id
stringlengths 2
7
| title
stringlengths 1
182
| text
stringlengths 200
369k
| url
stringlengths 31
212
| timestamp
stringdate 2025-04-05 18:25:13
2025-04-05 23:52:07
|
|---|---|---|---|---|
6007
|
Foreign relations of the Comoros
|
<!-- "none" is preferred when the title is sufficiently descriptive; see WP:SDNONE -->
In November 1975, Comoros became the 143rd member of the United Nations. The new nation was defined as consisting of the entire archipelago, despite the fact that France maintains control over Mayotte.
Overview
Comoros also is a member of the African Union, the Arab League, the European Development Fund, the World Bank, the International Monetary Fund, the Indian Ocean Commission, and the African Development Bank.
The government fostered close relationships with the more conservative (and oil-rich) Arab states, such as Saudi Arabia and Kuwait.
|-
|2
|
|
|-
|3
|
|
|-
|4
|
|
|-
|5
|
|
|-
|6
|
|
|-
|7
|
|
|-
|8
|
|
|-
|9
|
|
|-
|10
|
|
|-
|11
|
|
|-
|12
|
|
|-
|13
|
|
|-
|14
|
|
|-
|15
|
|
|-
|16
|
|
|-
|17
|
|
|-
|18
|
|
|-
|19
|
|
|-
|20
|
|
|-
|21
|
|
|-
|22
|
|
|-
|23
|
|
|-
|24
|
|
|-
|25
|
|
|-
|26
|
|
|-
|27
|
|
|-
|28
|
|
|-
|29
|
|
|-
|30
|
|
|-
|31
|
|
|-
|32
|
|
|-
|33
|
|
|-
|34
|
|
|-
|35
|
|
|-
|36
|
|
|-
|37
|
|
|-
|38
|
|
|-
|39
|
|
|-
|40
|
|
|-
|41
|
|
|-
|42
|
|
|-
|43
|
|
|-
|44
|
|
|-
|45
|
|
|-
|46
|
|
|-
|47
|
|
|-
|48
|
|
|-
|49
|
|
|-
|50
|
|
|-
|51
|
|
|-
|52
|
|
|-
|53
|
|
|-
|54
|
|
|-
|55
|
|
|-
|57
|
|
|-
|60
|
|
|-
|—
|
|
|-
|61
|
|
|-
|62
|
|
|-
|63
|
|
|-
|64
|
|
|-
|67
|
|
|-
|68
|
|
|-
|69
|
|
|-
|71
|
|
|-
|72
|
|
|-
|73
|
|
|-
|74
|
|
|-
|75
|
|
|-
|76
|
|
|-
|81
|
|
|-
|84
|
|
|-
|86
|
|
|-
|90
|
|
|-
|91
|
|
|-
|95
|
|
|-
|96
|
|
|-
|99
|
|
|-
|100
|
|
|-
|103
|
|
|-
|104
|
|
|-
|105
|
|
|-
|106
|
|
|-
|107
|
|
|-
|108
|
|
|-
|109
|
|
|-
|111
|
|
|-
|113
|
|
|-
|114
|
|
|-
|116
|
|
|-
|117
|
|
|-
|118
|
|
|-
|119
|
|
|-
|120
|
|
|-
|121
|
|
|-
|122
|
|
|-
|124
|
|Unknown
|-
|125
|
|Unknown
|-
|126
|
|Unknown
|-
|127
|
|Unknown
|-
|128
|
|Unknown
|-
|129
|
|Unknown
|-style="background:#D3D3D3"
|—
| (suspended)
|Unknown
|}
Bilateral relations
{| class"wikitable sortable" style"width:100%; margin:auto;"
|-
! style="width:15%;"| Country
! style="width:12%;"| Formal Relations Began
!Notes
|-
|
|15 November 1976
|
* Both countries established diplomatic relations on 15 November 1976
|- valign="top"
|||13 November 1975|| See China–Comoros relations
Both countries established diplomatic relations on 13 November 1975
A comprehensive Chinese-assisted treatment campaign has apparently eliminated malaria from the Comorian island of Moheli (population 36,000). Administered by Li Guoqiao at the Tropical Medicine Institute, the program relies on hybrid Artemisia annua of hybrid ancestry, which was used for a drug regimen by which all residents of the island, whether or not visibly ill, took two doses at a 40-day interval. This eliminated the human reservoir of the disease and reduced hospital admissions to 1% or less of January 2008 levels. Visitors to Moheli are now required to take antimalarial drugs, a mix of artemisinin, primaquine and pyrimethamine that China provides for free. When asked about Artemisia exports, Li was quoted, "We want to grow them in China and whatever we export depends on bilateral relationships." Comoros has requested a similar program for Grande Comore and Anjouan, total population 760,000, and Li said that Beijing has agreed in principle.
|-
|
|
|The countries maintain diplomatic relations and Congolese President Félix Tshisekedi visited Comoros in 2023.
|- valign="top"
|||<!--Date started-->||
Cyprus is represented in Comoros by its embassy in Pretoria.
|- valign="top"
|||1 December 1981||
Denmark is represented in Comoros by its embassy in Dar es Salaam, Tanzania.
|- valign="top"
|||19 December 1977||
Both countries established diplomatic relations on 19 December 1977
Comoros is represented in Finland by its embassy in Paris, France.
|- valign="top"
|||1 July 1978|| See France–Comoros relations
Both countries established diplomatic relations on 1 July 1978
Comoros' most significant international relationship is that with France. The three years of estrangement following the unilateral declaration of independence and the nationalistic Soilih regime were followed during the conservative Abdallah and Djohar regimes by a period of growing trade, aid, cultural, and defense links between the former colony and France, punctuated by frequent visits to Paris by the head of state and occasional visits by the French president to Moroni.
*Both countries are full members of the Indian-Ocean Rim Association.
|- valign="top"
|||23 June 1983||Both countries established diplomatic relations on 23 June 1983
*Indonesia is represented in Comoros by their embassy in Dar es Salaam.
*Both countries are full members of the Organisation of Islamic Cooperation and of the Indian-Ocean Rim Association.
|- valign="top"
|||24 October 2018||
Ireland is represented in Comoros by its embassy in Dar es Salaam, Tanzania.
|- valign="top"
|||1 November 1976||Both countries established diplomatic relations on 1 November 1976
*Comoros is represented in Italy by its embassy in Paris, France and an honorary consulate in Rome. and an honorary consulate in Anjouan.
|- valign="top"
|||14 November 1977||
Comorian relations with Japan were also significant because Japan was the second largest provider of aid, consisting of funding for fisheries, food, and highway development.
|-
|
|2000
|Both countries established diplomatic relations in 2000.
|- valign="top"
|||13 October 2008||Both countries established diplomatic relations on 13 October 2008
* The Comoros does not have an accreditation to Mexico.
* Mexico is accredited to the Comoros from its embassy in Nairobi, Kenya.
|-
|
|
|The two countries maintain diplomatic relations and signed 11 agreements in 2022.
|- valign="top"
|||21 February 1977||
*Comoros is represented in Netherlands by their embassy in Brussels, Belgium.
*The Netherlands are represented in Comoros by their embassy in Dar es Salaam.
|-
|
|
|The two countries maintain cordial relations.
|- valign="top"
||| || See Comoros–North Korea relations
Both countries established diplomatic relations on November 13, 1975.
|- valign="top"
||| || See Comoros–Qatar relations
Comoros severed the diplomatic relations with Qatar in June 2017.
|-
|
|
|Saudi Arabia has an embassy in Comoros.
|- valign="top"
|||24 November 1976||
Both countries established diplomatic relations on 24 November 1976.
Serbia is represented in Comoros by its embassy in Nairobi, Kenya.
|- valign="top"
|||14 May 1993||
Both countries established diplomatic relations on 14 May 1993
The close relationship Comoros developed with South Africa in the 1980s was much less significant to both countries in the 1990s.||See Comoros–Turkey relations
*The Embassy of the Comoros in Cairo is accredited to Turkey.
*The Turkish ambassador in Antananarivo to Madagascar is also accredited to the Union of the Comoros.
*Comoros has an honorary consulate in Kyiv.
*Ukraine is represented in Comoros by its embassy in Nairobi, Kenya.
|- valign="top"
|||3 October 1977||
Both countries established diplomatic relations on 3 October 1977.
|- valign="top"
|||15 August 1977|| See Comoros–United States relations
Both countries established diplomatic relations on 15 August 1977.
The American Embassy at Moroni was established on August 26, 1985, with Edward Brynn as Chargé d'Affaires ad interim. The American Embassy at Moroni was closed on September 30, 1993. Subsequent American Ambassadors to Comoros also have been accredited to Mauritius, and resident at Port Louis. On March 6, 2006, responsibilities for Comoros were transferred from Embassy Port Louis to Embassy Antananarivo. The two countries enjoy friendly relations. Future friendly relations continue to look promising between the Comoros and America.
|- valign="top"
|||21 May 2005||
*Both countries established diplomatic relations on 21 May 2005
*Both countries are full members of the Organisation of Islamic Cooperation.
|- valign="top"
|||6 January 1985||
Both countries established diplomatic relations on 6 January 1985
In April 2008, the Ministry of Agriculture and Irrigation of Yemen and Comoros Ministry of Fishery and Environment signed a "Memo of Understanding" (MOU) concerning agricultural cooperation.
|}
See also
* List of diplomatic missions in Comoros
* List of diplomatic missions of Comoros
References
|
https://en.wikipedia.org/wiki/Foreign_relations_of_the_Comoros
|
2025-04-05T18:27:41.063720
|
6008
|
Army of National Development
|
| image | alt
| caption = Comorian Coat of Arms
| image2 | alt2
| caption2 | motto
| founded =1997
| current_form | disbanded
| branches | headquartersMoroni
| flying_hours | website <!---->
<!-- Leadership -->
| commander-in-chief = Azali Assoumani
| commander-in-chief_title = Commander-in-chief
| minister =M. Yousoufa Mohamed Ali
| minister_title = Minister of Defense
| commander =Colonel Youssouf Idjihadi
| commander_title = Chief of the Defence Staff (Comoros)
<!-- Manpower -->
| age | conscription
| manpower_data | manpower_age
| available | available_f
| fit | fit_f
| reaching | reaching_f
| active | ranked
| reserve | deployed
<!-- Financial -->
| amount | percent_GDP
<!-- Industrial -->
| domestic_suppliers | foreign_suppliers <br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />
| imports | exports
<!-- Related articles -->
| history | ranks Military ranks of Comoros
|Battles=}}
The Comorian Armed Forces (; ) are the national military of the Comoros. The armed forces consist of a small standing army and a 500-member police force, as well as a 500-member defense force. A defense treaty with France provides naval resources for protection of territorial waters, training of Comorian military personnel, and air surveillance. France maintains a small troop presence in the Comoros at government request. France maintains a small Navy base and a Foreign Legion Detachment (DLEM) in Mayotte.
Structure
The AND consists of the following components:
* Comorian Ground Defense Force
* Comorian National Gendarmerie
* National School of the Armed Forces and Gendarmerie
* Comorian Air Force
* Comorian Presidential Guard
* Comorian Military Health Services
* Comorian Coast Guard
Equipment inventory
* FN FAL battle rifle
* AK-47 assault rifle
* Type 81 assault rifle
* NSV HMG
* RPG-7 anti-tank weapon
* Mitsubishi L200 pickup truck
Aircraft
Note: The last comprehensive aircraft inventory list was from Aviation Week & Space Technology in 2007.
{| class="wikitable"
! style="text-align:center; background:#acc;"|Aircraft
! style="text-align: center; background:#acc;"|Origin
! style="text-align:l center; background:#acc;"|Type
! style="text-align:left; background:#acc;"|Variant
! style="text-align:center; background:#acc;"|In service
! style="text-align: center; background:#acc;"|Notes
|-
! style"align: center; background: lavender;" colspan"7" | Transport
|-
| Cessna 402
| United States
| Transport
|
| 1
|
|-
| L-410 Turbolet
| Czech Republic
| Transport
|
| 1
|
|-
! style"align: center; background: lavender;" colspan"7" | Trainer aircraft
|-
| SIAI-Marchetti SF.260
| Italy
| Patrol / Trainer
|
| 5
|
|}
References
Category:Government of the Comoros
Comoros
|
https://en.wikipedia.org/wiki/Army_of_National_Development
|
2025-04-05T18:27:41.070198
|
6010
|
Computer worm
|
thumb|right|325px|Hex dump of the Blaster worm, showing a message left for Microsoft CEO Bill Gates by the worm's creator
thumb|Spread of Conficker worm
A computer worm is a standalone malware computer program that replicates itself in order to spread to other computers. It often uses a computer network to spread itself, relying on security failures on the target computer to access it. It will use this machine as a host to scan and infect other computers. When these new worm-invaded computers are controlled, the worm will continue to scan and infect other computers using these computers as hosts, and this behaviour will continue. Computer worms use recursive methods to copy themselves without host programs and distribute themselves based on exploiting the advantages of exponential growth, thus controlling and infecting more and more computers in a short time. Worms almost always cause at least some harm to the network, even if only by consuming bandwidth, whereas viruses almost always corrupt or modify files on a targeted computer.
Many worms are designed only to spread, and do not attempt to change the systems they pass through. However, as the Morris worm and Mydoom showed, even these "payload-free" worms can cause major disruption by increasing network traffic and other unintended effects.
History
The term "worm" was first used in this sense in John Brunner's 1975 novel, The Shockwave Rider. In the novel, Nichlas Haflinger designs and sets off a data-gathering worm in an act of revenge against the powerful people who run a national electronic information web that induces mass conformity. "You have the biggest-ever worm loose in the net, and it automatically sabotages any attempt to monitor it. There's never been a worm with that tough a head or that long a tail!" "Then the answer dawned on him, and he almost laughed. Fluckner had resorted to one of the oldest tricks in the store and turned loose in the continental net a self-perpetuating tapeworm, probably headed by a denunciation group "borrowed" from a major corporation, which would shunt itself from one nexus to another every time his credit-code was punched into a keyboard. It could take days to kill a worm like that, and sometimes weeks." During the Morris appeal process, the U.S. Court of Appeals estimated the cost of removing the worm from each installation at between $200 and $53,000; this work prompted the formation of the CERT Coordination Center and Phage mailing list. Morris himself became the first person tried and convicted under the 1986 Computer Fraud and Abuse Act.
Conficker, a computer worm discovered in 2008 that primarily targeted Microsoft Windows operating systems, is a worm that employs three different spreading strategies: local probing, neighborhood probing, and global probing. This worm was considered a hybrid epidemic and affected millions of computers. The term "hybrid epidemic" is used because of the three separate methods it employed to spread, which was discovered through code analysis.
Features
Independence
Computer viruses generally require a host program. The virus writes its own code into the host program. When the program runs, the written virus program is executed first, causing infection and damage. A worm does not need a host program, as it is an independent program or code chunk. Therefore, it is not restricted by the host program, but can run independently and actively carry out attacks.
Exploit attacks
Because a worm is not limited by the host program, worms can take advantage of various operating system vulnerabilities to carry out active attacks. For example, the "Nimda" virus exploits vulnerabilities to attack.
Complexity
Some worms are combined with web page scripts, and are hidden in HTML pages using VBScript, ActiveX and other technologies. When a user accesses a webpage containing a virus, the virus automatically resides in memory and waits to be triggered. There are also some worms that are combined with backdoor programs or Trojan horses, such as "Code Red".
Contagiousness
Worms are more infectious than traditional viruses. They not only infect local computers, but also all servers and clients on the network based on the local computer. Worms can easily spread through shared folders, e-mails, malicious web pages, and servers with a large number of vulnerabilities in the network.
Harm
Any code designed to do more than spread the worm is typically referred to as the "payload". Typical malicious payloads might delete files on a host system (e.g., the ExploreZip worm), encrypt files in a ransomware attack, or exfiltrate data such as confidential documents or passwords.
Some worms may install a backdoor. This allows the computer to be remotely controlled by the worm author as a "zombie". Networks of such machines are often referred to as botnets and are very commonly used for a range of malicious purposes, including sending spam or performing DoS attacks.
Some special worms attack industrial systems in a targeted manner. Stuxnet was primarily transmitted through LANs and infected thumb-drives, as its targets were never connected to untrusted networks, like the internet. This virus can destroy the core production control computer software used by chemical, power generation and power transmission companies in various countries around the world - in Stuxnet's case, Iran, Indonesia and India were hardest hit - it was used to "issue orders" to other equipment in the factory, and to hide those commands from being detected. Stuxnet used multiple vulnerabilities and four different zero-day exploits (e.g.: ) in Windows systems and Siemens SIMATICWinCC systems to attack the embedded programmable logic controllers of industrial machines. Although these systems operate independently from the network, if the operator inserts a virus-infected drive into the system's USB interface, the virus will be able to gain control of the system without any other operational requirements or prompts.
Countermeasures
Worms spread by exploiting vulnerabilities in operating systems. If user interaction is required for the malware to spread, it is called a Trojan horse.
-->
Vendors with security problems supply regular security updates (see "Patch Tuesday"), and if these are installed to a machine, then the majority of worms are unable to spread to it. If a vulnerability is disclosed before the security patch released by the vendor, a zero-day attack is possible.
Users need to be wary of opening unexpected emails, and should not run attached files or programs, or visit web sites that are linked to such emails. However, as with the ILOVEYOU worm, and with the increased growth and efficiency of phishing attacks, it remains possible to trick the end-user into running malicious code.
Anti-virus and anti-spyware software are helpful, but must be kept up-to-date with new pattern files at least every few days. The use of a firewall is also recommended.
Users can minimize the threat posed by worms by keeping their computers' operating system and other software up to date, avoiding opening unrecognized or unexpected emails and running firewall and antivirus software.
Mitigation techniques include:
ACLs in routers and switches
Packet-filters
TCP Wrapper/ACL enabled network service daemons
EPP/EDR software
Nullroute
Infections can sometimes be detected by their behavior - typically scanning the Internet randomly, looking for vulnerable hosts to infect. In addition, machine learning techniques can be used to detect new worms, by analyzing the behavior of the suspected computer.
Helpful worms
A helpful worm or anti-worm is a worm designed to do something that its author feels is helpful, though not necessarily with the permission of the executing computer's owner. Beginning with the first research into worms at Xerox PARC, there have been attempts to create useful worms. Those worms allowed John Shoch and Jon Hupp to test the Ethernet principles on their network of Xerox Alto computers. Similarly, the Nachi family of worms tried to download and install patches from Microsoft's website to fix vulnerabilities in the host system by exploiting those same vulnerabilities. In practice, although this may have made these systems more secure, it generated considerable network traffic, rebooted the machine in the course of patching it, and did its work without the consent of the computer's owner or user. Regardless of their payload or their writers' intentions, security experts regard all worms as malware. Another example of this approach is Roku OS patching a bug allowing for Roku OS to be rooted via an update to their screensaver channels, which the screensaver would attempt to connect to the telnet and patch the device.
One study proposed the first computer worm that operates on the second layer of the OSI model (Data link Layer), utilizing topology information such as Content-addressable memory (CAM) tables and Spanning Tree information stored in switches to propagate and probe for vulnerable nodes until the enterprise network is covered.
Anti-worms have been used to combat the effects of the Code Red, Blaster, and Santy worms. Welchia is an example of a helpful worm. Utilizing the same deficiencies exploited by the Blaster worm, Welchia infected computers and automatically began downloading Microsoft security updates for Windows without the users' consent. Welchia automatically reboots the computers it infects after installing the updates. One of these updates was the patch that fixed the exploit.
See also
List of computer worms
BlueKeep
Botnet
Code Shikara (Worm)
Computer and network surveillance
Computer virus
Computer security
Email spam
Father Christmas (computer worm)
Self-replicating machine
Technical support scam – unsolicited phone calls from a fake "tech support" person, claiming that the computer has a virus or other problems
Timeline of computer viruses and worms
Trojan horse (computing)
Worm memory test
XSS worm
Zombie (computer science)
References
External links
Malware Guide (archived link) – Guide for understanding, removing and preventing worm infections on Vernalex.com.
"The 'Worm' Programs – Early Experience with a Distributed Computation", John Shoch and Jon Hupp, Communications of the ACM, Volume 25 Issue 3 (March 1982), pp. 172–180.
"The Case for Using Layered Defenses to Stop Worms", Unclassified report from the U.S. National Security Agency (NSA), 18 June 2004.
Worm Evolution (archived link), paper by Jago Maniscalchi on Digital Threat, 31 May 2009.
Category:Computer worms
Category:Security breaches
Category:Types of malware
|
https://en.wikipedia.org/wiki/Computer_worm
|
2025-04-05T18:27:41.088621
|
6011
|
Chomsky hierarchy
|
thumb|right|200px|alt=The Chomsky hierarchy|Set inclusions described by the Chomsky hierarchy
The Chomsky hierarchy in the fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formal grammars. A formal grammar describes how to form strings from a language's vocabulary (or alphabet) that are valid according to the language's syntax. The linguist Noam Chomsky theorized that four different classes of formal grammars existed that could generate increasingly complex languages. Each class can also completely generate the language of all inferior classes (set inclusive).
History
The general idea of a hierarchy of grammars was first described by Noam Chomsky in "Three models for the description of language" during the formalization of transformational-generative grammar (TGG). Marcel-Paul Schützenberger also played a role in the development of the theory of formal languages; the paper "The algebraic theory of context free languages" describes the modern hierarchy, including context-free grammars.
Independently, alongside linguists, mathematicians were developing models of computation (via automata). Parsing a sentence in a language is similar to computation, and the grammars described by Chomsky proved to both resemble and be equivalent in computational power to various machine models.
The hierarchy
The following table summarizes each of Chomsky's four types of grammars, the class of language it generates, the type of automaton that recognizes it, and the form its rules must have. The classes are defined by the constraints on the productions rules.
Grammar Languages Recognizing automaton Production rules (constraints) Examples Type-3 Regular Finite-state automaton A \rightarrow \text{a}A \rightarrow \text{a}B (right regular)orA \rightarrow \text{a}A \rightarrow B\text{a} (left regular) L \{a^n \mid n > 0\} Type-2 Context-free Non-deterministic pushdown automatonA \rightarrow \alpha L \{a^nb^n \mid n > 0\} Type-1 Context-sensitive Linear-bounded non-deterministic Turing machine \alpha A \beta \rightarrow \alpha \gamma \beta L \{a^nb^nc^n \mid n > 0\} Type-0 Recursively enumerable Turing machine \gamma \rightarrow \alpha (\gamma non-empty) L \{w \mid w describes a terminating Turing machine \}
Note that the set of grammars corresponding to recursive languages is not a member of this hierarchy; these would be properly between Type-0 and Type-1.
Every regular language is context-free, every context-free language is context-sensitive, every context-sensitive language is recursive and every recursive language is recursively enumerable. These are all proper inclusions, meaning that there exist recursively enumerable languages that are not context-sensitive, context-sensitive languages that are not context-free and context-free languages that are not regular.
Regular (Type-3) grammars
Type-3 grammars generate the regular languages. Such a grammar restricts its rules to a single nonterminal on the left-hand side and a right-hand side consisting of a single terminal, possibly followed by a single nonterminal, in which case the grammar is right regular. Alternatively, all the rules can have their right-hand sides consist of a single terminal, possibly preceded by a single nonterminal (left regular). These generate the same languages. However, if left-regular rules and right-regular rules are combined, the language need no longer be regular. The rule S \rightarrow \varepsilon is also allowed here if S does not appear on the right side of any rule. These languages are exactly all languages that can be decided by a finite-state automaton. Additionally, this family of formal languages can be obtained by regular expressions. Regular languages are commonly used to define search patterns and the lexical structure of programming languages.
For example, the regular language L \{a^n \mid n > 0\} is generated by the Type-3 grammar G (\{S\}, \{a, b\}, P, S) with the productions P being the following.
Context-free (Type-2) grammars
Type-2 grammars generate the context-free languages. These are defined by rules of the form A \rightarrow \alpha with A being a nonterminal and \alpha being a string of terminals and/or nonterminals. These languages are exactly all languages that can be recognized by a non-deterministic pushdown automaton. Context-free languages—or rather its subset of deterministic context-free languages—are the theoretical basis for the phrase structure of most programming languages, though their syntax also includes context-sensitive name resolution due to declarations and scope. Often a subset of grammars is used to make parsing easier, such as by an LL parser.
For example, the context-free language L \{a^nb^n \mid n > 0\} is generated by the Type-2 grammar G (\{S\}, \{a, b\}, P, S) with the productions P being the following.
The language is context-free but not regular (by the pumping lemma for regular languages).
Context-sensitive (Type-1) grammars
Type-1 grammars generate context-sensitive languages. These grammars have rules of the form \alpha A\beta \rightarrow \alpha\gamma\beta with A a nonterminal and \alpha, \beta and \gamma strings of terminals and/or nonterminals. The strings \alpha and \beta may be empty, but \gamma must be nonempty. The rule S \rightarrow \epsilon is allowed if S does not appear on the right side of any rule. The languages described by these grammars are exactly all languages that can be recognized by a linear bounded automaton (a nondeterministic Turing machine whose tape is bounded by a constant times the length of the input.)
For example, the context-sensitive language L \{a^nb^nc^n \mid n > 0\} is generated by the Type-1 grammar G (\{S,A,B,C,W,Z\}, \{a, b, c\}, P, S) with the productions P being the following.
The language is context-sensitive but not context-free (by the pumping lemma for context-free languages).
A proof that this grammar generates L = \{a^nb^nc^n \mid n > 0\} is sketched in the article on Context-sensitive grammars.
Recursively enumerable (Type-0) grammars
Type-0 grammars include all formal grammars. There are no constraints on the productions rules. They generate exactly all languages that can be recognized by a Turing machine, thus any language that is possible to be generated can be generated by a Type-0 grammar. Note that this is different from the recursive languages, which can be decided by an always-halting Turing machine.
See also
Chomsky normal form
Citations
References
Category:1956 in computing
Category:Formal languages
Category:Generative linguistics
Hierarchy, Chomsky
|
https://en.wikipedia.org/wiki/Chomsky_hierarchy
|
2025-04-05T18:27:41.105388
|
6013
|
CRT
|
CRT or Crt most commonly refers to:
Cathode-ray tube, a display
Critical race theory, an academic framework of analysis
CRT may also refer to:
Law
Charitable remainder trust, United States
Civil Resolution Tribunal, Canada
Columbia River Treaty, Canada–US, 1960s
Science, technology, and mathematics
Medicine and biology
Calreticulin, a protein
Capillary refill time, for blood to refill capillaries
Cardiac resynchronization therapy and CRT defibrillator (CRT-D)
Catheter-related thrombosis, the development of a blood clot related to long-term use of central venous catheters
Certified Respiratory Therapist
Chemoradiotherapy, chemo- and radiotherapy combined
Cognitive Retention Therapy, for dementia
Corneal Refractive Therapy, in optometrics
CRT (genetics), a gene cluster
Social sciences
Cognitive reflection test, in psychology
Current reality tree (theory of constraints), in process management
Culturally relevant teaching, in pedagogy
Technology
Microsoft C Run-Time library
SecureCRT, formerly CRT, a telnet client
.crt, X.509 Certificate filename extension
Other uses in science and mathematics
Chinese remainder theorem, in number theory
Crater (constellation), in astronomy (abbreviated )
Transport
Canal & River Trust, England and Wales
Changchun Rail Transit, China
Chongqing Rail Transit, China
Connecticut River Transit, a defunct American bus service
Cross River Tram, a defunct proposal in London, England
CRT Group, an Australian transport company
Chicago Rapid Transit Company, a defunct American rail company
Colchester Rapid Transit, a rapid-transit system in Colchester, England.
Other uses
Canadian Railway Troops, WWI
Claiming Rule Teams, in motorcycle racing
Connecticut Repertory Theatre, University of Connecticut
Correctional Emergency Response Team
Iyojwaʼja Chorote, a language in Salta province, Argentina, ISO 639 code
|
https://en.wikipedia.org/wiki/CRT
|
2025-04-05T18:27:41.108299
|
6014
|
Cathode-ray tube
|
(not to scale) with its focused and deflected electron beam (in green)|220x220px]]
cathode-ray tube|220x220px]]
thumb|Cutaway rendering of a color CRT:|220x220px
thumb|Cutaway rendering of a monochrome CRT:The only visible differences are the single electron gun, the uniform white phosphor coating, and the lack of a shadow mask.|220x220px
A cathode-ray tube (CRT) is a vacuum tube containing one or more electron guns, which emit electron beams that are manipulated to display images on a phosphorescent screen. The images may represent electrical waveforms on an oscilloscope, a frame of video on an analog television set (TV), digital raster graphics on a computer monitor, or other phenomena like radar targets. A CRT in a TV is commonly called a picture tube. CRTs have also been used as memory devices, in which case the screen is not intended to be visible to an observer. The term cathode ray was used to describe electron beams when they were first discovered, before it was understood that what was emitted from the cathode was a beam of electrons.
In CRT TVs and computer monitors, the entire front area of the tube is scanned repeatedly and systematically in a fixed pattern called a raster. In color devices, an image is produced by controlling the intensity of each of three electron beams, one for each additive primary color (red, green, and blue) with a video signal as a reference. In modern CRT monitors and TVs the beams are bent by magnetic deflection, using a deflection yoke. Electrostatic deflection is commonly used in oscilloscopes. As such, handling a CRT carries the risk of violent implosion that can hurl glass at great velocity. The face is typically made of thick lead glass or special barium-strontium glass to be shatter-resistant and to block most X-ray emissions. This tube makes up most of the weight of CRT TVs and computer monitors.
Since the early 2010s, CRTs have been superseded by flat-panel display technologies such as LCD, plasma display, and OLED displays which are cheaper to manufacture and run, as well as significantly lighter and thinner. Flat-panel displays can also be made in very large sizes whereas was about the largest size of a CRT.
A CRT works by electrically heating a tungsten coil which in turn heats a cathode in the rear of the CRT, causing it to emit electrons which are modulated and focused by electrodes. The electrons are steered by deflection coils or plates, and an anode accelerates them towards the phosphor-coated screen, which generates light when hit by the electrons.HistoryDiscoveries
Cathode rays were discovered by Julius Plücker and Johann Wilhelm Hittorf. Hittorf observed that some unknown rays were emitted from the cathode (negative electrode) which could cast shadows on the glowing wall of the tube, indicating the rays were travelling in straight lines. In 1890, Arthur Schuster demonstrated cathode rays could be deflected by electric fields, and William Crookes showed they could be deflected by magnetic fields. In 1897, J. J. Thomson succeeded in measuring the mass-to-charge ratio of cathode rays, showing that they consisted of negatively charged particles smaller than atoms, the first "subatomic particles", which had already been named electrons by Irish physicist George Johnstone Stoney in 1891.
The earliest version of the CRT was known as the "Braun tube", invented by the German physicist Ferdinand Braun in 1897. It was a cold-cathode diode, a modification of the Crookes tube with a phosphor-coated screen. Braun was the first to conceive the use of a CRT as a display device. The Braun tube became the foundation of 20th century TV.
In 1908, Alan Archibald Campbell-Swinton, fellow of the Royal Society (UK), published a letter in the scientific journal Nature, in which he described how "distant electric vision" could be achieved by using a cathode-ray tube (or "Braun" tube) as both a transmitting and receiving device. He expanded on his vision in a speech given in London in 1911 and reported in The Times and the Journal of the Röntgen Society.
The first cathode-ray tube to use a hot cathode was developed by John Bertrand Johnson (who gave his name to the term Johnson noise) and Harry Weiner Weinhart of Western Electric, and became a commercial product in 1922. The introduction of hot cathodes allowed for lower acceleration anode voltages and higher electron beam currents, since the anode now only accelerated the electrons emitted by the hot cathode, and no longer had to have a very high voltage to induce electron emission from the cold cathode.
Development
In 1926, Kenjiro Takayanagi demonstrated a CRT TV receiver with a mechanical video camera that received images with a 40-line resolution. By 1927, he improved the resolution to 100 lines, which was unrivaled until 1931. By 1928, he was the first to transmit human faces in half-tones on a CRT display.
In 1927, Philo Farnsworth created a TV prototype.
The CRT was named in 1929 by inventor Vladimir K. Zworykin.
In the 1930s, Allen B. DuMont made the first CRTs to last 1,000 hours of use, which was one of the factors that led to the widespread adoption of TV.
The first commercially made electronic TV sets with cathode-ray tubes were manufactured by Telefunken in Germany in 1934.
In 1947, the cathode-ray tube amusement device, the earliest known interactive electronic game as well as the first to incorporate a cathode-ray tube screen, was created.
From 1949 to the early 1960s, there was a shift from circular CRTs to rectangular CRTs, although the first rectangular CRTs were made in 1938 by Telefunken. While circular CRTs were the norm, European TV sets often blocked portions of the screen to make it appear somewhat rectangular while American sets often left the entire front of the CRT exposed or only blocked the upper and lower portions of the CRT.
In 1954, RCA produced some of the first color CRTs, the 15GP22 CRTs used in the CT-100, the first color TV set to be mass produced. The first rectangular color CRTs were also made in 1954. However, the first rectangular color CRTs to be offered to the public were made in 1963. One of the challenges that had to be solved to produce the rectangular color CRT was convergence at the corners of the CRT.
The size of CRTs increased over time, from 20 inches in 1938, to 21 inches in 1955, 25 inches by 1974, 30 inches by 1980, 35 inches by 1985, and 43 inches by 1989. The world largest was the Sony KX-45ED1 at 45 inches but only one known working model exists.
In 1960, the Aiken tube was invented. It was a CRT in a flat-panel display format with a single electron gun. Deflection was electrostatic and magnetic, but due to patent problems, it was never put into production. It was also envisioned as a head-up display in aircraft. By the time patent issues were solved, RCA had already invested heavily in conventional CRTs.
1968 marked the release of Sony Trinitron brand with the model KV-1310, which was based on Aperture Grille technology. It was acclaimed to have improved the output brightness. The Trinitron screen was identical with its upright cylindrical shape due to its unique triple cathode single gun construction.
In 1987, flat-screen CRTs were developed by Zenith for computer monitors, reducing reflections and helping increase image contrast and brightness. Such CRTs were expensive, which limited their use to computer monitors. Attempts were made to produce flat-screen CRTs using inexpensive and widely available float glass.
In 1990, the first CRT with HD resolution, the Sony KW-3600HD, was released to the market. It is considered to be "historical material" by Japan's national museum.
The Sony KWP-5500HD, an HD CRT projection TV, was released in 1992.
In the mid-1990s, some 160 million CRTs were made per year.
In the mid-2000s, Canon and Sony presented the surface-conduction electron-emitter display and field-emission displays, respectively. They both were flat-panel displays that had one (SED) or several (FED) electron emitters per subpixel in place of electron guns. The electron emitters were placed on a sheet of glass and the electrons were accelerated to a nearby sheet of glass with phosphors using an anode voltage. The electrons were not focused, making each subpixel essentially a flood beam CRT. They were never put into mass production as LCD technology was significantly cheaper, eliminating the market for such displays.
The last large-scale manufacturer of (in this case, recycled) CRTs, Videocon, ceased in 2015. CRT TVs stopped being made around the same time.
In 2012, Samsung SDI and several other major companies were fined by the European Commission for price fixing of TV cathode-ray tubes.
The same occurred in 2015 in the US and in Canada in 2018.
Worldwide sales of CRT computer monitors peaked in 2000, at 90 million units, while those of CRT TVs peaked in 2005 at 130 million units.DeclineBeginning in the late 1990s to the early 2000s, CRTs began to be replaced with LCDs, starting first with computer monitors smaller than 15 inches in size, largely because of their lower bulk. Among the first manufacturers to stop CRT production was Hitachi in 2001, followed by Sony in Japan in 2004, Flat-panel displays dropped in price and started significantly displacing cathode-ray tubes in the 2000s. LCD monitor sales began exceeding those of CRTs in 2003–2004 and LCD TV sales started exceeding those of CRTs in some markets in 2005. Samsung SDI stopped CRT production in 2012.
Despite being a mainstay of display technology for decades, CRT-based computer monitors and TVs are now obsolete. Demand for CRT screens dropped in the late 2000s. Despite efforts from Samsung and LG to make CRTs competitive with their LCD and plasma counterparts, offering slimmer and cheaper models to compete with similarly sized and more expensive LCDs, CRTs eventually became obsolete and were relegated to developing markets and vintage enthusiasts once LCDs fell in price, with their lower bulk, weight and ability to be wall mounted coming as advantages.
Some industries still use CRTs because it is too much effort, downtime, or cost to replace them, or there is no substitute available; a notable example is the airline industry. Planes such as the Boeing 747-400 and the Airbus A320 used CRT instruments in their glass cockpits instead of mechanical instruments. Airlines such as Lufthansa still use CRT technology, which also uses floppy disks for navigation updates. They are also used in some military equipment for similar reasons. , at least one company manufactures new CRTs for these markets.
A popular consumer usage of CRTs is for retro gaming. Some games are impossible to play without CRT display hardware. Light guns only work on CRTs because they depend on the progressive timing properties of CRTs. Another reason people use CRTs due to the natural blending of these displays. Some games designed for CRT displays exploit this, which allows them to look more aesthetically pleasing on these displays.ConstructionsBody
CRT computer monitor]]
computer]]
The body of a CRT is usually made up of three parts: A screen/faceplate/panel, a cone/funnel, and a neck. The joined screen, funnel and neck are known as the bulb or envelope. while the funnel and screen are made by pouring and then pressing glass into a mold. The glass, known as CRT glass or TV glass, needs special properties to shield against x-rays while providing adequate light transmission in the screen or being very electrically insulating in the funnel and neck. The formulation that gives the glass its properties is also known as the melt. The glass is of very high quality, being almost contaminant and defect free. Most of the costs associated with glass production come from the energy used to melt the raw materials into glass. Glass furnaces for CRT glass production have several taps to allow molds to be replaced without stopping the furnace, to allow production of CRTs of several sizes. Only the glass used on the screen needs to have precise optical properties.
The optical properties of the glass used on the screen affect color reproduction and purity in color CRTs. Transmittance, or how transparent the glass is, may be adjusted to be more transparent to certain colors (wavelengths) of light. Transmittance is measured at the center of the screen with a 546 nm wavelength light, and a 10.16mm thick screen. Transmittance goes down with increasing thickness. Standard transmittances for Color CRT screens are 86%, 73%, 57%, 46%, 42% and 30%. Lower transmittances are used to improve image contrast but they put more stress on the electron gun, requiring more power on the electron gun for a higher electron beam power to light the phosphors more brightly to compensate for the reduced transmittance. The transmittance must be uniform across the screen to ensure color purity. The radius (curvature) of screens has increased (grown less curved) over time, from 30 to 68 inches, ultimately evolving into completely flat screens, reducing reflections. The thickness of both curved and flat screens gradually increases from the center outwards, and with it, transmittance is gradually reduced. This means that flat-screen CRTs may not be completely flat on the inside.
The glass used in CRTs arrives from the glass factory to the CRT factory as either separate screens and funnels with fused necks, for Color CRTs, or as bulbs made up of a fused screen, funnel and neck. There were several glass formulations for different types of CRTs, that were classified using codes specific to each glass manufacturer. The compositions of the melts were also specific to each manufacturer. Those optimized for high color purity and contrast were doped with Neodymium, while those for monochrome CRTs were tinted to differing levels, depending on the formulation used and had transmittances of 42% or 30%. Purity is ensuring that the correct colors are activated (for example, ensuring that red is displayed uniformly across the screen) while convergence ensures that images are not distorted. Convergence may be modified using a cross hatch pattern.
CRT glass used to be made by dedicated companies such as AGC Inc., O-I Glass, Samsung Corning Precision Materials, Corning Inc., and Nippon Electric Glass; others such as Videocon, Sony for the US market and Thomson made their own glass.
The funnel and the neck are made of leaded potash-soda glass or lead silicate glass The amount of x-rays emitted by a CRT can also lowered by reducing the brightness of the image. while also shielding heavily against x-rays, although some funnels may also contain barium. Another glass formulation uses 2–3% of lead on the screen.
Monochrome CRTs may have a tinted barium-lead glass formulation in both the screen and funnel, with a potash-soda lead glass in the neck; the potash-soda and barium-lead formulations have different thermal expansion coefficients. The glass used in the neck must be an excellent electrical insulator to contain the voltages used in the electron optics of the electron gun, such as focusing lenses. The lead in the glass causes it to brown (darken) with use due to x-rays, usually the CRT cathode wears out due to cathode poisoning before browning becomes apparent. The glass formulation determines the highest possible anode voltage and hence the maximum possible CRT screen size. For color, maximum voltages are often 24–32 kV, while for monochrome it is usually 21 or 24.5 kV, limiting the size of monochrome CRTs to 21 inches, or ~1 kV per inch. The voltage needed depends on the size and type of CRT. Since the formulations are different, they must be compatible with one another, having similar thermal expansion coefficients. or be ground to prevent reflections. CRTs may also have an anti-static coating. and the screen may contain 12% of barium oxide, and 12% of strontium oxide. Before this, CRTs used lead on the faceplate. Early CRTs did not have a dedicated anode cap connection; the funnel was the anode connection, so it was live during operation.
The funnel is coated on the inside and outside with a conductive coating, making the funnel a capacitor, helping stabilize and filter the anode voltage of the CRT, and significantly reducing the amount of time needed to turn on a CRT. The stability provided by the coating solved problems inherent to early power supply designs, as they used vacuum tubes. Because the funnel is used as a capacitor, the glass used in the funnel must be an excellent electrical insulator (dielectric). The inner coating has a positive voltage (the anode voltage that can be several kV) while the outer coating is connected to ground. CRTs powered by more modern power supplies do not need to be connected to ground, due to the more robust design of modern power supplies. The value of the capacitor formed by the funnel is 5–10 nF, although at the voltage the anode is normally supplied with. The capacitor formed by the funnel can also suffer from dielectric absorption, similarly to other types of capacitors. before handling to prevent injury.
The depth of a CRT is related to its screen size. Usual deflection angles were 90° for computer monitor CRTs and small CRTs and 110° which was the standard in larger TV CRTs, with 120 or 125° being used in slim CRTs made since 2001–2005 in an attempt to compete with LCD TVs. Over time, deflection angles increased as they became practical, from 50° in 1938 to 110° in 1959,
<gallery mode"packed" heights"180px">
File:Cinescopio per televisore a schermo rettangolare, 17 pollici, deflessione 110°, bianco e nero - Museo scienza tecnologia Milano 10081 dia.jpg|A monochrome CRT with 110° deflection
File:Cinescopio per televisore a schermo rettangolare, 13 pollici, deflessione 90°, bianco e nero - Museo scienza tecnologia Milano 10082 dia.jpg|A monochrome CRT with 90° deflection
</gallery>
Size and weight
The size of a CRT can be measured by the screen's entire area (or face diagonal) or alternatively by only its viewable area (or diagonal) that is coated by phosphor and surrounded by black edges.
While the viewable area may be rectangular, the edges of the CRT may have a curvature (e.g. black stripe CRTs, first made by Toshiba in 1972) or the viewable area may follow the curvature of the edges of the CRT (with or without black edges or curved edges).
Most of the weight of a CRT comes from the thick glass screen, which comprises 65% of the total weight of a CRT and limits its practical size (see ). The funnel and neck glass comprise the remaining 30% and 5% respectively. The glass in the funnel can vary in thickness, to join the thin neck with the thick screen.
Anode <!--Expand: how anode voltage is derived from horizontal deflection circuitry, the horiz. deflection coil and its voltage, which is created by the flyback so it creates anode voltage that is then multiplied and fed and horiz. deflection coil voltage that contributes to anode voltage, maybe flyback first creates 120v horiz. high current voltage, goes to the coil, returns from the coil, then its fed and voltage multiplied and energy added and fed to the anode-->
The outer conductive coating is connected to ground while the inner conductive coating is connected using the anode button/cap through a series of capacitors and diodes (a Cockcroft–Walton generator) to the high voltage flyback transformer; the inner coating is the anode of the CRT, which, together with an electrode in the electron gun, is also known as the final anode. The inner coating is connected to the electrode using springs. The electrode forms part of a bipotential lens. The capacitors and diodes serve as a voltage multiplier for the current delivered by the flyback.
For the inner funnel coating, monochrome CRTs use aluminum while color CRTs use aquadag; use aquadag. Aquadag is an electrically conductive graphite-based paint. In color CRTs, the aquadag is sprayed onto the interior of the funnel The connection is insulated by a silicone suction cup, possibly also using silicone grease to prevent corona discharge.
The anode button must be specially shaped to establish a hermetic seal between the button and funnel. X-rays may leak through the anode button, although that may not be the case in newer CRTs starting from the late 1970s to early 1980s, thanks to a new button and clip design. The button may consist of a set of 3 nested cups, with the outermost cup being made of a Nickel–Chromium–Iron alloy containing 40–49% of Nickel and 3–6% of Chromium to make the button easy to fuse to the funnel glass, with a first inner cup made of thick inexpensive iron to shield against x-rays, and with the second innermost cup also being made of iron or any other electrically conductive metal to connect to the clip. The cups must be heat resistant enough and have similar thermal expansion coefficients similar to that of the funnel glass to withstand being fused to the funnel glass. The inner side of the button is connected to the inner conductive coating of the CRT.
The flyback transformer is also known as an IHVT (Integrated High Voltage Transformer) if it includes a voltage multiplier. The flyback uses a ceramic or powdered iron core to enable efficient operation at high frequencies. The flyback contains one primary and many secondary windings that provide several different voltages. The main secondary winding supplies the voltage multiplier with voltage pulses to ultimately supply the CRT with the high anode voltage it uses, while the remaining windings supply the CRT's filament voltage, keying pulses, focus voltage and voltages derived from the scan raster. When the transformer is turned off, the flyback's magnetic field quickly collapses which induces high voltage in its windings. The speed at which the magnetic field collapses determines the voltage that is induced, so the voltage increases alongside its speed. A capacitor (Retrace Timing Capacitor) or series of capacitors (to provide redundancy) is used to slow the collapse of the magnetic field.
The design of the high voltage power supply in a product using a CRT has an influence in the amount of x-rays emitted by the CRT. The amount of emitted x-rays increases with both higher voltages and currents. If the product such as a TV set uses an unregulated high voltage power supply, meaning that anode and focus voltage go down with increasing electron current when displaying a bright image, the amount of emitted x-rays is as its highest when the CRT is displaying a moderately bright images, since when displaying dark or bright images, the higher anode voltage counteracts the lower electron beam current and vice versa respectively. The high voltage regulator and rectifier vacuum tubes in some old CRT TV sets may also emit x-rays.
Electron gun
The electron gun emits the electrons that ultimately hit the phosphors on the screen of the CRT. The electron gun contains a heater, which heats a cathode, which generates electrons that, using grids, are focused and ultimately accelerated into the screen of the CRT. The acceleration occurs in conjunction with the inner aluminum or aquadag coating of the CRT. The electron gun is positioned so that it aims at the center of the screen. The electron gun is made separately and then placed inside the neck through a process called "winding", or sealing. The electron gun has a glass wafer that is fused to the neck of the CRT. The connections to the electron gun penetrate the glass wafer. Once the electron gun is inside the neck, its metal parts (grids) are arced between each other using high voltage to smooth any rough edges in a process called spot knocking, to prevent the rough edges in the grids from generating secondary electrons.
Construction and method of operation
The electron gun has an indirectly heated hot cathode that is heated by a tungsten filament heating element; the heater may draw 0.5–2 A of current depending on the CRT. The voltage applied to the heater can affect the life of the CRT. Heating the cathode energizes the electrons in it, aiding electron emission, while at the same time current is supplied to the cathode; typically anywhere from 140 mA at 1.5 V to 600 mA at 6.3 V. The cathode creates an electron cloud (emits electrons) whose electrons are extracted, accelerated and focused into an electron beam.
There are several short circuits that can occur in a CRT electron gun. One is a heater-to-cathode short, that causes the cathode to permanently emit electrons which may cause an image with a bright red, green or blue tint with retrace lines, depending on the cathode (s) affected. Alternatively, the cathode may short to the control grid, possibly causing similar effects, or, the control grid and screen grid (G2) can short causing a very dark image or no image at all. The cathode may be surrounded by a shield to prevent sputtering.
The cathode is a layer of barium oxide which is coated on a piece of nickel for electrical and mechanical support. In color CRTs with red, green and blue cathodes, one or more cathodes may be affected independently of the others, causing total or partial loss of one or more colors. In color CRTs, since there are three cathodes, one for red, green and blue, a single or more poisoned cathode may cause the partial or complete loss of one or more colors, tinting the image.
The amount of electrons generated by the cathodes is related to their surface area. A cathode with more surface area creates more electrons, in a larger electron cloud, which makes focusing the electron cloud into an electron beam more difficult. is applied to the first (control) grid (G1) to converge the electrons from the hot cathode, creating an electron beam. G1 in practice is a Wehnelt cylinder. The brightness of the screen is not controlled by varying the anode voltage nor the electron beam current (they are never varied) despite them having an influence on image brightness, rather image brightness is controlled by varying the difference in voltage between the cathode and the G1 control grid. The second (screen) grid of the gun (G2) then accelerates the electrons towards the screen using several hundred DC volts. Then a third grid (G3) electrostatically focuses the electron beam before it is deflected and later accelerated by the anode voltage onto the screen. Electrostatic focusing of the electron beam may be accomplished using an einzel lens energized at up to 600 volts. Before electrostatic focusing, focusing the electron beam required a large, heavy and complex mechanical focusing system placed outside the electron gun. electrode, together with an electrode at the final anode voltage of the CRT, may be used for focusing instead. Such an arrangement is called a bipotential lens, which also offers higher performance than an einzel lens, or, focusing may be accomplished using a magnetic focusing coil together with a high anode voltage of dozens of kilovolts. However, magnetic focusing is expensive to implement, so it is rarely used in practice. Some CRTs may use two grids and lenses to focus the electron beam.
There is a voltage called cutoff voltage which is the voltage that creates black on the screen since it causes the image on the screen created by the electron beam to disappear, the voltage is applied to G1. In a color CRT with three guns, the guns have different cutoff voltages. Many CRTs share grid G1 and G2 across all three guns, increasing image brightness and simplifying adjustment since on such CRTs there is a single cutoff voltage for all three guns (since G1 is shared across all guns). Alternatively, the amplifier may be driven by a video processor that also introduces an OSD (On Screen Display) into the video stream that is fed into the amplifier, using a fast blanking signal. TV sets and computer monitors that incorporate CRTs need a DC restoration circuit to provide a video signal to the CRT with a DC component, restoring the original brightness of different parts of the image.
The electron beam may be affected by the Earth's magnetic field, causing it to normally enter the focusing lens off-center; this can be corrected using astigmation controls. Astigmation controls are both magnetic and electronic (dynamic); magnetic does most of the work while electronic is used for fine adjustments. One of the ends of the electron gun has a glass disk, the edges of which are fused with the edge of the neck of the CRT, possibly using frit; the metal leads that connect the electron gun to the outside pass through the disk.
Some electron guns have a quadrupole lens with dynamic focus to alter the shape and adjust the focus of the electron beam, varying the focus voltage depending on the position of the electron beam to maintain image sharpness across the entire screen, specially at the corners. They may also have a bleeder resistor to derive voltages for the grids from the final anode voltage.
After the CRTs were manufactured, they were aged to allow cathode emission to stabilize.
The electron guns in color CRTs are driven by a video amplifier which takes a signal per color channel and amplifies it to 40–170 V per channel, to be fed into the electron gun's cathodes; The amplifier's capabilities limit the resolution, refresh rate and contrast ratio of the CRT, as the amplifier needs to provide high bandwidth and voltage variations at the same time; higher resolutions and refresh rates need higher bandwidths (speed at which voltage can be varied and thus switching between black and white) and higher contrast ratios need higher voltage variations or amplitude for lower black and higher white levels. 30 MHz of bandwidth can usually provide 720p or 1080i resolution, while 20 MHz usually provides around 600 (horizontal, from top to bottom) lines of resolution, for example.
Deflection
<!--split deflection yoke-->
There are two types of deflection: magnetic and electrostatic. Magnetic is usually used in TVs and monitors as it allows for higher deflection angles (and hence shallower CRTs) and deflection power (which allows for higher electron beam current and hence brighter images) while avoiding the need for high voltages for deflection of up to 2 kV,Magnetic deflection
Those that use magnetic deflection may use a yoke that has two pairs of deflection coils; one pair for vertical, and another for horizontal deflection. The yoke can be bonded (be integral) or removable. Those that were bonded used glue or a plastic to bond the yoke to the area between the neck and the funnel of the CRT while those with removable yokes are clamped. and monochrome CRTs. The yoke may be connected using a connector, the order in which the deflection coils of the yoke are connected determines the orientation of the image displayed by the CRT. A CRT needs two deflection circuits: a horizontal and a vertical circuit, which are similar except that the horizontal circuit runs at a much higher frequency (a Horizontal scan rate) of 15–240 kHz depending on the refresh rate of the CRT and the number of horizontal lines to be drawn (the vertical resolution of the CRT). The higher frequency makes it more susceptible to interference, so an automatic frequency control (AFC) circuit may be used to lock the phase of the horizontal deflection signal to that of a sync signal, to prevent the image from becoming distorted diagonally. The vertical frequency varies according to the refresh rate of the CRT. So a CRT with a 60 Hz refresh rate has a vertical deflection circuit running at 60 Hz. The horizontal and vertical deflection signals may be generated using two circuits that work differently; the horizontal deflection signal may be generated using a voltage controlled oscillator (VCO) while the vertical signal may be generated using a triggered relaxation oscillator. In many TVs, the frequencies at which the deflection coils run is in part determined by the inductance value of the coils. for a given screen size, but at the cost of more deflection power and lower optical performance.
Higher deflection power means more current is sent to the deflection coils to bend the electron beam at a higher angle, The deflection power is measured in mA per inch. The horizontal deflection coils may also be driven in part by the horizontal output stage of a TV set. The stage contains a capacitor that is in series with the horizontal deflection coils that performs several functions, among them are: shaping the sawtooth deflection signal to match the curvature of the CRT and centering the image by preventing a DC bias from developing on the coil. At the beginning of retrace, the magnetic field of the coil collapses, causing the electron beam to return to the center of the screen, while at the same time the coil returns energy into capacitors, the energy of which is then used to force the electron beam to go to the left of the screen. The voltage on the horizontal deflection coils is negative when the electron beam is on the left side of the screen and positive when the electron beam is on the right side of the screen. The energy required for deflection is dependent on the energy of the electrons. Higher energy (voltage and/or current) electron beams need more energy to be deflected,
Burn-in
Burn-in is when images are physically "burned" into the screen of the CRT; this occurs due to degradation of the phosphors due to prolonged electron bombardment of the phosphors, and happens when a fixed image or logo is left for too long on the screen, causing it to appear as a "ghost" image or, in severe cases, also when the CRT is off. To counter this, screensavers were used in computers to minimize burn-in. Burn-in is not exclusive to CRTs, as it also happens to plasma displays and OLED displays.
Evacuation
The CRT's partial vacuum of to or less is evacuated or exhausted in a ~375–475 °C oven in a process called baking or bake-out. The evacuation process also outgasses any materials inside the CRT, while decomposing others such as the polyvinyl alcohol used to apply the phosphors. The heating and cooling are done gradually to avoid inducing stress, stiffening and possibly cracking the glass; the oven heats the gases inside the CRT, increasing the speed of the gas molecules which increases the chances of them getting drawn out by the vacuum pump. The temperature of the CRT is kept to below that of the oven, and the oven starts to cool just after the CRT reaches 400 °C, or, the CRT was kept at a temperature higher than 400 °C for up to 15–55 minutes. The CRT was heated during or after evacuation, and the heat may have been used simultaneously to melt the frit in the CRT, joining the screen and funnel. The pump used is a turbomolecular pump or a diffusion pump. Formerly mercury vacuum pumps were also used. After baking, the CRT is disconnected ("sealed or tipped off") from the vacuum pump. The getter is then fired using an RF (induction) coil. The getter is usually in the funnel or in the neck of the CRT. The getter material which is often barium-based, catches any remaining gas particles as it evaporates due to heating induced by the RF coil (that may be combined with exothermic heating within the material); the vapor fills the CRT, trapping any gas molecules that it encounters and condenses on the inside of the CRT forming a layer that contains trapped gas molecules. Hydrogen may be present in the material to help distribute the barium vapor. The material is heated to temperatures above 1000 °C, causing it to evaporate. Partial loss of vacuum in a CRT can result in a hazy image, blue glowing in the neck of the CRT, flashovers, loss of cathode emission or focusing problems. and the last in Europe, RACS, which was located in France, closed in 2013.
Reactivation
Also known as rejuvenation, the goal is to temporarily restore the brightness of a worn CRT. This is often done by carefully increasing the voltage on the cathode heater and the current and voltage on the control grids of the electron gun manually. Some rejuvenators can also fix heater-to-cathode shorts by running a capacitive discharge through the short. and some black and white CRT phosphors also contained beryllium in the form of Zinc beryllium silicate, The phosphors adhere to the screen because of Van der Waals and electrostatic forces. Phosphors composed of smaller particles adhere more strongly to the screen. The phosphors together with the carbon used to prevent light bleeding (in color CRTs) can be easily removed by scratching.
Several dozen types of phosphors were available for CRTs. Phosphors were classified according to color, persistence, luminance rise and fall curves, color depending on anode voltage (for phosphors used in penetration CRTs), Intended use, chemical composition, safety, sensitivity to burn-in, and secondary emission properties. Examples of rare earth phosphors are yttrium oxide for red and yttrium silicide for blue in beam index tubes, while examples of earlier phosphors are copper cadmium sulfide for red,
SMPTE-C phosphors have properties defined by the SMPTE-C standard, which defines a color space of the same name. The standard prioritizes accurate color reproduction, which was made difficult by the different phosphors and color spaces used in the NTSC and PAL color systems. PAL TV sets have subjectively better color reproduction due to the use of saturated green phosphors, which have relatively long decay times that are tolerated in PAL since there is more time in PAL for phosphors to decay, due to its lower framerate. SMPTE-C phosphors were used in professional video monitors.
The phosphor coating on monochrome and color CRTs may have an aluminum coating on its rear side used to reflect light forward, provide protection against ions to prevent ion burn by negative ions on the phosphor, manage heat generated by electrons colliding against the phosphor, prevent static build up that could repel electrons from the screen, form part of the anode and collect the secondary electrons generated by the phosphors in the screen after being hit by the electron beam, providing the electrons with a return path. This is known as filming. The lacquer contains solvents that are later evaporated; the lacquer may be chemically roughened to cause an aluminum coating with holes to be created to allow the solvents to escape. For visual observation of brief transient events, a long persistence phosphor may be desirable. For events which are fast and repetitive, or high frequency, a short-persistence phosphor is generally preferable. The phosphor persistence must be low enough to avoid smearing or ghosting artifacts at high refresh rates. Some blooming is unavoidable, which can be seen as bright areas of an image that expand, distorting or pushing aside surrounding darker areas of the same image. Blooming occurs because bright areas have a higher electron beam current from the electron gun, making the beam wider and harder to focus. Poor voltage regulation causes focus and anode voltage to go down with increasing electron beam current. Thermal expansion causes the shadow mask to expand by around 100 microns.
During normal operation, the shadow mask is heated to around 80–90 °C. Bright areas of images heat the shadow mask more than dark areas, leading to uneven heating of the shadow mask and warping (blooming) due to thermal expansion caused by heating by increased electron beam current. The shadow mask is usually made of steel but it can be made of Invar Coatings that dissipate heat may be applied on the shadow mask to limit blooming in a process called blackening.
Bimetal springs may be used in CRTs used in TVs to compensate for warping that occurs as the electron beam heats the shadow mask, causing thermal expansion. or a rail or frame that is fused to the funnel or the screen glass respectively, 80–85%High voltageImage brightness is related to the anode voltage and to the CRTs size, so higher voltages are needed for both larger screens and higher image brightness. Image brightness is also controlled by the current of the electron beam. since a CRT's exterior is exposed to the full atmospheric pressure, which for instance totals on a 27-inch (400 in<sup>2</sup>) screen. For example, the large 43-inch Sony PVM-4300 weighs , much heavier than 32-inch CRTs (up to ) and 19-inch CRTs (up to ). Much lighter flat panel TVs are only ~ for 32-inch and for 19-inch.
Size is also limited by anode voltage, as it would require a higher dielectric strength to prevent arcing and the electrical losses and ozone generation it causes, without sacrificing image brightness.
Shadow masks also become more difficult to make with increasing resolution and size. Higher deflection angles in color CRTs directly affect convergence at the corners of the screen which requires additional compensation circuitry to handle electron beam power and shape, leading to higher costs and power consumption. Higher deflection angles allow a CRT of a given size to be slimmer, however they also impose more stress on the CRT envelope, specially on the panel, the seal between the panel and funnel and on the funnel. The funnel needs to be long enough to minimize stress, as a longer funnel can be better shaped to have lower stress.
Comparison with other technologies
* LCD advantages over CRT: Lower bulk, power consumption and heat generation, higher refresh rates (up to 360 Hz)
* CRT advantages over LCD: Better color reproduction, no motion blur, multisyncing available in many monitors, no input lag except for computer monitors.
On CRTs, refresh rate depends on resolution, both of which are ultimately limited by the maximum horizontal scanning frequency of the CRT. Motion blur also depends on the decay time of the phosphors. Phosphors that decay too slowly for a given refresh rate may cause smearing or motion blur on the image. In practice, CRTs are limited to a refresh rate of 160 Hz. LCDs that can compete with OLED (Dual Layer, and mini-LED LCDs) are not available in high refresh rates, although quantum dot LCDs (QLEDs) are available in high refresh rates (up to 144 Hz) and are competitive in color reproduction with OLEDs.
CRT monitors can still outperform LCD and OLED monitors in input lag, as there is no signal processing between the CRT and the display connector of the monitor, since CRT monitors often use VGA which provides an analog signal that can be fed to a CRT directly. Video cards designed for use with CRTs may have a RAMDAC to generate the analog signals needed by the CRT. Due to these reasons, CRTs are often preferred for playing video games made in the early 2000s and prior in spite of their bulk, weight and heat generation, with some pieces of technology requiring a CRT to function due to not being built with the functionality of modern displays in mind.
CRTs tend to be more durable than their flat panel counterparts, or sometimes underscan.
Picture tube CRTs have overscan, meaning the actual edges of the image are not shown; this is deliberate to allow for adjustment variations between CRT TVs, preventing the ragged edges (due to blooming) of the image from being shown on screen. The shadow mask may have grooves that reflect away the electrons that do not hit the screen due to overscan. CRTs are also sometimes called Braun tubes.Monochrome CRTsIf the CRT is a black and white (B&W or monochrome) CRT, there is a single electron gun in the neck and the funnel is coated on the inside with aluminum that has been applied by evaporation; the aluminum is evaporated in a vacuum and allowed to condense on the inside of the CRT. In aluminized monochrome CRTs, Aquadag is used on the outside. There is a single aluminum coating covering the funnel and the screen.
Monochrome CRTs may use ring magnets to adjust the centering of the electron beam and magnets around the deflection yoke to adjust the geometry of the image.
When a monochrome CRT is shut off, the screen itself retracts to a small, white dot in the center, along with the phosphors shutting down, shot by the electron gun; it sometimes takes a while for it to go away.
<gallery mode"packed" heights"110px">
File:Osziroehre.jpg|Older monochrome CRT without aluminum, only aquadag
File:Monochrome CRT electron gun close up.jpg|The electron gun of a monochrome CRT
</gallery>
Color CRTs
color CRT]]
(aperture grille) color CRT. A thin horizontal support wire is visible.]]
Color CRTs use three different phosphors which emit red, green, and blue light respectively. They are packed together in stripes (as in aperture grille designs) or clusters called "triads" (as in shadow mask CRTs).
Color CRTs have three electron guns, one for each primary color, (red, green and blue) arranged either in a straight line (in-line) or in an equilateral triangular configuration (the guns are usually constructed as a single unit). The triangular configuration is often called delta-gun, based on its relation to the shape of the Greek letter delta (Δ). The arrangement of the phosphors is the same as that of the electron guns. A grille or mask absorbs the electrons that would otherwise hit the wrong phosphor.
A shadow mask tube uses a metal plate with tiny holes, typically in a delta configuration, placed so that the electron beam only illuminates the correct phosphors on the face of the tube; so that the electrons that strike the inside of any hole will be reflected back, if they are not absorbed (e.g. due to local charge accumulation), instead of bouncing through the hole to strike a random (wrong) spot on the screen. Another type of color CRT (Trinitron) uses an aperture grille of tensioned vertical wires to achieve the same result.
The three electron guns are in the neck (except for Trinitrons) and the red, green and blue phosphors on the screen may be separated by a black grid or matrix (called black stripe by Toshiba). The aluminum coating protects the phosphor from ions, absorbs secondary electrons, providing them with a return path, preventing them from electrostatically charging the screen which would then repel electrons and reduce image brightness, reflects the light from the phosphors forwards and helps manage heat. It also serves as the anode of the CRT together with the inner aquadag coating. The inner coating is electrically connected to an electrode of the electron gun using springs, forming the final anode.Shadow mask
The shadow mask absorbs or reflects electrons that would otherwise strike the wrong phosphor dots,
Shadow masks were replaced in TVs by slot masks in the 1970s, since slot masks let more electrons through, increasing image brightness. Shadow masks may be connected electrically to the anode of the CRT. Trinitron used a single electron gun with three cathodes instead of three complete guns. CRT PC monitors usually use shadow masks, except for Sony's Trinitron, Mitsubishi's Diamondtron and NEC's Cromaclear; Trinitron and Diamondtron use aperture grilles while Cromaclear uses a slot mask. Some shadow mask CRTs have color phosphors that are smaller in diameter than the electron beams used to light them, with the intention being to cover the entire phosphor, increasing image brightness. Shadow masks may be pressed into a curved shape.Screen manufactureEarly color CRTs did not have a black matrix, which was introduced by Zenith in 1969, and Panasonic in 1970.
The phosphors are applied using photolithography. The inner side of the screen is coated with phosphor particles suspended in PVA photoresist slurry, which is then dried using infrared light, exposed, and developed. The exposure is done using a "lighthouse" that uses an ultraviolet light source with a corrector lens to allow the CRT to achieve color purity. Removable shadow masks with spring-loaded clips are used as photomasks. The process is repeated with all colors. Usually the green phosphor is the first to be applied. After phosphor application, the screen is baked to eliminate any organic chemicals (such as the PVA that was used to deposit the phosphor) that may remain on the screen. Alternatively, the phosphors may be applied in a vacuum chamber by evaporating them and allowing them to condense on the screen, creating a very uniform coating. Poor exposure due to insufficient light leads to poor phosphor adhesion to the screen, which limits the maximum resolution of a CRT, as the smaller phosphor dots required for higher resolutions cannot receive as much light due to their smaller size.
After the screen is coated with phosphor and aluminum and the shadow mask installed onto it the screen is bonded to the funnel using a glass frit that may contain 65–88% of lead oxide by weight. The lead oxide is necessary for the glass frit to have a low melting temperature. Boron oxide (III) may also present to stabilize the frit, with alumina powder as filler powder to control the thermal expansion of the frit. The CRT is then baked in an oven in what is called a Lehr bake, to cure the frit, sealing the funnel and screen together. The frit contains a large quantity of lead, causing color CRTs to contain more lead than their monochrome counterparts. Monochrome CRTs on the other hand do not require frit; the funnel can be fused directly to the glass The Lehr bake consists of several successive steps that heat and then cool the CRT gradually until it reaches a temperature of 435–475 °C After the Lehr bake, the CRT is flushed with air or nitrogen to remove contaminants, the electron gun is inserted and sealed into the neck of the CRT, and a vacuum is formed on the CRT. More specifically, the convergence at the center of the screen (with no deflection field applied by the yoke) is called static convergence, and the convergence over the rest of the screen area (specially at the edges and corners) is called dynamic convergence. These movable weak permanent magnets are usually mounted on the back end of the deflection yoke assembly and are set at the factory to compensate for any static purity and convergence errors that are intrinsic to the unadjusted tube. Typically there are two or three pairs of two magnets in the form of rings made of plastic impregnated with a magnetic material, with their magnetic fields parallel to the planes of the magnets, which are perpendicular to the electron gun axes. Often, one pair of rings has 2 poles, another has 4, and the remaining ring has 6 poles. Each pair of magnetic rings forms a single effective magnet whose field vector can be fully and freely adjusted (in both direction and magnitude). By rotating a pair of magnets relative to each other, their relative field alignment can be varied, adjusting the effective field strength of the pair. (As they rotate relative to each other, each magnet's field can be considered to have two opposing components at right angles, and these four components [two each for two magnets] form two pairs, one pair reinforcing each other and the other pair opposing and canceling each other. Rotating away from alignment, the magnets' mutually reinforcing field components decrease as they are traded for increasing opposed, mutually cancelling components.) By rotating a pair of magnets together, preserving the relative angle between them, the direction of their collective magnetic field can be varied. Overall, adjusting all of the convergence/purity magnets allows a finely tuned slight electron beam deflection or lateral offset to be applied, which compensates for minor static convergence and purity errors intrinsic to the uncalibrated tube. Once set, these magnets are usually glued in place, but normally they can be freed and readjusted in the field (e.g. by a TV repair shop) if necessary.
On some CRTs, additional fixed adjustable magnets are added for dynamic convergence or dynamic purity at specific points on the screen, typically near the corners or edges. Further adjustment of dynamic convergence and purity typically cannot be done passively, but requires active compensation circuits, one to correct convergence horizontally and another to correct it vertically. In this case the deflection yoke contains convergence coils, a set of two per color, wound on the same core, to which the convergence signals are applied. That means 6 convergence coils in groups of 3, with 2 coils per group, with one coil for horizontal convergence correction and another for vertical convergence correction, with each group sharing a core. The groups are separated 120° from one another. Dynamic convergence is necessary because the front of the CRT and the shadow mask are not spherical, compensating for electron beam defocusing and astigmatism. The fact that the CRT screen is not spherical leads to geometry problems which may be corrected using a circuit. The signals used for convergence are parabolic waveforms derived from three signals coming from a vertical output circuit. The parabolic signal is fed into the convergence coils, while the other two are sawtooth signals that, when mixed with the parabolic signals, create the necessary signal for convergence. A resistor and diode are used to lock the convergence signal to the center of the screen to prevent it from being affected by the static convergence. The horizontal and vertical convergence circuits are similar. Each circuit has two resonators, one usually tuned to 15,625 Hz and the other to 31,250 Hz, which set the frequency of the signal sent to the convergence coils. Dynamic convergence may be accomplished using electrostatic quadrupole fields in the electron gun. Dynamic convergence means that the electron beam does not travel in a perfectly straight line between the deflection coils and the screen, since the convergence coils cause it to become curved to conform to the screen.
The convergence signal may instead be a sawtooth signal with a slight sine wave appearance, the sine wave part is created using a capacitor in series with each deflection coil. In this case, the convergence signal is used to drive the deflection coils. The sine wave part of the signal causes the electron beam to move more slowly near the edges of the screen. The capacitors used to create the convergence signal are known as the s-capacitors. This type of convergence is necessary due to the high deflection angles and flat screens of many CRT computer monitors. The value of the s-capacitors must be chosen based on the scan rate of the CRT, so multi-syncing monitors must have different sets of s-capacitors, one for each refresh rate. 90° deflection angle CRTs may use "self-convergence" without dynamic convergence, which together with the in-line triad arrangement, eliminates the need for separate convergence coils and related circuitry, reducing costs. complexity and CRT depth by 10 millimeters. Self-convergence works by means of "nonuniform" magnetic fields. Dynamic convergence is necessary in 110° deflection angle CRTs, and quadrupole windings on the deflection yoke at a certain frequency may also be used for dynamic convergence.
Dynamic color convergence and purity are one of the main reasons why until late in their history, CRTs were long-necked (deep) and had biaxially curved faces; these geometric design characteristics are necessary for intrinsic passive dynamic color convergence and purity. Only starting around the 1990s did sophisticated active dynamic convergence compensation circuits become available that made short-necked and flat-faced CRTs workable. These active compensation circuits use the deflection yoke to finely adjust beam deflection according to the beam target location. The same techniques (and major circuit components) also make possible the adjustment of display image rotation, skew, and other complex raster geometry parameters through electronics under user control. Other CRTs may instead use magnets that are pushed in and out instead of rings. The magnetic shield and shadow mask may be permanently magnetized by the earth's magnetic field, adversely affecting color purity when the CRT is moved. This problem is solved with a built-in degaussing coil, found in many TVs and computer monitors. Degaussing may be automatic, occurring whenever the CRT is turned on.
Color CRT displays in TV sets and computer monitors often have a built-in degaussing (demagnetizing) coil mounted around the perimeter of the CRT face. Upon power-up of the CRT display, the degaussing circuit produces a brief, alternating current through the coil which fades to zero over a few seconds, producing a decaying alternating magnetic field from the coil. This degaussing field is strong enough to remove shadow mask magnetization in most cases, maintaining color purity. In unusual cases of strong magnetization where the internal degaussing field is not sufficient, the shadow mask may be degaussed externally with a stronger portable degausser or demagnetizer. However, an excessively strong magnetic field, whether alternating or constant, may mechanically deform (bend) the shadow mask, causing a permanent color distortion on the display which looks very similar to a magnetization effect.
Resolution
Dot pitch defines the maximum resolution of the display, assuming delta-gun CRTs. In these, as the scanned resolution approaches the dot pitch resolution, moiré appears, as the detail being displayed is finer than what the shadow mask can render. Aperture grille monitors do not suffer from vertical moiré, however, because their phosphor stripes have no vertical detail. In smaller CRTs, these strips maintain position by themselves, but larger aperture-grille CRTs require one or two crosswise (horizontal) support strips; one for smaller CRTs, and two for larger ones. The support wires block electrons, causing the wires to be visible. In aperture grille CRTs, dot pitch is replaced by stripe pitch. Hitachi developed the Enhanced Dot Pitch (EDP) shadow mask, which uses oval holes instead of circular ones, with respective oval phosphor dots. and are similar in construction to other monochrome CRTs. Larger projection CRTs in general lasted longer, and were able to provide higher brightness levels and resolution, but were also more expensive. Projection CRTs have an unusually high anode voltage for their size (such as 27 or 25 kV for a 5 or 7-inch projection CRT respectively), and a specially made tungsten/barium cathode (instead of the pure barium oxide normally used) that consists of barium atoms embedded in 20% porous tungsten or barium and calcium aluminates or of barium, calcium and aluminum oxides coated on porous tungsten; the barium diffuses through the tungsten to emit electrons. The special cathode can deliver 2 mA of current instead of the 0.3mA of normal cathodes, or colorless glycol may be used inside a container which may be colored (forming a lens known as a c-element). Colored lenses or glycol are used for improving color reproduction at the cost of brightness, and are only used on red and green CRTs. Each CRT has its own glycol, which has access to an air bubble to allow the glycol to shrink and expand as it cools and warms. Projector CRTs may have adjustment rings just like color CRTs to adjust astigmatism, which is flaring of the electron beam (stray light similar to shadows). They have three adjustment rings; one with two poles, one with four poles, and another with 6 poles. When correctly adjusted, the projector can display perfectly round dots without flaring. The screens used in projection CRTs were more transparent than usual, with 90% transmittance.
Projector CRTs were available with electrostatic and electromagnetic focusing, the latter being more expensive. Electrostatic focusing used electronics to focus the electron beam, together with focusing magnets around the neck of the CRT for fine focusing adjustments. This type of focusing degraded over time. Electromagnetic focusing was introduced in the early 1990s and included an electromagnetic focusing coil in addition to the already existing focusing magnets. Electromagnetic focusing was much more stable over the lifetime of the CRT, retaining 95% of its sharpness by the end of life of the CRT.Beam-index tubeBeam-index tubes, also known as Uniray, Apple CRT or Indextron, was an attempt in the 1950s by Philco to create a color CRT without a shadow mask, eliminating convergence and purity problems, and allowing for shallower CRTs with higher deflection angles. It also required a lower voltage power supply for the final anode since it did not use a shadow mask, which normally blocks around 80% of the electrons generated by the electron gun. The lack of a shadow mask also made it immune to the earth's magnetic field while also making degaussing unnecessary and increasing image brightness. It was constructed similarly to a monochrome CRT, with an aquadag outer coating, an aluminum inner coating, and a single electron gun but with a screen with an alternating pattern of red, green, blue and UV (index) phosphor stripes (similarly to a Trinitron) with a side mounted photomultiplier tube It was revived by Sony in the 1980s as the Indextron but its adoption was limited, at least in part due to the development of LCD displays. Beam-index CRTs also suffered from poor contrast ratios of only around 50:1 since some light emission by the phosphors was required at all times by the photodiodes to track the electron beam. It allowed for single CRT color CRT projectors due to a lack of shadow mask; normally CRT projectors use three CRTs, one for each color, since a lot of heat is generated due to the high anode voltage and beam current, making a shadow mask impractical and inefficient since it would warp under the heat produced (shadow masks absorb most of the electron beam, and, hence, most of the energy carried by the relativistic electrons); the three CRTs meant that an involved calibration and adjustment procedure had to be carried out during installation of the projector, and moving the projector would require it to be recalibrated. A single CRT meant the need for calibration was eliminated, but brightness was decreased since the CRT screen had to be used for three colors instead of each color having its own CRT screen. LG's Flatron technology is based on this technology developed by Zenith, now a subsidiary of LG.
Flat CRTs have a number of challenges, like deflection. Vertical deflection boosters are required to increase the amount of current that is sent to the vertical deflection coils to compensate for the reduced curvature. The TV80 used electrostatic deflection while the Watchman used magnetic deflection with a phosphor screen that was curved inwards. Similar CRTs were used in video door bells.
<gallery mode"packed" heights"150px">
File:SONY 03JM 2.5" Monochrome Flat Watchman CRT side.jpg|The side of a Sony Watchman monochrome CRT. One of the pairs of deflection coils is easily noticeable.
</gallery>
Radar CRTs
Radar CRTs such as the 7JP4 had a circular screen and scanned the beam from the center outwards. The deflection yoke rotated, causing the beam to rotate in a circular fashion. The screen often had two colors, often a bright short persistence color that only appeared as the beam scanned the display and a long persistence phosphor afterglow. When the beam strikes the phosphor, the phosphor brightly illuminates, and when the beam leaves, the dimmer long persistence afterglow would remain lit where the beam struck the phosphor, alongside the radar targets that were "written" by the beam, until the beam re-struck the phosphor.
Oscilloscope CRTs
]]
In oscilloscope CRTs, electrostatic deflection is used, rather than the magnetic deflection commonly used with TV and other large CRTs. The beam is deflected horizontally by applying an electric field between a pair of plates to its left and right, and vertically by applying an electric field to plates above and below. TVs use magnetic rather than electrostatic deflection because the deflection plates obstruct the beam when the deflection angle is as large as is required for tubes that are relatively short for their size. Some Oscilloscope CRTs incorporate post deflection anodes (PDAs) that are spiral-shaped to ensure even anode potential across the CRT and operate at up to 15 kV. In PDA CRTs the electron beam is deflected before it is accelerated, improving sensitivity and legibility, specially when analyzing voltage pulses with short duty cycles.
Microchannel plate
When displaying fast one-shot events, the electron beam must deflect very quickly, with few electrons impinging on the screen, leading to a faint or invisible image on the display. Oscilloscope CRTs designed for very fast signals can give a brighter display by passing the electron beam through a micro-channel plate just before it reaches the screen. Through the phenomenon of secondary emission, this plate multiplies the number of electrons reaching the phosphor screen, giving a significant improvement in writing rate (brightness) and improved sensitivity and spot size as well.GraticulesMost oscilloscopes have a graticule as part of the visual display, to facilitate measurements. The graticule may be permanently marked inside the face of the CRT, or it may be a transparent external plate made of glass or acrylic plastic. An internal graticule eliminates parallax error, but cannot be changed to accommodate different types of measurements. Oscilloscopes commonly provide a means for the graticule to be illuminated from the side, which improves its visibility.
Image storage tubes
These are found in analog phosphor storage oscilloscopes. These are distinct from digital storage oscilloscopes which rely on solid state digital memory to store the image.
Where a single brief event is monitored by an oscilloscope, such an event will be displayed by a conventional tube only while it actually occurs. The use of a long persistence phosphor may allow the image to be observed after the event, but only for a few seconds at best. This limitation can be overcome by the use of a direct view storage cathode-ray tube (storage tube). A storage tube will continue to display the event after it has occurred until such time as it is erased. A storage tube is similar to a conventional tube except that it is equipped with a metal grid coated with a dielectric layer located immediately behind the phosphor screen. An externally applied voltage to the mesh initially ensures that the whole mesh is at a constant potential. This mesh is constantly exposed to a low velocity electron beam from a 'flood gun' which operates independently of the main gun. This flood gun is not deflected like the main gun but constantly 'illuminates' the whole of the storage mesh. The initial charge on the storage mesh is such as to repel the electrons from the flood gun which are prevented from striking the phosphor screen.
When the main electron gun writes an image to the screen, the energy in the main beam is sufficient to create a 'potential relief' on the storage mesh. The areas where this relief is created no longer repel the electrons from the flood gun which now pass through the mesh and illuminate the phosphor screen. Consequently, the image that was briefly traced out by the main gun continues to be displayed after it has occurred. The image can be 'erased' by resupplying the external voltage to the mesh restoring its constant potential. The time for which the image can be displayed was limited because, in practice, the flood gun slowly neutralises the charge on the storage mesh. One way of allowing the image to be retained for longer is temporarily to turn off the flood gun. It is then possible for the image to be retained for several days. The majority of storage tubes allow for a lower voltage to be applied to the storage mesh which slowly restores the initial charge state. By varying this voltage a variable persistence is obtained. Turning off the flood gun and the voltage supply to the storage mesh allows such a tube to operate as a conventional oscilloscope tube.
Vector monitors
Vector monitors were used in early computer aided design systems and are in some late-1970s to mid-1980s arcade games such as Asteroids.
They draw graphics point-to-point, rather than scanning a raster. Either monochrome or color CRTs can be used in vector displays, and the essential principles of CRT design and operation are the same for either type of display; the main difference is in the beam deflection patterns and circuits.
Data storage tubes
The Williams tube or Williams-Kilburn tube was a cathode-ray tube used to electronically store binary data. It was used in computers of the 1940s as a random-access digital storage device. In contrast to other CRTs in this article, the Williams tube was not a display device, and in fact could not be viewed since a metal plate covered its screen.
Cat's eye
In some vacuum tube radio sets, a "Magic Eye" or "Tuning Eye" tube was provided to assist in tuning the receiver. Tuning would be adjusted until the width of a radial shadow was minimized. This was used instead of a more expensive electromechanical meter, which later came to be used on higher-end tuners when transistor sets lacked the high voltage required to drive the device. The same type of device was used with tape recorders as a recording level meter, and for various other applications including electrical test equipment.Charactrons
Some displays for early computers (those that needed to display more text than was practical using vectors, or that required high speed for photographic output) used Charactron CRTs. These incorporate a perforated metal character mask (stencil), which shapes a wide electron beam to form a character on the screen. The system selects a character on the mask using one set of deflection circuits, but that causes the extruded beam to be aimed off-axis, so a second set of deflection plates has to re-aim the beam so it is headed toward the center of the screen. A third set of plates places the character wherever required. The beam is unblanked (turned on) briefly to draw the character at that position. Graphics could be drawn by selecting the position on the mask corresponding to the code for a space (in practice, they were simply not drawn), which had a small round hole in the center; this effectively disabled the character mask, and the system reverted to regular vector behavior. Charactrons had exceptionally long necks, because of the need for three deflection systems.
Nimo
Nimo was the trademark of a family of small specialised CRTs manufactured by Industrial Electronic Engineers. These had 10 electron guns which produced electron beams in the form of digits in a manner similar to that of the charactron. The tubes were either simple single-digit displays or more complex 4- or 6- digit displays produced by means of a suitable magnetic deflection system. Having little of the complexities of a standard CRT, the tube required a relatively simple driving circuit, and as the image was projected on the glass face, it provided a much wider viewing angle than competitive types (e.g., nixie tubes). However, their requirement for several voltages and their high voltage made them uncommon.Flood-beam CRT
Flood-beam CRTs are small tubes that are arranged as pixels for large video walls like Jumbotrons. The first screen using this technology (called Diamond Vision by Mitsubishi Electric) was introduced by Mitsubishi Electric for the 1980 Major League Baseball All-Star Game. It differs from a normal CRT in that the electron gun within does not produce a focused controllable beam. Instead, electrons are sprayed in a wide cone across the entire front of the phosphor screen, basically making each unit act as a single light bulb. Each one is coated with a red, green or blue phosphor, to make up the color sub-pixels. This technology has largely been replaced with light-emitting diode displays. Unfocused and undeflected CRTs were used as grid-controlled stroboscope lamps since 1958. Electron-stimulated luminescence (ESL) lamps, which use the same operating principle, were released in 2011.
Print-head CRT
CRTs with an unphosphored front glass but with fine wires embedded in it were used as electrostatic print heads in the 1960s. The wires would pass the electron beam current through the glass onto a sheet of paper where the desired content was therefore deposited as an electrical charge pattern. The paper was then passed near a pool of liquid ink with the opposite charge. The charged areas of the paper attract the ink and thus form the image.
Zeus – thin CRT display
In the late 1990s and early 2000s Philips Research Laboratories experimented with a type of thin CRT known as the Zeus display, which contained CRT-like functionality in a flat-panel display. The cathode of this display was mounted under the front of the display, and the electrons from the cathode would be directed to the back to the display where they would stay until extracted by electrodes near the front of the display, and directed to the front of the display which had phosphor dots. The devices were demonstrated but never marketed.
Slimmer CRT
Some CRT manufacturers, both LG.Philips Displays (later LP Displays) and Samsung SDI, innovated CRT technology by creating a slimmer tube. Slimmer CRT had the trade names Superslim, Ultraslim, Vixlim (by Samsung) and Cybertube and Cybertube+ (both by LG Philips displays). A flat CRT has a depth. The depth of Superslim was and Ultraslim was .Health concernsIonizing radiationCRTs can emit a small amount of X-ray radiation; this is a result of the electron beam's bombardment of the shadow mask/aperture grille and phosphors, which produces bremsstrahlung (braking radiation) as the high-energy electrons are decelerated. The amount of radiation escaping the front of the monitor is widely considered to be not harmful. The Food and Drug Administration regulations in are used to strictly limit, for instance, TV receivers to 0.5 milliroentgens per hour at a distance of from any external surface; since 2007, most CRTs have emissions that fall well below this limit. Note that the roentgen is an outdated unit and does not account for dose absorption. The conversion rate is about .877 roentgen per rem. Assuming that the viewer absorbed the entire dose (which is unlikely), and that they watched TV for 2 hours a day, a .5 milliroentgen hourly dose would increase the viewers yearly dose by 320 millirem. For comparison, the average background radiation in the United States is 310 millirem a year. Negative effects of chronic radiation are not generally noticeable until doses over 20,000 millirem.
The density of the x-rays that would be generated by a CRT is low because the raster scan of a typical CRT distributes the energy of the electron beam across the entire screen. Voltages above 15,000 volts are enough to generate "soft" x-rays. However, since CRTs may stay on for several hours at a time, the amount of x-rays generated by the CRT may become significant, hence the importance of using materials to shield against x-rays, such as the thick leaded glass and barium-strontium glass used in CRTs.ToxicityOlder color and monochrome CRTs may have been manufactured with toxic substances, such as cadmium, in the phosphors. The rear glass tube of modern CRTs may be made from leaded glass, which represent an environmental hazard if disposed of improperly. Since 1970, glass in the front panel (the viewable portion of the CRT) used strontium oxide rather than lead, though the rear of the CRT was still produced from leaded glass. Monochrome CRTs typically do not contain enough leaded glass to fail EPA TCLP tests. While the TCLP process grinds the glass into fine particles in order to expose them to weak acids to test for leachate, intact CRT glass does not leach (The lead is vitrified, contained inside the glass itself, similar to leaded glass crystalware).
Flicker
At low refresh rates (60 Hz and below), the periodic scanning of the display may produce a flicker that some people perceive more easily than others, especially when viewed with peripheral vision. Flicker is commonly associated with CRT as most TVs run at 50 Hz (PAL) or 60 Hz (NTSC), although there are some 100 Hz PAL TVs that are flicker-free. Typically only low-end monitors run at such low frequencies, with most computer monitors supporting at least 75 Hz and high-end monitors capable of 100 Hz or more to eliminate any perception of flicker. Though the 100 Hz PAL was often achieved using interleaved scanning, dividing the circuit and scan into two beams of 50 Hz. Non-computer CRTs or CRT for sonar or radar may have long persistence phosphor and are thus flicker free. If the persistence is too long on a video display, moving images will be blurred.
High-frequency audible noise
50 Hz/60 Hz CRTs used for TV operate with horizontal scanning frequencies of 15,750 and 15,734.27 Hz (for NTSC systems) or 15,625 Hz (for PAL systems). These frequencies are at the upper range of human hearing and are inaudible to many people; however, some people (especially children) will perceive a high-pitched tone near an operating CRT TV. The sound is due to magnetostriction in the magnetic core and periodic movement of windings of the flyback transformer but the sound can also be created by movement of the deflection coils, yoke or ferrite beads.
This problem does not occur on 100/120 Hz TVs and on non-CGA (Color Graphics Adapter) computer displays, because they use much higher horizontal scanning frequencies that produce sound which is inaudible to humans (22 kHz to over 100 kHz).
Implosion
If the glass wall is damaged, atmospheric pressure can implode the vacuum tube into dangerous fragments which accelerate inward and then spray at high speed in all directions. Although modern cathode-ray tubes used in TVs and computer displays have epoxy-bonded face-plates or other measures to prevent shattering of the envelope, CRTs must be handled carefully to avoid injury.Implosion protection
1500 terminal with exposed chassis, with its CRT suffering from a "cataract" due to aging PVA]]
Early CRTs had a glass plate over the screen that was bonded to it using glue, while later versions such as the LG Flatron used a resin, perhaps a UV-curable resin.
Older CRTs were mounted to the TV set using a frame. The band is tensioned by heating it, then mounting it on the CRT; the band cools afterwards, shrinking in size and putting the glass under compression, which strengthens the glass and reduces the necessary thickness (and hence weight) of the glass. This makes the band an integral component that should never be removed from an intact CRT that still has a vacuum; attempting to remove it may cause the CRT to implode. to achieve sufficient image brightness, a very high voltage (EHT or extra-high tension) is required, from a few thousand volts for a small oscilloscope CRT to tens of thousands for a larger screen color TV. This is many times greater than household power supply voltage. Even after the power supply is turned off, some associated capacitors and the CRT itself may retain a charge for some time and therefore dissipate that charge suddenly through a ground such as an inattentive human grounding a capacitor discharge lead. An average monochrome CRT may use 1–1.5 kV of anode voltage per inch. Special TEMPEST shielding can mitigate this effect. Such radiation of a potentially exploitable signal, however, occurs also with other display technologies and with electronics in general.
Recycling
Due to the toxins contained in CRT monitors the United States Environmental Protection Agency created rules (in October 2001) stating that CRTs must be brought to special e-waste recycling facilities. In November 2002, the EPA began fining companies that disposed of CRTs through landfills or incineration. Regulatory agencies, local and statewide, monitor the disposal of CRTs and other computer equipment.
As electronic waste, CRTs are considered one of the hardest types to recycle. CRTs have relatively high concentration of lead and , both of which are necessary for the display. There are several companies in the United States that charge a small fee to collect CRTs, then subsidize their labor by selling the harvested copper, wire, and printed circuit boards. The United States Environmental Protection Agency (EPA) includes discarded CRT monitors in its category of "hazardous household waste" but considers CRTs that have been set aside for testing to be commodities if they are not discarded, speculatively accumulated, or left unprotected from weather and other damage.
Various states participate in the recycling of CRTs, each with their reporting requirements for collectors and recycling facilities. For example, in California the recycling of CRTs is governed by CALRecycle, the California Department of Resources Recycling and Recovery through their Payment System. Recycling facilities that accept CRT devices from business and residential sector must obtain contact information such as address and phone number to ensure the CRTs come from a California source in order to participate in the CRT Recycling Payment System.
In Europe, disposal of CRT TVs and monitors is covered by the WEEE Directive.
Multiple methods have been proposed for the recycling of CRT glass. The methods involve thermal, mechanical and chemical processes. All proposed methods remove the lead oxide content from the glass. Some companies operated furnaces to separate the lead from the glass. A coalition called the Recytube project was once formed by several European companies to devise a method to recycle CRTs.
The funnel can be separated from the screen of the CRT using laser cutting, diamond saws or wires or using a resistively heated nichrome wire.
Leaded CRT glass was sold to be remelted into other CRTs, concrete, concrete and cement bricks, fiberglass insulation or used as flux in metals smelting.
A considerable portion of CRT glass is landfilled, where it can pollute the surrounding environment.
See also
* Cathodoluminescence
* Crookes tube
* Scintillation (physics)
*Laser-powered phosphor display, similar to a CRT, replaces the electron beam with a laser beam
Applying CRT in different display-purpose:
* Analog television
* Image displaying
* Comparison of CRT, LCD, plasma, and OLED displays
* Overscan
* Raster scan
* Scan line
Historical aspects:
* Direct-view bistable storage tube
* Flat-panel display
* Geer tube
* History of display technology
* Image dissector
* LCD television, LED-backlit LCD, LED display
* Penetron
* Surface-conduction electron-emitter display
* Trinitron
Safety and precautions:
* Monitor filter
* Photosensitive epilepsy
* TCO Certification
Notes
References
Selected patents
* : Zworykin Television System
External links
*
*
*
Category:Consumer electronics
Category:Display technology
Category:Television technology
Category:Vacuum tube displays
Category:Audiovisual introductions in 1897
Category:Telecommunications-related introductions in 1897
Category:Articles containing video clips
Category:Legacy hardware
Category:Retro style
|
https://en.wikipedia.org/wiki/Cathode-ray_tube
|
2025-04-05T18:27:41.248663
|
6015
|
Crystal
|
thumb|upright=1.25|Crystals of amethyst quartz
thumb|upright=1.25|Microscopically, a single crystal has atoms in a near-perfect periodic arrangement; a polycrystal is composed of many microscopic crystals (called "crystallites" or "grains"); and an amorphous solid (such as glass) has no periodic arrangement even microscopically.
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification.
The word crystal derives from the Ancient Greek word (), meaning both "ice" and "rock crystal", from (), "icy cold, frost".
Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most metals, rocks, ceramics, and ice. A third category of solids is amorphous solids, where the atoms have no periodic structure whatsoever. Examples of amorphous solids include glass, wax, and many plastics.
Despite the name, lead crystal, crystal glass, and related products are not crystals, but rather types of glass, i.e. amorphous solids.
Crystals, or crystalline solids, are often used in pseudoscientific practices such as crystal therapy, and, along with gemstones, are sometimes associated with spellwork in Wiccan beliefs and related religious movements.
Crystal structure (microscopic)
The scientific definition of a "crystal" is based on the microscopic arrangement of atoms inside it, called the crystal structure. A crystal is a solid where the atoms form a periodic arrangement. (Quasicrystals are an exception, see below).
Not all solids are crystals. For example, when liquid water starts freezing, the phase change begins with small ice crystals that grow until they fuse, forming a polycrystalline structure. In the final block of ice, each of the small crystals (called "crystallites" or "grains") is a true crystal with a periodic arrangement of atoms, but the whole polycrystal does not have a periodic arrangement of atoms, because the periodic pattern is broken at the grain boundaries. Most macroscopic inorganic solids are polycrystalline, including almost all metals, ceramics, ice, rocks, etc. Solids that are neither crystalline nor polycrystalline, such as glass, are called amorphous solids, also called glassy, vitreous, or noncrystalline. These have no periodic order, even microscopically. There are distinct differences between crystalline solids and amorphous solids: most notably, the process of forming a glass does not release the latent heat of fusion, but forming a crystal does.
A crystal structure (an arrangement of atoms in a crystal) is characterized by its unit cell, a small imaginary box containing one or more atoms in a specific spatial arrangement. The unit cells are stacked in three-dimensional space to form the crystal.
The symmetry of a crystal is constrained by the requirement that the unit cells stack perfectly with no gaps. There are 219 possible crystal symmetries (230 is commonly cited, but this treats chiral equivalents as separate entities), called crystallographic space groups. These are grouped into 7 crystal systems, such as cubic crystal system (where the crystals may form cubes or rectangular boxes, such as halite shown at right) or hexagonal crystal system (where the crystals may form hexagons, such as ordinary water ice).
Crystal faces, shapes and crystallographic forms
thumb|upright=1.6|As a halite crystal is growing, new atoms can very easily attach to the parts of the surface with rough atomic-scale structure and many dangling bonds. Therefore, these parts of the crystal grow out very quickly (yellow arrows). Eventually, the whole surface consists of smooth, stable faces, where new atoms cannot as easily attach themselves.
Crystals are commonly recognized, macroscopically, by their shape, consisting of flat faces with sharp angles. These shape characteristics are not necessary for a crystal—a crystal is scientifically defined by its microscopic atomic arrangement, not its macroscopic shape—but the characteristic macroscopic shape is often present and easy to see.
Euhedral crystals are those that have obvious, well-formed flat faces. Anhedral crystals do not, usually because the crystal is one grain in a polycrystalline solid.
The flat faces (also called facets) of a euhedral crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal: they are planes of relatively low Miller index. This occurs because some surface orientations are more stable than others (lower surface energy). As a crystal grows, new atoms attach easily to the rougher and less stable parts of the surface, but less easily to the flat, stable surfaces. Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces. (See diagram on right.)
One of the oldest techniques in the science of crystallography consists of measuring the three-dimensional orientations of the faces of a crystal, and using them to infer the underlying crystal symmetry.
A crystal's crystallographic forms are sets of possible faces of the crystal that are related by one of the symmetries of the crystal. For example, crystals of galena often take the shape of cubes, and the six faces of the cube belong to a crystallographic form that displays one of the symmetries of the isometric crystal system. Galena also sometimes crystallizes as octahedrons, and the eight faces of the octahedron belong to another crystallographic form reflecting a different symmetry of the isometric system. A crystallographic form is described by placing the Miller indices of one of its faces within brackets. For example, the octahedral form is written as {111}, and the other faces in the form are implied by the symmetry of the crystal.
Forms may be closed, meaning that the form can completely enclose a volume of space, or open, meaning that it cannot. The cubic and octahedral forms are examples of closed forms. All the forms of the isometric system are closed, while all the forms of the monoclinic and triclinic crystal systems are open. A crystal's faces may all belong to the same closed form, or they may be a combination of multiple open or closed forms.
A crystal's habit is its visible external shape. This is determined by the crystal structure (which restricts the possible facet orientations), the specific crystal chemistry and bonding (which may favor some facet types over others), and the conditions under which the crystal formed.
Occurrence in nature
thumb|right|Ice crystals
thumb|Fossil shell with calcite crystals
Rocks
By volume and weight, the largest concentrations of crystals in the Earth are part of its solid bedrock. Crystals found in rocks typically range in size from a fraction of a millimetre to several centimetres across, although exceptionally large crystals are occasionally found. , the world's largest known naturally occurring crystal is a crystal of beryl from Malakialina, Madagascar, long and in diameter, and weighing .
Some crystals have formed by magmatic and metamorphic processes, giving origin to large masses of crystalline rock. The vast majority of igneous rocks are formed from molten magma and the degree of crystallization depends primarily on the conditions under which they solidified. Such rocks as granite, which have cooled very slowly and under great pressures, have completely crystallized; but many kinds of lava were poured out at the surface and cooled very rapidly, and in this latter group a small amount of amorphous or glassy matter is common. Other crystalline rocks, the metamorphic rocks such as marbles, mica-schists and quartzites, are recrystallized. This means that they were at first fragmental rocks like limestone, shale and sandstone and have never been in a molten condition nor entirely in solution, but the high temperature and pressure conditions of metamorphism have acted on them by erasing their original structures and inducing recrystallization in the solid state.
Other rock crystals have formed out of precipitation from fluids, commonly water, to form druses or quartz veins. Evaporites such as halite, gypsum and some limestones have been deposited from aqueous solution, mostly owing to evaporation in arid climates.
Ice
Water-based ice in the form of snow, sea ice, and glaciers are common crystalline/polycrystalline structures on Earth and other planets. A single snowflake is a single crystal or a collection of crystals, while an ice cube is a polycrystal. Ice crystals may form from cooling liquid water below its freezing point, such as ice cubes or a frozen lake. Frost, snowflakes, or small ice crystals suspended in the air (ice fog) more often grow from a supersaturated gaseous-solution of water vapor and air, when the temperature of the air drops below its dew point, without passing through a liquid state. Another unusual property of water is that it expands rather than contracts when it crystallizes.
Organigenic crystals
Many living organisms are able to produce crystals grown from an aqueous solution, for example calcite and aragonite in the case of most molluscs or hydroxylapatite in the case of bones and teeth in vertebrates.
Polymorphism and allotropy
The same group of atoms can often solidify in many different ways. Polymorphism is the ability of a solid to exist in more than one crystal form. For example, water ice is ordinarily found in the hexagonal form Ice Ih, but can also exist as the cubic Ice Ic, the rhombohedral ice II, and many other forms. The different polymorphs are usually called different phases.
In addition, the same atoms may be able to form noncrystalline phases. For example, water can also form amorphous ice, while SiO2 can form both fused silica (an amorphous glass) and quartz (a crystal). Likewise, if a substance can form crystals, it can also form polycrystals.
For pure chemical elements, polymorphism is referred to as allotropy. For example, diamond and graphite are two crystalline forms of carbon, while amorphous carbon is a noncrystalline form. Polymorphs, despite having the same atoms, may have very different properties. For example, diamond is the hardest substance known, while graphite is so soft that it is used as a lubricant. Chocolate can form six different types of crystals, but only one has the suitable hardness and melting point for candy bars and confections. Polymorphism in steel is responsible for its ability to be heat treated, giving it a wide range of properties.
Polyamorphism is a similar phenomenon where the same atoms can exist in more than one amorphous solid form.
Crystallization
thumb|upright|Vertical cooling crystallizer in a beet sugar factory.
Crystallization is the process of forming a crystalline structure from a fluid or from materials dissolved in a fluid. (More rarely, crystals may be deposited directly from gas; see: epitaxy and frost.)
Crystallization is a complex and extensively-studied field, because depending on the conditions, a single fluid can solidify into many different possible forms. It can form a single crystal, perhaps with various possible phases, stoichiometries, impurities, defects, and habits. Or, it can form a polycrystal, with various possibilities for the size, arrangement, orientation, and phase of its grains. The final form of the solid is determined by the conditions under which the fluid is being solidified, such as the chemistry of the fluid, the ambient pressure, the temperature, and the speed with which all these parameters are changing.
Specific industrial techniques to produce large single crystals (called boules) include the Czochralski process and the Bridgman technique. Other less exotic methods of crystallization may be used, depending on the physical properties of the substance, including hydrothermal synthesis, sublimation, or simply solvent-based crystallization.
Large single crystals can be created by geological processes. For example, selenite crystals in excess of 10 m are found in the Cave of the Crystals in Naica, Mexico. For more details on geological crystal formation, see above.
Crystals can also be formed by biological processes, see above. Conversely, some organisms have special techniques to prevent crystallization from occurring, such as antifreeze proteins.
Defects, impurities, and twinning
thumb|left|upright=1.25|Two types of crystallographic defects. Top right: edge dislocation. Bottom right: screw dislocation.
An ideal crystal has every atom in a perfect, exactly repeating pattern. However, in reality, most crystalline materials have a variety of crystallographic defects: places where the crystal's pattern is interrupted. The types and structures of these defects may have a profound effect on the properties of the materials.
A few examples of crystallographic defects include vacancy defects (an empty space where an atom should fit), interstitial defects (an extra atom squeezed in where it does not fit), and dislocations (see figure at right). Dislocations are especially important in materials science, because they help determine the mechanical strength of materials.
Another common type of crystallographic defect is an impurity, meaning that the "wrong" type of atom is present in a crystal. For example, a perfect crystal of diamond would only contain carbon atoms, but a real crystal might perhaps contain a few boron atoms as well. These boron impurities change the diamond's color to slightly blue. Likewise, the only difference between ruby and sapphire is the type of impurities present in a corundum crystal.
thumb|Twinned pyrite crystal group.
In semiconductors, a special type of impurity, called a dopant, drastically changes the crystal's electrical properties. Semiconductor devices, such as transistors, are made possible largely by putting different semiconductor dopants into different places, in specific patterns.
Twinning is a phenomenon somewhere between a crystallographic defect and a grain boundary. Like a grain boundary, a twin boundary has different crystal orientations on its two sides. But unlike a grain boundary, the orientations are not random, but related in a specific, mirror-image way.
Mosaicity is a spread of crystal plane orientations. A mosaic crystal consists of smaller crystalline units that are somewhat misaligned with respect to each other.
Chemical bonds
In general, solids can be held together by various types of chemical bonds, such as metallic bonds, ionic bonds, covalent bonds, van der Waals bonds, and others. None of these are necessarily crystalline or non-crystalline. However, there are some general trends as follows:
Metals crystallize rapidly and are almost always polycrystalline, though there are exceptions like amorphous metal and single-crystal metals. The latter are grown synthetically, for example, fighter-jet turbines are typically made by first growing a single crystal of titanium alloy, increasing its strength and melting point over polycrystalline titanium. A small piece of metal may naturally form into a single crystal, such as Type 2 telluric iron, but larger pieces generally do not unless extremely slow cooling occurs. For example, iron meteorites are often composed of single crystal, or many large crystals that may be several meters in size, due to very slow cooling in the vacuum of space. The slow cooling may allow the precipitation of a separate phase within the crystal lattice, which form at specific angles determined by the lattice, called Widmanstatten patterns.
Ionic compounds typically form when a metal reacts with a non-metal, such as sodium with chlorine. These often form substances called salts, such as sodium chloride (table salt) or potassium nitrate (saltpeter), with crystals that are often brittle and cleave relatively easily. Ionic materials are usually crystalline or polycrystalline. In practice, large salt crystals can be created by solidification of a molten fluid, or by crystallization out of a solution. Some ionic compounds can be very hard, such as oxides like aluminium oxide found in many gemstones such as ruby and synthetic sapphire.
Covalently bonded solids (sometimes called covalent network solids) are typically formed from one or more non-metals, such as carbon or silicon and oxygen, and are often very hard, rigid, and brittle. These are also very common, notable examples being diamond and quartz respectively.
Weak van der Waals forces also help hold together certain crystals, such as crystalline molecular solids, as well as the interlayer bonding in graphite. Substances such as fats, lipids and wax form molecular bonds because the large molecules do not pack as tightly as atomic bonds. This leads to crystals that are much softer and more easily pulled apart or broken. Common examples include chocolates, candles, or viruses. Water ice and dry ice are examples of other materials with molecular bonding.Polymer materials generally will form crystalline regions, but the lengths of the molecules usually prevent complete crystallization—and sometimes polymers are completely amorphous.
Quasicrystals
thumb|The material holmium–magnesium–zinc (Ho–Mg–Zn) forms quasicrystals, which can take on the macroscopic shape of a pentagonal dodecahedron. Only quasicrystals can take this 5-fold symmetry. The edges are 2 mm long.
A quasicrystal consists of arrays of atoms that are ordered but not strictly periodic. They have many attributes in common with ordinary crystals, such as displaying a discrete pattern in x-ray diffraction, and the ability to form shapes with smooth, flat faces.
Quasicrystals are most famous for their ability to show five-fold symmetry, which is impossible for an ordinary periodic crystal (see crystallographic restriction theorem).
The International Union of Crystallography has redefined the term "crystal" to include both ordinary periodic crystals and quasicrystals ("any solid having an essentially discrete diffraction diagram").
Quasicrystals, first discovered in 1982, are quite rare in practice. Only about 100 solids are known to form quasicrystals, compared to about 400,000 periodic crystals known in 2004. The 2011 Nobel Prize in Chemistry was awarded to Dan Shechtman for the discovery of quasicrystals.
Special properties from anisotropy
Crystals can have certain special electrical, optical, and mechanical properties that glass and polycrystals normally cannot. These properties are related to the anisotropy of the crystal, i.e. the lack of rotational symmetry in its atomic arrangement. One such property is the piezoelectric effect, where a voltage across the crystal can shrink or stretch it. Another is birefringence, where a double image appears when looking through a crystal. Moreover, various properties of a crystal, including electrical conductivity, electrical permittivity, and Young's modulus, may be different in different directions in a crystal. For example, graphite crystals consist of a stack of sheets, and although each individual sheet is mechanically very strong, the sheets are rather loosely bound to each other. Therefore, the mechanical strength of the material is quite different depending on the direction of stress.
Not all crystals have all of these properties. Conversely, these properties are not quite exclusive to crystals. They can appear in glasses or polycrystals that have been made anisotropic by working or stress—for example, stress-induced birefringence.
Crystallography
Crystallography is the science of measuring the crystal structure (in other words, the atomic arrangement) of a crystal. One widely used crystallography technique is X-ray diffraction. Large numbers of known crystal structures are stored in crystallographic databases.
Image gallery
File:Insulincrystals.jpg|Insulin crystals grown in earth orbit. The low gravity allows crystals to be grown with minimal defects.
File:Hoar frost macro2.jpg|Hoar frost: A type of ice crystal (picture taken from a distance of about 5 cm).
File:Gallium crystals.jpg|Gallium, a metal that easily forms large crystals.
File:Apatite-Rhodochrosite-Fluorite-169799.jpg|An apatite crystal sits front and center on cherry-red rhodochroite rhombs, purple fluorite cubes, quartz and a dusting of brass-yellow pyrite cubes.
File:Monokristalines Silizium für die Waferherstellung.jpg|Boules of silicon, like this one, are an important type of industrially-produced single crystal.
File:Bornite-Chalcopyrite-Pyrite-180794.jpg|A specimen consisting of a bornite-coated chalcopyrite crystal nestled in a bed of clear quartz crystals and lustrous pyrite crystals. The bornite-coated crystal is up to 1.5 cm across.
File:Calcite-millerite association.jpg|Needle-like millerite crystals partially encased in calcite crystal and oxidized on their surfaces to zaratite; from the Devonian Milwaukee Formation of Wisconsin
File:Crystallized sugar, multiple crystals and a single crystal grown from seed.jpg|Crystallized sugar. Crystals on the right were grown from a sugar cube, while the left from a single seed crystal taken from the right. Red dye was added to the solution when growing the larger crystal, but, insoluble with the solid sugar, all but small traces were forced to precipitate out as it grew.
See also
Atomic packing factor
Anticrystal
Cocrystal
Colloidal crystal
Crystal growth
Crystal oscillator
Liquid crystal
Time crystal
References
Further reading
|
https://en.wikipedia.org/wiki/Crystal
|
2025-04-05T18:27:41.278456
|
6016
|
Cytosine
|
| ChemSpiderID = 577
| ChEMBL_Ref =
| ChEMBL = 15913
| StdInChI_Ref =
| StdInChI = 1S/C4H5N3O/c5-3-1-2-6-4(8)7-3/h1-2H,(H3,5,6,7,8)
| StdInChIKey_Ref =
| StdInChIKey = OPTASPLRGRRNAP-UHFFFAOYSA-N
| CASNo = 71-30-7
| CASNo_Ref =
| PubChem = 597
| UNII_Ref =
| UNII = 8J337D1HZY
| ChEBI_Ref =
| ChEBI = 16040
| SMILES OC1Nccc(N)n1
| KEGG_Ref =
| KEGG = C00380
| InChI = 1/C4H5N3O/c5-3-1-2-6-4(8)7-3/h1-2H,(H3,5,6,7,8)
| InChIKey = OPTASPLRGRRNAP-UHFFFAOYAY
| MeSHName = Cytosine
}}
| Section2 =
| Section3 =
}}
Cytosine () (symbol C or Cyt) is one of the four nucleotide bases found in DNA and RNA, along with adenine, guanine, and thymine (uracil in RNA). It is a pyrimidine derivative, with a heterocyclic aromatic ring and two substituents attached (an amine group at position 4 and a keto group at position 2). The nucleoside of cytosine is cytidine. In Watson–Crick base pairing, it forms three hydrogen bonds with guanine.
History
Cytosine was discovered and named by Albrecht Kossel and Albert Neumann in 1894 when it was hydrolyzed from calf thymus tissues. A structure was proposed in 1903, and was synthesized (and thus confirmed) in the laboratory in the same year.
In 1998, cytosine was used in an early demonstration of quantum information processing when Oxford University researchers implemented the Deutsch–Jozsa algorithm on a two qubit nuclear magnetic resonance quantum computer (NMRQC).
In March 2015, NASA scientists reported the formation of cytosine, along with uracil and thymine, from pyrimidine under the space-like laboratory conditions, which is of interest because pyrimidine has been found in meteorites although its origin is unknown.Chemical reactions<div class'skin-invert-image'>
</div>
Cytosine can be found as part of DNA, as part of RNA, or as a part of a nucleotide. As cytidine triphosphate (CTP), it can act as a co-factor to enzymes, and can transfer a phosphate to convert adenosine diphosphate (ADP) to adenosine triphosphate (ATP).
In DNA and RNA, cytosine is paired with guanine. However, it is inherently unstable, and can change into uracil (spontaneous deamination). This can lead to a point mutation if not repaired by the DNA repair enzymes such as uracil glycosylase, which cleaves a uracil in DNA.
Cytosine can also be methylated into 5-methylcytosine by an enzyme called DNA methyltransferase or be methylated and hydroxylated to make 5-hydroxymethylcytosine. The difference in rates of deamination of cytosine and 5-methylcytosine (to uracil and thymine) forms the basis of bisulfite sequencing.
Biological function
When found third in a codon of RNA, cytosine is synonymous with uracil, as they are interchangeable as the third base.
When found as the second base in a codon, the third is always interchangeable. For example, UCU, UCC, UCA and UCG are all serine, regardless of the third base.
Active enzymatic deamination of cytosine or 5-methylcytosine by the APOBEC family of cytosine deaminases could have both beneficial and detrimental implications on various cellular processes as well as on organismal evolution. The implications of deamination on 5-hydroxymethylcytosine, on the other hand, remains less understood.
Theoretical aspects
Until October 2021, Cytosine had not been found in meteorites, which suggested the first strands of RNA and DNA had to look elsewhere to obtain this building block. Cytosine likely formed within some meteorite parent bodies, however did not persist within these bodies due to an effective deamination reaction into uracil.
In October 2021, Cytosine was announced as having been found in meteorites by researchers in a joint Japan/NASA project, that used novel methods of detection which avoided damaging nucleotides as they were extracted from meteorites.
References
External links and citations
* [https://web.archive.org/web/20190416021636/http://gmd.mpimp-golm.mpg.de/Spectrums/04ef65b4-ae00-4bbf-b115-64d1aa7e0fcd.aspx Cytosine MS Spectrum]
*
*
Category:Nucleobases
Category:Amines
Category:Pyrimidones
|
https://en.wikipedia.org/wiki/Cytosine
|
2025-04-05T18:27:41.284831
|
6019
|
Computational chemistry
|
thumb|C60 molecule with isosurface of ground-state electron density as calculated with density functional theory
Computational chemistry is a branch of chemistry that uses computer simulations to assist in solving chemical problems. It uses methods of theoretical chemistry incorporated into computer programs to calculate the structures and properties of molecules, groups of molecules, and solids. The importance of this subject stems from the fact that, with the exception of some relatively recent findings related to the hydrogen molecular ion (dihydrogen cation), achieving an accurate quantum mechanical depiction of chemical systems analytically, or in a closed form, is not feasible. The complexity inherent in the many-body problem exacerbates the challenge of providing detailed descriptions of quantum mechanical systems. While computational results normally complement information obtained by chemical experiments, it can occasionally predict unobserved chemical phenomena.
Overview
Computational chemistry differs from theoretical chemistry, which involves a mathematical description of chemistry. However, computational chemistry involves the usage of computer programs and additional mathematical skills in order to accurately model various chemical problems. In theoretical chemistry, chemists, physicists, and mathematicians develop algorithms and computer programs to predict atomic and molecular properties and reaction paths for chemical reactions. Computational chemists, in contrast, may simply apply existing computer programs and methodologies to specific chemical questions.
Historically, computational chemistry has had two different aspects:
Finding a starting point for a laboratory synthesis or assisting in understanding experimental data, such as the position and source of spectroscopic peaks.
Predicting the possibility of so-far unknown molecules or exploring reaction mechanisms not readily studied via experiments. The books that were influential in the early development of computational quantum chemistry include Linus Pauling and E. Bright Wilson's 1935 Introduction to Quantum Mechanics – with Applications to Chemistry, Eyring, Walter and Kimball's 1944 Quantum Chemistry, Heitler's 1945 Elementary Wave Mechanics – with Applications to Quantum Chemistry, and later Coulson's 1952 textbook Valence, each of which served as primary references for chemists in the decades to follow.
With the development of efficient computer technology in the 1940s, the solutions of elaborate wave equations for complex atomic systems began to be a realizable objective. In the early 1950s, the first semi-empirical atomic orbital calculations were performed. Theoretical chemists became extensive users of the early digital computers. One significant advancement was marked by Clemens C. J. Roothaan's 1951 paper in the Reviews of Modern Physics. This paper focused largely on the "LCAO MO" approach (Linear Combination of Atomic Orbitals Molecular Orbitals). For many years, it was the second-most cited paper in that journal. The first ab initio Hartree–Fock method calculations on diatomic molecules were performed in 1956 at MIT, using a basis set of Slater orbitals. For diatomic molecules, a systematic study using a minimum basis set and the first calculation with a larger basis set were published by Ransil and Nesbet respectively in 1960. The first polyatomic calculations using Gaussian orbitals were performed in the late 1950s. The first configuration interaction calculations were performed in Cambridge on the EDSAC computer in the 1950s using Gaussian orbitals by Boys and coworkers. By 1971, when a bibliography of ab initio calculations was published, the largest molecules included were naphthalene and azulene. Abstracts of many earlier developments in ab initio theory have been published by Schaefer.
In 1964, Hückel method calculations (using a simple linear combination of atomic orbitals (LCAO) method to determine electron energies of molecular orbitals of π electrons in conjugated hydrocarbon systems) of molecules, ranging in complexity from butadiene and benzene to ovalene, were generated on computers at Berkeley and Oxford. These empirical methods were replaced in the 1960s by semi-empirical methods such as CNDO.
In the early 1970s, efficient ab initio computer programs such as ATMOL, Gaussian, IBMOL, and POLYAYTOM, began to be used to speed ab initio calculations of molecular orbitals. Of these four programs, only Gaussian, now vastly expanded, is still in use, but many other programs are now in use.
One of the first mentions of the term computational chemistry can be found in the 1970 book Computers and Their Role in the Physical Sciences by Sidney Fernbach and Abraham Haskell Taub, where they state "It seems, therefore, that 'computational chemistry' can finally be more and more of a reality." During the 1970s, widely different methods began to be seen as part of a new emerging discipline of computational chemistry. The Journal of Computational Chemistry was first published in 1980.
Computational chemistry has featured in several Nobel Prize awards, most notably in 1998 and 2013. Walter Kohn, "for his development of the density-functional theory", and John Pople, "for his development of computational methods in quantum chemistry", received the 1998 Nobel Prize in Chemistry. Martin Karplus, Michael Levitt and Arieh Warshel received the 2013 Nobel Prize in Chemistry for "the development of multiscale models for complex chemical systems".
Applications
There are several fields within computational chemistry.
The prediction of the molecular structure of molecules by the use of the simulation of forces, or more accurate quantum chemical methods, to find stationary points on the energy surface as the position of the nuclei is varied.
Storing and searching for data on chemical entities (see chemical databases).
Identifying correlations between chemical structures and properties (see quantitative structure–property relationship (QSPR) and quantitative structure–activity relationship (QSAR)).
Computational approaches to help in the efficient synthesis of compounds.
Computational approaches to design molecules that interact in specific ways with other molecules (e.g. drug design and catalysis).
These fields can give rise to several applications as shown below.
Catalysis
thumb|Computational chemistry can help predict values like activation energy from catalysis. The presence of the catalyst opens a different reaction pathway (shown in red) with lower activation energy. The final result and the overall thermodynamics are the same.
Computational chemistry is a tool for analyzing catalytic systems without doing experiments. Modern electronic structure theory and density functional theory has allowed researchers to discover and understand catalysts. Computational studies apply theoretical chemistry to catalysis research. Density functional theory methods calculate the energies and orbitals of molecules to give models of those structures. Using these methods, researchers can predict values like activation energy, site reactivity and other thermodynamic properties. Methods like density functional theory can be used to model drug molecules and find their properties, like their HOMO and LUMO energies and molecular orbitals. Computational chemists also help companies with developing informatics, infrastructure and designs of drugs.
Aside from drug synthesis, drug carriers are also researched by computational chemists for nanomaterials. It allows researchers to simulate environments to test the effectiveness and stability of drug carriers. Understanding how water interacts with these nanomaterials ensures stability of the material in human bodies. These computational simulations help researchers optimize the material find the best way to structure these nanomaterials before making them.
Computational chemistry databases
Databases are useful for both computational and non computational chemists in research and verifying the validity of computational methods. Empirical data is used to analyze the error of computational methods against experimental data. Empirical data helps researchers with their methods and basis sets to have greater confidence in the researchers results. Computational chemistry databases are also used in testing software or hardware for computational chemistry.
Databases can also use purely calculated data. Purely calculated data uses calculated values over experimental values for databases. Purely calculated data avoids dealing with these adjusting for different experimental conditions like zero-point energy. These calculations can also avoid experimental errors for difficult to test molecules. Though purely calculated data is often not perfect, identifying issues is often easier for calculated data than experimental.
RCSB: Stores publicly available 3D models of macromolecules (proteins, nucleic acids) and small molecules (drugs, inhibitors)
ChEMBL: Contains data from research on drug development such as assay results. Methods that do not include any empirical or semi-empirical parameters in their equations – being derived directly from theory, with no inclusion of experimental data – are called ab initio methods. A theoretical approximation is rigorously defined on first principles and then solved within an error margin that is qualitatively known beforehand. If numerical iterative methods must be used, the aim is to iterate until full machine accuracy is obtained (the best that is possible with a finite word length on the computer, and within the mathematical and/or physical approximations made).
Ab initio methods need to define a level of theory (the method) and a basis set. A basis set consists of functions centered on the molecule's atoms. These sets are then used to describe molecular orbitals via the linear combination of atomic orbitals (LCAO) molecular orbital method ansatz.
thumb|right|300px|Diagram illustrating various ab initio electronic structure methods in terms of energy. Spacings are not to scale.
A common type of ab initio electronic structure calculation is the Hartree–Fock method (HF), an extension of molecular orbital theory, where electron-electron repulsions in the molecule are not specifically taken into account; only the electrons' average effect is included in the calculation. As the basis set size increases, the energy and wave function tend towards a limit called the Hartree–Fock limit. These types of calculations are termed post–Hartree–Fock methods. By continually improving these methods, scientists can get increasingly closer to perfectly predicting the behavior of atomic and molecular systems under the framework of quantum mechanics, as defined by the Schrödinger equation. To obtain exact agreement with the experiment, it is necessary to include specific terms, some of which are far more important for heavy atoms than lighter ones.
In most cases, the Hartree–Fock wave function occupies a single configuration or determinant. In some cases, particularly for bond-breaking processes, this is inadequate, and several configurations must be used.
The total molecular energy can be evaluated as a function of the molecular geometry; in other words, the potential energy surface. Such a surface can be used for reaction dynamics. The stationary points of the surface lead to predictions of different isomers and the transition structures for conversion between isomers, but these can be determined without full knowledge of the complete surface.
Chemical dynamics
After the electronic and nuclear variables are separated within the Born–Oppenheimer representation), the wave packet corresponding to the nuclear degrees of freedom is propagated via the time evolution operator (physics) associated to the time-dependent Schrödinger equation (for the full molecular Hamiltonian). In the complementary energy-dependent approach, the time-independent Schrödinger equation is solved using the scattering theory formalism. The potential representing the interatomic interaction is given by the potential energy surfaces. In general, the potential energy surfaces are coupled via the vibronic coupling terms.
The most popular methods for propagating the wave packet associated to the molecular geometry are:
the Chebyshev (real) polynomial,
the multi-configuration time-dependent Hartree method (MCTDH),
the semiclassical method
and the split operator technique explained below.
Split operator technique
How a computational method solves quantum equations impacts the accuracy and efficiency of the method. The split operator technique is one of these methods for solving differential equations. In computational chemistry, split operator technique reduces computational costs of simulating chemical systems. Computational costs are about how much time it takes for computers to calculate these chemical systems, as it can take days for more complex systems. Quantum systems are difficult and time-consuming to solve for humans. Split operator methods help computers calculate these systems quickly by solving the sub problems in a quantum differential equation. The method does this by separating the differential equation into two different equations, like when there are more than two operators. Once solved, the split equations are combined into one equation again to give an easily calculable solution.
Semi-empirical methods
Semi-empirical quantum chemistry methods are based on the Hartree–Fock method formalism, but make many approximations and obtain some parameters from empirical data. They were very important in computational chemistry from the 60s to the 90s, especially for treating large molecules where the full Hartree–Fock method without the approximations were too costly. The use of empirical parameters appears to allow some inclusion of correlation effects into the methods.
Primitive semi-empirical methods were designed even before, where the two-electron part of the Hamiltonian is not explicitly included. For π-electron systems, this was the Hückel method proposed by Erich Hückel, and for all valence electron systems, the extended Hückel method proposed by Roald Hoffmann. Sometimes, Hückel methods are referred to as "completely empirical" because they do not derive from a Hamiltonian. Yet, the term "empirical methods", or "empirical force fields" is usually used to describe molecular mechanics.
thumb|Molecular mechanics potential energy function with continuum solvent
Molecular mechanics
In many cases, large molecular systems can be modeled successfully while avoiding quantum mechanical calculations entirely. Molecular mechanics simulations, for example, use one classical expression for the energy of a compound, for instance, the harmonic oscillator. All constants appearing in the equations must be obtained beforehand from experimental data or ab initio calculations.thumb|Molecular Dynamics for Argon Gas
Molecular dynamics
Molecular dynamics (MD) use either quantum mechanics, molecular mechanics or a mixture of both to calculate forces which are then used to solve Newton's laws of motion to examine the time-dependent behavior of systems. The result of a molecular dynamics simulation is a trajectory that describes how the position and velocity of particles varies with time. The phase point of a system described by the positions and momenta of all its particles on a previous time point will determine the next phase point in time by integrating over Newton's laws of motion.
Monte Carlo
Monte Carlo (MC) generates configurations of a system by making random changes to the positions of its particles, together with their orientations and conformations where appropriate. It is a random sampling method, which makes use of the so-called importance sampling. Importance sampling methods are able to generate low energy states, as this enables properties to be calculated accurately. The potential energy of each configuration of the system can be calculated, together with the values of other properties, from the positions of the atoms.
Quantum mechanics/molecular mechanics (QM/MM)
QM/MM is a hybrid method that attempts to combine the accuracy of quantum mechanics with the speed of molecular mechanics. It is useful for simulating very large molecules such as enzymes.
Quantum Computational Chemistry
Quantum computational chemistry aims to exploit quantum computing to simulate chemical systems, distinguishing itself from the QM/MM (Quantum Mechanics/Molecular Mechanics) approach. While QM/MM uses a hybrid approach, combining quantum mechanics for a portion of the system with classical mechanics for the remainder, quantum computational chemistry exclusively uses quantum computing methods to represent and process information, such as Hamiltonian operators.
Conventional computational chemistry methods often struggle with the complex quantum mechanical equations, particularly due to the exponential growth of a quantum system's wave function. Quantum computational chemistry addresses these challenges using quantum computing methods, such as qubitization and quantum phase estimation, which are believed to offer scalable solutions.
Qubitization involves adapting the Hamiltonian operator for more efficient processing on quantum computers, enhancing the simulation's efficiency. Quantum phase estimation, on the other hand, assists in accurately determining energy eigenstates, which are critical for understanding the quantum system's behavior.
While these techniques have advanced the field of computational chemistry, especially in the simulation of chemical systems, their practical application is currently limited mainly to smaller systems due to technological constraints. Nevertheless, these developments may lead to significant progress towards achieving more precise and resource-efficient quantum chemistry simulations.
In quantum chemistry, particularly, the complexity can grow exponentially with the number of electrons involved in the system. This exponential growth is a significant barrier to simulating large or complex systems accurately.
Advanced algorithms in both fields strive to balance accuracy with computational efficiency. For instance, in MD, methods like Verlet integration or Beeman's algorithm are employed for their computational efficiency. In quantum chemistry, hybrid methods combining different computational approaches (like QM/MM) are increasingly used to tackle large biomolecular systems.
Algorithmic complexity examples
The following list illustrates the impact of computational complexity on algorithms used in chemical computations. It is important to note that while this list provides key examples, it is not comprehensive and serves as a guide to understanding how computational demands influence the selection of specific computational methods in chemistry.
Molecular dynamics
Algorithm
Solves Newton's equations of motion for atoms and molecules.
thumb|Molecular dynamics simulation of liquid water at 298 K
Complexity
The standard pairwise interaction calculation in MD leads to an \mathcal{O}(N^2)complexity for N particles. This is because each particle interacts with every other particle, resulting in \frac{N(N-1)}{2} interactions. Advanced algorithms, such as the Ewald summation or Fast Multipole Method, reduce this to \mathcal{O}(N \log N) or even \mathcal{O}(N) by grouping distant particles and treating them as a single entity or using clever mathematical approximations.
Quantum mechanics/molecular mechanics (QM/MM)
Algorithm
Combines quantum mechanical calculations for a small region with molecular mechanics for the larger environment.
Complexity
The complexity of QM/MM methods depends on both the size of the quantum region and the method used for quantum calculations. For example, if a Hartree-Fock method is used for the quantum part, the complexity can be approximated as \mathcal{O}(M^2), where M is the number of basis functions in the quantum region. This complexity arises from the need to solve a set of coupled equations iteratively until self-consistency is achieved.
thumb|Algorithmic flowchart illustrating the Hartree–Fock method
Hartree-Fock method
Algorithm
Finds a single Fock state that minimizes the energy.
Complexity
NP-hard or NP-complete as demonstrated by embedding instances of the Ising model into Hartree-Fock calculations. The Hartree-Fock method involves solving the Roothaan-Hall equations, which scales as \mathcal{O}(N^3) to \mathcal{O}(N) depending on implementation, with N being the number of basis functions. The computational cost mainly comes from evaluating and transforming the two-electron integrals. This proof of NP-hardness or NP-completeness comes from embedding problems like the Ising model into the Hartree-Fock formalism.
Density functional theory
Algorithm
Investigates the electronic structure or nuclear structure of many-body systems such as atoms, molecules, and the condensed phases.
Complexity
Traditional implementations of DFT typically scale as \mathcal{O}(N^3), mainly due to the need to diagonalize the Kohn-Sham matrix. The diagonalization step, which finds the eigenvalues and eigenvectors of the matrix, contributes most to this scaling. Recent advances in DFT aim to reduce this complexity through various approximations and algorithmic improvements.
Standard CCSD and CCSD(T) method
Algorithm
CCSD and CCSD(T) methods are advanced electronic structure techniques involving single, double, and in the case of CCSD(T), perturbative triple excitations for calculating electronic correlation effects.
Complexity
CCSD
Scales as \mathcal{O}(M^6) where M is the number of basis functions. This intense computational demand arises from the inclusion of single and double excitations in the electron correlation calculation.
For other methods like MD or DFT, the computational complexity is often empirically observed and supported by algorithm analysis. In these cases, the proof of correctness is less about formal mathematical proofs and more about consistently observing the computational behaviour across various systems and implementations.
Molecules consist of nuclei and electrons, so the methods of quantum mechanics apply. Computational chemists often attempt to solve the non-relativistic Schrödinger equation, with relativistic corrections added, although some progress has been made in solving the fully relativistic Dirac equation. In principle, it is possible to solve the Schrödinger equation in either its time-dependent or time-independent form, as appropriate for the problem in hand; in practice, this is not possible except for very small systems. Therefore, a great number of approximate methods strive to achieve the best trade-off between accuracy and computational cost.
Accuracy can always be improved with greater computational cost. Significant errors can present themselves in ab initio models comprising many electrons, due to the computational cost of full relativistic-inclusive methods.
There is some dispute within the field whether or not the latter methods are sufficient to describe complex chemical reactions, such as those in biochemistry. Large molecules can be studied by semi-empirical approximate methods. Even larger molecules are treated by classical mechanics methods that use what are called molecular mechanics (MM).In QM-MM methods, small parts of large complexes are treated quantum mechanically (QM), and the remainder is treated approximately (MM).
Software packages
Many self-sufficient computational chemistry software packages exist. Some include many methods covering a wide range, while others concentrate on a very specific range or even on one method. Details of most of them can be found in:
Biomolecular modelling programs: proteins, nucleic acid.
Molecular mechanics programs.
Quantum chemistry and solid state-physics software supporting several methods.
Molecular design software
Semi-empirical programs.
Valence bond programs.
Specialized journals on computational chemistry
Annual Reports in Computational Chemistry
Computational and Theoretical Chemistry
Computational and Theoretical Polymer Science
Computers & Chemical Engineering
Journal of Chemical Information and Modeling
Journal of Chemical Software
Journal of Chemical Theory and Computation
Journal of Cheminformatics
Journal of Computational Chemistry
Journal of Computer Aided Chemistry
Journal of Computer Chemistry Japan
Journal of Computer-aided Molecular Design
Journal of Theoretical and Computational Chemistry
Molecular Informatics
Theoretical Chemistry Accounts
External links
NIST Computational Chemistry Comparison and Benchmark DataBase – Contains a database of thousands of computational and experimental results for hundreds of systems
American Chemical Society Division of Computers in Chemistry – American Chemical Society Computers in Chemistry Division, resources for grants, awards, contacts and meetings.
CSTB report Mathematical Research in Materials Science: Opportunities and Perspectives – CSTB Report
3.320 Atomistic Computer Modeling of Materials (SMA 5107) Free MIT Course
Chem 4021/8021 Computational Chemistry Free University of Minnesota Course
Technology Roadmap for Computational Chemistry
Applications of molecular and materials modelling.
Impact of Advances in Computing and Communications Technologies on Chemical Science and Technology CSTB Report
MD and Computational Chemistry applications on GPUs
Susi Lehtola, Antti J. Karttunen:"Free and open source software for computational chemistry education", First published: 23 March 2022, https://doi.org/10.1002/wcms.1610 (Open Access)
CCL.NET: Computational Chemistry List, Ltd.
See also
References
Category:Computational fields of study
Category:Theoretical chemistry
Category:Physical chemistry
Category:Chemical physics
Category:Computational physics
|
https://en.wikipedia.org/wiki/Computational_chemistry
|
2025-04-05T18:27:41.377508
|
6020
|
Crash (Ballard novel)
|
Crash is a novel by British author J. G. Ballard, first published in 1973 with cover designed by Bill Botten. It follows a group of car-crash fetishists who, inspired by the famous crashes of celebrities, become sexually aroused by staging and participating in car accidents.
The novel was released to divided critical reception, with many reviewers horrified by its provocative content. It was adapted into a controversial 1996 film of the same name by David Cronenberg.
Synopsis
The story is told through the eyes of narrator James Ballard, named after the author himself, but it centers on the sinister figure of Dr. Robert Vaughan, a former TV scientist turned "nightmare angel of the highways". James meets Vaughan after being injured in a car crash near London Airport. Gathering around Vaughan is a group of alienated people, all of them former crash victims, who follow him in his pursuit to re-enact the crashes of Hollywood celebrities such as Jayne Mansfield and James Dean, in order to experience what the narrator calls "a new sexuality, born from a perverse technology". Vaughan's ultimate fantasy is to die in a head-on collision with movie star Elizabeth Taylor.
Development
The Papers of J. G. Ballard at the British Library include two revised drafts of Crash (Add MS 88938/3/8). Scanned extracts from Ballard's drafts are included in ''Crash: The Collector's Edition,'' ed. Chris Beckett.
In 1971, Harley Cokeliss directed a short film entitled Crash! based on a chapter in J. G. Ballard's book The Atrocity Exhibition, where Ballard is featured, talking about the ideas in his book. British actress Gabrielle Drake appeared as a passenger and car-crash victim. Ballard later developed the idea, resulting in Crash. In his draft of the novel he mentioned Drake by name, but references to her were removed from the published version.
Interpretation
Crash has been difficult to characterize as a novel. At some points in his career, Ballard claimed that Crash was a "cautionary tale", a view that he would later regret, asserting that it is in fact "a psychopathic hymn. But it is a psychopathic hymn which has a point". Likewise, Ballard previously characterized it a science fiction novel, a position he would later take back.
Jean Baudrillard wrote an analysis of Crash in Simulacra and Simulation in which he declared it "the first great novel of the universe of simulation". He made note of how the fetish in the story conflates the functionality of the automobiles with that of the human body and how the characters' injuries and the damage to the vehicles are used as equivalent signs. To him, the hyperfunctionality leads to the dysfunction in the story. Quotes were used extensively to illustrate that the language of the novel employs plain, mechanical terms for the parts of the automobile and proper, medical language for human sex organs and acts. The story is interpreted as showing a merger between technology, sexuality, and death, and he further argued that by pointing out Vaughan's character takes and keeps photos of the car crashes and the mutilated bodies involved. Baudrillard stated that there is no moral judgment about the events within the novel but that Ballard himself intended it as a warning against a cultural trend.
The story can be classed as dystopic. A 1973 review in The New York Times was equally horrified: "Crash is, hands-down, the most repulsive book I've yet to come across."
However, retrospective opinion now considers Crash to be one of Ballard's best and most challenging works. Reassessing Crash in The Guardian, Zadie Smith wrote, "Crash is an existential book about how everybody uses everything. How everything uses everybody. And yet it is not a hopeless vision." On Ballard's legacy, she writes: "In Ballard's work there is always this mix of futuristic dread and excitement, a sweet spot where dystopia and utopia converge. For we cannot say we haven't got precisely what we dreamed of, what we always wanted, so badly."References in popular artMusic
The Normal's 1978 song "Warm Leatherette" was inspired by the novel, and later covered in 1980 by Grace Jones. Similarly inspired was "Miss the Girl," a 1983 single by The Creatures.
The Manic Street Preachers' song "Mausoleum" from 1994's The Holy Bible contains the famous Ballard quote about his reasons for writing the book, "I wanted to rub the human face in its own vomit. I wanted to force it to look in the mirror." John Foxx's album Metamatic contains songs that have Ballardian themes, such as "No-one Driving".Other film adaptationsAn apparently unauthorized adaptation of Crash called Nightmare Angel was filmed in 1986 by Susan Emerling and Zoe Beloff. This short film bears the credit "Inspired by J. G. Ballard".
See also
*Autassassinophilia
References
External links
* [http://www.jgballard.ca/terminal_collection/1968_73.html The Terminal Collection: JG Ballard First Editions]
*[http://www.bl.uk/works/crash Crash] at the British Library
<!--* James Ballard-IMDb-->
Category:1973 British novels
Category:1973 science fiction novels
Category:Novels about infidelity
Category:Books about cars
Category:BDSM literature
Category:Bisexual fiction
Category:British erotic novels
Category:British novels adapted into films
Category:Jonathan Cape books
Category:Postmodern novels
Category:Dystopian novels
Category:Psychological novels
Category:Novels about necrophilia
Category:Novels by J. G. Ballard
Category:Obscenity controversies in literature
Category:Literature about pedophilia
Category:Fiction about sexual addiction
Category:Fiction about casual sex
Category:Female bisexuality in fiction
Category:Male bisexuality in fiction
Category:Science fiction erotica
Category:LGBTQ speculative fiction novels
Category:British LGBTQ novels
Category:Novels about transgender topics
Category:Novels about gay topics
Category:Novels about technology
Category:Works about cars
|
https://en.wikipedia.org/wiki/Crash_(Ballard_novel)
|
2025-04-05T18:27:41.384079
|
6021
|
C (programming language)
|
C#}}
| latest preview version = C2y (N3220)
| latest preview date
| typing = Static, weak, manifest, nominal
| implementations = pcc, GCC, Clang, , C++Builder, ,
| dialects = Cyclone, Unified Parallel C, Split-C, Cilk, C*
| influenced Numerous: AMPL, AWK, csh, C++, C--, C#, Objective-C, D, Go, Java, JavaScript, JS++, Julia, Limbo, LPC, Perl, PHP, Pike, Processing, Python, Rust, Seed7, V (Vlang), Vala, Verilog (HDL), Nim, Zig
| operating system = Cross-platform
| year
| influenced by B (BCPL, CPL), ALGOL 68, PL/I, FORTRAN
| file ext = .c, .h
| website = <br /> <br />
| wikibooks = C Programming
}}
C (pronounced – like the letter c) is a general-purpose programming language. It was created in the 1970s by Dennis Ritchie and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems code (especially in kernels), device drivers, and protocol stacks, but its use in application software has been decreasing. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems.
A successor to the programming language B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. with C compilers available for practically all modern computer architectures and operating systems. The book The C Programming Language, co-authored by the original language designer, served for many years as the de facto standard for the language.
Overview
(right), the inventor of the C programming language, with Ken Thompson]]
C is an imperative, procedural language in the ALGOL tradition. It has a static type system. In C, all executable code is contained within subroutines (also called "functions", though not in the sense of functional programming). Function parameters are passed by value, although arrays are passed as pointers, i.e. the address of the first item in the array. Pass-by-reference is simulated in C by explicitly passing pointers to the thing being referenced.
C program source text is free-form code. Semicolons terminate statements, while curly braces are used to group statements into blocks.
The C language also exhibits the following characteristics:
* The language has a small, fixed number of keywords, including a full set of control flow primitives: <code>if/else</code>, <code>for</code>, <code>do/while</code>, <code>while</code>, and <code>switch</code>. User-defined names are not distinguished from keywords by any kind of sigil.
* It has a large number of arithmetic, bitwise, and logic operators: |++|&||d,}}, etc.
* More than one assignment may be performed in a single statement.
* Functions:
** Function return values can be ignored, when not needed.
** Function and data pointers permit ad hoc run-time polymorphism.
** Functions may not be defined within the lexical scope of other functions.
** Variables may be defined within a function, with scope.
** A function may call itself, so recursion is supported.
* Data typing is static, but weakly enforced; all data has a type, but implicit conversions are possible.
* User-defined (typedef) and compound types are possible.
** Heterogeneous aggregate data types (<code>struct</code>) allow related data elements to be accessed and assigned as a unit. The contents of whole structs cannot be compared using a single built-in operator (the elements must be compared individually).
** Union is a structure with overlapping members; it allows multiple data types to share the same memory location.
** Array indexing is a secondary notation, defined in terms of pointer arithmetic. Whole arrays cannot be assigned or compared using a single built-in operator. There is no "array" keyword in use or definition; instead, square brackets indicate arrays syntactically, for example <code>month[11]</code>.
** Enumerated types are possible with the <code>enum</code> keyword. They are freely interconvertible with integers.
** Strings are not a distinct data type, but are conventionally implemented as null-terminated character arrays.
* Low-level access to computer memory is possible by converting machine addresses to pointers.
* Procedures (subroutines not returning values) are a special case of function, with an empty return type <code>void</code>.
* Memory can be allocated to a program with calls to library routines.
* A preprocessor performs macro definition, source code file inclusion, and conditional compilation.
* There is a basic form of modularity: files can be compiled separately and linked together, with control over which functions and data objects are visible to other files via <code>static</code> and <code>extern</code> attributes.
* Complex functionality such as I/O, string manipulation, and mathematical functions are consistently delegated to library routines.
* The generated code after compilation has relatively straightforward needs on the underlying platform, which makes it suitable for creating operating systems and for use in embedded systems.
While C does not include certain features found in other languages (such as object orientation and garbage collection), these can be implemented or emulated, often through the use of external libraries (e.g., the GLib Object System or the Boehm garbage collector).
Relations to other languages
Many later languages have borrowed directly or indirectly from C, including C++, C#, Unix's C shell, D, Go, Java, JavaScript (including transpilers), Julia, Limbo, LPC, Objective-C, Perl, PHP, Python, Ruby, Rust, Swift, Verilog and SystemVerilog (hardware description languages). and Thompson modified the syntax to be less 'wordy' and similar to a simplified ALGOL known as SMALGOL. He called the result B,
Structures and Unix kernel re-write
At Version 4 Unix, released in November 1973, the Unix kernel was extensively re-implemented in C.
Unix was one of the first operating system kernels implemented in a language other than assembly. Earlier instances include the Multics system (which was written in PL/I) and Master Control Program (MCP) for the Burroughs B5000 (which was written in ALGOL) in 1961. In around <!--Better?: --> 1977, Ritchie and Stephen C. Johnson made further changes to the language to facilitate portability of the Unix operating system. Johnson's Portable C Compiler served as the basis for several implementations of C on new platforms. K&R C <!--K&R C redirects here-->
and Dennis Ritchie]]
In 1978 Brian Kernighan and Dennis Ritchie published the first edition of The C Programming Language. Known as K&R from the initials of its authors, the book served for many years as an informal specification of the language. The version of C that it describes is commonly referred to as "K&R C<!--boldface per WP:R#PLA-->". As this was released in 1978, it is now also referred to as C78. The second edition of the book covers the later ANSI C standard, described below.
K&R introduced several language features:
* Standard I/O library
* <code>long int</code> data type
* <code>unsigned int</code> data type
* Compound assignment operators of the form <code>op</code> (such as <code>-</code>) were changed to the form <code>op</code> (that is, <code>-</code>) to remove the semantic ambiguity created by constructs such as <code>i-10</code>, which had been interpreted as <code>i - 10</code> (decrement <code>i</code> by 10) instead of the possibly intended <code>i = -10</code> (let <code>i</code> be −10).
Even after the publication of the 1989 ANSI standard, for many years K&R C was still considered the "lowest common denominator" to which C programmers restricted themselves when maximum portability was desired, since many older compilers were still in use, and because carefully written K&R C code can be legal Standard C as well.
In early versions of C, only functions that return types other than <code>int</code> must be declared if used before the function definition; functions used without prior declaration were presumed to return type <code>int</code>.
For example:
<syntaxhighlight lang="c">
long some_function(); /* This is a function declaration, so the compiler can know the name and return type of this function. */
/* int */ other_function(); /* Another function declaration. Because this is an early version of C, there is an implicit 'int' type here. A comment shows where the explicit 'int' type specifier would be required in later versions. */
/* int */ calling_function() /* This is a function definition, including the body of the code following in the { curly brackets }. Because no return type is specified, the function implicitly returns an 'int' in this early version of C. */
{
long test1;
register /* int */ test2; /* Again, note that 'int' is not required here. The 'int' type specifier */
/* in the comment would be required in later versions of C. */
/* The 'register' keyword indicates to the compiler that this variable should */
/* ideally be stored in a register as opposed to within the stack frame. */
test1 = some_function();
if (test1 > 1)
test2 = 0;
else
test2 = other_function();
return test2;
}
</syntaxhighlight>
The <code>int</code> type specifiers which are commented out could be omitted in K&R C, but are required in later standards.
Since K&R function declarations did not include any information about function arguments, function parameter type checks were not performed, although some compilers would issue a warning message if a local function was called with the wrong number of arguments, or if different calls to an external function used different numbers or types of arguments. Separate tools such as Unix's lint utility were developed that (among other things) could check for consistency of function use across multiple source files.
In the years following the publication of K&R C, several features were added to the language, supported by compilers from AT&T (in particular PCC) and some other vendors. These included:
* <code>void</code> functions (i.e., functions with no return value)
* functions returning <code>struct</code> or <code>union</code> types (previously only a single pointer, integer or float could be returned)
* assignment for <code>struct</code> data types
* enumerated types (previously, preprocessor definitions for integer fixed values were used, e.g. <code>#define GREEN 3</code>)
The large number of extensions and lack of agreement on a standard library, together with the language popularity and the fact that not even the Unix compilers precisely implemented the K&R specification, led to the necessity of standardization. ANSI C and ISO C
<!-- WP:NFCC violation: '', second edition by Brian Kernighan and Dennis Ritchie covering ANSI C]] -->
During the late 1970s and 1980s, versions of C were implemented for a wide variety of mainframe computers, minicomputers, and microcomputers, including the IBM PC, as its popularity began to increase significantly.
In 1983 the American National Standards Institute (ANSI) formed a committee, X3J11, to establish a standard specification of C. X3J11 based the C standard on the Unix implementation; however, the non-portable portion of the Unix C library was handed off to the IEEE working group 1003 to become the basis for the 1988 POSIX standard. In 1989, the C standard was ratified as ANSI X3.159-1989 "Programming Language C". This version of the language is often referred to as ANSI C, Standard C, or sometimes C89.
In 1990 the ANSI C standard (with formatting changes) was adopted by the International Organization for Standardization (ISO) as ISO/IEC 9899:1990, which is sometimes called C90. Therefore, the terms "C89" and "C90" refer to the same programming language.
ANSI, like other national standards bodies, no longer develops the C standard independently, but defers to the international C standard, maintained by the working group ISO/IEC JTC1/SC22/WG14. National adoption of an update to the international standard typically occurs within a year of ISO publication.
One of the aims of the C standardization process was to produce a superset of K&R C, incorporating many of the subsequently introduced unofficial features. The standards committee also included several additional features such as function prototypes (borrowed from C++), <code>void</code> pointers, support for international character sets and locales, and preprocessor enhancements. Although the syntax for parameter declarations was augmented to include the style used in C++, the K&R interface continued to be permitted, for compatibility with existing source code.
C89 is supported by current C compilers, and most modern C code is based on it. Any program written only in Standard C and without any hardware-dependent assumptions will run correctly on any platform with a conforming C implementation, within its resource limits. Without such precautions, programs may compile only on a certain platform or with a particular compiler, due, for example, to the use of non-standard libraries, such as GUI libraries, or to a reliance on compiler- or platform-specific attributes such as the exact size of data types and byte endianness.
In cases where code must be compilable by either standard-conforming or K&R C-based compilers, the <code>__STDC__</code> macro can be used to split the code into Standard and K&R sections to prevent the use on a K&R C-based compiler of features available only in Standard C.
After the ANSI/ISO standardization process, the C language specification remained relatively static for several years. In 1995, Normative Amendment 1 to the 1990 C standard (ISO/IEC 9899/AMD1:1995, known informally as C95) was published, to correct some details and to add more extensive support for international character sets.
C99
The C standard was further revised in the late 1990s, leading to the publication of ISO/IEC 9899:1999 in 1999, which is commonly referred to as "C99". It has since been amended three times by Technical Corrigenda.
C99 introduced several new features, including inline functions, several new data types (including <code>long long int</code> and a <code>complex</code> type to represent complex numbers), variable-length arrays and flexible array members, improved support for IEEE 754 floating point, support for variadic macros (macros of variable arity), and support for one-line comments beginning with <code>//</code>, as in BCPL or C++. Many of these had already been implemented as extensions in several C compilers.
C99 is for the most part backward compatible with C90, but is stricter in some ways; in particular, a declaration that lacks a type specifier no longer has <code>int</code> implicitly assumed. A standard macro <code>__STDC_VERSION__</code> is defined with value <code>199901L</code> to indicate that C99 support is available. GCC, Solaris Studio, and other C compilers now support many or all of the new features of C99. The C compiler in Microsoft Visual C++, however, implements the C89 standard and those parts of C99 that are required for compatibility with C++11.
In addition, the C99 standard requires support for identifiers using Unicode in the form of escaped characters (e.g. or ) and suggests support for raw Unicode names.
C11
Work began in 2007 on another revision of the C standard, informally called "C1X" until its official publication of ISO/IEC 9899:2011 on December 8, 2011. The C standards committee adopted guidelines to limit the adoption of new features that had not been tested by existing implementations.
The C11 standard adds numerous new features to C and the library, including type generic macros, anonymous structures, improved Unicode support, atomic operations, multi-threading, and bounds-checked functions. It also makes some portions of the existing C99 library optional, and improves compatibility with C++. The standard macro <code>__STDC_VERSION__</code> is defined as <code>201112L</code> to indicate that C11 support is available.
C17
C17 is an informal name for ISO/IEC 9899:2018, a standard for the C programming language published in June 2018. It introduces no new language features, only technical corrections, and clarifications to defects in C11. The standard macro <code>__STDC_VERSION__</code> is defined as <code>201710L</code> to indicate that C17 support is available.
C23
C23 is an informal name for the current major C language standard revision. It was informally known as "C2X" through most of its development. C23 was published in October 2024 as ISO/IEC 9899:2024. The standard macro <code>__STDC_VERSION__</code> is defined as <code>202311L</code> to indicate that C23 support is available.
C2Y
C2Y is an informal name for the next major C language standard revision, after C23 (C2X), that is hoped to be released later in the 2020s decade, hence the '2' in "C2Y". An early working draft of C2Y was released in February 2024 as N3220 by the working group ISO/IEC JTC1/SC22/WG14.
Embedded C
Historically, embedded C programming requires non-standard extensions to the C language to support exotic features such as fixed-point arithmetic, multiple distinct memory banks, and basic I/O operations.
In 2008, the C Standards Committee published a technical report extending the C language to address these issues by providing a common standard for all implementations to adhere to. It includes a number of features not available in normal C, such as fixed-point arithmetic, named address spaces, and basic I/O hardware addressing.
Syntax
C has a formal grammar specified by the C standard. Line endings are generally not significant in C; however, line boundaries do have significance during the preprocessing phase. Comments may appear either between the delimiters <code>/*</code> and <code>*/</code>, or (since C99) following <code>//</code> until the end of the line. Comments delimited by <code>/*</code> and <code>*/</code> do not nest, and these sequences of characters are not interpreted as comment delimiters if they appear inside string or character literals.
C source files contain declarations and function definitions. Function definitions, in turn, contain declarations and statements. Declarations either define new types using keywords such as <code>struct</code>, <code>union</code>, and <code>enum</code>, or assign types to and perhaps reserve storage for new variables, usually by writing the type followed by the variable name. Keywords such as <code>char</code> and <code>int</code> specify built-in types. Sections of code are enclosed in braces (<code>{</code> and <code>}</code>, sometimes called "curly brackets") to limit the scope of declarations and to act as a single statement for control structures.
As an imperative language, C uses statements to specify actions. The most common statement is an expression statement, consisting of an expression to be evaluated, followed by a semicolon; as a side effect of the evaluation, functions may be called and variables assigned new values. To modify the normal sequential execution of statements, C provides several control-flow statements identified by reserved keywords. Structured programming is supported by <code>if</code> ... [<code>else</code>] conditional execution and by <code>do</code> ... <code>while</code>, <code>while</code>, and <code>for</code> iterative execution (looping). The <code>for</code> statement has separate initialization, testing, and reinitialization expressions, any or all of which can be omitted. <code>break</code> and <code>continue</code> can be used within the loop. Break is used to leave the innermost enclosing loop statement and continue is used to skip to its reinitialisation. There is also a non-structured <code>goto</code> statement which branches directly to the designated label within the function. <code>switch</code> selects a <code>case</code> to be executed based on the value of an integer expression. Different from many other languages, control-flow will fall through to the next <code>case</code> unless terminated by a <code>break</code>.
Expressions can use a variety of built-in operators and may contain function calls. The order in which arguments to functions and operands to most operators are evaluated is unspecified. The evaluations may even be interleaved. However, all side effects (including storage to variables) will occur before the next "sequence point"; sequence points include the end of each expression statement, and the entry to and return from each function call. Sequence points also occur during evaluation of expressions containing certain operators (<code>&&</code>, <code>||</code>, <code>?:</code> and the comma operator). This permits a high degree of object code optimization by the compiler, but requires C programmers to take more care to obtain reliable results than is needed for other programming languages.
Kernighan and Ritchie say in the Introduction of The C Programming Language: "C, like any other language, has its blemishes. Some of the operators have the wrong precedence; some parts of the syntax could be better." The C standard did not attempt to correct many of these blemishes, because of the impact of such changes on already existing software. Character set
The basic C source character set includes the following characters:
* Lowercase and uppercase letters of the ISO basic Latin alphabet: <code>a</code>–<code>z</code>, <code>A</code>–<code>Z</code>
* Decimal digits: <code>0</code>–<code>9</code>
* Graphic characters: <code>! " # % & ' ( ) * + , - . / : ; < = > ? [ \ ] ^ _ { | } ~</code>
* Whitespace characters: space, horizontal tab, vertical tab, form feed, newline
The newline character indicates the end of a text line; it need not correspond to an actual single character, although for convenience C treats it as such.
Additional multi-byte encoded characters may be used in string literals, but they are not entirely portable. Since C99 multi-national Unicode characters can be embedded portably within C source text by using <code>\uXXXX</code> or <code>\UXXXXXXXX</code> encoding (where <code>X</code> denotes a hexadecimal character).
The basic C execution character set contains the same characters, along with representations for alert, backspace, and carriage return. Run-time support for extended character sets has increased with each revision of the C standard.
Reserved words
The following reserved words are case sensitive.
C89 has 32 reserved words, also known as 'keywords', which cannot be used for any purposes other than those for which they are predefined:
* <code>auto</code>
* <code>break</code>
* <code>case</code>
* <code>char</code>
* <code>const</code>
* <code>continue</code>
* <code>default</code>
* <code>do</code>
* <code>double</code>
* <code>else</code>
* <code>enum</code>
* <code>extern</code>
* <code>float</code>
* <code>for</code>
* <code>goto</code>
* <code>if</code>
* <code>int</code>
* <code>long</code>
* <code>register</code>
* <code>return</code>
* <code>short</code>
* <code>signed</code>
* <code>sizeof</code>
* <code>static</code>
* <code>struct</code>
* <code>switch</code>
* <code>typedef</code>
* <code>union</code>
* <code>unsigned</code>
* <code>void</code>
* <code>volatile</code>
* <code>while</code>
C99 added five more reserved words: (‡ indicates an alternative spelling alias for a C23 keyword)
* <code>inline</code>
* <code>restrict</code>
* <code>_Bool</code> ‡
* <code>_Complex</code>
* <code>_Imaginary</code>
C11 added seven more reserved words: (‡ indicates an alternative spelling alias for a C23 keyword)
* <code>_Alignas</code> ‡
* <code>_Alignof</code> ‡
* <code>_Atomic</code>
* <code>_Generic</code>
* <code>_Noreturn</code>
* <code>_Static_assert</code> ‡
* <code>_Thread_local</code> ‡
C23 reserved fifteen more words:
* <code>alignas</code>
* <code>alignof</code>
* <code>bool</code>
* <code>constexpr</code>
* <code>false</code>
* <code>nullptr</code>
* <code>static_assert</code>
* <code>thread_local</code>
* <code>true</code>
* <code>typeof</code>
* <code>typeof_unqual</code>
* <code>_BitInt</code>
* <code>_Decimal32</code>
* <code>_Decimal64</code>
* <code>_Decimal128</code>
Most of the recently reserved words begin with an underscore followed by a capital letter, because identifiers of that form were previously reserved by the C standard for use only by implementations. Since existing program source code should not have been using these identifiers, it would not be affected when C implementations started supporting these extensions to the programming language. Some standard headers do define more convenient synonyms for underscored identifiers. Some of those words were added as keywords with their conventional spelling in C23 and the corresponding macros were removed.
Prior to C89, <code>entry</code> was reserved as a keyword. In the second edition of their book The C Programming Language, which describes what became known as C89, Kernighan and Ritchie wrote, "The ... [keyword] <code>entry</code>, formerly reserved but never used, is no longer reserved." and "The stillborn <code>entry</code> keyword is withdrawn." Operators
C supports a rich set of operators, which are symbols used within an expression to specify the manipulations to be performed while evaluating that expression. C has operators for:
* arithmetic: <code>+</code>, <code>-</code>, <code>*</code>, <code>/</code>, <code>%</code>
* assignment: <code>=</code>
* augmented assignment: |-|*|/|%|&||^|<<|>>|d=,}}
* bitwise logic: <code>~</code>, <code>&</code>, <code>|</code>, <code>^</code>
* bitwise shifts: <code><<</code>, <code>>></code>
* Boolean logic: <code>!</code>, <code>&&</code>, <code>||</code>
* conditional evaluation: <code>? :</code>
* equality testing: <code></code>, <code>!</code>
* calling functions: <code>( )</code>
* increment and decrement: <code>++</code>, <code>--</code>
* member selection: <code>.</code>, <code>-></code>
* object size: <code>sizeof</code>
* type: <code>typeof</code>, <code>typeof_unqual</code> since C23
* order relations: <code><</code>, <code><</code>, <code>></code>, <code>></code>
* reference and dereference: <code>&</code>, <code>*</code>, <code>[ ]</code>
* sequencing: <code>,</code>
* subexpression grouping: <code>( )</code>
* type conversion: <code>(typename)</code>
C uses the operator <code></code> (used in mathematics to express equality) to indicate assignment, following the precedent of Fortran and PL/I, but unlike ALGOL and its derivatives. C uses the operator <code></code> to test for equality. The similarity between the operators for assignment and equality may result in the accidental use of one in place of the other, and in many cases the mistake does not produce an error message (although some compilers produce warnings). For example, the conditional expression <code>if (a b + 1)</code> might mistakenly be written as <code>if (a b + 1)</code>, which will be evaluated as <code>true</code> unless the value of <code>a</code> is <code>0</code> after the assignment.
The C operator precedence is not always intuitive. For example, the operator <code></code> binds more tightly than (is executed prior to) the operators <code>&</code> (bitwise AND) and <code>|</code> (bitwise OR) in expressions such as <code>x & 1 0</code>, which must be written as <code>(x & 1) 0</code> if that is the coder's intent. <span class"anchor" id"HELLOWORLD"></span>"Hello, world" example
(1978)]]
The "hello, world" example that appeared in the first edition of K&R has become the model for an introductory program in most programming textbooks. The program prints "hello, world" to the standard output, which is usually a terminal or screen display.
The original version was:
<syntaxhighlight lang="c">
main()
{
printf("hello, world\n");
}
</syntaxhighlight>
A standard-conforming "hello, world" program is:
<!-- READ THIS BEFORE YOU EDIT! If you think there is a better way, first see talk page archive No. 8 for why. If you still want to change it, discuss it first.
-->
<syntaxhighlight lang="c">
#include <stdio.h>
int main(void)
{
printf("hello, world\n");
}
</syntaxhighlight>
The first line of the program contains a preprocessing directive, indicated by <code>#include</code>. This causes the compiler to replace that line of code with the entire text of the <code>stdio.h</code> header file, which contains declarations for standard input and output functions such as <code>printf</code> and <code>scanf</code>. The angle brackets surrounding <code>stdio.h</code> indicate that the header file can be located using a search strategy that prefers headers provided with the compiler to other headers having the same name (as opposed to double quotes which typically include local or project-specific header files).
The second line indicates that a function named <code>main</code> is being defined. The <code>main</code> function serves a special purpose in C programs; the run-time environment calls the <code>main</code> function to begin program execution. The type specifier <code>int</code> indicates that the value returned to the invoker (in this case the run-time environment) as a result of evaluating the <code>main</code> function, is an integer. The keyword <code>void</code> as a parameter list indicates that the <code>main</code> function takes no arguments.
The opening curly brace indicates the beginning of the code that defines the <code>main</code> function.
The next line of the program is a statement that calls (i.e. diverts execution to) a function named <code>printf</code>, which in this case is supplied from a system library. In this call, the <code>printf</code> function is passed (i.e. provided with) a single argument, which is the address of the first character in the string literal <code>"hello, world\n"</code>. The string literal is an unnamed array set up automatically by the compiler, with elements of type <code>char</code> and a final NULL character (ASCII value 0) marking the end of the array (to allow <code>printf</code> to determine the length of the string). The NULL character can also be written as the escape sequence <code>\0</code>. The <code>\n</code> is a standard escape sequence that C translates to a newline character, which, on output, signifies the end of the current line. The return value of the <code>printf</code> function is of type <code>int</code>, but it is silently discarded since it is not used. (A more careful program might test the return value to check that the <code>printf</code> function succeeded.) The semicolon <code>;</code> terminates the statement.
The closing curly brace indicates the end of the code for the <code>main</code> function. According to the C99 specification and newer, the <code>main</code> function (unlike any other function) will implicitly return a value of <code>0</code> upon reaching the <code>}</code> that terminates the function. The return value of <code>0</code> is interpreted by the run-time system as an exit code indicating successful execution of the function.
Data types
The type system in C is static and weakly typed, which makes it similar to the type system of ALGOL descendants such as Pascal. There are built-in types for integers of various sizes, both signed and unsigned, floating-point numbers, and enumerated types (<code>enum</code>). Integer type <code>char</code> is often used for single-byte characters. C99 added a Boolean data type. There are also derived types including arrays, pointers, records (<code>struct</code>), and unions (<code>union</code>).
C is often used in low-level systems programming where escapes from the type system may be necessary. The compiler attempts to ensure type correctness of most expressions, but the programmer can override the checks in various ways, either by using a type cast to explicitly convert a value from one type to another, or by using pointers or unions to reinterpret the underlying bits of a data object in some other way.
Some find C's declaration syntax unintuitive, particularly for function pointers. (Ritchie's idea was to declare identifiers in contexts resembling their use: "declaration reflects use".)
C's usual arithmetic conversions allow for efficient code to be generated, but can sometimes produce unexpected results. For example, a comparison of signed and unsigned integers of equal width requires a conversion of the signed value to unsigned. This can generate unexpected results if the signed value is negative.
Pointers
C supports the use of pointers, a type of reference that records the address or location of an object or function in memory. Pointers can be dereferenced to access data stored at the address pointed to, or to invoke a pointed-to function. Pointers can be manipulated using assignment or pointer arithmetic. The run-time representation of a pointer value is typically a raw memory address (perhaps augmented by an offset-within-word field), but since a pointer's type includes the type of the thing pointed to, expressions including pointers can be type-checked at compile time. Pointer arithmetic is automatically scaled by the size of the pointed-to data type.
Pointers are used for many purposes in C. Text strings are commonly manipulated using pointers into arrays of characters. Dynamic memory allocation is performed using pointers; the result of a <code>malloc</code> is usually cast to the data type of the data to be stored. Many data types, such as trees, are commonly implemented as dynamically allocated <code>struct</code> objects linked together using pointers. Pointers to other pointers are often used in multi-dimensional arrays and arrays of <code>struct</code> objects. Pointers to functions (function pointers) are useful for passing functions as arguments to higher-order functions (such as qsort or bsearch), in dispatch tables, or as callbacks to event handlers. Array bounds violations are therefore possible and can lead to various repercussions, including illegal memory accesses, corruption of data, buffer overruns, and run-time exceptions.
C does not have a special provision for declaring multi-dimensional arrays, but rather relies on recursion within the type system to declare arrays of arrays, which effectively accomplishes the same thing. The index values of the resulting "multi-dimensional array" can be thought of as increasing in row-major order. Multi-dimensional arrays are commonly used in numerical algorithms (mainly from applied linear algebra) to store matrices. The structure of the C array is well suited to this particular task. However, in early versions of C the bounds of the array must be known fixed values or else explicitly passed to any subroutine that requires them, and dynamically sized arrays of arrays cannot be accessed using double indexing. (A workaround for this was to allocate the array with an additional "row vector" of pointers to the columns.) C99 introduced "variable-length arrays" which address this issue.
The following example using modern C (C99 or later) shows allocation of a two-dimensional array on the heap and the use of multi-dimensional array indexing for accesses (which can use bounds-checking on many C compilers):
<syntaxhighlight lang="c">
int func(int N, int M)
{
float (*p)[N] [M] = malloc(sizeof *p);
if (p 0)
return -1;
for (int i = 0; i < N; i++)
for (int j = 0; j < M; j++)
(*p)[i] [j] = i + j;
print_array(N, M, p);
free(p);
return 1;
}
</syntaxhighlight>
And here is a similar implementation using C99's Auto VLA feature: too.}}
<syntaxhighlight lang="c">
int func(int N, int M)
{
// Caution: checks should be made to ensure N*M*sizeof(float) does NOT exceed limitations for auto VLAs and is within available size of stack.
float p[N] [M]; // auto VLA is held on the stack, and sized when the function is invoked
for (int i = 0; i < N; i++)
for (int j = 0; j < M; j++)
p[i] [j] = i + j;
print_array(N, M, p);
// no need to free(p) since it will disappear when the function exits, along with the rest of the stack frame
return 1;
}
</syntaxhighlight>
Array–pointer interchangeability
The subscript notation <code>x[i]</code> (where <code>x</code> designates a pointer) is syntactic sugar for <code>*(x+i)</code>. Taking advantage of the compiler's knowledge of the pointer type, the address that <code>x + i</code> points to is not the base address (pointed to by <code>x</code>) incremented by <code>i</code> bytes, but rather is defined to be the base address incremented by <code>i</code> multiplied by the size of an element that <code>x</code> points to. Thus, <code>x[i]</code> designates the <code>i+1</code>th element of the array.
Furthermore, in most expression contexts (a notable exception is as operand of <code>sizeof</code>), an expression of array type is automatically converted to a pointer to the array's first element. This implies that an array is never copied as a whole when named as an argument to a function, but rather only the address of its first element is passed. Therefore, although function calls in C use pass-by-value semantics, arrays are in effect passed by reference.
The total size of an array <code>x</code> can be determined by applying <code>sizeof</code> to an expression of array type. The size of an element can be determined by applying the operator <code>sizeof</code> to any dereferenced element of an array <code>A</code>, as in <code>n sizeof A[0]</code>. Thus, the number of elements in a declared array <code>A</code> can be determined as <code>sizeof A / sizeof A[0]</code>. Note, that if only a pointer to the first element is available as it is often the case in C code because of the automatic conversion described above, the information about the full type of the array and its length are lost. Memory management One of the most important functions of a programming language is to provide facilities for managing memory and the objects that are stored in memory. C provides three principal ways to allocate memory for objects:
There are also compilers, libraries, and operating system level mechanisms for performing actions that are not a standard part of C, such as bounds checking for arrays, detection of buffer overflow, serialization, dynamic memory tracking, and automatic garbage collection.
Memory management checking tools like Purify or Valgrind and linking with libraries containing special versions of the memory allocation functions can help uncover runtime errors in memory usage.
Uses
Rationale for use in systems programming
C is widely used for systems programming in implementing operating systems and embedded system applications. This is for several reasons:
* The C language permits platform hardware and memory to be accessed with pointers and type punning, so system-specific features (e.g. Control/Status Registers, I/O registers) can be configured and used with code written in C – it allows fullest control of the platform it is running on.
* The code generated after compilation does not demand many system features, and can be invoked from some boot code in a straightforward manner – it is simple to execute.
* The C language statements and expressions typically map well on to sequences of instructions for the target processor, and consequently there is a low run-time demand on system resources – it is fast to execute.
* With its rich set of operators, the C language can use many of the features of target CPUs. Where a particular CPU has more esoteric instructions, a language variant can be constructed with perhaps intrinsic functions to exploit those instructions – it can use practically all the target CPU's features.
* The language makes it easy to overlay structures onto blocks of binary data, allowing the data to be comprehended, navigated and modified – it can write data structures, even file systems.
* The language supports a rich set of operators, including bit manipulation, for integer arithmetic and logic, and perhaps different sizes of floating point numbers – it can process appropriately-structured data effectively.
* C is a fairly small language, with only a handful of statements, and without too many features that generate extensive target code – it is comprehensible.
* C has direct control over memory allocation and deallocation, which gives reasonable efficiency and predictable timing to memory-handling operations, without any concerns for sporadic stop-the-world garbage collection events – it has predictable performance.
* C permits the use and implementation of different memory allocation schemes, including a typical and ; a more sophisticated mechanism with arenas; or a version for an OS kernel that may suit DMA, use within interrupt handlers, or integrated with the virtual memory system.
* Depending on the linker and environment, C code can also call libraries written in assembly language, and may be called from assembly language – it interoperates well with other lower-level code.
* C and its calling conventions and linker structures are commonly used in conjunction with other high-level languages, with calls both to C and from C supported – it interoperates well with other high-level code.
* C has a very mature and broad ecosystem, including libraries, frameworks, open source compilers, debuggers and utilities, and is the de facto standard. It is likely the drivers already exist in C, or that there is a similar CPU architecture as a back-end of a C compiler, so there is reduced incentive to choose another language.
Used for computationally-intensive libraries
C enables programmers to create efficient implementations of algorithms and data structures, because the layer of abstraction from hardware is thin, and its overhead is low, an important criterion for computationally intensive programs. For example, the GNU Multiple Precision Arithmetic Library, the GNU Scientific Library, Mathematica, and MATLAB are completely or partially written in C. Many languages support calling library functions in C, for example, the Python-based framework NumPy uses C for the high-performance and hardware-interacting aspects.
Games
Computer games are often built from a combination of languages. C has featured significantly, especially for those games attempting to obtain best performance from computer platforms. Examples include Doom from 1993
C as an intermediate language
C is sometimes used as an intermediate language by implementations of other languages. This approach may be used for portability or convenience; by using C as an intermediate language, additional machine-specific code generators are not necessary. C has some features, such as line-number preprocessor directives and optional superfluous commas at the end of initializer lists, that support compilation of generated code. However, some of C's shortcomings have prompted the development of other C-based languages specifically designed for use as intermediate languages, such as C--. Also, contemporary major compilers GCC and LLVM both feature an intermediate representation that is not C, and those compilers support front ends for many languages including C.
Other languages written in C
A consequence of C's wide availability and efficiency is that compilers, libraries and interpreters of other programming languages are often implemented in C. For example, the reference implementations of Python, Perl, Ruby, and PHP are written in C.Once used for web developmentHistorically, C was sometimes used for web development using the Common Gateway Interface (CGI) as a "gateway" for information between the web application, the server, and the browser. C may have been chosen over interpreted languages because of its speed, stability, and near-universal availability. It is no longer common practice for web development to be done in C, and many other web development languages are popular. Applications where C-based web development continues include the HTTP configuration pages on routers, IoT devices and similar, although even here some projects have parts in higher-level languages e.g. the use of Lua within OpenWRT.
Web servers
The two most popular web servers, Apache HTTP Server and Nginx, are both written in C. These web servers interact with the operating system, listen on TCP ports for HTTP requests, and then serve up static web content, or cause the execution of other languages handling to 'render' content such as PHP, which is itself primarily written in C. C's close-to-the-metal approach allows for the construction of these high-performance software systems.
End-user applications
C has also been widely used to implement end-user applications. However, such applications can also be written in newer, higher-level languages.Limitations
While C has been popular, influential and hugely successful, it has drawbacks, including:
* The standard dynamic memory handling with <code>malloc</code> and <code>free</code> is error prone. Improper use can lead to memory leaks and dangling pointers.
* The use of pointers and the direct manipulation of memory means corruption of memory is possible, perhaps due to programmer error, or insufficient checking of bad data.
* There is some type checking, but it does not apply to areas like variadic functions, and the type checking can be trivially or inadvertently circumvented. It is weakly typed.
* Since the code generated by the compiler contains few checks itself, there is a burden on the programmer to consider all possible outcomes, to protect against buffer overruns, array bounds checking, stack overflows, memory exhaustion, and consider race conditions, thread isolation, etc.
* The use of pointers and the run-time manipulation of these means there may be two ways to access the same data (aliasing), which is not determinable at compile time. This means that some optimisations that may be available to other languages are not possible in C. FORTRAN is considered faster.
* Some of the standard library functions, e.g. <code>scanf</code> or , can lead to buffer overruns.
* There is limited standardisation in support for low-level variants in generated code, for example: different function calling conventions and ABI; different structure packing conventions; different byte ordering within larger integers (including endianness). In many language implementations, some of these options may be handled with the preprocessor directive <code>#pragma</code>, and some with additional keywords e.g. use <code>__cdecl</code> calling convention. The directive and options are not consistently supported.
* String handling using the standard library is code-intensive, with explicit memory management required.
* The language does not directly support object orientation, introspection, run-time expression evaluation, generics, etc.
* There are few guards against inappropriate use of language features, which may lead to unmaintainable code. In particular, the C preprocessor can hide troubling effects such as double evaluation and worse. This facility for tricky code has been celebrated with competitions such as the International Obfuscated C Code Contest and the Underhanded C Contest.
* C lacks standard support for exception handling and only offers return codes for error checking. The <code>setjmp</code> and <code>longjmp</code> standard library functions have been used to implement a try-catch mechanism via macros.
For some purposes, restricted styles of C have been adopted, e.g. MISRA C or CERT C, in an attempt to reduce the opportunity for bugs. Databases such as CWE attempt to count the ways C etc. has vulnerabilities, along with recommendations for mitigation.
There are tools that can mitigate against some of the drawbacks. Contemporary C compilers include checks which may generate warnings to help identify many potential bugs.
Related languages
graph, showing a comparison of the popularity of various programming languages]]
C has both directly and indirectly influenced many later languages such as C++ and Java. The most pervasive influence has been syntactical; all of the languages mentioned combine the statement and (more or less recognizably) expression syntax of C with type systems, data models or large-scale program structures that differ from those of C, sometimes radically.
Several C or near-C interpreters exist, including Ch and CINT, which can also be used for scripting.
When object-oriented programming languages became popular, C++ and Objective-C were two different extensions of C that provided object-oriented capabilities. Both languages were originally implemented as source-to-source compilers; source code was translated into C, and then compiled with a C compiler.
The C++ programming language (originally named "C with Classes") was devised by Bjarne Stroustrup as an approach to providing object-oriented functionality with a C-like syntax. C++ adds greater typing strength, scoping, and other tools useful in object-oriented programming, and permits generic programming via templates. Nearly a superset of C, C++ now supports most of C, with a few exceptions.
Objective-C was originally a very "thin" layer on top of C, and remains a strict superset of C that permits object-oriented programming using a hybrid dynamic/static typing paradigm. Objective-C derives its syntax from both C and Smalltalk: syntax that involves preprocessing, expressions, function declarations, and function calls is inherited from C, while the syntax for object-oriented features was originally taken from Smalltalk.
In addition to C++ and Objective-C, Ch, Cilk, and Unified Parallel C are nearly supersets of C.
See also
* Compatibility of C and C++
* Comparison of Pascal and C
* Comparison of programming languages
* International Obfuscated C Code Contest
* List of C-family programming languages
* List of C compilers
Notes
References
Sources
*
** By courtesy of the author, also at
*
* Further reading * <small>[https://github.com/wuzhouhui/c_standard_lib (source)]</small>
* <small>[https://github.com/wardvanwanrooij/thecbook (free)]</small>
*
* <small>[https://archive.org/details/creferencemanual00harb (archive)]</small>
* <small>[https://archive.org/details/cprogrammingmode0000king (archive)]</small>
*
*
*
* <small>[https://gustedt.gitlabpages.inria.fr/modern-c/ (free)]</small> External links
* [https://www.open-std.org/jtc1/sc22/wg14/ ISO C Working Group official website]
** [https://www.open-std.org/JTC1/SC22/WG14/www/standards ISO/IEC 9899], publicly available official C documents, including the C99 Rationale
**
* [https://c-faq.com/ comp.lang.c Frequently Asked Questions]
* [https://csapp.cs.cmu.edu/3e/docs/chistory.html A History of C], by Dennis Ritchie
* [https://en.cppreference.com/w/c C Library Reference and Examples]
Category:American inventions
Category:Articles with example C code
Category:C programming language family
Category:Cross-platform software
Category:High-level programming languages
Category:Procedural programming languages
Category:Structured programming languages
Category:Programming languages created in 1972
Category:Programming languages with an ISO standard
Category:Statically typed programming languages
Category:Systems programming languages
|
https://en.wikipedia.org/wiki/C_(programming_language)
|
2025-04-05T18:27:41.452040
|
6023
|
Castle of the Winds
|
Castle of the Winds is a tile-based roguelike video game for Microsoft Windows. It was developed by Rick Saada in 1989 and distributed by Epic MegaGames in 1993. The game was released around 1998 as a freeware download by the author. Though it is secondary to its hack and slash gameplay, Castle of the Winds has a plot loosely based on Norse mythology, told with setting changes, unique items, and occasional passages of text. The game is composed of two parts: A Question of Vengeance, released as shareware, and Lifthransir's Bane, sold commercially. A combined license for both parts was also sold.
Gameplay
The game differs from most roguelikes in a number of ways. Its interface is mouse-dependent, but supports keyboard shortcuts (such as 'g' to get an item). Castle of the Winds also allows the player to restore saved games after dying.
The game favors the use of magic in combat, as spells are the only weapons that work from a distance. The player character automatically gains a spell with each experience level, and can permanently gain others using corresponding books, until all thirty spells available are learned. There are two opposing pairs of elements: cold vs. fire and lightning vs. acid/poison. Spells are divided into six categories: attack, defense, healing, movement, divination, and miscellaneous.
Castle of the Winds possesses an inventory system that limits a player's load based on weight and bulk, rather than by number of items. It allows the character to use different containers, including packs, belts, chests, and bags. Other items include weapons, armor, protective clothing, purses, and ornamental jewellery. Almost every item in the game can be normal, cursed, or enchanted, with curses and enchantments working in a manner similar to NetHack. Although items do not break with use, they may already be broken or rusted when found. Most objects that the character currently carries can be renamed.
Wherever the player goes before entering the dungeon, there is always a town which offers the basic services of a temple for healing and curing curses, a junk store where anything can be sold for a few copper coins, a sage who can identify items and (from the second town onwards) a bank for storing the total capacity of coins to lighten the player's load. Other services that differ and vary in what they sell are outfitters, weaponsmiths, armoursmiths, magic shops and general stores.
The game tracks how much time has been spent playing the game. Although story events are not triggered by the passage of time, it does determine when merchants rotate their stock. Victorious players are listed as "Valhalla's Champions" in the order of time taken, from fastest to slowest. If the player dies, they are still put on the list, but are categorized as "Dead", with their experience point total listed as at the final killing blow. The amount of time spent also determines the difficulty of the last boss.
Plot
The player begins in a tiny hamlet, near which they used to live. Their farm has been destroyed and godparents killed. After clearing out an abandoned mine, the player finds a scrap of parchment that reveals the death of the player's godparents was ordered by an unknown enemy. The player then returns to the hamlet to find it pillaged, and decides to travel to Bjarnarhaven.
Once in Bjarnarhaven, the player explores the levels beneath a nearby fortress, eventually facing Hrungnir, the Hill Giant Lord, responsible for ordering the player's godparents' death. Hrungnir carries the Enchanted Amulet of Kings. Upon activating the amulet, the player is informed of their past by their dead father, after which the player is transported to the town of Crossroads, and Part I ends. The game can be imported or started over in Part II.
The town of Crossroads is run by a Jarl who at first does not admit the player, but later (on up to three occasions) provides advice and rewards. The player then enters the nearby ruined titular Castle of the Winds. There the player meets his/her deceased grandfather, who instructs them to venture into the dungeons below, defeat Surtur, and reclaim their birthright. Venturing deeper, the player encounters monsters run rampant, a desecrated crypt, a necromancer, and the installation of various special rooms for elementals. The player eventually meets and defeats the Wolf-Man leader, Bear-Man leader, the four Jotun kings, a Demon Lord, and finally Surtur. Upon defeating Surtur and escaping the dungeons, the player sits upon the throne, completing the game.
Development
Inspired by his love of RPGs and while learning Windows programming in the 80s, Rick Saada designed and completed Castle of the Winds. The game sold 13,500 copies. By 1998, the game's author, Rick Saada, decided to distribute the entirety of Castle of the Winds free of charge.
References
External links
Category:1989 video games
Category:Epic Games games
Category:Freeware games
Category:Public-domain software
Category:Roguelike video games
Category:Shareware games
Category:Single-player video games
Category:Video games based on Norse mythology
Category:Video games developed in the United States
Category:Video games set in castles
Category:Video games using procedural generation
Category:Video games with gender-selectable protagonists
Category:Windows games
Category:Windows-only games
|
https://en.wikipedia.org/wiki/Castle_of_the_Winds
|
2025-04-05T18:27:41.457287
|
6024
|
Reformed Christianity
|
Reformed Christianity, also called Calvinism,}} is a major branch of Protestantism that began during the 16th-century Protestant Reformation. In the modern day, it is largely represented by the Continental Reformed, Presbyterian, and Congregational traditions, as well as parts of the Anglican (known as "Episcopal" in some regions) and Baptist traditions.
Reformed theology emphasizes the authority of the Bible and the sovereignty of God, as well as covenant theology, a framework for understanding the Bible based on God's covenants with people. Reformed churches have emphasized simplicity in worship. Several forms of ecclesiastical polity are exercised by Reformed churches, including presbyterian, congregational, and some episcopal. Articulated by John Calvin, the Reformed faith holds to a spiritual (pneumatic) presence of Christ in the Lord's Supper.
Emerging in the 16th century, the Reformed tradition developed over several generations, especially in Switzerland, Scotland and the Netherlands. In the 17th century, Jacobus Arminius and the Remonstrants were expelled from the Dutch Reformed Church over disputes regarding predestination and salvation, and from that time Arminians are usually considered to be a distinct tradition from the Reformed. This dispute produced the Canons of Dort, the basis for the "doctrines of grace" also known as the "five points" of Calvinism.
Definition and terminology
Reformed Christianity is often called Calvinism after John Calvin (born Jehan Cauvin), influential reformer of Geneva. The term was first used by opposing Lutherans in the 1550s. Calvin did not approve of the use of this term, and scholars have argued its use is misleading, inaccurate, unhelpful, and "inherently distortive."
The definitions and boundaries of the terms Reformed Christianity and Calvinism are contested by scholars. As a historical movement, Reformed Christianity began during the Reformation with Huldrych Zwingli in Zürich, Switzerland. Following the failure of the Marburg Colloquy between Zwingli's followers and those of Martin Luther in 1529 to mediate disputes regarding the real presence of Christ in the Lord's Supper, Reformed Protestants were defined by their opposition to Lutherans. The Reformed also opposed Anabaptist radicals thus remaining within the Magisterial Reformation. During the 17th-century Arminian Controversy, followers of Jacobus Arminius were forcibly removed from the Dutch Reformed Church for their views regarding predestination and salvation, and thenceforth Arminians would be considered outside the pale of Reformed orthodoxy, though some use the term Reformed to include Arminians while using the term Calvinist to exclude Arminians.
Reformed Christianity also has a complicated relationship with Anglicanism, the branch of Christianity originating in the Church of England. The Anglican confessions are considered Protestant, and more specifically, Reformed, and leaders of the English Reformation were influenced by Calvinist rather than Lutheran theologians. Still the Church of England retained elements of Catholicism such as bishops and vestments, unlike continental Reformed churches, and thus was sometimes called "but halfly Reformed." Beginning in the 17th century, Anglicanism broadened to the extent that Reformed theology is no longer dominant in Anglicanism.
Some scholars argue that Reformed Baptists, who hold many of the same beliefs as Reformed Christians but not infant baptism, should be considered part of Reformed Christianity, though this would not have been the view of early modern Reformed theologians. Others disagree, asserting that Baptists should be considered a separate religious tradition.
History
in Geneva.]]
The first wave of Reformed theologians included Zwingli, Martin Bucer, Wolfgang Capito, John Oecolampadius, and Guillaume Farel. While from diverse academic backgrounds, their work already contained key themes within Reformed theology, especially the priority of scripture as a source of authority. Scripture was also viewed as a unified whole, which led to a covenantal theology of the sacraments of baptism and the Lord's Supper as visible signs of the covenant of grace. Another shared perspective was their denial of the real presence of Christ in the Eucharist. Each understood salvation to be by grace alone and affirmed a doctrine of unconditional election, the teaching that some people are chosen by God to be saved. Luther and his successor Philipp Melanchthon were significant influences on these theologians and, to a larger extent, those who followed. The doctrine of justification by faith alone, also known as sola fide, was a direct inheritance from Luther.
The second generation featured John Calvin, Heinrich Bullinger, Thomas Cranmer, Wolfgang Musculus, Peter Martyr Vermigli, Andreas Hyperius and John à Lasco. Written between 1536 and 1539, Calvin's Institutes of the Christian Religion was one of the most influential works of the era. Toward the middle of the 16th century, these beliefs were formed into one consistent creed which would shape the future definition of the Reformed faith. The 1549 Consensus Tigurinus unified Zwingli and Bullinger's memorialist theology of the Eucharist, which taught that it was simply a reminder of Christ's death, with Calvin's view of it as a means of grace with Christ actually present, though spiritually rather than bodily as in Catholic doctrine. The document demonstrates the diversity as well as unity in early Reformed theology, giving it a stability that enabled it to spread rapidly throughout Europe. This stands in marked contrast to the bitter controversy experienced by Lutherans prior to the 1579 Formula of Concord.
Through Calvin's missionary work in France, his program of reform eventually reached the French-speaking provinces of the Netherlands. Calvinism was adopted in the Electorate of the Palatinate under Frederick III, which led to the formulation of the Heidelberg Catechism in 1563. This and the Belgic Confession were adopted as confessional standards in the first synod of the Dutch Reformed Church in 1571.
In 1573 William the Silent joined the Calvinist Church. Calvinism was declared the official religion of the Kingdom of Navarre by the queen regnant Jeanne d'Albret after her conversion in 1560. Leading divines, either Calvinist or those sympathetic to Calvinism, settled in England, including Bucer, Martyr, and John Łaski, as did John Knox in Scotland. During the First English Civil War, English and Scots Presbyterians produced the Westminster Confession, which became the confessional standard for Presbyterians in the English-speaking world. Having established itself in Europe, the movement continued to spread to areas including North America, South Africa and Korea. While Calvin did not live to see the foundation of his work grow into an international movement, his death allowed his ideas to spread far beyond their city of origin and their borders and to establish their own distinct character. Spread
.]]
Although much of Calvin's work was in Geneva, his publications spread his ideas of a correctly Reformed church to many parts of Europe. In Switzerland, some cantons are still Reformed, and some are Catholic. Calvinism became the dominant doctrine within the Church of Scotland, the Dutch Republic, some communities in Flanders, and parts of Germany, especially those adjacent to the Netherlands in the Palatinate, Kassel, and Lippe, spread by Caspar Olevian and Zacharias Ursinus among others. Protected by the local nobility, Calvinism became a significant religion in eastern Hungary and Hungarian-speaking areas of Transylvania. there are about 3.5 million Hungarian Reformed people worldwide.
Calvinism was influential in France, Lithuania, and Poland before being mostly erased during the Counter-Reformation. One of the most important Polish reformed theologists was Łaski, who was also involved into organising churches in East Frisia and Stranger's Church in London. Later, a faction called the Polish Brethren broke away from Calvinism on January 22, 1556, when Piotr of Goniądz, a Polish student, spoke out against the doctrine of the Trinity during the general synod of the Reformed churches of Poland held in the village of Secemin. Calvinism gained some popularity in Scandinavia, especially Sweden, but was rejected in favor of Lutheranism after the Synod of Uppsala in 1593.
Many 17th century European settlers in the Thirteen Colonies in British America were Calvinists, who emigrated because of arguments over church structure, including the Pilgrim Fathers. Others were forced into exile, including the French Huguenots. Dutch and French Calvinist settlers were also among the first European colonizers of South Africa, beginning in the 17th century, who became known as Boers or Afrikaners.
Sierra Leone was largely colonized by Calvinist settlers from Nova Scotia, many of whom were Black Loyalists who fought for the British Empire during the American War of Independence. John Marrant had organized a congregation there under the auspices of the Huntingdon Connection. Some of the largest Calvinist communions were started by 19th- and 20th-century missionaries. Especially large are those in Indonesia, Korea and Nigeria. In South Korea there are 20,000 Presbyterian congregations with about 9–10 million church members, scattered in more than 100 Presbyterian denominations. In South Korea, Presbyterianism is the largest Christian denomination.
Demography
A 2011 report of the Pew Forum on Religious and Public Life estimates that members of Presbyterian or Reformed churches make up 7% of the estimated 801 million Protestants globally, or approximately 56 million people.
Though the broadly defined Reformed faith is much larger, as it constitutes Congregationalist (0.5%), most of the United and uniting churches (unions of different denominations) (7.2%) and most likely some of the other Protestant denominations (38.2%). All three are distinct categories from Presbyterian or Reformed (7%) in this report. The Reformed family of churches is one of the largest Christian denominations, representing 75 million believers worldwide.
According to Global Christianity: A Guide to the World’s Largest Religion from Afghanistan to Zimbabwe, in 2020, Presbyterian and Reformed Christians numbered around 65,446,000 people, or 0.8% of the world's population. Congregationalists were listed at 4,986,000, with 0.1% of the world's population. Therefore, the three branches of Reformed Christianity totaled 70,432,000 people, or 0.9% of the global population.
World Communions
The World Communion of Reformed Churches (WCRC), which includes some United Churches, has 80 million believers. WCRC is the fourth largest Christian communion in the world, after the Roman Catholic Church, the Eastern Orthodox Churches, and the Anglican Communion. Reformed theologians emphasize that this sinfulness affects all of a person's nature, including their will. This view, that sin so dominates people that they are unable to avoid sin, has been called total depravity. As a consequence, every one of their descendants inherited a stain of corruption and depravity. This condition, innate to all humans, is known in Christian theology as original sin.
Calvin thought original sin was "a hereditary corruption and depravity of our nature, extending to all the parts of the soul." Calvin asserted people were so warped by original sin that "everything which our mind conceives, meditates, plans, and resolves, is always evil." The depraved condition of every human being is not the result of sins people commit during their lives. Instead, before we are born, while we are in our mother's womb, "we are in God's sight defiled and polluted." Calvin thought people were justly condemned to hell because their corrupted state is "naturally hateful to God."
In colloquial English, the term "total depravity" can be easily misunderstood to mean that people are absent of any goodness or unable to do any good. However the Reformed teaching is actually that while people continue to bear God's image and may do things that appear outwardly good, their sinful intentions affect all of their nature and actions so that they are not pleasing to God.
Justification is the part of salvation where God pardons the sin of those who believe in Christ. It is historically held by Protestants to be the most important article of Christian faith, though more recently it is sometimes given less importance out of ecumenical concerns. People are not on their own able to fully repent of their sin or prepare themselves to repent because of their sinfulness. Therefore, justification is held to arise solely from God's free and gracious act.
Sanctification is the part of salvation in which God makes believers holy, by enabling them to exercise greater love for God and for other people. The good works accomplished by believers as they are sanctified are considered to be the necessary outworking of the believer's salvation, though they do not cause the believer to be saved. Sanctification, like justification, is by faith, because doing good works is simply living as the child of God one has become. Predestination
Stemming from the theology of John Calvin, Reformed theologians teach that sin so affects human nature that they are unable even to exercise faith in Christ by their own will. While people are said to retain free will, in that they willfully sin, they are unable not to sin because of the corruption of their nature due to original sin. Reformed Christians believe that God predestined some people to be saved and others were predestined to eternal damnation. This choice by God to save some is held to be unconditional and not based on any characteristic or action on the part of the person chosen. The Calvinist view is opposed to the Arminian view that God's choice of whom to save is conditional or based on his foreknowledge of who would respond positively to God.
Karl Barth reinterpreted the doctrine of predestination to apply only to Christ. Individual people are only said to be elected through their being in Christ. Reformed theologians who followed Barth, including Jürgen Moltmann, David Migliore, and Shirley Guthrie, have argued that the traditional Reformed concept of predestination is speculative and have proposed alternative models. These theologians claim that a properly trinitarian doctrine emphasizes God's freedom to love all people, rather than choosing some for salvation and others for damnation. God's justice towards and condemnation of sinful people is spoken of by these theologians as out of his love for them and a desire to reconcile them to himself.
Five Points of Calvinism
Much attention surrounding Calvinism focuses on the "Five Points of Calvinism" (also called the doctrines of grace). The five points have been summarized under the acrostic TULIP. The five points are popularly said to summarize the Canons of Dort; however, there is no historical relationship between them, and some scholars argue that their language distorts the meaning of the Canons, Calvin's theology, and the theology of 17th-century Calvinistic orthodoxy, particularly in the language of total depravity and limited atonement. The five points were more recently popularized in the 1963 booklet The Five Points of Calvinism Defined, Defended, Documented by David N. Steele and Curtis C. Thomas. The origins of the five points and the acrostic are uncertain, but they appear to be outlined in the Counter Remonstrance of 1611, a lesser-known Reformed reply to the Arminians, which was written prior to the Canons of Dort. The acrostic was used by Cleland Boyd McAfee as early as circa 1905. An early printed appearance of the acrostic can be found in Loraine Boettner's 1932 book, The Reformed Doctrine of Predestination.
Church
]]
Reformed Christians see the Christian Church as the community with which God has made the covenant of grace, a promise of eternal life and relationship with God. This covenant extends to those under the "old covenant" whom God chose, beginning with Abraham and Sarah. The church is conceived of as both invisible and visible. The invisible church is the body of all believers, known only to God. The visible church is the institutional body which contains both members of the invisible church as well as those who appear to have faith in Christ, but are not truly part of God's elect.
In order to identify the visible church, Reformed theologians have spoken of certain marks of the Church. For some, the only mark is the pure preaching of the gospel of Christ. Others, including John Calvin, also include the right administration of the sacraments. Others, such as those following the Scots Confession, include a third mark of rightly administered church discipline, or exercise of censure against unrepentant sinners. These marks allowed the Reformed to identify the church based on its conformity to the Bible rather than the magisterium or church tradition. Worship Regulative principle of worship
described what should (and should not) occur in worship.]]
The regulative principle of worship is a teaching shared by some Calvinists and Anabaptists on how the Bible orders public worship. The substance of the doctrine regarding worship is that God institutes in the Scriptures everything he requires for worship in the Church and that everything else is prohibited. As the regulative principle is reflected in Calvin's own thought, it is driven by his evident antipathy toward the Roman Catholic Church and its worship practices, and it associates musical instruments with icons, which he considered violations of the Ten Commandments' prohibition of graven images.
On this basis, many early Calvinists also eschewed musical instruments and advocated a cappella exclusive psalmody in worship, though Calvin himself allowed other scriptural songs as well as psalms,
Since the 19th century, however, some of the Reformed churches have modified their understanding of the regulative principle and make use of musical instruments, believing that Calvin and his early followers went beyond the biblical requirements
Sacraments
The Westminster Confession of Faith limits the sacraments to baptism and the Lord's Supper. Sacraments are denoted "signs and seals of the covenant of grace." Westminster speaks of "a sacramental relation, or a sacramental union, between the sign and the thing signified; whence it comes to pass that the names and effects of the one are attributed to the other." Baptism is for infant children of believers as well as believers, as it is for all the Reformed except Baptists and some Congregationalists. Baptism admits the baptized into the visible church, and in it all the benefits of Christ are offered to the baptized. On the Lord's supper, the Westminster Confession takes a position between Lutheran sacramental union and Zwinglian memorialism: "the Lord's supper really and indeed, yet not carnally and corporally, but spiritually, receive and feed upon Christ crucified, and all benefits of his death: the body and blood of Christ being then not corporally or carnally in, with, or under the bread and wine; yet, as really, but spiritually, present to the faith of believers in that ordinance as the elements themselves are to their outward senses."
The 1689 London Baptist Confession of Faith does not use the term sacrament, but describes baptism and the Lord's supper as ordinances, as do most Baptists, Calvinist or otherwise. Baptism is only for those who "actually profess repentance towards God", and not for the children of believers. Baptists also insist on immersion or dipping, in contradistinction to other Reformed Christians. The Baptist Confession describes the Lord's supper as "the body and blood of Christ being then not corporally or carnally, but spiritually present to the faith of believers in that ordinance", similarly to the Westminster Confession. There is significant latitude in Baptist congregations regarding the Lord's supper, and many hold the Zwinglian view. Logical order of God's decree
There are two schools of thought regarding the logical order of God's decree to ordain the fall of man: supralapsarianism (from the Latin: , "above", here meaning "before" + , "fall") and infralapsarianism (from the Latin: , "beneath", here meaning "after" + , "fall"). The former view, sometimes called "high Calvinism", argues that the Fall occurred partly to facilitate God's purpose to choose some individuals for salvation and some for damnation. Infralapsarianism, sometimes called "low Calvinism", is the position that, while the Fall was indeed planned, it was not planned with reference to who would be saved.
Supralapsarianism is based on the belief that God chose which individuals to save logically prior to the decision to allow the race to fall and that the Fall serves as the means of realization of that prior decision to send some individuals to hell and others to heaven (that is, it provides the grounds of condemnation in the reprobate and the need for salvation in the elect). In contrast, infralapsarians hold that God planned the race to fall logically prior to the decision to save or damn any individuals because, it is argued, in order to be "saved", one must first need to be saved from something and therefore the decree of the Fall must precede predestination to salvation or damnation.
These two views vied with each other at the Synod of Dort, an international body representing Calvinist Christian churches from around Europe, and the judgments that came out of that council sided with infralapsarianism (Canons of Dort, First Point of Doctrine, Article 7). The Westminster Confession of Faith also teaches (in Hodge's words "clearly impl[ies]") the infralapsarian view, but is sensitive to those holding to supralapsarianism. The Lapsarian controversy has a few vocal proponents on each side today, but overall it does not receive much attention among modern Calvinists.
Branches
The Reformed tradition is historically represented by the Continental, Presbyterian, Reformed Anglican, Congregationalist, and Reformed Baptist denominational families.
Reformed churches practice several forms of church government, primarily presbyterian and congregational, but some adhere to episcopal polity. The largest interdenominational association is the World Communion of Reformed Churches with more than 100 million members in 211 member denominations around the world. Smaller, conservative Reformed associations include the World Reformed Fellowship and the International Conference of Reformed Churches. Continental
"Continental" Reformed churches originate in continental Europe, a term used by English speakers to distinguish them from traditions from the British Isles. Many uphold the Helvetic Confessions and Heidelberg Catechism, which were adopted in Zurich and Heidelberg, respectively. In the United States, immigrants belonging to the continental Reformed churches joined the Dutch Reformed Church there, as well as the Anglican Church. Presbyterian
Presbyterian churches are named for their order of government by assemblies of elders, or presbyters. They are especially influenced by John Knox, who brought Reformed theology and polity to the Church of Scotland after spending time on the continent in Calvin's Geneva. Presbyterians historically uphold the Westminster Confession of Faith.
Congregational
Congregationalism originates in Puritanism, a sixteenth-century movement to reform the Church of England. Unlike the Presbyterians, Congregationalists consider the local church to be rightfully self-ruled by their own officers, not higher ecclesiastical courts. The Savoy Declaration, a revision of Westminster, is the primary confession of historic Congregationalism. Evangelical Congregationalists are internationally represented by the World Evangelical Congregational Fellowship. Christian denominations in the Congregationalist tradition include the United Church of Christ, the National Association of Congregational Christian Churches and the Conservative Congregational Christian Conference in the United States, Evangelical Congregational Church in Argentina and Evangelical Fellowship of Congregational Churches in the United Kingdom, among others.
Anglican
Though Anglicanism today is often described as a separate branch from the Reformed, historic Anglicanism is a part of the wider Reformed tradition. The foundational documents of the Anglican church "express a theology in keeping with the Reformed theology of the Swiss and South German Reformation." The Most Rev. Peter Robinson, presiding bishop of the United Episcopal Church of North America, writes:}}
Baptist
Reformed or Calvinistic Baptists, unlike other Reformed traditions, exclusively practice believer's baptism. They observe congregational polity like the Congregationalists. Their primary confession is the 1689 Baptist Confession of Faith, a revision of the Savoy Declaration of the Congregationalist Church, but other Baptist Confessions are also used. Not all Baptists are Reformed. Some Reformed Baptists accept Reformed theology, especially soteriology, but do not hold to a specific confession or to covenant theology. Variants in Reformed theology Amyraldism
formulated Amyraldism, a modified Calvinist theology regarding the nature of Jesus' atonement.]]
Amyraldism (or sometimes Amyraldianism, also known as the School of Saumur, hypothetical universalism, post redemptionism, moderate Calvinism, or four-point Calvinism) is the belief that God, prior to his decree of election, decreed Christ's atonement for all alike if they believe, but seeing that none would believe on their own, he then elected those whom he will bring to faith in Christ, thereby preserving the Calvinist doctrine of unconditional election. The efficacy of the atonement remains limited to those who believe.
Named after its formulator Moses Amyraut, this doctrine is still viewed as a variety of Calvinism in that it maintains the particularity of sovereign grace in the application of the atonement. However, detractors like B. B. Warfield have termed it "an inconsistent and therefore unstable form of Calvinism."
Hyper-Calvinism
Hyper-Calvinism first referred to a view that appeared among the early English Particular Baptists in the 18th century. Their system denied that the call of the gospel to "repent and believe" is directed to every single person and that it is the duty of every person to trust in Christ for salvation. The term also occasionally appears in both theological and secular controversial contexts, where it usually connotes a negative opinion about some variety of theological determinism, predestination, or a version of Evangelical Christianity or Calvinism that is deemed by the critic to be unenlightened, harsh, or extreme.
The Westminster Confession of Faith says that the gospel is to be freely offered to sinners, and the Larger Catechism makes clear that the gospel is offered to the non-elect.
Neo-Calvinism
initiated Neo-Calvinism.]]
Beginning in the 1880s, Neo-Calvinism, a form of Dutch Calvinism, is the movement initiated by the theologian and later Dutch prime minister Abraham Kuyper. James Bratt has identified a number of different types of Dutch Calvinism: The Seceders—split into the Reformed Church "West" and the Confessionalists; and the Neo-Calvinists—the Positives and the Antithetical Calvinists. The Seceders were largely infralapsarian and the Neo-Calvinists usually supralapsarian.
Kuyper wanted to awaken the church from what he viewed as its pietistic slumber. He declared:
<blockquote>No single piece of our mental world is to be sealed off from the rest and there is not a square inch in the whole domain of human existence over which Christ, who is sovereign over all, does not cry: 'Mine!' </blockquote>
This refrain has become something of a rallying call for Neo-Calvinists.
Christian Reconstructionism
Christian Reconstructionism is a fundamentalist Calvinist theonomic movement that has remained rather obscure. Founded by R. J. Rushdoony, the movement has had an important influence on the Christian Right in the United States. The movement peaked in the 1990s. However, it lives on in small denominations such as the Reformed Presbyterian Church in the United States and as a minority position in other denominations. Christian Reconstructionists are usually postmillennialists and followers of the presuppositional apologetics of Cornelius Van Til. They tend to support a decentralized political order resulting in laissez-faire capitalism. New Calvinism
New Calvinism is a growing perspective within conservative Evangelicalism that embraces the fundamentals of 16th century Calvinism while also trying to be relevant in the present day world. In March 2009, Time magazine described the New Calvinism as one of the "10 ideas changing the world". Some of the major figures who have been associated with the New Calvinism are John Piper, C. J. Mahaney, and Tim Keller. New Calvinists have been criticized for blending Calvinist soteriology with popular Evangelical positions on the sacraments and continuationism and for rejecting tenets seen as crucial to the Reformed faith such as confessionalism and covenant theology.
Social and economic influences
Calvin expressed himself on usury in a 1545 letter to a friend, Claude de Sachin, in which he criticized the use of certain passages of scripture invoked by people opposed to the charging of interest. He reinterpreted some of these passages, and suggested that others of them had been rendered irrelevant by changed conditions. He also dismissed the argument (based upon the writings of Aristotle) that it is wrong to charge interest for money because money itself is barren. He said that the walls and the roof of a house are barren, too, but it is permissible to charge someone for allowing him to use them. In the same way, money can be made fruitful.
He qualified his view, however, by saying that money should be lent to people in dire need without hope of interest, while a modest interest rate of 5% should be permitted in relation to other borrowers.
In The Protestant Ethic and the Spirit of Capitalism, Max Weber wrote that capitalism in Northern Europe evolved when the Protestant (particularly Calvinist) ethic influenced large numbers of people to engage in work in the secular world, developing their own enterprises and engaging in trade and the accumulation of wealth for investment. In other words, the Protestant work ethic was an important force behind the unplanned and uncoordinated emergence of modern capitalism.
Expert researchers and authors have referred to the United States as a "Protestant nation" or "founded on Protestant principles," specifically emphasizing its Calvinist heritage.Politics and society
during the Marian persecutions in 1556]]
, leader of Hungarian Calvinists in the anti-Habsburg rebellion and first Calvinist prince of Transylvania ()]]
in the Netherlands in the 19th century]]
in Haarlem in the Dutch Republic, ]]
Calvin's concepts of God and man led to ideas which were gradually put into practice after his death, in particular in the fields of politics and society. After their fight for independence from Spain (1579), the Netherlands, under Calvinist leadership, granted asylum to religious minorities, including French Huguenots, English Independents (Congregationalists), and Jews from Spain and Portugal. The ancestors of the philosopher Baruch Spinoza were Portuguese Jews. Aware of the trial against Galileo, René Descartes lived in the Netherlands, out of reach of the Inquisition, from 1628 to 1649. Pierre Bayle, a Reformed Frenchman, also felt safer in the Netherlands than in his home country. He was the first prominent philosopher who demanded tolerance for atheists. Hugo Grotius (1583–1645) was able to publish a rather liberal interpretation of the Bible and his ideas about natural law in the Netherlands. Moreover, the Calvinist Dutch authorities allowed the printing of books that could not be published elsewhere, such as Galileo's Discorsi (1638).
Alongside the liberal development of the Netherlands came the rise of modern democracy in England and North America. In the Middle Ages, state and church had been closely connected. Martin Luther's doctrine of the two kingdoms separated state and church in principle. His doctrine of the priesthood of all believers raised the laity to the same level as the clergy. Going one step further, Calvin included elected laymen (church elders, presbyters) in his concept of church government. The Huguenots added synods whose members were also elected by the congregations. The other Reformed churches took over this system of church self-government, which was essentially a representative democracy. Baptists, Quakers, and Methodists are organized in a similar way. These denominations and the Anglican Church were influenced by Calvin's theology in varying degrees.
In another factor in the rise of democracy in the Anglo-American world, Calvin favored a mixture of democracy and aristocracy as the best form of government (mixed government). He appreciated the advantages of democracy. His political thought aimed to safeguard the rights and freedoms of ordinary men and women. In order to minimize the misuse of political power he suggested dividing it among several institutions in a system of checks and balances (separation of powers). Finally, Calvin taught that if worldly rulers rise up against God they should be put down. In this way, he and his followers stood in the vanguard of resistance to political absolutism and furthered the cause of democracy. The Congregationalists who founded Plymouth Colony (1620) and Massachusetts Bay Colony (1628) were convinced that the democratic form of government was the will of God. Enjoying self-rule, they practiced separation of powers. Rhode Island, Connecticut, and Pennsylvania, founded by Roger Williams, Thomas Hooker, and William Penn, respectively, combined democratic government with a limited freedom of religion that did not extend to Catholics (Congregationalism being the established, tax-supported religion in Connecticut). These colonies became safe havens for persecuted religious minorities, including Jews.
In England, Baptists Thomas Helwys ( 1575– 1616), and John Smyth ( 1554–) influenced the liberal political thought of the Presbyterian poet and politician John Milton (1608–1674) and of the philosopher John Locke (1632–1704), who in turn had both a strong impact on the political development in their home country (English Civil War of 1642–1651, Glorious Revolution of 1688) as well as in North America. The ideological basis of the American Revolution was largely provided by the radical Whigs, who had been inspired by Milton, Locke, James Harrington (1611–1677), Algernon Sidney (1623–1683), and other thinkers. The Whigs' "perceptions of politics attracted widespread support in America because they revived the traditional concerns of a Protestantism that had always verged on Puritanism". The United States Declaration of Independence, the United States Constitution and (American) Bill of Rights initiated a tradition of human and civil rights that continued in the French Declaration of the Rights of Man and of the Citizen and the constitutions of numerous countries around the world, e.g. Latin America, Japan, India, Germany, and other European countries. It is also echoed in the United Nations Charter and the Universal Declaration of Human Rights.
In the 19th century, churches based on or influenced by Calvin's theology became deeply involved in social reforms, e.g. the abolition of slavery (William Wilberforce, Harriet Beecher Stowe, Abraham Lincoln, and others), women suffrage, and prison reforms. Members of these churches formed co-operatives to help the impoverished masses. The founders of the Red Cross Movement, including Henry Dunant, were Reformed Christians. Their movement also initiated the Geneva Conventions.
Others view Calvinist influence as not always being solely positive. The Boers and Afrikaner Calvinists combined ideas from Calvinism and Kuyperian theology to justify apartheid in South Africa. As late as 1974 the majority of the Dutch Reformed Church in South Africa was convinced that their theological stances (including the story of the Tower of Babel) could justify apartheid. In 1990 the Dutch Reformed Church document Church and Society maintained that although they were changing their stance on apartheid, they believed that within apartheid and under God's sovereign guidance, "...everything was not without significance, but was of service to the Kingdom of God." These views were not universal and were condemned by many Calvinists outside South Africa. Pressure from both outside and inside the Dutch Reformed Calvinist church helped reverse apartheid in South Africa.
Throughout the world, the Reformed churches operate hospitals, homes for handicapped or elderly people, and educational institutions on all levels. For example, American Congregationalists founded Harvard University (1636), Yale University (1701), and about a dozen other colleges. A particular stream of influence of Calvinism concerns art. Visual art cemented society in the first modern nation state, the Netherlands, and also Neo-Calvinism put much weight on this aspect of life. Hans Rookmaaker is the most prolific example. In literature one can think of Marilynne Robinson. In her non-fiction she powerfully demonstrates the modernity of Calvin's thinking, calling him a humanist scholar (p. 174, The Death of Adam).
See also
* List of Calvinist educational institutions in North America
* List of Reformed denominations
* Synod of Jerusalem (1672): Eastern Orthodox council rejecting Calvinist beliefs
* Criticism of Protestantism
* The Protestant Ethic and the Spirit of Capitalism (1905) – Max Weber's analysis of Calvinism's influence on society and economics
Doctrine
* Common grace
* Reformed confessions of faith
Related
* Boer Calvinists: Boere-Afrikaners that hold to Reformed theology
* Continental Reformed church: Calvinist churches originating in continental Europe
* Augustinian soteriology : Augustine of Hippo's soteriology, which later influenced Calvinism
* Huguenots: followers of Calvinism in France, originating in the 16th and 17th century
* Pilgrims: English Separatists who left Europe for America in search of religious toleration, eventually settling in New England
* Presbyterians: Calvinists in countries worldwide
* Puritans: English Protestants who wanted to purify the Church of England
* Waldensians: Italian Protestants, preceded Calvinism but today identify with Reformed theology
* Finished Work Pentecostalism: Pentecostal doctrine, which retains progressive sanctification from its Reformed roots, propagated by ministers with Presbyterian and Baptist backgrounds.
Opposing views
* Arminianism
* Catholicism
** Augustinianism
* Christian universalism
* Eastern Orthodoxy
** Palamism
* Free Grace theology
* Open theism
* Lutheranism
* Molinism
* Socinianism
Notes
References
Bibliography
*
*
* 218 |urlhttp://cruciality.files.wordpress.com/2009/10/reformed-identity-by-eberhard-busch-reformed-world-december2008.pdf |access-date20 September 2014 }}
* .
*
* 310 |languageen-us}}
*
* .
*
*
*
*
*
*
*
*
*
*
*
* .
*
* .
*
*
*
* }}
Further reading
*
*
*
* Bratt, James D. (1984) Dutch Calvinism in Modern America: A History of a Conservative Subculture [https://www.amazon.com/Dutch-Calvinism-Modern-America-Conservative/dp/0802800092/ excerpt and text search]
*
* Hart, D. G. (2013). Calvinism: A History. New Haven, Connecticut: Yale University Press, [https://www.amazon.com/Calvinism-Darryl-Hart-ebook/dp/B00D6II2JO/ excerpt and text search]
*
*
*
*
*
*
External links
*
* [https://reformed.org/wp-content/uploads/2019/04/RLDabney5PointsofCalvinism.pdf "Five Points of Calvinism"] by Robert Lewis Dabney (PDF)
Category:Calvinist theology
Category:Trinitarianism
|
https://en.wikipedia.org/wiki/Reformed_Christianity
|
2025-04-05T18:27:41.504868
|
6026
|
Countable set
|
}}
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements.
In more technical terms, assuming the axiom of countable choice, a set is countable if its cardinality (the number of elements of the set) is not greater than that of the natural numbers. A countable set that is not finite is said to be countably infinite.
The concept is attributed to Georg Cantor, who proved the existence of uncountable sets, that is, sets that are not countable; for example the set of the real numbers.
A note on terminology <span class"anchor" id"Terminology"></span>
Although the terms "countable" and "countably infinite" as defined here are quite common, the terminology is not universal. An alternative style uses countable to mean what is here called countably infinite, and at most countable to mean what is here called countable.
The terms enumerable and denumerable may also be used, e.g. referring to countable and countably infinite respectively, definitions vary and care is needed respecting the difference with recursively enumerable.
Definition
A set <math>S</math> is countable if:
* Its cardinality <math>|S|</math> is less than or equal to <math>\aleph_0</math> (aleph-null), the cardinality of the set of natural numbers <math>\N</math>.
* <math>S</math> is empty or there exists a surjective function from <math>\N</math> to <math>S</math>.
* <math>S</math> is either finite (<math>|S|<\aleph_0</math>) or countably infinite.
* The elements of <math>S</math> can be arranged in an infinite sequence <math>a_0, a_1, a_2, \ldots</math>, where <math>a_i</math> is distinct from <math>a_j</math> for <math>i\neq j</math> and every element of <math>S</math> is listed.
A set is uncountable if it is not countable, i.e. its cardinality is greater than <math>\aleph_0</math>.HistoryIn 1874, in his first set theory article, Cantor proved that the set of real numbers is uncountable, thus showing that not all infinite sets are countable. In 1878, he used one-to-one correspondences to define and compare cardinalities. In 1883, he extended the natural numbers with his infinite ordinals, and used sets of ordinals to produce an infinity of sets having different infinite cardinalities.IntroductionA set is a collection of elements, and may be described in many ways. One way is simply to list all of its elements; for example, the set consisting of the integers 3, 4, and 5 may be denoted <math>\{3, 4, 5\}</math>, called roster form. This is only effective for small sets, however; for larger sets, this would be time-consuming and error-prone. Instead of listing every single element, sometimes an ellipsis ("...") is used to represent many elements between the starting element and the end element in a set, if the writer believes that the reader can easily guess what ... represents; for example, <math>\{1, 2, 3, \dots, 100\}</math> presumably denotes the set of integers from 1 to 100. Even in this case, however, it is still possible to list all the elements, because the number of elements in the set is finite. If we number the elements of the set 1, 2, and so on, up to <math>n</math>, this gives us the usual definition of "sets of size <math>n</math>".
Some sets are infinite; these sets have more than <math>n</math> elements where <math>n</math> is any integer that can be specified. (No matter how large the specified integer <math>n</math> is, such as <math>n10^{1000}</math>, infinite sets have more than <math>n</math> elements.) For example, the set of natural numbers, denotable by <math>\{0, 1, 2, 3, 4, 5,\dots\}</math>,{{efn|nameZeroN|Since there is an obvious bijection between <math>\N</math> and <math>\N^*=\{1,2,3,\dots\}</math>, it makes no difference whether one considers 0 a natural number or not. In any case, this article follows ISO 31-11 and the standard convention in mathematical logic, which takes 0 as a natural number.}} has infinitely many elements, and we cannot use any natural number to give its size. It might seem natural to divide the sets into different classes: put all the sets containing one element together; all the sets containing two elements together; ...; finally, put together all infinite sets and consider them as having the same size. This view works well for countably infinite sets and was the prevailing assumption before Georg Cantor's work. For example, there are infinitely many odd integers, infinitely many even integers, and also infinitely many integers overall. We can consider all these sets to have the same "size" because we can arrange things such that, for every integer, there is a distinct even integer:
<math display="block">\ldots \, -\! 2\! \rightarrow \! - \! 4, \, -\! 1\! \rightarrow \! - \! 2, \, 0\! \rightarrow \! 0, \, 1\! \rightarrow \! 2, \, 2\! \rightarrow \! 4 \, \cdots</math>
or, more generally, <math>n \rightarrow 2n</math> (see picture). What we have done here is arrange the integers and the even integers into a one-to-one correspondence (or bijection), which is a function that maps between two sets such that each element of each set corresponds to a single element in the other set. This mathematical notion of "size", cardinality, is that two sets are of the same size if and only if there is a bijection between them. We call all sets that are in one-to-one correspondence with the integers countably infinite and say they have cardinality <math>\aleph_0</math>.
Georg Cantor showed that not all infinite sets are countably infinite. For example, the real numbers cannot be put into one-to-one correspondence with the natural numbers (non-negative integers). The set of real numbers has a greater cardinality than the set of natural numbers and is said to be uncountable.
Formal overview
By definition, a set <math>S</math> is countable if there exists a bijection between <math>S</math> and a subset of the natural numbers <math>\N=\{0,1,2,\dots\}</math>. For example, define the correspondence
<math display=block>
a \leftrightarrow 1,\ b \leftrightarrow 2,\ c \leftrightarrow 3
</math>
Since every element of <math>S=\{a,b,c\}</math> is paired with precisely one element of <math>\{1,2,3\}</math>, and vice versa, this defines a bijection, and shows that <math>S</math> is countable. Similarly we can show all finite sets are countable.
As for the case of infinite sets, a set <math>S</math> is countably infinite if there is a bijection between <math>S</math> and all of <math>\N</math>. As examples, consider the sets <math>A\{1,2,3,\dots\}</math>, the set of positive integers, and <math>B\{0,2,4,6,\dots\}</math>, the set of even integers. We can show these sets are countably infinite by exhibiting a bijection to the natural numbers. This can be achieved using the assignments <math>n \leftrightarrow n+1</math> and <math>n \leftrightarrow 2n</math>, so that
<math display=block>\begin{matrix}
0 \leftrightarrow 1, & 1 \leftrightarrow 2, & 2 \leftrightarrow 3, & 3 \leftrightarrow 4, & 4 \leftrightarrow 5, & \ldots \\[6pt]
0 \leftrightarrow 0, & 1 \leftrightarrow 2, & 2 \leftrightarrow 4, & 3 \leftrightarrow 6, & 4 \leftrightarrow 8, & \ldots
\end{matrix}</math>
Every countably infinite set is countable, and every infinite countable set is countably infinite. Furthermore, any subset of the natural numbers is countable, and more generally:
The set of all ordered pairs of natural numbers (the Cartesian product of two sets of natural numbers, <math>\N\times\N</math> is countably infinite, as can be seen by following a path like the one in the picture: assigns one natural number to each pair of natural numbers]] The resulting mapping proceeds as follows:
<math display=block>
0 \leftrightarrow (0, 0), 1 \leftrightarrow (1, 0), 2 \leftrightarrow (0, 1), 3 \leftrightarrow (2, 0), 4 \leftrightarrow (1, 1), 5 \leftrightarrow (0, 2), 6 \leftrightarrow (3, 0), \ldots
</math>
This mapping covers all such ordered pairs.
This form of triangular mapping recursively generalizes to <math>n</math>-tuples of natural numbers, i.e., <math>(a_1,a_2,a_3,\dots,a_n)</math> where <math>a_i</math> and <math>n</math> are natural numbers, by repeatedly mapping the first two elements of an <math>n</math>-tuple to a natural number. For example, <math>(0, 2, 3)</math> can be written as <math>((0, 2), 3)</math>. Then <math>(0, 2)</math> maps to 5 so <math>((0, 2), 3)</math> maps to <math>(5, 3)</math>, then <math>(5, 3)</math> maps to 39. Since a different 2-tuple, that is a pair such as <math>(a,b)</math>, maps to a different natural number, a difference between two n-tuples by a single element is enough to ensure the n-tuples being mapped to different natural numbers. So, an injection from the set of <math>n</math>-tuples to the set of natural numbers <math>\N</math> is proved. For the set of <math>n</math>-tuples made by the Cartesian product of finitely many different sets, each element in each tuple has the correspondence to a natural number, so every tuple can be written in natural numbers then the same logic is applied to prove the theorem.
}}
The set of all integers <math>\Z</math> and the set of all rational numbers <math>\Q</math> may intuitively seem much bigger than <math>\N</math>. But looks can be deceiving. If a pair is treated as the numerator and denominator of a vulgar fraction (a fraction in the form of <math>a/b</math> where <math>a</math> and <math>b\neq 0</math> are integers), then for every positive fraction, we can come up with a distinct natural number corresponding to it. This representation also includes the natural numbers, since every natural number <math>n</math> is also a fraction <math>n/1</math>. So we can conclude that there are exactly as many positive rational numbers as there are positive integers. This is also true for all rational numbers, as can be seen below.
{{math theorem | math_statement <math>\Z</math> (the set of all integers) and <math>\Q</math> (the set of all rational numbers) are countable.{{efn|Proof: The integers <math>\Z</math> are countable because the function <math>f:\Z\to\N</math> given by <math>f(n)2^n</math> if <math>n</math> is non-negative and <math>f(n)3^{-n}</math> if <math>n</math> is negative, is an injective function. The rational numbers <math>\Q</math> are countable because the function <math>g:\Z\times\N\to\Q</math> given by <math>g(m,n)m/(n+1)</math> is a surjection from the countable set <math>\Z\times\N</math> to the rationals <math>\Q</math>.}}}}
In a similar manner, the set of algebraic numbers is countable.{{efn|1Proof: Per definition, every algebraic number (including complex numbers) is a root of a polynomial with integer coefficients. Given an algebraic number <math>\alpha</math>, let <math>a_0x^0 + a_1 x^1 + a_2 x^2 + \cdots + a_n x^n</math> be a polynomial with integer coefficients such that <math>\alpha</math> is the <math>k</math>-th root of the polynomial, where the roots are sorted by absolute value from small to big, then sorted by argument from small to big. We can define an injection (i. e. one-to-one) function <math>f:\mathbb{A}\to\Q</math> given by <math>f(\alpha) = 2^{k-1} \cdot 3^{a_0} \cdot 5^{a_1} \cdot 7^{a_2} \cdots {p_{n+2}}^{a_n}</math>, where <math>p_n</math> is the <math>n</math>-th prime.}}
Sometimes more than one mapping is useful: a set <math>A</math> to be shown as countable is one-to-one mapped (injection) to another set <math>B</math>, then <math>A</math> is proved as countable if <math>B</math> is one-to-one mapped to the set of natural numbers. For example, the set of positive rational numbers can easily be one-to-one mapped to the set of natural number pairs (2-tuples) because <math>p/q</math> maps to <math>(p,q)</math>. Since the set of natural number pairs is one-to-one mapped (actually one-to-one correspondence or bijection) to the set of natural numbers as shown above, the positive rational number set is proved as countable.
{{math theorem | math_statement Any finite union of countable sets is countable.{{efn|1Proof: If <math>A_i</math> is a countable set for each <math>i</math> in <math>I=\{1,\dots,n\}</math>, then for each <math>i</math> there is a surjective function <math>g_i:\N\to A_i</math> and hence the function
<math display="block">G : I \times \mathbf{N} \to \bigcup_{i \in I} A_i,</math>
given by <math>G(i,m)g_i(m)</math> is a surjection. Since <math>I\times \N</math> is countable, the union <math display"inline">\bigcup_{i \in I} A_i</math> is countable.
}}}}
With the foresight of knowing that there are uncountable sets, we can wonder whether or not this last result can be pushed any further. The answer is "yes" and "no", we can extend it, but we need to assume a new axiom to do so.
{{math theorem | math_statement (Assuming the axiom of countable choice) The union of countably many countable sets is countable.{{efn|1Proof: As in the finite case, but <math>I\N</math> and we use the axiom of countable choice to pick for each <math>i</math> in <math>\N</math> a surjection <math>g_i</math> from the non-empty collection of surjections from <math>\N</math> to <math>A_i</math>. Note that since we are considering the surjection <math>G : \mathbf{N} \times \mathbf{N} \to \bigcup_{i \in I} A_i</math>, rather than an injection, there is no requirement that the sets be disjoint.}}}}
For example, given countable sets <math>\textbf{a},\textbf{b},\textbf{c},\dots</math>, we first assign each element of each set a tuple, then we assign each tuple an index using a variant of the triangular enumeration we saw above:
<math display=block>
\begin{array}{ c|c|c }
\text{Index} & \text{Tuple} & \text {Element} \\ \hline
0 & (0,0) & \textbf{a}_0 \\
1 & (0,1) & \textbf{a}_1 \\
2 & (1,0) & \textbf{b}_0 \\
3 & (0,2) & \textbf{a}_2 \\
4 & (1,1) & \textbf{b}_1 \\
5 & (2,0) & \textbf{c}_0 \\
6 & (0,3) & \textbf{a}_3 \\
7 & (1,2) & \textbf{b}_2 \\
8 & (2,1) & \textbf{c}_1 \\
9 & (3,0) & \textbf{d}_0 \\
10 & (0,4) & \textbf{a}_4 \\
\vdots & &
\end{array}
</math>
We need the axiom of countable choice to index all the sets <math>\textbf{a},\textbf{b},\textbf{c},\dots</math> simultaneously.
This set is the union of the length-1 sequences, the length-2 sequences, the length-3 sequences, and so on, each of which is a countable set (finite Cartesian product). Thus the set is a countable union of countable sets, which is countable by the previous theorem.
The elements of any finite subset can be ordered into a finite sequence. There are only countably many finite sequences, so also there are only countably many finite subsets.
These follow from the definitions of countable set as injective / surjective functions.
'''Cantor's theorem''' asserts that if <math>A</math> is a set and <math>\mathcal{P}(A)</math> is its power set, i.e. the set of all subsets of <math>A</math>, then there is no surjective function from <math>A</math> to <math>\mathcal{P}(A)</math>. A proof is given in the article Cantor's theorem. As an immediate consequence of this and the Basic Theorem above we have:
{{math theorem | name Proposition | math_statement The set <math>\mathcal{P}(\N)</math> is not countable; i.e. it is uncountable.}}
For an elaboration of this result see Cantor's diagonal argument.
The set of real numbers is uncountable, and so is the set of all infinite sequences of natural numbers.
Minimal model of set theory is countable
If there is a set that is a standard model (see inner model) of ZFC set theory, then there is a minimal standard model (see Constructible universe). The Löwenheim–Skolem theorem can be used to show that this minimal model is countable. The fact that the notion of "uncountability" makes sense even in this model, and in particular that this model M contains elements that are:
* subsets of M, hence countable,
* but uncountable from the point of view of M,
was seen as paradoxical in the early days of set theory; see Skolem's paradox for more.
The minimal standard model includes all the algebraic numbers and all effectively computable transcendental numbers, as well as many other kinds of numbers.
Total orders
Countable sets can be totally ordered in various ways, for example:
*Well-orders (see also ordinal number):
**The usual order of natural numbers (0, 1, 2, 3, 4, 5, ...)
**The integers in the order (0, 1, 2, 3, ...; −1, −2, −3, ...)
*Other (not well orders):
**The usual order of integers (..., −3, −2, −1, 0, 1, 2, 3, ...)
**The usual order of rational numbers (Cannot be explicitly written as an ordered list!)
In both examples of well orders here, any subset has a least element; and in both examples of non-well orders, some subsets do not have a least element.
This is the key definition that determines whether a total order is also a well order.
See also
* Aleph number
* Counting
* Hilbert's paradox of the Grand Hotel
* Uncountable set
Notes
Citations
References
*
*
*
*
*
* Reprinted by Springer-Verlag, New York, 1974. (Springer-Verlag edition). Reprinted by Martino Fine Books, 2011. (Paperback edition).
*
*
*
*
Category:Basic concepts in infinite set theory
Category:Cardinal numbers
Category:Infinity
|
https://en.wikipedia.org/wiki/Countable_set
|
2025-04-05T18:27:41.521194
|
6034
|
Cahn–Ingold–Prelog priority rules
|
<!--This article is in US English-->
In organic chemistry, the Cahn–Ingold–Prelog (CIP) sequence rules (also the CIP priority convention; named after Robert Sidney Cahn, Christopher Kelk Ingold, and Vladimir Prelog) are a standard process to completely and unequivocally name a stereoisomer of a molecule. The purpose of the CIP system is to assign an R or S descriptor to each stereocenter and an E or Z descriptor to each double bond so that the configuration of the entire molecule can be specified uniquely by including the descriptors in its systematic name. A molecule may contain any number of stereocenters and any number of double bonds, and each usually gives rise to two possible isomers. A molecule with an integer describing the number of stereocenters will usually have }} stereoisomers, and }} diastereomers each having an associated pair of enantiomers.
The key article setting out the CIP sequence rules was published in 1966, and was followed by further refinements, before it was incorporated into the rules of the International Union of Pure and Applied Chemistry (IUPAC), the official body that defines organic nomenclature, in 1974. as part of the IUPAC book Nomenclature of Organic Chemistry. The IUPAC presentation of the rules constitute the official, formal standard for their use, and it notes that "the method has been developed to cover all compounds with ligancy up to 4... and… [extended to the case of] ligancy 6… [as well as] for all configurations and conformations of such compounds." However, a different problem remains: in rare cases, two different stereoisomers of the same molecule can have the same CIP descriptors, so the CIP system may not be able to unambiguously name a stereoisomer, and other systems may be preferable.
Steps for naming
The steps for naming molecules using the CIP system are often presented as:
# Identification of stereocenters and double bonds;
# Assignment of priorities to the groups attached to each stereocenter or double-bonded atom; and
# Assignment of R/S and E/Z descriptors.
Assignment of priorities
R/S and E/Z descriptors are assigned by using a system for ranking priority of the groups attached to each stereocenter. This procedure, often known as the sequence rules, is the heart of the CIP system. The overview in this section omits some rules that are needed only in rare cases.
#Compare the atomic number (Z) of the atoms directly attached to the stereocenter; the group having the atom of higher atomic number Z receives higher priority (i.e. number 1).
#If there is a tie, the atoms at distance 2 from the stereocenter have to be considered: a list is made for each group of further atoms bonded to the one directly attached to the stereocenter. Each list is arranged in order of decreasing atomic number Z. Then the lists are compared atom by atom; at the earliest difference, the group containing the atom of higher atomic number Z receives higher priority.
#If there is still a tie, each atom in each of the two lists is replaced with a sublist of the other atoms bonded to it (at distance 3 from the stereocenter), the sublists are arranged in decreasing order of atomic number Z, and the entire structure is again compared atom by atom. This process is repeated recursively, each time with atoms one bond farther from the stereocenter, until the tie is broken.
Isotopes
If two groups differ only in isotopes, then the larger atomic mass is used to set the priority.
Double and triple bonds
If an atom, A, is double-bonded to another atom, then atom A should be treated as though it is "connected to the same atom twice". An atom that is double-bonded has a higher priority than an atom that is single bonded.
When B is replaced with a list of attached atoms, A itself, but not its "phantom", is excluded in accordance with the general principle of not doubling back along a bond that has just been followed. A triple bond is handled the same way except that A and B are each connected to two phantom atoms of the other.
Cyclic molecules
To handle a molecule containing one or more cycles, one must first expand it into a tree (called a hierarchical digraph) by traversing bonds in all possible paths starting at the stereocenter. When the traversal encounters an atom through which the current path has already passed, a phantom atom is generated in order to keep the tree finite. A single atom of the original molecule may appear in many places (some as phantoms, some not) in the tree. Assigning descriptors Stereocenters: R/S A chiral sp<sup>3</sup> hybridized isomer contains four different substituents. All four substituents are assigned prorites based on its atomic numbers. After the substituents of a stereocenter have been assigned their priorities, the molecule is oriented in space so that the group with the lowest priority is pointed away from the observer. If the substituents are numbered from 1 (highest priority) to 4 (lowest priority), then the sense of rotation of a curve passing through 1, 2 and 3 distinguishes the stereoisomers. In a configurational isomer, the lowest priority group (most times hydrogen) is positioned behind the plane or the hatched bond going away from the reader. The highest priority group will have an arc drawn connecting to the rest of the groups, finishing at the group of third priority. An arc drawn clockwise, has the rectus (R) assignment. An arc drawn counterclockwise, has the sinister (S) assignment. The names are derived from the Latin for 'right' and 'left', respectively. When naming an organic isomer, the abbreviation for either rectus or sinister assignment is placed in front of the name in parentheses. For example, 3-methyl-1-pentene with a rectus assignment is formatted as (R)-3-methyl-1-pentene.
Double bonds: E/Z
For double bonded molecules, Cahn–Ingold–Prelog priority rules (CIP rules) are followed to determine the priority of substituents of the double bond. If both of the high priority groups are on the same side of the double bond (cis configuration), then the stereoisomer is assigned the configuration Z (zusammen, German word meaning "together"). If the high priority groups are on opposite sides of the double bond (trans configuration), then the stereoisomer is assigned the configuration E (entgegen, German word meaning "opposed") Coordination compounds In some cases where stereogenic centers are formed, the configuration must be specified. Without the presence of a non-covalent interaction, a compound is achiral. Some professionals have proposed a new rule to account for this. This rule states that "non-covalent interactions have a fictitious number between 0 and 1" when assigning priority. Compounds in which this occurs are referred to as coordination compounds.
Spiro compounds
Some spiro compounds, for example the SDP ligands ((R)- and (S)-7,7'-bis(diphenylphosphaneyl)-2,2',3,3'-tetrahydro-1,1'-spirobi[indene]), represent chiral, C<sub>2</sub>-symmetrical molecules where the rings lie approximately at right angles to each other and each molecule cannot be superposed on its mirror image.
:{| align"center" class"wikitable skin-invert-image" width=800px
|-
!colspan="2"|R/S assignments for several compounds
|-
||
| valigntop| The hypothetical molecule bromochlorofluoroiodomethane shown in its (R)-configuration would be a very simple chiral compound. The priorities are assigned based on atomic number (Z): iodine (Z 53) > bromine (Z 35) > chlorine (Z 17) > fluorine (Z = 9). Allowing fluorine (lowest priority, number 4) to point away from the viewer the rotation is clockwise hence the R assignment.
|-
||
| valign"top" | In the assignment of <small>L</small>-serine highest priority (i.e. number 1) is given to the nitrogen atom (Z 7) in the amino group (NH<sub>2</sub>). Both the hydroxymethyl group (CH<sub>2</sub>OH) and the carboxylic acid group (COOH) have carbon atoms (Z 6) but priority is given to the latter because the carbon atom in the COOH group is connected to a second oxygen (Z 8) whereas in the CH<sub>2</sub>OH group carbon is connected to a hydrogen atom (Z = 1). Lowest priority (i.e. number 4) is given to the hydrogen atom and as this atom points away from the viewer, the counterclockwise decrease in priority over the three remaining substituents completes the assignment as S.
|-
||
| valign=top| The stereocenter in (S)-carvone is connected to one hydrogen atom (not shown, priority 4) and three carbon atoms. The isopropenyl group has priority 1 (carbon atoms only), and for the two remaining carbon atoms, priority is decided with the carbon atoms two bonds removed from the stereocenter, one part of the keto group (O, O, C, priority number 2) and one part of an alkene (C, C, H, priority number 3). The resulting counterclockwise rotation results in S.
|}
Describing multiple centers
If a compound has more than one chiral stereocenter, each center is denoted by either R or S. For example, ephedrine exists in (1R,2S) and (1S,2R) stereoisomers, which are distinct mirror-image forms of each other, making them enantiomers. This compound also exists as the two enantiomers written (1R,2R) and (1S,2S), which are named pseudoephedrine rather than ephedrine. All four of these isomers are named 2-methylamino-1-phenyl-1-propanol in systematic nomenclature. However, ephedrine and pseudoephedrine are diastereomers, or stereoisomers that are not enantiomers because they are not related as mirror-image copies. Pseudoephedrine and ephedrine are given different names because, as diastereomers, they have different chemical properties, even for racemic mixtures of each.
More generally, for any pair of enantiomers, all of the descriptors are opposite: (R,R) and (S,S) are enantiomers, as are (R,S) and (S,R). Diastereomers have at least one descriptor in common; for example (R,S) and (R,R) are diastereomers, as are (S,R) and (S,S). This holds true also for compounds having more than two stereocenters: if two stereoisomers have at least one descriptor in common, they are diastereomers. If all the descriptors are opposite, they are enantiomers.
A meso compound is an achiral molecule, despite having two or more stereogenic centers. A meso compound is superposable on its mirror image, therefore it reduces the number of stereoisomers predicted by the 2<sup>n</sup> rule. This occurs because the molecule obtains a plane of symmetry that causes the molecule to rotate around the central carbon–carbon bond.
Relative configuration
The relative configuration of two stereoisomers may be denoted by the descriptors R and S with an asterisk (*). (R*,R*) means two centers having identical configurations, (R,R) or (S,S); (R*,S*) means two centers having opposite configurations, (R,S) or (S,R). To begin, the lowest-numbered (according to IUPAC systematic numbering) stereogenic center is given the R* descriptor.
To designate two anomers the relative stereodescriptors alpha (α) and beta (β) are used. In the α anomer the anomeric carbon atom and the reference atom do have opposite configurations (R,S) or (S,R), whereas in the β anomer they are the same (R,R) or (S,S).
Faces
and α-phenylethanol. The H atom has the lowest priority number 4.]]
Stereochemistry also plays a role assigning faces to trigonal molecules such as ketones. A nucleophile in a nucleophilic addition can approach the carbonyl group from two opposite sides or faces. When an achiral nucleophile attacks acetone, both faces are identical and there is only one reaction product. When the nucleophile attacks butanone, the faces are not identical (enantiotopic) and a racemic product results. When the nucleophile is a chiral molecule diastereoisomers are formed. When one face of a molecule is shielded by substituents or geometric constraints compared to the other face the faces are called diastereotopic. The same rules that determine the stereochemistry of a stereocenter (R or S) also apply when assigning the face of a molecular group. The faces are then called the '''Re-face and Si-face'. In the example displayed on the right, the compound acetophenone is viewed from the Re-face. Hydride addition as in a reduction process from this side will form the (S)-enantiomer and attack from the opposite Si-face will give the (R)-enantiomer. However, one should note that adding a chemical group to the prochiral center from the Re-face will not always lead to an (S)-stereocenter, as the priority of the chemical group has to be taken into account. That is, the absolute stereochemistry of the product is determined on its own and not by considering which face it was attacked from. In the above-mentioned example, if chloride (Z 17) were added to the prochiral center from the Re-face, this would result in an (R)-enantiomer. See also
* Chirality (chemistry)
* Descriptor (chemistry)
* E–Z'' notation
* Isomer
* Stereochemistry
References
Category:Chemical nomenclature
Category:Eponymous chemical rules
Category:Stereochemistry
|
https://en.wikipedia.org/wiki/Cahn–Ingold–Prelog_priority_rules
|
2025-04-05T18:27:41.537076
|
6035
|
Celibacy
|
Celibacy (from Latin caelibatus) is the state of voluntarily being unmarried, sexually abstinent,<!--NOTE: Sources differ on the and/or matter -- whether celibacy is both unmarried and sexually abstinent, or one or the other; this line follows the sources with WP:Due weight, and the WP:ANDOR guideline. --> or both, usually for religious reasons. It is often in association with the role of a religious official or devotee. In its narrow sense, the term celibacy is applied only to those for whom the unmarried state is the result of a sacred vow, act of renunciation, or religious conviction. In a wider sense, it is commonly understood to only mean abstinence from sexual activity.
Celibacy has existed in one form or another throughout history, in virtually all the major religions of the world, and views on it have varied. Classical Hindu culture encouraged asceticism and celibacy in the later stages of life, after one has met one's societal obligations. Jainism, on the other hand, preached complete celibacy even for young monks and considered celibacy to be an essential behavior to attain moksha. Buddhism is similar to Jainism in this respect. There were, however, significant cultural differences in the various areas where Buddhism spread, which affected the local attitudes toward celibacy. A somewhat similar situation existed in Japan, where the Shinto tradition also opposed celibacy. In most native African and Native American religious traditions, celibacy has been viewed negatively as well, although there were exceptions like periodic celibacy practiced by some Mesoamerican warriors.
The Romans viewed celibacy as an aberration and legislated fiscal penalties against it, with the exception of the Vestal Virgins, who took a 30-year vow of chastity in order to devote themselves to the study and correct observance of state rituals. In Christianity, celibacy means the promise to live either virginal or celibate in the future. Such a vow of celibacy has been normal for some centuries for Catholic priests, Catholic and Eastern Orthodox monks, and nuns. In addition, a promise or vow of celibacy may be made in the Anglican Communion and some Protestant churches or communities, such as the Shakers; for members of religious orders and religious congregations; and for hermits, consecrated virgins, and deaconesses. Judaism and Islam have denounced celibacy, as both religions emphasize marriage and family life; however, the priests of the Essenes, a Jewish sect during the Second Temple period, practised celibacy. Several hadiths indicate that the Islamic prophet Muhammad denounced celibacy.
Etymology
The English word celibacy derives from the Latin caelibatus, "state of being unmarried", from Latin , meaning "unmarried". This word derives from two Proto-Indo-European stems, "alone" and "living".Abstinence and celibacyThe words abstinence and celibacy are often used interchangeably, but are not necessarily the same thing. Sexual abstinence, also known as continence'', is abstaining from some or all aspects of sexual activity, often for some limited period of time, while celibacy may be defined as a voluntary religious vow not to marry or engage in sexual activity. Asexuality is commonly conflated with celibacy and sexual abstinence, but it is considered distinct from the two, as celibacy and sexual abstinence are behavioral and those who use those terms for themselves are generally motivated by factors such as an individual's personal or religious beliefs.
A. W. Richard Sipe, while focusing on the topic of celibacy in Catholicism, states that "the most commonly assumed definition of celibate is simply an unmarried or single person, and celibacy is perceived as synonymous with sexual abstinence or restraint." Sipe adds that even in the relatively uniform milieu of Catholic priests in the United States there seems to be "simply no clear operational definition of celibacy". Elizabeth Abbott commented on the terminology in her A History of Celibacy (2001) writing that she "drafted a definition of celibacy that discarded the rigidly pedantic and unhelpful distinctions between celibacy, chastity, and virginity..."
The concept of "new" celibacy was introduced by Gabrielle Brown in her 1980 book The New Celibacy. In a revised version (1989) of her book, she claims abstinence to be "a response on the outside to what's going on, and celibacy is a response from the inside". According to her definition, celibacy (even short-term celibacy that is pursued for non-religious reasons) is much more than not having sex. It is more intentional than abstinence, and its goal is personal growth and empowerment. Although Brown repeatedly states that celibacy is a matter of choice, she clearly suggests that those who do not choose this route are somehow missing out. This new perspective on celibacy is echoed by several authors including Elizabeth Abbott, Wendy Keller, and Wendy Shalit.Buddhism
]]
The rule of celibacy in the Buddhist religion, whether Mahayana or Theravada, has a long history. Celibacy was advocated as an ideal rule of life for all monks and nuns by Gautama Buddha, except in Japan where it is not strictly followed due to historical and political developments following the Meiji Restoration. In Japan, celibacy was an ideal among Buddhist clerics for hundreds of years. But violations of clerical celibacy were so common for so long that finally, in 1872, state laws made marriage legal for Buddhist clerics. Subsequently, ninety percent of Buddhist monks/clerics married. An example is Higashifushimi Kunihide, a prominent Buddhist priest of Japanese royal ancestry who was married and a father whilst serving as a monk for most of his lifetime.
Gautama, later known as the Buddha, is known for his renunciation of his wife, Princess Yasodharā, and son, Rahula. In order to pursue an ascetic life, he needed to renounce aspects of the impermanent world, including his wife and son. Later on both his wife and son joined the ascetic community and are mentioned in the Buddhist texts to have become enlightened. In another sense, a buddhavacana recorded the zen patriarch Vimalakirti as being an advocate of marital continence instead of monastic renunciation. This sutra became somewhat popular due to its brash humour as well as its integration of the role of women in lay and spiritual life.
Christianity
, an Algonquin-Mohawk Catholic laywoman who took a private vow of perpetual virginity]]
, . John is considered the forerunner of Christ, who lived a celibate life of abnegation and penance.]]
<!--According to a view, when Jesus discusses marriage, he points out that there is some responsibility for a man marrying a woman. Not having assets of their own, women needed to be protected from the risk of their husbands' putting them on the street at whim. In those times marriage was an economic matter. A woman and her children could easily be rejected. Restriction of divorce was based on the necessity of protecting the woman and her position in society, not necessarily in a religious context, but in an economic context. However, Jesus primarily points out that a married couple, man and woman, becomes but one flesh rather than two and thus their union as an absolute, for "no man can separate what God united", and does not mention any context when stating that divorce and remarriage, resulting from the "hardness of the heart", constitutes adultery. He also points out that there are those "which were made eunuchs of men: and there be eunuchs, which have made themselves eunuchs for the kingdom of heaven's sake", but in the original Greek, the word εὐνοῦχος means "castrated person". It was the custom at the time Jesus lived for priests of some ancient gods and goddesses to be castrated. In the pre-Christian period Vestals, who served the virgin goddess of the hearth, were obliged to forgo marriage, and so were some priests and servants of some ancient deities such as Isis. However, it is a general view that Christ himself lived a life of perfect chastity; thus, "Voluntary chastity is the imitation of him who was the virgin Son of a virgin Mother". One of his invocations is "King of virgins and lover of stainless chastity" (Rex virginum, amator castitatis).
Furthermore, Christ, when his disciples suggest it is "better not to marry," stated "Not everyone can accept this word, but only those to whom it has been given. For there are eunuchs who have been so from birth, and there are eunuchs who have been made eunuchs by others, and there are eunuchs who have made themselves eunuchs for the sake of the kingdom of heaven. Let anyone accept this who can" (Matthew 19:10-12, NRSV). While eunuchs were not generally celibate, over subsequent centuries this statement has come to be interpreted as referring to celibacy.
<!--While the Jewish sect of essenes practiced celibacy the general practice of the Jewish community by that time prescribed marriage for everybody, and at an early age. In fact, in 1 Corinthians 7:8–9, he explicitly writes, "Now to the unmarried and the widows I say: It is good for them to stay unmarried, as I do. But if they cannot control themselves, they should marry, for it is better to marry than to burn with passion."-->
Paul the Apostle emphasized the importance of overcoming the desires of the flesh and saw the state of celibacy being superior to that of marriage. Paul made parallels between the relations between spouses and God's relationship with the church. "Husbands, love your wives even as Christ loved the church. Husbands should love their wives as their own bodies" (Ephesians 5:25–28). Paul himself was celibate and said that his wish was "that all of you were as I am" (1 Corinthians 7:7). In fact, this entire chapter endorses celibacy while also clarifying that marriage is also acceptable.
The early Christians lived in the belief that the end of the world would soon come upon them, and saw no point in planning new families and having children. According to Chadwick, this was why Paul encouraged both celibate and marital lifestyles
A number of early Christian martyrs were women or girls who had given themselves to Christ in perpetual virginity, such as Saint Agnes and Saint Lucy. According to most Christian thought, the first sacred virgin was Mary, the mother of Jesus, who was consecrated by the Holy Spirit during the Annunciation. Tradition also has it that the Apostle Matthew consecrated virgins. In the Catholic Church and the Orthodox churches, a consecrated virgin is a woman who has been consecrated by the church to a life of perpetual virginity in the service of the church.
Desert Fathers
and a Cherub'' from Saint Catherine's Monastery, Sinai, Egypt]]
The Desert Fathers were Christian hermits and ascetics Sometime around AD 270, Anthony heard a Sunday sermon stating that perfection could be achieved by selling all of one's possessions, giving the proceeds to the poor, and following Christ (Matthew 19:21). He followed the advice and made the further step of moving deep into the desert to seek complete solitude.
Over time, the model of Anthony and other hermits attracted many followers, who lived alone in the desert or in small groups. They chose a life of extreme asceticism, renouncing all the pleasures of the senses, rich food, baths, rest, and anything that made them comfortable. Thousands joined them in the desert, mostly men but also a handful of women. Religious seekers also began going to the desert seeking advice and counsel from the early Desert Fathers. By the time of Anthony's death, there were so many men and women living in the desert in celibacy that it was described as "a city" by Anthony's biographer.
According to the later St. Jerome (420), celibacy is a moral virtue, consisting of living in the flesh, but outside the flesh, and so being not corrupted by it (vivere in carne praeter carnem). Celibacy excludes not only libidinous acts, but also sinful thoughts or desires of the flesh. Jerome referred to marriage prohibition for priests when he claimed in Against Jovinianus that Peter and the other apostles had been married before they were called, but subsequently gave up their marital relations.
In the Catholic, Orthodox and Oriental Orthodox traditions, bishops are required to be celibate. In the Eastern Catholic and Orthodox traditions, priests and deacons are allowed to be married, yet have to remain celibate if they are unmarried at the time of ordination.Augustinian viewIn the early Church, higher clerics lived in marriages. Augustine taught that the original sin of Adam and Eve was either an act of foolishness (insipientia) followed by pride and disobedience to God, or else inspired by pride. The first couple disobeyed God, who had told them not to eat of the tree of the knowledge of good and evil (Gen 2:17). The tree was a symbol of the order of creation. Self-centeredness made Adam and Eve eat of it, thus failing to acknowledge and respect the world as it was created by God, with its hierarchy of beings and values. They would not have fallen into pride and lack of wisdom, if Satan had not sown into their senses "the root of evil" (radix mali). Their nature was wounded by concupiscence or libido, which affected human intelligence and will, as well as affections and desires, including sexual desire.
The sin of Adam is inherited by all human beings. Already in his pre-Pelagian writings, Augustine taught that original sin was transmitted by concupiscence, which he regarded as the passion of both soul and body, making humanity a massa damnata (mass of perdition, condemned crowd) and much enfeebling, though not destroying, the freedom of the will.
In the early 3rd century, the Canons of the Apostolic Constitutions decreed that only lower clerics might still marry after their ordination, but marriage of bishops, priests, and deacons were not allowed.<!-- Augustine's view of sexual feelings as sinful affected his view of women. For example, he considered a man's erection to be sinful, though involuntary, because it did not take place under his conscious control. His solution was to place controls on women to limit their ability to influence men. He equated flesh with woman and spirit with man.
He believed that the serpent approached Eve because she was less rational and lacked self-control, while Adam's choice to eat was viewed as an act of kindness so that Eve would not be left alone. Augustine's views on women were not all negative, however. In his Tractates on the Gospel of John, Augustine, commenting on the Samaritan woman from John 4:1–42, uses the woman as a figure of the church.
According to Raming, the authority of the Decretum Gratiani, a collection of Roman Catholic canon law which prohibits women from leading, teaching, or being a witness, rests largely on the views of the early church fathers, especially St. Augustine. The laws and traditions founded upon St. Augustine's views of sexuality and women continue to exercise considerable influence over church doctrinal positions regarding the role of women in the church.-->
After Augustine
One explanation for the origin of obligatory celibacy is that it is based on the writings of Saint Paul, who wrote of the advantages of celibacy allowed a man in serving the Lord. Celibacy was popularised by the early Christian theologians like Saint Augustine of Hippo and Origen. Another possible explanation for the origins of obligatory celibacy revolves around more practical reason, "the need to avoid claims on church property by priests' offspring". It remains a matter of Canon Law (and often a criterion for certain religious orders, especially Franciscans) that priests may not own land and therefore cannot pass it on to legitimate or illegitimate children. The land belongs to the Church through the local diocese as administered by the Local Ordinary (usually a bishop), who is often an ex officio corporation sole. Celibacy is viewed differently by the Catholic Church and the various Protestant communities. It includes clerical celibacy, celibacy of the consecrated life and voluntary celibacy.
The Protestant Reformation rejected celibate life and sexual continence for preachers. Protestant celibate communities have emerged, especially from Anglican and Lutheran backgrounds. A few minor Christian sects advocate celibacy as a better way of life. These groups included the Shakers, the Harmony Society and the Ephrata Cloister.
Many evangelicals prefer the term "abstinence" to "celibacy". Assuming everyone will marry, they focus their discussion on refraining from premarital sex and focusing on the joys of a future marriage. But some evangelicals, particularly older singles, desire a positive message of celibacy that moves beyond the "wait until marriage" message of abstinence campaigns. They seek a new understanding of celibacy that is focused on God rather than a future marriage or a lifelong vow to the Church.
There are also many Pentecostal churches which practice celibate ministry. For instance, the full-time ministers of the Pentecostal Mission are celibate and generally single. Married couples who enter full-time ministry may become celibate and could be sent to different locations.Catholic Church
During the first three or four centuries, no law was promulgated prohibiting clerical marriage. Celibacy was a matter of choice for bishops, priests, and deacons.
friar, 2012]]
Statutes forbidding clergy from having wives were written beginning with the Council of Elvira (306) but these early statutes were not universal and were often defied by clerics and then retracted by hierarchy. The Synod of Gangra (345) condemned a false asceticism whereby worshipers boycotted celebrations presided over by married clergy. The Apostolic Constitutions () excommunicated a priest or bishop who left his wife "under the pretense of piety" (Mansi, 1:51).
"A famous letter of Synesius of Cyrene () is evidence both for the respecting of personal decision in the matter and for contemporary appreciation of celibacy. For priests and deacons clerical marriage continued to be in vogue".
"The Second Lateran Council (1139) seems to have enacted the first written law making sacred orders a direct impediment to marriage for the universal Church." In places, coercion and enslavement of clerical wives and children was apparently involved in the enforcement of the law. "The earliest decree in which the children [of clerics] were declared to be slaves and never to be enfranchised [freed] seems to have been a canon of the Synod of Pavia in 1018. Similar penalties were promulgated against wives and concubines (see the Synod of Melfi, 1189 can. xii), who by the very fact of their unlawful connexion with a subdeacon or clerk of higher rank became liable to be seized by the over-lord". In contrast, Saint Peter, whom the Church considers its first Pope, was married given that he had a mother-in-law whom Christ healed (Matthew 8). But some argue that Peter was a widower, due to the fact that this passage does not mention his wife, and that his mother-in-law is the one who serves Christ and the apostles after she is healed. Furthermore, Peter himself states: "Then Peter spoke up, 'We have left everything to follow you!' 'Truly I tell you', Jesus replied, 'no one who has left home or brothers or sisters or mother or father or children or fields for me and the gospel will fail to receive a hundred times as much'" (Mark 10,28–30).
Usually, only celibate men are ordained as priests in the Latin Church. Married clergy who have converted from other Christian denominations can be ordained Roman Catholic priests without becoming celibate. Priestly celibacy is not doctrine of the Church (such as the belief in the Assumption of Mary) but a matter of discipline, like the use of the vernacular (local) language in Mass or Lenten fasting and abstinence. As such, it can theoretically change at any time though it still must be obeyed by Catholics until the change were to take place. The Eastern Catholic Churches ordain both celibate and married men. However, in both the East and the West, bishops are chosen from among those who are celibate. In Ireland, several priests have fathered children, the two most prominent being bishop Eamonn Casey and Michael Cleary.
The classical heritage flourished throughout the Middle Ages in both the Byzantine Greek East and the Latin West. When discerning the population of Christendom in medieval Europe during the Middle Ages, Will Durant, referring to Plato's ideal community, stated on the oratores (clergy):
"The clergy, like Plato's guardians, were placed in authority not by the suffrages of the people, but by their talent as shown in ecclesiastical studies and administration, by their disposition to a life of meditation and simplicity, and (perhaps it should be added) by the influence of their relatives with the powers of state and church. In the latter half of the period in which they ruled [AD 800 onwards], the clergy were as free from family cares as even Plato could desire; and in some cases it would seem they enjoyed no little of the reproductive freedom accorded to the guardians. Celibacy was part of the psychological structure of the power of the clergy; for on the one hand they were unimpeded by the narrowing egoism of the family, and on the other their apparent superiority to the call of the flesh added to the awe in which lay sinners held them …"Celibate homosexual ChristiansSome homosexual Christians choose to be celibate following their denomination's teachings on homosexuality.
In 2014, the American Association of Christian Counselors amended its code of ethics to eliminate the promotion of conversion therapy for homosexuals and encouraged them to be celibate instead.
Islam
Islamic attitudes toward celibacy have been complex, Muhammad denounced it, however some Sufi orders embrace it. Islam does not promote celibacy; rather it condemns premarital sex and extramarital sex. In fact, according to Islam, marriage enables one to attain the highest form of righteousness within this sacred spiritual bond but the Qur'an does not state it as an obligation. The Qur'an (Q57:27) states, "But the Monasticism which they (who followed Jesus) invented for themselves, We did not prescribe for them but only to please God therewith, but that they did not observe it with the right observance." Therefore, religion is clearly not a reason to stay unmarried although people are allowed to live their lives however they are comfortable; but relationships and sex outside of marriage, let alone forced marriage, is definitely a sin, "Oh you who believe! You are forbidden to inherit women against their will" (Q4:19). In addition, marriage partners can be distractions from practicing religion at the same time, "Your mates and children are only a trial for you" (Q64:15) however that still does not mean Islam does not encourage people who have sexual desires and are willing to marry. Anyone who does not (intend to) get married in this life can always do it in the Hereafter instead.
Celibacy appears as a peculiarity among some Sufis.
Celibacy was practiced by women saints in Sufism. Celibacy was debated along with women's roles in Sufism in medieval times.
Celibacy, poverty, meditation, and mysticism within an ascetic context along with worship centered around saints' tombs were promoted by the Qadiri Sufi order among Hui Muslims in China. In China, unlike other Muslim sects, the leaders (Shaikhs) of the Qadiriyya Sufi order are celibate. Unlike other Sufi orders in China, the leadership within the order is not a hereditary position, rather, one of the disciples of the celibate Shaikh is chosen by the Shaikh to succeed him. The 92-year-old celibate Shaikh Yang Shijun was the leader of the Qadiriya order in China as of 1998.
Celibacy is practiced by Haydariya Sufi dervishes.
Zoroastrianism
Zoroastrian text Videvdad (4:47) praises a married man by saying:<blockquote>The man who has a wife is far above him who is unmarried...</blockquote>
Meher Baba
The spiritual teacher Meher Baba stated that "[F]or the [spiritual] aspirant a life of strict celibacy is preferable to married life, if restraint comes to him easily without undue sense of self-repression. Such restraint is difficult for most persons and sometimes impossible, and for them married life is decidedly more helpful than a life of celibacy. For ordinary persons, married life is undoubtedly advisable unless they have a special aptitude for celibacy". Baba also asserted that "The value of celibacy lies in the habit of restraint and the sense of detachment and independence which it gives" and that "The aspirant must choose one of the two courses which are open to him. He must take to the life of celibacy or to the married life, and he must avoid at all costs a cheap compromise between the two. Promiscuity in sex gratification is bound to land the aspirant in a most pitiful and dangerous chaos of ungovernable lust."
Ancient Greece and Rome
In Sparta and many other Greek cities, failure to marry was grounds for loss of citizenship, and could be prosecuted as a crime. Both Cicero and Dionysius of Halicarnassus stated that Roman law forbade celibacy. There are no records of such a prosecution, nor is the Roman punishment for refusing to marry known.
Pythagoreanism was the system of esoteric and metaphysical beliefs held by Pythagoras and his followers. Pythagorean thinking was dominated by a profoundly mystical view of the world. The Pythagorean code further restricted his members from eating meat, fish, and beans which they practised for religious, ethical and ascetic reasons, in particular the idea of metempsychosis – the transmigration of souls into the bodies of other animals.
"Pythagoras himself established a small community that set a premium on study, vegetarianism, and sexual restraint or abstinence. Later philosophers believed that celibacy would be conducive to the detachment and equilibrium required by the philosopher's calling."
The Balkans
The tradition of sworn virgins developed out of the Kanuni i Lekë Dukagjinit (, or simply the Kanun). The Kanun is not a religious document – many groups follow this code, including Roman Catholics, the Albanian Orthodox, and Muslims.
Women who become sworn virgins make a vow of celibacy, and are allowed to take on the social role of men: inheriting land, wearing male clothing, etc.
Political contexts
During the May Fourth Movement in China, pledges of celibacy were a means through which participants resisted traditional marriage and devote themselves to revolutionary causes.
See also
* Abstinence in Judaism
* Feminism and celibacy
References
Bibliography
*
* Donald Cozzens (2006). [https://archive.org/details/freeingcelibacy0000cozz Freeing Celibacy]. Collegeville, Minn.: Liturgical Press.
*
* Rafael Domingo (2020): [https://canopyforum.org/2020/03/03/why-does-the-catholic-church-insist-on-celibacy-by-rafael-domingo/ "Why Does the Catholic Church Insist on Celibacy?" by Rafael Domingo]
External links
<!--()-->
<!--| DO NOT ADD MORE LINKS TO THIS ARTICLE. WIKIPEDIA IS NOT A COLLECTION OF |-->
<!--| LINKS. If you think that your link might be useful, do not add it here, |-->
<!--| but put it on this article's discussion page first or submit your link |-->
<!--| to the appropriate category at the Open Directory Project (www.dmoz.org)|-->
<!--| and link back to that category using the template. |-->
<!--| |-->
<!--| Links that have not been verified WILL BE DELETED. |-->
<!--| See Wikipedia:External links and Wikipedia:Spam for details |-->
<!--()-->
* [https://www.vatican.va/roman_curia/congregations/cclergy/documents/rc_con_cclergy_doc_01011993_bfoun_en.html The Biblical foundation of priestly celibacy]
* [http://www.vor.org/rbdisk/calvin/ci_html/4_12#4.12.23 The Reformation view of Celibacy]
* [http://www.hbo.com/docs/programs/celibacy/synopsis.html HBO documentary film Celibacy]
|
https://en.wikipedia.org/wiki/Celibacy
|
2025-04-05T18:27:41.597832
|
6036
|
Coalition government
|
A coalition government, or coalition cabinet, is a government by political parties that enter into a power-sharing arrangement of the executive. Coalition governments usually occur when no single party has achieved an absolute majority after an election. A party not having majority is common under proportional representation, but not in nations with majoritarian electoral systems.
A coalition government may also be created in a time of national difficulty or crisis (for example, during wartime or economic crisis) to give a government the high degree of perceived political legitimacy or collective identity, it can also play a role in diminishing internal political strife. In such times, parties have formed all-party coalitions (national unity governments, grand coalitions).
If a coalition collapses, the prime minister and cabinet may be ousted by a vote of no confidence, call snap elections, form a new majority coalition, or continue as a minority government.
Formation of coalition governments
For a coalition to come about the coalition partners need to compromise on their policy expectations. One coalition or probing partner must lose for the other one to win, to achieve a Nash equilibrium, which is necessary for a coalition to form. If the parties are not willing to compromise, the coalition will not come about.
Before parties form a coalition government, they formulate a coalition agreement, in which they state what policies they try to adapt in the legislative period.
Coalition agreement
(SPD), Angela Merkel (CDU) and Horst Seehofer (CSU) presenting the 2013 coalition agreement for Germany's third Merkel cabinet.]]
In multi-party states, a coalition agreement is an agreement negotiated between the parties that form a coalition government. It codifies the most important shared goals and objectives of the cabinet. It is often written by the leaders of the parliamentary groups. Coalitions that have a written agreement are more productive than those that do not.
If an issue is discussed more deeply and in more detail in chamber than what appears in the coalition agreement, it indicates that the coalition parties do not share the same policy ideas. Hence, a more detailed written formulation of the issue helps parties in the coalition to limit 'agency loss' when the ministry overseeing that issue is managed by another coalition party. Electoral accountability
Coalition governments can also impact voting behavior by diminishing the clarity of responsibility.
Electoral accountability is harder to achieve in coalition governments than in single party governments because there is no direct responsibility within the governing parties in the coalition.
Retrospective voting has a huge influence on the outcome of an election. However, the risk of retrospective voting is a lot weaker with coalition governments than in single party governments. Within the coalition, the party with the head of state has the biggest risk of retrospective voting.Distribution
Countries which often operate with coalition cabinets include: the Nordic countries, the Benelux countries, Australia, Austria, Brazil, Chile, Cyprus, East Timor, France, Germany, Greece, Guinea-Bissau, India, Indonesia, Ireland, Israel, Italy, Japan, Kenya, Kosovo, Latvia, Lebanon, Lesotho, Lithuania, Malaysia, Nepal, New Zealand, Pakistan, Thailand, Spain, Trinidad and Tobago, Turkey, and Ukraine. Switzerland has been ruled by a consensus government with a coalition of the four strongest parties in parliament since 1959, called the "Magic Formula". Between 2010 and 2015, the United Kingdom also operated a formal coalition between the Conservative and the Liberal Democrat parties, but this was unusual: the UK usually has a single-party majority government. Not every parliament forms a coalition government, for example the European Parliament.
Armenia
Armenia became an independent state in 1991, following the collapse of the Soviet Union. Since then, many political parties were formed in it, who mainly work with each other to form coalition governments. The country was governed by the My Step Alliance coalition after successfully gaining a majority in the National Assembly of Armenia following the 2018 Armenian parliamentary election.
Australia
In federal Australian politics, the conservative Liberal, National, Country Liberal and Liberal National parties are united in a coalition, known simply as the Coalition.
While nominally two parties, the Coalition has become so stable, at least at the federal level, that in practice the lower house of Parliament has become a two-party system, with the Coalition and the Labor Party being the major parties. This coalition is also found in the states of New South Wales and Victoria. In South Australia and Western Australia the Liberal and National parties compete separately, while in the Northern Territory and Queensland the two parties have merged, forming the Country Liberal Party, in 1978, and the Liberal National Party, in 2008, respectively.
Coalition governments involving the Labor Party and the Australian Greens have occurred at state and territory level, for example following the 2010 Tasmanian state election and the 2016 and 2020 Australian Capital Territory elections.
Belgium
In Belgium, a nation internally divided along linguistic lines (primarily between Dutch-speaking Flanders in the north and French-speaking Wallonia in the south, with Brussels also being by and large Francophone), each main political disposition (Social democracy, liberalism, right-wing populism, etc.) is, with the exception of the far-left Workers' Party of Belgium, split between Francophone and Dutch-speaking parties (e.g. the Dutch-speaking Vooruit and French-speaking Socialist Party being the two social-democratic parties). In the 2019 federal election, no party got more than 17% of the vote. Thus, forming a coalition government is an expected and necessary part of Belgian politics. In Belgium, coalition governments containing ministers from six or more parties are not uncommon; consequently, government formation can take an exceptionally long time. Between 2007 and 2011, Belgium operated under a caretaker government as no coalition could be formed.
Canada
In Canada, the Great Coalition was formed in 1864 by the Clear Grits, , and Liberal-Conservative Party. During the First World War, Prime Minister Robert Borden attempted to form a coalition with the opposition Liberals to broaden support for controversial conscription legislation. The Liberal Party refused the offer but some of their members did cross the floor and join the government. Although sometimes referred to as a coalition government, according to the definition above, it was not. It was disbanded after the end of the war.
During the 2008–09 Canadian parliamentary dispute, two of Canada's opposition parties signed an agreement to form what would become the country's second federal coalition government since Confederation if the minority Conservative government was defeated on a vote of non-confidence, unseating Stephen Harper as Prime Minister. The agreement outlined a formal coalition consisting of two opposition parties, the Liberal Party and the New Democratic Party. The Bloc Québécois agreed to support the proposed coalition on confidence matters for 18 months. In the end, parliament was prorogued by the Governor General, and the coalition dispersed before parliament was reconvened.
According to historian Christopher Moore, coalition governments in Canada became much less possible in 1919, when the leaders of parties were no longer chosen by elected MPs but instead began to be chosen by party members. Such a manner of leadership election had never been tried in any parliamentary system before. According to Moore, as long as that kind of leadership selection process remains in place and concentrates power in the hands of the leader, as opposed to backbenchers, then coalition governments will be very difficult to form. Moore shows that the diffusion of power within a party tends to also lead to a diffusion of power in the parliament in which that party operates, thereby making coalitions more likely.
Provincial
Several coalition governments have been formed within provincial politics. As a result of the 1919 Ontario election, the United Farmers of Ontario and the Labour Party, together with three independent MLAs, formed a coalition that governed Ontario until 1923.
In British Columbia, the governing Liberals formed a coalition with the opposition Conservatives in order to prevent the surging, left-wing Cooperative Commonwealth Federation from taking power in the 1941 British Columbia general election. Liberal premier Duff Pattullo refused to form a coalition with the third-place Conservatives, so his party removed him. The Liberal–Conservative coalition introduced a winner-take-all preferential voting system (the "Alternative Vote") in the hopes that their supporters would rank the other party as their second preference; however, this strategy backfired in the subsequent 1952 British Columbia general election where, to the surprise of many, the right-wing populist BC Social Credit Party won a minority. They were able to win a majority in the subsequent election as Liberal and Conservative supporters shifted their anti-CCF vote to Social Credit.
Manitoba has had more formal coalition governments than any other province. Following gains by the United Farmer's/Progressive movement elsewhere in the country, the United Farmers of Manitoba unexpectedly won the 1921 election. Like their counterparts in Ontario, they had not expected to win and did not have a leader. They asked John Bracken, a professor in animal husbandry, to become leader and premier. Bracken changed the party's name to the Progressive Party of Manitoba. During the Great Depression, Bracken survived at a time when other premiers were being defeated by forming a coalition government with the Manitoba Liberals (eventually, the two parties would merge into the Liberal-Progressive Party of Manitoba, and decades later, the party would change its name to the Manitoba Liberal Party). In 1940, Bracken formed a wartime coalition government with almost every party in the Manitoba Legislature (the Conservatives, CCF, and Social Credit; however, the CCF broke with the coalition after a few years over policy differences). The only party not included was the small, communist Labor-Progressive Party, which had a handful of seats.
In Saskatchewan, NDP premier Roy Romanow formed a formal coalition with the Saskatchewan Liberals in 1999 after being reduced to a minority. After two years, the newly elected Liberal leader David Karwacki ordered the coalition be disbanded, the Liberal caucus disagreed with him and left the Liberals to run as New Democrats in the upcoming election. The Saskatchewan NDP was re-elected with a majority under its new leader Lorne Calvert, while the Saskatchewan Liberals lost their remaining seats and have not been competitive in the province since.
Denmark
From the creation of the Folketing in 1849 through the introduction of proportional representation in 1918, there were only single-party governments in Denmark. Thorvald Stauning formed his second government and Denmark's first coalition government in 1929. Since then, the norm has been coalition governments, though there have been periods where single-party governments were frequent, such as the decade after the end of World War II, during the 1970s, and in the late 2010s. Every government from 1982 until the 2015 elections were coalitions. While Mette Frederiksen's first government only consisted of her own Social Democrats, her second government is a coalition of the Social Democrats, Venstre, and the Moderates.
When the Social Democrats under Stauning won 46% of the votes in the 1935 election, this was the closest any party has gotten to winning an outright majority in parliament since 1918. One party has thus never held a majority alone, and even one-party governments have needed to have confidence agreements with at least one other party to govern. For example, though Frederiksen's first government only consisted of the Social Democrats, it also relied on the support of the Social Liberal Party, the Socialist People's Party, and the Red–Green Alliance.
Finland
In Finland, no party has had an absolute majority in the parliament since independence, and multi-party coalitions have been the norm. Finland experienced its most stable government (Lipponen I and II) since independence with a five-party governing coalition, a so-called "rainbow government". The Lipponen cabinets set the stability record and were unusual in the respect that both the centre-left (SDP) and radical left-wing (Left Alliance) parties sat in the government with the major centre-right party (National Coalition). The Katainen cabinet was also a rainbow coalition of a total of five parties.
Germany
In Germany, coalition governments are the norm, as it is rare for any single party to win a majority in parliament. The German political system makes extensive use of the constructive vote of no confidence, which requires governments to control an absolute majority of seats. Every government since the foundation of the Federal Republic in 1949 has involved at least two political parties. Typically, governments involve one of the two major parties forming a coalition with a smaller party. For example, from 1982 to 1998, the country was governed by a coalition of the CDU/CSU with the minor Free Democratic Party (FDP); from 1998 to 2005, a coalition of the Social Democratic Party of Germany (SPD) and the minor Greens held power. The CDU/CSU comprises an alliance of the Christian Democratic Union of Germany and Christian Social Union in Bavaria, described as "sister parties" which form a joint parliamentary group, and for this purpose are always considered a single party. Coalition arrangements are often given names based on the colours of the parties involved, such as "red-green" for the SPD and Greens. Coalitions of three parties are often named after countries whose flags contain those colours, such as the black-yellow-green Jamaica coalition.
Grand coalitions of the two major parties also occur, but these are relatively rare, as they typically prefer to associate with smaller ones. However, if the major parties are unable to assemble a majority, a grand coalition may be the only practical option. This was the case following the 2005 federal election, in which the incumbent SPD–Green government was defeated but the opposition CDU/CSU–FDP coalition also fell short of a majority. A grand coalition government was subsequently formed between the CDU/CSU and the SPD. Partnerships like these typically involve carefully structured cabinets: Angela Merkel of the CDU/CSU became Chancellor while the SPD was granted the majority of cabinet posts.
Coalition formation has become increasingly complex as voters increasingly migrate away from the major parties during the 2000s and 2010s. While coalitions of more than two parties were extremely rare in preceding decades, they have become common on the state level. These often include the liberal FDP and the Greens alongside one of the major parties, or "red–red–green" coalitions of the SPD, Greens, and The Left. In the eastern states, dwindling support for moderate parties has seen the rise of new forms of grand coalitions such as the Kenya coalition. The rise of populist parties also increases the time that it takes for a successful coalition to form. By 2016, the Greens were participating eleven governing coalitions on the state level in seven different constellations. During campaigns, parties often declare which coalitions or partners they prefer or reject. This tendency toward fragmentation also spread to the federal level, particularly during the 2021 federal election, which saw the CDU/CSU and SPD fall short of a combined majority of votes for the first time in history.IndiaAfter India's Independence on 15 August 1947, the Indian National Congress, the major political party instrumental in the Indian independence movement, ruled the nation. The first Prime Minister, Jawaharlal Nehru, his successor Lal Bahadur Shastri, and the third Prime Minister, Indira Gandhi, were all members of the Congress party. However, Raj Narain, who had unsuccessfully contested an election against Indira from the constituency of Rae Bareli in 1971, lodged a case alleging electoral malpractice. In June 1975, Indira was found guilty and barred by the High Court from holding public office for six years. In response, a state of emergency was declared under the pretext of national security. The next election resulted in the formation of India's first ever national coalition government under the prime ministership of Morarji Desai, which was also the first non-Congress national government. It existed from 24 March 1977 to 15 July 1979, headed by the Janata Party, an amalgam of political parties opposed to the emergency imposed between 1975 and 1977. As the popularity of the Janata Party dwindled, Desai had to resign, and Chaudhary Charan Singh, a rival of his, became the fifth Prime Minister. However, due to lack of support, this coalition government did not complete its five-year term.
Congress returned to power in 1980 under Indira Gandhi, and later under Rajiv Gandhi as the sixth Prime Minister. However, the general election of 1989 once again brought a coalition government under National Front, which lasted until 1991, with two Prime Ministers, the second one being supported by Congress. The 1991 election resulted in a Congress-led stable minority government for five years. The eleventh parliament produced three Prime Ministers in two years and forced the country back to the polls in 1998. The first successful coalition government in India which completed a whole five-year term was the Bharatiya Janata Party (BJP)-led National Democratic Alliance with Atal Bihari Vajpayee as Prime Minister from 1999 to 2004. Then another coalition, the Congress-led United Progressive Alliance, consisting of 13 separate parties, ruled India for two terms from 2004 to 2014 with Manmohan Singh as PM. However, in the 16th general election in May 2014, the BJP secured a majority on its own (becoming the first party to do so since the 1984 election), and the National Democratic Alliance came into power, with Narendra Modi as Prime Minister. In 2019, Narendra Modi was re-elected as Prime Minister as the National Democratic Alliance again secured a majority in the 17th general election. India returned to an NDA led coalition government in 2024 as the BJP failed to achieve an outright majority.
Indonesia
As a result of the toppling of Suharto, political freedom is significantly increased. Compared to only three parties allowed to exist in the New Order era, a total of 48 political parties participated in the 1999 election and always a total of more than 10 parties in next elections. There are no majority winner of those elections and coalition governments are inevitable. The current government is a coalition of five parliamentary parties led by the major centre-right Gerindra to let governing big tent Advanced Indonesia Coalition.
Ireland
In Ireland, coalition governments are common; not since 1977 has a single party formed a majority government. Coalition governments to date have been led by either Fianna Fáil or Fine Gael. They have been joined in government by one or more smaller parties or independent members of parliament (TDs).
Ireland's first coalition government was formed after the 1948 general election, with five parties and independents represented at cabinet. Before 1989, Fianna Fáil had opposed participation in coalition governments, preferring single-party minority government instead. It formed a coalition government with the Progressive Democrats in that year.
The Labour Party has been in government on eight occasions. On all but one of those occasions, it was as a junior coalition party to Fine Gael. The exception was a government with Fianna Fáil from 1993 to 1994. The 29th Government of Ireland (2011–16), was a grand coalition of the two largest parties, as Fianna Fáil had fallen to third place in the Dáil.
The current government is a Fianna Fáil, Fine Gael and the Independents. Although Fianna Fáil and Fine Gael have been serving in government together since 2020, they haven't formed coalition before due to their different roots that goes back to Irish Civil War (1922–23).
Israel
A similar situation exists in Israel, which typically has at least 10 parties holding representation in the Knesset. The only faction to ever gain the majority of Knesset seats was Alignment, an alliance of the Labor Party and Mapam that held an absolute majority for a brief period from 1968 to 1969. Historically, control of the Israeli government has alternated between periods of rule by the right-wing Likud in coalition with several right-wing and religious parties and periods of rule by the center-left Labor in coalition with several left-wing parties. Ariel Sharon's formation of the centrist Kadima party in 2006 drew support from former Labor and Likud members, and Kadima ruled in coalition with several other parties.
Israel also formed a national unity government from 1984–1988. The premiership and foreign ministry portfolio were held by the head of each party for two years, and they switched roles in 1986.
Japan
In Japan, controlling a majority in the House of Representatives is enough to decide the election of the prime minister (=recorded, two-round votes in both houses of the National Diet, yet the vote of the House of Representatives decision eventually overrides a dissenting House of Councillors vote automatically after the mandatory conference committee procedure fails which, by precedent, it does without real attempt to reconcile the different votes). Therefore, a party that controls the lower house can form a government on its own. It can also pass a budget on its own. But passing any law (including important budget-related laws) requires either majorities in both houses of the legislature or, with the drawback of longer legislative proceedings, a two-thirds majority in the House of Representatives.
In recent decades, single-party full legislative control is rare, and coalition governments are the norm: Most governments of Japan since the 1990s and, as of 2020, all since 1999 have been coalition governments, some of them still fell short of a legislative majority. The Liberal Democratic Party (LDP) held a legislative majority of its own in the National Diet until 1989 (when it initially continued to govern alone)<!--, it came close enough to call it de facto control (through accessions) from the dissolution of the NFP (December 1997) until its defeat in the 1998 House of Councillors election (leading to the formation of a coalition cabinet in January 1999)!-->, and between the 2016 and 2019 elections (when it remained in its previous ruling coalition). The Democratic Party of Japan (through accessions in the House of Councillors) briefly controlled a single-party legislative majority for a few weeks before it lost the 2010 election (it, too, continued to govern as part of its previous ruling coalition).
From the constitutional establishment of parliamentary cabinets and the introduction of the new, now directly elected upper house of parliament in 1947 until the formation of the LDP and the reunification of the Japanese Socialist Party in 1955, no single party formally controlled a legislative majority on its own. Only few formal coalition governments (46th, 47th, initially 49th cabinet<!--:ja:第3次吉田内閣; Yoshida III was a bit complicated as the Democratic Party was splitting: Initially, the Democrats were in government with one wing (Inukai), and in opposition with the other (Tomabechi); later, the coalition wing merged with the Liberals, while the opposition wing merged with other opposition groups to form the kokumin-Democrats!-->) interchanged with technical minority governments and cabinets without technical control of the House of Councillors (later called "twisted Diets", nejire kokkai, when they were not only technically, but actually divided). But during most of that period, the centrist Ryokufūkai was the strongest overall or decisive cross-bench group in the House of Councillors, and it was willing to cooperate with both centre-left and centre-right governments even when it was not formally part of the cabinet; and in the House of Representatives, minority governments of Liberals or Democrats (or their precursors; loose, indirect successors to the two major pre-war parties) could usually count on support from some members of the other major conservative party or from smaller conservative parties and independents. Finally in 1955, when Hatoyama Ichirō's Democratic Party minority government called early House of Representatives elections and, while gaining seats substantially, remained in the minority, the Liberal Party refused to cooperate until negotiations on a long-debated "conservative merger" of the two parties were agreed upon, and eventually successful.
After it was founded in 1955, the Liberal Democratic Party dominated Japan's governments for a long period: The new party governed alone without interruption until 1983, again from 1986 to 1993 and most recently between 1996 and 1999. The first time the LDP entered a coalition government followed its third loss of its House of Representatives majority in the 1983 House of Representatives general election. The LDP-New Liberal Club coalition government lasted until 1986 when the LDP won landslide victories in simultaneous double elections to both houses of parliament.
There have been coalition cabinets where the post of prime minister was given to a junior coalition partner: the JSP-DP-Cooperativist coalition government in 1948 of prime minister Ashida Hitoshi (DP) who took over after his JSP predecessor Tetsu Katayama had been toppled by the left wing of his own party, the JSP-Renewal-Kōmei-DSP-JNP-Sakigake-SDF-DRP coalition in 1993 with Morihiro Hosokawa (JNP) as compromise PM for the Ichirō Ozawa-negotiated rainbow coalition that removed the LDP from power for the first time to break up in less than a year, and the LDP-JSP-Sakigake government that was formed in 1994 when the LDP had agreed, if under internal turmoil and with some defections, to bury the main post-war partisan rivalry and support the election of JSP prime minister Tomiichi Murayama in exchange for the return to government.
Malaysia
Ever since Malaysia gained independence in 1957, none of its federal governments have ever been controlled by a single political party. Due to the social nature of the country, the first federal government was formed by a three-party Alliance coalition, composed of the United Malays National Organisations (UMNO), the Malaysian Chinese Association (MCA), and the Malaysian Indian Congress (MIC). It was later expanded and rebranded as Barisan Nasional (BN), which includes parties representing the Malaysian states of Sabah and Sarawak.
The 2018 Malaysian general election saw the first non-BN coalition federal government in the country's electoral history, formed through an alliance between the Pakatan Harapan (PH) coalition and the Sabah Heritage Party (WARISAN). The federal government formed after the 2020–2022 Malaysian political crisis was the first to be established through coordination between multiple political coalitions. This occurred when the newly formed Perikatan Nasional (PN) coalition partnered with BN and Gabungan Parti Sarawak (GPS). In 2022 after its registration, Sabah-based Gabungan Rakyat Sabah (GRS) formally joined the government (though it had been a part of an informal coalition since 2020). The current government led by Prime Minister Anwar Ibrahim is composed of four political coalitions and 19 parties.
New Zealand
MMP was introduced in New Zealand in the 1996 election.
In order to get into power, parties need to get a total of 50% of the approximately (there can be more if an Overhang seat exists) 120 seats in parliament – 61. Since it is rare for a party to win a full majority, they must form coalitions with other parties. For example, from 1996 to 1998, the country was governed by a coalition of the National with the minor NZ First; from 1999 to 2002, a coalition of the Labour and the minor Alliance and with confidence and supply from the Green Party held power. Between 2017 and 2020, Labour, New Zealand First formed a Coalition Government with confidence and supply from the Green Party. During the 2023 general election, National won 49 seats, ACT won eleven and New Zealand First won eight formed a coalition government.
Spain
Since 2015, there are many more coalition governments than previously in municipalities, autonomous regions and, since 2020 (coming from the November 2019 Spanish general election), in the Spanish Government. There are two ways of conforming them: all of them based on a program and its institutional architecture, one consists on distributing the different areas of government between the parties conforming the coalition and the other one is, like in the Valencian Community, where the ministries are structured with members of all the political parties being represented, so that conflicts that may occur are regarding competences and not fights between parties.
Coalition governments in Spain had already existed during the 2nd Republic, and have been common in some specific Autonomous Communities since the 1980s. Nonetheless, the prevalence of two big parties overall has been eroded and the need for coalitions appears to be the new normal since around 2015.
Turkey
Turkey's first coalition government was formed after the 1961 general election, with two political parties and independents represented at cabinet. It was also Turkey's first grand coalition as the two largest political parties of opposing political ideologies (Republican People's Party and Justice Party) united. Between 1960 and 2002, 17 coalition governments were formed in Turkey. The media and the general public view coalition governments as unfavorable and unstable due to their lack of effectiveness and short lifespan. Following Turkey's transition to a presidential system in 2017, political parties focussed more on forming electoral alliances. Due to separation of powers, the government doesn't have to be formed by parliamentarians and therefore not obliged to result in a coalition government. However, the parliament can dissolve the cabinet if the parliamentary opposition is in majority.United Kingdom
In the United Kingdom, coalition governments (sometimes known as "national governments") usually have only been formed at times of national crisis. The most prominent was the National Government of 1931 to 1940. There were multi-party coalitions during both world wars. Apart from this, when no party has had a majority, minority governments normally have been formed with one or more opposition parties agreeing to vote in favour of the legislation which governments need to function: for instance the Labour government of James Callaghan formed a pact with the Liberals from March 1977 until July 1978, following a series of by-election defeats had eroded Labour's majority of three seats which had been gained at the October 1974 election. However, in the run-up to the 1997 general election, Labour opposition leader Tony Blair was in talks with Liberal Democrat leader Paddy Ashdown about forming a coalition government if Labour failed to win a majority at the election; but there proved to be no need for a coalition as Labour won the election by a landslide. The 2010 general election resulted in a hung parliament (Britain's first for 36 years), and the Conservatives, led by David Cameron, which had won the largest number of seats, formed a coalition with the Liberal Democrats in order to gain a parliamentary majority, ending 13 years of Labour government. This was the first time that the Conservatives and Lib Dems had made a power-sharing deal at Westminster. It was also the first full coalition in Britain since 1945, having been formed 70 years virtually to the day after the establishment of Winston Churchill's wartime coalition,
Labour and the Liberal Democrats have entered into a coalition twice in the Scottish Parliament, as well as twice in the Welsh Assembly.
Uruguay
Since the 1989 election, there have been 4 coalition governments, all including at least both the conservative National Party and the liberal Colorado Party. The first one was after the election of the blanco Luis Alberto Lacalle and lasted until 1992 due to policy disagreements, the longest lasting coalition was the Colorado-led coalition under the second government of Julio María Sanguinetti, in which the national leader Alberto Volonté was frequently described as a "Prime Minister", the next coalition (under president Jorge Batlle) was also Colorado-led, but it lasted only until after the 2002 Uruguay banking crisis, when the blancos abandoned the government. Following the 2019 Uruguayan general election, the blanco Luis Lacalle Pou formed the coalición multicolor, composed of his own National Party, the liberal Colorado Party, the eclectic Open Cabildo and the center left Independent Party.Support and criticism
Advocates of proportional representation suggest that a coalition government leads to more consensus-based politics, as a government comprising differing parties (often based on different ideologies) need to compromise about governmental policy. Another stated advantage is that a coalition government better reflects the popular opinion of the electorate within a country; this means, for instance, that the political system contains just one majority-based mechanism. Contrast this with district voting in which the majority mechanism occurs twice: first, the majority of voters pick the representative and, second, the body of representatives make a subsequent majority decision. The doubled majority decision undermines voter support for that decision. The benefit of proportional representation is that it contains that majority mechanism just once. Additionally, coalition partnership may play an important role in moderating the level of affective polarization over parties, that is, the animosity and hostility against the opponent party identifiers/supporters.
Those who disapprove of coalition governments believe that such governments have a tendency to be fractious and prone to disharmony, as their component parties hold differing beliefs and thus may not always agree on policy. Sometimes the results of an election mean that the coalitions which are mathematically most probable are ideologically infeasible, for example in Flanders or Northern Ireland. A second difficulty might be the ability of minor parties to play "kingmaker" and, particularly in close elections, gain far more power in exchange for their support than the size of their vote would otherwise justify.
Germany is the largest nation ever to have had proportional representation during the interbellum. After WW II, the German system, district based but then proportionally adjusted afterward, contains a threshold that keeps the number of parties limited. The threshold is set at five percent, resulting in empowered parties with at least a minimum amount of political gravity.
Coalition governments have also been criticized for sustaining a consensus on issues when disagreement and the consequent discussion would be more fruitful. To forge a consensus, the leaders of ruling coalition parties can agree to silence their disagreements on an issue to unify the coalition against the opposition. The coalition partners, if they control the parliamentary majority, can collude to make the parliamentary discussion on the issue irrelevant by consistently disregarding the arguments of the opposition and voting against the opposition's proposals — even if there is disagreement within the ruling parties about the issue. However, in winner-take-all this seems always to be the case.
Powerful parties can also act in an oligocratic way to form an alliance to stifle the growth of emerging parties. Of course, such an event is rare in coalition governments when compared to two-party systems, which typically exist because of stifling of the growth of emerging parties, often through discriminatory nomination rules regulations and plurality voting systems, and so on.
A single, more powerful party can shape the policies of the coalition disproportionately. Smaller or less powerful parties can be intimidated to not openly disagree. In order to maintain the coalition, they would have to vote against their own party's platform in the parliament. If they do not, the party has to leave the government and loses executive power. However, this is contradicted by the "kingmaker" factor mentioned above.
Finally, a strength that can also be seen as a weakness is that proportional representation puts the emphasis on collaboration. All parties involved are looking at the other parties in the best light possible, since they may be (future) coalition partners. The pendulum may therefore show less of a swing between political extremes. Still, facing external issues may then also be approached from a collaborative perspective, even when the outside force is not benevolent.
Legislative coalitions and agreements
A legislative coalition or voting coalition is when political parties in a legislature align on voting to push forward specific policies or legislation, but do not engage in power-sharing of the executive branch like in coalition governments.
In a parliamentary system, political parties may form a confidence and supply arrangement, pledging to support the governing party on legislative bills and motions that carry a vote of confidence. Unlike a coalition government, which is a more formalised partnership characterised by the sharing of the executive branch, a confidence and supply arrangement does not entail executive "power-sharing". Instead, it involves the governing party supporting specific proposals and priorities of the other parties in the arrangement, in return for their continued support on motions of confidence.
United States
In the United States, political parties have formed legislative coalitions in the past in order to push forward specific policies or legislation in the United States Congress. The most recent legislative coalition took place in 1917, a coalition was formed between members of the Democratic Party, Progressive Party and Socialist Party of America to elect Champ Clark as the speaker of the United States House of Representatives.
More recently, during the 118th Congress, an informal legislative coalition formed between Democrats and mainline Republicans to pass critical legislation opposed by the Freedom Caucus, an extreme right-wing faction controlling a minority of seats in the Republican Conference.
A coalition government, in which "power-sharing" of executive offices is performed, has not occurred in the United States. The norms that allow coalition governments to form and persist do not exist in the United States.<ref namemarktush/>
See also
* Cohabitation
* Collaborative leadership
* Electoral alliance
* Electoral fusion
* Hung parliament
* List of democracy and election-related topics
* List of countries with coalition governments
* Majority government
* Minority government
* Parliamentary system
* Plurality voting system
* Political coalition
* Political organisation
* :Category:Political party alliances
* Popular front
* Power sharing
* Unholy alliance
* United front
References
Works cited
* }}
cs:Koalice#Vládní koalice
|
https://en.wikipedia.org/wiki/Coalition_government
|
2025-04-05T18:27:41.638808
|
6038
|
Chemical engineering
|
s.]]
Chemical engineering is an engineering field which deals with the study of the operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials into useful products. Chemical engineering uses principles of chemistry, physics, mathematics, biology, and economics to efficiently use, produce, design, transport and transform energy and materials. The work of chemical engineers can range from the utilization of nanotechnology and nanomaterials in the laboratory to large-scale industrial processes that convert chemicals, raw materials, living cells, microorganisms, and energy into useful forms and products. Chemical engineers are involved in many aspects of plant design and operation, including safety and hazard assessments, process design and analysis, modeling, control engineering, chemical reaction engineering, nuclear engineering, biological engineering, construction specification, and operating instructions.
Chemical engineers typically hold a degree in Chemical Engineering or Process Engineering. Practicing engineers may have professional certification and be accredited members of a professional body. Such bodies include the Institution of Chemical Engineers (IChemE) or the American Institute of Chemical Engineers (AIChE). A degree in chemical engineering is directly linked with all of the other engineering disciplines, to various extents.
Etymology
]]
A 1996 article cites James F. Donnelly for mentioning an 1839 reference to chemical engineering in relation to the production of sulfuric acid. In the same paper, however, George E. Davis, an English consultant, was credited with having coined the term. Davis also tried to found a Society of Chemical Engineering, but instead, it was named the Society of Chemical Industry (1881), with Davis as its first secretary. The History of Science in United States: An Encyclopedia puts the use of the term around 1890. "Chemical engineering", describing the use of mechanical equipment in the chemical industry, became common vocabulary in England after 1850. By 1910, the profession, "chemical engineer," was already in common use in Britain and the United States.
History
New concepts and innovations
. The actual fuel cell stack is the layered cube shape in the center of the image.]]
In the 1940s, it became clear that unit operations alone were insufficient in developing chemical reactors. While the predominance of unit operations in chemical engineering courses in Britain and the United States continued until the 1960s, transport phenomena started to receive greater focus. Along with other novel concepts, such as process systems engineering (PSE), a "second paradigm" was defined. Transport phenomena gave an analytical approach to chemical engineering while PSE focused on its synthetic elements, such as those of a control system and process design. Developments in chemical engineering before and after World War II were mainly incited by the petrochemical industry; however, advances in other fields were made as well. Advancements in biochemical engineering in the 1940s, for example, found application in the pharmaceutical industry, and allowed for the mass production of various antibiotics, including penicillin and streptomycin. Meanwhile, progress in polymer science in the 1950s paved way for the "age of plastics".
Safety and hazard developments
Concerns regarding large-scale chemical manufacturing facilities' safety and environmental impact were also raised during this period. Silent Spring, published in 1962, alerted its readers to the harmful effects of DDT, a potent insecticide. The 1974 Flixborough disaster in the United Kingdom resulted in 28 deaths, as well as damage to a chemical plant and three nearby villages. 1984 Bhopal disaster in India resulted in almost 4,000 deaths. These incidents, along with other incidents, affected the reputation of the trade as industrial safety and environmental protection were given more focus. In response, the IChemE required safety to be part of every degree course that it accredited after 1982. By the 1970s, legislation and monitoring agencies were instituted in various countries, such as France, Germany, and the United States. In time, the systematic application of safety principles to chemical and other process plants began to be considered a specific discipline, known as process safety.
Recent progress
Advancements in computer science found applications for designing and managing plants, simplifying calculations and drawings that previously had to be done manually. The completion of the Human Genome Project is also seen as a major development, not only advancing chemical engineering but genetic engineering and genomics as well. Chemical engineering principles were used to produce DNA sequences in large quantities.Concepts
Chemical engineering involves the application of several principles. Key concepts are presented below.
Plant design and construction
Chemical engineering design concerns the creation of plans, specifications, and economic analyses for pilot plants, new plants, or plant modifications. Design engineers often work in a consulting role, designing plants to meet clients' needs. Design is limited by several factors, including funding, government regulations, and safety standards. These constraints dictate a plant's choice of process, materials, and equipment.
Plant construction is coordinated by project engineers and project managers, depending on the size of the investment. A chemical engineer may do the job of project engineer full-time or part of the time, which requires additional training and job skills or act as a consultant to the project group. In the USA the education of chemical engineering graduates from the Baccalaureate programs accredited by ABET do not usually stress project engineering education, which can be obtained by specialized training, as electives, or from graduate programs. Project engineering jobs are some of the largest employers for chemical engineers.
Process design and analysis
A unit operation is a physical step in an individual chemical engineering process. Unit operations (such as crystallization, filtration, drying and evaporation) are used to prepare reactants, purifying and separating its products, recycling unspent reactants, and controlling energy transfer in reactors. On the other hand, a unit process is the chemical equivalent of a unit operation. Along with unit operations, unit processes constitute a process operation. Unit processes (such as nitration, hydrogenation, and oxidation involve the conversion of materials by biochemical, thermochemical and other means. Chemical engineers responsible for these are called process engineers.
Process design requires the definition of equipment types and sizes as well as how they are connected and the materials of construction. Details are often printed on a Process Flow Diagram which is used to control the capacity and reliability of a new or existing chemical factory.
Education for chemical engineers in the first college degree 3 or 4 years of study stresses the principles and practices of process design. The same skills are used in existing chemical plants to evaluate the efficiency and make recommendations for improvements.
Transport phenomena
Modeling and analysis of transport phenomena is essential for many industrial applications. Transport phenomena involve fluid dynamics, heat transfer and mass transfer, which are governed mainly by momentum transfer, energy transfer and transport of chemical species, respectively. Models often involve separate considerations for macroscopic, microscopic and molecular level phenomena. Modeling of transport phenomena, therefore, requires an understanding of applied mathematics.Applications and practiceChemical engineers develop economic ways of using materials and energy. Chemical engineers use chemistry and engineering to turn raw materials into usable products, such as medicine, petrochemicals, and plastics on a large-scale, industrial setting. They are also involved in waste management and research. Both applied and research facets could make extensive use of computers.
Chemical engineers may be involved in industry or university research where they are tasked with designing and performing experiments, by scaling up theoretical chemical reactions, to create better and safer methods for production, pollution control, and resource conservation. They may be involved in designing and constructing plants as a project engineer. Chemical engineers serving as project engineers use their knowledge in selecting optimal production methods and plant equipment to minimize costs and maximize safety and profitability. After plant construction, chemical engineering project managers may be involved in equipment upgrades, troubleshooting, and daily operations in either full-time or consulting roles. See also Related topics
* Education for Chemical Engineers
* English Engineering units
* List of chemical engineering societies
* List of chemical engineers
* List of chemical process simulators
* Outline of chemical engineering
Related fields and concepts
* Biochemical engineering
* Bioinformatics
* Biological engineering
* Biomedical engineering
* Biomolecular engineering
* Bioprocess engineering
* Biotechnology
* Biotechnology engineering
* Catalysts
* Ceramics
* Chemical process modeling
* Chemical reactor
* Chemical technologist
* Chemical weapons
* Cheminformatics
* Computational fluid dynamics
* Corrosion engineering
* Cost estimation
* Earthquake engineering
* Electrochemistry
* Electrochemical engineering
* Environmental engineering
* Fischer Tropsch synthesis
* Fluid dynamics
* Food engineering
* Fuel cell
* Gasification
* Heat transfer
* Industrial catalysts
* Industrial chemistry
* Industrial gas
* Mass transfer
* Materials science
* Metallurgy
* Microfluidics
* Mineral processing
* Molecular engineering
* Nanotechnology
* Natural environment
* Natural gas processing
* Nuclear reprocessing
* Oil exploration
* Oil refinery
* Paper engineering
* Petroleum engineering
* Pharmaceutical engineering
* Plastics engineering
* Polymers
* Process control
* Process design
* Process development
* Process engineering
* Process miniaturization
* Process safety
* Semiconductor device fabrication
* Separation processes (see also: separation of mixture)
** Crystallization processes
** Distillation processes
** Membrane processes
* Syngas production
* Textile engineering
* Thermodynamics
* Transport phenomena
* Unit operations
* Water technology
Associations
* American Institute of Chemical Engineers
* Chemical Institute of Canada
* European Federation of Chemical Engineering
* Indian Institute of Chemical Engineers
* Institution of Chemical Engineers
* National Organization for the Professional Advancement of Black Chemists and Chemical Engineers
References
Bibliography
* .
* |lccn=2001023739}}.
* |lccn2001017315 |date2001-07-24}}.
* .
* .
* |lccn=2002027208}}.
* .
* |lccn=92036218}}.
* .
* .
* |lastReynolds |firstTerry S. |chapterEngineering, Chemical |lccn99043757}}.
* .
* .
* .
Category:Process engineering
Category:Engineering disciplines
|
https://en.wikipedia.org/wiki/Chemical_engineering
|
2025-04-05T18:27:41.660272
|
6041
|
List of comedians
|
A comedian is one who entertains through comedy, such as jokes and other forms of humour. Following is a list of comedians, comedy groups, and comedy writers.
Comedians
(sorted alphabetically by surname)
A
Rose Abdoo (born 1962)
Raymond Ablack (born 1989)
John Aboud (born 1973)
Silvia Abril (born 1971)
James Acaster (born 1985)
Jayde Adams (born 1984)
Kev Adams (born 1991)
Mark Addy (born 1964)
Lolly Adefope (born 1990)
Demi Adejuyigbe (born 1992)
Pamela Adlon (born 1966)
James Adomian (born 1980)
Scott Adsit (born 1965)
Bayani Agbayani (born 1969)
Steve Agee (born 1969)
Alex Agnew (born 1973)
Rubén Aguirre (1934–2016)
Dan Ahdoot (born 1981)
Caroline Aherne (1963–2016)
Ahmed Ahmed (born 1970)
Sohail Ahmed (born 1963)
Franklyn Ajaye (born 1949)
Anna Akana (born 1989)
Malin Akerman (born 1978)
Nawaal Akram (born 1990)
Nasser Al Qasabi (born 1963)
Lori Alan (born 1966)
Joe Alaskey (1952–2016)
Carlos Alazraqui (born 1962)
Rory Albanese (born 1977)
Lou Albano (1933–2009)
Eddie Albert (1906–2005)
Ogie Alcasid (born 1967)
Alan Alda (born 1936)
Jason Alexander (born 1959)
Mo Alexander (born 1970)
Ted Alexandro (born 1969)
Allan K. (born 1958)
Barbara Jo Allen (1906–1974)
Dave Allen (1936–2005)
Gracie Allen (1895–1964)
Krista Allen (born 1971)
Leo Allen (born 1972)
Marty Allen (1922–2018)
Steve Allen (1921–2000)
Tim Allen (born 1953)
Woody Allen (born 1935)
Kirstie Alley (1951–2022)
Kevin Allison (born 1970)
Stephanie Allynne (born 1986)
Anabel Alonso (born 1964)
Cristela Alonzo (born 1979)
Jeff Altman (born 1951)
Brian Jordan Alvarez (born 1987)
The Amazing Johnathan (1958–2022)
Utkarsh Ambudkar (born 1983)
Don Ameche (1908–1993)
Robbie Amell (born 1988)
Mo Amer (born 1981)
John Amos (1939–2024)
Megan Amram (born 1987)
Simon Amstell (born 1979)
Morey Amsterdam (1908–1996)
Andrea Anders (born 1975)
Siw Anita Andersen (born 1966)
Amy Anderson (born 1972)
Anthony Anderson (born 1970)
Blake Anderson (born 1984)
Harry Anderson (1952–2018)
James Anderson
Louie Anderson (1953–2022)
Wil Anderson (born 1974)
Eric André (born 1983)
Alex Anfanger (born 1985)
Michael Angarano (born 1987)
Lucia Aniello (born 1983)
Jennifer Aniston (born 1969)
Aziz Ansari (born 1983)
Ant (born 1967)
Dave Anthony (born 1967)
Craig Anton (born 1962)
Judd Apatow (born 1967)
Ingo Appelt (born 1967)
Christina Applegate (born 1971)
John Aprea (born 1941)
Carly Aquilino (born 1990)
Nicole Arbour (born 1985)
Lisa Arch (born 1971)
Roscoe "Fatty" Arbuckle (1887–1933)
Geoffrey Arend (born 1978)
Lesley Arfin (born 1979)
Marcella Arguello (born 1985)
Fred Armisen (born 1966)
Alexander Armstrong (born 1970)
Desi Arnaz (1917–1986)
Will Arnett (born 1970)
David A. Arnold (1968–2022)
Tichina Arnold (born 1969)
Tom Arnold (born 1959)
David Arquette (born 1971)
Bea Arthur (1922–2009)
Aaron Aryanpur (born 1978)
Katie Aselton (born 1978)
Erica Ash (1977–2024)
Lauren Ash (born 1983)
Annaleigh Ashford (born 1985)
Arthur Askey (1900–1982)
Ed Asner (1929–2021)
Sean Astin (born 1971)
Skylar Astin (born 1987)
Emily Atack (born 1989)
Anthony Atamanuik (born 1974)
Aristotle Athari (born 1991)
Essence Atkins (born 1972)
Rowan Atkinson (born 1955)
Helen Atkinson-Wood (born 1955)
Dave Attell (born 1965)
Michael "Atters" Attree (born 1965)
Scott Aukerman (born 1970)
Phil Austin (1941–2015)
Joe Avati (born 1974)
Shondrella Avery (born 1971)
Awkwafina (born 1988)
Ayelet the Kosher Komic
Dan Aykroyd (born 1952)
Peter Aykroyd (1955–2021)
Damali Ayo (born 1972)
Richard Ayoade (born 1977)
Hank Azaria (born 1964)
Hannan Azlan
Valerie Azlynn (born 1980)
B
Baba Ali (born 1975)
Dirk Bach (1961–2012)
King Bach (born 1988)
Jim Backus (1913–1989)
Diedrich Bader (born 1966)
Max Baer Jr. (born 1937)
Ross Bagley (born 1988)
Tim Bagley (born 1957)
Iris Bahr (born 1977)
Ainsley Bailey (born 1992)
Ben Bailey (born 1970)
Bill Bailey (born 1965)
Conrad Bain (1923–2013)
Scott Baio (born 1960)
Nick Bakay (born 1959)
Bobbie Baker
Leslie David Baker (born 1958)
Rosebud Baker (born 1985)
Sarah Baker (born 1973)
Dan Bakkedahl (born 1969)
Carlos Balá (1925–2022)
Bob Balaban (born 1945)
Josiane Balasko (born 1950)
Hugo Egon Balder (born 1950)
Alec Baldwin (born 1958)
Dougie Baldwin (born 1996)
Lucille Ball (1911–1989)
Kaye Ballard (1925–2019)
Reginald Ballard (born 1965)
Tom Ballard (born 1989)
Paolo Ballesteros (born 1982)
Colleen Ballinger (born 1986)
Tim Baltz (born 1981)
Maria Bamford (born 1970)
Eric Bana (born 1968)
Elizabeth Banks (born 1974)
Morwenna Banks (born 1961)
Zach Barack (born 1995)
Edward Barbanell (born 1977)
Celeste Barber (born 1982)
Ralph Barbosa (born 1996)
Nate Bargatze (born 1979)
Robert Baril (born 1986/1987)
Ike Barinholtz (born 1977)
Jon Barinholtz (born 1982)
Arj Barker (born 1974)
Ronnie Barker (1929–2005)
Caitlin Barlow (born 1983)
Angela Barnes (born 1976)
Cooper Barnes (born 1979)
Kevin Barnett (1986–2019)
Ty Barnett (born 1975)
Vince Barnett (1902–1977)
Sandy Baron (1937–2001)
Anita Barone (born 1964)
Roseanne Barr (born 1952)
Julian Barratt (born 1968)
Amanda Barrie (born 1935)
Kenya Barris (born 1974)
Carl Barron (born 1968)
Todd Barry (born 1964)
Mario Barth (born 1972)
Justin Bartha (born 1978)
Jay Baruchel (born 1982)
Frank-Markus Barwasser (born 1960)
David Alan Basche (born 1968)
Jason Bateman (born 1969)
Angelique Bates (born 1980)
David Batra (born 1972)
Brian Baumgartner (born 1972)
Eric Bauza (born 1979)
Stanley Baxter (born 1926)
Vanessa Bayer (born 1981)
Matthew Baynton (born 1980)
Wally Bayola (born 1972)
Carter Bays (born 1975)
Aisling Bea (born 1984)
Allyce Beasley (born 1954)
Anne Beatts (1947–2021)
Lucy Beaumont (born 1983)
David Beck (born 1970)
Alison Becker (born 1977)
Jürgen Becker (born 1959)
Rob Beckett (born 1986)
Samantha Bee (born 1969)
Beetlejuice (born 1968)
Joy Behar (born 1942)
Natasha Behnam (born 1996)
Greg Behrendt (born 1963)
Beth Behrs (born 1985)
Ashley Bell (born 1986)
Jillian Bell (born 1984)
Lake Bell (born 1979)
Tone Bell (born 1983)
W. Kamau Bell (born 1973)
Bill Bellamy (born 1965)
Ryan Belleville (born 1979)
Jim Belushi (born 1954)
John Belushi (1949–1982)
Richard Belzer (1944–2023)
Bea Benaderet (1906–1968)
H. Jon Benjamin (born 1966)
Owen Benjamin (born 1980)
Beck Bennett (born 1984)
Jeff Bennett (born 1962)
Ron Bennington (born 1958)
D.C. Benny
Jack Benny (1894–1974)
Doug Benson (born 1964)
Alec Berg (born 1969)
Candice Bergen (born 1946)
Edgar Bergen (1903–1978)
Tom Bergeron (born 1955)
Peter Paul Bergman (1939–2012)
Kate Berlant (born 1987)
Milton Berle (1908–2002)
Andy Berman (born 1968)
Shelley Berman (1925–2017)
Crystal Bernard (born 1961)
Sandra Bernhard (born 1955)
Matt Berry (born 1974)
Joe Besser (1907–1988)
Matt Besser (born 1967)
Ilka Bessin (born 1971)
Beetlejuice (born 1968)
Danny Bhoy (born 1976)
Mayim Bialik (born 1975)
Leslie Bibb (born 1974)
Craig Bierko (born 1964)
Jason Biggs (born 1978)
Mike Birbiglia (born 1978)
Simon Bird (born 1984)
Mary Birdsong (born 1968)
Des Bishop (born 1975)
Joey Bishop (1918–2007)
John Bishop (born 1966)
Kevin Bishop (born 1980)
Danielle Bisutti (born 1976)
Ashley Nicole Black (born 1985)
Jack Black (born 1969)
Jordan Black (born 1970)
Lewis Black (born 1948)
Michael Ian Black (born 1971)
Michael Blackson (born 1972)
Mark Blankfield (1950–2024)
Hamish Blake (born 1981)
Susanne Blakeslee (born 1956)
Mel Blanc (1908–1989)
Maria Blasucci (born 1986)
Brian Blessed (born 1936)
Rich Blomquist (born 1977)
Rachel Bloom (born 1987)
Ben Blue (1901–1975)
Josh Blue (born 1978)
Sarayu Blue (born 1975)
Amir Blumenfeld (born 1983)
John Bluthal (1929–2018)
Raphael Bob-Waksberg (born 1984)
Alonzo Bodden (born 1967)
Steve Bodow
Mirja Boes (born 1971)
Catherine Bohart (born 1988)
Danny Bonaduce (born 1959)
Sue Bond (born 1945)
Peter Bonerz (born 1938)
Bobby Bones (born 1980)
Wigald Boning (born 1967)
Sonny Bono (1935–1998)
Elayne Boosler (born 1952)
Joel Kim Booster (born 1988)
Connie Booth (born 1940)
Tato Bores (1927–1996)
Flula Borg (born 1982)
Victor Borge (1909–2000)
Ernest Borgnine (1917–2012)
Kyle Bornheimer (born 1975)
Alex Borstein (born 1971)
Loren Bouchard (born 1969)
Lilan Bowden (born 1985)
Andrew Bowen (born 1972)
Julie Bowen (born 1970)
Byron Bowers (born 1978)
John Ross Bowie (born 1971)
Max Boyce (born 1945)
Steven Boyer (born 1979)
Frankie Boyle (born 1972)
Peter Boyle (1935–2006)
Fern Brady
Wayne Brady (born 1972)
Harriet Braine
Zach Braff (born 1975)
Joey Bragg (born 1996)
Patrick Brammall (born 1976)
Jo Brand (born 1957)
Russell Brand (born 1975)
Betsy Brandt (born 1973)
Guy Branum (born 1975)
Larry Brantley (born 1966)
John Branyan (born 1965)
Matt Braunger (born 1974)
Kurt Braunohler (born 1976)
Daniel Breaker (born 1980)
El Brendel (1890–1964)
Josh Brener (born 1984)
Kevin Brennan (born 1960)
Neal Brennan (born 1974)
David Brenner (1936–2014)
Jim Breuer (born 1967)
Blonde Brewer
Paget Brewster (born 1969)
Fanny Brice (1891–1951)
Todd Bridges (born 1965)
Alison Brie (born 1982)
Sabrina Brier (born 1994)
Richard Briers (1934–2013)
Joe Bob Briggs (born 1953)
Awra Briguela (born 2004)
Patrick Bristow (born 1962)
Janine Brito
Paul Brittain (born 1977)
Doug Brochu (born 1990)
Matthew Broderick (born 1962)
Adam Brody (born 1979)
Jimmy Brogan (born 1948)
Benjy Bronk (born 1967)
Tim Brooke-Taylor (1940–2020)
Albert Brooks (born 1947)
Foster Brooks (1912–2001)
James L. Brooks (born 1940)
Max Brooks (born 1972)
Mel Brooks (born 1926)
Brittany Broski (born 1997)
Brother Theodore (1906–2001)
Alan Brough (born 1967)
A. Whitney Brown (born 1952)
Alton Brown (born 1962)
Candace Brown (born 1980)
Clancy Brown (born 1959)
Joe E. Brown (1891–1973)
Kevin Brown (born 1972)
Wally Brown (1904–1961)
Cocoa Brown (born 1972)
Yvette Nicole Brown (born 1971)
Carrie Brownstein (born 1974)
Lenny Bruce (1925–1966)
Hazel Brugger (born 1993)
Quinta Brunson (born 1989)
Aidy Bryant (born 1987)
Cubby Bryant (born 1971)
Rob Brydon (born 1965)
Andy Buckley (born 1965)
James Buckley (born 1987)
Sophie Buddle (born 1994)
Herlene Budol (born 1999)
Jim J. Bullock (born 1955)
Sandra Bullock (born 1964)
Vicco von Bülow (1923–2011)
Rodger Bumpass (born 1951)
Michael Bunin (born 1970)
John Bunny (1863–1915)
David Burd (aka) Lil Dicky (born 1988)
Hannibal Buress (born 1983)
Tituss Burgess (born 1979)
Delta Burke (born 1956)
Kathy Burke (born 1964)
Carol Burnett (born 1933)
Bo Burnham (born 1990)
Burnie Burns (born 1973)
George Burns (1896–1996)
Jack Burns (1933–2020)
Regan Burns (born 1968)
Sarah Burns (born 1981)
Bill Burr (born 1968)
Maryedith Burrell (born 1952)
Ty Burrell (born 1967)
Abe Burrows (1910–1985)
James Burrows (born 1940)
Steve Buscemi (born 1957)
Adam Busch (born 1978)
Mikey Bustos (born 1981)
River Butcher (born 1982)
Michelle Buteau (born 1977)
Brett Butler (born 1958)
Red Buttons (1919–2006)
Adam Buxton (born 1969)
Ruth Buzzi (born 1936)
Nicole Byer (born 1986)
John Byner (born 1938)
Ed Byrne (born 1972)
Jason Byrne (born 1972)
P. J. Byrne (born 1974)
Rose Byrne (born 1979)
Steve Byrne (born 1974)
C
Louis C.K. (born 1967)
Vladimir Caamaño (born 1979)
Mike Cabellon
Angelique Cabral (born 1979)
Liz Cackowski
Sid Caesar (1922–2014)
Frank Caeti (born 1973)
Frank Caliendo (born 1975)
Charlie Callas (1924–2011)
Bryan Callen (born 1967)
Frances Callier (born 1969)
Kirk Cameron (born 1970)
Rhona Cameron (born 1965)
Jaime Camil (born 1973)
Anna Camp (born 1982)
Colleen Camp (born 1953)
Adam Campbell (born 1980)
Archie Campbell (1914–1987)
Bruce Campbell (born 1958)
Craig Campbell (born 1969)
Heather Anne Campbell
Larry Joe Campbell (born 1970)
Neil Campbell
Sam Campbell (born 1991)
Tisha Campbell (born 1968)
Maria Canals-Barrera (born 1966)
John Candy (1950–1994)
Bobby Cannavale (born 1970)
Kay Cannon (born 1974)
Nick Cannon (born 1980)
Judy Canova (1913–1983)
Melai Cantiveros (born 1988)
Mario Cantone (born 1959)
Nicolas Cantu (born 2003)
John Caparulo (born 1975)
Blaine Capatch (born 1965)
Lizzy Caplan (born 1982)
Twink Caplan (born 1947)
Scott Capurro (born 1962)
Perry Caravello (born 1963)
Matty Cardarople (born 1983)
Linda Cardellini (born 1975)
D'Arcy Carden (born 1980)
Nancy Carell (born 1966)
Steve Carell (born 1962)
Anthony Carelli (aka) Santino Marella (born 1974)
Drew Carey (born 1958)
Liz Carey (born 1978)
Maggie Carey (born 1975)
George Carl (1916–2000)
George Carlin (1937–2008)
Jordan Carlos (born 1978)
Urzila Carlson (born 1976)
Jerrod Carmichael (born 1987)
Alan Carney (1909–1973)
Art Carney (1918–2003)
Adam Carolla (born 1964)
Alan Carr (born 1976)
Jimmy Carr (born 1972)
Jim Carrey (born 1962)
Rodney Carrington (born 1968)
Jack Carroll (born 1998)
Pat Carroll (1927–2022)
Carrot Top (Scott Thompson) (born 1965)
Jasper Carrott (born 1945)
Johnny Carson (1925–2005)
Nell Carter (1948–2003)
Nancy Cartwright (born 1957)
Dana Carvey (born 1955)
Neil Casey (born 1981)
Aya Cash (born 1982)
Cliff Cash (born 1981)
Craig Cash (born 1960)
Michael Cassidy (born 1983)
Dan Castellaneta (born 1957)
Mike Castle (born 1989)
Roy Castle (1932–1994)
Arturo Castro (born 1985)
Jade Catta-Preta (born 1984)
Mary Jo Catlett (born 1938)
Walter Catlett (1889–1960)
Kim Cattrall (born 1956)
John Catucci (born 1973)
Jo Caulfield (born 1965)
Tony Cavalero (born 1983)
Elise Cavanna (1902–1963)
Dick Cavett (born 1936)
Adam Cayton-Holland (born 1980)
Kyle Cease (born 1977)
Cedric the Entertainer (born 1964)
Kiray Celis (born 1995)
Wyatt Cenac (born 1976)
Michael Cera (born 1988)
Bülent Ceylan (born 1976)
Jessica Chaffin (born 1974)
Rachel Chagall (born 1952)
Sarah Chalke (born 1976)
Kevin Chamberlin (born 1963)
Emma Chambers (1964–2018)
Jackie Chan (born 1954)
Melanie Chandra (born 1984)
Jay Chandrasekhar (born 1968)
Carol Channing (1921–2019)
Jay Chanoine (born 1986/1987)
Zoë Chao (born 1985)
Omar Chaparro (born 1974)
Charlie Chaplin (1889–1977)
Graham Chapman (1941–1989)
Doug Chappel (born 1975)
Dave Chappelle (born 1973)
Charlamagne tha God (born 1978)
Craig Charles (born 1964)
Josh Charles (born 1971)
Charo
Melanie Chartoff (born 1948)
Charley Chase (1893–1940)
Chevy Chase (born 1943)
Michael Che (born 1983)
Karen Chee (born 1995)
Parvesh Cheena (born 1979)
Richard Cheese (born 1965)
Aaron Chen (born 1995)
Hank Chen (born 1989)
Kristin Chenoweth (born 1968)
Zach Cherry (born 1987)
Cherry Chevapravatdumrong (born 1977)
Ronny Chieng (born 1985)
Autumn Chiklis (born 1993)
Michael Chiklis (born 1963)
Feodor Chin (born 1974)
Chingo Bling (Pedro Herrera) (born 1979)
Lori Tan Chinn (born 1948)
Nasir Chinyoti (born 1970)
Ted Chippington (born 1960)
Whitney Chitwood
Henry Cho (born 1962)
John Cho (born 1972)
Margaret Cho (born 1968)
Jessica Chobot (born 1977)
Chokoleit (1970–2019)
Tommy Chong (born 1938)
Bill Chott (born 1969)
Stephen Chow (born 1962)
Paul Chowdhry (born 1974)
Bridget Christie (born 1971)
Richard Christy (born 1974)
Thomas Haden Church (born 1960)
Papa CJ (born 1977)
Anthony Clark (born 1964)
Bobby Clark (1888–1960)
Laurence Clark (born 1974)
Mystro Clark (born 1966)
Lenny Clarke (born 1953)
Julian Clary (born 1959)
Andrew "Dice" Clay (born 1958)
John Cleese (born 1939)
Ellen Cleghorne (born 1965)
Jemaine Clement (born 1974)
Sean Clements (born 1981)
Del Close (1934–1999)
Jerry Clower (1926–1998)
Martin Clunes (born 1961)
Andy Clyde (1892–1967)
Imogene Coca (1908–2001)
Michaela Coel (born 1987)
Andy Cohen (born 1968)
Catherine Cohen (born 1991)
Sacha Baron Cohen (born 1971)
Mindy Cohn (born 1966)
Diablo Cody (born 1978)
Sherry Cola (born 1989)
Enrico Colantoni (born 1963)
Stephen Colbert (born 1964)
Coldmirror (born 1984)
Deon Cole (born 1972)
Gary Coleman (1968–2010)
Jonathan Coleman (1956–2021)
Kelen Coleman (born 1984)
Ryan Coleman (born 1991)
Kim Coles (born 1962)
Bobby Collins (born 1951)
Michelle Collins (born 1981)
Misha Collins (born 1974)
Mo Collins (born 1965)
Katy Colloton (born 1984)
Olivia Colman (born 1974)
Sarah Colonna (born 1974)
Michael Colton (born 1975)
Robbie Coltrane (1950–2022)
Ray Combs (1956–1996)
Roisin Conaty (born 1979)
Pat Condell (born 1949)
Brian Conley (born 1961)
Kurtis Conner (born 1994)
Frank Conniff (born 1956)
Billy Connolly (born 1942)
Kevin Connolly (born 1974)
Adam Conover (born 1983)
Nina Conti (born 1974)
Paolo Contis (born 1984)
Tim Conway (1933–2019)
Steve Coogan (born 1965)
Carole Cook (1924–2023)
Dane Cook (born 1972)
Matt Cook (born 1984)
Peter Cook (1937–1995)
Josh Cooke (born 1979)
Danny Cooksey (born 1975)
Jennifer Coolidge (born 1961)
Bradley Cooper (born 1975)
Calico Cooper (born 1981)
Pat Cooper (born 1929)
Sarah Cooper (born 1977)
Tommy Cooper (1921–1984)
Alicia Coppola (born 1968)
Bill Corbett (born 1960)
Ronnie Corbett (1930–2016)
Nate Corddry (born 1977)
Rob Corddry (born 1971)
James Corden (born 1978)
Eugene Cordero (born 1978)
Professor Irwin Corey (1914–2017)
Joe Cornish (born 1968)
Judy Cornwell (born 1940)
Pete Correale (born 1970)
Rebecca Corry (born 1971)
Bud Cort (born 1948)
Paola Cortellesi (born 1973)
Bill Cosby (born 1937)
Lou Costello (1906–1959)
Sue Costello (born 1968)
Camille Cottin (born 1978)
Antony Cotton (born 1975)
Dave Coulier (born 1959)
Jonathan Coulton (born 1970)
Eliza Coupe (born 1981)
Stephanie Courtney (born 1970)
Allen Covert (born 1964)
Courteney Cox (born 1964)
Nikki Cox (born 1978)
Wally Cox (1924–1973)
Carly Craig (born 1980)
Billy Crawford (born 1982)
Lavell Crawford (born 1968)
Zach Cregger (born 1980)
Amanda Crew (born 1986)
Terry Crews (born 1968)
Chelsey Crisp (born 1983)
John Crist (born 1984)
Affion Crockett (born 1974)
Ben Crompton (born 1974)
Mackenzie Crook (born 1971)
Norm Crosby (1927–2020)
David Cross (born 1964)
Trae Crowder (born 1986)
Lucas Cruikshank (born 1993)
Hal Cruttenden (born 1969)
Barry Cryer (1935–2022)
Jon Cryer (born 1965)
Billy Crystal (born 1948)
Ice Cube (born 1969)
Seán Cullen (born 1965)
Whitney Cummings (born 1982)
Dan Cummins (born 1977)
James Cunningham (born 1973)
Mark Curry (born 1961)
Stephen Curry (born 1976)
Jane Curtin (born 1947)
Joan Cusack (born 1962)
John Cusack (born 1966)
Jack Cutmore-Scott (born 1987)
D
Peter F. Dailey (1868–1908)
E.G. Daily (born 1961)
Charlie Dale (1885–1971)
Jim Dale (born 1935)
Karl Dall (1941–2020)
John Francis Daley (born 1985)
Andrew Daly (born 1971)
Jon Daly (born 1977)
Tim Daly (born 1956)
Bill Dana (1924–2017)
Rodney Dangerfield (1921–2004)
Chad Daniels (born 1975)
Greg Daniels (born 1963)
Ted Danson (born 1947)
Dante (born 1970)
Tony Danza (born 1951)
Khalid Abbas Dar (born 1955)
Rhys Darby (born 1974)
Severn Darden (1929–1995)
Vir Das (born 1979)
Hayes Davenport (born 1986)
Jim David (born 1954)
Keith David (born 1956)
Larry David (born 1947)
Dov Davidoff (born 1973)
Hugh Davidson
Jim Davidson (born 1953)
Pete Davidson (born 1993)
Alan Davies (born 1966)
Greg Davies (born 1968)
Ann B. Davis (1926–2014)
Clifton Davis (born 1945)
DeRay Davis (born 1982)
Jeff B. Davis (born 1973)
Julia Davis (born 1966)
Kristin Davis (born 1965)
LaVan Davis (born 1966)
Lucy Davis (born 1973)
Matt Davis (born 1979)
Nore Davis (born 1984)
Tanyalee Davis (born 1970)
Tom Davis (born 1979)
Tom Davis (1952–2012)
Ken Davitian (born 1953)
Richard Dawson (1932–2012)
Les Dawson (1931–1993)
Shane Dawson (born 1988)
Charlie Day (born 1976)
Dennis Day (1916–1988)
Felicia Day (born 1979)
Mikey Day (born 1980)
Andy de la Tour (born 1954)
Ai-Ai delas Alas (born 1964)
Mark DeCarlo (born 1962)
Frank DeCaro (born 1962)
Enchong Dee (born 1988)
Gerry Dee (born 1968)
Jack Dee (born 1962)
Rob Deering (born 1972)
Rick Dees (born 1950)
Eddie Deezen (born 1957)
Ellen DeGeneres (born 1958)
Vance DeGeneres (born 1954)
Neil Delamere (born 1980)
Rob Delaney (born 1977)
Lea DeLaria (born 1958)
Jessica Delfino (born 1976)
Chris D'Elia (born 1980)
Joey de Leon (born 1946)
Grey DeLisle (born 1973)
Bianca Del Rio (born 1975)
David DeLuise (born 1971)
Dom DeLuise (1933–2009)
Ivor Dembina (born 1951)
Dr. Demento (born 1941)
Jamie Demetriou (born 1987)
Natasia Demetriou (born 1984)
Dustin Demri-Burns (born 1978)
Lori Beth Denberg (born 1976)
Jamie Denbo (born 1973)
Kat Dennings (born 1986)
Gabrielle Dennis (born 1981)
Hugh Dennis (born 1962)
Les Dennis (born 1953)
Bob Denver (1935–2005)
Joe DeRita (1909–1993)
Joe DeRosa (born 1977)
Portia de Rossi (born 1973)
Zooey Deschanel (born 1980)
Jack DeSena (born 1987)
Mike DeStefano (1966–2011)
Patti Deutsch (1943–2017)
Adam DeVine (born 1983)
Danny DeVito (born 1944)
Tommy Dewey (born 1978)
Joyce DeWitt (born 1949)
Eugenio Derbez (born 1962)
Dustin Diamond (1977–2021)
Chris Diamantopoulos (born 1975)
Joey Diaz (born 1963)
Ogie Diaz (born 1970)
Vic DiBitetto (born 1961)
Andy Dick (born 1965)
Daniel Dickey (born 1986)
John Di Domenico (born 1962)
Dominic Dierkes (born 1984)
Richard Digance (born 1949)
Debra DiGiovanni (born 1972)
Wendy van Dijk (born 1971)
Phyllis Diller (1917–2012)
Brooke Dillman (born 1966)
Kevin Dillon (born 1965)
Tim Dillon (born 1985)
John DiMaggio (born 1968)
Amelia Dimoldenberg (born 1994)
David Dineen-Porter (born 1979)
Paul Dinello (born 1962)
Juan Pablo Di Pace (born 1979)
Nick DiPaolo (born 1962)
Katie Dippold (born 1980)
Andrew Dismukes (born 1995)
Chris Distefano (born 1984)
Olli Dittrich (born 1956)
Gina DiVittorio (born 1995)
Omid Djalili (born 1965)
Anh Do (born 1977)
David Dobrik (born 1996)
Nik Dodani (born 1993)
Ken Dodd (1927–2018)
Mark Dolan (born 1974)
Dolphy (1928–2012)
Eugene Domingo (born 1971)
Joel Dommett (born 1985)
Kether Donohue (born 1985)
Lisa Donovan (born 1980)
Tate Donovan (born 1963)
Paul Dooley (born 1928)
Jimmy Dore (born 1965)
Jon Dore (born 1975)
Jeff Doucette (born 1947)
Doug E. Doug (born 1970)
Donna Douglas (1932–2015)
Jack Douglass (born 1988)
Beth Dover (born 1978)
John Dowie (born 1950)
Jim Downey (born 1952)
Paul W. Downs (born 1982)
Brian Doyle-Murray (born 1945)
Charlie Drake (1925–2006)
Larry Drake (1949–2016)
Ruth Draper (1884–1956)
Rachel Dratch (born 1966)
Tom Dreesen (born 1939)
Fran Drescher (born 1957)
Marie Dressler (1868–1934)
James Dreyfus (born 1968)
Anna Drezen
Drew Droege
Mike Drucker (born 1984)
Ryan Drummond (born 1973)
Eric Drysdale (born 1969)
Rebecca Drysdale (born 1978/1979)
Rick Ducommun (1952–2015)
Julia Duffy (born 1951)
Dennis Dugan (born 1946)
Christian Duguay (born 1970)
Josh Duhamel (born 1972)
Jean Dujardin (born 1972)
Clark Duke (born 1985)
Patty Duke (1946–2016)
Robin Duke (born 1954)
Sandy Duncan (born 1946)
Shane Dundas (born 1959)
Jeff Dunham (born 1962)
Lena Dunham (born 1986)
Barbara Dunkelman (born 1989)
Colton Dunn (born 1977)
Gabe Dunn (born 1988)
George Dunn (1914–1982)
Jimmy Dunn
Nora Dunn (born 1952)
Ryan Dunn (1977–2011)
Kyle Dunnigan (born 1971)
Debbe Dunning (born 1966)
Jay Duplass (born 1973)
Mark Duplass (born 1976)
Elvis Duran (born 1964)
Jimmy Durante (1893–1980)
Sanjay Dutt (born 1959)
Clea DuVall (born 1977)
Shelley Duvall (1949–2024)
Bil Dwyer (born 1962)
Jeff Dye (born 1983)
Harriet Dyer (born 1988)
Rob Dyrdek (born 1974)
Jeremy Dyson (born 1966)
E
Open Mike Eagle (born 1980)
Jason Earles (born 1977)
John Early (born 1988)
Christine Ebersole (born 1953)
Buddy Ebsen (1908–2003)
Chris Eckert (born 1986)
Lisa Eckhart (born 1992)
Costaki Economopoulos (born 1965)
Paul Eddington (1927–1995)
Ayo Edebiri (born 1995)
Alex Edelman (born 1989)
Eric Edelstein (born 1977)
Barbara Eden (born 1931)
Ade Edmondson (born 1957)
Dean Edwards (born 1970)
Derek Edwards (born 1958)
Ian Edwards
Justin Edwards (born 1972)
Christian Ehring (born 1972)
Billy Eichner (born 1978)
Hannah Einbinder (born 1995)
Bob Einstein (1942–2019)
Rich Eisen (born 1969)
Ophira Eisenberg (born 1972)
Naomi Ekperigin (born 1983)
Kevin Eldon (born 1959)
Jenna Elfman (born 1971)
Laurie Elliot (born 1971)
Abby Elliott (born 1987)
Bob Elliott (1923–2016)
Bridey Elliott (born 1990)
Chris Elliott (born 1960)
Mary Elizabeth Ellis (born 1979)
Gad Elmaleh (born 1971)
Ethan Embry (born 1978)
Dick Emery (1915–1983)
Harry Enfield (born 1961)
Georgia Engel (1948–2019)
Anke Engelke (born 1965)
Bill Engvall (born 1957)
John Ennis
Mike Epps (born 1970)
Molly Erdman (born 1974)
Heinz Erhardt (1909–1979)
Paco Erhard (born 1975)
Andy Erikson (born 1987)
Leon Errol (1881–1951)
Blaire Erskine (born 1991)
Maya Erskine (born 1987)
Cole Escola (born 1986)
Ennis Esmer (born 1978)
Felipe Esparza (born 1970)
Cameron Esposito (born 1981)
Charles Esten (born 1965)
Chris Estrada
Karla Estrada (born 1974)
Chris Evans (born 1966)
Lee Evans (born 1964)
Sean Evans (born 1986)
Bridget Everett (born 1972)
Kenny Everett (1944–1995)
Justine Ezarick (born 1984)
F
Ana Fabrega (born 1991)
Jackie Fabulous (born 1970)
Josh Fadem (born 1980)
Bill Fagerbakke (born 1957)
Damien Fahey (born 1980)
Donald Faison (born 1974)
Jimmy Fallon (born 1974)
Richard Fancy (born 1943)
Simon Fanshawe (born 1956)
Ali Farahnakian (born 1967)
Anna Faris (born 1976)
Chris Farley (1964–1997)
John Farley (born 1968)
Kevin Farley (born 1965)
Bill Farmer (born 1952)
Simon Farnaby (born 1973)
Jamie Farr (born 1934)
Bobby Farrelly (born 1958)
Peter Farrelly (born 1956)
Negin Farsad (born 1978)
Mitch Fatel (born 1968)
David Faustino (born 1974)
Jon Favreau (born 1966)
Nat Faxon (born 1975)
Isabel Fay (born 1979)
Joey Faye (1909–1997)
Helga Feddersen (1930–1990)
Wayne Federman (born 1959)
Paul Feig (born 1962)
Fortune Feimster (born 1980)
Rachel Feinstein
Ben Feldman (born 1980)
David Feldman
Liz Feldman (born 1977)
Marty Feldman (1934–1982)
Beanie Feldstein (born 1993)
Graham Fellowes (born 1959)
Randy Feltface (born 1980)
Spike Feresten (born 1964)
Craig Ferguson (born 1962)
Don Ferguson (born 1946)
Jay R. Ferguson (born 1974)
Jesse Tyler Ferguson (born 1975)
Keith Ferguson (born 1972)
Shelby Fero (born 1993)
Adam Ferrara (born 1966)
Jerry Ferrara (born 1979)
America Ferrera (born 1984)
Conchata Ferrell (1943–2020)
Will Ferrell (born 1967)
Herbert Feuerstein (1937–2020)
Tina Fey (born 1970)
Sally Field (born 1946)
Nathan Fielder (born 1983)
Michael Fielding (born 1982)
Noel Fielding (born 1973)
Totie Fields (1930–1978)
W. C. Fields (1880–1946)
Nathan Fillion (born 1971)
Larry Fine (1902–1975)
Chloe Fineman (born 1988)
Christian Finnegan (born 1973)
Katie Finneran (born 1971)
Dan Finnerty (born 1970)
Kathryn Fiore (born 1979)
Jo Firestone (born 1987)
Jordan Firstman (born 1991)
Mark Fischbach (aka) Markiplier (born 1989)
Jenna Fischer (born 1974)
Joely Fisher (born 1967)
Lang Fisher (born 1980)
Miles Fisher (born 1983)
Greg Fitzsimmons (born 1966)
Fannie Flagg (born 1944)
Joe Flaherty (1941–2024)
Crista Flanagan (born 1976)
Tom Flanigan
Kate Flannery (born 1964)
Charles Fleischer (born 1950)
Chris Fleming (born 1987)
Jim Florentine (born 1964)
Jake Flores
Neil Flynn (born 1960)
Jake Fogelnest (born 1979)
Dan Fogler (born 1976)
Lisa Foiles (born 1986)
Dave Foley (born 1963)
Mick Foley (born 1965)
Evan Fong (aka) Vanoss (born 1992)
Paul Foot (born 1973)
Faith Ford (born 1964)
Thomas Mikal Ford (1964–2016)
Matt Forde (born 1982)
Joey Forman (1929–1982)
George Formby (1904–1961)
George Formby Sr. (1875–1921)
Will Forte (born 1970)
Kat Foster (born 1978)
Jermaine Fowler (born 1988)
Jimmy Fowlie (born 1985)
Kirk Fox (born 1969)
Michael J. Fox (born 1961)
Zack Fox (born 1990)
Jeff Foxworthy (born 1958)
Jamie Foxx (born 1967)
Redd Foxx (1922–1991)
Leigh Francis (born 1974)
Stewart Francis (born 1964)
Jason Francisco (born 1987)
Pablo Francisco (born 1974)
Dave Franco (born 1985)
Eduardo Franco (born 1995)
James Franco (born 1978)
Al Franken (born 1951)
Bonnie Franklin (1944–2013)
Marina Franklin
Nelson Franklin (born 1985)
Daniel Franzese (born 1978)
Alice Fraser
William Frawley (1887–1966)
Stan Freberg (1926–2015)
Gavin Free (born 1988)
Travon Free (born 1985)
Cate Freedman
Martin Freeman (born 1971)
Jared Freid (born 1985)
Dawn French (born 1957)
Matt Frewer (born 1958)
Judah Friedlander (born 1969)
Will Friedle (born 1976)
Budd Friedman (1932–2022)
Jena Friedman (born 1983)
Matt Friend (born 1998)
Annette Frier (born 1974)
Leon Frierson (born 1986)
Don Friesen
Freddie Frinton (1909–1968)
Rebecca Front (born 1964)
David Frost (1939–2013)
Nick Frost (born 1972)
Stephen Fry (born 1957)
Pamela Fryman (born 1959)
Daisy Fuentes (born 1966)
John Fugelsang (born 1969)
Rich Fulcher (born 1968)
Kurt Fuller (born 1953)
Ned Fulmer (born 1987)
Ziwe Fumudoh (born 1992)
Ron Funches (born 1983)
Brittany Furlan (born 1986)
Fakkah Fuzz (born 1986)
G
Eva Gabor (1919–1995)
Jon Gabrus (born 1982)
Josh Gad (born 1981)
Richard Gadd (born 1989)
Hannah Gadsby (born 1978)
Jim Gaffigan (born 1966)
Mo Gaffney (born 1958)
Megan Gailey (born 1986)
Jayson Gainza (born 1980)
Daniele Gaither (born 1970)
Johnny Galecki (born 1975)
Zach Galifianakis (born 1969)
Gallagher (1946–2022)
Brian Gallivan
Sue Galloway
Mayce Galoni (born 1994)
Ed Gamble (born 1986)
Joross Gamboa (born 1984)
Megan Ganz (born 1984)
Robert Ben Garant (born 1970)
Jorge Garcia (born 1973)
Billy Gardell (born 1969)
Graeme Garden (born 1943)
Blanche Gardin (born 1977)
Brother Dave Gardner (1926–1983)
Heidi Gardner (born 1983)
Pete Gardner
Tony Gardner (born 1964)
Zarna Garg (born 1975)
Jeff Garlin (born 1962)
Ralph Garman (born 1964)
Paul Garner (1909–2004)
Janeane Garofalo (born 1964)
Teri Garr (1944–2024)
Betty Garrett (1919–2011)
Brad Garrett (born 1960)
Susie Garrett (1929–2002)
Kyle Gass (born 1960)
Ana Gasteyer (born 1967)
Alison Gates (born 1988/1989)
Kimmy Gatewood
Mark Gatiss (born 1966)
Joe Gatto (born 1976)
Ryan Gaul (born 1973)
Richard Gautier (1931–2017)
Joey Gay (born 1971)
George Gaynes (1917–2016)
Dustin Gee (1942–1986)
Chris Geere (born 1981)
Brett Gelman (born 1976)
John Gemberling (born 1981)
Genevieve (1920–2004)
Tom Gerhardt (born 1957)
Ricky Gervais (born 1961)
Chris Gethard (born 1980)
Estelle Getty (1923–2008)
Alice Ghostley (1923–2007)
Tom Gianas
Janno Gibbs (born 1969)
Marla Gibbs (born 1931)
Erin Gibson
Kathie Lee Gifford (born 1953)
Billy Gilbert (1894–1971)
Rhod Gilbert (born 1968)
Russell Gilbert (born 1959)
Sara Gilbert (born 1975)
Kevin Gillese (born 1980)
Terry Gilliam (born 1940)
Mo Gilligan (born 1988)
Shane Gillis (born 1987)
Paul Gilmartin (born 1963)
Ewen Gilmour (1963–2014)
Lisa Gilroy (born 1990)
Greg Giraldo (1965–2010)
Adele Givens (born 1960)
Jon Glaser (born 1968)
Nikki Glaser (born 1984)
Ira Glass (born 1959)
Todd Glass (born 1964)
Rick Glassman (born 1984)
Ilana Glazer (born 1987)
Jackie Gleason (1916–1987)
Tom Gleeson (born 1974)
Ben Gleib (born 1978)
Donald Glover (aka) Childish Gambino (born 1983)
Stephen Glover (aka) Steve-O (born 1974)
GloZell (born 1972)
George Gobel (1919–1991)
Godfrey (born 1969)
Janey Godley (born 1961)
Paul Goebel (born 1968)
Loyiso Gola (born 1983)
Judy Gold (born 1962)
Adam Goldberg (born 1970)
Adam F. Goldberg (born 1976)
Andrew Goldberg (born 1978)
Evan Goldberg (born 1982)
Whoopi Goldberg (born 1955)
Brett Goldstein (born 1980)
Jonathan Goldstein (born 1968)
Bobcat Goldthwait (born 1962)
Ian Gomez (born 1965)
Roberto Gómez Bolaños (Chespirito) (1929–2014)
Josh Gondelman (born 1985)
Jami Gong (born 1969)
Alex Gonzaga (born 1988)
Ginger Gonzaga (born 1983)
Toni Gonzaga (born 1984)
Cuba Gooding Jr. (born 1968)
Omar Gooding (born 1976)
John Goodman (born 1952)
Ken Goodwin (1933–2012)
Dan Goor (born 1975)
Leo Gorcey (1917–1969)
Joseph Gordon-Levitt (born 1981)
Christopher Gorham (born 1974)
Dave Gorman (born 1971)
Frank Gorshin (1933–2005)
Freeman Gosden (1899–1982)
Mark-Paul Gosselaar (born 1974)
Gilbert Gottfried (1955–2022)
Theodore Gottlieb (1906–2001)
Dana Gould (born 1964)
Sandra Gould (1916–1999)
Ray Goulding (1922–1990)
Sal Governale (born 1968)
Luba Goy (born 1945)
Jeff Grace
Topher Grace (born 1978)
Boothby Graffoe (born 1962)
Heather Graham (born 1970)
Matt Graham
Kelsey Grammer (born 1955)
Charlie Grandy (born 1974)
Fred Grandy (born 1948)
Corinne Grant (born 1973)
David Grant (born 1956)
Stephen Grant (born 1973)
Judy Graubart (born 1943)
Ari Graynor (born 1983)
Jeff Green (born 1964)
Seth Green (born 1974)
Tom Green (born 1971)
Bryan Greenberg (born 1978)
Shecky Greene (1926–2023)
Max Greenfield (born 1979)
Kathy Greenwood (born 1962)
Judy Greer (born 1975)
Melvin Gregg (born 1988)
Dick Gregory (1932–2017)
James Gregory (born 1946)
Tamsin Greig (born 1966)
Adrian Grenier (born 1976)
Stacey Grenrock-Woods (born 1975)
David Alan Grier (born 1955)
Erik Griffin (born 1972)
Eddie Griffin (born 1968)
Kathy Griffin (born 1960)
Andy Griffith (1926–2012)
Scott Grimes (born 1971)
Todd Grinnell (born 1976)
Asher Grodman (born 1987)
Charles Grodin (1935–2021)
Matt Groening (born 1954)
David Groh (1939–2008)
Kirsten Gronfield (born 1977)
Mary Gross (born 1953)
Michael Gross (born 1947)
Peter Grosz (born 1974)
Rene Gube (born 1979)
Matthew Gray Gubler (born 1980)
Christopher Guest (born 1948)
Patty Guggenheim (born 1984)
Ariana Guido (born 1999)
Ann Morgan Guilbert (1928–2016)
Robert Guillaume (1927–2017)
Harvey Guillen (born 1990)
Ingrid Guimarães (born 1972)
Gary Gulman (born 1970)
Appurv Gupta (born 1990)
Broti Gupta (born 1993)
Annabelle Gurwitch (born 1961)
Björn Gustafsson (born 1986)
Greg Gutfeld (born 1964)
Steve Guttenberg (born 1958)
Deryck Guyler (1914–1999)
H
Buddy Hackett (1924–2003)
Tiffany Haddish (born 1979)
Bill Hader (born 1978)
Sarah Hadland (born 1971)
Jenny Hagel
Hallie Haglund (born 1982)
Meredith Hagner (born 1987)
Kathryn Hahn (born 1973)
Tony Hale (born 1970)
Brian Haley (born 1961)
Jack Haley (1897–1979)
Stavros Halkias (born 1989)
Anthony Michael Hall (born 1968)
Brad Hall (born 1958)
Brandon Micheal Hall (born 1993)
Daheli Hall (born 1976)
Huntz Hall (1919–1999)
Rich Hall (born 1954)
Dieter Hallervorden (born 1935)
Katie Halper (born 1980)
Evelyn Hamann (1942–2007)
Neil Hamburger (born 1967)
Argus Hamilton
Lloyd Hamilton (1891–1935)
Ryan Hamilton (born 1976)
Jon Hamm (born 1971)
Darrell Hammond (born 1955)
Nick Hancock (born 1962)
Tony Hancock (1924–1968)
Jack Handey (born 1949)
Chelsea Handler (born 1975)
Colin Hanks (born 1977)
Tom Hanks (born 1956)
Gabbie Hanna (born 1991)
Alyson Hannigan (born 1974)
Ryan Hansen (born 1981)
Malcolm Hardee (1950–2005)
Brandon Hardesty (born 1987)
Mike Harding (born 1944)
Chris Hardwick (born 1971)
Johnny Hardwick (1958–2023)
Jeremy Hardy (1961–2019)
Oliver Hardy (1890–1957)
Allana Harkin
Otis Harlan (1865–1940)
Dan Harmon (born 1973)
Tim Harmston (born 1971/1972)
Valerie Harper (1939–2019)
William Jackson Harper (born 1980)
Neil Patrick Harris (born 1973)
Rachael Harris (born 1968)
Robin Harris (1953–1990)
Blake Harrison (born 1985)
Bret Harrison (born 1982)
Patti Harrison (born 1990)
Hannah Hart (born 1986)
Kevin Hart (born 1979)
Mamrie Hart (born 1983)
Melissa Joan Hart (born 1976)
Miranda Hart (born 1972)
Adam Hartle (born 1979)
Phil Hartman (1948–1998)
Steve Harvey (born 1957)
Ian Harvie
Murtaza Hassan (1965–2011)
Paul Walter Hauser (born 1986)
Allan Havey (born 1954)
Kali Hawk (born 1986)
Tim Hawkins (born 1968)
Tony Hawks (born 1960)
Goldie Hawn (born 1945)
Charles Hawtrey (1858–1923)
Charles Hawtrey (1914–1988)
Will Hay (1888–1949)
Richard Haydn (1905–1985)
Erinn Hayes (born 1976)
Sean Hayes (born 1970)
Mike Hayley
Natalie Haynes (born 1974)
Ted Healy (1896–1937)
Richard Hearne (1890–1987)
Caleb Hearon (born 1995)
Patricia Heaton (born 1958)
Ian Hecox (born 1987)
Mitch Hedberg (1968–2005)
Jon Heder (born 1977)
Briga Heelan (born 1987)
Bobby Heenan (1943–2017)
Kevin Heffernan (born 1968)
John Heffron (born 1970)
John Hegley (born 1953)
Robert Hegyes (1951–2012)
Tim Heidecker (born 1976)
Jesse Heiman (born 1978)
Hans-Joachim Heist (born 1949)
Simon Helberg (born 1980)
Grace Helbig (born 1985)
Emily Heller (born 1985)
Peter Helliar (born 1975)
Nick Helm (born 1980)
Katherine Helmond (1929–2019)
Ed Helms (born 1974)
Greg Hemphill (born 1969)
Shirley Hemphill (1947–1999)
Sherman Hemsley (1938–2012)
Dickie Henderson (1922–1985)
Christina Hendricks (born 1975)
Elaine Hendrix (born 1970)
Vic Henley (1962–2020)
Marilu Henner (born 1952)
Carolyn Hennesy (born 1962)
Buck Henry (1930–2020)
Ely Henry (born 1991)
Lenny Henry (born 1958)
Mike Henry (born 1964)
John Henton (born 1960)
Dai Henwood (born 1978)
Hugh Herbert (1884–1952)
Christoph Maria Herbst (born 1966)
Tim Herlihy (born 1966)
David Herman (born 1967)
Thomas Hermanns (born 1963)
Marcello Hernández (born 1997)
Mark Herras (born 1986)
Richard Herring (born 1967)
Edward Herrmann (1943–2014)
Seth Herzog (born 1970)
Howard Hesseman (1940–2022)
Bill Hicks (1961–1994)
Ryan Higa (born 1990)
David Anthony Higgins (born 1961)
John Michael Higgins (born 1963)
Maeve Higgins
Steve Higgins (born 1963)
Jhong Hilario (born 1976)
Dieter Hildebrandt (1927–2013)
Amy Hill (born 1953)
Bec Hill (born 1986)
Benny Hill (1924–1992)
Dave Hill (born 1974)
Dulé Hill (born 1975)
Ed Hill (born 1984)
Harry Hill (born 1964)
Jonah Hill (born 1983)
Martina Hill (born 1974)
Melinda Hill (born 1972)
Murray Hill
Thelma Hill (1906–1938)
Tymberlee Hill
Jeff Hiller
Adam Hills (born 1970)
Tony Hinchcliffe (born 1984)
Cheryl Hines (born 1965)
Gregory Hines (1946–2003)
Skip Hinnant (born 1940)
Michael Hitchcock (born 1958)
Thora Hird (1911–2003)
Justin Hires (born 1985)
Judd Hirsch (born 1935)
Matt Hobby (born 1985)
Stephanie Hodge (born 1956)
Jessy Hodges (born 1986)
John Hodgman (born 1971)
Joel Hodgson (born 1960)
Jackie Hoffman (born 1960)
Robby Hoffman (born 1989)
Gaby Hoffmann (born 1982)
Steve Hofstetter (born 1979)
Chris Hogan (born 1970)
Paul Hogan (born 1939)
Siobhan Fallon Hogan (born 1961)
Amy Hoggart (born 1986)
Corey Holcomb (born 1969)
Dominic Holland (born 1967)
Mary Holland (born 1985)
Judy Holliday (1921–1965)
Vanessa Hollingshead
Stanley Holloway (1890–1982)
Anders Holm (born 1981)
Chelsea Holmes (born 1993/1994)
Dave Holmes (born 1971)
Eamonn Holmes (born 1959)
Jessica Holmes (born 1973)
Pete Holmes (born 1979)
Todd Holoubek (born 1969)
Lauren Holt (born 1991)
Helen Hong (born 1985)
James Hong (born 1929)
Brian Hooks (born 1974)
Jan Hooks (1957–2014)
Bob Hope (1903–2003)
Sharon Horgan (born 1970)
Alex Horne (born 1978)
Kenneth Horne (1907–1969)
Mathew Horne (born 1978)
Alex Kapp Horner (born 1969)
David Hornsby (born 1975)
Don Hornsby (1924–1950)
Jane Horrocks (born 1964)
Lutz van der Horst (born 1975)
Edward Everett Horton (1886–1970)
Richard Steven Horvitz (born 1966)
Curly Howard (1903–1952)
Frankie Howerd (1917–1992)
Ken Howard (1944–2016)
Kyle Howard (born 1978)
Moe Howard (1897–1975)
Ron Howard (born 1954)
Russell Howard (born 1980)
Shemp Howard (1895–1955)
Kirby Howell-Baptiste (born 1987)
Glenn Howerton (born 1976)
Lil Rel Howery (born 1979)
Jeremy Hotz (born 1966)
Roy Hudd (1936–2020)
Oliver Hudson (born 1976)
Rob Huebel (born 1969)
Akilah Hughes (born 1989)
Dave Hughes (born 1970)
John Hughes (1950–2009)
London Hughes (born 1989)
Sean Hughes (1965–2017)
Steve Hughes (born 1966)
D. L. Hughley (born 1963)
Daniel Humbarger
Barry Humphries (1934–2023)
Bonnie Hunt (born 1961)
Brendan Hunt (born 1972)
Bill Hunter (1940–2011)
Reginald D. Hunter (born 1969)
David Huntsberger (born 1979)
Michelle Hurd (born 1966)
Carl Hurley (born 1941)
Elizabeth Hurley (born 1965)
Lillian Hurst (born 1943)
Jake Hurwitz (born 1985)
Jon Hurwitz (born 1977)
Brian Huskey (born 1968)
Toby Huss (born 1966)
Warren Hutcherson (born 1963)
Melanie Hutsell (born 1968)
Betty Hutton (1921–2007)
Sam Hyde (born 1985)
Jessica Hynes (born 1972)
I
Paul Iacono (born 1988)
Sal Iacono (born 1971)
Armando Iannucci (born 1963)
Adrienne Iapalucci
Eric Idle (born 1943)
Eddie Ifft (born 1974)
Gabriel Iglesias (born 1976)
Sabrina Impacciatore (born 1968)
Celia Imrie (born 1952)
Robin Ince (born 1969)
Neil Innes (1944–2019)
Scott Innes (born 1966)
Tino Insana (1948–2017)
Dom Irrera (born 1948)
Bill Irwin (born 1950)
Matt Iseman (born 1971)
Harith Iskander (born 1966)
Eddie Izzard (born 1962)
J
Brandon T. Jackson (born 1984)
Marc Evan Jackson (born 1970)
Shantira Jackson
Victoria Jackson (born 1959)
Manny Jacinto (born 1987)
Gillian Jacobs (born 1982)
Abbi Jacobson (born 1984)
Jon Jafari (aka) JonTron (born 1990)
Javed Jaffrey (born 1963)
T.J. Jagodowski (born 1971)
Gerburg Jahnke (born 1955)
Sabrina Jalees (born 1985)
Billy T. James (1948–1991)
Elis James (born 1980)
Janelle James (born 1979)
Kevin James (born 1965)
Nick Jameson (born 1948)
Jameela Jamil (born 1986)
Gary Janetti (born 1966)
Alia Janine (born 1978)
Michael Patrick Jann (born 1970)
Allison Janney (born 1959)
Zoe Jarman (born 1982)
David Jason (born 1940)
Jay Jason (1915–2001)
Sam Jay (born 1982)
Kavin Jayaram (born 1980)
Jim Jefferies (born 1977)
Richard Jeni (1957–2007)
Ken Jeong (born 1969)
Anthony Jeselnik (born 1978)
Jess Hilarious (born 1992)
Michael Jeter (1952–2003)
Geri Jewell (born 1956)
Penn Jillette (born 1955)
Andrea Jin (born 1996)
Maz Jobrani (born 1972)
Jake Johannsen (born 1960)
Anjelah Johnson (born 1982)
Anthony Johnson (1966–2021)
Chic Johnson (1891–1962)
Jake Johnson (born 1978)
James Austin Johnson (born 1989)
Josh Johnson (born 1990)
Lia Marie Johnson (born 1996)
Nicole Randall Johnson (born 1973)
Punkie Johnson (born 1985)
Rebekka Johnson
Slink Johnson
Zainab Johnson
Jay Johnston (born 1968)
Kristen Johnston (born 1967)
Brandon Scott Jones (born 1984)
"Hamburger" Jones
Jason Jones (born 1967)
Leslie Jones (born 1967)
Luka Jones (born 1975)
Matt Jones (born 1981)
Orlando Jones (born 1968)
Rashida Jones (born 1976)
Shirley Jones (born 1934)
Terry Jones (1942–2020)
Leslie Jordan (1955–2022)
Lesley Joseph (born 1945)
Colin Jost (born 1982)
Mitra Jouhari (born 1992)
Jesse Joyce (born 1978)
Mario Joyner (born 1961)
Mike Judge (born 1962)
Andy Juett (born 1977)
Phill Jupitus (born 1962)
Jay Jurden (born 1988)
K
Daniel Kaluuya (born 1989)
Madeline Kahn (1942–1999)
Bess Kalb (born 1987)
Jamie Kaler (born 1964)
Mindy Kaling (born 1979)
Adhir Kalyan (born 1983)
Carol Kane (born 1952)
Russell Kane (born 1975)
Gabe Kaplan (born 1945)
Myq Kaplan (born 1978)
Fabiana Karla (born 1975)
J. P. Karliak (born 1981)
Uğur Rıfat Karlova (born 1980)
Ian Karmel (born 1984)
Richard Karn (born 1956)
Aaron Karo (born 1979)
Jensen Karp (born 1979)
Moshe Kasher (born 1979)
Jackie Kashian (born 1963)
John Kassir (born 1957)
Rosanne Katon (born 1954)
Sierra Katow (born 1994)
Chris Kattan (born 1970)
Jonathan Katz (born 1946)
Mickey Katz (1909–1985)
Andy Kaufman (1949–1984)
Julie Kavner (born 1950)
Peter Kay (born 1973)
Phil Kay (born 1969)
Spencer Kayden (born 1971)
Danny Kaye (1911–1987)
Paul Kaye (born 1964)
Stubby Kaye (1918–1997)
Samson Kayo (born 1991/1992)
Zoe Kazan (born 1983)
Molly Kearney (born 1992)
Diane Keaton (born 1946)
Michael Keaton (born 1951)
Carolin Kebekus (born 1980)
Jared Keeso (born 1984)
Garrison Keillor (born 1942)
John Keister (born 1956)
Penelope Keith (born 1940)
Peter Kelamis (born 1967)
Echo Kellum (born 1982)
Chris Kelly (born 1983)
Frank Kelly (1938–2016)
Martha Kelly (born 1968)
Patsy Kelly (1910–1981)
Robert Kelly (born 1970)
Pert Kelton (1907–1968)
Brandis Kemp (1944–2020)
Ellie Kemper (born 1980)
Luke Kempner (born 1987)
Suzanna Kempner (born 1985)
Harriet Kemsley (born 1987)
Sarah Kendall (born 1976)
Edgar Kennedy (1890–1948)
Graham Kennedy (1934–2005)
Jamie Kennedy (born 1970)
Mimi Kennedy (born 1948)
Tom Kennedy (1885–1965)
Trey Kennedy
Kerri Kenney-Silver (born 1970)
Jon Kenny (born 1957)
Tom Kenny (born 1962)
Sean Kent
Humphrey Ker (born 1982)
Langston Kerman (born 1987)
Hape Kerkeling (born 1964)
Michael Kessler (born 1967)
Keegan-Michael Key (born 1971)
Kristin Key (born 1980)
Sarah Keyworth (born 1993)
Amanullah Khan (born 1970)
Guz Khan (born 1986)
Shappi Khorsandi (born 1973)
The Kid Mero (born 1983)
Ford Kiernan (born 1962)
Laura Kightlinger (born 1969)
Pat Kilbane (born 1969)
Craig Kilborn (born 1962)
Karen Kilgariff (born 1970)
Taran Killam (born 1982)
Ronnie Killings (aka) R-Truth (born 1972)
Laurie Kilmartin (born 1965)
Jimmy Kimmel (born 1967)
Jonathan Kimmel (born 1976)
Kyle Kinane (born 1976)
Richard Kind (born 1956)
Andy Kindler (born 1956)
Alan King (1927–2004)
Anthony King
Dave King (1929–2002)
Georgia King (born 1986)
Jaime King (born 1979)
Matt King (born 1968)
Michael Patrick King (born 1954)
Nika King
Sam Kinison (1953–1992)
Greg Kinnear (born 1963)
Roy Kinnear (1934–1988)
Kathy Kinney (born 1954)
Angela Kinsey (born 1971)
Bruno Kirby (1949–2006)
Bill Kirchenbauer (born 1953)
Jen Kirkman (born 1974)
Matt Kirshen (born 1980)
Jessica Kirson (born 1969)
Takeshi Kitano (born 1947)
Jonathan Kite (born 1979)
Daniel Kitson (born 1977)
Roger Kitter (1949–2015)
Felix Kjellberg (aka) PewDiePie (born 1989)
Julie Klausner (born 1978)
Chris Klein (born 1979)
Jessi Klein (born 1975)
Robert Klein (born 1942)
Jordan Klepper (born 1979)
Kevin Kline (born 1947)
Jack Klugman (1922–2012)
Jessica Knappett (born 1984)
Christopher Knight (born 1957)
Jak Knight (1993–2022)
Ted Knight (1923–1986)
Wayne Knight (born 1955)
Don Knotts (1924–2006)
Christy Knowings (born 1980)
Johnny Knoxville (born 1971)
Chris Knutson
Christine Ko (born 1988)
Cody Ko (born 1990)
Olga Koch (born 1992)
David Koechner (born 1962)
Stephanie Koenig (born 1987)
Matt Koff
Gaby Köster (born 1961)
Michael Koman (born 1977)
Hari Kondabolu (born 1982)
Dada Kondke (1932–1998)
Anna Konkle (born 1987)
Jenni Konner (born 1971)
Lynne Koplitz (born 1969)
Harvey Korman (1927–2008)
Annie Korzen (born 1938)
Liza Koshy (born 1996)
Michael Kosta (born 1979)
Ernie Kovacs (1919–1962)
Jo Koy (born 1971)
Lindsey Kraft (born 1980)
Jane Krakowski (born 1968)
Eric Allan Kramer (born 1962)
John Krasinski (born 1979)
Jan Kraus (born 1953)
Diether Krebs (1947–2000)
Bert Kreischer (born 1972)
Howard Kremer (born 1971)
Jonathan Krisel (born 1979)
Kurt Krömer (born 1974)
Nick Kroll (born 1978)
Maren Kroymann (born 1949)
Mike Krüger (born 1951)
David Krumholtz (born 1978)
Esther Ku (born 1980)
Lisa Kudrow (born 1963)
Akshay Kumar (born 1967)
Nish Kumar (born 1985)
Mila Kunis (born 1983)
Elvira Kurt (born 1961)
Swoosie Kurtz (born 1944)
Ashton Kutcher (born 1978)
Sarah Kuttner (born 1979)
Eugenia Kuzmina (born 1981)
L
Shia LaBeouf (born 1986)
Tyler Labine (born 1978)
Jake Lacy (born 1985)
Preston Lacy (born 1969)
Cathy Ladman
Jon Lajoie (born 1980)
Don Lake (born 1956)
Patricia Lake (1919–1993)
Maurice LaMarche (born 1958)
Leah Lamarr (born 1988)
Phil LaMarr (born 1967)
Kate Lambert (born 1981)
Lisa Lampanelli (born 1961)
Amy Landecker (born 1969)
David Lander (1947–2020)
Steve Landesberg (1936–2010)
Matteo Lane (born 1986)
Nathan Lane (born 1956)
Richard Lane (1899–1982)
Harry Langdon (1894–1944)
Artie Lange (born 1967)
Ted Lange (born 1948)
Chris Langham (born 1949)
Ruth Langsford (born 1960)
Beth Lapides
Lauren Lapkus (born 1985)
Rocky LaPorte
John Lapus (born 1973)
John Larroquette (born 1947)
Larry the Cable Guy (born 1963)
Jay Larson
Queen Latifah (born 1970)
Stan Laurel (1890–1965)
Dan Lauria (born 1947)
Hugh Laurie (born 1959)
Ed Lauter (1938–2013)
Lauren Laverne (born 1978)
Linda Lavin (1937–2024)
Tony Law (born 1969)
Bill Lawrence (born 1968)
Carolyn Lawrence (born 1967)
Doug Lawrence (Mr Lawrence) (born 1969)
Martin Lawrence (born 1965)
Mike Lawrence (born 1983)
Vicki Lawrence (born 1949)
Josh Lawson (born 1981)
Maggie Lawson (born 1980)
Preacher Lawson (born 1991)
Cloris Leachman (1926–2021)
Denis Leary (born 1957)
Matt LeBlanc (born 1967)
Annie Lederman (born 1983)
Andy Lee (born 1981)
Bobby Lee (born 1972)
C.S. Lee (born 1971)
Daniel Curtis Lee (born 1991)
Greg Lee (born 1962)
Hana Mae Lee (born 1988)
Jamie Lee (born 1983)
Jason Lee (born 1970)
Paul Sun-Hyung Lee (born 1972)
Raquel Lee (born 1986)
Rex Lee (born 1969)
Stewart Lee (born 1968)
Terence Lee (born 1964)
Andrew Leeds (born 1981)
Mekki Leeper (born 1994)
Jane Leeves (born 1961)
Michael Legge (born 1968)
Natasha Leggero (born 1974)
Jay Leggett (1963–2013)
John Leguizamo (born 1960)
John Lehr (born 1965)
Tom Lehrer (born 1928)
Carol Leifer (born 1956)
Ismo Leikola (born 1979)
Steve Lemme (born 1968)
Jack Lemmon (1925–2001)
Nancy Lenehan (born 1953)
Tom Lenk (born 1976)
Thomas Lennon (born 1970)
Jay Leno (born 1950)
Jack E. Leonard (1910–1973)
Chauncey Leopardi (born 1981)
Yassir Lester (born 1984)
James Lesure (born 1970)
David Letterman (born 1947)
Sam Levenson (1911–1980)
Johnny Lever (born 1950)
Zachary Levi (born 1980)
Kristine Levine (born 1970)
Samm Levine (born 1982)
Cash Levy
Dan Levy (born 1981)
Dan Levy (born 1983)
Eugene Levy (born 1946)
Clea Lewis (born 1965)
Jenifer Lewis (born 1957)
Jerry Lewis (1926–2017)
Kimrie Lewis (born 1982)
Phill Lewis (born 1968)
Richard Lewis (1947–2024)
Robert Q. Lewis (1921–1991)
Shari Lewis (1933–1998)
Vicki Lewis (born 1960)
Leslie Liao (born 1987)
Kobi Libii
Ali Liebegott (born 1971)
Paul Lieberstein (born 1967)
Wendy Liebman (born 1961)
Gabe Liedman (born 1982)
Judith Light (born 1949)
Lil Dicky (born 1988)
Lil' JJ (born 1990)
Matthew Lillard (born 1970)
Hal Linden (born 1931)
Riki Lindhome (born 1979)
George Lindsey (1928–2012)
Joe Lipari (born 1979)
Maureen Lipman (born 1946)
Joe List (born 1982)
Zoe Lister-Jones (born 1982)
Ian Lithgow (born 1972)
John Lithgow (born 1945)
Luciana Littizzetto (born 1964)
Ralf Little (born 1980)
Rich Little (born 1938)
Rob Little (born 1972)
Steve Little (born 1972)
Beth Littleford (born 1968)
Lucy Liu (born 1968)
Ron Livingston (born 1967)
Christopher Lloyd (born 1938)
Eric Lloyd (born 1986)
Harold Lloyd (1893–1971)
Roger Lloyd-Pack (1944–2014)
Joe Lo Truglio (born 1970)
Daniel Lobell (born 1982/1983)
Sean Lock (1963–2021)
Freddy Lockhart (born 1979)
Jamie Loftus (born 1993)
Greg London (born 1966)
Jay London (born 1966)
Josie Long (born 1982)
Justin Long (born 1978)
Shelley Long (born 1949)
Michael Longfellow (born 1994)
Mike Lookinland (born 1960)
Andrés López (born 1971)
George Lopez (born 1961)
Mario Lopez (born 1973)
Dave Losso
Julia Louis-Dreyfus (born 1961)
Faizon Love (born 1968)
Jason Love
Judi Love (born 1980)
Loni Love (born 1971)
Jon Lovett (born 1982)
Jon Lovitz (born 1957)
Rob Lowe (born 1964)
Chris Lowell (born 1984)
Britt Lower (born 1985)
Adam Lowitt
Mark Lowry (born 1958)
Matt Lucas (born 1974)
Luenell (born 1959)
Joanna Lumley (born 1946)
Eric Lutes (born 1962)
John Lutz (born 1973)
Joe Lycett (born 1988)
Desi Lydic (born 1981)
Carmen Lynch (born 1972)
Drew Lynch (born 1991)
Jane Lynch (born 1960)
Katherine Lynch (born 1972)
Stephen Lynch (born 1971)
Paul Lynde (1926–1982)
Nicholas Lyndhurst (born 1961)
Chelcie Lynn (born 1987)
Darci Lynne (born 2004)
Melanie Lynskey (born 1977)
Natasha Lyonne (born 1979)
M
Moms Mabley (1894–1975)
Sunny Mabrey (born 1975)
Bernie Mac (1957–2008)
Hayes MacArthur (born 1977)
Scott MacArthur (born 1979)
Norm Macdonald (1959–2021)
Rachael MacFarlane (born 1976)
Seth MacFarlane (born 1973)
Gavin MacLeod (1931–2021)
Fred MacMurray (1908–1991)
Justina Machado (born 1972)
April Macie (born 1975)
Laird Macintosh (born 1962)
Charles Mack (1888–1934)
Lee Mack (born 1968)
Mary Mack (born 1975)
Doon Mackichan (born 1962)
Mike MacRae (born 1977)
Sheila MacRae (1921–2014)
Chris Maddock (born 1977/1978)
Kathleen Madigan (born 1965)
Al Madrigal (born 1971)
Jolina Magdangal (born 1978)
Scooter Magruder (born 1988)
Sean Maguire (born 1976)
Naveed Mahbub
Bill Maher (born 1956)
Bruce Mahler (born 1950)
John Mahoney (1940–2018)
Bobby Mair (born 1986)
Shaun Majumder (born 1972)
Ally Maki (born 1986)
Wendie Malick (born 1950)
Joshua Malina (born 1966)
Keith Malley (born 1974)
Jose Manalo (born 1966)
Joe Mande (born 1983)
David Mandel (born 1970)
Howie Mandel (born 1955)
Dylan Mandlsohn (born 1980/1981)
Aasif Mandvi (born 1966)
Jason Manford (born 1981)
Stephen Mangan (born 1968)
Jonathan Mangum (born 1971)
Sunita Mani (born 1986)
Sebastian Maniscalco (born 1973)
Leslie Mann (born 1972)
Charlie Manna (1920–1970)
Bernard Manning (1930–2007)
Taryn Manning (born 1978)
J.P. Manoux (born 1969)
Jason Mantzoukas (born 1972)
Edu Manzano (born 1955)
Luis Manzano (born 1981)
Alec Mapa (born 1965)
Jenna Marbles (born 1986)
Joseph Marcell (born 1948)
Cheech Marin (born 1946)
Ken Marino (born 1968)
Pigmeat Markham (1904–1981)
Alfred Marks (1921–1996)
Bob Marley (born 1967)
Marc Maron (born 1963)
Ross Marquand (born 1981)
Empoy Marquez (born 1981)
Zoë Coombs Marr
Elizabeth Marrero (born 1963)
Dylan Marron (born 1988)
Betty Marsden (1919–1998)
James Marsden (born 1973)
Garry Marshall (1934–2016)
Paula Marshall (born 1964)
Penny Marshall (1943–2018)
Andrea Martin (born 1947)
Dean Martin (1917–1995)
Demetri Martin (born 1973)
Dick Martin (1922–2008)
Duane Martin (born 1965)
Mae Martin (born 1987)
Millicent Martin (born 1934)
Steve Martin (born 1945)
Adrian Martinez (born 1972)
Jackie Martling (born 1947)
Karen Maruyama (born 1958)
Chico Marx (1887–1961)
Groucho Marx (1890–1977)
Gummo Marx (1892–1977)
Harpo Marx (1888–1964)
Patricia Marx
Zeppo Marx (1901–1979)
Jackie Mason (1928–2021)
Christopher Massey (born 1990)
Kyle Massey (born 1991)
Christopher Masterson (born 1980)
Danny Masterson (born 1976)
Sean Masterson
Rose Matafeo (born 1992)
Ross Mathews (born 1979)
Shane Mauss (born 1980)
Andrew Maxwell (born 1974)
Elaine May (born 1932)
Ralphie May (1972–2017)
Rik Mayall (1958–2014)
Wendy Maybury (born 1974/1975)
Youngmi Mayer (born 1984)
Ayden Mayeri (born 1990)
Bill Maynard (1928–2018)
X Mayo (born 1987)
Jayma Mays (born 1979)
Dan Mazer (born 1971)
Jennie McAlpine (born 1984)
Alphonso McAuley (born 1984)
Jack McBrayer (born 1973)
Danny McBride (born 1976)
Jenny McCarthy (born 1972)
Matt McCarthy (born 1979)
Melissa McCarthy (born 1970)
Dave McCary (born 1985)
Rue McClanahan (1934–2010)
Fancy Ray McCloney
Edie McClurg (born 1945)
Matthew McConaughey (born 1969)
Brian McConnachie (1942–2024)
Eric McCormack (born 1963)
Dan McCoy (born 1978)
Michael McCullers (born 1971)
Bruce McCulloch (born 1961)
Julian McCullough (born 1979)
Paul McCullough (1883–1936)
Suli McCullough (born 1968)
Paul McDermott (born 1962)
Josh McDermitt (born 1978)
Heather McDonald (born 1970)
Kevin McDonald (born 1961)
Michael McDonald (born 1964)
Charlotte McDonnell (born 1990)
Charlie McDowell (born 1983)
Rob McElhenney (born 1977)
Griffin McElroy (born 1987)
Justin McElroy (born 1980)
Travis McElroy (born 1983)
Reba McEntire (born 1955)
Bonnie McFarlane (born 1973)
Caitlin McGee (born 1988)
John C. McGinley (born 1959)
Ted McGinley (born 1958)
Mike McGlone (born 1972)
Joel McHale (born 1971)
Jan McInnis
Michael McIntyre (born 1976)
Rose McIver (born 1988)
Adam McKay (born 1968)
Antoine McKay (born 1970)
Michael McKean (born 1947)
Jessica McKenna (born 1987)
Patrick McKenna (born 1960)
Bret McKenzie (born 1976)
Brian McKim
Mark McKinney (born 1959)
Kate McKinnon (born 1984)
Des McLean
Wendi McLendon-Covey (born 1969)
Seán McLoughlin (aka) jacksepticeye (born 1990)
Pauline McLynn (born 1962)
Heather McMahan (born 1987)
Ed McMahon (1923–2009)
Rove McManus (born 1974)
Don McMillan
Joanne McNally (born 1983)
Ryan McPartlin (born 1975)
Vaughn Meader (1936–2004)
Audrey Meadows (1922–1996)
Tim Meadows (born 1961)
Kevin Meaney (1956–2016)
Angela Means (born 1963)
Tatanka Means (born 1985)
Anne Meara (1929–2015)
Tallie Medel
Matt Meese (born 1983)
Keyla Monterroso Mejia (born 1998)
Fred Melamed (born 1956)
Stuttering John Melendez (born 1965)
Jill-Michele Melean (born 1979)
Doug Mellard
Carlos Mencia (born 1967)
Maine Mendoza (born 1995)
Rick Mercer (born 1969)
Stephen Merchant (born 1974)
Dave Merheje
Liz Meriwether (born 1981)
Buster Merryfield (1920–1999)
Paul Merton (born 1957)
Chris Messina (born 1974)
Debra Messing (born 1968)
Laurie Metcalf (born 1955)
Art Metrano (1936–2021)
Rebecca Metz (born 1973)
Kurt Metzger (born 1977)
Jason Mewes (born 1974)
Breckin Meyer (born 1974)
Josh Meyers (born 1976)
Seth Meyers (born 1973)
Florinda Meza (born 1948)
Shaun Micallef (born 1962)
Michael V. (born 1969)
Vic Michaelis (born 1993)
Felicia Michaels (born 1964)
Lorne Michaels (born 1944)
Kate Micucci (born 1980)
Thomas Middleditch (born 1982)
Bette Midler (born 1945)
A.D. Miles (born 1971)
John Milhiser (born 1981)
Cristin Milioti (born 1985)
Ben Miller (born 1966)
Christa Miller (born 1964)
Dennis Miller (born 1953)
George Miller (aka) Joji/Filthy Frank (born 1993)
Karlous Miller (born 1983)
Larry Miller (born 1953)
Marilyn Suzanne Miller (born 1950)
Max Miller (1894–1963)
Murray Miller (born 1976)
T.J. Miller (born 1981)
Sarah Millican (born 1975)
Spike Milligan (1918–2002)
Florence Mills (1896–1927)
Andy Milonakis (born 1976)
Tim Minchin (born 1975)
Brian Miner (born 1981)
Hasan Minhaj (born 1985)
Jerry Minor (born 1969)
Dan Mintz (born 1981)
Christopher Mintz-Plasse (born 1989)
Matt Mira (born 1983)
Lin-Manuel Miranda (born 1980)
Eugene Mirman (born 1975)
David Mitchell (born 1974)
Duke Mitchell (1926–1981)
Finesse Mitchell (born 1972)
Kel Mitchell (born 1978)
Mike Mitchell (born 1982)
Aditi Mittal
Michael Mittermeier (born 1966)
Jerod Mixon (born 1981)
Katy Mixon (born 1981)
Kenice Mobley (born 1985)
Colin Mochrie (born 1957)
Mehran Modiri (born 1967)
Alex Moffat (born 1982)
Kausar Mohammed (born 1992)
Nick Mohammed (born 1980)
Jay Mohr (born 1970)
Al Molinaro (1919–2015)
Richard Moll (1943–2023)
John Moloney
Dominic Monaghan (born 1976)
Mo'Nique (born 1967)
Bob Monkhouse (1928–2003)
Elizabeth Montgomery (1933–1995)
Lucy Montgomery (born 1975)
Adam Montoya (aka) SeaNanners (born 1984)
Lou Moon
Kyle Mooney (born 1984)
Nate Mooney
Paul Mooney (1941–2021)
Christina Moore (born 1973)
Dudley Moore (1935–2002)
Mary Tyler Moore (1936–2017)
Michael Moore (born 1954)
Phil Moore (born 1961)
Rudy Ray Moore (1927–2008)
Tim Moore (1887–1958)
Trevor Moore (1980–2021)
Victor Moore (1876–1962)
Agnes Moorehead (1900–1974)
Maribeth Monroe (born 1978)
Steve Monroe (born 1972)
Natalie Morales (born 1985)
Dylan Moran (born 1971)
George Moran (1881–1949)
Polly Moran (1883–1952)
Rick Moranis (born 1953)
Dave Mordal (born c. 1950–1960s)
Eric Morecambe (1926–1984)
German Moreno (1933–2016)
Harley Morenstein (born 1985)
Dermot Morgan (1952–1998)
Diane Morgan (born 1975)
Elliott Morgan (born 1987)
John Morgan (1930–2004)
Leanne Morgan (born 1965)
Matt Morgan (born 1977)
Tracy Morgan (born 1968)
Richie Moriarty (born 1980)
Brent Morin (born 1986)
Pat Morita (1932–2005)
Sam Morril (born 1986)
Brad Morris (born 1975)
Chris Morris (born 1965)
Garrett Morris (born 1937)
Lamorne Morris (born 1983)
Seth Morris (born 1970)
Neil Morrissey (born 1962)
Eleanor Morton
Howard Morton (1925–1997)
Lew Morton
Laci Mosley (born 1991)
Don Most (born 1953)
Zero Mostel (1915–1977)
José Sánchez Mota (born 1965)
Tahj Mowry (born 1986)
Matthew Moy (born 1984)
Bobby Moynihan (born 1977)
Teacher Mpamire (born 1983)
John Mulaney (born 1982)
Martin Mull (1943–2024)
Megan Mullally (born 1958)
Mitch Mullany (1968–2008)
Neil Mullarkey (born 1961)
Ina Müller (born 1965)
Brennan Lee Mulligan (born 1988)
Annie Mumolo (born 1973)
Noah Munck (born 1996)
Olivia Munn (born 1980)
Simon Munnery (born 1967)
Richard Murdoch (1907–1990)
Annie Murphy (born 1986)
Charlie Murphy (1959–2017)
Colin Murphy (born 1968)
Eddie Murphy (born 1961)
Kevin Murphy (born 1956)
Larry Murphy (born 1972)
Morgan Murphy (born 1981)
Noel Murphy (born 1961)
Al Murray (born 1968)
Bill Murray (born 1950)
James Murray (born 1976)
Jan Murray (1916–2006)
Joel Murray (born 1963)
Lorenzo Music (1937–2001)
Erik Myers
Mike Myers (born 1963)
Arden Myrin (born 1973)
N
Jim Nabors (1930–2017)
David Nagle (aka) Nogla (born 1992)
Suzy Nakamura (born 1968)
Kevin Nalty (born 1969)
Leonardo Nam (born 1979)
Philomaine Nanema (born 1982)
Aparna Nancherla (born 1982)
Kumail Nanjiani (born 1978)
Paul Nardizzi
Jason Narvy (born 1974)
Amber Nash (born 1977)
Jason Nash (born 1973)
Niecy Nash (born 1970)
Rex Navarette (born 1969)
Vhong Navarro (born 1977)
Henry Naylor (born 1966)
Kunal Nayyar (born 1981)
Cliff Nazarro (1904–1961)
Kevin Nealon (born 1953)
Lucas Neff (born 1985)
Taylor Negron (1957–2015)
Jamar Neighbors (born 1986)
Bob Nelson (born 1958)
Bridget Jones Nelson (born 1964)
Craig T. Nelson (born 1944)
Michael J. Nelson (born 1964)
Ozzie Nelson (1906–1975)
Thomas Nelstrop (born 1980)
Nick Nemeroff (1989–2022)
Nephew Tommy (born 1967)
Felipe Neto (born 1988)
Bebe Neuwirth (born 1958)
Kyle Newacheck (born 1984)
Bob Newhart (1929–2024)
Griffin Newman (born 1989)
Laraine Newman (born 1952)
Robert Newman (born 1964)
Tawny Newsome (born 1983)
Bert Newton (1938–2021)
Lee Newton (born 1985)
Desus Nice (born 1981)
Phil Nichol
Brittani Nichols (born 1988)
Mike Nichols (1931–2014)
Rhys Nicholson (born 1990)
Leslie Nielsen (1926–2010)
Trevor Noah (born 1984)
Ross Noble (born 1976)
Coleen Nolan (born 1965)
Katie Nolan (born 1987)
Henry Normal (born 1956)
Hayley Marie Norman (born 1989)
Mark Normand (born 1983)
Nolan North (born 1970)
Graham Norton (born 1963)
Jim Norton (born 1968)
Duncan Norvelle (born 1958)
Tig Notaro (born 1971)
B. J. Novak (born 1979)
Jacqueline Novak (born 1982)
Kayvan Novak (born 1978)
Don Novello (born 1943)
Dieter Nuhr (born 1960)
Luke Null (born 1990)
Whindersson Nunes (born 1995)
Oscar Nunez (born 1958)
Ego Nwodim (born 1988)
Bill Nye (born 1955)
Louis Nye (1913–2005)
O
Jay Oakerson (born 1977)
Matt Oberg (born 1976)
Dara Ó Briain (born 1972)
Conan O'Brien (born 1963)
Katie O'Brien (born 1983)
Mike O'Brien (born 1976)
Jerry O'Connell (born 1974)
Ryan O'Connell (born 1986)
Carroll O'Connor (1924–2001)
Des O'Connor (1932–2020)
Donald O'Connor (1925–2003)
Sean O'Connor (born 1985)
Bill Oddie (born 1941)
Bob Odenkirk (born 1962)
Claudia O'Doherty (born 1983)
David O'Doherty (born 1975)
Mark O'Donnell (1954–2012)
Rosie O'Donnell (born 1962)
Steve O'Donnell (born 1954)
Michael O'Donoghue (1940–1994)
Chris O'Dowd (born 1979)
Nick Offerman (born 1970)
Paul O'Grady (1955–2023)
Ardal O'Hanlon (born 1965)
Catherine O'Hara (born 1954)
Jim O'Heir (born 1962)
John O'Hurley (born 1954)
Atsuko Okatsuka (born 1988)
Tricia O'Kelley (born 1968)
Earl Okin (born 1947)
Amy Okuda (born 1989)
John Oliver (born 1977)
Alberto Olmedo (1933–1988)
Ole Olsen (1892–1963)
Kaitlin Olson (born 1975)
Conner O'Malley (born 1986)
Mike O'Malley (born 1966)
Timothy Omundson (born 1969)
Patrice O'Neal (1969–2011)
Ed O'Neill (born 1946)
Steve Oram (born 1973)
Yvonne Orji (born 1983)
Taylor Ortega (born 1989)
Zak Orth (born 1970)
Andrew Orvedahl (born 1976)
Barunka O'Shaughnessy
Andi Osho (born 1973)
Aida Osman (born 1996)
David Ossman (born 1936)
Dan Oster (born 1981)
Patton Oswalt (born 1969)
Cheri Oteri (born 1962)
Rick Overton (born 1954)
Bill Owen (1914–1999)
Gary Owen (born 1974)
Larry Owens
Zac Oyama (born 1987)
Gil Ozeri
P
Jack Paar (1918–2004)
Frankie Pace
Celia Pacquola (born 1983)
Anthony Padilla (born 1987)
Ashley Padilla (born 1993)
Robin Padilla (born 1969)
Monica Padman (born 1987)
Elliot Page (born 1987)
LaWanda Page (1920–2002)
Natalie Palamides (born 1990)
Brian Palermo
Ron Palillo (1949–2012)
Michael Palin (born 1943)
Adam Pally (born 1982)
Candy Palmater (1968–2021)
Sam Pancake (born 1964)
Maulik Pancholy (born 1974)
Angelica Panganiban (born 1986)
Franklin Pangborn (1889–1958)
John Pankow (born 1954)
Tom Papa (born 1968)
Yannis Pappas (born 1975)
John Paragon (1954–2021)
Zhubin Parang (born 1981)
Jimmy Pardo (born 1966)
Ron Pardo (born 1967)
Lennon Parham (born 1976)
Sandeep Parikh (born 1980)
Randall Park (born 1974)
Sydney Park (born 1997)
Nicole Parker (born 1978)
Pardis Parker
Paula Jai Parker (born 1969)
Sarah Jessica Parker (born 1965)
Trey Parker (born 1969)
Katherine Parkinson (born 1977/1978)
Chris Parnell (born 1967)
Grace Parra (born 1984)
Rachel Parris (born 1984)
Andy Parsons (born 1967)
Jim Parsons (born 1973)
Karyn Parsons (born 1966)
Jean-Claude Pascal (1927–1992)
Sara Pascoe (born 1981)
Joe Pasquale (born 1961)
David Pasquesi (born 1960)
Bastian Pastewka (born 1972)
Kasha Patel (born 1991)
Nimesh Patel (born 1986)
Punam Patel (born 1993)
Ravi Patel (born 1978)
Edi Patterson (born 1972)
Jake Paul (born 1997)
Pat Paulsen (1927–1997)
Rob Paulsen (born 1956)
David Paymer (born 1954)
Allen Payne (born 1968)
Khary Payton (born 1972)
Christina Pazsitzky (born 1976)
Ray Peacock (born 1973)
Trevor Peacock (1931–2021)
Jack Pearl (1894–1982)
Minnie Pearl (1912–1996)
Zack Pearlman (born 1988)
Josh Peck (born 1986)
Artemis Pebdani (born 1977)
Ron Pederson (born 1978)
Nasim Pedrad (born 1981)
Jordan Peele (born 1979)
Simon Pegg (born 1970)
Paula Pell (born 1963)
Jessimae Peluso (born 1982)
Johnny Pemberton (born 1981)
Steve Pemberton (born 1967)
Kal Penn (born 1977)
Joe Penner (1904–1941)
Eddie Pepitone (born 1958)
Jack Pepper (1902–1979)
Joe Pera (born 1988/1989)
Kevin Pereira (born 1982)
Chelsea Peretti (born 1978)
Danielle Perez
Ion Perez (born 1990)
Dewayne Perkins (born 1990)
Kathleen Rose Perkins (born 1974)
Sue Perkins (born 1969)
Rhea Perlman (born 1948)
Matthew Perry (1969–2023)
Tyler Perry (born 1969)
Jon Pertwee (1919–1996)
Tammy Pescatelli (born 1969)
Melissa Peterman (born 1971)
Bernadette Peters (born 1948)
Russell Peters (born 1970)
Paul Petersen (born 1945)
Cassandra Peterson (born 1951)
Alexandra Petri (born 1988)
Dat Phan (born 1975)
Jay Pharoah (born 1987)
J.J. Philbin (born 1974)
Regis Philbin (1931–2020)
Busy Philipps (born 1979)
Emo Philips (born 1956)
Henry Phillips (born 1969)
Sally Phillips (born 1970)
Philomaine Nanema, aka Philo (born 1982)
Dannah Phirman (born 1975)
Andrew Phung (born 1984)
Bobby Pickett (1938–2007)
Chonda Pierce (born 1960)
David Hyde Pierce (born 1959)
Amy Pietz (born 1969)
Karl Pilkington (born 1972)
Daniella Pineda (born 1987)
John Pinette (1964–2014)
Ryan Pinkston (born 1988)
Danielle Pinnock (born 1988)
Joe Piscopo (born 1951)
ZaSu Pitts (1894–1963)
Jeremy Piven (born 1965)
Nigel Planer (born 1953)
Ben Platt (born 1993)
Aubrey Plaza (born 1984)
Amy Poehler (born 1971)
Greg Poehler (born 1974)
Jon Pointing (born 1986)
Pokwang (born 1972)
Kevin Pollak (born 1957)
Mike Pollock (born 1965)
Jorge Porcel (1936–2006)
Javier Portales (1937–2003)
Chris Porter (born 1979)
Don Porter (1912–1997)
Lucy Porter (born 1973)
Tommy Pope (born 1979)
Brian Posehn (born 1966)
Parker Posey (born 1968)
Tom Poston (1921–2007)
Lauren Potter (born 1990)
Annie Potts (born 1952)
Paula Poundstone (born 1959)
Dan Povenmire (born 1963)
Esther Povitsky (born 1988)
Chris Powell (born 1983)
Dana Powell (born 1974)
Dante Powell (born 1987/1988)
Glen Powell (born 1988)
DeStorm Power (born 1982)
Navin Prabhakar
John Prats (born 1984)
Chris Pratt (born 1979)
Guy Pratt (born 1962)
Kyla Pratt (born 1986)
Laura Prepon (born 1980)
Jaime Pressly (born 1977)
Amber Preston
Eric Price (born 1974)
Tom Price (born 1980)
Freddie Prinze (1954–1977)
Freddie Prinze Jr. (born 1976)
Kiri Pritchard Mclean (born 1986)
Lauren Pritchard (born 1977)
Michael Pritchard (born 1950)
Philip Proctor (born 1940)
Markus Maria Profitlich (born 1960)
Greg Proops (born 1959)
Mark Proksch (born 1978)
Paul Provenza (born 1957)
Kelly Pryce (born 1986/1987)
DJ Pryor (born 1988)
Richard Pryor (1940–2005)
Cristina Pucelli (born 1969)
Danny Pudi (born 1979)
Rolo Puente (1939–2011)
Lucy Punch (born 1977)
Steve Punt (born 1962)
Missi Pyle (born 1972)
Q
DJ Qualls (born 1978)
Caroline Quentin (born 1960)
Adam Quesnell (born 1981/1982)
Steven Michael Quezada (born 1963)
Kate Quigley (born 1982)
Brian Quinn (born 1976)
Colin Quinn (born 1959)
Frankie Quiñones (born 1983)
Rufa Mae Quinto (born 1978)
Pauline Quirke (born 1959)
R
Stefan Raab (born 1966)
Allyn Rachel (born 1983)
Alan Rachins (1942–2024)
Gilda Radner (1946–1989)
Josh Radnor (born 1974)
Kat Radley (born 1985)
Charlotte Rae (1926–2018)
Issa Rae (born 1985)
Rags Ragland (1905–1946)
Jeff Ragsdale (1971–2023)
Randy Rainbow (born 1981)
Mary Lynn Rajskub (born 1971)
Sheryl Lee Ralph (born 1956)
Louis Ramey
Harold Ramis (1944–2014)
Rachel Ramras (born 1974)
Chris Ramsey (born 1986)
Franchesca Ramsey (born 1983)
Tony Randall (1920–2004)
Joe Randazzo (born 1978)
Frank Randle (1901–1957)
Romesh Ranganathan (born 1978)
Richard Rankin (born 1983)
Stephen Rannazzisi (born 1977)
Andrew Rannells (born 1978)
Esnyr Ranollo (born 2001)
Michael Rapaport (born 1970)
June Diane Raphael (born 1980)
Jim Rash (born 1971)
Allison Raskin (born 1989)
Meaghan Rath (born 1986)
Connor Ratliff
John Ratzenberger (born 1947)
Melissa Rauch (born 1980)
Raven-Symoné (born 1985)
Donnell Rawlings (born 1968)
Adam Ray (born 1982)
Jonah Ray (born 1981)
Ted Ray (1905–1977)
Martha Raye (1916–1994)
Al Read (1909–1987)
Howard Read (born 1984)
Diona Reasonover (born 1992)
Spoken Reasons (born 1988)
Andreas Rebers (born 1958)
Chris Redd (born 1985)
Jasper Redd (born 1979)
JR Reed (born 1967)
Jon Reep (born 1972)
Vic Reeves (born 1959)
Brian Regan (born 1958)
Jason Reich
Leo Reich (born 1998)
Sam Reich (born 1984)
Anne Reid (born 1935)
Noah Reid (born 1987)
Tara Reid (born 1975)
Tim Reid (born 1944)
Caitlin Reilly (born 1989)
Charles Nelson Reilly (1931–2007)
John C. Reilly (born 1965)
Carl Reiner (1922–2020)
Rob Reiner (born 1947)
Paul Reiser (born 1956)
Ivan Reitman (1946–2022)
Leah Remini (born 1970)
Roy Rene (1892–1954)
Adam Resnick
Retta (born 1970)
Paul Reubens (1952–2023)
Willie Revillame (born 1961)
Tony Revolori (born 1996)
Simon Rex (born 1974)
Gladys Reyes (born 1977)
Alex Reymundo
Manilyn Reynes (born 1972)
Burt Reynolds (1936–2018)
John Reynolds (born 1991)
Rick Reynolds (born 1951)
Ryan Reynolds (born 1976)
Caroline Rhea (born 1964)
Erica Rhodes (born 1983)
Tom Rhodes (born 1967)
Alfonso Ribeiro (born 1971)
Giovanni Ribisi (born 1974)
Alison Rich
Katie Rich
Simon Rich (born 1984)
Jeff Richards (born 1974)
Michael Richards (born 1949)
April Richardson (born 1979)
Jon Richardson (born 1982)
Matt Richardson (born 1991)
Miranda Richardson (born 1958)
Sam Richardson (born 1984)
Shane Richie (born 1964)
Mathias Richling (born 1953)
Jeff Richmond (born 1961)
Andy Richter (born 1966)
Laurence Rickard (born 1975)
Don Rickles (1926–2017)
Matt Rife (born 1995)
Daniel Rigby (born 1982)
Rob Riggle (born 1970)
Gina Riley (born 1961)
Jack Riley (1935–2016)
Lisa Riley (born 1976)
Kelly Ripa (born 1970)
Jason Ritter (born 1980)
John Ritter (1948–2003)
Tyler Ritter (born 1985)
Al Ritz (1901–1965)
Harry Ritz (1907–1986)
Jimmy Ritz (1904–1985)
Emilio Rivera (born 1961)
Joan Rivers (1933–2014)
Rowland Rivron (born 1958)
Steve Rizzo
Ted Robbins (born 1955)
Lyda Roberti (1906–1938)
Doris Roberts (1925–2016)
Ian Roberts (born 1965)
John Roberts (born 1971)
Jeanne Robertson (1943–2021)
Noah Robertson (born 1983)
Craig Robinson (born 1971)
Joe Robinson (born 1968)
Leonard Robinson
Phoebe Robinson (born 1984)
Tim Robinson (born 1981)
Linda Robson (born 1958)
Mo Rocca (born 1969)
Chris Rock (born 1965)
Tony Rock (born 1974)
Charles Rocket (1949–2005)
Glenn Rockowitz (born 1970)
Aida Rodriguez (born 1977)
Guillermo Rodriguez (born 1971)
Paul Rodriguez (born 1955)
Valente Rodriguez (born 1964)
Daniel Roebuck (born 1963)
Joe Rogan (born 1967)
Lauren Miller Rogen (born 1982)
Seth Rogen (born 1982)
Matt Rogers (born 1990)
Will Rogers (1879–1935)
Justin Roiland (born 1980)
Henry Rollins (born 1961)
Freddie Roman (1937–2022)
Rick Roman (1966–1992)
Larry Romano (born 1963)
Ray Romano (born 1957)
Michael Roof (1976–2009)
Mickey Rooney (1920–2014)
Rebecca Root (born 1969)
Stephen Root (born 1951)
George Roper (1934–2003)
Tony Rosato (1954–2017)
Patty Rosborough
Rose Marie (1923–2017)
Andrea Rosen (born 1974)
Michael Rosenbaum (born 1972)
Tom Rosenthal (born 1988)
Jeffrey Ross (born 1965)
Jonathan Ross (born 1960)
Lonny Ross (born 1978)
Tracee Ellis Ross (born 1972)
Steve Rossi (1932–2014)
Eli Roth (born 1972)
Barry Rothbart (born 1983)
Natasha Rothwell (born 1980)
Mitch Rouse (born 1964)
Patricia Routledge (born 1929)
Dan Rowan (1922–1987)
Patsy Rowlands (1931–2005)
Ben Roy (born 1979)
Alex Rubens
Michael Rubens
Alan Ruck (born 1956)
Paul Rudd (born 1969)
Rita Rudner (born 1953)
Jon Rudnitsky (born 1989)
Maya Rudolph (born 1972)
Amber Ruffin (born 1979)
Kevin Ruf (born 1961)
Sara Rue (born 1979)
Charlie Ruggles (1886–1970)
Debra Jo Rupp (born 1951)
Chris Rush (1946–2018)
Deborah Rush (born 1954)
Lenny Rush (born 2009)
Willie Rushton (1937–1996)
Anna Russell (1911–2006)
Mark Russell (1932–2023)
Nipsey Russell (1918–2005)
Rosalind Russell (1907–1976)
Paul Rust (born 1981)
Nick Rutherford (born 1985)
Irene Ryan (1902–1973)
Katherine Ryan (born 1983)
Roz Ryan (born 1951)
Ryan Bang (born 1991)
Stevie Ryan (1984–2017)
Tommy Ryman (born 1983)
S
Thomas Sadoski (born 1976)
Jerry Sadowitz (born 1961)
Bryan Safi
Katey Sagal (born 1954)
Bob Saget (1956–2022)
Tami Sagher
Mort Sahl (1927–2021)
Nichole Sakura (born 1989)
Rosa Salazar (born 1985)
Charles "Chic" Sale (1885–1936)
Soupy Sales (1926–2009)
Peter Sallis (1921–2017)
Tony Sam
Andy Samberg (born 1978)
Sugar Sammy (born 1976)
Angus Sampson (born 1978/1979)
Paul Sand (born 1932)
Beverly Sanders (born 1940)
Adam Sandler (born 1966)
Isabel Sanford (1917–2004)
Randy Santiago (born 1960)
Andrew Santino (born 1983)
Carlos Santos (born 1986)
Nico Santos (born 1979)
Horatio Sanz (born 1969)
Herb Sargent (1923–2005)
Martin Sargent (born 1975)
Will Sasso (born 1975)
Drake Sather (1959–2004)
Sabrina Sato (born 1981)
Rajiv Satyal (born 1976)
Jennifer Saunders (born 1958)
Andrea Savage (born 1973)
Ben Savage (born 1980)
Fred Savage (born 1976)
Julia Sawalha (born 1968)
Alexei Sayle (born 1952)
Prunella Scales (born 1932)
Brendan Scannell (born 1990)
Kristen Schaal (born 1978)
Sara Schaefer (born 1978)
Akiva Schaffer (born 1977)
Jackie Schaffer
Jeff Schaffer (born 1970)
Lewis Schaffer (born 1957)
Tom Scharpling (born 1969)
Mary Scheer (born 1963)
Paul Scheer (born 1976)
Ronnie Schell (born 1931)
Gus Schilling (1908–1957)
Robert Schimmel (1950–2010)
Hayden Schlossberg (born 1978)
Art Paul Schlosser (born 1960)
Wilfried Schmickler (born 1954)
Harald Schmidt (born 1957)
Jana Schmieding (born 1981)
Ralf Schmitz (born 1974)
Danielle Schneider (born 1975)
Helge Schneider (born 1955)
Martin Schneider (born 1964)
Rob Schneider (born 1963)
Sarah Schneider (born 1983)
Stephen Schneider (born 1980)
Barbara Schöneberger (born 1974)
Avery Schreiber (1935–2002)
Paul Schrier (born 1970)
Atze Schröder (born 1965)
Olaf Schubert (born 1967)
Richard Schull (1929–1999)
Andrew Schulz (born 1983)
Amy Schumer (born 1981)
Michael Schur (born 1975)
Leon Schuster (born 1951)
Samba Schutte (born 1983)
Ben Schwartz (born 1981)
Jason Schwartzman (born 1980)
Esther Schweins (born 1970)
David Schwimmer (born 1966)
Peter Scolari (1955–2021)
Brian Scolaro (born 1973)
Adam Scott (born 1973)
Reid Scott (born 1977)
Tom Everett Scott (born 1970)
Seann William Scott (born 1976)
Rory Scovel (born 1980)
Amanda Seales (born 1981)
Kenny Sebastian (born 1990)
Harry Secombe (1921–2001)
Amy Sedaris (born 1961)
Sam Seder (born 1966)
Rhea Seehorn (born 1972)
George Segal (1934–2021)
Jason Segel (born 1980)
Tom Segura (born 1979)
Streeter Seidell (born 1982)
Jerry Seinfeld (born 1954)
Scott Seiss (born 1994)
Jeffery Self (born 1987)
Peter Sellers (1925–1980)
Larry Semon (1889–1928)
Mack Sennett (1880–1960)
Rachel Sennott (born 1995)
Peter Serafinowicz (born 1972)
Josh Server (born 1979)
Joshua Seth (born 1970)
Glenn Shadix (1952–2010)
Ross Shafer (born 1954)
Paul Shaffer (born 1949)
Ari Shaffir (born 1974)
Ahir Shah (born 1990)
Tony Shalhoub (born 1953)
Garry Shandling (1949–2016)
Jake Shane (born 1999)
Paul Shane (1940–2013)
Rekha Shankar (born 1990)
Molly Shannon (born 1964)
Kapil Sharma (born 1981)
Josh Sharp (born 1987)
Timm Sharp (born 1978)
William Shatner (born 1931)
Alia Shawkat (born 1989)
Dick Shawn (1923–1987)
Wallace Shawn (born 1943)
Lin Shaye (born 1943)
Brendan Schaub (born 1983)
Harry Shearer (born 1943)
Reece Shearsmith (born 1969)
Charlie Sheen (born 1965)
Derek Sheen (born 1970/1971)
David Sheffield (born 1948)
Angela V. Shelton (born 1970)
Dax Shepard (born 1975)
Sherri Shepherd (born 1967)
Waen Shepherd (born 1971)
Eden Sher (born 1991)
Rondell Sheridan (born 1958)
Allan Sherman (1924–1973)
Sarah Sherman (born 1993)
Brad Sherwood (born 1964)
Tom Shillue (born 1966)
Ken Shimura (1950–2020)
Kevin Shinick (born 1969)
Iliza Shlesinger (born 1983)
Craig Shoemaker (born 1962)
Pauly Shore (born 1968)
Sammy Shore (1928–2019)
Martin Short (born 1950)
Pat Shortt (born 1967)
Michael Showalter (born 1970)
Wil Shriner (born 1953)
Jimmy Shubert
Rosie Shuster (born 1950)
Ritch Shydner (born 1952)
Ali Siddiq (born 1973/1974)
Emma Sidi (born 1991)
George Sidney (1876–1945)
Denny Siegel
Darien Sills-Evans (born 1974)
Laura Silverman (born 1966)
Sarah Silverman (born 1970)
Phil Silvers (1911–1985)
Arthur Simeon (born 1974)
John Simmit (born 1963)
Sam Simmons (born 1977)
Hannah Simone (born 1980)
Timothy Simons (born 1978)
Jimmi Simpson (born 1975)
Joan Sims (1930–2001)
Sinbad (born 1956)
Akaash Singh (born 1984)
Lilly Singh (born 1988)
Hella von Sinnen (born 1959)
Tiya Sircar (born 1982)
Dave Sirus
Red Skelton (1913–1997)
Benito Skinner (born 1993)
Frank Skinner (born 1957)
Chuck Sklar
Jenny Slate (born 1982)
Tony Slattery (1959–2025)
Jonathan Slavin (born 1969)
Bobby Slayton (born 1955)
Dulcé Sloan (born 1983)
Lindsay Sloane (born 1977)
Daniel Sloss (born 1990)
Veronika Slowikowska (born 1995)
Brendon Small (born 1975)
Lucien "Saluche" Small (1948–2007)
Andy Smart (1959–2023)
Jean Smart (born 1951)
Robert Smigel (born 1960)
Rickey Smiley (born 1968)
Yakov Smirnoff (born 1951)
Arthur Smith (born 1954)
Brandon Mychal Smith (born 1989)
Brian Thomas Smith (born 1977)
Daniel Browning Smith (born 1979)
DeAnne Smith (born 1979)
Joe Smith (1884–1981)
Kevin Smith (born 1970)
Kurtwood Smith (born 1943)
Linda Smith (1958–2006)
Margaret Smith
Phyllis Smith (born 1949)
Steve Smith (born 1945)
Will Smith (born 1968)
Will Smith (born 1971)
Yeardley Smith (born 1964)
JB Smoove (born 1965)
Cobie Smulders (born 1982)
Dana Snyder (born 1973)
Liza Snyder (born 1968)
David So (born 1987)
Barry Sobel (born 1959)
Betsy Sodaro (born 1984)
Dan Soder (born 1983)
John Solomon (born 1970)
Laura Solon (born 1979)
Lion Solser (1877–1915)
Kira Soltanovich (born 1973)
Suzanne Somers (1946–2023)
Rich Sommer (born 1978)
Sommore (born 1966)
Karan Soni (born 1989)
Gianmarco Soresi (born 1989)
Arleen Sorkin (1955–2023)
Ann Sothern (1909–2001)
Tito Sotto (born 1948)
Vic Sotto (born 1954)
Karla Souza (born 1985)
Kevin Spacey (born 1959)
David Spade (born 1964)
Hal Sparks (born 1969)
Ron Sparks (born 1977)
Aries Spears (born 1975)
Rachel Specter (born 1980)
Chris Spencer (born 1968)
Dave Spikey (born 1950)
Brent Spiner (born 1949)
Justin Spitzer
Thomas Spitzer (born 1988)
Emily Spivey (born 1971)
Brian Stack (born 1964)
Jessica St. Clair (born 1976)
Megan Stalter (born 1990)
John Stamos (born 1963)
Arnold Stang (1918–2009)
Doug Stanhope (born 1967)
Vivian Stanshall (1943–1995)
Martin Starr (born 1982)
Jen Statsky (born 1985)
Mark Steel (born 1960)
Steve Steen (born 1954)
Mary Steenburgen (born 1953)
Rob Stefaniuk (born 1971)
Axel Stein (born 1982)
Ben Stein (born 1944)
David Steinberg (born 1942)
Beth Stelling (born 1986)
Brian Stepanek (born 1971)
Jason Stephens
Pamela Stephenson (born 1949)
Skip Stephenson (1940–1992)
Ford Sterling (1883–1939)
Mindy Sterling (born 1953)
Howard Stern (born 1954)
Steve-O (born 1974)
Michael Fenton Stevens (born 1958)
Brody Stevens (1970–2019)
Ray Stevens (born 1939)
French Stewart (born 1964)
Jon Stewart (born 1962)
Paul Stewart (1908–1986)
David Ogden Stiers (1942–2018)
Ryan Stiles (born 1959)
Ben Stiller (born 1965)
Jerry Stiller (1927–2020)
Jeff Stilson (born 1959)
Hannah Stocking (born 1992)
Fred Stoller (born 1958)
Nicholas Stoller (born 1976)
Matt Stone (born 1971)
Eric Stonestreet (born 1971)
Larry Storch (1923–2022)
Gale Storm (1922–2009)
Moses Storm (born 1990)
Tom Stourton (born 1987)
Ryan Stout (born 1982)
Michael Strahan (born 1971)
Cordula Stratmann (born 1963)
Paul Strickland (born ?)
Cecily Strong (born 1984)
Rider Strong (born 1979)
Jessica Stroup (born 1986/1987)
Jud Strunk (1936–1981)
James Patrick Stuart (born 1968)
Geoff Stults (born 1977)
Jason Sudeikis (born 1975)
Chris Sugden (born 1952)
Alec Sulkin (born 1973)
Nancy Sullivan (born 1969)
Nicole Sullivan (born 1970)
Marc Summers (born 1951)
Jiaoying Summers (born 1990)
Slim Summerville (1892–1946)
Tika Sumpter (born 1980)
Josh Sundquist (born 1984)
Ethan Suplee (born 1976)
Kevin Sussman (born 1970)
Mena Suvari (born 1979)
Nick Swardson (born 1976)
John Swartzwelder (born 1949)
Barret Swatek (born 1977)
Jim Sweeney (born 1955)
Julia Sweeney (born 1959)
Steve Sweeney (born 1949)
Terry Sweeney (born 1950)
C. C. Swiney (born 1981)
JoAnna Garcia Swisher (born 1979)
Eric Sykes (1923–2012)
Wanda Sykes (born 1964)
Cynthia Szigeti (1949–2016)
Magda Szubanski (born 1961)
T
Jorma Taccone (born 1977)
George Takei (born 1937)
Rich Talarico (born 1973)
Jill Talley (born 1962)
Chris Tallman (born 1970)
Kerry Talmage (1963–2004)
Kapil Talwalkar (born 1993)
Danny Tamberelli (born 1982)
Jeffrey Tambor (born 1944)
Jimmy Tarbuck (born 1940)
Liza Tarbuck (born 1964)
Carl Tart (born 1989)
Drew Tarver (born 1986)
Emily Tarver (born 1982)
Masashi Tashiro (born 1956)
Catherine Tate (born 1969)
Jacques Tati (1907–1982)
Jimmy Tatro (born 1992)
Jim Tavaré (born 1963)
Christine Taylor (born 1971)
Clarice Taylor (1917–2011)
Ellie Taylor (born 1983)
Johnny Taylor Jr.
Maddie Taylor (born 1966)
Paul Taylor (born 1986)
Renée Taylor (born 1933)
Rip Taylor (1931–2019)
Tariq Teddy
Teller (born 1948)
Miles Teller (born 1987)
Judy Tenuta (1949–2022)
Steve Terreberry (born 1987)
Maria Thayer (born 1975)
Robin Thede (born 1979)
Justin Theroux (born 1971)
Alan Thicke (1947–2016)
Terry-Thomas (1911–1990)
Danny Thomas (1914–1991)
Dave Thomas (born 1949)
Eddie Kaye Thomas (born 1980)
Jay Thomas (1948–2017)
Joe Thomas (born 1983)
Josh Thomas (born 1987)
Kathryn Renée Thomas
Mark Thomas (born 1967)
Marlo Thomas (born 1937)
Michelle Thomas (1968–1998)
Vinny Thomas (born 1997)
Whitmer Thomas (born 1989)
Tim Thomerson (born 1946)
Greg Thomey (born 1961)
Bobb'e J. Thompson (born 1996)
Dave Thompson (born 1959)
Emma Thompson (born 1959)
Josh Robert Thompson (born 1975)
Kenan Thompson (born 1978)
Lea Thompson (born 1961)
Scott Thompson (born 1959)
Siobhan Thompson (born 1984)
Nick Thune (born 1979)
Baratunde Thurston (born 1977)
Sarah Thyre (born 1968)
Kai Tier
Tommy Tiernan (born 1969)
Greta Titelman (born 1990)
Christopher Titus (born 1964)
Mukesh Tiwari (born 1969)
Stephen Tobolowsky (born 1951)
Thelma Todd (1905–1935)
Sandi Toksvig (born 1958)
Steph Tolev (born 1985)
Judy Toll (1958–2002)
Allison Tolman (born 1981)
Jes Tom (born 1990)
Lily Tomlin (born 1939)
David Tomlinson (1917–2000)
Taylor Tomlinson (born 1993)
Paul F. Tompkins (born 1968)
TomSka (born 1990)
Paul Tonkinson (born 1969)
Barry Took (1928–2002)
Shayne Topp (born 1991)
Rip Torn (1931–2019)
Nate Torrence (born 1977)
Julio Torres (born 1987)
Liz Torres (born 1947)
Guy Torry (born 1969)
Joe Torry (born 1965)
Daniel Tosh (born 1975)
Josie Totah (born 2001)
Robert Townsend (born 1957)
Jerry Trainor (born 1977)
Natalie Tran (born 1986)
Robin Tran (born 1986)
Rosie Tran (born 1984)
Tien Tran (born 1987)
Nancy Travis (born 1961)
Jesus Trejo (born 1986)
Harry Trevaldwyn (born 1994)
Angela Trimbur (born 1981)
Tommy Trinder (1909–1989)
Chloe Troast (born 1997)
Verne Troyer (1969–2018)
Duncan Trussell (born 1974)
Nora Tschirner (born 1981)
Irene Tu (born 1992)
Bryan Tucker
Chris Tucker (born 1971)
Alan Tudyk (born 1971)
Jane Turner (born 1960)
Toby Turner (born 1985)
Ben Turpin (1869–1940)
Aisha Tyler (born 1970)
U
Alanna Ubach (born 1975)
Bob Uecker (born 1935)
Ikechukwu Ufomadu (born 1986)
Tracey Ullman (born 1959)
Sheryl Underwood (born 1963)
Brian Unger (born 1965)
Gabrielle Union (born 1972)
Stanley Unwin (1911–2002)
James Urbaniak (born 1963)
Michael Urie (born 1980)
V
John Valby, aka Dr. Dirty (born 1944)
Wilmer Valderrama (born 1980)
Ramón Valdés (1923–1988)
Gary Valentine (born 1961)
Billy Van (1934–2003)
Dick Van Dyke (born 1925)
Jerry Van Dyke (1931–2018)
Dick Van Patten (1928–2015)
Danitra Vance (1954–1994)
Nia Vardalos (born 1962)
Tuesday Vargas (born 1980)
Janet Varney (born 1976)
Jim Varney (1949–2000)
Johnny Vaughan (born 1966)
Baron Vaughn (born 1980)
Vince Vaughn (born 1970)
Milana Vayntrub (born 1987)
Radhika Vaz (born 1973)
Jennifer Veal (born 1991)
Sindhu Vee (born 1969)
Johnny Vegas (born 1970)
Ricky Velez (born 1989)
Reginald VelJohnson (born 1952)
Vinny Vella (1947–2019)
Prashanth Venkataramanujam (born 1987)
Milo Ventimiglia (born 1977)
Sofia Vergara (born 1972)
Tom Verica (born 1964)
Andrée Vermeulen (born 1982)
Jackie Vernon (1924–1987)
Wally Vernon (1904–1970)
Vice Ganda (born 1976)
Eva Victor
John Viener (born 1972)
Gillian Vigman (born 1972)
Kulap Vilaysack (born 1980)
Nova Villa (born 1946)
Carlos Villagrán (born 1942)
Buboy Villar (born 1998)
Melissa Villaseñor (born 1987)
Hervé Villechaize (1943–1993)
Tim Vine (born 1967)
Geraldine Viswanathan (born 1995)
Jon Vitti (born 1960)
Édgar Vivar (born 1944)
Paul C. Vogt (born 1964)
Theo Von (born 1980)
Daniel von Bargen (1950–2015)
Rich Vos (born 1957)
Sal Vulcano (born 1976)
W
Otto Waalkes (born 1948)
Nina Wadia (born 1968)
Mark Wahlberg (born 1971)
David Wain (born 1969)
Lena Waithe (born 1984)
Taika Waititi (born 1975)
Emil Wakim (born 1998)
Eliot Wald (1946–2003)
Gary Waldhorn (1943–2022)
Christopher Walken (born 1943)
Benjamin Walker (born 1982)
Devon Walker (born 1991)
Doug Walker (born 1981)
Holly Walker (born 1967)
Jimmie Walker (born 1947)
Nancy Walker (1922–1992)
Roy Walker (born 1940)
Max Wall (1908–1990)
Danny Wallace (born 1976)
George Wallace (1895–1960)
George Wallace Jnr (1918–1968)
George Wallace (born 1952)
Trevor Wallace (born 1992)
Linda Wallem (born 1961)
Phoebe Waller-Bridge (born 1985)
David Walliams (born 1971)
Ruth Wallis (1920–2007)
Greg Walloch (born 1970)
Bradley Walsh (born 1960)
Brendon Walsh (born 1978)
Holly Walsh (born 1980)
Kate Walsh (born 1967)
Mary Walsh (born 1952)
Matt Walsh (born 1964)
Ray Walston (1914–2001)
Jessica Walter (1941–2021)
Lisa Ann Walter (born 1963)
Julie Walters (born 1950)
David Walton (born 1978)
Christoph Waltz (born 1956)
Phil Wang (born 1990)
Sheng Wang (born 1980)
Keith Wann (born 1969)
Patrick Warburton (born 1964)
Asha Ward (born 1999)
Mike Ward (born 1973)
Brandon Wardell (born 1992)
Eric Wareheim (born 1976)
Marsha Warfield (born 1954)
Malcolm-Jamal Warner (born 1970)
Mike Warnke (born 1946)
Rusty Warren (1930–2021)
Sydnee Washington
Derek Waters (born 1979)
Michaela Watkins (born 1971)
Reggie Watts (born 1972)
Ruby Wax (born 1953)
Damon Wayans (born 1960)
Damon Wayans Jr. (born 1982)
Keenen Ivory Wayans (born 1958)
Kim Wayans (born 1961)
Marlon Wayans (born 1972)
Shawn Wayans (born 1971)
Kountry Wayne (born 1987)
Robert Webb (born 1972)
Steven Weber (born 1961)
Fred Wedlock (1942–2010)
Lauren Weedman (born 1969)
Ed Weeks (born 1980)
Henning Wehn (born 1974)
Brent Weinbach
Stephnie Weir (born 1967)
Shaun Weiss (born 1979)
Oliver Welke (born 1966)
Danny Wells (1941–2013)
Noël Wells (born 1986)
George Wendt (born 1948)
Ali Wentworth (born 1965)
Tatá Werneck (born 1983)
Amber Stevens West (born 1986)
Billy West (born 1952)
Lindy West (born 1982)
Alice Wetterlund (born 1981)
Frank Whaley (born 1963)
Wil Wheaton (born 1972)
Brooks Wheelan (born 1986)
Bert Wheeler (1895–1968)
Jill Whelan (born 1966)
Betty White (1922–2021)
Ellie White (born 1989)
Jaleel White (born 1976)
Mike White (born 1970)
Ron White (born 1956)
Slappy White (1921–1995)
June Whitfield (1925–2018)
Jack Whitehall (born 1988)
Jason John Whitehead
Paul Whitehouse (born 1958)
Bradley Whitford (born 1959)
Kym Whitley (born 1961)
Mae Whitman (born 1988)
Jane Wickline (born 1999)
Josh Widdicombe (born 1983)
Nick Wiger (born 1980)
Tracey Wigfield (born 1983)
Kristen Wiig (born 1973)
Brian Wilde (1927–2008)
Stefanie Wilder-Taylor
Fred Willard (1933–2020)
Ben Willbond (born 1973)
Allison Williams (born 1988)
Anson Williams (born 1949)
Ashley Williams (born 1978)
Barney Williams (1824–1876)
Barry Williams (born 1954)
Bert Williams (1874–1922)
Brad Williams (born 1984)
Charlie Williams (1927–2006)
Chris Williams (born 1967)
Cindy Williams (1947–2023)
Gary Anthony Williams (born 1966)
Harland Williams (born 1962)
Jessica Williams (born 1986)
Katt Williams (born 1973)
Kenneth Williams (1926–1988)
Kimberly Williams-Paisley (born 1971)
Mason Williams (born 1938)
Robin Williams (1951–2014)
Tyler James Williams (born 1992)
Victor Williams (born 1970)
Wendy Williams (born 1964)
Dave Williamson
Taylor Williamson
Cardis Cardell Willis (1937–2007)
Dave Willis (born 1970)
Dave Willis (1895–1973)
Denny Willis (1920–1995)
Justin Willman (born 1980)
Emma Willmann (born 1985)
Holly Willoughby (born 1981)
Larry Wilmore (born 1961)
Cal Wilson (1970–2023)
Casey Wilson (born 1980)
Debra Wilson (born 1962)
Demond Wilson (born 1946)
Flip Wilson (1933–1998)
Lou Wilson (born 1991)
Luke Wilson (born 1971)
Mary Louise Wilson (born 1931)
Owen Wilson (born 1968)
Rainn Wilson (born 1966)
Rebel Wilson (born 1980)
Reno Wilson (born 1969)
Thomas F. Wilson (born 1959)
Bob Wiltfong (born 1969)
April Winchell (born 1960)
Henry Winkler (born 1945)
Lizz Winstead (born 1961)
Jonathan Winters (1925–2013)
Norman Wisdom (1915–2010)
Chris Witaske (born 1983)
Brenda Withers
Harris Wittels (1984–2015)
Fred Wolf (born 1964)
Michelle Wolf (born 1985)
Dennis Wolfberg (1946–1994)
Jason Woliner (born 1980)
Ali Wong (born 1982)
Jimmy Wong (born 1987)
Kristina Wong (born 1978)
Roy Wood Jr. (born 1978)
Victoria Wood (1953–2016)
Danny Woodburn (born 1964)
Kim Woodburn (born 1942)
Zach Woods (born 1984)
Glenn Wool (born 1974)
Sheb Wooley (1921–2003)
Robert Woolsey (1888–1938)
Harry Worth (1917–1989)
Mike Wozniak (born 1979)
Edgar Wright (born 1974)
Steven Wright (born 1955)
Sabrina Wu (born 1998)
Robert Wuhl (born 1951)
Chris Wylde (born 1976)
Ed Wynn (1886–1966)
Jacob Wysocki (born 1990)
X
Swami X (1925–2015)
Y
Rajpal Yadav (born 1971)
Marc Yaffee (born 1961)
Kaya Yanar (born 1973)
Alan Yang (born 1983)
Bowen Yang (born 1990)
Eugene Lee Yang (born 1986)
Jenny Yang (born 1990)
Jimmy O. Yang (born 1987)
"Weird Al" Yankovic (born 1959)
Cedric Yarbrough (born 1973)
Mike Yard
Mike Yarwood (1941–2023)
Gina Yashere (born 1974)
Lucky Yates (born 1967)
Dustin Ybarra (born 1989)
Steven Yeun (born 1983)
Charlyne Yi (born 1986)
Cem Yılmaz (born 1973)
Celeste Yim (born 1996)
Michael Yo (born 1974)
Aaron Yonda (born 1973)
Dwight York
Heléne Yorke (born 1985)
Alan Young (1919–2016)
Bill Young (died 2014)
Parker Young (born 1988)
Rick Younger (born 1969)
Henny Youngman (1906–1998)
Jaboukie Young-White (born 1994)
Hampton Yount (born 1984)
Bassem Youssef (born 1974)
Ramy Youssef (born 1991)
Joe Yule (1892–1950)
Imran Yusuf (born 1979)
Z
Tincho Zabala (1923–2001)
Hollywood Zakoshisyoh (born 1974)
Andy Zaltzman (born 1974)
Sasheer Zamata (born 1986)
Katya Zamolodchikova
Alex Zane (born 1979)
Bob Zany (born 1961)
Steve Zahn (born 1967)
Steve Zaragoza (born 1982)
Vitaly Zdorovetskiy (born 1992)
Volodymyr Zelenskyy (born 1978)
Henry Zebrowski (born 1984)
David Zed
Mather Zickel (born 1970)
Dolph Ziggler (born 1980)
Jenny Zigrino (born 1987)
Steve Zissis (born 1975)
Tay Zonday (born 1982)
Alan Zweibel (born 1950)
Comedy groups
Ant & Dec
Armstrong and Miller
Abbott and Costello
Barats and Bereta
Beyond the Fringe
Bob and Ray
Bonzo Dog Doo-Dah Band
BriTANicK
Broken Lizard
Brown and Carney
Burns and Allen
CollegeHumor
The Chaser
Les Charlots
Cheech and Chong
Clark and McCullough
The Comedy Store Players
The Comic Strip
Dalton Trumbo's Reluctant Cabaret
The Firesign Theatre
Flight of the Conchords
Frangela
The Frat Pack
French and Saunders
Fry and Laurie
Garfunkel and Oates
God's Pottery
The Goons
The Grumbleweeds
Hale and Pace
Hamish and Andy
Hard 'n Phirm
Homer and Jethro
Jackass
Key and Peele
The Kids in the Hall
The Kipper Kids
Kreisiraadio from Estonia
Lano and Woodley
Laurel and Hardy
The League of Gentlemen
Little Britain
The Little Rascals
The Lonely Island
Les Luthiers
The Lucas Brothers
Marijuana Logues
Martin and Lewis
Marx Brothers
McKenzie Brothers
The Mighty Boosh
Million Dollar Extreme
The Minnesota Wrecking Crew
Mitchell and Webb
Monty Python
Morecambe and Wise
Not Ready for Prime-Time Players (Saturday Night Live)
Paul and Storm
Penn & Teller
Pete and Dud
Phil Lord and Christopher Miller
Please Don't Destroy
Punt and Dennis
Reeves and Mortimer
The Ritz Brothers
Rowan and Martin
Royal Canadian Air Farce
Scotland the What?
Sklar Brothers
Smith and Dale
Smosh
Smothers Brothers
Stella
Stiller and Meara
Studio C
Tenacious D
The Tenderloins
The Three Stooges
Tim and Eric
The Try Guys
The Umbilical Brothers
Upright Citizens Brigade
Vanoss Crew/Banana Bus Squad
The Valleyfolk
Vinesauce
Wayne and Shuster
Wheeler and Woolsey
The Whitest Kids U' Know
Comedy writers
(sorted alphabetically by surname)
Douglas Adams (1952–2011)
Fred Allen (1894–1956)
Woody Allen (born 1935)
Tony Barbieri (born 1963)
Chesney and Wolfe
Roy Clarke (born 1930)
Dick Clement (born 1937)
David Croft (1922–2011)
Barry Cryer
Esmonde and Larbey
Galton and Simpson
W. S. Gilbert
Willis Hall
Antony Jay
Carla Lane
Ian La Frenais (born 1937)
Graham Linehan and Arthur Mathews
Jeremy Lloyd
David Nobbs
Simon Nye
Frank Muir
Denis Norden
S. J. Perelman
Jimmy Perry
David Renwick
Jack Rosenthal
David Sedaris
Gerardo Sofovich (1937–2015)
Hugo Sofovich (1939–2003)
Johnny Speight
John Sullivan
James Thurber
Peter Tinniswood
Zoë Tomalin
Keith Waterhouse
See also
Lists of comedians by nationality
List of Australian comedians
List of British comedians
List of Canadian comedians
List of Dutch comedians
List of Finnish comedians
List of German comedians
List of Indian comedians
List of Italian comedians
List of Japanese comedians
List of Mexican comedians
List of Norwegian comedians
List of Portuguese comedians
List of Puerto Rican comedians
List of United States stand-up comedians
Other related lists
List of comedy films
List of deadpan comedians
List of humorists
List of musical comedians
List of New York Improv comedians
List of stand-up comedians
Anglophone
|
https://en.wikipedia.org/wiki/List_of_comedians
|
2025-04-05T18:27:42.144545
|
6042
|
Compact space
|
, the interval (−∞, −2]}} is not compact because it is not bounded. The interval (2, 4)}} is not compact because it is not closed (but bounded). The interval [0, 1]}} is compact because it is both closed and bounded.]]
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval [0,1] would be compact. Similarly, the space of rational numbers <math>\mathbb{Q}</math> is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers <math>\mathbb{R}</math> is not compact either, because it excludes the two limiting values <math>+\infty</math> and <math>-\infty</math>. However, the extended real number line would be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other topological spaces.
One such generalization is that a topological space is sequentially compact if every infinite sequence of points sampled from the space has an infinite subsequence that converges to some point of the space. The Bolzano–Weierstrass theorem states that a subset of Euclidean space is compact in this sequential sense if and only if it is closed and bounded. Thus, if one chooses an infinite number of points in the closed unit interval , some of those points will get arbitrarily close to some real number in that space.
For instance, some of the numbers in the sequence , , , , , , ...}} accumulate to 0 (while others accumulate to 1).
Since neither 0 nor 1 are members of the open unit interval , those same sets of points would not accumulate to any point of it, so the open unit interval is not compact. Although subsets (subspaces) of Euclidean space can be compact, the entire space itself is not compact, since it is not bounded. For example, considering <math>\mathbb{R}^1</math> (the real number line), the sequence of points has no subsequence that converges to any real number.
Compactness was formally introduced by Maurice Fréchet in 1906 to generalize the Bolzano–Weierstrass theorem from spaces of geometrical points to spaces of functions. The Arzelà–Ascoli theorem and the Peano existence theorem exemplify applications of this notion of compactness to classical analysis. Following its initial introduction, various equivalent notions of compactness, including sequential compactness and limit point compactness, were developed in general metric spaces. In general topological spaces, however, these notions of compactness are not necessarily equivalent. The most useful notion — and the standard definition of the unqualified term compactness — is phrased in terms of the existence of finite families of open sets that "cover" the space, in the sense that each point of the space lies in some set contained in the family. This more subtle notion, introduced by Pavel Alexandrov and Pavel Urysohn in 1929, exhibits compact spaces as generalizations of finite sets. In spaces that are compact in this sense, it is often possible to patch together information that holds locally – that is, in a neighborhood of each point – into corresponding statements that hold throughout the space, and many theorems are of this character.
The term compact set is sometimes used as a synonym for compact space, but also often refers to a compact subspace of a topological space.
Historical development
In the 19th century, several disparate mathematical properties were understood that would later be seen as consequences of compactness. On the one hand, Bernard Bolzano (1817) had been aware that any bounded sequence of points (in the line or plane, for instance) has a subsequence that must eventually get arbitrarily close to some other point, called a limit point.
Bolzano's proof relied on the method of bisection: the sequence was placed into an interval that was then divided into two equal parts, and a part containing infinitely many terms of the sequence was selected.
The process could then be repeated by dividing the resulting smaller interval into smaller and smaller parts – until it closes down on the desired limit point. The full significance of Bolzano's theorem, and its method of proof, would not emerge until almost 50 years later when it was rediscovered by Karl Weierstrass.
In the 1880s, it became clear that results similar to the Bolzano–Weierstrass theorem could be formulated for spaces of functions rather than just numbers or geometrical points.
The idea of regarding functions as themselves points of a generalized space dates back to the investigations of Giulio Ascoli and Cesare Arzelà.
The culmination of their investigations, the Arzelà–Ascoli theorem, was a generalization of the Bolzano–Weierstrass theorem to families of continuous functions, the precise conclusion of which was that it was possible to extract a uniformly convergent sequence of functions from a suitable family of functions. The uniform limit of this sequence then played precisely the same role as Bolzano's "limit point". Towards the beginning of the twentieth century, results similar to that of Arzelà and Ascoli began to accumulate in the area of integral equations, as investigated by David Hilbert and Erhard Schmidt.
For a certain class of Green's functions coming from solutions of integral equations, Schmidt had shown that a property analogous to the Arzelà–Ascoli theorem held in the sense of mean convergence – or convergence in what would later be dubbed a Hilbert space. This ultimately led to the notion of a compact operator as an offshoot of the general notion of a compact space.
It was Maurice Fréchet who, in 1906, had distilled the essence of the Bolzano–Weierstrass property and coined the term compactness to refer to this general phenomenon (he used the term already in his 1904 paper which led to the famous 1906 thesis).
However, a different notion of compactness altogether had also slowly emerged at the end of the 19th century from the study of the continuum, which was seen as fundamental for the rigorous formulation of analysis.
In 1870, Eduard Heine showed that a continuous function defined on a closed and bounded interval was in fact uniformly continuous. In the course of the proof, he made use of a lemma that from any countable cover of the interval by smaller open intervals, it was possible to select a finite number of these that also covered it.
The significance of this lemma was recognized by Émile Borel (1895), and it was generalized to arbitrary collections of intervals by Pierre Cousin (1895) and Henri Lebesgue (1904). The Heine–Borel theorem, as the result is now known, is another special property possessed by closed and bounded sets of real numbers.
This property was significant because it allowed for the passage from local information about a set (such as the continuity of a function) to global information about the set (such as the uniform continuity of a function). This sentiment was expressed by , who also exploited it in the development of the integral now bearing his name. Ultimately, the Russian school of point-set topology, under the direction of Pavel Alexandrov and Pavel Urysohn, formulated Heine–Borel compactness in a way that could be applied to the modern notion of a topological space. showed that the earlier version of compactness due to Fréchet, now called (relative) sequential compactness, under appropriate conditions followed from the version of compactness that was formulated in terms of the existence of finite subcovers. It was this notion of compactness that became the dominant one, because it was not only a stronger property, but it could be formulated in a more general setting with a minimum of additional technical machinery, as it relied only on the structure of the open sets in a space.
<!--
One of the main reasons for studying compact spaces is because they are in some ways very similar to finite sets: there are many results which are easy to show for finite sets, whose proofs carry over with minimal change to compact spaces.
Here is an example:
* Suppose is a Hausdorff space, and we have a point and a finite subset of not containing . Then we can separate and by neighborhoods: for each , let and be disjoint neighborhoods containing and , respectively. Then the intersection of all the and the union of all the are the required neighborhoods of and .
Note that if is infinite, the proof fails, because the intersection of arbitrarily many neighborhoods of might not be a neighborhood of .
The proof can be "rescued", however, if is compact: we simply take a finite subcover of the cover } of , then intersect the corresponding finitely many .
In this way, we see that in a Hausdorff space, any point can be separated by neighborhoods from any compact set not containing it.
In fact, repeating the argument shows that any two disjoint compact sets in a Hausdorff space can be separated by neighborhoods – note that this is precisely what we get if we replace "point" (i.e. singleton set) with "compact set" in the Hausdorff separation axiom.
Many of the arguments and results involving compact spaces follow such a pattern.
-->
Basic examples
Any finite space is compact; a finite subcover can be obtained by selecting, for each point, an open set containing it. A nontrivial example of a compact space is the (closed) unit interval of real numbers. If one chooses an infinite number of distinct points in the unit interval, then there must be some accumulation point among these points in that interval. For instance, the odd-numbered terms of the sequence , , , , , , , ...}} get arbitrarily close to 0, while the even-numbered ones get arbitrarily close to 1. The given example sequence shows the importance of including the boundary points of the interval, since the limit points must be in the space itself — an open (or half-open) interval of the real numbers is not compact. It is also crucial that the interval be bounded, since in the interval , one could choose the sequence of points , of which no sub-sequence ultimately gets arbitrarily close to any given real number.
In two dimensions, closed disks are compact since for any infinite number of points sampled from a disk, some subset of those points must get arbitrarily close either to a point within the disc, or to a point on the boundary. However, an open disk is not compact, because a sequence of points can tend to the boundary – without getting arbitrarily close to any point in the interior. Likewise, spheres are compact, but a sphere missing a point is not since a sequence of points can still tend to the missing point, thereby not getting arbitrarily close to any point within the space. Lines and planes are not compact, since one can take a set of equally-spaced points in any given direction without approaching any point.
Definitions
Various definitions of compactness may apply, depending on the level of generality.
A subset of Euclidean space in particular is called compact if it is closed and bounded. This implies, by the Bolzano–Weierstrass theorem, that any infinite sequence from the set has a subsequence that converges to a point in the set. Various equivalent notions of compactness, such as sequential compactness and limit point compactness, can be developed in general metric spaces. That is, is compact if for every collection of open subsets of such that
<math display"block">X \bigcup_{S \in C}S\ ,</math>
there is a finite subcollection ⊆ such that
<math display"block">X \bigcup_{S \in F} S\ .</math>
Some branches of mathematics such as algebraic geometry, typically influenced by the French school of Bourbaki, use the term quasi-compact for the general notion, and reserve the term compact for topological spaces that are both Hausdorff and quasi-compact. A compact set is sometimes referred to as a compactum, plural compacta.
Compactness of subsets
A subset of a topological space is said to be compact if it is compact as a subspace (in the subspace topology). That is, is compact if for every arbitrary collection of open subsets of such that
<math display="block">K \subseteq \bigcup_{S \in C} S\ ,</math>
there is a finite subcollection ⊆ such that
<math display="block">K \subseteq \bigcup_{S \in F} S\ .</math>
Because compactness is a topological property, the compactness of a subset depends only on the subspace topology induced on it. It follows that, if <math>K \subset Z \subset Y</math>, with subset equipped with the subspace topology, then is compact in if and only if is compact in .
Characterization
If is a topological space then the following are equivalent:
# is compact; i.e., every open cover of has a finite subcover.
# has a sub-base such that every cover of the space, by members of the sub-base, has a finite subcover (Alexander's sub-base theorem).
# is Lindelöf and countably compact.
# Any collection of closed subsets of with the finite intersection property has nonempty intersection.
# Every net on has a convergent subnet (see the article on nets for a proof).
# Every filter on has a convergent refinement.
# Every net on has a cluster point.
# Every filter on has a cluster point.
# Every ultrafilter on converges to at least one point.
# Every infinite subset of has a complete accumulation point.
# For every topological space , the projection <math>X \times Y \to Y</math> is a closed mapping (see proper map).
# Every open cover linearly ordered by subset inclusion contains .
Bourbaki defines a compact space (quasi-compact space) as a topological space where each filter has a cluster point (i.e., 8. in the above).
Euclidean space
For any subset of Euclidean space, is compact if and only if it is closed and bounded; this is the Heine–Borel theorem.
As a Euclidean space is a metric space, the conditions in the next subsection also apply to all of its subsets. Of all of the equivalent conditions, it is in practice easiest to verify that a subset is closed and bounded, for example, for a closed interval or closed -ball.
Metric spaces
For any metric space , the following are equivalent (assuming countable choice):
# is compact.
# is complete and totally bounded (this is also equivalent to compactness for uniform spaces).
# is sequentially compact; that is, every sequence in has a convergent subsequence whose limit is in (this is also equivalent to compactness for first-countable uniform spaces).
# is limit point compact (also called weakly countably compact); that is, every infinite subset of has at least one limit point in .
# is countably compact; that is, every countable open cover of has a finite subcover.
# is an image of a continuous function from the Cantor set.
# Every decreasing nested sequence of nonempty closed subsets in has a nonempty intersection.
# Every increasing nested sequence of proper open subsets in fails to cover .
A compact metric space also satisfies the following properties:
# Lebesgue's number lemma: For every open cover of , there exists a number such that every subset of of diameter < is contained in some member of the cover.
# is second-countable, separable and Lindelöf – these three conditions are equivalent for metric spaces. The converse is not true; e.g., a countable discrete space satisfies these three conditions, but is not compact.
# is closed and bounded (as a subset of any metric space whose restricted metric is ). The converse may fail for a non-Euclidean space; e.g. the real line equipped with the discrete metric is closed and bounded but not compact, as the collection of all singletons of the space is an open cover which admits no finite subcover. It is complete but not totally bounded.
Ordered spaces
For an ordered space (i.e. a totally ordered set equipped with the order topology), the following are equivalent:
# is compact.
# Every subset of has a supremum (i.e. a least upper bound) in .
# Every subset of has an infimum (i.e. a greatest lower bound) in .
# Every nonempty closed subset of has a maximum and a minimum element.
An ordered space satisfying (any one of) these conditions is called a complete lattice.
In addition, the following are equivalent for all ordered spaces , and (assuming countable choice) are true whenever is compact. (The converse in general fails if is not also metrizable.):
# Every sequence in has a subsequence that converges in .
# Every monotone increasing sequence in converges to a unique limit in .
# Every monotone decreasing sequence in converges to a unique limit in .
# Every decreasing nested sequence of nonempty closed subsets <sub>1</sub> ⊇ <sub>2</sub> ⊇ ... in has a nonempty intersection.
# Every increasing nested sequence of proper open subsets <sub>1</sub> ⊆ <sub>2</sub> ⊆ ... in fails to cover .
Characterization by continuous functions
Let be a topological space and the ring of real continuous functions on .
For each , the evaluation map <math>\operatorname{ev}_p\colon C(X)\to \mathbb{R}</math>
given by is a ring homomorphism.
The kernel of is a maximal ideal, since the residue field }} is the field of real numbers, by the first isomorphism theorem. A topological space is pseudocompact if and only if every maximal ideal in has residue field the real numbers. For completely regular spaces, this is equivalent to every maximal ideal being the kernel of an evaluation homomorphism. There are pseudocompact spaces that are not compact, though.
In general, for non-pseudocompact spaces there are always maximal ideals in such that the residue field is a (non-Archimedean) hyperreal field. The framework of non-standard analysis allows for the following alternative characterization of compactness: a topological space is compact if and only if every point of the natural extension is infinitely close to a point of (more precisely, is contained in the monad of ). Hyperreal definition A space is compact if its hyperreal extension (constructed, for example, by the ultrapower construction) has the property that every point of is infinitely close to some point of . For example, an open real interval (0, 1)}}}} is not compact because its hyperreal extension contains infinitesimals, which are infinitely close to 0, which is not a point of .
Sufficient conditions
* A closed subset of a compact space is compact.
* A finite union of compact sets is compact.
* A continuous image of a compact space is compact.
* The intersection of any non-empty collection of compact subsets of a Hausdorff space is compact (and closed);
** If is not Hausdorff then the intersection of two compact subsets may fail to be compact (see footnote for example).{{efn|
Let {{math|1X {a, b} ∪ <math>\mathbb{N}</math>}}, {{math|1U {a} ∪ <math>\mathbb{N}</math>}}, and {{math|1V {b} ∪ <math>\mathbb{N}</math>}}. Endow with the topology generated by the following basic open sets: every subset of <math>\mathbb{N}</math> is open; the only open sets containing are and ; and the only open sets containing are and . Then and are both compact subsets but their intersection, which is <math>\mathbb{N}</math>, is not compact. Note that both and are compact open subsets, neither one of which is closed.
}}
* The product of any collection of compact spaces is compact. (This is Tychonoff's theorem, which is equivalent to the axiom of choice.)
* In a metrizable space, a subset is compact if and only if it is sequentially compact (assuming countable choice)
* A finite set endowed with any topology is compact.
Properties of compact spaces
* A compact subset of a Hausdorff space is closed.
** If is not Hausdorff then a compact subset of may fail to be a closed subset of (see footnote for example).{{efn|
Let {{math|1X {a, b}<!---->}} and endow with the topology {{math|{X, ∅, {a}<!---->}<!---->}}. Then {{math|{a}<!---->}} is a compact set but it is not closed.
}}
** If is not Hausdorff then the closure of a compact set may fail to be compact (see footnote for example). be the set of non-negative integers. We endow with the particular point topology by defining a subset to be open if and only if . Then {{math|1S : {0}<!---->}} is compact, the closure of is all of , but is not compact since the collection of open subsets {{math|{<!---->{0, x} : x ∈ X}<!---->}} does not have a finite subcover.
}}
* In any topological vector space (TVS), a compact subset is complete. However, every non-Hausdorff TVS contains compact (and thus complete) subsets that are not closed.
* If and are disjoint compact subsets of a Hausdorff space , then there exist disjoint open sets and in such that and .
* A continuous bijection from a compact space into a Hausdorff space is a homeomorphism.
* A compact Hausdorff space is normal and regular.
* If a space is compact and Hausdorff, then no finer topology on is compact and no coarser topology on is Hausdorff.
* If a subset of a metric space is compact then it is -bounded.
Functions and compact spaces
Since a continuous image of a compact space is compact, the extreme value theorem holds for such spaces: a continuous real-valued function on a nonempty compact space is bounded above and attains its supremum.
(Slightly more generally, this is true for an upper semicontinuous function.) As a sort of converse to the above statements, the pre-image of a compact space under a proper map is compact.
Compactifications
Every topological space is an open dense subspace of a compact space having at most one point more than , by the Alexandroff one-point compactification.
By the same construction, every locally compact Hausdorff space is an open dense subspace of a compact Hausdorff space having at most one point more than .
Ordered compact spaces
A nonempty compact subset of the real numbers has a greatest element and a least element.
Let be a simply ordered set endowed with the order topology.
Then is compact if and only if is a complete lattice (i.e. all subsets have suprema and infima). Examples
* Any finite topological space, including the empty set, is compact. More generally, any space with a finite topology (only finitely many open sets) is compact; this includes in particular the trivial topology.
* Any space carrying the cofinite topology is compact.
* Any locally compact Hausdorff space can be turned into a compact space by adding a single point to it, by means of Alexandroff one-point compactification. The one-point compactification of <math>\mathbb{R}</math> is homeomorphic to the circle ; the one-point compactification of <math>\mathbb{R}^2</math> is homeomorphic to the sphere . Using the one-point compactification, one can also easily construct compact spaces which are not Hausdorff, by starting with a non-Hausdorff space.
* The right order topology or left order topology on any bounded totally ordered set is compact. In particular, Sierpiński space is compact.
* No discrete space with an infinite number of points is compact. The collection of all singletons of the space is an open cover which admits no finite subcover. Finite discrete spaces are compact.
* In <math>\mathbb{R}</math> carrying the lower limit topology, no uncountable set is compact.
* In the cocountable topology on an uncountable set, no infinite set is compact. Like the previous example, the space as a whole is not locally compact but is still Lindelöf.
* The closed unit interval }} is compact. This follows from the Heine–Borel theorem. The open interval is not compact: the open cover <math display"inline">\left( \frac{1}{n}, 1 - \frac{1}{n} \right)</math> for 3, 4, ... }} does not have a finite subcover. Similarly, the set of rational numbers in the closed interval is not compact: the sets of rational numbers in the intervals <math display"inline">\left[0, \frac{1}{\pi} - \frac{1}{n}\right]\text{ and }\left[\frac{1}{\pi} + \frac{1}{n}, 1\right]</math> cover all the rationals in [0, 1] for 4, 5, ... }} but this cover does not have a finite subcover. Here, the sets are open in the subspace topology even though they are not open as subsets of <math>\mathbb{R}</math>.
* The set <math>\mathbb{R}</math> of all real numbers is not compact as there is a cover of open intervals that does not have a finite subcover. For example, intervals − 1, + 1}} }}, where takes all integer values in , cover <math>\mathbb{R}</math> but there is no finite subcover.
* On the other hand, the extended real number line carrying the analogous topology is compact; note that the cover described above would never reach the points at infinity and thus would not cover the extended real line. In fact, the set has the homeomorphism to [−1, 1] of mapping each infinity to its corresponding unit and every real number to its sign multiplied by the unique number in the positive part of interval that results in its absolute value when divided by one minus itself, and since homeomorphisms preserve covers, the Heine-Borel property can be inferred.
* For every natural number , the -sphere is compact. Again from the Heine–Borel theorem, the closed unit ball of any finite-dimensional normed vector space is compact. This is not true for infinite dimensions; in fact, a normed vector space is finite-dimensional if and only if its closed unit ball is compact.
* On the other hand, the closed unit ball of the dual of a normed space is compact for the weak-* topology. (Alaoglu's theorem)
* The Cantor set is compact. In fact, every compact metric space is a continuous image of the Cantor set.
* Consider the set of all functions {{math|f : <math>\mathbb{R}</math> → [0, 1]}} from the real number line to the closed unit interval, and define a topology on so that a sequence <math>\{f_n\}</math> in converges towards if and only if <math>\{f_n(x)\}</math> converges towards for all real numbers . There is only one such topology; it is called the topology of pointwise convergence or the product topology. Then is a compact topological space; this follows from the Tychonoff theorem.
* A subset of the Banach space of real-valued continuous functions on a compact Hausdorff space is relatively compact if and only if it is equicontinuous and pointwise bounded (Arzelà–Ascoli theorem).
* Consider the set of all functions → }} satisfying the Lipschitz condition ≤ }} for all }}. Consider on the metric induced by the uniform distance <math>d(f, g) = \sup_{x \in [0, 1]} |f(x) - g(x)|.</math> Then by the Arzelà–Ascoli theorem the space is compact.
* The spectrum of any bounded linear operator on a Banach space is a nonempty compact subset of the complex numbers <math>\mathbb{C}</math>. Conversely, any compact subset of <math>\mathbb{C}</math> arises in this manner, as the spectrum of some bounded linear operator. For instance, a diagonal operator on the Hilbert space <math>\ell^2</math> may have any compact nonempty subset of <math>\mathbb{C}</math> as spectrum.
* The space of Borel probability measures on a compact Hausdorff space is compact for the vague topology, by the Alaoglu theorem.
* A collection of probability measures on the Borel sets of Euclidean space is called tight if, for any positive epsilon, there exists a compact subset containing all but at most epsilon of the mass of each of the measures. Helly's theorem then asserts that a collection of probability measures is relatively compact for the vague topology if and only if it is tight.
Algebraic examples
* Topological groups such as an orthogonal group are compact, while groups such as a general linear group are not.
* Since the -adic integers are homeomorphic to the Cantor set, they form a compact set.
* Any global field K is a discrete additive subgroup of its adele ring, and the quotient space is compact. This was used in John Tate's thesis to allow harmonic analysis to be used in number theory.
* The spectrum of any commutative ring with the Zariski topology (that is, the set of all prime ideals) is compact, but never Hausdorff (except in trivial cases). In algebraic geometry, such topological spaces are examples of quasi-compact schemes, "quasi" referring to the non-Hausdorff nature of the topology.
* The spectrum of a Boolean algebra is compact, a fact which is part of the Stone representation theorem. Stone spaces, compact totally disconnected Hausdorff spaces, form the abstract framework in which these spectra are studied. Such spaces are also useful in the study of profinite groups.
* The structure space of a commutative unital Banach algebra is a compact Hausdorff space.
* The Hilbert cube is compact, again a consequence of Tychonoff's theorem.
* A profinite group (e.g. Galois group) is compact.
See also
* Compactly generated space
* Compactness theorem
* Eberlein compactum
* Exhaustion by compact sets
* Lindelöf space
* Metacompact space
* Noetherian topological space
* Orthocompact space
* Paracompact space
* Quasi-compact morphism
* Precompact set - also called totally bounded
* Relatively compact subspace
* Totally bounded
Notes
References
Bibliography
*
*.
*.
* (Purely analytic proof of the theorem that between any two values which give results of opposite sign, there lies at least one real root of the equation).
*
*
*
*
*
*
*
*
*
* <!-- -->
*
*
*
*
*
* .
*
*
External links
*
----
Category:Compactness (mathematics)
Category:General topology
Category:Properties of topological spaces
Category:Topology
|
https://en.wikipedia.org/wiki/Compact_space
|
2025-04-05T18:27:42.199084
|
6045
|
Clodius
|
thumb|Denarius issued for the anti-Neronian rebel Clodius Macer in 68 AD
Clodius is an alternate form of the Roman nomen Claudius, a patrician gens that was traditionally regarded as Sabine in origin. The alternation of o and au is characteristic of the Sabine dialect. The feminine form is Clodia.
Republican era
Publius Clodius Pulcher
During the Late Republic, the spelling Clodius is most prominently associated with Publius Clodius Pulcher, a popularis politician who gave up his patrician status through an order in order to qualify for the office of tribune of the plebs. Clodius positioned himself as a champion of the urban plebs, supporting free grain for the poor and the right of association in guilds (collegia); because of this individual's ideology, Clodius has often been taken as a more "plebeian" spelling and a gesture of political solidarity. Clodius's two elder brothers, the Appius Claudius Pulcher who was consul in 54 BC and the C. Claudius Pulcher who was praetor in 56 BC, conducted more conventional political careers and are referred to in contemporary sources with the traditional spelling.
The view that Clodius represents a plebeian or politicized form has been questioned by Clodius's chief modern-era biographer. In The Patrician Tribune, W. Jeffrey Tatum points out that the spelling is also associated with Clodius's sisters and that "the political explanation … is almost certainly wrong." A plebeian branch of the gens, the Claudii Marcelli, retained the supposedly patrician spelling, while there is some inscriptional evidence that the -o- form may also have been used on occasion by close male relatives of the "patrician tribune" Clodius. Tatum argues that the use of -o- by the "chic" Clodia was a fashionable affectation, and that Clodius, whose perhaps inordinately loving relationship with his sister was the subject of much gossip and insinuation, was imitating his stylish sibling. The linguistic variation of o for au was characteristic of the Umbrian language, of which Sabine was a branch. Forms using o were considered archaic or rustic in the 50s BC, and the use of Clodius would have been either a whimsical gesture of pastoral fantasy, or a trendy assertion of antiquarian authenticity.
Other Clodii of the Republic
In addition to Clodius, Clodii from the Republican era include:
Gnaeus Cornelius Lentulus Clodianus, presumably a "Clodius" before his adoption
Clodius Aesopus, a tragic actor in the 50s BC who may have been a freedman of one of the Clodii Pulchri.
Claudia, daughter of Clodius Pulcher and Fulvia, the first wife of emperor Augustus.
Clodia, sister of Publius Clodius Pulcher, sometimes identified in Catullus' poems as "Lesbia".
Women of the Claudii Marcelli branch were often called "Clodia" in the late Republic.
Imperial era
thumb|Funerary relief for Publius Clodius Philonicus, 70–100 AD
People using the name Clodius during the period of the Roman Empire include:
Gaius Clodius Licinus, consul suffectus in AD 4.
Gaius Clodius Vestalis, possible builder of the Via Clodia
Publius Clodius Thrasea Paetus, senator and philosopher during the reign of Nero
Lucius Clodius Macer, a legatus who revolted against Nero
Publius Clodius Quirinalis, from Arelate in Gaul, teacher of rhetoric in time of Nero
Decimus Clodius Septimius Albinus, commonly known as Clodius Albinus, rival emperor 196–197
Marcus Clodius Pupienus Maximus, known as Pupienus, co-emperor 238
Titus Clodius Pupienus Pulcher Maximus, son of emperor Pupienus and suffect consul c. 235
Clodii Celsini
The Clodii Celsini continued to practice the traditional religions of antiquity in the face of Christian hegemony through at least the 4th century, when Clodius Celsinus Adelphius (see below) converted. Members of this branch include:
Quintus Fabius Clodius Agrippianus Celsinus, proconsul of Caria in 249 and the son of Clodius Celsinus (b. ca. 185); see for other members of the family.
Clodius Celsinus Adelphius, praefectus urbi in 351.
Quintus Clodius Hermogenianus Olybrius, consul 379
See also
Clodio the Longhair, a chieftain of the Salian Franks, sometimes called "Clodius I"
Leges Clodiae, legislation sponsored by Clodius Pulcher as tribune
References
Selected bibliography
Tatum, W. Jeffrey. The Patrician Tribune: P. Clodius Pulcher. Studies in the History of Greece and Rome series. University of North Carolina Press, 1999. Limited preview online. Hardcover .
Further reading
Fezzi, L. Il tribuno Clodio. Roma-Bari, Laterza, 2008. .
Category:Ancient Roman prosopographical lists
Category:Ancient Roman names
|
https://en.wikipedia.org/wiki/Clodius
|
2025-04-05T18:27:42.204593
|
6046
|
Cicero
|
| birth_date = 3 January 106 BC<!--THIS ARTICLE USES THE BC/AD ERA CONVENTION THROUGHOUT; PLEASE READ WP:ERA AND DISCUSS ON CICERO'S TALK PAGE BEFORE CHANGING-->
| birth_place = Arpinum, Italy
| death_date = 7 December 43 BC (aged 63)
| death_place = Formia, Italy
| death_cause = Assassination (by order of Mark Antony)
| party = <!-- Optimates and populares not a political party. Cicero claimed both "affiliations" for himself and for others as well. MA Robb (2010). -->
| occupation = Statesman, lawyer, writer, orator
| opponents | spouse
| children = Tullia and Cicero Minor
| relatives = Quintus Tullius Cicero (brother)
| module }}
}}
| era = Hellenistic philosophy
| region = Western philosophy
| school_tradition =
| main_interests =
| notable_ideas =
}}
}}
Marcus Tullius Cicero ).}} ( ; <!-- please note that i is [i] before vowels, not [ɪ] -->; 3 January 106 BC – 7 December 43 BC) was a Roman statesman, lawyer, scholar, philosopher, orator, writer and Academic skeptic, who tried to uphold optimate principles during the political crises that led to the establishment of the Roman Empire. His extensive writings include treatises on rhetoric, philosophy and politics. He is considered one of Rome's greatest orators and prose stylists and the innovator of what became known as "Ciceronian rhetoric". Cicero was educated in Rome and in Greece. He came from a wealthy municipal family of the Roman equestrian order, and served as consul in 63 BC.
He greatly influenced both ancient and modern reception of the Latin language. A substantial part of his work has survived, and he was admired by both ancient and modern authors alike. Cicero adapted the arguments of the chief schools of Hellenistic philosophy in Latin and coined a large portion of Latin philosophical vocabulary via lexical innovation (e.g. neologisms such as , generator, , infinitio, , ), almost 150 of which were the result of translating Greek philosophical terms.
Though he was an accomplished orator and successful lawyer, Cicero believed his political career was his most important achievement. It was during his consulship that the Catiline conspiracy attempted to overthrow the government through an attack on the city by outside forces, and Cicero (by his own account) suppressed the revolt by summarily and controversially executing five conspirators without trial, an act which would later lead to his exile. During the chaotic middle period of the first century BC, marked by civil wars and the dictatorship of Julius Caesar, Cicero was a supporter of the Optimates faction. Following Caesar's death, Cicero became an enemy of Mark Antony in the ensuing power struggle, attacking him in a series of speeches. He was proscribed as an enemy of the state by the Second Triumvirate and consequently executed by soldiers operating on their behalf in 43 BC, having been intercepted during an attempted flight from the Italian peninsula. His severed hands and head (taken by order of Antony and displayed representing the repercussions of his anti-Antonian actions as a writer and as an orator, respectively) were then displayed on the Rostra.
Petrarch's rediscovery of Cicero's letters is often credited for initiating the 14th-century Renaissance in public affairs, humanism, and classical Roman culture. According to Polish historian Tadeusz Zieliński, "the Renaissance was above all things a revival of Cicero, and only after him and through him of the rest of Classical antiquity." The peak of Cicero's authority and prestige came during the 18th-century Enlightenment, and his impact on leading Enlightenment thinkers and political theorists such as John Locke, David Hume, Montesquieu, and Edmund Burke was substantial. His works rank among the most influential in global culture, and today still constitute one of the most important bodies of primary material for the writing and revision of Roman history, especially the last days of the Roman Republic.
Early life
, Italy, birthplace of Cicero|left]]
by Vincenzo Foppa (fresco, 1464), now at the Wallace Collection|left]]
Marcus Tullius Cicero was born on 3 January 106 BC in Arpinum, a hill town southeast of Rome. He belonged to the tribus Cornelia. His father was a wealthy member of the equestrian order and possessed good connections in Rome. However, not being of robust health (he experienced poor digestion and inflammation of the eyes), he could not enter public life and studied extensively to compensate. Little is known about Cicero's mother Helvia, but Cicero's brother Quintus wrote in a letter that she was a thrifty housewife.
Cicero's cognomen, a hereditary nickname, comes from the Latin for chickpea, . Plutarch explains that the name was originally given to one of Cicero's ancestors who had a cleft in the tip of his nose resembling a chickpea. }} The famous family names of Fabius, Lentulus, and Piso come from the Latin names of beans, lentils, and peas, respectively. Plutarch writes that Cicero was urged to change this deprecatory name when he entered politics, but refused, saying that he would make Cicero more glorious than Scaurus ("Swollen-ankled") and Catulus ("Puppy").
At the age of 15, in 90 BC, Cicero started serving under Pompey Strabo and later Sulla in the Social war between Rome and its Italian allies. When in Rome during the turbulent plebeian tribunate of Publius Sulpicius Rufus in 88 BC which saw a short bout of fighting between the Sulpicius and Sulla, who had been elected consul for that year, Cicero found himself greatly impressed by Sulpicius' oratory even if he disagreed with his politics. He continued his studies at Rome, writing a pamphlet titled On Invention relating to rhetorical argumentation and studying philosophy with Greek academics who had fled the ongoing First Mithridatic War. Education During this period in Roman history, Greek language and cultural studies were highly valued by the elite classes. Cicero was therefore educated in the teachings of the ancient Greek philosophers, poets and historians; as he obtained much of his understanding of the theory and practice of rhetoric from the Greek poet Archias. Cicero used his knowledge of Greek to translate many of the theoretical concepts of Greek philosophy into Latin, thus translating Greek philosophical works for a larger audience. It was precisely his broad education that tied him to the traditional Roman elite.
Cicero's interest in philosophy figured heavily in his later career and led to him providing a comprehensive account of Greek philosophy for a Roman audience, including creating a philosophical vocabulary in Latin. In 87 BC, Philo of Larissa, the head of the Platonic Academy that had been founded by Plato in Athens about 300 years earlier, arrived in Rome. Cicero, "inspired by an extraordinary zeal for philosophy", sat enthusiastically at his feet and absorbed Carneades' Academic Skeptic philosophy.
According to Plutarch, Cicero was an extremely talented student, whose learning attracted attention from all over Rome, affording him the opportunity to study Roman law under Quintus Mucius Scaevola. Cicero's fellow students were Gaius Marius Minor, Servius Sulpicius Rufus (who became a famous lawyer, one of the few whom Cicero considered superior to himself in legal matters), and Titus Pomponius. The latter two became Cicero's friends for life, and Pomponius (who later received the nickname "Atticus", and whose sister married Cicero's brother) would become, in Cicero's own words, "as a second brother", with both maintaining a lifelong correspondence.
In 79 BC, Cicero left for Greece, Asia Minor and Rhodes. This was perhaps to avoid the potential wrath of Sulla, as Plutarch claims, though Cicero himself says it was to hone his skills and improve his physical fitness. In Athens he studied philosophy with Antiochus of Ascalon, the 'Old Academic' and initiator of Middle Platonism. In Asia Minor, he met the leading orators of the region and continued to study with them. Cicero then journeyed to Rhodes to meet his former teacher, Apollonius Molon, who had taught him in Rome. Molon helped Cicero hone the excesses in his style, as well as train his body and lungs for the demands of public speaking. Charting a middle path between the competing Attic and Asiatic styles, Cicero would ultimately become considered second only to Demosthenes among history's orators.
Early career
Early legal activity
While Cicero had feared that the law courts would be closed forever, they were reopened in the aftermath of Sulla's civil war and the purging of Sulla's political opponents in the proscriptions. Many of the orators whom Cicero had admired in his youth were now dead from age or political violence. His first major appearance in the courts was in 81 BC at the age of 26 when he delivered Pro Quinctio, a speech defending certain commercial transactions which Cicero had recorded and disseminated.
His more famous speech defending Sextus Roscius of Ameria – – on charges of parricide in 80 BC was his first appearance in criminal court. In this high-profile case, Cicero accused a freedman of the dictator Sulla, Chrysogonus, of fabricating Roscius' father's proscription to obtain Roscius' family's property. Successful in his defence, Cicero tactfully avoided incriminating Sulla of any wrongdoing and developed a positive oratorical reputation for himself.
While Plutarch claims that Cicero left Rome shortly thereafter out of fear of Sulla's response, according to Kathryn Tempest, "most scholars now dismiss this suggestion" because Cicero left Rome after Sulla resigned his dictatorship. Cicero, for his part, later claimed that he left Rome, headed for Asia, to develop his physique and develop his oratory. After marrying his wife, Terentia, in 80 BC, he eventually left for Asia Minor with his brother Quintus, his friend Titus Atticus, and others on a long trip spanning most of 79 through 77 BC. Returning to Rome in 77 BC, Cicero again busied himself with legal defence.
Early political career
In 76 BC, at the quaestorian elections, Cicero was elected at the minimum age required – 30 years – in the first returns from the comitia tributa, to the post of quaestor. Ex officio, he also became a member of the Senate. In the quaestorian lot, he was assigned to Sicily for 75 BC. The post, which was largely one related to financial administration in support of the state or provincial governors, proved for Cicero an important place where he could gain clients in the provinces. His time in Sicily saw him balance his duties – largely in terms of sending more grain back to Rome – with his support for the provincials, Roman businessmen in the area, and local potentates. Adeptly balancing those responsibilities, he won their gratitude. He was also appreciated by local Syracusans for the rediscovery of the lost tomb of Archimedes, which he personally financed.
Promising to lend the Sicilians his oratorical voice, he was called on a few years after his quaestorship to prosecute the Roman province's governor Gaius Verres, for abuse of power and corruption. In 70 BC, at the age of 36, Cicero launched his first high-profile prosecution against Verres, an emblem of the corrupt Sullan supporters who had risen in the chaos of the civil war.
The prosecution of Gaius Verres was a great forensic success for Cicero. While Verres hired the prominent lawyer, Quintus Hortensius, after a lengthy period in Sicily collecting testimonials and evidence and persuading witnesses to come forward, Cicero returned to Rome and won the case in a series of dramatic court battles. His unique style of oratory set him apart from the flamboyant Hortensius. On the conclusion of this case, Cicero came to be considered the greatest orator in Rome. The view that Cicero may have taken the case for reasons of his own is viable. Hortensius was, at this point, known as the best lawyer in Rome; to beat him would guarantee much success and the prestige that Cicero needed to start his career. Cicero's oratorical ability is shown in his character assassination of Verres and various other techniques of persuasion used on the jury. One such example is found in the speech In Verrem, where he states "with you on this bench, gentlemen, with Marcus Acilius Glabrio as your president, I do not understand what Verres can hope to achieve". Oratory was considered a great art in ancient Rome and an important tool for disseminating knowledge and promoting oneself in elections, in part because there were no regular newspapers or mass media. Cicero was neither a patrician nor a plebeian noble; his rise to political office despite his relatively humble origins has traditionally been attributed to his brilliance as an orator.
Cicero grew up in a time of civil unrest and war. Sulla's victory in the first of a series of civil wars led to a new constitutional framework that undermined (liberty), the fundamental value of the Roman Republic. Nonetheless, Sulla's reforms strengthened the position of the equestrian class, contributing to that class's growing political power. Cicero was both an Italian and a , but more importantly he was a Roman constitutionalist. His social class and loyalty to the Republic ensured that he would "command the support and confidence of the people as well as the Italian middle classes". The optimates faction never truly accepted Cicero, and this undermined his efforts to reform the Republic while preserving the constitution. Nevertheless, he successfully ascended the cursus honorum, holding each magistracy at or near the youngest possible age: quaestor in 75 BC (age 30), aedile in 69 BC (age 36), and praetor in 66 BC (age 39), when he served as president of the extortion court. He was then elected consul at age 42.<!-- WP:CALC -->
Consulship
by Cesare Maccari, 1882–1888|alt|upright1.2]]
Cicero, seizing the opportunity offered by optimate fear of reform, was elected consul for the year 63 BC; he was elected with the support of every unit of the centuriate assembly, rival members of the post-Sullan establishment, and the leaders of municipalities throughout post-Social War Italy. His co-consul for the year, Gaius Antonius Hybrida, played a minor role.
He began his consular year by opposing a land bill proposed by a plebeian tribune which would have appointed commissioners with semi-permanent authority over land reform.
Catiline fled and left behind his followers to start the revolution from within while he himself assaulted the city with an army of "moral and financial bankrupts, or of honest fanatics and adventurers". It is alleged that Catiline had attempted to involve the Allobroges, a tribe of Transalpine Gaul, in their plot, but Cicero, working with the Gauls, was able to seize letters that incriminated the five conspirators and forced them to confess in front of the Senate. The senate then deliberated upon the conspirators' punishment. As it was the dominant advisory body to the various legislative assemblies rather than a judicial body, there were limits to its power; however, martial law was in effect, and it was feared that simple house arrest or exile – the standard options – would not remove the threat to the state. At first Decimus Junius Silanus spoke for the "extreme penalty"; but during the debate many were swayed by Julius Caesar, who decried the precedent it would set and argued in favor of life imprisonment in various Italian towns. Cato the Younger then rose in defense of the death penalty and the Senate finally agreed on the matter, and came down in support of the death penalty. Cicero had the conspirators taken to the Tullianum, the notorious Roman prison, where they were strangled. Cicero himself accompanied the former consul Publius Cornelius Lentulus Sura, one of the conspirators, to the Tullianum.
Cicero received the honorific "pater patriae" for his efforts to suppress the conspiracy, but lived thereafter in fear of trial or exile for having put Roman citizens to death without trial. While the senatus consultum ultimum gave some legitimacy to the use of force against the conspirators, }} Cicero also argued that Catiline's conspiracy, by virtue of its treason, made the conspirators enemies of the state and forfeited the protections intrinsically possessed by Roman citizens. The consuls moved decisively. Antonius Hybrida was dispatched to defeat Catiline in battle that year, preventing Crassus or Pompey from exploiting the situation for their own political aims.
After the suppression of the conspiracy, Cicero was proud of his accomplishment. Some of his political enemies argued that though the act gained Cicero popularity, he exaggerated the extent of his success. He overestimated his popularity again several years later after being exiled from Italy and then allowed back from exile. At this time, he claimed that the republic would be restored along with him.
Shortly after completing his consulship, in late 62 BC, Cicero arranged the purchase of a large townhouse on the Palatine Hill previously owned by Rome's richest citizen, Marcus Licinius Crassus. To finance the purchase, Cicero borrowed some two million sesterces from Publius Cornelius Sulla, whom he had previously defended from court. <!-- It cost an exorbitant sum, 3.5 million sesterces, which required Cicero to arrange for a loan from his co-consul Gaius Antonius Hybrida based on the expected profits from Antonius's proconsulship in Macedonia. --> Cicero boasted his house was "in conspectu prope totius urbis" ("in sight of nearly the whole city"), only a short walk from the Roman Forum.
Exile and return
In 60 BC, Julius Caesar invited Cicero to be the fourth member of his existing partnership with Pompey and Marcus Licinius Crassus, an assembly that would eventually be called the First Triumvirate. Cicero refused the invitation because he suspected it would undermine the Republic, and because he was strongly opposed to anything unconstitutional that limited the powers of the consuls and replaced them with non-elected officials.
During Caesar's consulship of 59 BC, the triumvirate had achieved many of their goals of land reform, publicani debt forgiveness, ratification of Pompeian conquests, etc. With Caesar leaving for his provinces, they wished to maintain their hold on politics. They engineered the adoption of patrician Publius Clodius Pulcher into a plebeian family and had him elected as one of the ten tribunes of the plebs for 58 BC. Clodius used the triumvirate's backing to push through legislation that benefited them. He introduced several laws (the leges Clodiae) that made him popular with the people, strengthening his power base, then he turned on Cicero. Clodius passed a law which made it illegal to offer "fire and water" (i.e. shelter or food) to anyone who executed a Roman citizen without a trial.
Cicero, having executed members of the Catiline conspiracy four years previously without formal trial, was clearly the intended target. Furthermore, many believed that Clodius acted in concert with the triumvirate who feared that Cicero would seek to abolish many of Caesar's accomplishments while consul the year before. Cicero argued that the senatus consultum ultimum indemnified him from punishment, and he attempted to gain the support of the senators and consuls, especially of Pompey.
Cicero grew out his hair, dressed in mourning and toured the streets. Clodius' gangs dogged him, hurling abuse, stones and even excrement. Hortensius, trying to rally to his old rival's support, was almost lynched. The Senate and the consuls were cowed. Caesar, who was still encamped near Rome, was apologetic but said he could do nothing when Cicero brought himself to grovel in the proconsul's tent. Everyone seemed to have abandoned Cicero.
After Clodius passed a law to deny to Cicero fire and water (i.e. shelter) within four hundred miles of Rome, Cicero went into exile. He arrived at Thessalonica, on 23 May 58 BC. In his absence, Clodius, who lived next door to Cicero on the Palatine, arranged for Cicero's house to be confiscated by the state, and was even able to purchase a part of the property in order to extend his own house. After the intervention of recently elected tribune Titus Annius Milo, acting on the behalf of Pompey who wanted Cicero as a client, the Senate voted in favor of recalling Cicero from exile. Clodius cast the single vote against the decree. Cicero returned to Italy on 5 August 57 BC, landing at Brundisium. He was greeted by a cheering crowd, and, to his delight, his beloved daughter Tullia. In his Oratio De Domo Sua Ad Pontifices, Cicero convinced the College of Pontiffs to rule that the consecration of his land was invalid, thereby allowing him to regain his property and rebuild his house on the Palatine.
Cicero tried to re-enter politics as an independent operator, but his attempts to attack portions of Caesar's legislation were unsuccessful and encouraged Caesar to re-solidify his political alliance with Pompey and Crassus. The conference at Luca in 56 BC left the three-man alliance in domination of the republic's politics; this forced Cicero to recant and support the triumvirate out of fear from being entirely excluded from public life. After the conference, Cicero lavishly praised Caesar's achievements, got the Senate to vote a thanksgiving for Caesar's victories, and grant money to pay his troops. He also delivered a speech 'On the consular provinces' () which checked an attempt by Caesar's enemies to strip him of his provinces in Gaul. After this, a cowed Cicero concentrated on his literary works. It is uncertain whether he was directly involved in politics for the following few years. His legal work largely consisted of defending allies of the ruling and his own personal friends and allies; he defended his former pupil Marcus Caelius Rufus against a charge of murder in 56. Under the influence of the triumvirs, he had also defended his former enemies Publius Vatinius (in August 54 BCE), Marcus Aemilius Scaurus (between July and September) and Gnaeus Plancius (with the ) in September, which weakened his prestige and sparked attacks on his integrity: Luca Grillo has suggested these cases as the source of the poet Catullus's double-edged comment that Cicero was "the best defender of anybody".Governorship of Ciliciaminted by Cicero in Apamea Cibotus in 51–50 BC, while serving as proconsul of Cilicia.]]
In 51 BC he reluctantly accepted a promagistracy (as proconsul) in Cilicia for the year; there were few other former consuls eligible as a result of a legislative requirement enacted by Pompey in 52 BC specifying an interval of five years between a consulship or praetorship and a provincial command. He served as proconsul of Cilicia from May 51 BC, arriving in the provinces three months later around August.
In 53 BC Marcus Licinius Crassus had been defeated by the Parthians at the Battle of Carrhae. This opened the Roman East for a Parthian invasion, causing unrest in Syria and Cilicia. Cicero restored calm by his mild system of government. He discovered that a great amount of public property had been embezzled by corrupt previous governors and members of their staff, and did his utmost to restore it. Thus he greatly improved the condition of the cities. He retained the civil rights of, and exempted from penalties, the men who gave the property back. Besides this, he was extremely frugal in his outlays for staff and private expenses during his governorship, and this made him highly popular among the natives.
Besides his activity in ameliorating the hard pecuniary situation of the province, Cicero was also creditably active in the military sphere. Early in his governorship he received information that prince Pacorus, son of Orodes II the king of the Parthians, had crossed the Euphrates, and was ravaging the Syrian countryside and had even besieged Cassius (the interim Roman commander in Syria) in Antioch. Cicero eventually marched with two understrength legions and a large contingent of auxiliary cavalry to Cassius's relief. Pacorus and his army had already given up on besieging Antioch and were heading south through Syria, ravaging the countryside again. Cassius and his legions followed them, harrying them wherever they went, eventually ambushing and defeating them near Antigonea.
Another large troop of Parthian horsemen was defeated by Cicero's cavalry who happened to run into them while scouting ahead of the main army. Cicero next defeated some robbers who were based on Mount Amanus and was hailed as imperator by his troops. Afterwards he led his army against the independent Cilician mountain tribes, besieging their fortress of Pindenissum. It took him 47 days to reduce the place, which fell in December. On 30 July 50 BC Cicero left the province to his brother Quintus, who had accompanied him on his governorship as his legate. On his way back to Rome he stopped in Rhodes and then went to Athens, where he caught up with his old friend Titus Pomponius Atticus and met men of great learning.Julius Caesar's civil warCicero arrived in Rome on 4 January 49 BC. He stayed outside the pomerium, to retain his promagisterial powers: either in expectation of a triumph or to retain his independent command authority in the coming civil war. The struggle between Pompey and Julius Caesar grew more intense in 50 BC. Cicero favored Pompey, seeing him as a defender of the senate and Republican tradition, but at that time avoided openly alienating Caesar. When Caesar invaded Italy in 49 BC, Cicero fled Rome. Caesar, seeking an endorsement by a senior senator, courted Cicero's favor, but even so Cicero slipped out of Italy and traveled to Dyrrhachium where Pompey's staff was situated. Cicero traveled with the Pompeian forces to Pharsalus in Macedonia in 48 BC, though he was quickly losing faith in the competence and righteousness of the Pompeian side. Eventually, he provoked the hostility of his fellow senator Cato, who told him that he would have been of more use to the cause of the optimates if he had stayed in Rome. After Caesar's victory at the Battle of Pharsalus on 9 August, Cicero refused to take command of the Pompeian forces and continue the war. He returned to Rome, still as a promagistrate with his lictors, in 47 BC, and dismissed them upon his crossing the pomerium and renouncing his command.
In a letter to Varro on , Cicero outlined his strategy under Caesar's dictatorship. Cicero, however, was taken by surprise when the Liberatores assassinated Caesar on the ides of March, 44 BC. Cicero was not included in the conspiracy, even though the conspirators were sure of his sympathy. Marcus Junius Brutus called out Cicero's name, asking him to restore the republic when he lifted his bloodstained dagger after the assassination. A letter Cicero wrote in February 43 BC to Trebonius, one of the conspirators, began, "How I could wish that you had invited me to that most glorious banquet on the Ides of March!" Cicero became a popular leader during the period of instability following the assassination. He had no respect for Mark Antony, who was scheming to take revenge upon Caesar's murderers. In exchange for amnesty for the assassins, he arranged for the Senate to agree not to declare Caesar to have been a tyrant, which allowed the Caesarians to have lawful support and kept Caesar's reforms and policies intact.
Opposition to Mark Antony and death
In April 43 BC, "diehard republicans" may have revived the ancient position of princeps senatus (leader of the senate) for Cicero. This position had been very prestigious until the constitutional reforms of Sulla in 82–80 BC, which removed most of its importance.
On the other side, Antony was consul and leader of the Caesarian faction, and unofficial executor of Caesar's public will. Relations between the two were never friendly and worsened after Cicero claimed that Antony was taking liberties in interpreting Caesar's wishes and intentions. Octavian was Caesar's adopted son and heir. After he returned to Italy, Cicero began to play him against Antony. He praised Octavian, declaring he would not make the same mistakes as his father. He attacked Antony in a series of speeches he called the Philippics, named after Demosthenes's denunciations of Philip II of Macedon. At the time, Cicero's popularity as a public figure was unrivalled.
Cicero supported Decimus Junius Brutus Albinus as governor of Cisalpine Gaul (Gallia Cisalpina) and urged the Senate to name Antony an enemy of the state. The speech of Lucius Piso, Caesar's father-in-law, delayed proceedings against Antony. Antony was later declared an enemy of the state when he refused to lift the siege of Mutina, which was in the hands of Decimus Brutus. Cicero's plan to drive out Antony failed. Antony and Octavian reconciled and allied with Lepidus to form the Second Triumvirate after the successive battles of Forum Gallorum and Mutina. The alliance came into official existence with the lex Titia, passed on 27 November 43 BC, which gave each triumvir a consular imperium for five years. The Triumvirate immediately began a proscription of their enemies, modeled after that of Sulla in 82 BC. Cicero and all of his contacts and supporters were numbered among the enemies of the state, even though Octavian argued for two days against Cicero being added to the list.
Cicero was one of the most viciously and doggedly hunted among the proscribed. He was viewed with sympathy by a large segment of the public and many people refused to report that they had seen him. He was caught on 7 December 43 BC leaving his villa in Formiae in a litter heading to the seaside, where he hoped to embark on a ship destined for Macedonia. When his killers – Herennius (a Centurion) and Popilius (a Tribune) – arrived, Cicero's own slaves said they had not seen him, but he was given away by Philologus, a freedman of his brother Quintus Cicero.
}}
He bowed to his captors, leaning his head out of the litter in a gladiatorial gesture to ease the task. By baring his neck and throat to the soldiers, he was indicating that he would not resist. According to Plutarch, Herennius first slew him, then cut off his head. On Antony's instructions his hands, which had penned the Philippics against Antony, were cut off as well; these were nailed along with his head on the Rostra in the Forum Romanum according to the tradition of Marius and Sulla, both of whom had displayed the heads of their enemies in the Forum. Cicero was the only victim of the proscriptions who was displayed in that manner. According to Cassius Dio, in a story often mistakenly attributed to Plutarch, Antony's wife Fulvia took Cicero's head, pulled out his tongue, and jabbed it repeatedly with her hairpin in final revenge against Cicero's power of speech.
Cicero's son, Marcus Tullius Cicero Minor, during his year as a consul in 30 BC, avenged his father's death, to a certain extent, when he announced to the Senate Mark Antony's naval defeat at Actium in 31 BC by Octavian.
Octavian is reported to have praised Cicero as a patriot and a scholar of meaning in later times, within the circle of his family. However, it was Octavian's acquiescence that had allowed Cicero to be killed, as Cicero was condemned by the new triumvirate.
Cicero's career as a statesman was marked by inconsistencies and a tendency to shift his position in response to changes in the political climate. His indecision may be attributed to his sensitive and impressionable personality; he was prone to overreaction in the face of political and private change. "Would that he had been able to endure prosperity with greater self-control, and adversity with more fortitude!" wrote C. Asinius Pollio, a contemporary Roman statesman and historian. Personal life and family
Cicero married Terentia probably at the age of 27, in 79 BC. According to the upper-class mores of the day it was a marriage of convenience but lasted harmoniously for nearly 30 years. Terentia's family was wealthy, probably the plebeian noble house of Terenti Varrones, thus meeting the needs of Cicero's political ambitions in both economic and social terms. She had a half-sister named Fabia, who as a child had become a Vestal Virgin, a great honour. Terentia was a strong-willed woman and (citing Plutarch) "took more interest in her husband's political career than she allowed him to take in household affairs".
In the 50s BC, Cicero's letters to Terentia became shorter and colder. He complained to his friends that Terentia had betrayed him but did not specify in which sense. Perhaps the marriage could not outlast the strain of the political upheaval in Rome, Cicero's involvement in it, and various other disputes between the two. The divorce appears to have taken place in 51 BC or shortly before. In 46 or 45 BC, Cicero married a young girl, Publilia, who had been his ward. It is thought that Cicero needed her money, particularly after having to repay the dowry of Terentia, who came from a wealthy family.
Although his marriage to Terentia was one of convenience, it is commonly known that Cicero held great love for his daughter Tullia. When she suddenly became ill in February 45 BC and died after having seemingly recovered from giving birth to a son in January, Cicero was stunned. "I have lost the one thing that bound me to life," he wrote to Atticus. Atticus told him to come for a visit during the first weeks of his bereavement, so that he could comfort him when his pain was at its greatest. In Atticus's large library, Cicero read everything that the Greek philosophers had written about overcoming grief, "but my sorrow defeats all consolation." Caesar and Brutus, as well as Servius Sulpicius Rufus, sent him letters of condolence.
Cicero hoped that his son Marcus would become a philosopher like him, but Marcus himself wished for a military career. He joined the army of Pompey in 49 BC, and after Pompey's defeat at Pharsalus 48 BC, he was pardoned by Caesar. Cicero sent him to Athens to study as a disciple of the peripatetic philosopher Kratippos in 48 BC, but he used this absence from "his father's vigilant eye" to "eat, drink, and be merry." After Cicero's death, he joined the army of the Liberatores but was later pardoned by Augustus. Augustus's bad conscience for having given in to Cicero's being put on the proscription list during the Second Triumvirate led him to aid considerably Marcus Minor's career. He became an augur and was nominated consul in 30 BC together with Augustus. As such, he was responsible for revoking the honors of Mark Antony, who was responsible for the proscription and could in this way take revenge. Later he was appointed proconsul of Syria and the province of Asia.Legacy
's childhood copy of De Officiis, bearing the inscription in his hand, "Thys boke is myne Prynce Henry"]]
Cicero has been traditionally considered the master of Latin prose, with Quintilian declaring that Cicero was "not the name of a man, but of eloquence itself." The English words Ciceronian (meaning "eloquent") and cicerone (meaning "local guide") derive from his name. He is credited with transforming Latin from a modest utilitarian language into a versatile literary medium capable of expressing abstract and complicated thoughts with clarity. Julius Caesar praised Cicero's achievement by saying "it is more important to have greatly extended the frontiers of the Roman spirit than the frontiers of the Roman empire". According to John William Mackail, "Cicero's unique and imperishable glory is that he created the language of the civilized world, and used that language to create a style which nineteen centuries have not replaced, and in some respects have hardly altered."
Cicero was also an energetic writer with an interest in a wide variety of subjects, in keeping with the Hellenistic philosophical and rhetorical traditions in which he was trained. The quality and ready accessibility of Ciceronian texts favored very wide distribution and inclusion in teaching curricula, as suggested by a graffito at Pompeii, admonishing: "You will like Cicero, or you will be whipped".
Cicero was greatly admired by influential Church Fathers such as Augustine of Hippo, who credited Cicero's lost Hortensius for his eventual conversion to Christianity, and St. Jerome, who had a feverish vision in which he was accused of being "follower of Cicero and not of Christ" before the judgment seat.
This influence further increased after the Early Middle Ages in Europe, where more of his writings survived than any other Latin author's. Medieval philosophers were influenced by Cicero's writings on natural law and innate rights.
Petrarch's rediscovery of Cicero's letters provided the impetus for searches for ancient Greek and Latin writings scattered throughout European monasteries, and the subsequent rediscovery of classical antiquity led to the Renaissance. Subsequently, Cicero became synonymous with classical Latin to such an extent that a number of humanist scholars began to assert that no Latin word or phrase should be used unless it appeared in Cicero's works, a stance criticised by Erasmus.
His voluminous correspondence, much of it addressed to his friend Atticus, has been especially influential, introducing the art of refined letter writing to European culture. Cornelius Nepos, the first century BC biographer of Atticus, remarked that Cicero's letters contained such a wealth of detail "concerning the inclinations of leading men, the faults of the generals, and the revolutions in the government" that their reader had little need for a history of the period.
Among Cicero's admirers were Desiderius Erasmus, Martin Luther, and John Locke. Following the invention of Johannes Gutenberg's printing press, De Officiis was the second book printed in Europe, after the Gutenberg Bible. Scholars note Cicero's influence on the rebirth of religious toleration in the 17th century.
Cicero was especially popular with the Philosophes of the 18th century, including Edward Gibbon, Diderot, David Hume, Montesquieu, and Voltaire. Gibbon wrote of his first experience reading the author's collective works thus: "I tasted the beauty of the language; I breathed the spirit of freedom; and I imbibed from his precepts and examples the public and private sense of a man...after finishing the great author, a library of eloquence and reason, I formed a more extensive plan of reviewing the Latin classics..."
Voltaire called Cicero "the greatest as well as the most elegant of Roman philosophers" and even staged a play based on Cicero's role in the Catilinarian conspiracy, called Rome Sauvée, ou Catilina, to "make young people who go to the theatre acquainted with Cicero." Voltaire was spurred to pen the drama as a rebuff to his rival Claude Prosper Jolyot de Crébillon's own play Catilina, which had portrayed Cicero as a coward and villain who hypocritically married his own daughter to Catiline.
Montesquieu produced his "Discourse on Cicero" in 1717, in which he heaped praise on the author because he rescued "philosophy from the hands of scholars, and freed it from the confusion of a foreign language". Montesquieu went on to declare that Cicero was "of all the ancients, the one who had the most personal merit, and whom I would prefer to resemble."
Cicero the republican inspired the Founding Fathers of the United States and the revolutionaries of the French Revolution. John Adams said, "As all the ages of the world have not produced a greater statesman and philosopher united than Cicero, his authority should have great weight." Thomas Jefferson names Cicero as one of a handful of major figures who contributed to a tradition "of public right" that informed his draft of the Declaration of Independence and shaped American understandings of "the common sense" basis for the right of revolution. Camille Desmoulins said of the French republicans in 1789 that they were "mostly young people who, nourished by the reading of Cicero at school, had become passionate enthusiasts for liberty".
In the modern era, American libertarian Jim Powell starts his history of liberty with the sentence: "Marcus Tullius Cicero expressed principles that became the bedrock of liberty in the modern world."
Likewise, no other ancient personality has inspired as much venomous dislike as Cicero, especially in more modern times. His commitment to the values of the Republic accommodated a hatred of the poor and persistent opposition to the advocates and mechanisms of popular representation. Friedrich Engels referred to him as "the most contemptible scoundrel in history" for upholding republican "democracy" while at the same time denouncing land and class reforms. Cicero has faced criticism for exaggerating the democratic qualities of republican Rome, and for defending the Roman oligarchy against the popular reforms of Caesar. Michael Parenti admits Cicero's abilities as an orator, but finds him a vain, pompous and hypocritical personality who, when it suited him, could show public support for popular causes that he privately despised. Parenti presents Cicero's prosecution of the Catiline conspiracy as legally flawed at least, and possibly unlawful.
Cicero also had an influence on modern astronomy. Nicolaus Copernicus, searching for ancient views on earth motion, said that he "first ... found in Cicero that Hicetas supposed the earth to move."
Notably, "Cicero" was the name attributed to size 12 font in typesetting table drawers. For ease of reference, type sizes 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, and 20 were all given different names.Works
Cicero was declared a righteous pagan by the Early Church. Subsequent Roman and medieval Christian writers quoted liberally from his works De re publica (On the Commonwealth) and De Legibus (On the Laws), and much of his work has been recreated from these surviving fragments. Cicero also articulated an early, abstract conceptualization of rights, based on ancient law and custom. Of Cicero's books, six on rhetoric have survived, as well as parts of seven on philosophy. Of his speeches, 88 were recorded, but only 52 survive.
In archaeology
Cicero's great repute in Italy has led to numerous ruins being identified as having belonged to him, though none have been substantiated with absolute certainty. In Formia, two Roman-era ruins are popularly believed to be Cicero's mausoleum, the Tomba di Cicerone, and the villa where he was assassinated in 43 BC. The latter building is centered around a central hall with Doric columns and a coffered vault, with a separate nymphaeum, on five acres of land near Formia. A modern villa was built on the site after the Rubino family purchased the land from Ferdinand II of the Two Sicilies in 1868. Cicero's supposed tomb is a 24-meter (79 feet) tall tower on an opus quadratum base on the ancient Via Appia outside of Formia. Some suggest that it is not in fact Cicero's tomb, but a monument built on the spot where Cicero was intercepted and assassinated while trying to reach the sea.
In Pompeii, a large villa excavated in the mid 18th century just outside the Herculaneum Gate was widely believed to have been Cicero's, who was known to have owned a holiday villa in Pompeii he called his Pompeianum. The villa was stripped of its fine frescoes and mosaics and then re-buried after 1763 – it has yet to be re-excavated. However, contemporaneous descriptions of the building from the excavators combined with Cicero's own references to his Pompeianum differ, making it unlikely that it is Cicero's villa.
In Rome, the location of Cicero's house has been roughly identified from excavations of the Republican-era stratum on the northwestern slope of the Palatine Hill. Cicero's domus has long been known to have stood in the area, according to his own descriptions and those of later authors, but there is some debate about whether it stood near the base of the hill, very close to the Roman Forum, or nearer to the summit. During his life the area was the most desirable in Rome, densely occupied with Patrician houses including the Domus Publica of Julius Caesar and the home of Cicero's mortal enemy Clodius.Notable fictional portrayalsIn Dante's 1320 poem the Divine Comedy, the author encounters Cicero, among other philosophers, in Limbo. Ben Jonson dramatised the conspiracy of Catiline in his play Catiline His Conspiracy, featuring Cicero as a character. Cicero also appears as a minor character in William Shakespeare's play Julius Caesar.
Cicero was portrayed on the motion picture screen by British actor Alan Napier in the 1953 film Julius Caesar, based on Shakespeare's play. He has also been played by such noted actors as Michael Hordern (in Cleopatra), and André Morell (in the 1970 Julius Caesar). Most recently, Cicero was portrayed by David Bamber in the HBO series Rome (2005–2007) and appeared in both seasons.
In the historical novel series Masters of Rome, Colleen McCullough presents a not-so-flattering depiction of Cicero's career, showing him struggling with an inferiority complex and vanity, morally flexible and fatally indiscreet, while his rival Julius Caesar is shown in a more approving light. Cicero is portrayed as a hero in the novel A Pillar of Iron by Taylor Caldwell (1965). Robert Harris' novels Imperium, Lustrum (published under the name Conspirata in the United States) and Dictator comprise a three-part series based on the life of Cicero. In these novels Cicero's character is depicted in a more favorable way than in those of McCullough, with his positive traits equaling or outweighing his weaknesses (while conversely Caesar is depicted as more sinister than in McCullough). Cicero is a major recurring character in the Roma Sub Rosa series of mystery novels by Steven Saylor. He also appears several times as a peripheral character in John Maddox Roberts' SPQR series.
Samuel Barnett portrays Cicero in a 2017 audio drama series pilot produced by Big Finish Productions. A full series was released the following year. All episodes are written by David Llewellyn and directed and produced by Scott Handcock.
Giancarlo Esposito portrays Mayor Franklyn Cicero, a character from Francis Ford Coppola's 2024 sci-fi epic film Megalopolis, which is a modern futuristic interpretation of the Catiline Conspiracy. In the film, Esposito stars opposite Adam Driver, who portrays a character named Cesar Catilina.See also
* Caecilia Attica
* Caecilia Metella (daughter of Celer)
* Civis romanus sum
* Clausula (rhetoric)
* A Dialogue Concerning Oratorical Partitions
* E pluribus unum
* Esse quam videri
* Ipse dixit
* List of ancient Romans
* Lorem ipsum
* Marcantonius Majoragio
* Marcus Tullius Tiro
* Marius Nizolius
* Otium
* Socratici viri
* Tempest in a teapot
* Translation
Notes
References
Citations
Modern sources
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
* Reprinted 1968.
*
*
*
*
*
*
*
*
*
*
*
Ancient sources
* <!-- Att --> }}
* <!-- Brut --> }}
* <!-- Cat --> }}
* <!-- Fam --> }}
* <!-- Off --> |access-date26 November 2023 |archive-date26 November 2023 |archive-urlhttps://web.archive.org/web/20231126074729/http://www.perseus.tufts.edu/hopper/text?docurn:cts:latinLit:phi0474.phi055 |url-status=live }}
* |access-date19 February 2021 |archive-date31 July 2022 |archive-urlhttps://web.archive.org/web/20220731043828/https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Sallust/Bellum_Catilinae%2A.html |url-status=live }}
* <!-- Plut Vit -->
** |access-date26 November 2023 |archive-date10 April 2020 |archive-urlhttps://web.archive.org/web/20200410020040/http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Lives/Crassus*.html |url-status=live }}
** |access-date19 February 2021 |archive-date31 January 2024 |archive-urlhttps://web.archive.org/web/20240131100133/https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Lives/Cicero%2A.html |url-status=live }}
** |access-date26 November 2023 |archive-date10 April 2020 |archive-urlhttps://web.archive.org/web/20200410020040/http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Lives/Crassus*.html |url-status=live }}
** |access-date26 November 2023 |archive-date20 April 2008 |archive-urlhttps://web.archive.org/web/20080420154411/http://www.perseus.tufts.edu/cgi-bin/ptext?lookupCic.+Q.+fr.+2.3 |url-statuslive }}
** |access-date26 November 2023 |archive-date19 June 2024 |archive-urlhttps://web.archive.org/web/20240619070053/http://www.perseus.tufts.edu/hopper/text?docurn:cts:greekLit:tlg0007.tlg033.perseus-eng1 |url-statuslive }}
External links
Works by Cicero
* [http://catalog.perseus.org/catalog/urn:cite:perseus:author.364 Works by Cicero at Perseus Digital Library]
*
*
*
*
* [https://www.stoictherapy.com/elibrary#cicero Works by Cicero] at the Stoic Therapy eLibrary
* The Latin Library (Latin): [http://www.thelatinlibrary.com/cic.html Works of Cicero]
* [http://dcc.dickinson.edu/cicero-verres/preface-and-acknowledgements Dickinson College Commentaries: Against Verres 2.1.53–86]
* [http://dcc.dickinson.edu/cicero-de-imperio/preface-and-acknowledgments Dickinson College Commentaries: ''On Pompey's Command (De Imperio) 27–49]
* [http://openn.library.upenn.edu/Data/0023/html/horace_ms_1b.html Horace MS 1b Laelius de Amicitia at OPenn]
* [http://openn.library.upenn.edu/Data/0023/html/lewis_e_066.html Lewis E 66 Epistolae ad familiares (Letters to friends)]
'Biographies and descriptions of Cicero's time'''
Plutarch's biography of Cicero contained in the Parallel Lives
* Life of Cicero by Anthony Trollope, Volume I & Volume II
* Cicero by Rev. W. Lucas Collins (Ancient Classics for English Readers)
* Roman life in the days of Cicero by Rev. Alfred J. Church
* Social life at Rome in the Age of Cicero by W. Warde Fowler
*
* [http://classics.mit.edu/Plutarch/cicero.html Dryden's translation of Cicero from Plutarch's Parallel Lives]
* [http://community.middlebury.edu/~harris/LatinAuthors/Cicero.html At Middlebury College website]
*
}}
Category:106 BC births
Category:43 BC deaths
Category:2nd-century BC Romans
Category:1st-century BC executions
Category:1st-century BC philosophers
Category:1st-century BC Roman augurs
Category:1st-century BC Roman consuls
Category:1st-century BC writers in Latin
Category:Academic skeptics
Category:Ancient landowners
Category:Ancient Roman equites
Category:Ancient Roman exiles
Category:Ancient Roman jurists
Category:Ancient Roman rhetoricians
Category:Ancient Roman scholars of religion
Category:Classical humanists
Category:Deaths by edged and bladed weapons
Category:Executed ancient Roman people
Category:Executed philosophers
Category:Executed writers
Category:Golden Age Latin writers
Category:Letter writers in Latin
Category:Optimates
Category:People executed by the Roman Republic
Category:People from Arpino
Category:Plebeian aediles
Category:Philosophers of Roman Italy
Category:Recipients of ancient Roman pardons
Category:Roman governors of Cilicia
Category:Roman quaestors
Category:1st-century BC Roman praetors
Category:Roman Republican praetors
Category:Roman-era Skeptic philosophers
Category:Roman-era students in Athens
Category:Translation scholars
Category:Translators of Ancient Greek texts
Category:Trope theorists
Category:Tullii
Category:People of the War of Mutina
Category:Natural law ethicists
|
https://en.wikipedia.org/wiki/Cicero
|
2025-04-05T18:27:42.259565
|
6047
|
Consul
|
Consul (abbrev. cos.; Latin plural consules) was the title of one of the two chief magistrates of the Roman Republic, and subsequently also an important title under the Roman Empire. The title was used in other European city-states through antiquity and the Middle Ages, in particular in the Republics of Genoa and Pisa, then revived in modern states, notably in the First French Republic. The related adjective is consular, from the Latin consularis.
This usage contrasts with modern terminology, where a consul is a type of diplomat.
Roman consul
A consul held the highest elected political office of the Roman Republic (509 to 27 BC), and ancient Romans considered the consulship the highest level of the cursus honorum (an ascending sequence of public offices to which politicians aspired). Consuls were elected to office and held power for one year. There were always two consuls in power at any time.
Other uses in antiquity
Private sphere
It was not uncommon for an organization under Roman private law to copy the terminology of state and city institutions for its own statutory agents. The founding statute, or contract, of such an organisation was called lex, 'law'. The people elected each year were patricians, members of the upper class.
City-states
While many cities, including the Gallic states and the Carthaginian Republic, had a double-headed chief magistracy, another title was often used, such as the Punic sufet, Duumvir, or native styles like Meddix.
Medieval city-states, communes and municipalities
thumb|Caffaro di Rustico da Caschifellone, statesman of the Genoese Republic in the 12th century, for which he served eight terms as a consul.|282x282px
Republic of Genoa
The city-state of Genoa, unlike ancient Rome, bestowed the title of consul on various state officials, not necessarily restricted to the highest. Among these were Genoese officials stationed in various Mediterranean ports, whose role included helping Genoese merchants and sailors in difficulties with the local authorities. Great Britain reciprocated by appointing consuls to Genoa from 1722. This institution, with its name, was later emulated by other powers and is reflected in the modern usage of the word (see Consul (representative)).
Republic of Pisa
In addition to the Genoese Republic, the Republic of Pisa also took the form of "Consul" in the early stages of its government. The Consulate of the Republic of Pisa was the major government institution present in Pisa from 1087 to 1189. Despite losing space within the government since 1190 in favor of the Podestà, for some periods of the 13th century some citizens were again elected as consuls.
Other uses in the Medieval period
thumb|left|In this painting, Alphonse, Count of Poitiers and Count of Toulouse takes an oath before the Consuls of the town of Agen, with his right hand on the town ordinances, committing himself to recognize the autonomy of the town's commune, while sitting on a pedestal. The consul administering the oath is forced to go on his knees, symbolizing Alphonse's lordship and the town's loyalty.
Throughout most of southern France, a consul ( or ) was an office equivalent to the of the north and roughly similar with English aldermen. The most prominent were those of Bordeaux and Toulouse, which came to be known as jurats and capitouls, respectively. The capitouls of Toulouse were granted transmittable nobility. In many other smaller towns the first consul was the equivalent of a mayor today, assisted by a variable number of secondary consuls and jurats. His main task was to levy and collect tax.
The Dukes of Gaeta often used also the title of "consul" in its Greek form "Hypatos" (see List of Hypati and Dukes of Gaeta).
French Revolution
French Republic 1799–1804
thumb|right|220px|A portrait of the three consuls, Jean-Jacques-Régis de Cambacérès, Napoleon Bonaparte and Charles-François Lebrun (left to right)
After Napoleon Bonaparte staged a coup against the Directory government in November 1799, the French Republic adopted a constitution which conferred executive powers upon three consuls, elected for a period of ten years. In reality, the first consul, Bonaparte, dominated his two colleagues and held supreme power, soon making himself consul for life (1802) and eventually, in 1804, emperor.
The office was held by:
Napoleon Bonaparte, Emmanuel-Joseph Sieyès, Roger Ducos, provisional consuls (10 November – 12 December 1799)
Napoleon Bonaparte (first consul), Jean-Jacques Cambacérès (second consul), Charles-François Lebrun (third consul), consuls (12 December 1799 – 18 May 1804)
Bolognese Republic, 1796
The short-lived Bolognese Republic, proclaimed in 1796 as a French client republic in the Central Italian city of Bologna, had a government consisting of nine consuls and its head of state was the Presidente del Magistrato, i.e., chief magistrate, a presiding office held for four months by one of the consuls. Bologna already had consuls at some parts of its Medieval history.
Roman Republic, 1798–1800
The French-sponsored Roman Republic (15 February 1798 – 23 June 1800) was headed by multiple consuls:
Francesco Riganti, Carlo Luigi Costantini, Duke Bonelli-Crescenzi, Antonio Bassi, Gioacchino Pessuti, Angelo Stampa, Domenico Maggi, provisional consuls (15 February – 20 March 1798)
Liborio Angelucci, Giacomo De Mattheis, Panazzi, Reppi, Ennio Quirino Visconti, consuls (20 March – September 1798)
Brigi, Calisti, Francesco Pierelli, Giuseppe Rey, Federico Maria Domenico Michele, Zaccaleoni, consuls (September – 24 July 1799)
Consular rule was interrupted by the Neapolitan occupation (27 November – 12 December 1798), which installed a Provisional Government:
Prince Giambattista Borghese, Prince Paolo-Maria Aldobrandini, Prince Gibrielli, Marchese Camillo Massimo, Giovanni Ricci (29 November 1798 - 12 December 1798)
Rome was occupied by France (11 July – 28 September 1799) and again by Naples (30 September 1799 – 23 June 1800), bringing an end to the Roman Republic.
Revolutionary Greece, 1821
Among the many petty local republics that were formed during the first year of the Greek Revolution, prior to the creation of a unified Provisional Government at the First National Assembly at Epidaurus, were:
The Consulate of Argos (from 26 May 1821, under the Senate of the Peloponnese) had a single head of state, styled consul, 28 March 1821 – 26 May 1821: Stamatellos Antonopoulos
The Consulate of East Greece (Livadeia) (from 15 November 1821, under the Areopagus of East Greece) was headed 1 April 1821 – 15 November 1821 by three consuls: Lambros Nakos, Ioannis Logothetis & Ioannis Filon
Note: in Greek, the term for "consul" is "hypatos" (ὕπατος), which translates as "supreme one", and hence does not necessarily imply a joint office.
Paraguay, 1813–1844
In between a series of juntas and various other short-lived regimes, the young republic was governed by "consuls of the republic", with two consuls alternating in power every 4 months:
12 October 1813 – 12 February 1814, José Gaspar Rodríguez de Francia y Velasco
12 February 1814 – 12 June 1814, Fulgencio Yegros y Franco de Torres
12 June 1814 – 3 October 1814, José Gaspar Rodríguez de Francia y Velasco; he stayed on as "supreme dictator" 3 October 1814 – 20 September 1840 (from 6 June 1816 styled "perpetual supreme dictator")
After a few presidents of the Provisional Junta, there were again consuls of the republic, 14 March 1841 – 13 March 1844 (ruling jointly, but occasionally styled "first consul", "second consul"): Carlos Antonio López Ynsfrán (b. 1792 – d. 1862) + Mariano Roque Alonzo Romero (d. 1853) (the lasts of the aforementioned juntistas, Commandant-General of the Army)
Thereafter all republican rulers were styled "president".
Modern uses of the term
In modern terminology, a consul is a type of diplomat. The American Heritage Dictionary defines consul as "an official appointed by a government to reside in a foreign country and represent its interests there." The Devil's Dictionary defines Consul as "in American politics, a person who having failed to secure an office from the people is given one by the Administration on condition that he leave the country".
In most governments, the consul is the head of the consular section of an embassy, and is responsible for all consular services such as immigrant and non-immigrant visas, passports, and citizen services for expatriates living or traveling in the host country.
A less common modern usage is when the consul of one country takes a governing role in the host country.
See also
Differently named, but same function
Captain Regent (similar modern position in San Marino's government)
Consularis (Roman gubernatorial style)
Modern UN System
Consulate
Sources and references
WorldStatesmen.org, see each present country
Specific
Category:Ancient Roman titles
Category:Heads of government
Category:Heads of state
Category:Military ranks of ancient Rome
Category:Latin political words and phrases
Category:Collective heads of state
Category:Cursus honorum
Category:Diplomats by role
cs:Konzul (antický Řím)
hr:Konzul
io:Konsulo
ku:Konsûl
sr:Конзул
tl:Konsulado
|
https://en.wikipedia.org/wiki/Consul
|
2025-04-05T18:27:42.266597
|
6050
|
List of equations in classical mechanics
|
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of reference. The point of concurrency of the three axes is known as the origin of the particular space.
Classical mechanics utilises many equations—as well as other mathematical concepts—which relate various physical quantities to one another. These include differential equations, manifolds, Lie groups, and ergodic theory. This article gives a summary of the most important of these.
This article lists equations from Newtonian mechanics, see analytical mechanics for the more general formulation of classical mechanics (which includes Lagrangian and Hamiltonian mechanics).
Classical mechanics
Mass and inertia
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Linear, surface, volumetric mass density λ or μ (especially in acoustics, see below) for Linear, σ for surface, ρ for volume. m = \int \lambda \, \mathrm{d} \ell
m = \iint \sigma \, \mathrm{d} S
m \iiint \rho \, \mathrm{d} V kg m−n, n 1, 2, 3 M L−n Moment of mass m (No common symbol) Point mass:
\mathbf{m} = \mathbf{r}m
Discrete masses about an axis x_i :
\mathbf{m} \sum_{i1}^N \mathbf{r}_i m_i
Continuum of mass about an axis x_i :
\mathbf{m} = \int \rho \left ( \mathbf{r} \right ) x_i \mathrm{d} \mathbf{r} kg m M L Center of mass rcom
(Symbols vary) i-th moment of mass \mathbf{m}_i = \mathbf{r}_i m_i
Discrete masses:
\mathbf{r}_\mathrm{com} \frac{1}{M} \sum_i \mathbf{r}_i m_i \frac{1}{M} \sum_i \mathbf{m}_i
Mass continuum:
\mathbf{r}_\mathrm{com} \frac{1}{M} \int \mathrm{d}\mathbf{m} \frac{1}{M} \int \mathbf{r} \, \mathrm{d}m \frac{1}{M}\int \mathbf{r} \rho \, \mathrm{d}V m L 2-Body reduced mass m12, μ Pair of masses m1 and m2 \mu = \frac{m_1 m_2}{m_1 + m_2} kg M Moment of inertia (MOI) I Discrete Masses:
I \sum_i \mathbf{m}_i \cdot \mathbf{r}_i \sum_i \left | \mathbf{r}_i \right | ^2 m
Mass continuum:
I \int \left | \mathbf{r} \right | ^2 \mathrm{d} m \int \mathbf{r} \cdot \mathrm{d} \mathbf{m} = \int \left | \mathbf{r} \right | ^2 \rho \, \mathrm{d}V kg m2 M L2
Derived kinematic quantities
thumb|300px|Kinematic quantities of a classical particle: mass m, position r, velocity v, acceleration a.
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Velocity v \mathbf{v} \frac{\mathrm{d} \mathbf{r}}{\mathrm{d} t} m s−1 L T−1 Acceleration a \mathbf{a} \frac{\mathrm{d} \mathbf{v}}{\mathrm{d} t} \frac{\mathrm{d}^2 \mathbf{r}}{\mathrm{d} t^2 } m s−2 L T−2 Jerk j \mathbf{j} \frac{\mathrm{d} \mathbf{a}}{\mathrm{d} t} \frac{\mathrm{d}^3 \mathbf{r}}{\mathrm{d} t^3} m s−3 L T−3 Jounce s \mathbf{s} \frac{\mathrm{d} \mathbf{j}}{\mathrm{d} t} = \frac{\mathrm{d}^4 \mathbf{r}}{\mathrm{d} t^4}
|| m s−4 || L T−4 Angular velocity ω \boldsymbol{\omega} \mathbf{\hat{n}} \frac{ \mathrm{d} \theta }{\mathrm{d} t} rad s−1 T−1 Angular Acceleration α \boldsymbol{\alpha} \frac{\mathrm{d} \boldsymbol{\omega}}{\mathrm{d} t} \mathbf{\hat{n}} \frac{\mathrm{d}^2 \theta}{\mathrm{d} t^2} rad s−2 T−2 Angular jerk ζ \boldsymbol{\zeta} \frac{\mathrm{d} \boldsymbol{\alpha}}{\mathrm{d} t} = \mathbf{\hat{n}} \frac{ \mathrm{d}^3 \theta}{\mathrm{d} t^3} rad s−3 T−3
Derived dynamic quantities
350px|thumb|Angular momenta of a classical object.Left: intrinsic "spin" angular momentum S is really orbital angular momentum of the object at every point,right: extrinsic orbital angular momentum L about an axis,top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω)bottom: momentum p and its radial position r from the axis.The total angular momentum (spin + orbital) is J.
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Momentum p \mathbf{p} m\mathbf{v} kg m s−1 M L T−1 Force F \mathbf{F} \mathrm{d} \mathbf{p}/\mathrm{d} t N kg m s−2 M L T−2 Impulse J, Δp, I \mathbf{J} \Delta \mathbf{p} \int_{t_1}^{t_2} \mathbf{F} \, \mathrm{d} t kg m s−1 M L T−1 Angular momentum about a position point r0, L, J, S \mathbf{L} \left ( \mathbf{r} - \mathbf{r}_0 \right ) \times \mathbf{p}
Most of the time we can set r0 = 0 if particles are orbiting about axes intersecting at a common point. kg m2 s−1 M L2 T−1 Moment of a force about a position point r0,
Torque τ, M \boldsymbol{\tau} \left ( \mathbf{r} - \mathbf{r}_0 \right ) \times \mathbf{F} \frac{\mathrm{d} \mathbf{L}}{\mathrm{d} t} N m kg m2 s−2 M L2 T−2 Angular impulse ΔL (no common symbol) \Delta \mathbf{L} \int_{t_1}^{t_2} \boldsymbol{\tau} \, \mathrm{d} t kg m2 s−1 M L2 T−1
General energy definitions
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Mechanical work due to a Resultant Force W W \int_C \mathbf{F} \cdot \mathrm{d} \mathbf{r} J N m kg m2 s−2 M L2 T−2 Work done ON mechanical system, Work done BY WON, WBY \Delta W_\mathrm{ON} - \Delta W_\mathrm{BY} J N m kg m2 s−2 M L2 T−2 Potential energy φ, Φ, U, V, Ep \Delta W - \Delta V J N m kg m2 s−2 M L2 T−2 Mechanical power P P \frac{\mathrm{d}E}{\mathrm{d}t} W = J s−1 M L2 T−3
Every conservative force has a potential energy. By following two principles one can consistently assign a non-relative value to U:
Wherever the force is zero, its potential energy is defined to be zero as well.
Whenever the force does work, potential energy is lost.
Generalized mechanics
Quantity (common name/s) (Common) symbol/s Defining equation SI units DimensionGeneralized coordinates q, Q varies with choice varies with choiceGeneralized velocities \dot{q},\dot{Q} \dot{q}\equiv \mathrm{d}q/\mathrm{d}t varies with choice varies with choiceGeneralized momenta p, P p \partial L /\partial \dot{q} varies with choice varies with choice Lagrangian L L(\mathbf{q},\mathbf{\dot{q}},t) T(\mathbf{\dot{q}}) - V(\mathbf{q},\mathbf{\dot{q}},t)
where \mathbf{q} \mathbf{q}(t) and p p(t) are vectors of the generalized coords and momenta, as functions of time J M L2 T−2 Hamiltonian H H(\mathbf{p},\mathbf{q},t) \mathbf{p}\cdot\mathbf{\dot{q}} - L(\mathbf{q},\mathbf{\dot{q}},t) J M L2 T−2 Action, Hamilton's principal function S, \scriptstyle{\mathcal{S}} \mathcal{S} \int_{t_1}^{t_2} L(\mathbf{q},\mathbf{\dot{q}},t) \mathrm{d}t J s M L2 T−1
Kinematics
In the following rotational definitions, the angle can be any angle about the specified axis of rotation. It is customary to use θ, but this does not have to be the polar angle used in polar coordinate systems. The unit axial vector
\mathbf{\hat{n}} = \mathbf{\hat{e}}_r\times\mathbf{\hat{e}}_\theta
defines the axis of rotation, \scriptstyle \mathbf{\hat{e}}_r unit vector in direction of , \scriptstyle \mathbf{\hat{e}}_\theta unit vector tangential to the angle.
Translation RotationVelocityAverage:
\mathbf{v}_{\mathrm{average}} = {\Delta \mathbf{r} \over \Delta t}
Instantaneous:
\mathbf{v} {d\mathbf{r} \over dt}Angular velocity \boldsymbol{\omega} \mathbf{\hat{n}}\frac{{\rm d} \theta}{{\rm d} t}Rotating rigid body: \mathbf{v} = \boldsymbol{\omega} \times \mathbf{r} AccelerationAverage:
\mathbf{a}_{\mathrm{average}} = \frac{\Delta\mathbf{v}}{\Delta t}
Instantaneous:
\mathbf{a} \frac{d\mathbf{v}}{dt} \frac{d^2\mathbf{r}}{dt^2} Angular acceleration
\boldsymbol{\alpha} \frac{{\rm d} \boldsymbol{\omega}}{{\rm d} t} \mathbf{\hat{n}}\frac{{\rm d}^2 \theta}{{\rm d} t^2}
Rotating rigid body:
\mathbf{a} = \boldsymbol{\alpha} \times \mathbf{r} + \boldsymbol{\omega} \times \mathbf{v} JerkAverage:
\mathbf{j}_{\mathrm{average}} = \frac{\Delta\mathbf{a}}{\Delta t}
Instantaneous:
\mathbf{j} \frac{d\mathbf{a}}{dt} \frac{d^2\mathbf{v}}{dt^2} = \frac{d^3\mathbf{r}}{dt^3} Angular jerk
\boldsymbol{\zeta} \frac{{\rm d} \boldsymbol{\alpha}}{{\rm d} t} \mathbf{\hat{n}}\frac{{\rm d}^2 \omega}{{\rm d} t^2} = \mathbf{\hat{n}}\frac{{\rm d}^3 \theta}{{\rm d} t^3}
Rotating rigid body:
\mathbf{j} = \boldsymbol{\zeta} \times \mathbf{r} + \boldsymbol{\alpha} \times \mathbf{a}
Dynamics
Translation RotationMomentumMomentum is the "amount of translation"
\mathbf{p} = m\mathbf{v}
For a rotating rigid body:
\mathbf{p} = \boldsymbol{\omega} \times \mathbf{m} Angular momentum
Angular momentum is the "amount of rotation":
\mathbf{L} \mathbf{r} \times \mathbf{p} \mathbf{I} \cdot \boldsymbol{\omega}
and the cross-product is a pseudovector i.e. if r and p are reversed in direction (negative), L is not.
In general I is an order-2 tensor, see above for its components. The dot · indicates tensor contraction.Force and Newton's 2nd lawResultant force acts on a system at the center of mass, equal to the rate of change of momentum:
\begin{align} \mathbf{F} & \frac{d\mathbf{p}}{dt} \frac{d(m\mathbf{v})}{dt} \\
& = m\mathbf{a} + \mathbf{v}\frac{{\rm d}m}{{\rm d}t} \\
\end{align}
For a number of particles, the equation of motion for one particle i is:
\frac{\mathrm{d}\mathbf{p}_i}{\mathrm{d}t} = \mathbf{F}_{E} + \sum_{i \neq j} \mathbf{F}_{ij}
where pi momentum of particle i, Fij force on particle i by particle j, and FE = resultant external force (due to any agent not part of system). Particle i does not exert a force on itself.Torque
Torque τ is also called moment of a force, because it is the rotational analogue to force:
\boldsymbol{\tau} \frac{{\rm d}\mathbf{L}}{{\rm d}t} \mathbf{r}\times\mathbf{F} = \frac{{\rm d}(\mathbf{I} \cdot \boldsymbol{\omega})}{{\rm d}t}
For rigid bodies, Newton's 2nd law for rotation takes the same form as for translation:
\begin{align}
\boldsymbol{\tau} & \frac{{\rm d}\mathbf{L}}{{\rm d}t} \frac{{\rm d}(\mathbf{I}\cdot\boldsymbol{\omega})}{{\rm d}t} \\
& = \frac{{\rm d}\mathbf{I}}{{\rm d}t}\cdot\boldsymbol{\omega} + \mathbf{I}\cdot\boldsymbol{\alpha} \\
\end{align}
Likewise, for a number of particles, the equation of motion for one particle i is:
\frac{\mathrm{d}\mathbf{L}_i}{\mathrm{d}t} = \boldsymbol{\tau}_E + \sum_{i \neq j} \boldsymbol{\tau}_{ij} YankYank is rate of change of force:
\begin{align} \mathbf{Y} & \frac{d\mathbf{F}}{dt} \frac{d^2\mathbf{p}}{dt^2} = \frac{d^2(m\mathbf{v})}{dt^2} \\[1ex]
& = m\mathbf{j} + \mathbf{2a}\frac{{\rm d}m}{{\rm d}t} + \mathbf{v}\frac{{\rm d^2}m}{{\rm d}t^2}
\end{align}
For constant mass, it becomes;
\mathbf{Y} = m\mathbf{j}Rotatum
Rotatum Ρ is also called moment of a Yank, because it is the rotational analogue to yank:
\boldsymbol{\Rho} \frac{{\rm d}\boldsymbol{\tau}}{{\rm d}t} \mathbf{r}\times\mathbf{Y} = \frac{{\rm d}(\mathbf{I} \cdot \boldsymbol{\alpha})}{{\rm d}t} ImpulseImpulse is the change in momentum:
\Delta \mathbf{p} = \int \mathbf{F} \, dt
For constant force F:
\Delta \mathbf{p} = \mathbf{F} \Delta t Twirl/angular impulse is the change in angular momentum:
\Delta \mathbf{L} = \int \boldsymbol{\tau} \, dt
For constant torque τ:
\Delta \mathbf{L} = \boldsymbol{\tau} \Delta t
Precession
The precession angular speed of a spinning top is given by:
\boldsymbol{\Omega} = \frac{wr}{I\boldsymbol{\omega}}
where w is the weight of the spinning flywheel.
Energy
The mechanical work done by an external agent on a system is equal to the change in kinetic energy of the system:
General work-energy theorem (translation and rotation)
The work done W by an external agent which exerts a force F (at r) and torque τ on an object along a curved path C is:
W \Delta T \int_C \left ( \mathbf{F} \cdot \mathrm{d} \mathbf{r} + \boldsymbol{\tau} \cdot \mathbf{n} \, {\mathrm{d} \theta} \right )
where θ is the angle of rotation about an axis defined by a unit vector n.
Kinetic energy
The change in kinetic energy for an object initially traveling at speed v_0 and later at speed v is:
\Delta E_k W \frac{1}{2} m(v^2 - {v_0}^2)
Elastic potential energy
For a stretched spring fixed at one end obeying Hooke's law, the elastic potential energy is
\Delta E_p = \frac{1}{2} k(r_2-r_1)^2
where r2 and r1 are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant.
Euler's equations for rigid body dynamics
Euler also worked out analogous laws of motion to those of Newton, see Euler's laws of motion. These extend the scope of Newton's laws to rigid bodies, but are essentially the same as above. A new equation Euler formulated is:
\mathbf{I} \cdot \boldsymbol{\alpha} + \boldsymbol{\omega} \times \left ( \mathbf{I} \cdot \boldsymbol{\omega} \right ) = \boldsymbol{\tau}
where I is the moment of inertia tensor.
General planar motion
The previous equations for planar motion can be used here: corollaries of momentum, angular momentum etc. can immediately follow by applying the above definitions. For any object moving in any path in a plane,
\mathbf{r} \mathbf{r}(t) r\hat\mathbf r
the following general results apply to the particle.
Kinematics Dynamics Position
\mathbf{r} \mathbf{r}\left ( r,\theta, t \right ) r \hat\mathbf r Velocity
\mathbf{v} = \hat\mathbf r \frac{\mathrm{d} r}{\mathrm{d}t} + r \omega \hat\mathbf\theta Momentum
\mathbf{p} = m \left(\hat\mathbf r \frac{\mathrm{d} r}{\mathrm{d}t} + r \omega \hat\mathbf\theta \right)
Angular momenta
\mathbf{L} = m \mathbf{r}\times \left(\hat\mathbf{r} \frac{\mathrm{d} r}{\mathrm{d}t} + r\omega\hat\mathbf\theta\right) Acceleration
\mathbf{a} =\left ( \frac{\mathrm{d}^2 r}{\mathrm{d}t^2} - r\omega^2\right )\hat\mathbf r + \left ( r \alpha + 2 \omega \frac{\mathrm{d}r}{{\rm d}t} \right )\hat\mathbf\theta The centripetal force is
\mathbf{F}_\bot - m \omega^2 R \hat\mathbf r - \omega^2 \mathbf{m}
where again m is the mass moment, and the Coriolis force is
\mathbf{F}_c 2\omega m \frac{{\rm d}r}{{\rm d}t} \hat\mathbf\theta 2\omega m v \hat\mathbf\theta
The Coriolis acceleration and force can also be written:
\mathbf{F}_c m\mathbf{a}_c -2 m \boldsymbol{ \omega \times v}
Central force motion
For a massive body moving in a central potential due to another object, which depends only on the radial separation between the centers of masses of the two objects, the equation of motion is:
\frac{d^2}{d\theta^2}\left(\frac{1}{\mathbf{r}}\right) + \frac{1}{\mathbf{r}} = -\frac{\mu\mathbf{r}^2}{\mathbf{l}^2}\mathbf{F}(\mathbf{r})
Equations of motion (constant acceleration)
These equations can be used only when acceleration is constant. If acceleration is not constant then the general calculus equations above must be used, found by integrating the definitions of position, velocity and acceleration (see above).
Linear motionAngular motion\mathbf{v-v_0}\mathbf at \boldsymbol{\omega - \omega_0} \boldsymbol\alpha t \mathbf{x - x_0} \tfrac{1}{2}(\mathbf{v_0+v})t \boldsymbol{\theta - \theta_0} \tfrac{1}{2}(\boldsymbol{\omega_0 + \omega})t\mathbf{x - x_0} \mathbf v_0t+\tfrac{1}{2}\mathbf at^2 \boldsymbol{\theta - \theta_0} \boldsymbol\omega _0 t + \tfrac{1}{2} \boldsymbol\alpha t^2 \mathbf x_{n^{th}} \mathbf v_0+\mathbf a(n-\tfrac{1}{2}) \boldsymbol\theta_{n^{th}}\boldsymbol\omega_0+\boldsymbol\alpha(n-\tfrac{1}{2})v^2 - v_0^2 2\mathbf{a(x-x_0)} \omega^2 - \omega_0^2 2\boldsymbol{\alpha(\theta-\theta_0)}
Galilean frame transforms
For classical (Galileo-Newtonian) mechanics, the transformation law from one inertial or accelerating (including rotation) frame (reference frame traveling at constant velocity - including zero) to another is the Galilean transform.
Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F' moving at translational velocity V or angular velocity Ω relative to F. Conversely F moves at velocity (—V or —Ω) relative to F'. The situation is similar for relative accelerations.
Motion of entities Inertial frames Accelerating framesTranslation
V = Constant relative velocity between two inertial frames F and F'.
A = (Variable) relative acceleration between two accelerating frames F and F'.Relative position
\mathbf{r}' = \mathbf{r} + \mathbf{V}t
Relative velocity
\mathbf{v}' = \mathbf{v} + \mathbf{V}
Equivalent accelerations
\mathbf{a}' = \mathbf{a} Relative accelerations
\mathbf{a}' = \mathbf{a} + \mathbf{A}
Apparent/fictitious forces
\mathbf{F}' = \mathbf{F} - \mathbf{F}_\mathrm{app} Rotation
Ω = Constant relative angular velocity between two frames F and F'.
Λ = (Variable) relative angular acceleration between two accelerating frames F and F'.Relative angular position
\theta' = \theta + \Omega t
Relative velocity
\boldsymbol{\omega}' = \boldsymbol{\omega} + \boldsymbol{\Omega}
Equivalent accelerations
\boldsymbol{\alpha}' = \boldsymbol{\alpha} Relative accelerations
\boldsymbol{\alpha}' = \boldsymbol{\alpha} + \boldsymbol{\Lambda}
Apparent/fictitious torques
\boldsymbol{\tau}' = \boldsymbol{\tau} - \boldsymbol{\tau}_\mathrm{app} Transformation of any vector T to a rotating frame
\frac{{\rm d}\mathbf{T}'}{{\rm d}t} = \frac{{\rm d}\mathbf{T}}{{\rm d}t} - \boldsymbol{\Omega} \times \mathbf{T}
Mechanical oscillators
SHM, DHM, SHO, and DHO refer to simple harmonic motion, damped harmonic motion, simple harmonic oscillator and damped harmonic oscillator respectively.
+ Equations of motion Physical situation Nomenclature Translational equations Angular equations SHM
x = Transverse displacement
θ = Angular displacement
A = Transverse amplitude
Θ Angular amplitude \frac{\mathrm{d}^2 x}{\mathrm{d}t^2} - \omega^2 x
Solution:
x A \sin\left ( \omega t + \phi \right ) \frac{\mathrm{d}^2 \theta}{\mathrm{d}t^2} - \omega^2 \theta
Solution:
\theta = \Theta \sin\left ( \omega t + \phi \right ) Unforced DHM
b = damping constant
κ torsion constant \frac{\mathrm{d}^2 x}{\mathrm{d}t^2} + b \frac{\mathrm{d}x}{\mathrm{d}t} + \omega^2 x 0
Solution (see below for ω'):
x=Ae^{-bt/2m}\cos\left ( \omega' \right )
Resonant frequency:
\omega_\mathrm{res} = \sqrt{\omega^2 - \left ( \frac{b}{4m} \right )^2 }
Damping rate:
\gamma = b/m
Expected lifetime of excitation:
\tau 1/\gamma \frac{\mathrm{d}^2 \theta}{\mathrm{d}t^2} + b \frac{\mathrm{d}\theta}{\mathrm{d}t} + \omega^2 \theta 0
Solution:
\theta=\Theta e^{-\kappa t/2m}\cos\left ( \omega \right )
Resonant frequency:
\omega_\mathrm{res} = \sqrt{\omega^2 - \left ( \frac{\kappa}{4m} \right )^2 }
Damping rate:
\gamma = \kappa/m
Expected lifetime of excitation:
\tau = 1/\gamma
+ Angular frequencies Physical situation Nomenclature Equations Linear undamped unforced SHO
k = spring constant
m mass of oscillating bob \omega \sqrt{\frac{k}{m}} Linear unforced DHO
k = spring constant
b Damping coefficient \omega' \sqrt{\frac{k}{m}-\left ( \frac{b}{2m} \right )^2 } Low amplitude angular SHO
I = Moment of inertia about oscillating axis
κ torsion constant \omega \sqrt{\frac{\kappa}{I}} Low amplitude simple pendulum
L = Length of pendulum
g = Gravitational acceleration
Θ = Angular amplitude Approximate value
\omega = \sqrt{\frac{g}{L}}
Exact value can be shown to be:
\omega \sqrt{\frac{g}{L}} \left [ 1 + \sum_{k1}^\infty \frac{\prod_{n1}^k \left ( 2n-1 \right )}{\prod_{n1}^m \left ( 2n \right )} \sin^{2n} \Theta \right ]
+ Energy in mechanical oscillations Physical situation Nomenclature Equations SHM energy
T = kinetic energy
U = potential energy
E = total energy Potential energy
U \frac{m}{2} \left ( x \right )^2 \frac{m \left( \omega A \right )^2}{2} \cos^2(\omega t + \phi)
Maximum value at x = A:
U_\mathrm{max} = \frac{m}{2} \left ( \omega A \right )^2
Kinetic energy
T \frac{\omega^2 m}{2} \left ( \frac{\mathrm{d} x}{\mathrm{d} t} \right )^2 \frac{m \left ( \omega A \right )^2}{2}\sin^2\left ( \omega t + \phi \right )
Total energy
E T + U DHM energy E \frac{m \left ( \omega A \right )^2}{2}e^{-bt/m}
See also
List of physics formulae
Defining equation (physical chemistry)
Constitutive equation
Mechanics
Optics
Electromagnetism
Thermodynamics
Acoustics
Isaac Newton
List of equations in wave theory
List of relativistic equations
List of equations in fluid mechanics
List of equations in gravitation
List of electromagnetism equations
List of photonics equations
List of equations in quantum mechanics
List of equations in nuclear and particle physics
Notes
References
Category:Classical mechanics
Classical Mechanics
|
https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics
|
2025-04-05T18:27:42.342976
|
6051
|
Cursus honorum
|
The , or more colloquially 'ladder of offices'; ) was the sequential order of public offices held by aspiring politicians in the Roman Republic and the early Roman Empire. It was designed for men of senatorial rank. The cursus honorum comprised a mixture of military and political administration posts; the ultimate prize for winning election to each "rung" in the sequence was to become one of the two consuls in a given year.
These rules were altered and flagrantly ignored in the course of the last century of the Republic. For example, Gaius Marius held consulships for five years in a row between 104 BC and 100 BC. He was consul seven times in all, also serving in 107 and 86. Officially presented as opportunities for public service, the offices often became mere opportunities for self-aggrandizement. The constitutional reforms of Sulla between 82 and 79 BC required a ten-year interval before holding the same office again for another term.
To have held each office at the youngest possible age (suo anno, 'in his year') was considered a great political success. For instance, to miss out on a praetorship at 39 meant that one could not become consul at 42. Cicero expressed extreme pride not only in being a novus homo ('new man'; comparable to a "self-made man") who became consul even though none of his ancestors had ever served as a consul, but also in having become consul "in his year".
Military service
Prior to entering political life and the cursus honorum, a young man of senatorial rank was expected to serve around ten years of military duty. The years of service were intended to be mandatory in order to qualify for political office.
Advancement and honors would improve his political prospects, and a successful military career might culminate in the office of military tribune, to which 24 men were elected by the Tribal Assembly each year. From the time of Augustus onwards, twenty quaestors served in the financial administration at Rome or as second-in-command to a governor in the provinces. They could also serve as the paymaster for a legion.
Aedile
At 36 years of age, a promagistrate could stand for election to one of the aediles (pronounced , from aedes, "temple edifice") positions. Of these aediles, two were plebeian and two were patrician, with the patrician aediles called curule aediles. The plebeian aediles were elected by the Plebeian Council and the curule aediles were either elected by the Tribal Assembly or appointed by the reigning consul. The aediles had administrative responsibilities in Rome. They had to take care of the temples (whence their title, from the Latin aedes, "temple"), organize games, and be responsible for the maintenance of the public buildings in Rome. Moreover, they took charge of Rome's water and food supplies; in their capacity as market superintendents, they served sometimes as judges in mercantile affairs.
The aedile was the supervisor of public works; the words "edifice" and "edification" stem from the same root. He oversaw the public works, temples and markets. Therefore, the aediles would have been in some cooperation with the current censors, who had similar or related duties. Also, they oversaw the organization of festivals and games (ludi), which made this a very sought-after office for a career minded politician of the late Republic, as it was a good means of gaining popularity by staging spectacles.
Curule aediles were added at a later date in the 4th century BC; their duties do not differ substantially from plebeian aediles. However, unlike plebeian aediles, curule aediles were allowed certain symbols of rank—the sella curulis or curule chair, for example—and only patricians could stand for election to curule aedile. This later changed, and both plebeians and patricians could stand for curule aedileship.
The elections for curule aedile were at first alternated between patricians and plebeians, until late in the 2nd century BC, when the practice was abandoned and both classes became free to run during all years.
While part of the cursus honorum, this step was optional and not required to hold future offices. Though the office was usually held after the quaestorship and before the praetorship, there are some cases with former praetors serving as aediles. Praetor
After serving either as quaestor or as aedile, a man of 39 years could run for praetor. During the reign of Augustus this requirement was lowered to 30, at the request of Gaius Maecenas. The number of praetors elected varied through history, generally increasing with time. During the republic, six or eight were generally elected each year to serve judicial functions throughout Rome and other governmental responsibilities. In the absence of the consuls, a praetor would be given command of the garrison in Rome or in Italy. Also, a praetor could exercise the functions of the consuls throughout Rome, but their main function was that of a judge. They would preside over trials involving criminal acts, grant court orders and validate "illegal" acts as acts of administering justice. A praetor was escorted by six lictors, and wielded imperium. After a term as praetor, the magistrate could serve as a provincial governor with the title of propraetor, wielding propraetor imperium, commanding the province's legions, and possessing ultimate authority within his province(s).
Two of the praetors were more prestigious than the others. The first was the Praetor Peregrinus, who was the chief judge in trials involving one or more foreigners. The other was the Praetor Urbanus, the chief judicial office in Rome. He had the power to overturn any verdict by any other courts, and served as judge in cases involving criminal charges against provincial governors. The Praetor Urbanus was not allowed to leave the city for more than ten days. If one of these two praetors was absent from Rome, the other would perform the duties of both. Consul
The office of consul was the most prestigious of all of the offices on the cursus honorum, and represented the summit of a successful career. The minimum age was 42. Years were identified by the names of the two consuls elected for a particular year; for instance, M. Messalla et M. Pisone consulibus, "in the consulship of Messalla and Piso", dates an event to 61 BC. Consuls were responsible for the city's political agenda, commanded large-scale armies and controlled important provinces. The consuls served for only a year (a restriction intended to limit the amassing of power by individuals) and could only rule when they agreed, because each consul could veto the other's decision.
The consuls would alternate monthly as the chairman of the Senate. They also were the supreme commanders in the Roman army, with each being granted two legions during their consular year. Consuls also exercised the highest juridical power in the Republic, being the only office with the power to override the decisions of the Praetor Urbanus. Only laws and the decrees of the Senate or the People's assembly limited their powers, and only the veto of a fellow consul or a tribune of the plebs could supersede their decisions.
A consul was escorted by twelve lictors, held imperium and wore the toga praetexta. Because the consul was the highest executive office within the Republic, they had the power to veto any action or proposal by any other magistrate, save that of the Tribune of the Plebs. After a consulship, a consul was assigned one of the more important provinces and acted as the governor in the same way that a propraetor did, only owning proconsular imperium. A second consulship could only be attempted after an interval of 10 years to prevent one man holding too much power. Dictator and magister equitum
Of all the offices within the Roman Republic, none granted as much power and authority as the position of dictator, known as the Master of the People. In times of emergency, the Senate would declare that a dictator was required, and the current consuls would appoint a dictator. This was the only decision that could not be vetoed by the Tribune of the Plebs. The dictator was the sole exception to the Roman legal principles of having multiple magistrates in the same office and being legally able to be held to answer for actions in office. Essentially by definition, only one dictator could serve at a time, and no dictator could ever be held legally responsible for any action during his time in office for any reason.
The dictator was the highest magistrate in degree of imperium and was attended by twenty-four lictors (as were the former Kings of Rome). Although his term lasted only six months instead of twelve (except for the Dictatorships of Sulla and Caesar), all other magistrates reported to the dictator (except for the tribunes of the plebs – although they could not veto any of the dictator's acts), granting the dictator absolute authority in both civil and military matters throughout the Republic. The dictator was free from the control of the Senate in all that he did, could execute anyone without a trial for any reason, and could ignore any law in the performance of his duties. The dictator was the sole magistrate under the Republic that was truly independent in discharging his duties. All of the other offices were extensions of the Senate's executive authority and thus answerable to the Senate. Since the dictator exercised his own authority, he did not suffer this limitation, which was the cornerstone of the office's power.
When a dictator entered office, he appointed to serve as his second-in-command a magister equitum, the Master of the Horse, whose office ceased to exist once the dictator left office. The magister equitum held praetorian imperium, was attended by six lictors, and was charged with assisting the dictator in managing the State. When the dictator was away from Rome, the magister equitum usually remained behind to administer the city. The magister equitum, like the dictator, had unchallengeable authority in all civil and military affairs, with his decisions only being overturned by the dictator himself.
The dictatorship was definitively abolished in 44 BC after the assassination of Gaius Julius Caesar (Lex Antonia).
See also
* Outline of ancient Rome – overview of and topical guide to ancient Rome
* Political institutions of ancient Rome – lists of political institutions of ancient Rome
* Roman Senate – political institution in ancient Rome
* Vigintisexviri – college of minor magistrates of the Roman Republic
* Tres militiae – the equestrian order version of the cursus honorum
References
External links
*[http://www.vroma.org/~bmcmanus/romangvt.html Diagram of the cursus honorum]
*[https://www.livius.org/articles/concept/cursus-honorum/ Livius.org: Cursus honorum]
Category:Ancient Roman government
Category:Roman law
|
https://en.wikipedia.org/wiki/Cursus_honorum
|
2025-04-05T18:27:42.354240
|
6056
|
Continental drift
|
Continental drift is a highly supported scientific theory, originating in the early 20th century, that Earth's continents move or drift relative to each other over geologic time. The concept was independently and more fully developed by Alfred Wegener in his 1915 publication, <nowiki/>"The Origin of Continents and Oceans".
Wegener was the first to use the phrase "continental drift" (1912, 1915) In 1939 an international geological conference was held in Frankfurt. See also
*
* Israel C. White
Citations
General and cited sources
*
*
* (pb: )
* <!-- CAUTION: catalogs are inconsistent. This is from the printed book. -->
* (First edition published 1570, [https://books.google.com/books?idYG1EAAAAcAAJ&pgPR4 1587 edition online])
*
* . External links
* [http://www.age-of-the-sage.org/tectonic_plates/boundaries_boundary_types.html#franklin_emerson_continental_drift Benjamin Franklin (1782) and Ralph Waldo Emerson (1834) noted Continental Drift]
* [http://www.ux1.eiu.edu/~cfjps/1300/cont_drift.html A brief introduction to Plate Tectonics, based on the work of Alfred Wegener]
* [https://www.nytimes.com/2021/02/06/science/tectonic-plates-continental-drift.html Animation of continental drift for last 1 billion years]
* [http://www.scotese.com/earth.htm Maps of continental drift, from the Precambrian to the future]
* [https://dinosaurpictures.org/ancient-earth 3D visualization of what did Earth look like from 750 million years ago to present (at present location of your choice)]
Category:Obsolete geology theories
Category:Plate tectonics
|
https://en.wikipedia.org/wiki/Continental_drift
|
2025-04-05T18:27:42.402760
|
6057
|
Commodores
|
Commodores (album)|other uses|Commodore (disambiguation)Commodore}}
| instrument | years_active 1968–present
| label =
| associated_acts | website
| current_members = * William King
* Walter Orange
* J.D. Nicholas
| past_members = * Milan Williams
* Thomas McClary
* Lionel Richie
* Ronald LaPread
* Andre Callahan
* Michael Gilbert
* James Ingram
* Skyler Jett
* Sheldon Reynolds
* Eugene Ward
* Mikael Manley
* David Hodges
* Chelsea Powell
* Kyra Avery
* Tom Joyner
}}
Commodores, often billed as The Commodores, is an American funk and soul group. The group's most successful period was in the late 1970s and early 1980s when Lionel Richie was the co-lead singer.
The members of the group met as mostly freshmen at Tuskegee Institute (now Tuskegee University) in 1968, and signed with Motown in November 1972, having first caught the public eye opening for the Jackson 5 while on tour.
The band's biggest hit singles are ballads such as "Easy", "Three Times a Lady", and "Nightshift"; and funk-influenced dance songs, including "Brick House", "Fancy Dancer", "Lady (You Bring Me Up)", and "Too Hot ta Trot".
Commodores were inducted into the Alabama Music Hall of Fame and Vocal Group Hall of Fame. The new six-man band featured Lionel Richie, Thomas McClary, and William King from the Mystics, and Andre Callahan, Michael Gilbert, and Milan Williams from the Jays. They chose their present name when King flipped open a dictionary and ran his finger down the page. "We lucked out," he remarked with a laugh when telling this story to People magazine. "We almost became 'The Commodes.'"
The bandmembers attended Tuskegee University in Alabama. After winning the university's annual freshman talent contest, they played at fraternity parties as well as a weekend gig at the Black Forest Inn, one of a few clubs in Tuskegee that catered to college students. They performed cover tunes and some original songs with their first singer, James Ingram (not the famous solo artist). and is also heard in many films, including Boogie Nights and Looking for Mr. Goodbar. It reached No. 22 on the Billboard Hot 100 in 1974. Another 1974 song "I Feel Sanctified" has been called a "prototype" of Wild Cherry's 1976 big hit "Play That Funky Music". Of the three albums released in 1975 and 1976, Caught in the Act was funk album, but ''Movin' On and Hot on the Tracks'' were pop albums. After those recordings the group developed the mellower sound hinted at in their 1976 top-ten hits, "Sweet Love" and "Just to Be Close to You".
Founding member McClary left in 1984 (shortly after Richie) to pursue a solo career,
The group gradually abandoned its funk roots and moved into the more commercial pop arena. The Commodores were on a European tour performing at Wembley Arena, London, on June 25, 2009, when they walked off the stage after they were told that Michael Jackson had died. Initially the band thought it was a hoax. However, back in their dressing rooms they received confirmation and broke down in tears. The next night at Birmingham's NIA Arena, J.D. Nicholas added Jackson's name to the lyrics of the song, and henceforth the Commodores have mentioned Jackson and other deceased R&B singers. Thus came the inspiration upon the first anniversary of Jackson's death to re-record, with new lyrics, the hit song "Nightshift" as a tribute.
In 1990, they formed Commodores Records and re-recorded their 20 greatest hits as Commodores Hits Vol. I & II. They have recorded a live album, Commodores Live, along with a DVD of the same name, and a Christmas album titled Commodores Christmas. In 2012, the band was working on new material, with some contributions written by current and former members.
Commodores as of 2020 consist of Walter "Clyde" Orange, James Dean "J.D." Nicholas, and William "WAK" King, along with their five-piece band The Mean Machine.They continue to perform, playing at arenas, theaters, and festivals around the world.PersonnelCurrent members
* William "WAK" King – trumpet, guitar, keyboards, vocals (1968–present)
* Walter Orange – vocals, drums (1972–present)
* James Dean "J.D." Nicholas – vocals (1984–2024)
Former members
* Lionel Richie – vocals, keyboards, saxophone (1968–82)
* Milan Williams – keyboards, rhythm guitar (1968–89)
* Thomas McClary – lead guitar, vocals (1968–83)
* Andre Callahan – drums, vocals, keyboards (1968–70)
* Michael Gilbert – bass guitar, trumpet (1968–70)
* Eugene Ward – keyboards (1968–70)
* Ronald LaPread – bass guitar (1970–86)
* James Ingram – vocals, drums (1970–72)
* Skyler Jett – vocals (1982–84)
* Sheldon Reynolds – lead guitar (1983–87)
* Mikael Manley – lead guitar (1995–2005)
* Don Williams Sr - keyboards (1999–2001)
Timeline
TimeAxis = orientation:horizontal format:yyyy
Legend = orientation:vertical position:bottom columns:4
ScaleMajor = increment:5 start:1968
ScaleMinor = increment:1 start:1968
Colors =
id:vocals value:red legend:Vocals
id:trump value:skyblue legend:Trumpet
id:sax value:tan2 legend:Saxophone
id:guitar value:green legend:Guitar
id:keys value:purple legend:Keyboards
id:bass value:blue legend:Bass
id:drums value:orange legend:Drums
id:studio value:black legend:Studio_album
id:bars value:gray(0.93)
BackgroundColors = bars:bars
LineData =
layer:back color:studio
at:22/07/1974
at:15/02/1975
at:15/10/1975
at:15/06/1976
at:30/03/1977
at:15/05/1978
at:15/07/1979
at:15/06/1980
at:22/06/1981
at:15/09/1983
at:15/01/1985
at:15/10/1986
at:15/07/1988
at:15/11/1992
at:29/03/1993
BarData =
bar:WK text:"William King"
bar:LR text:"Lionel Richie"
bar:SJ text:"Skyler Jett"
bar:JN text:"J.D. Nicholas"
bar:TM text:"Thomas McClary"
bar:SR text:"Sheldon Reynolds"
bar:MM text:"Mikael Manley"
bar:MW text:"Milan Williams"
bar:EW text:"Eugene Ward"
bar:MG text:"Michael Gilbert"
bar:RL text:"Ronald LaPread"
bar:AC text:"Andre Callahan"
bar:JI text:"James Ingram"
bar:WO text:"Walter Orange"
PlotData =
bar:LR from:start till:30/08/1982 color:sax width:11
bar:LR from:start till:30/08/1982 color:keys width:7
bar:LR from:start till:30/08/1982 color:vocals width:3
bar:TM from:start till:01/02/1983 color:guitar width:11
bar:TM from:start till:01/02/1983 color:vocals width:3
bar:MW from:start till:01/01/1989 color:keys width:11
bar:MW from:start till:01/01/1975 color:guitar width:3
bar:EW from:start till:01/01/1970 color:keys width:11
bar:MG from:start till:01/01/1970 color:bass width:11
bar:MG from:start till:01/01/1970 color:trump width:3
bar:AC from:start till:01/01/1970 color:drums width:11
bar:AC from:start till:01/01/1970 color:vocals width:3
bar:AC from:start till:01/01/1970 color:keys width:7
bar:WK from:start till:end color:trump width:11
bar:WK from:01/09/1982 till:end color:keys width:3
bar:WK from:01/05/1985 till:end color:guitar width:7
bar:RL from:01/02/1970 till:01/08/1986 color:bass width:11
bar:JI from:20/08/1970 till:01/04/1972 color:drums width:11
bar:JI from:20/08/1970 till:01/04/1972 color:vocals width:3
bar:WO from:01/05/1972 till:end color:drums width:11
bar:WO from:01/05/1972 till:end color:vocals width:3
bar:SJ from:01/10/1982 till:01/05/1984 color:vocals width:11
bar:SR from:01/01/1983 till:01/03/1987 color:guitar width:11
bar:JN from:01/06/1984 till:end color:vocals width:11
bar:MM from:01/03/1995 till:15/06/2005 color:guitar width:11
}}
Discography
;Studio albums
* Machine Gun (1974)
* Caught in the Act (1975)
* ''Movin' On (1975)
* Hot on the Tracks (1976)
* Commodores (1977)
* Natural High (1978)
* Midnight Magic (1979)
* Heroes (1980)
* In the Pocket (1981)
* Commodores 13 (1983)
* Nightshift (1985)
* United (1986)
* Rock Solid (1988)
* No Tricks'' (1993)
Accolades
Grammy awards
The Commodores have won one Grammy Award out of ten nominations.
{|class="wikitable sortable plainrowheaders"
|-
|+Grammy Awards
! scope="col" | Year
! scope="col" | Category
! scope="col" | Work
! scope="col" | Result
|-
| 1978
| rowspan=2|Best Rhythm & Blues Vocal Performance – Duo, Group Or Chorus
| "Easy" "Brick House"
|
|-
| rowspan=2|1979
| "Natural High"
|
|-
| rowspan=2|Best Pop Vocal Performance by a Duo or Group
| "Three Times A Lady"
|
|-
| rowspan=2|1980
| "Sail On"
|
|-
| rowspan=2|Best Rhythm & Blues Vocal Performance – Duo, Group Or Chorus
| "Midnight Magic"
|
|-
| rowspan=2|1981
| "Heroes"
|
|-
| Best Inspirational Performance
| "Jesus Is Love"
|
|-
| 1982
| rowspan=2|Best Rhythm & Blues Vocal Performance – Duo, Group Or Chorus
| "Lady (You Bring Me Up)"
|
|-
| 1986
| "Nightshift"
|
|}
Alabama Music Hall of Fame
During 1995 the Commodores were inducted into the Alabama Music Hall of Fame.Vocal Group Hall of FameDuring 2003 the Commodores were also inducted into the Vocal Group Hall of Fame.
References
External links
*
* [http://www.bluesandsoul.com/feature/395/lionel_richie_three_times_a_superstar/ Lionel Richie interview by Pete Lewis, 'Blues & Soul' 03/2009]
* [https://web.archive.org/web/20070312071212/http://www.vocalgroup.org/inductees/the_commodores.html 'The Commodores' Vocal Group Hall of Fame Page]
Category:American rhythm and blues musical groups
Category:American pop music groups
Category:American funk musical groups
Category:American musical sextets
Category:American soul musical groups
Category:Motown artists
Category:Musical groups from Alabama
Category:Grammy Award winners
Category:Musical groups established in 1968
Category:Tuskegee University alumni
Category:Lionel Richie
Category:African-American musical groups
Category:Universal Motown Records artists
Category:1968 establishments in Alabama
|
https://en.wikipedia.org/wiki/Commodores
|
2025-04-05T18:27:42.414334
|
6058
|
Collagen
|
thumb|upright=1.5|The triple helix: three left-handed polyproline type II helices (red, green, blue) assemble by an axial hydrogen bond to form a right-handed triple helix, the tertiary structure of collagen.
Collagen () is the main structural protein in the extracellular matrix of the connective tissues of many animals. It is the most abundant protein in mammals, making up 25% to 35% of protein content. Amino acids are bound together to form a triple helix of elongated fibril known as a collagen helix. It is mostly found in cartilage, bones, tendons, ligaments, and skin. Vitamin C is vital for collagen synthesis.
Depending on the degree of mineralization, collagen tissues may be rigid (bone) or compliant (tendon) or have a gradient from rigid to compliant (cartilage). Collagen is also abundant in corneas, blood vessels, the gut, intervertebral discs, and the dentin in teeth. In muscle tissue, it serves as a major component of the endomysium. Collagen constitutes 1% to 2% of muscle tissue and 6% by weight of skeletal muscle. The fibroblast is the most common cell creating collagen in animals. Gelatin, which is used in food and industry, is collagen that was irreversibly hydrolyzed using heat, basic solutions, or weak acids.
Etymology
thumb|Collagen
The name collagen comes from the Greek κόλλα (kólla), meaning "glue", and suffix -γέν, -gen, denoting "producing".
Types
As of 2011, 28 types of human collagen have been identified, described, and classified according to their structure. This diversity shows collagen's diverse functionality. All of the types contain at least one triple helix.
Fibrillar (type I, II, III, V, XI)
Non-fibrillar
FACIT (fibril-associated collagens with interrupted triple helices) (types IX, XII, XIV, XIX, XXI)
Short-chain (types VIII, X)
Basement membrane (type IV)
Multiplexin (multiple triple helix domains with interruptions) (types XV, XVIII)
MACIT (membrane-associated collagens with interrupted triple helices) (types XIII, XVII)
Microfibril-forming (type VI)
Anchoring fibrils (type VII)
The five most common types are:
Type I: skin, tendon, vasculature, organs, bone (main component of the organic part of bone)
Type II: cartilage (main collagenous component of cartilage)
Type III: reticulate (main component of reticular fibers), commonly found alongside type I
Type IV: forms basal lamina, the epithelium-secreted layer of the basement membrane
Type V: cell surfaces, hair, and placenta
In humans
Cardiac
The collagenous cardiac skeleton, which includes the four heart valve rings, is histologically, elastically and uniquely bound to cardiac muscle. The cardiac skeleton also includes the separating septa of the heart chambers – the interventricular septum and the atrioventricular septum. Collagen contribution to the measure of cardiac performance summarily represents a continuous torsional force opposed to the fluid mechanics of blood pressure emitted from the heart. The collagenous structure that divides the upper chambers of the heart from the lower chambers is an impermeable membrane that excludes both blood and electrical impulses through typical physiological means. With support from collagen, atrial fibrillation never deteriorates to ventricular fibrillation. Collagen is layered in variable densities with smooth muscle mass. The mass, distribution, age, and density of collagen all contribute to the compliance required to move blood back and forth. Individual cardiac valvular leaflets are folded into shape by specialized collagen under variable pressure. Gradual calcium deposition within collagen occurs as a natural function of aging. Calcified points within collagen matrices show contrast in a moving display of blood and muscle, enabling methods of cardiac imaging technology to arrive at ratios essentially stating blood in (cardiac input) and blood out (cardiac output). Pathology of the collagen underpinning of the heart is understood within the category of connective tissue disease.
Bone grafts
As the skeleton forms the structure of the body, it is vital that it maintains its strength, even after breaks and injuries. Collagen is used in bone grafting because its triple-helix structure makes it a very strong molecule. It is ideal for use in bones, as it does not compromise the structural integrity of the skeleton. The triple helical structure prevents collagen from being broken down by enzymes, it enables adhesiveness of cells and it is important for the proper assembly of the extracellular matrix.
Tissue regeneration
Collagen scaffolds are used in tissue regeneration, whether in sponges, thin sheets, gels, or fibers. Collagen has favorable properties for tissue regeneration, such as pore structure, permeability, hydrophilicity, and stability in vivo. Collagen scaffolds also support deposition of cells, such as osteoblasts and fibroblasts, and once inserted, facilitate growth to proceed normally.
Reconstructive surgery
Collagens are widely used in the construction of artificial skin substitutes used for managing severe burns and wounds. These collagens may be derived from cow, horse, pig, or even human sources; and are sometimes used in combination with silicones, glycosaminoglycans, fibroblasts, growth factors and other substances.
Wound healing
Collagen is one of the body's key natural resources and a component of skin tissue that can benefit all stages of wound healing. When collagen is made available to the wound bed, closure can occur. This avoids wound deterioration and procedures such as amputation.
Collagen is used as a natural wound dressing because it has properties that artificial wound dressings do not have. It resists bacteria, which is vitally important in wound dressing. As a burn dressing, collagen helps it heal fast by helping granulation tissue to grow over the burn. Collagen is also widely used as a bioink for 3D bioprinting and biofabrication of 3D tissue models.
Biology
The collagen protein is composed of a triple helix, which generally consists of two identical chains (α1) and an additional chain that differs slightly in its chemical composition (α2). The amino acid composition of collagen is atypical for proteins, particularly with respect to its high hydroxyproline content. The most common motifs in collagen's amino acid sequence are glycine-proline-X and glycine-X-hydroxyproline, where X is any amino acid other than glycine, proline or hydroxyproline.
The table below lists average amino acid composition for fish and mammal skin.
Amino acid Abundance in mammal skin(residues/1000) Abundance in fish skin(residues/1000) Glycine 329 339 Proline 126 108 Alanine 109 114 Hydroxyproline 95 67 Glutamic acid 74 76 Arginine 49 52 Aspartic acid 47 47 Serine 36 46 Lysine 29 26 Leucine 24 23 Valine 22 21 Threonine 19 26 Phenylalanine 13 14 Isoleucine 11 11 Hydroxylysine 6 8 Methionine 6 13 Histidine 5 7 Tyrosine 3 3 Cysteine 1 1 Tryptophan 0 0
Synthesis
First, a three-dimensional stranded structure is assembled, mostly composed of the amino acids glycine and proline. This is the collagen precursor procollagen. Then, procollagen is modified by the addition of hydroxyl groups to the amino acids proline and lysine. This step is important for later glycosylation and the formation of collagen's triple helix structure. Because the hydroxylase enzymes performing these reactions require vitamin C as a cofactor, a long-term deficiency in this vitamin results in impaired collagen synthesis and scurvy. These hydroxylation reactions are catalyzed by the enzymes prolyl 4-hydroxylase and lysyl hydroxylase. The reaction consumes one ascorbate molecule per hydroxylation. Collagen synthesis occurs inside and outside cells.
The most common form of collagen is fibrillary collagen. Another common form is meshwork collagen, which is often involved in the formation of filtration systems. All types of collagen are triple helices, but differ in the make-up of their alpha peptides created in step 2. Below we discuss the formation of fibrillary collagen.
Transcription of mRNA: Synthesis begins with turning on genes associated with the formation of a particular alpha peptide (typically alpha 1, 2 or 3). About 44 genes are associated with collagen formation, each coding for a specific mRNA sequence, and are typically named with the "COL" prefix.
Pre-pro-peptide formation: The created mRNA exits the cell nucleus into the cytoplasm. There, it links with the ribosomal subunits and is translated into a peptide. The peptide goes into the endoplasmic reticulum for post-translational processing. It is directed there by a signal recognition particle on the endoplasmic reticulum, which recognizes the peptide's signal sequence (the early part of the sequence). The processed product is a pre-pro-peptide called preprocollagen.
Pro-collagen formation: Three modifications of the pre-pro-peptide form the alpha peptide:
The signal peptide on the N-terminal is removed. The molecule is now called propeptide.
Lysines and prolines are hydroxylated by the enzymes 'prolyl hydroxylase' and 'lysyl hydroxylase', producing hydroxyproline and hydroxylysine. This helps in cross-linking the alpha peptides. This enzymatic step requires vitamin C as a cofactor. In scurvy, the lack of hydroxylation of prolines and lysines causes a looser triple helix (which is formed by three alpha peptides).
Glycosylation occurs by adding either glucose or galactose monomers onto the hydroxyl groups that were placed onto lysines, but not on prolines.
Three of the hydroxylated and glycosylated propeptides twist into a triple helix (except for its ends), forming procollagen. It is packaged into a transfer vesicle destined for the Golgi apparatus.
Modification and secretion: In the Golgi apparatus, the procollagen goes through one last post-translational modification, adding oligosaccharides (not monosaccharides as in step 3). Then it is packaged into a secretory vesicle to be secreted from the cell.
Tropocollagen formation: Outside the cell, membrane-bound enzymes called collagen peptidases remove the unwound ends of the molecule, producing tropocollagen. Defects in this step produce various collagenopathies called Ehlers–Danlos syndrome. This step is absent when synthesizing type III, a type of fibrillar collagen.
Collagen fibril formation: Lysyl oxidase, a copper-dependent enzyme, acts on lysines and hydroxylysines, producing aldehyde groups, which eventually form covalent bonds between tropocollagen molecules. This polymer of tropocollagen is called a collagen fibril.
thumb|upright=1.3|Action of lysyl oxidase
Amino acids
Collagen has an unusual amino acid composition and sequence:
Glycine is found at almost every third residue.
Proline makes up about 17% of collagen.
Collagen contains two unusual derivative amino acids not directly inserted during translation. These amino acids are found at specific locations relative to glycine and are modified post-translationally by different enzymes, both of which require vitamin C as a cofactor.
Hydroxyproline derived from proline
Hydroxylysine derived from lysine – depending on the type of collagen, varying numbers of hydroxylysines are glycosylated (mostly having disaccharides attached).
Cortisol stimulates degradation of (skin) collagen into amino acids.
Collagen I formation
Most collagen forms in a similar manner, but the following process is typical for type I:
Inside the cell
Two types of alpha chains – alpha-1 and alpha 2, are formed during translation on ribosomes along the rough endoplasmic reticulum (RER). These peptide chains known as preprocollagen, have registration peptides on each end and a signal peptide.
Polypeptide chains are released into the lumen of the RER.
Signal peptides are cleaved inside the RER and the chains are now known as pro-alpha chains.
Hydroxylation of lysine and proline amino acids occurs inside the lumen. This process is dependent on and consumes ascorbic acid (vitamin C) as a cofactor.
Glycosylation of specific hydroxylysine residues occurs.
Triple alpha helical structure is formed inside the endoplasmic reticulum from two alpha-1 chains and one alpha-2 chain.
Procollagen is shipped to the Golgi apparatus, where it is packaged and secreted into extracellular space by exocytosis.
Outside the cell
Registration peptides are cleaved and tropocollagen is formed by procollagen peptidase.
Multiple tropocollagen molecules form collagen fibrils, via covalent cross-linking (aldol reaction) by lysyl oxidase which links hydroxylysine and lysine residues. Multiple collagen fibrils form into collagen fibers.
Collagen may be attached to cell membranes via several types of protein, including fibronectin, laminin, fibulin and integrin.
Molecular structure
A single collagen molecule, tropocollagen, is used to make up larger collagen aggregates, such as fibrils. It is approximately 300 nm long and 1.5 nm in diameter, and it is made up of three polypeptide strands (called alpha peptides, see step 2), each of which has the conformation of a left-handed helix – this should not be confused with the right-handed alpha helix. These three left-handed helices are twisted together into a right-handed triple helix or "super helix", a cooperative quaternary structure stabilized by many hydrogen bonds. With type I collagen and possibly all fibrillar collagens, if not all collagens, each triple-helix associates into a right-handed super-super-coil referred to as the collagen microfibril. Each microfibril is interdigitated with its neighboring microfibrils to a degree that might suggest they are individually unstable, although within collagen fibrils, they are so well ordered as to be crystalline.
thumb|upright=1.3|Three polypeptides coil to form tropocollagen. Many tropocollagens then bind together to form a fibril, and many of these then form a fibre.
A distinctive feature of collagen is the regular arrangement of amino acids in each of the three chains of these collagen subunits. The sequence often follows the pattern Gly-Pro-X or Gly-X-Hyp, where X may be any of various other amino acid residues. Additional assembly of fibrils is guided by fibroblasts, which deposit fully formed fibrils from fibripositors. In the fibrillar collagens, molecules are staggered to adjacent molecules by about 67 nm (a unit that is referred to as 'D' and changes depending upon the hydration state of the aggregate). In each D-period repeat of the microfibril, there is a part containing five molecules in cross-section, called the "overlap", and a part containing only four molecules, called the "gap". Larger fibrillar bundles are formed with the aid of several different classes of proteins (including different collagen types), glycoproteins, and proteoglycans to form the different types of mature tissues from alternate combinations of the same key players. These later advances are particularly important to better understanding the way in which collagen structure affects cell–cell and cell–matrix communication and how tissues are constructed in growth and repair and changed in development and disease. For example, using AFM–based nanoindentation it has been shown that a single collagen fibril is a heterogeneous material along its axial direction with significantly different mechanical properties in its gap and overlap regions, correlating with its different molecular organizations in these two regions.
Collagen fibrils/aggregates are arranged in different combinations and concentrations in various tissues to provide varying tissue properties. In bone, entire collagen triple helices lie in a parallel, staggered array. 40 nm gaps between the ends of the tropocollagen subunits (approximately equal to the gap region) probably serve as nucleation sites for the deposition of long, hard, fine crystals of the mineral component, which is hydroxylapatite (approximately) Ca10(OH)2(PO4)6. Type I collagen gives bone its tensile strength.
Associated disorders
Collagen-related diseases most commonly arise from genetic defects or nutritional deficiencies that affect the biosynthesis, assembly, posttranslational modification, secretion, or other processes involved in normal collagen production.
+Genetic defects of collagen genes Type Notes Gene(s) Disorders
I This is the most abundant collagen of the human body. It is present in scar tissue, the end product when tissue heals by repair. It is found in tendons, skin, artery walls, cornea, the endomysium surrounding muscle fibers, fibrocartilage, and the organic part of bones and teeth. COL1A1, COL1A2 Osteogenesis imperfecta, Ehlers–Danlos syndrome, infantile cortical hyperostosis a.k.a. Caffey's disease
II Hyaline cartilage, makes up 50% of all cartilage protein. Vitreous humour of the eye. COL2A1 Collagenopathy, types II and XI
III This is the collagen of granulation tissue and is produced quickly by young fibroblasts before the tougher type I collagen is synthesized. Reticular fiber. Also found in artery walls, skin, intestines and the uterus COL3A1 Ehlers–Danlos syndrome, Dupuytren's contracture
IV Basal lamina; eye lens. Also serves as part of the filtration system in capillaries and the glomeruli of nephron in the kidney. COL4A1, COL4A2, COL4A3, COL4A4, COL4A5, COL4A6 Alport syndrome, Goodpasture's syndrome
V Most interstitial tissue, assoc. with type I, associated with placenta COL5A1, COL5A2, COL5A3 Ehlers–Danlos syndrome (classical)
VI Most interstitial tissue, assoc. with type I COL6A1, COL6A2, COL6A3, COL6A5 Ulrich myopathy, Bethlem myopathy, atopic dermatitis
VII Forms anchoring fibrils in dermoepidermal junctions COL7A1 Epidermolysis bullosa dystrophica
VIII Some endothelial cells COL8A1, COL8A2 Posterior polymorphous corneal dystrophy 2
IX FACIT collagen, cartilage, assoc. with type II and XI fibrils COL9A1, COL9A2, COL9A3 EDM2 and EDM3
X Hypertrophic and mineralizing cartilage COL10A1 Schmid metaphyseal dysplasia
XI Cartilage COL11A1, COL11A2 Collagenopathy, types II and XI
XII FACIT collagen, interacts with type I containing fibrils, decorin and glycosaminoglycans COL12A1 –
XIII Transmembrane collagen, interacts with integrin a1b1, fibronectin and components of basement membranes like nidogen and perlecan. COL13A1 –
XIV FACIT collagen, also known as undulin COL14A1 –
XV – COL15A1 –
XVI FACIT collagen COL16A1 –
XVII Transmembrane collagen, also known as BP180, a 180 kDa protein COL17A1 Bullous pemphigoid and certain forms of junctional epidermolysis bullosa
XVIII Source of endostatin COL18A1 –
XIX FACIT collagen COL19A1 –
XX – COL20A1 –
XXI FACIT collagen COL21A1 –
XXII FACIT collagen COL22A1 –
XXIII MACIT collagen COL23A1 –
XXIV – COL24A1 –
XXV – COL25A1 –
XXVI – EMID2 –
XXVII – COL27A1 –
XXVIII – COL28A1 –
In addition to the above-mentioned disorders, excessive deposition of collagen occurs in scleroderma.
Diseases
One thousand mutations have been identified in 12 out of more than 20 types of collagen. These mutations can lead to various diseases at the tissue level.
Osteogenesis imperfecta – Caused by a mutation in type 1 collagen, dominant autosomal disorder, results in weak bones and irregular connective tissue, some cases can be mild while others can be lethal. Mild cases have lowered levels of collagen type 1 while severe cases have structural defects in collagen.
Chondrodysplasias – Skeletal disorder believed to be caused by a mutation in type 2 collagen, further research is being conducted to confirm this.
Ehlers–Danlos syndrome – Thirteen different types of this disorder, which lead to deformities in connective tissue, are known. Some of the rarer types can be lethal, leading to the rupture of arteries. Each syndrome is caused by a different mutation. For example, the vascular type (vEDS) of this disorder is caused by a mutation in collagen type 3.
Alport syndrome – Can be passed on genetically, usually as X-linked dominant, but also as both an autosomal dominant and autosomal recessive disorder, those with the condition have problems with their kidneys and eyes, loss of hearing can also develop during the childhood or adolescent years.
Knobloch syndrome – Caused by a mutation in the COL18A1 gene that codes for the production of collagen XVIII. Patients present with protrusion of the brain tissue and degeneration of the retina; an individual who has family members with the disorder is at an increased risk of developing it themselves since there is a hereditary link.
Characteristics
Collagen is one of the long, fibrous structural proteins whose functions are quite different from those of globular proteins, such as enzymes. Tough bundles of collagen called collagen fibers are a major component of the extracellular matrix that supports most tissues and gives cells structure from the outside, but collagen is also found inside certain cells. Collagen has great tensile strength, and is the main component of fascia, cartilage, ligaments, tendons, bone and skin. Along with elastin and soft keratin, it is responsible for skin strength and elasticity, and its degradation leads to wrinkles that accompany aging. It strengthens blood vessels and plays a role in tissue development. It is present in the cornea and lens of the eye in crystalline form. It may be one of the most abundant proteins in the fossil record, given that it appears to fossilize frequently, even in bones from the Mesozoic and Paleozoic.
Mechanical properties
Collagen is a complex hierarchical material with mechanical properties that vary significantly across different scales.
On the molecular scale, atomistic and course-grained modeling simulations, as well as numerous experimental methods, have led to several estimates of the Young's modulus of collagen at the molecular level. Only above a certain strain rate is there a strong relationship between elastic modulus and strain rate, possibly due to the large number of atoms in a collagen molecule. The length of the molecule is also important, where longer molecules have lower tensile strengths than shorter ones due to short molecules having a large proportion of hydrogen bonds being broken and reformed.
On the fibrillar scale, collagen has a lower modulus compared to the molecular scale, and varies depending on geometry, scale of observation, deformation state, and hydration level.
Limited tests have been done on the tensile strength of the collagen fiber, but generally it has been shown to have a lower Young's modulus compared to fibrils.
When studying the mechanical properties of collagen, tendon is often chosen as the ideal material because it is close to a pure and aligned collagen structure. However, at the macro, tissue scale, the vast number of structures that collagen fibers and fibrils can be arranged into results in highly variable properties. For example, tendon has primarily parallel fibers, whereas skin consists of a net of wavy fibers, resulting in a much higher strength and lower ductility in tendon compared to skin. The mechanical properties of collagen at multiple hierarchical levels is given.
+Young's Modulus of Collagen at Multiple Hierarchical LevelsHierarchical LevelYoung's ModulusMolecular (via atomistic modeling)2.4-7 GPaFibril0.2-0.8 GPaFiber (measured from cross-linked rat tail tendon)1.10 GPaFiber (measured from non-cross-linked rat tail tendon)50-250 MPa
Uses
right|150px|thumb|A salami and the collagen casing (below) it came in
Collagen has a wide variety of applications. In the medical industry, it is used in cosmetic surgery and burn surgery. An example of collagen use for food manufacturing is in casings for sausages.
If collagen is subject to sufficient denaturation, such as by heating, the three tropocollagen strands separate partially or completely into globular domains, containing a different secondary structure to the normal collagen polyproline II (PPII) of random coils. This process describes the formation of gelatin, which is used in many foods, including flavored gelatin desserts. Besides food, gelatin has been used in pharmaceutical, cosmetic, and photography industries. It is also used as a dietary supplement, and has been advertised as a potential remedy against the ageing process.
From the Greek for glue, kolla, the word collagen means "glue producer" and refers to the early process of boiling the skin and sinews of horses and other animals to obtain glue. Collagen adhesive was used by Egyptians about 4,000 years ago, and Native Americans used it in bows about 1,500 years ago. The oldest glue in the world, carbon-dated as more than 8,000 years old, was found to be collagen – used as a protective lining on rope baskets and embroidered fabrics, to hold utensils together, and in crisscross decorations on human skulls. Collagen normally converts to gelatin, but survived due to dry conditions. Animal glues are thermoplastic, softening again upon reheating, so they are still used in making musical instruments such as fine violins and guitars, which may have to be reopened for repairs – an application incompatible with tough, synthetic plastic adhesives, which are permanent. Animal sinews and skins, including leather, have been used to make useful articles for millennia.
Gelatin-resorcinol-formaldehyde glue (and with formaldehyde replaced by less-toxic pentanedial and ethanedial) has been used to repair experimental incisions in rabbit lungs.
Cosmetics
Bovine collagen is widely used in dermal fillers for aesthetic correction of wrinkles and skin aging. Collagen cremes are also widely sold even though collagen cannot penetrate the skin because its fibers are too large. Collagen is a vital protein in skin, hair, nails, and other tissues. Its production decreases with age and factors like sun damage and smoking. Collagen supplements, derived from sources like fish and cattle, are marketed to improve skin, hair, and nails. Studies show some skin benefits, but these supplements often contain other beneficial ingredients, making it unclear if collagen alone is effective. There's minimal evidence supporting collagen's benefits for hair and nails. Overall, the effectiveness of oral collagen supplements is not well-proven, and focusing on a healthy lifestyle and proven skincare methods like sun protection is recommended.
History
The molecular and packing structures of collagen eluded scientists over decades of research. The first evidence that it possesses a regular structure at the molecular level was presented in the mid-1930s. Research then concentrated on the conformation of the collagen monomer, producing several competing models, although correctly dealing with the conformation of each individual peptide chain. The triple-helical "Madras" model, proposed by G. N. Ramachandran in 1955, provided an accurate model of quaternary structure in collagen. This model was supported by further studies of higher resolution in the late 20th century.
The packing structure of collagen has not been defined to the same degree outside of the fibrillar collagen types, although it has been long known to be hexagonal. As with its monomeric structure, several conflicting models propose either that the packing arrangement of collagen molecules is 'sheet-like', or is microfibrillar. The microfibrillar structure of collagen fibrils in tendon, cornea and cartilage was imaged directly by electron microscopy in the late 20th century and early 21st century. The microfibrillar structure of rat tail tendon was modeled as being closest to the observed structure, although it oversimplified the topological progression of neighboring collagen molecules, and so did not predict the correct conformation of the discontinuous D-periodic pentameric arrangement termed microfibril.
See also
Collagen hybridizing peptide, a peptide that can bind to denatured collagen
Hypermobility spectrum disorder
Metalloprotease inhibitor
Osteoid, a collagen-containing component of bone
Collagen loss
References
*
Category:Structural proteins
Category:Edible thickening agents
Category:Aging-related proteins
|
https://en.wikipedia.org/wiki/Collagen
|
2025-04-05T18:27:42.532401
|
6059
|
Calvin and Hobbes
|
Watterson took a second sabbatical from April 3 through December 31, 1994. His return came with an announcement that Calvin and Hobbes would be concluding at the end of 1995. Stating his belief that he had achieved everything that he wanted to within the medium, he announced his intention to work on future projects at a slower pace with fewer artistic compromises.
Speaking to NPR in 2005, animation critic Charles Solomon opined that the final strip "left behind a hole in the comics page that no strip has been able to fill."
Sunday formatting
, third, and quarter pages (optionally discarding panels 1 and 2). However, Watterson wished to draw comics which did not conform to the standard panel division.|alt=|205x205px]]
Syndicated comics were typically published six times a week in black and white, with a Sunday supplement version in a larger, full color format. This larger format version of the strip was constrained by mandatory layout requirements that made it possible for newspaper editors to format the strip for different page sizes and layouts.
Watterson grew increasingly frustrated by the shrinking of the available space for comics in the newspapers and the mandatory panel divisions that restricted his ability to produce better artwork and more creative storytelling. He felt that without space for anything more than simple dialogue or sparse artwork, comics as an art form were becoming dilute, bland, and unoriginal.
Watterson longed for the artistic freedom allotted to classic strips such as Little Nemo and Krazy Kat, and in 1989 he gave a sample of what could be accomplished with such liberty in the opening pages of the Sunday strip compilation, The Calvin and Hobbes Lazy Sunday Book—an 8-page previously unpublished Calvin story fully illustrated in watercolor. The same book contained an afterword from the artist himself, reflecting on a time when comic strips were allocated a whole page of the newspaper and every comic was like a "color poster".
Within two years, Watterson was ultimately successful in negotiating a deal that provided him more space and creative freedom. Following his 1991 sabbatical, Universal Press announced that Watterson had decided to sell his Sunday strip as an unbreakable half of a newspaper or tabloid page. Many editors and even a few cartoonists including Bil Keane (The Family Circus) and Bruce Beattie (Snafu) criticized him for what they perceived as arrogance and an unwillingness to abide by the normal practices of the cartoon business. Others, including Bill Amend (Foxtrot), Johnny Hart (BC, Wizard of Id) and Barbara Brandon (''Where I'm Coming From'') supported him. The American Association of Sunday and Feature Editors even formally requested that Universal reconsider the changes. Watterson's own comments on the matter was that "editors will have to judge for themselves whether or not Calvin and Hobbes deserves the extra space. If they don't think the strip carries its own weight, they don't have to run it." Ultimately only 15 newspapers cancelled the strip in response to the layout changes.
Sabbaticals
Bill Watterson took two sabbaticals from the daily requirements of producing the strip. The first took place from May 5, 1991, to February 1, 1992, and the second from April 3 through December 31, 1994. These sabbaticals were included in the new contract Watterson managed to negotiate with Universal Features in 1990. The sabbaticals were proposed by the syndicate themselves, who, fearing Watterson's complete burnout, endeavored to get another five years of work from their star artist.MerchandisingCalvin and Hobbes had almost no official product merchandising. Watterson held that comic strips should stand on their own as an art form and although he did not start out completely opposed to merchandising in all forms (or even for all comic strips), he did reject an early syndication deal that involved incorporating a more marketable, licensed character into his strip. Almost no legitimate Calvin and Hobbes merchandise exists. Exceptions produced during the strip's original run include two 16-month calendars (1988–89 and 1989–90), a t-shirt for the Smithsonian Exhibit, Great American Comics: 100 Years of Cartoon Art (1990) and the textbook Teaching with Calvin and Hobbes, which has been described as "perhaps the most difficult piece of official Calvin and Hobbes memorabilia to find." In 2010, Watterson did allow his characters to be included in a series of United States Postal Service stamps honoring five classic American comics. Licensed prints of Calvin and Hobbes were made available and have also been included in various academic works.
The strip's immense popularity has led to the appearance of various counterfeit items such as window decals and T-shirts that often feature crude humor, binge drinking and other themes that are not found in Watterson's work. Images from one strip in which Calvin and Hobbes dance to loud music at night were commonly used for copyright violations. After threat of a lawsuit alleging infringement of copyright and trademark, some sticker makers replaced Calvin with a different boy, while other makers made no changes. Watterson wryly commented, "I clearly miscalculated how popular it would be to show Calvin urinating on a Ford logo,"
Animation
Watterson has expressed admiration for animation as an artform. In a 1989 interview in The Comics Journal he described the appeal of being able to do things with a moving image that cannot be done by a simple drawing: the distortion, the exaggeration and the control over the length of time an event is viewed. However, although the visual possibilities of animation appealed to Watterson, the idea of finding a voice for Calvin made him uncomfortable, as did the idea of working with a team of animators. Calls from major Hollywood figures interested in an adaptation of his work, including Jim Henson, George Lucas and Steven Spielberg, were never returned Schulz and Kelly particularly influenced Watterson's outlook on comics during his formative years. He also makes a point of not showing certain things explicitly: the "Noodle Incident" and the children's book Hamster Huey and the Gooey Kablooie are left to the reader's imagination, where Watterson was sure they would be "more outrageous" than he could portray. Production and technique Watterson's technique started with minimalist pencil sketches drawn with a light pencil (though the larger Sunday strips often required more elaborate work) on a piece of Bristol board, with his brand of choice being Strathmore because he felt it held the drawings better on the page as opposed to the cheaper brands (Watterson said he initially used any cheap pad of Bristol board his local supply store had but switched to Strathmore after he found himself growing more and more displeased with the results). He would then use a small sable brush and India ink to fill in the rest of the drawing, saying that he did not want to simply trace over his penciling and thus make the inking more spontaneous. He lettered dialogue with a Rapidograph fountain pen, and he used a crowquill pen for odds and ends. Mistakes were covered with various forms of correction fluid, including the type used on typewriters. Watterson was careful in his use of color, often spending a great deal of time in choosing the right colors to employ for the weekly Sunday strip; his technique was to cut the color tabs the syndicate sent him into individual squares, lay out the colors, and then paint a watercolor approximation of the strip on tracing paper over the Bristol board and then mark the strip accordingly before sending it on. When Calvin and Hobbes began there were 64 colors available for the Sunday strips. For the later Sunday strips Watterson had 125 colors as well as the ability to fade the colors into each other. He begins exploring the medium of snow when a warm day melts his snowman. His next sculpture "speaks to the horror of our own mortality, inviting the viewer to contemplate the evanescence of life." In later strips, Calvin's creative instincts diversify to include sidewalk drawings (or, as he terms them, examples of "suburban postmodernism").
Watterson also lampooned the academic world. In one example, Calvin carefully crafts an "artist's statement", claiming that such essays convey more messages than artworks themselves ever do (Hobbes blandly notes, "You misspelled Weltanschauung"). He indulges in what Watterson calls "pop psychobabble" to justify his destructive rampages and shift blame to his parents, citing "toxic codependency." In one instance, he pens a book report based on the theory that the purpose of academic writing is to "inflate weak ideas, obscure poor reasoning and inhibit clarity," entitled The Dynamics of Interbeing and Monological Imperatives in Dick and Jane: A Study in Psychic Transrelational Gender Modes. Displaying his creation to Hobbes, he remarks, "Academia, here I come!" Watterson explains that he adapted this jargon (and similar examples from several other strips) from an actual book of art criticism.
Overall, Watterson's satirical essays serve to attack both sides, criticizing both the commercial mainstream and the artists who are supposed to be "outside" it. The strip on Sunday, June 21, 1992, criticized the naming of the Big Bang theory as not evocative of the wonders behind it and coined the term "Horrendous Space Kablooie", an alternative that achieved some informal popularity among scientists and was often shortened to "the HSK". The term has also been referred to in newspapers, books and university courses.Calvin's alter-egosCalvin imagines himself as many great creatures and other people, including dinosaurs, elephants, jungle-farers and superheroes. Three of his alter egos are well-defined and recurrent:
*"Spaceman Spiff" is a heroic spacefarer who narrates his adventures in the third person. As Spiff, Calvin battles aliens (typically his parents or teacher, but also sometimes other kids his age) with a ray gun known as a "zorcher" (later "frap-ray blaster", "death ray blaster" or "atomic napalm neutralizer") and travels to distant planets (his house, school or neighborhood), often crashing unhurt on a planet. Calvin's self-narration as Spaceman Spiff is frequently riddled with alliteration: "Zounds! Zorched by Zarches, Spaceman Spiff's crippled craft crashes on planet Plootarg!" Watterson has stated the idea of Spaceman Spiff came from an earlier attempt as a cartoon, and is meant as a parody of Flash Gordon. The canyons and deserts that many of the Spaceman Spiff stories are set in are based on the landscapes of southern Utah.
* "Tracer Bullet" is a hardboiled private eye, who says he has eight slugs in him ("One's lead, and the rest are bourbon."). In one story, Bullet is called to a case in which a "pushy dame" (Calvin's mother) accuses him of destroying an expensive lamp (broken during an indoor football game between Calvin and Hobbes). Later, he is snatched by the pushy dame's "hired goon" (Calvin's father having a talk with him). In another, he "investigates" a math word problem during class, "closing the case" with an answer of 1,000,000,000 when the correct response was 15. He made his debut when Calvin donned a fedora in order to hide a terrible haircut Hobbes had given him. These strips are drawn in elaborate, shadowy black-and-white that evoke film noir. Watterson did not attempt Tracer Bullet stories often, due to the time-consuming way the strip needed to be drawn and inked.
* "Stupendous Man" is a superhero who wears a mask and a cape (made by Calvin's mother) and narrates his own adventures. While Calvin is in character as Stupendous Man, he refers to his alter ego as a mild-mannered millionaire playboy. Stupendous Man almost always "suffers defeat" at the hands of his opponent. When Hobbes asks if Stupendous Man has ever won any battles, Calvin says all his battles are "moral victories." Stupendous Man's nemeses include "Mom-Lady" (Calvin's mom), "Annoying Girl" (Susie Derkins), "Crab Teacher" (Miss Wormwood) and "Baby-Sitter Girl" (Rosalyn). Some of the "super powers" of the villains have been revealed: Mom-Lady has a "mind scrambling eyeball ray" that wills the victim to "do her nefarious bidding"; and Baby Sitter Girl has a similar power of using a "psycho beam" which weakens "Stupendous Man's stupendous will". The "powers" of Annoying Girl and Crab Teacher are never revealed. Calvin often tries to pretend he and "Stupendous Man" are two different people, but it fails to work. Stupendous Man has multiple "superpowers", including, but not limited to, super strength, the ability to fly, various vision powers such as "high-speed vision", "muscles of magnitude" and a "stomach of steel".
Cardboard boxes
Calvin also has several adventures involving corrugated cardboard boxes, which he adapts for many imaginative and elaborate uses. In one strip, when Calvin shows off his Transmogrifier, a device that transforms its user into any desired creature or item, Hobbes remarks, "It's amazing what they do with corrugated cardboard these days." Calvin is able to change the function of the boxes by rewriting the label and flipping the box onto another side. In this way, a box can be used not only for its conventional purposes (a storage container for water balloons, for example), but also as a flying time machine, a duplicator, a transmogrifier or, with the attachment of a few wires and a colander, a "Cerebral Enhance-o-tron."
In the real world, Calvin's antics with his box have had varying effects. When he transmogrified into a tiger, he still appeared as a regular human child to his parents. However, in a story where he made several duplicates of himself, his parents are seen interacting with what does seem like multiple Calvins, including in a strip where two of him are seen in the same panel as his father. It is ultimately unknown what his parents do or do not see, as Calvin tries to hide most of his creations (or conceal their effects) so as not to traumatize them.
In addition, Calvin uses a cardboard box as a sidewalk kiosk to sell things. Often, Calvin offers merchandise no one would want, such as "suicide drink", "a swift kick in the butt" for one dollar or a "frank appraisal of your looks" for fifty cents. In one strip, he sells "happiness" for ten cents, hitting the customer in the face with a water balloon and explaining that he meant his own happiness. In another strip, he sold "insurance", firing a slingshot at those who refused to buy it. In some strips, he tried to sell "great ideas" and, in one earlier strip, he attempted to sell the family car to obtain money for a grenade launcher. In yet another strip, he sells "life" for five cents, where the customer receives nothing in return, which, in Calvin's opinion, is life.
The box has also functioned as an alternate secret meeting place for G.R.O.S.S., as the "Box of Secrecy".
Calvinball
<!-- Courtesy note per WP:LiNK2SECT: Calvinball redirects here -->
Calvinball is an improvisational sport/game introduced in a 1990 storyline that involved Calvin's negative experience of joining the school baseball team. Calvinball is a nomic or self-modifying game, a contest of wits, skill and creativity rather than stamina or athletic skill. The game is portrayed as a rebellion against conventional team sports and became a staple of the final five years of the comic. The only consistent rules of the game are that Calvinball may never be played with the same rules twice and that each participant must wear a mask.
When asked how to play, Watterson stated: "It's pretty simple: you make up the rules as you go." In most appearances of the game, a comical array of conventional and non-conventional sporting equipment is involved, including a croquet set, a badminton set, assorted flags, bags, signs, a hobby horse, water buckets and balloons, with humorous allusions to unseen elements such as "time-fracture wickets". Scoring is portrayed as arbitrary and nonsensical ("Q to 12" and "oogy to boogy") and the lack of fixed rules leads to lengthy argument between the participants as to who scored, where the boundaries are, and when the game is finished. Usually, the contest results in Calvin being outsmarted by Hobbes. The game has been described in one academic work not as a new game based on fragments of an older one, but as the "constant connecting and disconnecting of parts, the constant evasion of rules or guidelines based on collective creativity."Snowmen and other snow artCalvin often creates horrendous/dark humor scenes with his snowmen and other snow sculptures. He uses the snowman for social commentary, revenge or pure enjoyment. Examples include Snowman Calvin being yelled at by Snowman Dad to shovel the snow; one snowman eating snow cones scooped out of a second snowman, who is lying on the ground with an ice-cream scoop in his back; a "snowman house of horror"; and snowmen representing people he hates. "The ones I really hate are small, so they'll melt faster," he says. There was even an occasion on which Calvin accidentally brought a snowman to life and it made itself and a small army into "deranged mutant killer monster snow goons."
Calvin's snow art is often used as a commentary on art in general. For example, Calvin has complained more than once about the lack of originality in other people's snow art and compared it with his own grotesque snow sculptures. In one of these instances, Calvin and Hobbes claim to be the sole guardians of high culture; in another, Hobbes admires Calvin's willingness to put artistic integrity above marketability, causing Calvin to reconsider and make an ordinary snowman.
Wagon and sled rides
Calvin and Hobbes frequently ride downhill in a wagon or sled (depending on the season), as a device to add some physical comedy to the strip and because, according to Watterson, "it's a lot more interesting ... than talking heads." While the ride is sometimes the focus of the strip, it also frequently serves as a counterpoint or visual metaphor while Calvin ponders the meaning of life, death, God, philosophy or a variety of other weighty subjects. Many of their rides end in spectacular crashes which leave them battered, beaten up and broken, a fact which convinces Hobbes to sometimes hop off before a ride even begins. In the final strip, Calvin and Hobbes depart on their sled to go exploring.G.R.O.S.S. (Get Rid of Slimy GirlS) G.R.O.S.S. (which is a backronym for Get Rid Of Slimy GirlS, "otherwise it doesn't spell anything") is a club in which Calvin and Hobbes are the only members. The club was founded in the garage of their house, but to clear space for its activities, Calvin and (purportedly) Hobbes push Calvin's parents' car, causing it to roll into a ditch (but not suffer damage); the incident prompts the duo to change the club's location to Calvin's treehouse. They hold meetings that involve finding ways to annoy and discomfort Susie Derkins, a girl and enemy of their club. Actions include planting a fake secret tape near her in attempt to draw her in to a trap, trapping her in a closet at their house and creating elaborate water balloon traps. Calvin gave himself and Hobbes important positions in the club, Calvin being "Dictator-for-Life" and Hobbes being "President-and-First-Tiger". They go into Calvin's treehouse for their club meetings and often get into fights during them. The password to get into the treehouse is intentionally long and difficult, which has on at least one occasion ruined Calvin's plans. As Hobbes is able to climb the tree without the rope, he is usually the one who comes up with the password, which often involves heaping praise upon tigers. An example of this can be seen in the comic strip where Calvin, rushing to get into the treehouse to throw things at a passing Susie Derkins, insults Hobbes, who is in the treehouse and thus has to let down the rope. Hobbes forces Calvin to say the password for insulting him. By the time Susie arrives, in time to hear Calvin saying some of the password, causing him to stumble, Calvin is on "Verse Seven: Tigers are perfect!/The E-pit-o-me/of good looks and grace/and quiet..uh..um..dignity". The opportunity to pelt Susie with something having passed, Calvin threatens to turn Hobbes into a rug.
Dinosaurs
Dinosaurs play a heavy role in many of Calvin's imagination sequences. These strips will often begin with hyper-realistic scenes of dinosaur interactions, only to end with a cut to Calvin acting out these scenes as part of a day-dream, often to his embarrassment. Watterson placed a heavy focus on accurately depicting dinosaurs, due to his own interest in them as well as to reinforce how real they are to Calvin.
Books
There are 18 Calvin and Hobbes books, published from 1987 to 1997. These include 11 collections, which form a complete archive of the newspaper strips, except for a single daily strip from November 28, 1985. (The collections do contain a strip for this date, but it is not the same strip that appeared in some newspapers.) Treasuries usually combine the two preceding collections with bonus material and include color reprints of Sunday comics.
Watterson included some new material in the treasuries. In The Essential Calvin and Hobbes, which includes cartoons from the collections Calvin and Hobbes and Something Under the Bed Is Drooling, the back cover features a scene of a giant Calvin rampaging through a town. The scene is based on Watterson's home town of Chagrin Falls, Ohio, and Calvin is holding the Chagrin Falls Popcorn Shop, an iconic candy and ice cream shop overlooking the town's namesake falls. Several of the treasuries incorporate additional poetry; The Indispensable Calvin and Hobbes book features a set of poems, ranging from just a few lines to an entire page, that cover topics such as Calvin's mother's "hindsight" and exploring the woods. In The Essential Calvin and Hobbes, Watterson presents a long poem explaining a night's battle against a monster from Calvin's perspective. The Authoritative Calvin and Hobbes includes a story based on Calvin's use of the Transmogrifier to finish his reading homework.
A complete collection of Calvin and Hobbes strips, in three hardcover volumes totaling 1440 pages, was released on October 4, 2005, by Andrews McMeel Publishing. It includes color prints of the art used on paperback covers, the treasuries' extra illustrated stories and poems and a new introduction by Bill Watterson in which he talks about his inspirations and his story leading up to the publication of the strip. The alternate 1985 strip is still omitted, and three other strips (January 7 and November 24, 1987, and November 25, 1988) have altered dialogue. A four-volume paperback version was released November 13, 2012.
To celebrate the release (which coincided with the strip's 20th anniversary and the tenth anniversary of its absence from newspapers), Bill Watterson answered 15 questions submitted by readers.
Early books were printed in smaller format in black and white. These were later reproduced in twos in color in the "Treasuries" (Essential, Authoritative and Indispensable), except for the contents of Attack of the Deranged Mutant Killer Monster Snow Goons. Those Sunday strips were not reprinted in color until the Complete collection was finally published in 2005.
Watterson claims he named the books the "Essential, Authoritative and Indispensable" because, as he says in The Calvin and Hobbes Tenth Anniversary Book, the books are "obviously none of these things." It has been called the "Holy Grail" for Calvin and Hobbes collectors.ReceptionReviewing Calvin and Hobbes in 1990, Entertainment Weekly Ken Tucker gave the strip an A+ rating, writing "Watterson summons up the pain and confusion of childhood as much as he does its innocence and fun."
Academic response
In 1993, paleontologist and paleoartist Gregory S. Paul praised Bill Watterson for the scientific accuracy of the dinosaurs appearing in Calvin and Hobbes.
In her 1994 book When Toys Come Alive, Lois Rostow Kuznets theorizes that Hobbes serves both as a figure of Calvin's childish fantasy life and as an outlet for the expression of libidinous desires more associated with adults. Kuznets also analyzes Calvin's other fantasies, suggesting that they are a second tier of fantasies utilized in places like school where transitional objects such as Hobbes would not be socially acceptable.
Political scientist James Q. Wilson, in a paean to Calvin and Hobbes upon Watterson's decision to end the strip in 1995, characterized it as "our only popular explication of the moral philosophy of Aristotle."
Alisa White Coleman analyzed the strip's underlying messages concerning ethics and values in "'Calvin and Hobbes': A Critique of Society's Values," published in the Journal of Mass Media Ethics in 2000.
A collection of original Sunday strips was exhibited at Ohio State University's Billy Ireland Cartoon Library & Museum in 2001. Watterson himself selected the strips and provided his own commentary for the exhibition catalog, which was later published by Andrews McMeel as Calvin and Hobbes: Sunday Pages 1985–1995. and the university-level philosophy reader Open Questions: Readings for Critical Thinking and Writing in 2005; in the latter, the ethical views of Watterson and his characters Calvin and Hobbes are discussed in relation to the views of professional philosophers. In a 2009 evaluation of the entire body of Calvin and Hobbes strips using grounded theory methodology, Christijan D. Draper found that: "Overall, Calvin and Hobbes suggests that meaningful time use is a key attribute of a life well lived," and that "the strip suggests one way to assess the meaning associated with time use is through preemptive retrospection by which a person looks at current experiences through the lens of an anticipated future..."
Jamey Heit's Imagination and Meaning in Calvin and Hobbes, a critical and academic analysis of the strip, was published in 2012.
Calvin and Hobbes strips were again exhibited at the Billy Ireland Cartoon Library & Museum at The Ohio State University in 2014, in an exhibition entitled Exploring Calvin and Hobbes. An exhibition catalog by the same title, which also contained an interview with Watterson conducted by Jenny Robb, the curator of the museum, was published by Andrews McMeel in 2015.Legacy
Years after its original newspaper run, Calvin and Hobbes has continued to exert influence in entertainment, art, and fandom.
In television, Calvin and Hobbes have been satirically depicted in stop motion animation in the 2006 and 2018 Robot Chicken episodes "Lust for Puppets" and "Jew No. 1 Opens a Treasure Chest" respectively, and in traditional animation in the 2009 Family Guy episode "Not All Dogs Go to Heaven." In the 2013 Community episode "Paranormal Parentage," the characters Abed Nadir (Danny Pudi) and Troy Barnes (Donald Glover) dress as Calvin and Hobbes, respectively, for Halloween.
British artists, merchandisers, booksellers, and philosophers were interviewed for a 2009 BBC Radio 4 half-hour programme about the abiding popularity of the comic strip, narrated by Phill Jupitus.
The first book-length study of the strip, Looking for Calvin and Hobbes: The Unconventional Story of Bill Watterson and His Revolutionary Comic Strip by Nevin Martell, was first published in 2009; an expanded edition was published in 2010. The book chronicles Martell's quest to tell the story of Calvin and Hobbes and Watterson through research and interviews with people connected to the cartoonist and his work. The director of the later documentary Dear Mr. Watterson referenced Looking for Calvin and Hobbes in discussing the production of the movie, and Martell appears in the film.
The American documentary film Dear Mr. Watterson, released in 2013, explores the impact and legacy of Calvin and Hobbes through interviews with authors, curators, historians, and numerous professional cartoonists.
The enduring significance of Calvin and Hobbes to international cartooning was recognized by the jury of the Angoulême International Comics Festival in 2014 by the awarding of its Grand Prix to Watterson, only the fourth American to ever receive the honor (after Will Eisner, Robert Crumb, and Art Spiegelman).
From 2016 to 2021, author Berkeley Breathed included Calvin and Hobbes in various Bloom County cartoons. He launched the first cartoon on April Fool's Day 2016 and jokingly issued a statement suggesting that he had acquired Calvin and Hobbes from Bill Watterson, who was "out of the Arizona facility, continent and looking forward to some well-earned financial security." While bearing Watterson's signature and drawing style as well as featuring characters from both Calvin and Hobbes and Breathed's Bloom County, it is unclear whether Watterson had any input into these cartoons or not.
Calvin and Hobbes remains the most viewed comic on GoComics, which cycles through old strips with an approximately 30-year delay.Grown-up CalvinPortraying Calvin as a teenager/adult has inspired writers.
In 2011, a comic strip appeared by cartoonists Dan and Tom Heyerman called Hobbes and Bacon. The strip depicts Calvin as an adult, married to Susie Derkins with a young daughter named after philosopher Francis Bacon, to whom Calvin gives Hobbes. Though consisting of only four strips originally, Hobbes and Bacon received considerable attention when it appeared and was continued by other cartoonists and artists.
A novel titled Calvin by CLA Young Adult Book Award–winning author Martine Leavitt was published in 2015.
The titular character of the comic strip Frazz has been noted for his similar appearance and personality to a grown-up Calvin. Creator Jef Mallett has stated that although Watterson is an inspiration to him, the similarities are unintentional.
References
Bibliography
*
*
*
*
*
*
*
* Markstein, Donald D. [http://www.toonopedia.com/calhobbs.htm Calvin and Hobbes] at Don Markstein's Toonopedia. [https://archive.today/20120409215718/http://www.toonopedia.com/calhobbs.htm Archived] from the original on April 13, 2012.
* Lew, Michele. [https://case.edu/ech/articles/c/calvin-and-hobbes CALVIN AND HOBBES], April 5, 2022 at The Encyclopedia of Cleveland History. [https://web.archive.org/web/20220807230322/https://case.edu/ech/articles/c/calvin-and-hobbes Archived] from the original August 7, 2022.
External links
*
*
*
Category:1985 comics debuts
Category:1995 comics endings
Category:American comic strips
Category:Children's fiction books
Category:Comic strip duos
Category:Comics about anthropomorphic tigers
Category:Comics about sentient toys
Category:Comics about talking objects
Category:Comics about children
Category:Comics about friendship
Category:Comics characters introduced in 1985
Category:Comics set in the United States
Category:Gag-a-day comics
Category:Fantasy comics
|
https://en.wikipedia.org/wiki/Calvin_and_Hobbes
|
2025-04-05T18:27:42.574043
|
6060
|
Campaign for Real Ale
|
| type = Consumer organisation
| headquarters = St Albans
| location = United Kingdom
| membership 144,900
| language = English
| leader_title = National Chairman / Chief Executive
| leader_name = Ash Corbett-Collins / Tom Stainer
| key_people | num_staff
| budget | website
}}
The Campaign for Real Ale (CAMRA) is an independent voluntary consumer organisation headquartered in St Albans, which promotes real ale, cider and perry and traditional British pubs and clubs.
History
The organisation was founded on 16 March 1971 in Kruger's Bar, Dunquin, County Kerry, Ireland, by Michael Hardman, Graham Lees, Jim Makin, and Bill Mellor, who were opposed to the growing mass production of beer and the homogenisation of the British brewing industry. The original name was the Campaign for the Revitalisation of Ale. Following the formation of the Campaign, the first annual general meeting took place in 1972, at the Rose Inn in Coton Road, Nuneaton.
Early membership consisted of the four founders and their friends. Interest in CAMRA and its objectives spread rapidly, with 5,000 members signed up by 1973. Other early influential members included Christopher Hutt, author of Death of the English Pub, who succeeded Hardman as chairman, Frank Baillie, author of ''The Beer Drinker's Companion, and later the many times Good Beer Guide'' editor, Roger Protz.
In 1991, CAMRA had 30,000 members across the UK and abroad and, a year later, helped to launch the European Beer Consumers Union.ActivitiesCAMRA's campaigns include promoting small brewing and pub businesses, reforming licensing laws, reducing tax on beer, and stopping continued consolidation among local British brewers. It also makes an effort to promote less common varieties of beer, including stout, porter, and mild, as well as traditional cider and perry.
CAMRA's states that real ale should be served without the use of additional carbonation. This means that "any beer brand which is produced in both cask and keg versions" is not admitted to CAMRA festivals if the brewery's marketing is deemed to imply an equivalence of quality or character between the two versions.
Organisation
CAMRA is organised on a federal basis, over 200 local branches, each covering a particular geographical area of the UK, that contribute to the central body of the organisation based in St Albans. It is governed by a National Executive, made up of 12 voluntary unpaid directors elected by the membership. The local branches are grouped into 16 regions across the UK, such as the West Midlands or Wessex.Publications and websites
CAMRA publishes the Good Beer Guide, an annually compiled directory of the best 4,500 real ale outlets and listing of real ale brewers.
CAMRA members received a monthly newspaper called ''What's Brewing until its April 2021 issue and there is a quarterly colour magazine called Beer''. It also maintains a National Inventory of Historic Pub Interiors to help bring greater recognition and protection to Britain's most historic pubs.
Festivals
CAMRA supports and promotes beer and cider festivals around the country, which are organised by local CAMRA branches. Generally, each festival charges an entry fee which either covers entry only or also includes a commemorative glass showing the details of the festival. A festival programme is usually also provided, with a list and description of the drinks available. Members may get discounted entrance to CAMRA festivals.
The Campaign also organises the annual Great British Beer Festival in August. It is now held in the Great, National & West Halls at the Olympia Exhibition Centre, in Kensington, London, having been held for a few years at Earl's Court as well as regionally in the past at venues such as Brighton and Leeds. This is the UK's largest beer festival, with over 900 beers, ciders and perries available over the week long event.
For many years, CAMRA also organised the National Winter Ales Festival. However, in 2017 this was re-branded as the Great British Beer Festival Winter where they award the Champion Winter Beer of Britain. Unlike the Great British Beer Festival, the Winter event does not have a permanent venue and is rotated throughout the country every three years. Recent hosts have been Derby and Norwich, with the event currently held each February in Birmingham. In 2020 CAMRA also launched the Great Welsh Beer Festival, to be held in Cardiff in April.
Awards
CAMRA presents awards for beers and pubs, such as the National Pub of the Year. The competition begins in the preceding year with branches choosing their local pub of the year through either a ballot or a panel of judges. The branch winners are entered into 16 regional competitions which are then visited by several individuals who agree the best using a scoring system that considers beer quality, aesthetic and welcome. The four finalists are announced each year before a ceremony to crown the winner in the spring. There are also the Pub Design Awards, which are held in association with English Heritage and the Victorian Society. These comprise several categories, including new build, refurbished and converted pubs.
The best known CAMRA award is the Champion Beer of Britain, which is selected at the Great British Beer Festival. Other awards include the Champion Beer of Scotland and the Champion Beer of Wales.
National Beer Scoring Scheme
CAMRA developed the National Beer Scoring Scheme (NBSS) as an easy to use scheme for judging beer quality in pubs, to assist CAMRA branches in selecting pubs for the Good Beer Guide. CAMRA members input their beer scores online via WhatPub or through the Good Beer Guide app.Pub heritage
The CAMRA Pub Heritage Group identifies, records and helps to protect pub interiors of historic and/or architectural importance, and seeks to get them listed.
The group maintains two inventories of Heritage pubs, the National Inventory (NI), which contains only those pubs that have been maintained in their original condition (or have been modified very little) for at least thirty years, but usually since at least World War II. The second, larger, inventory is the Regional Inventory (RI), which is broken down by county and contains both those pubs listed in the NI and other pubs that are not eligible for the NI, for reasons such as having been overly modified, but are still considered historically important, or have particular architectural value.
LocAle
The LocAle scheme was launched in 2007 to promote locally brewed beers. The scheme functions slightly differently in each area, and is managed by each branch, but each is similar: if the beer is to be promoted as a LocAle it must come from a brewery within a predetermined number of miles set by each CAMRA branch, generally around 20, although the North London branch has set it at 30 miles from brewery to pub, even if it comes from a distribution centre further away; As of January 2021 the club had over 3,000 members and owned investments worth over £17 million. Although all investors must be CAMRA members, the CAMRA Members' Investment Club is not part of CAMRA Ltd.See also
*Society for the Preservation of Beers from the Wood
*Society of Independent Brewers
*Independent Family Brewers of Britain
*European Beer Consumers' Union
*Real Ale Twats
References
External links
*[http://www.camra.org.uk/ CAMRA website]
*[http://www.heritagepubs.org.uk/ Pub Heritage Group – Official Site]
*[http://www.gbbf.org.uk/ Great British Beer Festival]
Category:1971 establishments in the United Kingdom
Category:Beer in the United Kingdom
Category:Beer organizations
Category:British food and drink organisations
Category:Consumer organisations in the United Kingdom
Category:Organisations based in Hertfordshire
Category:Organizations established in 1971
|
https://en.wikipedia.org/wiki/Campaign_for_Real_Ale
|
2025-04-05T18:27:42.581720
|
6061
|
CNO cycle
|
of the relative energy output (ε) of proton–proton (p–p), CNO, and triple-α fusion processes at different temperatures (T). The dashed line shows the combined energy generation of the p–p and CNO processes within a star.]]
In astrophysics, the carbon–nitrogen–oxygen (CNO) cycle, sometimes called Bethe–Weizsäcker cycle, after Hans Albrecht Bethe and Carl Friedrich von Weizsäcker, is one of the two known sets of fusion reactions by which stars convert hydrogen to helium, the other being the proton–proton chain reaction (p–p cycle), which is more efficient at the Sun's core temperature. The CNO cycle is hypothesized to be dominant in stars that are more than 1.3 times as massive as the Sun. One nucleus goes on to become carbon, nitrogen, and oxygen isotopes through a number of transformations in a repeating cycle.
The proton–proton chain is more prominent in stars the mass of the Sun or less. This difference stems from temperature dependency differences between the two reactions; pp-chain reaction starts at temperatures around (4 megakelvin), making it the dominant energy source in smaller stars. A self-maintaining CNO chain starts at approximately , but its energy output rises much more rapidly with increasing temperatures so that it becomes the dominant source of energy at approximately .
The Sun has a core temperature of around , and only of nuclei produced in the Sun are
born in the CNO cycle.
The CNO-I process was independently proposed by Carl von Weizsäcker and Hans Bethe
Cold CNO cycles
Under typical conditions found in stars, catalytic hydrogen burning by the CNO cycles is limited by proton captures. Specifically, the timescale for beta decay of the radioactive nuclei produced is faster than the timescale for fusion. Because of the long timescales involved, the cold CNO cycles convert hydrogen to helium slowly, allowing them to power stars in quiescent equilibrium for many years.
CNO-I
The first proposed catalytic cycle for the conversion of hydrogen into helium was initially called the carbon–nitrogen cycle (CN-cycle), also referred to as the Bethe–Weizsäcker cycle in honor of the independent work of Carl Friedrich von Weizsäcker in 1937–38 drew on three earlier papers written in collaboration with Robert Bacher and Milton Stanley Livingston and which came to be known informally as ''Bethe's Bible''. It was considered the standard work on nuclear physics for many years and was a significant factor in his being awarded the 1967 Nobel Prize in Physics. Bethe's original calculations suggested the CN-cycle was the Sun's primary source of energy.
: → → → → → →
This cycle is now understood as being the first part of a larger process, the CNO-cycle, and the main reactions in this part of the cycle (CNO-I) are:)
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 122.24 seconds
The limiting (slowest) reaction in the CNO-I cycle is the proton capture on . In 2006 it was experimentally measured down to stellar energies, revising the calculated age of globular clusters by around 1 billion years.
The neutrinos emitted in beta decay will have a spectrum of energy ranges, because although momentum is conserved, the momentum can be shared in any way between the positron and neutrino, with either emitted at rest and the other taking away the full energy, or anything in between, so long as all the energy from the Q-value is used. The total momentum received by the positron and the neutrino is not great enough to cause a significant recoil of the much heavier daughter nucleus .}} and hence, its contribution to kinetic energy of the products, for the precision of values given here, can be neglected. Thus the neutrino emitted during the decay of nitrogen-13 can have an energy from zero up to , and the neutrino emitted during the decay of oxygen-15 can have an energy from zero up to . On average, about 1.7 MeV of the total energy output is taken away by neutrinos for each loop of the cycle, leaving about available for producing luminosity.
CNO-II
In a minor branch of the above reaction, occurring in the Sun's core 0.04% of the time, the final reaction involving shown above does not produce carbon-12 and an alpha particle, but instead produces oxygen-16 and a photon and continues
:|||||||separator= → }}
In detail:
<!-- Autogenerated using Phykiformulae 0.12 User:SkyLined#Phykiformulae
N-15 + H -> O-16 + y _ _ + 12.13 MeV
O-16 + H -> F-17 + γ _ _ + 0.60 MeV
F-17 _ _ -> O-17 + e+ + νe + 2.76 MeV
O-17 + H -> N-14 + He _ _ + 1.19 MeV
N-14 + H -> O-15 + y _ _ + 7.35 MeV
O-15 _ _ -> N-15 + e+ + ve + 2.75 MeV
-->:{| border="0"
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 64.49 seconds)
|- style="height:2em;"
| ||+ || ||→ || ||+ || || || ||+ ||
|- style="height:2em;"
| ||+ || ||→ || ||+ || || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 122.24 seconds)
|}
Like the carbon, nitrogen, and oxygen involved in the main branch, the fluorine produced in the minor branch is merely an intermediate product; at steady state, it does not accumulate in the star.
CNO-III
This subdominant branch is significant only for massive stars. The reactions are started when one of the reactions in CNO-II results in fluorine-18 and a photon instead of nitrogen-14 and an alpha particle, and continues
: → → → → → →
In detail:
:{| border="0"
|- style="height:2em;"
| || + || || → || || + ||}} || || || + ||
|- style="height:2em;"
| || || || → || || + || || + ||}} || + || || (half-life of )
|- style="height:2em;"
| || + || || → || || + || || || || + ||
|- style="height:2em;"
| || + || || → || || + || }} || || || + ||
|- style="height:2em;"
| || + || || → || || + || }} || || || + ||
|- style="height:2em;"
| || || || → || || + || || + || }} || + || || (half-life of )
|}
CNO-IV
Like the CNO-III, this branch is also only significant in massive stars. The reactions are started when one of the reactions in CNO-III results in fluorine-19 and a photon instead of nitrogen-15 and an alpha particle, and continues
:|||||||separator → }}
In detail:
:{| border="0"
| || + || ||→ || || + ||}} || || || + ||
|-
| ||+ || ||→ || ||+ || || || ||+ ||
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 64.49 seconds)
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 109.771 minutes)
|- style="height:2em;"
|}
In some instances can combine with a helium nucleus to start a neon-sodium cycle, in which:
|||||||separator → }}
The sodium-23 can also turn into magesium-24 after proton bombardment, initiating the magnesium-aluminum cycle.
Hot CNO cycles
Under conditions of higher temperature and pressure, such as those found in novae and X-ray bursts, the rate of proton captures exceeds the rate of beta-decay, pushing the burning to the proton drip line. The essential idea is that a radioactive species will capture a proton before it can beta decay, opening new nuclear burning pathways that are otherwise inaccessible. Because of the higher temperatures involved, these catalytic cycles are typically referred to as the hot CNO cycles; because the timescales are limited by beta decays instead of proton captures, they are also called the beta-limited CNO cycles. HCNO-I The difference between the CNO-I cycle and the HCNO-I cycle is that captures a proton instead of decaying, leading to the total sequence
:→→→→→→
In detail:
:{| border="0"
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 70.641 seconds)
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 122.24 seconds)
|- style="height:2em;"
| ||+ || ||→ || ||+ || || || ||+ ||
|}
HCNO-II
The notable difference between the CNO-II cycle and the HCNO-II cycle is that captures a proton instead of decaying, and neon is produced in a subsequent reaction on , leading to the total sequence
:→→→→→→
In detail:
:{| border="0"
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 1.672 seconds)
|- style="height:2em;"
| ||+ || ||→ || ||+ || || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 122.24 seconds)
|}
HCNO-III
An alternative to the HCNO-II cycle is that captures a proton moving towards higher mass and using the same helium production mechanism as the CNO-IV cycle as
:→→→→→→
In detail:
:{| border="0"
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 17.22 seconds)
|- style="height:2em;"
| ||+ || ||→ || ||+ || || || ||+ ||
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| ||+ || ||→ || ||+ ||}} || || ||+ ||
|- style="height:2em;"
| || || ||→ || ||+ || ||+ ||}} ||+ ||||(half-life of 1.672 seconds)
|}
Use in astronomy
While the total number of "catalytic" nuclei are conserved in the cycle, in stellar evolution the relative proportions of the nuclei are altered. When the cycle is run to equilibrium, the ratio of the carbon-12/carbon-13 nuclei is driven to 3.5, and nitrogen-14 becomes the most numerous nucleus, regardless of initial composition. During a star's evolution, convective mixing episodes moves material, within which the CNO cycle has operated, from the star's interior to the surface, altering the observed composition of the star. Red giant stars are observed to have lower carbon-12/carbon-13 and carbon-12/nitrogen-14 ratios than do main sequence stars, which is considered to be convincing evidence for the operation of the CNO cycle.See also
* Aneutronic fusion
* Cold fusion
* Fusion power
* Nuclear fusion
* Proton–proton chain, as found in stars like the Sun
* Stellar nucleosynthesis, the whole topic
* Triple-alpha process, how is produced from lighter nuclei
Footnotes
References
Further reading
*
*
Category:Nuclear fusion reactions
Category:Carbon
Category:Nitrogen
Category:Oxygen
Category:Fluorine
Category:Neon
Category:Nucleosynthesis
|
https://en.wikipedia.org/wiki/CNO_cycle
|
2025-04-05T18:27:42.631276
|
6062
|
Craps
|
crap}}
}}
Craps is a dice game in which players bet on the outcomes of the roll of a pair of dice. Players can wager money against each other (playing "street craps") or against a bank ("casino craps"). Because it requires little equipment, "street craps" can be played in informal settings. While shooting craps, players may use slang terminology to place bets and actions.
History
, circa 1912]]
Craps developed in the United States from a simplification of the western European game of Hazard, also spelled Hazzard a detailed description of Hazard was provided by Edmond Hoyle in ''Hoyle's Games, Improved'' (1790). which in Hazard are instant-losing numbers for the first dice roll, regardless of the shooter's selected main number.
According to some accounts, Hazard was brought from London to New Orleans in approximately 1805 by the returning Bernard Xavier Philippe de Marigny de Mandeville, the young gambler and scion of a family of wealthy landowners in colonial Louisiana. Hazard allows the dice shooter to choose any number from five to nine as their "main" number; in a pamphlet published in 1933, Edward Tinker claimed that Marigny simplified the game by making the main always seven, Field hands taught their friends and deckhands, who carried the new game up the Mississippi River and its tributaries, although the game was never popular amongst the riverboat gamblers. which eventually spread throughout America by the 1910s,
The craps numbers of 2, 3, and 12 are similarly derived from Hazard. If the main is seven, then the two-dice sum of twelve is added to the crabs as a losing number on the first dice roll. This condition is retained in the simplified game called Pass. All three losing numbers (2, 3, and 12) on the first roll of Pass are jointly called the craps numbers. As introduced by Winn, "Don't Pass" bets were taken with a 5 percent commission to ensure the house retained an edge in running the game; this was replaced by the Bar-3 push for "Don't Pass", and later by the Bar-12 (or Bar-2) push.
Craps exploded in popularity during World War II,Dice
have been retired by drilling a hole completely through between the 1-6 faces; the four-digit serial number on the 6 face has been partially obliterated, but it started and ended with a 4.]]
The dice used at casinos for craps and many other games are sometimes called perfect or gambling house dice. These are generally made from translucent extruded cellulose, with perfectly square edges each in length, with pips drilled deep and filled with opaque paint matching the density of cellulose, which ensures the dice remain balanced. The dice are buffed and polished to a high glossy finish after the pips are set, and the edges usually are left sharp, also called square or razor edge. To discourage cheating and dice substitution, each die carries a serial number and the casino's logo or name.
Under New Jersey regulations, the shooter selects two dice from a set of at least five.
Rules of play
<!--Previous section name-->
Each casino may set which bets are offered and different payouts for them, though a core set of bets and payouts is typical. Players take turns rolling two dice and whoever is throwing the dice is called the "shooter". Players can bet on the various options by placing chips directly on the appropriately-marked sections of the layout, or asking the base dealer or stickman to do so, depending on which bet is being made.
While acting as the shooter, a player must have a bet on either the "Pass" or the "Don't Pass" line or both. "Pass" and "Don't Pass" are sometimes called "Win" and "Lose", "Do" and "Don't", or "Right" and "Wrong". These frequently incorporate a reminder to the dealers as to which bets to pay or collect.
;Two — "Snake Eyes", "Two Craps Two", "Double Aces", "Loose Deuce", "Snickies": The two ones that compose it look like a pair of small, beady eyes. During actual play, more common terms are "two craps two" during the comeout roll because the Pass line bet is lost on a comeout crap roll and/or because a bet on any craps would win. "Aces; double the field" would be a more common call when not on the comeout roll to remind the dealers to pay double on the field bets and encourage the field bettor to place subsequent bets and/or when no crap bets have been placed. Another name for the two is "loose deuce" or "Snickies" due to it sounding like "Snake eyes" but spoken with an accent.
;Three — "Three Craps Three", "Ace Deuce", "Tracy", "Acey Deucy": Typically called as "three craps three" during the comeout roll, or "three, ace deuce, come away single" when not on the comeout to signify the come bet has been lost and to pay single to any field bettors. Three may also be referred to as "ace caught a deuce", "Tracy", or even less often "acey deucey".
;Four (hard) — "Little Joe", "Joe", "Little Dick", "Little Joe from Kokomo", "Little Joe on the Front Row", "Ballerina": usually hard, is sometimes referred to as "Little Joe from Kokomo" or "Little Joe on the front row" or just "Little Joe".
|-
!Hard 6 / Hard 8
| Hard way
|10:1||9:1||9.09%
|Multi
|6 as a pair (3-3)<hr/>8 as a pair (4-4)
|7<hr/>6 as a non-pair (1–5,2-4)<hr/>8 as a non-pair (2-6,3-5)
|style"text-align:left;" | In the UK and Australia, the payout is 9.5:1 lowering the house edge to 4.55%.
Bonus Craps: Prior to the initial "come out roll", players may place an optional wager (usually a $1 minimum to a maximum $25) on one or more of the three Bonus Craps wagers, "All Small", "All Tall", or "All or Nothing at All." For players to win the "All Small" wager, the shooter must hit all five small numbers (2, 3, 4, 5, 6) before a seven is rolled; similarly, "All Tall" wins if all five high numbers (8, 9, 10, 11, 12) are hit before a seven is rolled.
These bets pay 35-for-1, for a house advantage of 7.76%. "All or Nothing at All" wins if the shooter hits all 10 numbers before a seven is rolled. This pays 176-for-1, for a house edge of 7.46%. For all three wagers, the order in which the numbers are hit does not matter. Whenever a seven is hit, including on the come out roll, all bonus bets lose, the bonus board is reset, and new bonus bets may be placed.Multiple different betsA player may wish to make multiple different bets. For example, a player may be wish to bet $1 on all hard ways and the horn. If one of the bets win the dealer may automatically replenish the losing bet with profits from the winning bet. In this example, if the shooter rolls a hard 8 (pays 9:1), the horn loses. The dealer may return $5 to the player and place the other $4 on the horn bet which lost. If the player does not want the bet replenished, he or she should request any or all bets be taken down.
Working and not working bets
A working bet is a live bet. Bets may also be on the board, but not in play and therefore not working. Pass line and come bets are always working meaning the chips are in play and the player is therefore wagering live money. Other bets may be working or not working depending whether a point has been established or player's choice. Place and buy bets are working by default when a point is established and not working when the point is off unless the player specifies otherwise. Lay bets are always working even if a point has not been established unless the player requests otherwise. At any time, a player may wish to take any bet or bets out of play. The dealer will put an "Off" button on the player's specific bet or bets; this allows the player to keep his chips on the board without a live wager. For example, if a player decides not to wager a place bet mid-roll but wishes to keep the chips on the number, he or she may request the bet be "not working" or "Off". The chips remain on the table, but the player cannot win from or lose chips which are not working.
The opposite is also allowed. By default place and buy bets are not working without an established point; a player may wish to wager chips before a point has been established. In this case, the player would request the bet be working in which the dealer will place an "On" button on the specified chips.
Betting variants
These variants depend on the casino and the table, and sometimes a casino will have different tables that use or omit these variants and others.
* 11 is a point number instead of a natural. Rolling an 11 still pays "Yo" center-table bets, but the Pass line does not automatically win (and the Don't Pass line does not automatically lose) when 11 is rolled on the come-out. Making the point pays 3:1 on Pass/Come odds bets (1:3 on Don't Pass/Come odds); all line bets are still even money. This substantially reduces the odds of a natural (from 8/36 to 6/36) and of making the point in general (since a 3:1 dog is added to the mix). All other things equal, the house edge on the Pass Line and Come bets for this play variation jumps dramatically to 9.75%.
* 12 pays 3:1 on the field. This is generally seen in rooms that have two different table minimums, on the tables with the higher minimums. The lower minimum ones will then have 2:1 odds. For example, the Mirage casino in Las Vegas features 3:1 odds.
* 11 pays 2:1 on the field. This variant is normally used when 12 pays 3:1, and neutralizes the house edge on the field.
* Big 6/8 are unavailable. These bets are equivalent to placing or buying 6 or 8 as points, which have better payout for the same real odds, so Big 6/8 are rarely used and many casinos simply omit them from the layout. Casinos in Atlantic City are even prohibited by law from offering Big 6/8 bets.
Optimal betting
When craps is played in a casino, all bets have a house advantage. That is, it can be shown mathematically that a player will (with 100% probability) lose all his or her money to the casino in the long run, while in the short run the player is more likely to lose money than make money. There may be players who are lucky and get ahead for a period of time, but in the long run these winning streaks are eroded away. One can slow, but not eliminate, one's average losses by only placing bets with the smallest house advantage.
The Pass/Don't Pass line, Come/Don't Come line, place 6, place 8, buy 4 and buy 10 (only under the casino rules where commission is charged only on wins) have the lowest house edge in the casino, and all other bets will, on average, lose money between three and twelve times faster because of the difference in house edges.
The place bets and buy bets differ from the Pass line and come line, in that place bets and buy bets can be removed at any time, since, while they are multi-roll bets, their odds of winning do not change from roll to roll, whereas Pass line bets and come line bets are a combination of different odds on their first roll and subsequent rolls. The first roll of a Pass line bet is 2:1 advantage for the player (8 wins, 4 losses), but it is "paid for" by subsequent rolls that are at the same disadvantage to the player as the Don't Pass bets were at an advantage. As such, they cannot profitably let the player take down the bet after the first roll. Players can bet or lay odds behind an established point depending on whether it was a Pass/Come or Don't Pass/Don't Come to lower house edge by receiving true odds on the point. Casinos which allow put betting allows players to increase or make new pass/come bets after the come-out roll. This bet generally has a higher house edge than place betting, unless the casino offers high odds.
Conversely, a player can take back (pick up) a Don't Pass or Don't Come bet after the first roll, but this cannot be recommended, because they already endured the disadvantaged part of the combination – the first roll. On that come-out roll, they win just 3 times (2 and 3), while losing 8 of them (7 and 11) and pushing one (12) out of the 36 possible rolls. On the other 24 rolls that become a point, their Don't Pass bet is now to their advantage by 6:3 (4 and 10), 6:4 (5 and 9) and 6:5 (6 and 8). If a player chooses to remove the initial Don't Come and/or Don't Pass line bet, he or she can no longer lay odds behind the bet and cannot re-bet the same Don't Pass and/or Don't Come number (players must make a new Don't Pass or come bets if desired). However, players can still make standard lay bets odds on any of the point numbers (4,5,6,8,9,10).
Among these, and the remaining numbers and possible bets, there are a myriad of systems and progressions that can be used with many combinations of numbers.
An important alternative metric is house advantage per roll (rather than per bet), which may be expressed in loss per hour. The typical pace of rolls varies depending on the number of players, but 102 rolls per hour is a cited rate for a nearly full table.
When throwing the dice, the player is expected to hit the farthest wall at the opposite end of the table (these walls are typically augmented with pyramidal structures to ensure highly unpredictable bouncing after impact). Casinos will sometimes allow a roll that does not hit the opposite wall as long as the dice are thrown past the middle of the table; a very short roll will be nullified as a "no roll". The dice may not be slid across the table and must be tossed. These rules are intended to prevent dexterous players from physically influencing the outcome of the roll.
Players are generally asked not to throw the dice above a certain height (such as the eye level of the dealers). This is both for the safety of those around the table, and to eliminate the potential use of such a throw as a distraction device in order to cheat. Some may also discourage or disallow unsanitary practices such as kissing or spitting on the dice.
In most casinos, players are not allowed to hand anything directly to dealers, and vice versa. Items such as cash, checks, and chips are exchanged by laying them down on the table; for example, when "buying in" (paying cash for chips), players are expected to place the cash on the layout: the dealer will take it and then place the chips in front of the player. This rule is enforced in order to allow the casino to easily monitor and record all transfers via overhead surveillance cameras, and to reduce the opportunity for cheating via sleight-of-hand.
Most casinos prohibit "call bets", and may have a warning such as "No Call Bets" printed on the layout to make this clear. This means a player may not call out a bet without also placing the corresponding chips on the table. Such a rule reduces the potential for misunderstanding in loud environments, as well as disputes over the amount that the player intended to bet after the outcome has been decided. Some casinos choose to allow call bets once players have bought-in. When allowed, they are usually made when a player wishes to bet at the last second, immediately before the dice are thrown, to avoid the risk of obstructing the roll. An exhaustive list of these is beyond the scope of this article, but the guidelines below are most commonly given.
Tips
Tipping the dealers is universal and expected in Craps. As in most other casino games, a player may simply place (or toss) chips onto the table and say, "For the dealers", "For the crew", etc. In craps, it is also common to place a bet for the dealers. This is usually done one of three ways: by placing an ordinary bet and simply declaring it for the dealers, as a "two-way", or "on top". A "Two-Way" is a bet for both parties: for example, a player may toss in two chips and say "Two Way Hard Eight", which will be understood to mean one chip for the player and one chip for the dealers. Players may also place a stack of chips for a bet as usual, but leave the top chip off-center and announce "on top for the dealers". The dealer's portion is often called a "toke" bet, which comes from the practice of using $1 slot machine tokens to place dealer bets in some casinos.
Casinos take steps to prevent this. The dice are usually required to hit the back wall of the table, which is normally faced with a jagged angular texture such as pyramids, making controlled spins more difficult. There has been no independent evidence that such methods can be successfully applied in a real casino.
New York Craps is one of the variations of craps played mostly in the Eastern coast of the US, true to its name. History states that this game was actually found and played in casinos in Yugoslavia, the UK and the Bahamas. In this craps variant, the house edge is greater than Las Vegas Craps or Bank craps. The table layout is also different, and is called a double-end-dealer table. This variation is different from the original craps game in several ways, but the primary difference is that New York craps does not allow Come or Don't Come bets. New York Craps Players bet on box numbers like 4, 5, 6, 8, 9, or 10. The overall house edge in New York craps is 5%.
Cards replacing dice
To replicate the original dice odds exactly without dice or possibility of card-counting, one scheme uses two shuffle machines each with just one deck of Ace through 6 each. Each machine selects one of the 6 cards at random and this is the roll. The selected cards are replaced and the decks are reshuffled for the next roll.
The prayer or invocation "Baby needs a new pair of shoes!" is associated with shooting craps.
Floating craps
Floating craps is an illegal operation of craps. The term floating refers to the practice of the game's operators using portable tables and equipment to quickly move the game from location to location to stay ahead of the law enforcement authorities.
The 1950 Broadway musical Guys and Dolls features a major plot point revolving around a floating craps game.
In the 1950s and 1960s The Sands Hotel in Las Vegas had a craps table that floated in the swimming pool, as a joke reference to the notoriety of the term.RecordsA Golden Arm is a craps player who rolls the dice for longer than one hour without losing. Likely the first known Golden Arm was Oahu native Stanley Fujitake, who rolled 118 times without sevening out in 3 hours and 6 minutes at the California Hotel and Casino on May 28, 1989.
The current record for length of a "hand" (successive rounds won by the same shooter) is 154 rolls including 25 passes by Patricia DeMauro of New Jersey, lasting 4 hours and 18 minutes, at the Borgata in Atlantic City, New Jersey, on May 23–24, 2009. She bested by over an hour the record held for almost 20 years – that of Fujitake.
See also
References
External links
<!--
Please be cautious adding more external links.
Wikipedia is not a collection of links and should not be used for advertising.
Excessive or inappropriate links will be removed.
See Wikipedia:External links and Wikipedia:Spam for details.
If there are already suitable links, propose additions or replacements on the article's talk page.
-->
*
Category:Craps
Category:Dice games
Category:Gambling games
Category:African-American culture
|
https://en.wikipedia.org/wiki/Craps
|
2025-04-05T18:27:42.683673
|
6066
|
Carl von Clausewitz
|
| birth_place = Burg bei Magdeburg, Kingdom of Prussia, Holy Roman Empire
| death_date
| death_place = Breslau, Province of Silesia, Kingdom of Prussia
| placeofburial | allegiance
| branch = Prussian Army
| serviceyears = 1792–1831
| rank = Major general
| unit = Russian–German Legion (III Corps)
| commands = Kriegsakademie
| battles =
* French Revolutionary Wars
**Siege of Mainz
* Napoleonic Wars
**Battle of Jena–Auerstedt
**Battle of Borodino
**Battle of Ligny
**Battle of Wavre
| awards | spouse
| relations | laterwork
}}
Carl Philipp Gottfried (or Gottlieb) von Clausewitz}} ( , ; 1 July 1780 – 16 November 1831) was a Prussian general and military theorist who stressed the "moral" (in modern terms meaning psychological) and political aspects of waging war. His most notable work, (About War), though unfinished at his death, is considered a seminal treatise on military strategy and science.
Clausewitz stressed the multiplex interaction of diverse factors in war, noting how unexpected developments unfolding under the "fog of war" (i.e., in the face of incomplete, dubious, and often erroneous information and great fear, doubt, and excitement) call for rapid decisions by alert commanders. He saw history as a vital check on erudite abstractions that did not accord with experience. In contrast to the early work of Antoine-Henri Jomini, he argued that war could not be quantified or reduced to mapwork, geometry, and graphs. Clausewitz had many aphorisms, of which one of the most famous is, "War is the continuation of policy with other means."NameClausewitz's Christian names are sometimes given in non-German sources as "Karl", "Carl Philipp Gottlieb", or "Carl Maria". He spelled his own given name with a "C" in order to identify with the classical Western tradition; writers who use "Karl" are often seeking to emphasize their German (rather than European) identity. "Carl Philipp Gottfried" appears on Clausewitz's tombstone. Nonetheless, sources such as military historian Peter Paret and Encyclopædia Britannica continue to use Gottlieb instead of Gottfried.Life and military careerClausewitz was born on 1 July 1780 in Burg bei Magdeburg in the Prussian Duchy of Magdeburg as the fourth and youngest son of a family that made claims to a noble status which Carl accepted. Clausewitz's family claimed descent from the Barons of Clausewitz in Upper Silesia, though scholars question the connection. His grandfather, the son of a Lutheran pastor, had been a professor of theology. Clausewitz's father, once a lieutenant in the army of Frederick the Great, King of Prussia, held a minor post in the Prussian internal-revenue service. Clausewitz entered the Prussian military service at the age of twelve as a lance corporal, eventually attaining the rank of major general.
Clausewitz served in the Rhine campaigns (1793–1794) including the siege of Mainz, when the Prussian Army invaded France during the French Revolution, and fought in the Napoleonic Wars from 1806 to 1815. He entered the Kriegsakademie (also cited as "The German War School", the "Military Academy in Berlin", and the "Prussian Military Academy," later the "War College") in Berlin in 1801 (aged 21), probably studied the writings of the philosophers Immanuel Kant and/or Johann Gottlieb Fichte and Friedrich Schleiermacher and won the regard of General Gerhard von Scharnhorst, the future first chief-of-staff of the newly reformed Prussian Army (appointed 1809). Clausewitz, Hermann von Boyen (1771–1848) and Karl von Grolman (1777–1843) were among Scharnhorst's primary allies in his efforts to reform the Prussian army between 1807 and 1814.
Clausewitz served during the Jena Campaign as aide-de-camp to Prince August. At the Battle of Jena-Auerstedt on 14 October 1806—when Napoleon invaded Prussia and defeated the Prussian-Saxon army commanded by Karl Wilhelm Ferdinand, Duke of Brunswick—he was captured, one of the 25,000 prisoners taken that day as the Prussian army disintegrated. He was 26. Clausewitz was held prisoner with his prince in France from 1807 to 1808. Returning to Prussia, he assisted in the reform of the Prussian army and state. She also edited, published, and introduced his collected works.
Opposed to Prussia's enforced alliance with Napoleon, Clausewitz left the Prussian army and served in the Imperial Russian Army from 1812 to 1813 during the Russian campaign, taking part in the Battle of Borodino (1812). Like many Prussian officers serving in Russia, he joined the Russian–German Legion in 1813. In the service of the Russian Empire, Clausewitz helped negotiate the Convention of Tauroggen (1812), which prepared the way for the coalition of Prussia, Russia, and the United Kingdom that ultimately defeated Napoleon and his allies. He was soon appointed chief-of-staff of Johann von Thielmann's III Corps. In that capacity he served at the Battle of Ligny and the Battle of Wavre during the Waterloo campaign in 1815. An army led personally by Napoleon defeated the Prussians at Ligny (south of Mont-Saint-Jean and the village of Waterloo) on 16 June 1815, but they withdrew in good order. Napoleon's failure to destroy the Prussian forces led to his defeat a few days later at the Battle of Waterloo (18 June 1815), when the Prussian forces arrived on his right flank late in the afternoon to support the Anglo-Dutch-Belgian forces pressing his front. Napoleon had convinced his troops that the field grey uniforms were those of Marshal Grouchy's grenadiers. Clausewitz's unit fought heavily outnumbered at Wavre (18–19 June 1815), preventing large reinforcements from reaching Napoleon at Waterloo. After the war, Clausewitz served as the director of the Kriegsakademie, where he served until 1830. In that year he returned to active duty with the army. Soon afterward, the outbreak of several revolutions around Europe and a crisis in Poland appeared to presage another major European war. Clausewitz was appointed chief of staff of the only army Prussia was able to mobilise in this emergency, which was sent to the Polish border. Its commander, Gneisenau, died of cholera (August 1831), and Clausewitz took command of the Prussian army's efforts to construct a to contain the great cholera outbreak (the first time cholera had appeared in modern heartland Europe, causing a continent-wide panic). Clausewitz himself died of the same disease shortly afterwards, on 16 November 1831. She wrote the preface for On War and had published most of his collected works by 1835. who was involved in numerous military campaigns, but he is famous primarily as a military theorist interested in the examination of war, utilising the campaigns of Frederick the Great and Napoleon as frames of reference for his work. He wrote a careful, systematic, philosophical examination of war in all its aspects. The result was his principal book, On War, a major work on the philosophy of war. It was unfinished when Clausewitz died and contains material written at different stages in his intellectual evolution, producing some significant contradictions between different sections. The sequence and precise character of that evolution is a source of much debate as to the exact meaning behind some seemingly contradictory observations in discussions pertinent to the tactical, operational and strategic levels of war, for example (though many of these apparent contradictions are simply the result of his dialectical method). Clausewitz constantly sought to revise the text, particularly between 1827 and his departure on his last field assignments, to include more material on "people's war" and forms of war other than high-intensity warfare between states, but relatively little of this material was included in the book. Jomini did not attempt to define war but Clausewitz did, providing (and dialectically comparing) a number of definitions. The first is his dialectical thesis: "War is thus an act of force to compel our enemy to do our will." The second, often treated as Clausewitz's 'bottom line,' is in fact merely his dialectical antithesis: "War is merely the continuation of policy with other means." The synthesis of his dialectical examination of the nature of war is his famous "trinity," saying that war is "a fascinating trinity—composed of primordial violence, hatred, and enmity, which are to be regarded as a blind natural force; the play of chance and probability, within which the creative spirit is free to roam; and its element of subordination, as an instrument of policy, which makes it subject to pure reason." Christopher Bassford says the best shorthand for Clausewitz's trinity should be something like "violent emotion/chance/rational calculation." However, it is frequently presented as "people/army/government," a misunderstanding based on a later paragraph in the same section. This misrepresentation was popularised by U.S. Army Colonel Harry Summers' Vietnam-era interpretation, facilitated by weaknesses in the 1976 Howard/Paret translation.
The degree to which Clausewitz managed to revise his manuscript to reflect that synthesis is the subject of much debate. His final reference to war and Politik, however, goes beyond his widely quoted antithesis: "War is simply the continuation of political intercourse with the addition of other means. We deliberately use the phrase 'with the addition of other means' because we also want to make it clear that war in itself does not suspend political intercourse or change it into something entirely different. In essentials that intercourse continues, irrespective of the means it employs. The main lines along which military events progress, and to which they are restricted, are political lines that continue throughout the war into the subsequent peace."
}}
Clausewitz introduced systematic philosophical contemplation into Western military thinking, with powerful implications not only for historical and analytical writing but also for practical policy, military instruction, and operational planning. He relied on his own experiences, contemporary writings about Napoleon, and on deep historical research. His historiographical approach is evident in his first extended study, written when he was 25, of the Thirty Years' War. In On War, Clausewitz sees all wars as the sum of decisions, actions, and reactions in an uncertain and dangerous context, and also as a socio-political phenomenon. He also stressed the complex nature of war, which encompasses both the socio-political and the operational and stresses the primacy of state policy. (One should be careful not to limit his observations on war to war between states, however, as he certainly discusses other kinds of protagonists). Clausewitz, according to Azar Gat, expressed in the field of military theory the main themes of the Romantic reaction against the worldview of the Enlightenment, rejecting universal principles and stressing historical diversity and the forces of the human spirit. This explains the strength and value of many of his arguments, derived from this great cultural movement, but also his often harsh rhetoric against his predecessors.
Clausewitz's emphasis on the inherent superiority of the defense suggests that habitual aggressors are likely to end up as failures. The inherent superiority of the defense obviously does not mean that the defender will always win, however: there are other asymmetries to be considered. He was interested in co-operation between the regular army and militia or partisan forces, or citizen soldiers, as one possible—sometimes the only—method of defense. In the circumstances of the Wars of the French Revolution and those with Napoleon, which were energised by a rising spirit of nationalism, he emphasised the need for states to involve their entire populations in the conduct of war. This point is especially important, as these wars demonstrated that such energies could be of decisive importance and for a time led to a democratisation of the armed forces much as universal suffrage democratised politics.
While Clausewitz was intensely aware of the value of intelligence at all levels, he was also very skeptical of the accuracy of much military intelligence: "Many intelligence reports in war are contradictory; even more are false, and most are uncertain.... In short, most intelligence is false."Principal ideas
Key ideas discussed in On War include:
* the dialectical approach to military analysis
* the methods of "critical analysis"
* the economic profit-seeking logic of commercial enterprise is equally applicable to the waging of war and negotiating for peace
* the nature of the balance-of-power mechanism
* the relationship between political objectives and military objectives in war
* the asymmetrical relationship between attack and defense
* the nature of "military genius" (involving matters of personality and character, beyond intellect)
* the "fascinating trinity" (wunderliche Dreifaltigkeit) of war
* philosophical distinctions between "absolute war," "ideal war," and "real war"
* in "real war," the distinctive poles of a) limited objectives (political and/or military) and b) war to "render the enemy helpless"
* the idea that war and its conduct belong fundamentally to the social realm rather than to the realms of art or science
* "strategy" belongs primarily to the realm of art, but is constrained by quantitative analyses of political benefits versus military costs & losses
* "tactics" belongs primarily to the realm of science (most obvious in the development of siege warfare)
* the importance of "moral forces" (more than simply "morale") as opposed to quantifiable physical elements
* the "military virtues" of professional armies (which do not necessarily trump the rather different virtues of other kinds of fighting forces)
* conversely, the very real effects of a superiority in numbers and "mass"
* the essential unpredictability of war
* the "fog of war"
As described by Christopher Bassford, then-professor of strategy at the National War College of the United States:
") while accurate as far as it goes, was not intended as a statement of fact. It is the antithesis in a dialectical argument whose thesis is the point—made earlier in the analysis—that "war is nothing but a duel [or wrestling match, the extended metaphor in which that discussion was embedded] on a larger scale." His synthesis, which resolves the deficiencies of these two bold statements, says that war is neither "nothing but" an act of brute force nor "merely" a rational act of politics or policy. This synthesis lies in his "fascinating trinity" []: a dynamic, inherently unstable interaction of the forces of violent emotion, chance, and rational calculation. In what he called a "logical fantasy," war cannot be waged in a limited way: the rules of competition will force participants to use all means at their disposal to achieve victory. But in the real world, he said, such rigid logic is unrealistic and dangerous. As a practical matter, the military objectives in real war that support political objectives generally fall into two broad types: limited aims or the effective "disarming" of the enemy "to render [him] politically helpless or militarily impotent. Thus, the complete defeat of the enemy may not be necessary, desirable, or even possible.
According to Azar Gat, the opposing interpretations of Clausewitz are rooted in Clausewitz’s own conceptual journey. The centerpiece of Clausewitz’s theory of war throughout his life was his concept of all-out fighting and energetic conduct leading to the great battle of annihilation. He believed such conduct expressed the very “nature”, or “lasting spirit” of war. Accordingly, Clausewitz disparaged the significance of the maneuver, surprise, and cunning in war, as distracting from the centrality of battle, and argued that defense was legitimate only if and as long as one was weaker than the enemy. Nevertheless, in the last years of his life, after the first six out of the eight books of On War had already been drafted, Clausewitz came to recognize that this concept was not universal and did not even apply to the Napoleonic Wars, the supreme model of his theory of war. This was demonstrated by the Spanish and Russian campaigns and by guerrilla warfare, in all of which battle was systematically avoided. Consequently, from 1827 on, Clausewitz recognized the legitimacy of limited war and explained it by the influence of politics that harnessed the unlimited nature of war to serve its objectives. Clausewitz died in 1831 before he completed the revision he planned along these lines. He incorporated his new ideas only into the end of Book VI, Book VIII and the beginning of Book I of On War. As a result, when published, On War encompassed both his old and new ideas, at odds with each other.
Thus, against common interpretations of On War, Gat points out that Clausewitz’s transformed views regarding the relationship between politics and war and the admission of limited war into his theory constituted a U-turn against his own life-long fundamental view of the nature of war. Gat further argues the readers’ miscomprehension of the theory in On War as complete and dialectical, rather than a draft undergoing a radical change of mind, has thus generated a range of reactions. People of each age have found in On War the Clausewitz who suited their own views on war and its conduct. Between 1870 and 1914, he was celebrated mainly for his insistence on the clash of forces and the decisive battle, and his emphasis on moral forces. By contrast, after 1945, during the nuclear age, his reputation has reached a second pinnacle for his later acceptance of the primacy of politics and the concept of limited war.
Referring to much of the current interpretation of On War as the Emperor’s New Clothes syndrome, Gat argues that instead of critically addressing the puzzling contradictions in On War, Clausewitz has been set in stone and could not be wrong.
In modern times the reconstruction of Clausewitzian theory has been a matter of much dispute. One analysis was that of Panagiotis Kondylis, a Greek writer and philosopher, who opposed the interpretations of Raymond Aron in Penser la Guerre, Clausewitz, and other liberal writers. According to Aron, Clausewitz was one of the first writers to condemn the militarism of the Prussian general staff and its war-proneness, based on Clausewitz's argument that "war is a continuation of policy by other means." In Theory of War, Kondylis claims that this is inconsistent with Clausewitzian thought. He claims that Clausewitz was morally indifferent to war (though this probably reflects a lack of familiarity with personal letters from Clausewitz, which demonstrate an acute awareness of war's tragic aspects) and that his advice regarding politics' dominance over the conduct of war has nothing to do with pacifist ideas.
Other notable writers who have studied Clausewitz's texts and translated them into English are historians Peter Paret of the Institute for Advanced Study and Sir Michael Howard. Howard and Paret edited the most widely used edition of On War (Princeton University Press, 1976/1984) and have produced comparative studies of Clausewitz and other theorists, such as Tolstoy. Bernard Brodie's A Guide to the Reading of "On War," in the 1976 Princeton translation, expressed his interpretations of the Prussian's theories and provided students with an influential synopsis of this vital work. The 1873 translation by Colonel James John Graham was heavily—and controversially—edited by the philosopher, musician, and game theorist Anatol Rapoport.
The British military historian John Keegan attacked Clausewitz's theory in his book A History of Warfare. Keegan argued that Clausewitz assumed the existence of states, yet 'war antedates the state, diplomacy and strategy by many millennia.'
Influence
Clausewitz died without completing Vom Kriege, but despite this his ideas have been widely influential in military theory and have had a strong influence on German military thought specifically. Later Prussian and German generals, such as Helmuth Graf von Moltke, were clearly influenced by Clausewitz: Moltke's widely quoted statement that "No operational plan extends with high certainty beyond the first encounter with the main enemy force" is a classic reflection of Clausewitz's insistence on the roles of chance, friction, "fog," uncertainty, and interactivity in war.
Clausewitz's influence spread to British thinking as well, though at first more as a historian and analyst than as a theorist. That view assumes, however, a set of values as to what constitutes "rational" political objectives—in this case, values not shaped by the fervid Social Darwinism that was rife in 1914 Europe. One of the most influential British Clausewitzians today is Colin S. Gray; historian Hew Strachan (like Wilkinson also the Chichele Professor of Military History at Oxford University, since 2001) has been an energetic proponent of the study of Clausewitz, but his own views on Clausewitz's ideas are somewhat ambivalent.
With some interesting exceptions (e.g., John McAuley Palmer, Robert M. Johnston, Hoffman Nickerson), Clausewitz had little influence on American military thought before 1945 other than via British writers, though Generals Eisenhower and Patton were avid readers of English translations. He did influence Karl Marx, Friedrich Engels, Vladimir Lenin, Leon Trotsky, Võ Nguyên Giáp, Ferdinand Foch, and Mao Zedong, and thus the Communist Soviet and Chinese traditions, as Lenin emphasized the inevitability of wars among capitalist states in the age of imperialism and presented the armed struggle of the working class as the only path toward the eventual elimination of war. Because Lenin was an admirer of Clausewitz and called him "one of the great military writers," his influence on the Red Army was immense. The Russian historian A.N. Mertsalov commented that "It was an irony of fate that the view in the USSR was that it was Lenin who shaped the attitude towards Clausewitz, and that Lenin's dictum that war is a continuation of politics is taken from the work of this [allegedly] anti-humanist anti-revolutionary."}}
Henry A. Kissinger, however, described Lenin's approach as being that politics is a continuation of war by other means, thus turning Clausewitz's argument "on its head." The idea that war involves inherent "friction" that distorts, to a greater or lesser degree, all prior arrangements, has become common currency in fields such as business strategy and sport. The phrase fog of war derives from Clausewitz's stress on how confused warfare can seem while one is immersed within it. The term center of gravity, used in a military context derives from Clausewitz's usage, which he took from Newtonian mechanics. In U.S. military doctrine, "center of gravity" refers to the basis of an opponent's power at the operational, strategic, or political level, though this is only one aspect of Clausewitz's use of the term.
Late 20th and early 21st century
The deterrence strategy of the United States in the 1950s was closely inspired by President Dwight Eisenhower's reading of Clausewitz as a young officer in the 1920s. Eisenhower was greatly impressed by Clausewitz's example of a theoretical, idealized "absolute war" in Vom Kriege as a way of demonstrating how absurd it would be to attempt such a strategy in practice. For Eisenhower, the age of nuclear weapons had made what was for Clausewitz in the early-19th century only a theoretical vision an all too real possibility in the mid-20th century. From Eisenhower's viewpoint, the best deterrent to war was to show the world just how appalling and horrific a nuclear "absolute war" would be if it should ever occur, hence a series of much-publicized nuclear tests in the Pacific, giving first priority in the defense budget to nuclear weapons and to their delivery-systems over conventional weapons, and making repeated statements in public that the United States was able and willing at all times to use nuclear weapons. In this way, through the massive retaliation doctrine and the closely related foreign-policy concept of brinkmanship, Eisenhower hoped to hold out a credible vision of Clausewitzian nuclear "absolute war" in order to deter the Soviet Union and/or China from ever risking a war or even conditions that might lead to a war with the United States.
* Famous military writers
** Niccolò Machiavelli – The Prince
** Antoine-Henri Jomini
** B.H. Liddell Hart
** Sun Tzu
** Maurice de Saxe
* Absolute war
* Operation Clausewitz
* Philosophy of war
* Principles of War
* Strategic studies
* U.S. Army Strategist
References
Informational notes
Citations
Further reading
* See massive Clausewitz bibliographies in English, French, German, etc., on [http://www.clausewitz.com/mobile/bibl.htm The Clausewitz Homepage bibliography section].
* Aron, Raymond. Clausewitz: Philosopher of War. (1985). 418 pp.
* Bassford, Christopher. [http://www.clausewitz.com/readings/Bassford/CIE/TOC.htm Clausewitz in English: The Reception of Clausewitz in Britain and America, 1815–1945]. New York: Oxford University Press, 1994.
* Christopher Bassford, "[http://www.clausewitz.com/mobile/trinity8.htm Tiptoe Through the Trinity: The Strange Persistence of Trinitarian Warfare]." Working paper.
* Christopher Bassford, "[http://www.clausewitz.com/mobile/Bassford-Supersession5.pdf Clausewitz's Categories of War and the Supersession of 'Absolute War'] " (Clausewitz.com). This is a 'working paper' first posted in 2016."
*
* [http://www.mqup.ca/war-as-paradox-products-9780773547698.php Cormier, Youri]. "Fighting Doctrines and Revolutionary Ethics" Journal of Military and Security Studies, Vol 15, No 1 (2013) https://web.archive.org/web/20140729225332/http://jmss.synergiesprairies.ca/jmss/index.php/jmss/article/view/519
*
* [http://www.mqup.ca/war-as-paradox-products-9780773547698.php Cormier, Youri]. War As Paradox: Clausewitz & Hegel on Fighting Doctrines and Ethics, (Montreal & Kingston: McGill Queen's University Press, 2016) pp. 183–232
*
* Donker, Paul. "[https://www.clausewitzstudies.org/bibl/DonkerP-TheEvolutionOfClausewitzsVomKriege.pdf The Evolution of Clausewitz's Vom Kriege: a reconstruction on the basis of the earlier versions of his masterpiece]." Trans. Paul Donker and Christopher Bassford, ClausewitzStudies.org, August 2019. Originally "Die Entwicklung von Clausewitz' Vom Kriege: Eine Rekonstruktion auf der Grundlage der früheren Fassungen seines Meisterwerks," in the Clausewitz-Gesellschaft's Jahrbuch2017, pp. 14–39.
* Echevarria, Antulio J., II. After Clausewitz: German Military Thinkers before the Great War. (2001). 346 pp.
*
* Gat, Azar. The Origins of Military Thought from the Enlightenment to Clausewitz (1989)
* Gat, Azar. A history of military thought: from the Enlightenment to the Cold War (2001)
* Gat, Azar. ''The Clausewitz Myth: Or the Emperor's New Clothes (2024)
* Handel, Michael I., ed. Clausewitz and Modern Strategy. 1986. 324 pp.
* Handel, Michael I. Masters of War: Classical Strategic Thought.'' (2001) 482 pages. Based on comparison of Clausewitz's On War with Sun Tzu's The Art of War
* Heuser, Beatrice. Reading Clausewitz. (2002). 238 pages,
*
*
* Sir Michael Howard, Clausewitz, 1983 [originally a volume in the Oxford University Press "Past Masters" series, reissued in 2000 as Clausewitz: A Very Short Introduction].
*
** See critique of Keegan's arguments by Christopher Bassford, "[http://www.clausewitz.com/mobile/keegandelenda.htm John Keegan and the Grand Tradition of Trashing Clausewitz: A Polemic]," War in History, November 1994, pp. 319–336.
*
*
* Mertsalov, A.N. "Jomini versus Clausewitz" pp. 11–19 from Russia War, Peace and Diplomacy edited by Mark and Ljubica Erickson, London: Weidenfeld & Nicolson, 2004, .
* Paret, Peter. [http://www.berghahnbooks.com/title.php?rowtag=ParetClausewitzClausewitz in His Time: Essays in the Cultural and Intellectual History of Thinking about War]. New York and Oxford: Berghahn Books, 2015.
*
* Paret, Peter. Clausewitz and the State: The Man, His Theories, and His Times. Princeton: Princeton University Press, 1976.
*
*
* Paul Roques, Le général de Clausewitz. Sa vie et sa théorie de la guerre, Paris, Editions Astrée, 2013. http://www.editions-astree.fr/BC/Bon_de_commande_Roques.pdf
* Rothfels, Hans "Clausewitz" pp. 93–113 from The Makers of Modern Strategy edited by Edward Mead Earle, Gordon A. Craig & Felix Gilbert, Princeton, N.J.: Princeton University Press, 1943.
*
* Smith, Hugh. On Clausewitz: A Study of Military and Political Ideas. (2005). 303 pp.
* Stoker, Donald J. Clausewitz: His Life and Work (Oxford UP, 2014) 376 pp. [https://www.h-net.org/reviews/showrev.php?id=42780 online review]; also [https://www.amazon.com/Clausewitz-Life-Work-Donald-Stoker/dp/0199357943/ excerpt]
*
* Strachan, Hew, and Andreas Herberg-Rothe, eds. Clausewitz in the Twenty-First Century (2007) [https://www.amazon.com/dp/0199232024/ excerpt and text search]
*
* Sumida, Jon Tetsuro. Decoding Clausewitz: A New Approach to On War Lawrence, Kansas: University Press of Kansas, 2008.
* Villacres, Edward J. and Bassford, Christopher. [http://www.clausewitz.com/readings/Bassford/Trinity/TRININTR.htm "Reclaiming the Clausewitzian Trinity"]. Parameters, Autumn 95, pp. 9–19,
* Wallach, Jehuda L. The Dogma of the Battle of Annihilation: The Theories of Clausewitz and Schlieffen and Their Impact on the German Conduct of Two World Wars. (1986).
*
Primary sources (including translations)
* Clausewitz, Carl von. Historical and Political Writings, ed. Peter Paret and Daniel Moran (1992).
* Clausewitz, Carl von. [http://www.clausewitz.com/readings/VomKriege1832/TOC.htm Vom Kriege]. Berlin: Dümmlers Verlag, 1832.
*
* Clausewitz, Carl von. On War, abridged version translated by Michael Howard and Peter Paret, edited with an introduction by Beatrice Heuser Oxford World's Classics (Oxford University Press, 2007)
* Clausewitz, Carl von. [http://www.clausewitz.com/mobile/principlesofwar.htm Principles of War]. Translated by Hans Gatske. The Military Service Publishing Company, 1942. Originally "Die wichtigsten Grundsätze des Kriegführens zur Ergänzung meines Unterrichts bei Sr. Königlichen Hoheit dem Kronprinzen" (written 1812).
* Clausewitz, Carl von. Col. J. J. Graham, translator. Vom Kriege. [https://www.gutenberg.org/ebooks/1946 On War – Volume 1], Project Gutenberg eBook. The full text of the 1873 English translation can be seen in parallel with the original German text at [http://www.clausewitz.com/CompareFrameSource1.htm Compare VOM KRIEGE (1832) and ON WAR (1873 translation)] . [http://www.clausewitz.com/CompareFrameSource1.htm Compare VOM KRIEGE (1832) and ON WAR (1873 translation)]
* Clausewitz, Karl von. On War. Trans. O.J. Matthijs Jolles. New York: Random House, 1943. Though not currently the standard translation, this is increasingly viewed by many Clausewitz scholars as the most precise and accurate English translation.
* Clausewitz, Carl von (2018). ''Napoleon's 1796 Italian Campaign. Trans and ed. Nicholas Murray and Christopher Pringle. Lawrence, Kansas: University Press of Kansas.
* Clausewitz, Carl von (2020). Napoleon Absent, Coalition Ascendant: The 1799 Campaign in Italy and Switzerland, Volume 1. Trans and ed. Nicholas Murray and Christopher Pringle. Lawrence, Kansas: University Press of Kansas. [http://www.h-net.org/reviews/showrev.php?id=57772 online review]
* Clausewitz, Carl von (2021). The Coalition Crumbles, Napoleon Returns: The 1799 Campaign in Italy and Switzerland, Volume 2. Trans and ed. Nicholas Murray and Christopher Pringle. Lawrence, Kansas: University Press of Kansas.
* Clausewitz, Carl von. [http://www.clausewitz.com/readings/1812/Clausewitz-CampaignOf1812inRussia-EllesmereTranslation.pdf The Campaign of 1812 in Russia] ''. Trans. anonymous [Wellington's friend Francis Egerton, later Lord Ellesmere], London: John Murray Publishers, 1843. Originally Carl von Clausewitz, Hinterlassene Werke des Generals Carl von Clausewitz über Krieg und Krieg führung, 10 vols., Berlin, 1832–37, "Der Feldzug von 1812 in Russland" in Vol. 7, Berlin, 1835.
* Clausewitz, Carl von, and Wellesley, Arthur (First Duke of Wellington), ed./trans. Christopher Bassford, Gregory W. Pedlow, and Daniel Moran, [http://www.clausewitz.com/readings/1815/ On Waterloo: Clausewitz, Wellington, and the Campaign of 1815]. (Clausewitz.com, 2010). This collection of documents includes, in a modern English translation, the whole of Clausewitz's study, [http://www.clausewitz.com/readings/1815/five1-9.htm The Campaign of 1815: Strategic Overview] (Berlin: 1835). . It also includes [http://www.clausewitz.com/readings/1815/six.htm Wellington's reply] to Clausewitz's discussion of the campaign, as well as [http://www.clausewitz.com/readings/1815/three.htm two letters by Clausewitz] to his wife after the major battles of 1815 and other supporting documents and essays.
* Clausewitz, Carl von. [http://www.clausewitz.com/readings/TwoLetters/TwoLetters.htm Two Letters on Strategy]. Ed./trans. Peter Paret and Daniel Moran. Carlisle: Army War College Foundation, 1984.
External links
* [https://www.mindmeister.com/609061126/on-war Mind Map of On War]
* [http://www.clausewitz.com/index.htm Clausewitz homepage], large amounts of information.
* Corn, Tony. [http://www.hoover.org/publications/policy-review/article/6795 "Clausewitz in Wonderland"], Policy Review, September 2006. This is an article hostile to "Clausewitz and the Clausewitzians." See also [http://www.clausewitz.com/readings/Bassford/OnCornyIdeas.htm reply by Clausewitz Homepage], "Clausewitz's self-appointed PR Flack."
*
*
*
* [https://web.archive.org/web/20070926204024/http://www.homepage.bluewin.ch/abegglen/papers/clausewitz_influence_on_jomini.pdf The Influence of Clausewitz on Jomini's Le Précis de l'Art de la Guerre]
* [http://www.clausewitz.com/readings/TwoLetters/TwoLetters.htm Two Letters On Strategy], addressed to the Prussian general-staff officer, Major von Roeder, respectively of 22 and 24 December 1827.
* [https://www.academia.edu/attachments/35927726/download_file?st=MTQxODQ3NjcxNCwxMDguMjYuMTIzLjE2MSwxMzMzMjk5MA%3D%3D Erfourth M. & Bazin, A. (2014). Clausewitz's Military Genius and the #Human Dimension. The Bridge.]
Category:1780 births
Category:1831 deaths
Category:People from Burg bei Magdeburg
Category:People from the Duchy of Magdeburg
Category:Deaths from cholera
Category:German military writers
Category:German untitled nobility
Category:Prussian commanders of the Napoleonic Wars
Category:Major generals of Prussia
Category:Napoleonic Wars prisoners of war held by France
Category:Military theorists
Category:Political realists
Category:German prisoners of war
Category:19th-century German writers
Category:19th-century German male writers
Category:Russian military personnel of the Napoleonic Wars
Category:German male non-fiction writers
Category:Philosophers of war
Category:Theoretical historians
Category:Military personnel from Saxony-Anhalt
|
https://en.wikipedia.org/wiki/Carl_von_Clausewitz
|
2025-04-05T18:27:42.714554
|
6068
|
Common Lisp
|
, for ANSI Common Lisp
| designer = Scott Fahlman, Richard P. Gabriel, David A. Moon, Kent Pitman, Guy Steele, Dan Weinreb
| developer = ANSI X3J13 committee
| standard reference = Common Lisp HyperSpec
| latest release version | latest release date
| typing = Dynamic, strong
| scope = Lexical, optionally dynamic
| namespace style = Lisp-2
| implementations = Allegro CL, ABCL, Clasp, CLISP, Clozure CL, CMUCL, ECL, GCL, LispWorks, Scieneer CL, SBCL, Symbolics Common Lisp
| dialects = CLtL1, CLtL2, ANSI Common Lisp
| influenced by = Lisp, Lisp Machine Lisp, Maclisp, Scheme, Interlisp
| influenced = Clojure, Dylan, Emacs Lisp, EuLisp, ISLISP, *Lisp, AutoLisp, Julia, Moose, R, SKILL, SubL
| operating system = Cross-platform
| license | website
| file ext = .lisp, .lsp, .l, .cl, .fasl
}}
Common Lisp (CL) is a dialect of the Lisp programming language, published in American National Standards Institute (ANSI) standard document ANSI INCITS 226-1994 (S2018) (formerly X3.226-1994 (R1999)). The Common Lisp HyperSpec, a hyperlinked HTML version, has been derived from the ANSI Common Lisp standard.
The Common Lisp language was developed as a standardized and improved successor of Maclisp. By the early 1980s several groups were already at work on diverse successors to MacLisp: Lisp Machine Lisp (aka ZetaLisp), Spice Lisp, NIL and S-1 Lisp. Common Lisp sought to unify, standardise, and extend the features of these MacLisp dialects. Common Lisp is not an implementation, but rather a language specification. Several implementations of the Common Lisp standard are available, including free and open-source software and proprietary products.
Common Lisp is a general-purpose, multi-paradigm programming language. It supports a combination of procedural, functional, and object-oriented programming paradigms. As a dynamic programming language, it facilitates evolutionary and incremental software development, with iterative compilation into efficient run-time programs. This incremental development is often done interactively without interrupting the running application.
It also supports optional type annotation and casting, which can be added as necessary at the later profiling and optimization stages, to permit the compiler to generate more efficient code. For instance, <code>fixnum</code> can hold an unboxed integer in a range supported by the hardware and implementation, permitting more efficient arithmetic than on big integers or arbitrary precision types. Similarly, the compiler can be told on a per-module or per-function basis which type of safety level is wanted, using optimize declarations.
Common Lisp includes CLOS, an object system that supports multimethods and method combinations. It is often implemented with a Metaobject Protocol.
Common Lisp is extensible through standard features such as Lisp macros (code transformations) and reader macros (input parsers for characters).
Common Lisp provides partial backwards compatibility with Maclisp and John McCarthy's original Lisp. This allows older Lisp software to be ported to Common Lisp.
History
Work on Common Lisp started in 1981 after an initiative by ARPA manager Bob Engelmore to develop a single community standard Lisp dialect. Much of the initial language design was done via electronic mail. In 1982, Guy L. Steele Jr. gave the first overview of Common Lisp at the 1982 ACM Symposium on LISP and functional programming.
The first language documentation was published in 1984 as Common Lisp the Language (known as CLtL1), first edition. A second edition (known as CLtL2), published in 1990, incorporated many changes to the language, made during the ANSI Common Lisp standardization process: extended LOOP syntax, the Common Lisp Object System, the Condition System for error handling, an interface to the pretty printer and much more. But CLtL2 does not describe the final ANSI Common Lisp standard and thus is not a documentation of ANSI Common Lisp. The final ANSI Common Lisp standard then was published in 1994. Since then no update to the standard has been published. Various extensions and improvements to Common Lisp (examples are Unicode, Concurrency, CLOS-based IO) have been provided by implementations and libraries.
Syntax
Common Lisp is a dialect of Lisp. It uses S-expressions to denote both code and data structure. Function calls, macro forms and special forms are written as lists, with the name of the operator first, as in these examples:
<syntaxhighlight lang="lisp">
(+ 2 2) ; adds 2 and 2, yielding 4. The function's name is '+'. Lisp has no operators as such.
</syntaxhighlight>
<syntaxhighlight lang="lisp">
(defvar *x*) ; Ensures that a variable *x* exists,
; without giving it a value. The asterisks are part of
; the name, by convention denoting a special (global) variable.
; The symbol *x* is also hereby endowed with the property that
; subsequent bindings of it are dynamic, rather than lexical.
(setf *x* 42.1) ; Sets the variable *x* to the floating-point value 42.1
</syntaxhighlight>
<syntaxhighlight lang="lisp">
;; Define a function that squares a number:
(defun square (x)
(* x x))
</syntaxhighlight>
<syntaxhighlight lang="lisp">
;; Execute the function:
(square 3) ; Returns 9
</syntaxhighlight>
<!-- I truncated this a bit; in smaller browsers, it runs off the side-->
<syntaxhighlight lang="lisp">
;; The 'let' construct creates a scope for local variables. Here
;; the variable 'a' is bound to 6 and the variable 'b' is bound
;; to 4. Inside the 'let' is a 'body', where the last computed value is returned.
;; Here the result of adding a and b is returned from the 'let' expression.
;; The variables a and b have lexical scope, unless the symbols have been
;; marked as special variables (for instance by a prior DEFVAR).
(let ((a 6)
(b 4))
(+ a b)) ; returns 10
</syntaxhighlight>
Data types
Common Lisp has many data types.
Scalar types
Number types include integers, ratios, floating-point numbers, and complex numbers. Common Lisp uses bignums to represent numerical values of arbitrary size and precision. The ratio type represents fractions exactly, a facility not available in many languages. Common Lisp automatically coerces numeric values among these types as appropriate.
The Common Lisp character type is not limited to ASCII characters. Most modern implementations allow Unicode characters.
The symbol type is common to Lisp languages, but largely unknown outside them. A symbol is a unique, named data object with several parts: name, value, function, property list, and package. Of these, value cell and function cell are the most important. Symbols in Lisp are often used similarly to identifiers in other languages: to hold the value of a variable; however there are many other uses. Normally, when a symbol is evaluated, its value is returned. Some symbols evaluate to themselves, for example, all symbols in the keyword package are self-evaluating. Boolean values in Common Lisp are represented by the self-evaluating symbols T and NIL. Common Lisp has namespaces for symbols, called 'packages'.
A number of functions are available for rounding scalar numeric values in various ways. The function <code>round</code> rounds the argument to the nearest integer, with halfway cases rounded to the even integer. The functions <code>truncate</code>, <code>floor</code>, and <code>ceiling</code> round towards zero, down, or up respectively. All these functions return the discarded fractional part as a secondary value. For example, <code>(floor -2.5)</code> yields −3, 0.5; <code>(ceiling -2.5)</code> yields −2, −0.5; <code>(round 2.5)</code> yields 2, 0.5; and <code>(round 3.5)</code> yields 4, −0.5.
Data structures
Sequence types in Common Lisp include lists, vectors, bit-vectors, and strings. There are many operations that can work on any sequence type.
As in almost all other Lisp dialects, lists in Common Lisp are composed of conses, sometimes called cons cells or pairs. A cons is a data structure with two slots, called its car and cdr. A list is a linked chain of conses or the empty list. Each cons's car refers to a member of the list (possibly another list). Each cons's cdr refers to the next cons—except for the last cons in a list, whose cdr refers to the <code>nil</code> value. Conses can also easily be used to implement trees and other complex data structures; though it is usually advised to use structure or class instances instead. It is also possible to create circular data structures with conses.
Common Lisp supports multidimensional arrays, and can dynamically resize adjustable arrays if required. Multidimensional arrays can be used for matrix mathematics. A vector is a one-dimensional array. Arrays can carry any type as members (even mixed types in the same array) or can be specialized to contain a specific type of members, as in a vector of bits. Usually, only a few types are supported. Many implementations can optimize array functions when the array used is type-specialized. Two type-specialized array types are standard: a string is a vector of characters, while a bit-vector is a vector of bits.
Hash tables store associations between data objects. Any object may be used as key or value. Hash tables are automatically resized as needed.
Packages are collections of symbols, used chiefly to separate the parts of a program into namespaces. A package may export some symbols, marking them as part of a public interface. Packages can use other packages.
Structures, similar in use to C structs and Pascal records, represent arbitrary complex data structures with any number and type of fields (called slots). Structures allow single-inheritance.
Classes are similar to structures, but offer more dynamic features and multiple-inheritance. (See CLOS). Classes have been added late to Common Lisp and there is some conceptual overlap with structures. Objects created of classes are called Instances. A special case is Generic Functions. Generic Functions are both functions and instances.
Functions
Common Lisp supports first-class functions. For instance, it is possible to write functions that take other functions as arguments or return functions as well. This makes it possible to describe very general operations.
The Common Lisp library relies heavily on such higher-order functions. For example, the <code>sort</code> function takes a relational operator as an argument and key function as an optional keyword argument. This can be used not only to sort any type of data, but also to sort data structures according to a key.
<syntaxhighlight lang="lisp">
;; Sorts the list using the > and < function as the relational operator.
(sort (list 5 2 6 3 1 4) #'>) ; Returns (6 5 4 3 2 1)
(sort (list 5 2 6 3 1 4) #'<) ; Returns (1 2 3 4 5 6)
</syntaxhighlight>
<syntaxhighlight lang="lisp">
;; Sorts the list according to the first element of each sub-list.
(sort (list '(9 A) '(3 B) '(4 C)) #'< :key #'first) ; Returns ((3 B) (4 C) (9 A))
</syntaxhighlight>
The evaluation model for functions is very simple. When the evaluator encounters a form <code>(f a1 a2...)</code> then it presumes that the symbol named f is one of the following:
# A special operator (easily checked against a fixed list)
# A macro operator (must have been defined previously)
# The name of a function (default), which may either be a symbol, or a sub-form beginning with the symbol <code>lambda</code>.
If f is the name of a function, then the arguments a1, a2, ..., an are evaluated in left-to-right order, and the function is found and invoked with those values supplied as parameters.
Defining functions
The macro <code>defun</code> defines functions where a function definition gives the name of the function, the names of any arguments, and a function body:
<syntaxhighlight lang="lisp">
(defun square (x)
(* x x))
</syntaxhighlight>
Function definitions may include compiler directives, known as declarations, which provide hints to the compiler about optimization settings or the data types of arguments. They may also include documentation strings (docstrings), which the Lisp system may use to provide interactive documentation:
<syntaxhighlight lang="lisp">
(defun square (x)
"Calculates the square of the single-float x."
(declare (single-float x) (optimize (speed 3) (debug 0) (safety 1)))
(the single-float (* x x)))
</syntaxhighlight>
Anonymous functions (function literals) are defined using <code>lambda</code> expressions, e.g. <code>(lambda (x) (* x x))</code> for a function that squares its argument. Lisp programming style frequently uses higher-order functions for which it is useful to provide anonymous functions as arguments.
Local functions can be defined with <code>flet</code> and <code>labels</code>.
<syntaxhighlight lang="lisp">
(flet ((square (x)
(* x x)))
(square 3))
</syntaxhighlight>
There are several other operators related to the definition and manipulation of functions. For instance, a function may be compiled with the <code>compile</code> operator. (Some Lisp systems run functions using an interpreter by default unless instructed to compile; others compile every function).
Defining generic functions and methods
The macro <code>defgeneric</code> defines generic functions. Generic functions are a collection of methods.
The macro <code>defmethod</code> defines methods.
Methods can specialize their parameters over CLOS standard classes, system classes, structure classes or individual objects. For many types, there are corresponding system classes.
When a generic function is called, multiple-dispatch will determine the effective method to use.
<syntaxhighlight lang="lisp">
(defgeneric add (a b))
</syntaxhighlight>
<syntaxhighlight lang="lisp">
(defmethod add ((a number) (b number))
(+ a b))
</syntaxhighlight>
<syntaxhighlight lang="lisp">
(defmethod add ((a vector) (b number))
(map 'vector (lambda (n) (+ n b)) a))
</syntaxhighlight>
<syntaxhighlight lang="lisp">
(defmethod add ((a vector) (b vector))
(map 'vector #'+ a b))
</syntaxhighlight>
<syntaxhighlight lang="lisp">
(defmethod add ((a string) (b string))
(concatenate 'string a b))
</syntaxhighlight>
<syntaxhighlight lang="lisp">
(add 2 3) ; returns 5
(add #(1 2 3 4) 7) ; returns #(8 9 10 11)
(add #(1 2 3 4) #(4 3 2 1)) ; returns #(5 5 5 5)
(add "COMMON " "LISP") ; returns "COMMON LISP"
</syntaxhighlight>
Generic Functions are also a first class data type. There are many more features to Generic Functions and Methods than described above.
The function namespace
<!-- This section name is linked from several places; if you change it, update the links. -->
The namespace for function names is separate from the namespace for data variables. This is a key difference between Common Lisp and Scheme. For Common Lisp, operators that define names in the function namespace include <code>defun</code>, <code>flet</code>, <code>labels</code>, <code>defmethod</code> and <code>defgeneric</code>.
To pass a function by name as an argument to another function, one must use the <code>function</code> special operator, commonly abbreviated as <code>#'</code>. The first <code>sort</code> example above refers to the function named by the symbol <code>></code> in the function namespace, with the code <code>#'></code>. Conversely, to call a function passed in such a way, one would use the <code>funcall</code> operator on the argument.
Scheme's evaluation model is simpler: there is only one namespace, and all positions in the form are evaluated (in any order) – not just the arguments. Code written in one dialect is therefore sometimes confusing to programmers more experienced in the other. For instance, many Common Lisp programmers like to use descriptive variable names such as list or string which could cause problems in Scheme, as they would locally shadow function names.
Whether a separate namespace for functions is an advantage is a source of contention in the Lisp community. It is usually referred to as the Lisp-1 vs. Lisp-2 debate. Lisp-1 refers to Scheme's model and Lisp-2 refers to Common Lisp's model. These names were coined in a 1988 paper by Richard P. Gabriel and Kent Pitman, which extensively compares the two approaches.Multiple return valuesCommon Lisp supports the concept of multiple values, where any expression always has a single primary value, but it might also have any number of secondary values, which might be received and inspected by interested callers. This concept is distinct from returning a list value, as the secondary values are fully optional, and passed via a dedicated side channel. This means that callers may remain entirely unaware of the secondary values being there if they have no need for them, and it makes it convenient to use the mechanism for communicating information that is sometimes useful, but not always necessary. For example,
* The <code>TRUNCATE</code> function rounds the given number to an integer towards zero. However, it also returns a remainder as a secondary value, making it very easy to determine what value was truncated. It also supports an optional divisor parameter, which can be used to perform Euclidean division trivially:
<syntaxhighlight lang="cl">
(let ((x 1266778)
(y 458))
(multiple-value-bind (quotient remainder)
(truncate x y)
(format nil "~A divided by ~A is ~A remainder ~A" x y quotient remainder)))
;;;; => "1266778 divided by 458 is 2765 remainder 408"
</syntaxhighlight>
* <code>GETHASH</code> returns the value of a key in an associative map, or the default value otherwise, and a secondary Boolean indicating whether the value was found. Thus code that does not care about whether the value was found or provided as the default can simply use it as-is, but when such distinction is important, it might inspect the secondary Boolean and react appropriately. Both use cases are supported by the same call and neither is unnecessarily burdened or constrained by the other. Having this feature at the language level removes the need to check for the existence of the key or compare it to null as would be done in other languages.
<syntaxhighlight lang="cl">
(defun get-answer (library)
(gethash 'answer library 42))
(defun the-answer-1 (library)
(format nil "The answer is ~A" (get-answer library)))
;;;; Returns "The answer is 42" if ANSWER not present in LIBRARY
(defun the-answer-2 (library)
(multiple-value-bind (answer sure-p)
(get-answer library)
(if (not sure-p)
"I don't know"
(format nil "The answer is ~A" answer))))
;;;; Returns "I don't know" if ANSWER not present in LIBRARY
</syntaxhighlight>
Multiple values are supported by a handful of standard forms, most common of which are the <code>MULTIPLE-VALUE-BIND</code> special form for accessing secondary values and <code>VALUES</code> for returning multiple values:
<syntaxhighlight lang="cl">
(defun magic-eight-ball ()
"Return an outlook prediction, with the probability as a secondary value"
(values "Outlook good" (random 1.0)))
;;;; => "Outlook good"
;;;; => 0.3187
</syntaxhighlight>
Other types
Other data types in Common Lisp include:
*Pathnames represent files and directories in the filesystem. The Common Lisp pathname facility is more general than most operating systems' file naming conventions, making Lisp programs' access to files broadly portable across diverse systems.
*Input and output streams represent sources and sinks of binary or textual data, such as the terminal or open files.
*Common Lisp has a built-in pseudo-random number generator (PRNG). Random state objects represent reusable sources of pseudo-random numbers, allowing the user to seed the PRNG or cause it to replay a sequence.
*Conditions are a type used to represent errors, exceptions, and other "interesting" events to which a program may respond.
*Classes are first-class objects, and are themselves instances of classes called metaobject classes (metaclasses for short).
*Readtables are a type of object which control how Common Lisp's reader parses the text of source code. By controlling which readtable is in use when code is read in, the programmer can change or extend the language's syntax.
Scope
Like programs in many other programming languages, Common Lisp programs make use of names to refer to variables, functions, and many other kinds of entities. Named references are subject to scope.
The association between a name and the entity which the name refers to is called a binding.
Scope refers to the set of circumstances in which a name is determined to have a particular binding.
Determiners of scope
The circumstances which determine scope in Common Lisp include:
* the location of a reference within an expression. If it's the leftmost position of a compound, it refers to a special operator or a macro or function binding, otherwise to a variable binding or something else.
* the kind of expression in which the reference takes place. For instance, <code>(go x)</code> means transfer control to label <code>x</code>, whereas <code>(print x)</code> refers to the variable <code>x</code>. Both scopes of <code>x</code> can be active in the same region of program text, since tagbody labels are in a separate namespace from variable names. A special form or macro form has complete control over the meanings of all symbols in its syntax. For instance, in <code>(defclass x (a b) ())</code>, a class definition, the <code>(a b)</code> is a list of base classes, so these names are looked up in the space of class names, and <code>x</code> isn't a reference to an existing binding, but the name of a new class being derived from <code>a</code> and <code>b</code>. These facts emerge purely from the semantics of <code>defclass</code>. The only generic fact about this expression is that <code>defclass</code> refers to a macro binding; everything else is up to <code>defclass</code>.
* the location of the reference within the program text. For instance, if a reference to variable <code>x</code> is enclosed in a binding construct such as a <code>let</code> which defines a binding for <code>x</code>, then the reference is in the scope created by that binding.
* for a variable reference, whether or not a variable symbol has been, locally or globally, declared special. This determines whether the reference is resolved within a lexical environment, or within a dynamic environment.
* the specific instance of the environment in which the reference is resolved. An environment is a run-time dictionary which maps symbols to bindings. Each kind of reference uses its own kind of environment. References to lexical variables are resolved in a lexical environment, et cetera. More than one environment can be associated with the same reference. For instance, thanks to recursion or the use of multiple threads, multiple activations of the same function can exist at the same time. These activations share the same program text, but each has its own lexical environment instance.
To understand what a symbol refers to, the Common Lisp programmer must know what kind of reference is being expressed, what kind of scope it uses if it is a variable reference (dynamic versus lexical scope), and also the run-time situation: in what environment is the reference resolved, where was the binding introduced into the environment, et cetera.
Kinds of environment
Global
Some environments in Lisp are globally pervasive. For instance, if a new type is defined, it is known everywhere thereafter. References to that type look it up in this global environment.
Dynamic
One type of environment in Common Lisp is the dynamic environment. Bindings established in this environment have dynamic extent, which means that a binding is established at the start of the execution of some construct, such as a <code>let</code> block, and disappears when that construct finishes executing: its lifetime is tied to the dynamic activation and deactivation of a block. However, a dynamic binding is not just visible within that block; it is also visible to all functions invoked from that block. This type of visibility is known as indefinite scope. Bindings which exhibit dynamic extent (lifetime tied to the activation and deactivation of a block) and indefinite scope (visible to all functions which are called from that block) are said to have dynamic scope.
Common Lisp has support for dynamically scoped variables, which are also called special variables. Certain other kinds of bindings are necessarily dynamically scoped also, such as restarts and catch tags. Function bindings cannot be dynamically scoped using <code>flet</code> (which only provides lexically scoped function bindings), but function objects (a first-level object in Common Lisp) can be assigned to dynamically scoped variables, bound using <code>let</code> in dynamic scope, then called using <code>funcall</code> or <code>APPLY</code>.
Dynamic scope is extremely useful because it adds referential clarity and discipline to global variables. Global variables are frowned upon in computer science as potential sources of error, because they can give rise to ad-hoc, covert channels of communication among modules that lead to unwanted, surprising interactions.
In Common Lisp, a special variable which has only a top-level binding behaves just like a global variable in other programming languages. A new value can be stored into it, and that value simply replaces what is in the top-level binding. Careless replacement of the value of a global variable is at the heart of bugs caused by the use of global variables. However, another way to work with a special variable is to give it a new, local binding within an expression. This is sometimes referred to as "rebinding" the variable. Binding a dynamically scoped variable temporarily creates a new memory location for that variable, and associates the name with that location. While that binding is in effect, all references to that variable refer to the new binding; the previous binding is hidden. When execution of the binding expression terminates, the temporary memory location is gone, and the old binding is revealed, with the original value intact. Of course, multiple dynamic bindings for the same variable can be nested.
In Common Lisp implementations which support multithreading, dynamic scopes are specific to each thread of execution. Thus special variables serve as an abstraction for thread local storage. If one thread rebinds a special variable, this rebinding has no effect on that variable in other threads. The value stored in a binding can only be retrieved by the thread which created that binding. If each thread binds some special variable <code>*x*</code>, then <code>*x*</code> behaves like thread-local storage. Among threads which do not rebind <code>*x*</code>, it behaves like an ordinary global: all of these threads refer to the same top-level binding of <code>*x*</code>.
Dynamic variables can be used to extend the execution context with additional context information which is implicitly passed from function to function without having to appear as an extra function parameter. This is especially useful when the control transfer has to pass through layers of unrelated code, which simply cannot be extended with extra parameters to pass the additional data. A situation like this usually calls for a global variable. That global variable must be saved and restored, so that the scheme doesn't break under recursion: dynamic variable rebinding takes care of this. And that variable must be made thread-local (or else a big mutex must be used) so the scheme doesn't break under threads: dynamic scope implementations can take care of this also.
In the Common Lisp library, there are many standard special variables. For instance, all standard I/O streams are stored in the top-level bindings of well-known special variables. The standard output stream is stored in *standard-output*.
Suppose a function foo writes to standard output:
<syntaxhighlight lang="lisp">
(defun foo ()
(format t "Hello, world"))
</syntaxhighlight>
To capture its output in a character string, *standard-output* can be bound to a string stream and called:
<syntaxhighlight lang="lisp">
(with-output-to-string (*standard-output*)
(foo))
</syntaxhighlight>
-> "Hello, world" ; gathered output returned as a string
Lexical
Common Lisp supports lexical environments. Formally, the bindings in a lexical environment have lexical scope and may have either an indefinite extent or dynamic extent, depending on the type of namespace. Lexical scope means that visibility is physically restricted to the block in which the binding is established. References which are not textually (i.e. lexically) embedded in that block simply do not see that binding.
The tags in a TAGBODY have lexical scope. The expression (GO X) is erroneous if it is not embedded in a TAGBODY which contains a label X. However, the label bindings disappear when the TAGBODY terminates its execution, because they have dynamic extent. If that block of code is re-entered by the invocation of a lexical closure, it is invalid for the body of that closure to try to transfer control to a tag via GO:
<syntaxhighlight lang="lisp">
(defvar *stashed*) ;; will hold a function
(tagbody
(setf *stashed* (lambda () (go some-label)))
(go end-label) ;; skip the (print "Hello")
some-label
(print "Hello")
end-label)
-> NIL
</syntaxhighlight>
When the TAGBODY is executed, it first evaluates the setf form which stores a function in the special variable *stashed*. Then the (go end-label) transfers control to end-label, skipping the code (print "Hello"). Since end-label is at the end of the tagbody, the tagbody terminates, yielding NIL. Suppose that the previously remembered function is now called:
<syntaxhighlight lang="lisp">
(funcall *stashed*) ;; Error!
</syntaxhighlight>
This situation is erroneous. One implementation's response is an error condition containing the message, "GO: tagbody for tag SOME-LABEL has already been left". The function tried to evaluate (go some-label), which is lexically embedded in the tagbody, and resolves to the label. However, the tagbody isn't executing (its extent has ended), and so the control transfer cannot take place.
Local function bindings in Lisp have lexical scope, and variable bindings also have lexical scope by default. By contrast with GO labels, both of these have indefinite extent. When a lexical function or variable binding is established, that binding continues to exist for as long as references to it are possible, even after the construct which established that binding has terminated. References to lexical variables and functions after the termination of their establishing construct are possible thanks to lexical closures.
Lexical binding is the default binding mode for Common Lisp variables. For an individual symbol, it can be switched to dynamic scope, either by a local declaration, by a global declaration. The latter may occur implicitly through the use of a construct like DEFVAR or DEFPARAMETER. It is an important convention in Common Lisp programming that special (i.e. dynamically scoped) variables have names which begin and end with an asterisk sigil <code>*</code> in what is called the "earmuff convention". If adhered to, this convention effectively creates a separate namespace for special variables, so that variables intended to be lexical are not accidentally made special.
Lexical scope is useful for several reasons.
Firstly, references to variables and functions can be compiled to efficient machine code, because the run-time environment structure is relatively simple. In many cases it can be optimized to stack storage, so opening and closing lexical scopes has minimal overhead. Even in cases where full closures must be generated, access to the closure's environment is still efficient; typically each variable becomes an offset into a vector of bindings, and so a variable reference becomes a simple load or store instruction with a base-plus-offset addressing mode.
Secondly, lexical scope (combined with indefinite extent) gives rise to the lexical closure, which in turn creates a whole paradigm of programming centered around the use of functions being first-class objects, which is at the root of functional programming.
Thirdly, perhaps most importantly, even if lexical closures are not exploited, the use of lexical scope isolates program modules from unwanted interactions. Due to their restricted visibility, lexical variables are private. If one module A binds a lexical variable X, and calls another module B, references to X in B will not accidentally resolve to the X bound in A. B simply has no access to X. For situations in which disciplined interactions through a variable are desirable, Common Lisp provides special variables. Special variables allow for a module A to set up a binding for a variable X which is visible to another module B, called from A. Being able to do this is an advantage, and being able to prevent it from happening is also an advantage; consequently, Common Lisp supports both lexical and dynamic scope.
Macros
A macro in Lisp superficially resembles a function in usage. However, rather than representing an expression which is evaluated, it represents a transformation of the program source code. The macro gets the source it surrounds as arguments, binds them to its parameters and computes a new source form. This new form can also use a macro. The macro expansion is repeated until the new source form does not use a macro. The final computed form is the source code executed at runtime.
Typical uses of macros in Lisp:
* new control structures (example: looping constructs, branching constructs)
* scoping and binding constructs
* simplified syntax for complex and repeated source code
* top-level defining forms with compile-time side-effects
* data-driven programming
* embedded domain specific languages (examples: SQL, HTML, Prolog)
* implicit finalization forms
Various standard Common Lisp features also need to be implemented as macros, such as:
* the standard <code>setf</code> abstraction, to allow custom compile-time expansions of assignment/access operators
* <code>with-accessors</code>, <code>with-slots</code>, <code>with-open-file</code> and other similar <code>WITH</code> macros
* Depending on implementation, <code>if</code> or <code>cond</code> is a macro built on the other, the special operator; <code>when</code> and <code>unless</code> consist of macros
* The powerful <code>loop</code> domain-specific language
Macros are defined by the defmacro macro. The special operator macrolet allows the definition of local (lexically scoped) macros. It is also possible to define macros for symbols using define-symbol-macro and symbol-macrolet.
Paul Graham's book On Lisp describes the use of macros in Common Lisp in detail. Doug Hoyte's book Let Over Lambda extends the discussion on macros, claiming "Macros are the single greatest advantage that lisp has as a programming language and the single greatest advantage of any programming language." Hoyte provides several examples of iterative development of macros.
Example using a macro to define a new control structure
Macros allow Lisp programmers to create new syntactic forms in the language. One typical use is to create new control structures. The example macro provides an <code>until</code> looping construct. The syntax is:
<syntaxhighlight lang="text">
(until test form*)
</syntaxhighlight>
The macro definition for until:
<syntaxhighlight lang="lisp">
(defmacro until (test &body body)
(let ((start-tag (gensym "START"))
(end-tag (gensym "END")))
`(tagbody ,start-tag
(when ,test (go ,end-tag))
(progn ,@body)
(go ,start-tag)
,end-tag)))
</syntaxhighlight>
tagbody is a primitive Common Lisp special operator which provides the ability to name tags and use the go form to jump to those tags. The backquote ` provides a notation that provides code templates, where the value of forms preceded with a comma are filled in. Forms preceded with comma and at-sign are spliced in. The tagbody form tests the end condition. If the condition is true, it jumps to the end tag. Otherwise, the provided body code is executed and then it jumps to the start tag.
An example of using the above until macro:
<syntaxhighlight lang="lisp">
(until (= (random 10) 0)
(write-line "Hello"))
</syntaxhighlight>
The code can be expanded using the function macroexpand-1. The expansion for the above example looks like this:
<syntaxhighlight lang="lisp">
(TAGBODY
#:START1136
(WHEN (ZEROP (RANDOM 10))
(GO #:END1137))
(PROGN (WRITE-LINE "hello"))
(GO #:START1136)
#:END1137)
</syntaxhighlight>
During macro expansion the value of the variable test is (= (random 10) 0) and the value of the variable body is ((write-line "Hello")). The body is a list of forms.
Symbols are usually automatically upcased. The expansion uses the TAGBODY with two labels. The symbols for these labels are computed by GENSYM and are not interned in any package. Two go forms use these tags to jump to. Since tagbody is a primitive operator in Common Lisp (and not a macro), it will not be expanded into something else. The expanded form uses the when macro, which also will be expanded. Fully expanding a source form is called code walking.
In the fully expanded (walked) form, the when form is replaced by the primitive if:
<syntaxhighlight lang="lisp">
(TAGBODY
#:START1136
(IF (ZEROP (RANDOM 10))
(PROGN (GO #:END1137))
NIL)
(PROGN (WRITE-LINE "hello"))
(GO #:START1136))
#:END1137)
</syntaxhighlight>
All macros must be expanded before the source code containing them can be evaluated or compiled normally. Macros can be considered functions that accept and return S-expressions – similar to abstract syntax trees, but not limited to those. These functions are invoked before the evaluator or compiler to produce the final source code. Macros are written in normal Common Lisp, and may use any Common Lisp (or third-party) operator available.
Variable capture and shadowing
Common Lisp macros are capable of what is commonly called variable capture, where symbols in the macro-expansion body coincide with those in the calling context, allowing the programmer to create macros wherein various symbols have special meaning. The term variable capture is somewhat misleading, because all namespaces are vulnerable to unwanted capture, including the operator and function namespace, the tagbody label namespace, catch tag, condition handler and restart namespaces.
Variable capture can introduce software defects. This happens in one of the following two ways:
* In the first way, a macro expansion can inadvertently make a symbolic reference which the macro writer assumed will resolve in a global namespace, but the code where the macro is expanded happens to provide a local, shadowing definition which steals that reference. Let this be referred to as type 1 capture.
* The second way, type 2 capture, is just the opposite: some of the arguments of the macro are pieces of code supplied by the macro caller, and those pieces of code are written such that they make references to surrounding bindings. However, the macro inserts these pieces of code into an expansion which defines its own bindings that accidentally captures some of these references.
The Scheme dialect of Lisp provides a macro-writing system which provides the referential transparency that eliminates both types of capture problem. This type of macro system is sometimes called "hygienic", in particular by its proponents (who regard macro systems which do not automatically solve this problem as unhygienic).
In Common Lisp, macro hygiene is ensured one of two different ways.
One approach is to use gensyms: guaranteed-unique symbols which can be used in a macro-expansion without threat of capture. The use of gensyms in a macro definition is a manual chore, but macros can be written which simplify the instantiation and use of gensyms. Gensyms solve type 2 capture easily, but they are not applicable to type 1 capture in the same way, because the macro expansion cannot rename the interfering symbols in the surrounding code which capture its references. Gensyms could be used to provide stable aliases for the global symbols which the macro expansion needs. The macro expansion would use these secret aliases rather than the well-known names, so redefinition of the well-known names would have no ill effect on the macro.
Another approach is to use packages. A macro defined in its own package can simply use internal symbols in that package in its expansion. The use of packages deals with type 1 and type 2 capture.
However, packages don't solve the type 1 capture of references to standard Common Lisp functions and operators. The reason is that the use of packages to solve capture problems revolves around the use of private symbols (symbols in one package, which are not imported into, or otherwise made visible in other packages). Whereas the Common Lisp library symbols are external, and frequently imported into or made visible in user-defined packages.
The following is an example of unwanted capture in the operator namespace, occurring in the expansion of a macro:
<syntaxhighlight lang="lisp">
;; expansion of UNTIL makes liberal use of DO
(defmacro until (expression &body body)
`(do () (,expression) ,@body))
;; macrolet establishes lexical operator binding for DO
(macrolet ((do (...) ... something else ...))
(until (= (random 10) 0) (write-line "Hello")))
</syntaxhighlight>
The <code>until</code> macro will expand into a form which calls <code>do</code> which is intended to refer to the standard Common Lisp macro <code>do</code>. However, in this context, <code>do</code> may have a completely different meaning, so <code>until</code> may not work properly.
Common Lisp solves the problem of the shadowing of standard operators and functions by forbidding their redefinition. Because it redefines the standard operator <code>do</code>, the preceding is actually a fragment of non-conforming Common Lisp, which allows implementations to diagnose and reject it.
Condition system
The condition system is responsible for exception handling in Common Lisp. It provides conditions, handlers and restarts. Conditions are objects describing an exceptional situation (for example an error). If a condition is signaled, the Common Lisp system searches for a handler for this condition type and calls the handler. The handler can now search for restarts and use one of these restarts to automatically repair the current problem, using information such as the condition type and any relevant information provided as part of the condition object, and call the appropriate restart function.
These restarts, if unhandled by code, can be presented to users (as part of a user interface, that of a debugger for example), so that the user can select and invoke one of the available restarts. Since the condition handler is called in the context of the error (without unwinding the stack), full error recovery is possible in many cases, where other exception handling systems would have already terminated the current routine. The debugger itself can also be customized or replaced using the <code>*debugger-hook*</code> dynamic variable. Code found within unwind-protect forms such as finalizers will also be executed as appropriate despite the exception.
In the following example (using Symbolics Genera) the user tries to open a file in a Lisp function test called from the Read-Eval-Print-LOOP (REPL), when the file does not exist. The Lisp system presents four restarts. The user selects the Retry OPEN using a different pathname restart and enters a different pathname (lispm-init.lisp instead of lispm-int.lisp). The user code does not contain any error handling code. The whole error handling and restart code is provided by the Lisp system, which can handle and repair the error without terminating the user code.
<syntaxhighlight lang="text">
Command: (test ">zippy>lispm-int.lisp")
Error: The file was not found.
For lispm:>zippy>lispm-int.lisp.newest
LMFS:OPEN-LOCAL-LMFS-1
Arg 0: #P"lispm:>zippy>lispm-int.lisp.newest"
s-A, <Resume>: Retry OPEN of lispm:>zippy>lispm-int.lisp.newest
s-B: Retry OPEN using a different pathname
s-C, <Abort>: Return to Lisp Top Level in a TELNET server
s-D: Restart process TELNET terminal
-> Retry OPEN using a different pathname
Use what pathname instead [default lispm:>zippy>lispm-int.lisp.newest]:
lispm:>zippy>lispm-init.lisp.newest
...the program continues
</syntaxhighlight>
Common Lisp Object System (CLOS)
Common Lisp includes a toolkit for object-oriented programming, the Common Lisp Object System or CLOS. Peter Norvig explains how many Design Patterns are simpler to implement in a dynamic language with the features of CLOS (Multiple Inheritance, Mixins, Multimethods, Metaclasses, Method combinations, etc.).
Several extensions to Common Lisp for object-oriented programming have been proposed to be included into the ANSI Common Lisp standard, but eventually CLOS was adopted as the standard object-system for Common Lisp. CLOS is a dynamic object system with multiple dispatch and multiple inheritance, and differs radically from the OOP facilities found in static languages such as C++ or Java. As a dynamic object system, CLOS allows changes at runtime to generic functions and classes. Methods can be added and removed, classes can be added and redefined, objects can be updated for class changes and the class of objects can be changed.
CLOS has been integrated into ANSI Common Lisp. Generic functions can be used like normal functions and are a first-class data type. Every CLOS class is integrated into the Common Lisp type system. Many Common Lisp types have a corresponding class. There is more potential use of CLOS for Common Lisp. The specification does not say whether conditions are implemented with CLOS. Pathnames and streams could be implemented with CLOS. These further usage possibilities of CLOS for ANSI Common Lisp are not part of the standard. Actual Common Lisp implementations use CLOS for pathnames, streams, input–output, conditions, the implementation of CLOS itself and more.
Compiler and interpreter
A Lisp interpreter directly executes Lisp source code provided as Lisp objects (lists, symbols, numbers, ...) read from s-expressions. A Lisp compiler generates bytecode or machine code from Lisp source code. Common Lisp allows both individual Lisp functions to be compiled in memory and the compilation of whole files to externally stored compiled code (fasl files).
Several implementations of earlier Lisp dialects provided both an interpreter and a compiler. Unfortunately often the semantics were different. These earlier Lisps implemented lexical scoping in the compiler and dynamic scoping in the interpreter. Common Lisp requires that both the interpreter and compiler use lexical scoping by default. The Common Lisp standard describes both the semantics of the interpreter and a compiler. The compiler can be called using the function compile for individual functions and using the function compile-file for files. Common Lisp allows type declarations and provides ways to influence the compiler code generation policy. For the latter various optimization qualities can be given values between 0 (not important) and 3 (most important): speed, space, safety, debug and compilation-speed.
There is also a function to evaluate Lisp code: <code>eval</code>. <code>eval</code> takes code as pre-parsed s-expressions and not, like in some other languages, as text strings. This way code can be constructed with the usual Lisp functions for constructing lists and symbols and then this code can be evaluated with the function <code>eval</code>. Several Common Lisp implementations (like Clozure CL and SBCL) are implementing <code>eval</code> using their compiler. This way code is compiled, even though it is evaluated using the function <code>eval</code>.
The file compiler is invoked using the function compile-file. The generated file with compiled code is called a fasl (from fast load) file. These fasl files and also source code files can be loaded with the function load into a running Common Lisp system. Depending on the implementation, the file compiler generates byte-code (for example for the Java Virtual Machine), C language code (which then is compiled with a C compiler) or, directly, native code.
Common Lisp implementations can be used interactively, even though the code gets fully compiled. The idea of an Interpreted language thus does not apply for interactive Common Lisp.
The language makes a distinction between read-time, compile-time, load-time, and run-time, and allows user code to also make this distinction to perform the wanted type of processing at the wanted step.
Some special operators are provided to especially suit interactive development; for instance, <code>defvar</code> will only assign a value to its provided variable if it wasn't already bound, while <code>defparameter</code> will always perform the assignment. This distinction is useful when interactively evaluating, compiling and loading code in a live image.
Some features are also provided to help writing compilers and interpreters. Symbols consist of first-level objects and are directly manipulable by user code. The <code>progv</code> special operator allows to create lexical bindings programmatically, while packages are also manipulable. The Lisp compiler is available at runtime to compile files or individual functions. These make it easy to use Lisp as an intermediate compiler or interpreter for another language.
Code examples
Birthday paradox
The following program calculates the smallest number of people in a room for whom the probability of unique birthdays is less than 50% (the birthday paradox, where for 1 person the probability is obviously 100%, for 2 it is 364/365, etc.). The answer is 23.
In Common Lisp, by convention, constants are enclosed with + characters.
<syntaxhighlight lang="lisp">
(defconstant +year-size+ 365)
(defun birthday-paradox (probability number-of-people)
(let ((new-probability (* (/ (- +year-size+ number-of-people)
+year-size+)
probability)))
(if (< new-probability 0.5)
(1+ number-of-people)
(birthday-paradox new-probability (1+ number-of-people)))))
</syntaxhighlight>
Calling the example function using the REPL (Read Eval Print Loop):
<syntaxhighlight lang="text">
CL-USER > (birthday-paradox 1.0 1)
23
</syntaxhighlight>
Sorting a list of person objects
We define a class <code>person</code> and a method for displaying the name and age of a person.
Next we define a group of persons as a list of <code>person</code> objects.
Then we iterate over the sorted list.
<syntaxhighlight lang="lisp">
(defclass person ()
((name :initarg :name :accessor person-name)
(age :initarg :age :accessor person-age))
(:documentation "The class PERSON with slots NAME and AGE."))
(defmethod display ((object person) stream)
"Displaying a PERSON object to an output stream."
(with-slots (name age) object
(format stream "~a (~a)" name age)))
(defparameter *group*
(list (make-instance 'person :name "Bob" :age 33)
(make-instance 'person :name "Chris" :age 16)
(make-instance 'person :name "Ash" :age 23))
"A list of PERSON objects.")
(dolist (person (sort (copy-list *group*)
#'>
:key #'person-age))
(display person *standard-output*)
(terpri))
</syntaxhighlight>
It prints the three names with descending age.
<syntaxhighlight lang="text">
Bob (33)
Ash (23)
Chris (16)
</syntaxhighlight>
Exponentiating by squaring
Use of the LOOP macro is demonstrated:
<syntaxhighlight lang="lisp">
(defun power (x n)
(loop with result = 1
while (plusp n)
when (oddp n) do (setf result (* result x))
do (setf x (* x x)
n (truncate n 2))
finally (return result)))
</syntaxhighlight>
Example use:
<syntaxhighlight lang="lisp">
CL-USER > (power 2 200)
1606938044258990275541962092341162602522202993782792835301376
</syntaxhighlight>
Compare with the built in exponentiation:
<syntaxhighlight lang="lisp">
CL-USER > (= (expt 2 200) (power 2 200))
T
</syntaxhighlight>
Find the list of available shells
WITH-OPEN-FILE is a macro that opens a file and provides a stream. When the form is returning, the file is automatically closed. FUNCALL calls a function object. The LOOP collects all lines that match the predicate.
<syntaxhighlight lang="lisp">
(defun list-matching-lines (file predicate)
"Returns a list of lines in file, for which the predicate applied to
the line returns T."
(with-open-file (stream file)
(loop for line = (read-line stream nil nil)
while line
when (funcall predicate line)
collect it)))
</syntaxhighlight>
The function AVAILABLE-SHELLS calls the above function LIST-MATCHING-LINES with a pathname and an anonymous function as the predicate. The predicate returns the pathname of a shell or NIL (if the string is not the filename of a shell).
<syntaxhighlight lang="lisp">
(defun available-shells (&optional (file #p"/etc/shells"))
(list-matching-lines
file
(lambda (line)
(and (plusp (length line))
(char= (char line 0) #\/)
(pathname
(string-right-trim '(#\space #\tab) line))))))
</syntaxhighlight>
Example results (on Mac OS X 10.6):
<syntaxhighlight lang="lisp">
CL-USER > (available-shells)
(#P"/bin/bash" #P"/bin/csh" #P"/bin/ksh" #P"/bin/sh" #P"/bin/tcsh" #P"/bin/zsh")
</syntaxhighlight>
Comparison with other Lisps
<!-- needs lots -->
Common Lisp is most frequently compared with, and contrasted to, Scheme—if only because they are the two most popular Lisp dialects. Scheme predates CL, and comes not only from the same Lisp tradition but from some of the same engineers—Guy Steele, with whom Gerald Jay Sussman designed Scheme, chaired the standards committee for Common Lisp.
Common Lisp is a general-purpose programming language, in contrast to Lisp variants such as Emacs Lisp and AutoLISP which are extension languages embedded in particular products (GNU Emacs and AutoCAD, respectively). Unlike many earlier Lisps, Common Lisp (like Scheme) uses lexical variable scope by default for both interpreted and compiled code.
Most of the Lisp systems whose designs contributed to Common Lisp—such as ZetaLisp and Franz Lisp—used dynamically scoped variables in their interpreters and lexically scoped variables in their compilers. Scheme introduced the sole use of lexically scoped variables to Lisp; an inspiration from ALGOL 68. CL supports dynamically scoped variables as well, but they must be explicitly declared as "special". There are no differences in scoping between ANSI CL interpreters and compilers.
Common Lisp is sometimes termed a Lisp-2 and Scheme a Lisp-1, referring to CL's use of separate namespaces for functions and variables. (In fact, CL has many namespaces, such as those for go tags, block names, and <code>loop</code> keywords). There is a long-standing controversy between CL and Scheme advocates over the tradeoffs involved in multiple namespaces. In Scheme, it is (broadly) necessary to avoid giving variables names that clash with functions; Scheme functions frequently have arguments named <code>lis</code>, <code>lst</code>, or <code>lyst</code> so as not to conflict with the system function <code>list</code>. However, in CL it is necessary to explicitly refer to the function namespace when passing a function as an argument—which is also a common occurrence, as in the <code>sort</code> example above.
CL also differs from Scheme in its handling of Boolean values. Scheme uses the special values #t and #f to represent truth and falsity. CL follows the older Lisp convention of using the symbols T and NIL, with NIL standing also for the empty list. In CL, any non-NIL value is treated as true by conditionals, such as <code>if</code>, whereas in Scheme all non-#f values are treated as true. These conventions allow some operators in both languages to serve both as predicates (answering a Boolean-valued question) and as returning a useful value for further computation, but in Scheme the value '() which is equivalent to NIL in Common Lisp evaluates to true in a Boolean expression.
Lastly, the Scheme standards documents require tail-call optimization, which the CL standard does not. Most CL implementations do offer tail-call optimization, although often only when the programmer uses an optimization directive. Nonetheless, common CL coding style does not favor the ubiquitous use of recursion that Scheme style prefers—what a Scheme programmer would express with tail recursion, a CL user would usually express with an iterative expression in <code>do</code>, <code>dolist</code>, <code>loop</code>, or (more recently) with the <code>iterate</code> package.
Implementations
See the Category Common Lisp implementations.
Common Lisp is defined by a specification (like Ada and C) rather than by one implementation (like Perl). There are many implementations, and the standard details areas in which they may validly differ.
In addition, implementations tend to come with extensions, which provide functionality not covered in the standard:
* Interactive Top-Level (REPL)
* Garbage Collection
* Debugger, Stepper and Inspector
* Weak data structures (hash tables)
* Extensible sequences
* Extensible LOOP
* Environment access
* CLOS Meta-object Protocol
* CLOS based extensible streams
* CLOS based Condition System
* Network streams
* Persistent CLOS
* Unicode support
* Foreign-Language Interface (often to C)
* Operating System interface
* Java Interface
* Threads and Multiprocessing
* Application delivery (applications, dynamic libraries)
* Saving of images
Free and open-source software libraries have been created to support extensions to Common Lisp in a portable way, and are most notably found in the repositories of the Common-Lisp.net and CLOCC (Common Lisp Open Code Collection) projects.
Common Lisp implementations may use any mix of native code compilation, byte code compilation or interpretation. Common Lisp has been designed to support incremental compilers, file compilers and block compilers. Standard declarations to optimize compilation (such as function inlining or type specialization) are proposed in the language specification. Most Common Lisp implementations compile source code to native machine code. Some implementations can create (optimized) stand-alone applications. Others compile to interpreted bytecode, which is less efficient than native code, but eases binary-code portability. Some compilers compile Common Lisp code to C code. The misconception that Lisp is a purely interpreted language is most likely because Lisp environments provide an interactive prompt and that code is compiled one-by-one, in an incremental way. With Common Lisp incremental compilation is widely used.
Some Unix-based implementations (CLISP, SBCL) can be used as a scripting language; that is, invoked by the system transparently in the way that a Perl or Unix shell interpreter is.List of implementationsCommercial implementations
; Allegro Common Lisp: for Microsoft Windows, FreeBSD, Linux, Apple macOS and various UNIX variants. Allegro CL provides an Integrated Development Environment (IDE) (for Windows and Linux) and extensive capabilities for application delivery.
; Liquid Common Lisp: formerly called Lucid Common Lisp. Only maintenance, no new releases.
; LispWorks: for Microsoft Windows, FreeBSD, Linux, Apple macOS, iOS, Android and various UNIX variants. LispWorks provides an Integrated Development Environment (IDE) (available for most platforms, but not for iOS and Android) and extensive capabilities for application delivery.
; mocl: for iOS, Android and macOS.
; Open Genera: for DEC Alpha.
; Scieneer Common Lisp: which is designed for high-performance scientific computing.
Freely redistributable implementations
; Armed Bear Common Lisp (ABCL): A CL implementation that runs on the Java Virtual Machine. It includes a compiler to Java byte code, and allows access to Java libraries from CL. It was formerly just a component of the Armed Bear J Editor.
; Clasp: A LLVM based implementation that seamlessly interoperates with C++ libraries. Runs on several Unix and Unix-like systems (including macOS).
; CLISP: A bytecode-compiling implementation, portable and runs on several Unix and Unix-like systems (including macOS), as well as Microsoft Windows and several other systems.
; Clozure CL (CCL): Originally a free and open-source fork of Macintosh Common Lisp. As that history implies, CCL was written for the Macintosh, but Clozure CL now runs on macOS, FreeBSD, Linux, Solaris and Windows. 32 and 64 bit x86 ports are supported on each platform. Additionally there are Power PC ports for Mac OS and Linux. CCL was previously known as OpenMCL, but that name is no longer used, to avoid confusion with the open source version of Macintosh Common Lisp.
; CMUCL: Originally from Carnegie Mellon University, now maintained as free and open-source software by a group of volunteers. CMUCL uses a fast native-code compiler. It is available on Linux and BSD for Intel x86; Linux for Alpha; macOS for Intel x86 and PowerPC; and Solaris, IRIX, and HP-UX on their native platforms.
; Corman Common Lisp: for Microsoft Windows. In January 2015 Corman Lisp has been published under MIT license.
; Embeddable Common Lisp (ECL): ECL includes a bytecode interpreter and compiler. It can also compile Lisp code to machine code via a C compiler. ECL then compiles Lisp code to C, compiles the C code with a C compiler and can then load the resulting machine code. It is also possible to embed ECL in C programs, and C code into Common Lisp programs.
; GNU Common Lisp (GCL): The GNU Project's Lisp compiler. Not yet fully ANSI-compliant, GCL is however the implementation of choice for several large projects including the mathematical tools Maxima, AXIOM and (historically) ACL2. GCL runs on Linux under eleven different architectures, and also under Windows, Solaris, and FreeBSD.
; Macintosh Common Lisp (MCL): Version 5.2 for Apple Macintosh computers with a PowerPC processor running Mac OS X is open source. RMCL (based on MCL 5.2) runs on Intel-based Apple Macintosh computers using the Rosetta binary translator from Apple.
; ManKai Common Lisp (MKCL): A branch of ECL. MKCL emphasises reliability, stability and overall code quality through a heavily reworked, natively multi-threaded, runtime system. On Linux, MKCL features a fully POSIX compliant runtime system.
; Movitz: Implements a Lisp environment for x86 computers without relying on any underlying OS.
; Poplog: Poplog implements a version of CL, with POP-11, and optionally Prolog, and Standard ML (SML), allowing mixed language programming. For all, the implementation language is POP-11, which is compiled incrementally. It also has an integrated Emacs-like editor that communicates with the compiler.
; Steel Bank Common Lisp (SBCL): A branch from CMUCL. "Broadly speaking, SBCL is distinguished from CMU CL by a greater emphasis on maintainability." SBCL runs on the platforms CMUCL does, except HP/UX; in addition, it runs on Linux for AMD64, PowerPC, SPARC, MIPS, Windows x86 and AMD64. SBCL does not use an interpreter by default; all expressions are compiled to native code unless the user switches the interpreter on. The SBCL compiler generates fast native code according to a previous version of The Computer Language Benchmarks Game.
; Ufasoft Common Lisp: port of CLISP for windows platform with core written in C++.
Other implementations
; Austin Kyoto Common Lisp: an evolution of Kyoto Common Lisp by Bill Schelter
; Butterfly Common Lisp: an implementation written in Scheme for the BBN Butterfly multi-processor computer
; CLICC: a Common Lisp to C compiler
; CLOE: Common Lisp for PCs by Symbolics
; Codemist Common Lisp: used for the commercial version of the computer algebra system Axiom
; ExperCommon Lisp: an early implementation for the Apple Macintosh by ExperTelligence
; Golden Common Lisp: an implementation for the PC by GoldHill Inc.
; Ibuki Common Lisp: a commercialized version of Kyoto Common Lisp
; Kyoto Common Lisp: the first Common Lisp compiler that used C as a target language. GCL, ECL and MKCL originate from this Common Lisp implementation.
; L: a small version of Common Lisp for embedded systems developed by IS Robotics, now iRobot
; Lisp Machines (from Symbolics, TI and Xerox): provided implementations of Common Lisp in addition to their native Lisp dialect (Lisp Machine Lisp or Interlisp). CLOS was also available. Symbolics provides an enhanced version Common Lisp.
; Procyon Common Lisp: an implementation for Windows and Mac OS, used by Franz for their Windows port of Allegro CL
; Star Sapphire Common LISP: an implementation for the PC
; SubL: a variant of Common Lisp used for the implementation of the Cyc knowledge-based system
; Top Level Common Lisp: an early implementation for concurrent execution
; WCL: a shared library implementation
; VAX Common Lisp: Digital Equipment Corporation's implementation that ran on VAX systems running VMS or ULTRIX
; XLISP: an implementation written by David BetzApplications
Common Lisp is used to develop research applications (often in Artificial Intelligence), for rapid development of prototypes or for deployed applications.
Common Lisp is used in many commercial applications, including the Yahoo! Store web-commerce site, which originally involved Paul Graham and was later rewritten in C++ and Perl. Other notable examples include:
* ACT-R, a cognitive architecture used in a large number of research projects.
* Authorizer's Assistant, a large rule-based system used by American Express, analyzing credit requests.
* Cyc, a long running project to create a knowledge-based system that provides a huge amount of common sense knowledge.
* Gensym G2, a real-time expert system and business rules engine
* Genworks GDL, based on the open-source Gendl kernel.
* The development environment for the Jak and Daxter video game series, developed by Naughty Dog.
* ITA Software's low fare search engine, used by travel websites such as Orbitz and Kayak.com and airlines such as American Airlines, Continental Airlines and US Airways.
* Mirai, a 3D graphics suite.
* Opusmodus is a music composition system based on Common Lisp, used in Computer assisted composition.
* Prototype Verification System (PVS), a mechanized environment for formal specification and verification.
* PWGL is a sophisticated visual programming environment based on Common Lisp, used in Computer assisted composition and sound synthesis.
* Piano, a complete aircraft analysis suite, written in Common Lisp, used by companies like Boeing, Airbus, and Northrop Grumman.
* Grammarly, an English-language writing-enhancement platform, has its core grammar engine written in Common Lisp.
* The Dynamic Analysis and Replanning Tool (DART), which is said to alone have paid back during the years from 1991 to 1995 for all thirty years of DARPA investments in AI research.
* NASA's Jet Propulsion Lab's "Deep Space 1", an award-winning Common Lisp program for autopiloting the Deep Space One spaceship.
* SigLab, a Common Lisp platform for signal processing used in missile defense, built by Raytheon.
* SPIKE, a scheduling system for Earth or space based observatories and satellites, notably the Hubble Space Telescope, written in Common Lisp.
* Common Lisp has been used for prototyping the garbage collector of Microsoft's .NET Common Language Runtime.
* The original version of Reddit, though the developers later switched to Python due to the lack of libraries for Common Lisp, according to an official blog post by Reddit co-founder Steve Huffman.
There also exist open-source applications written in Common Lisp, such as:
* ACL2, a full-featured automated theorem prover for an applicative variant of Common Lisp.
* Axiom, a sophisticated computer algebra system.
* Maxima, a sophisticated computer algebra system, based on Macsyma.
* OpenMusic, an object-oriented visual programming environment based on Common Lisp, used in computer assisted composition.
* Pgloader, a data loader for PostgreSQL, which was re-written from Python to Common Lisp.
* Stumpwm, a tiling, keyboard driven X11 Window Manager written entirely in Common Lisp.
See also
*Common Lisp the Language
*On Lisp
*Practical Common Lisp
References
Bibliography
A chronological list of books published (or about to be published) about Common Lisp (the language) or about programming with Common Lisp (especially AI programming).
* Guy L. Steele: Common Lisp the Language, 1st Edition, Digital Press, 1984,
* Rodney Allen Brooks: Programming in Common Lisp, John Wiley and Sons Inc, 1985,
* Richard P. Gabriel: Performance and Evaluation of Lisp Systems, The MIT Press, 1985, , [http://www.dreamsongs.com/Files/Timrep.pdf PDF]
* Robert Wilensky: Common LISPcraft, W.W. Norton & Co., 1986,
* Eugene Charniak, Christopher K. Riesbeck, Drew V. McDermott, James R. Meehan: Artificial Intelligence Programming, 2nd Edition, Lawrence Erlbaum, 1987,
* Wendy L. Milner: Common Lisp: A Tutorial, Prentice Hall, 1987,
* Deborah G. Tatar: ''A Programmer's Guide to Common Lisp, Longman Higher Education, 1987,
* Taiichi Yuasa, Masami Hagiya: Introduction to Common Lisp, Elsevier Ltd, 1987,
* Christian Queinnec, Jerome Chailloux: Lisp Evolution and Standardization, Ios Pr Inc., 1988,
* Taiichi Yuasa, Richard Weyhrauch, Yasuko Kitajima: Common Lisp Drill, Academic Press Inc, 1988,
* Wade L. Hennessey: Common Lisp, McGraw-Hill Inc., 1989,
* Tony Hasemer, John Dominque: Common Lisp Programming for Artificial Intelligence, Addison-Wesley Educational Publishers Inc, 1989,
* Sonya E. Keene: Object-Oriented Programming in Common Lisp: A Programmer's Guide to CLOS, Addison-Wesley, 1989,
* David Jay Steele: Golden Common Lisp: A Hands-On Approach, Addison Wesley, 1989,
* David S. Touretzky: Common Lisp: A Gentle Introduction to Symbolic Computation, Benjamin-Cummings, 1989, . [https://www.cs.cmu.edu/~dst/LispBook/ Web/PDF] Dover reprint (2013)
* Christopher K. Riesbeck, Roger C. Schank: Inside Case-Based Reasoning, Lawrence Erlbaum, 1989,
* Patrick Winston, Berthold Horn: Lisp, 3rd Edition, Addison-Wesley, 1989, , [http://people.csail.mit.edu/phw/Books/LISPBACK.HTML Web]
* Gerard Gazdar, Chris Mellish: Natural Language Processing in LISP: An Introduction to Computational Linguistics, Addison-Wesley Longman Publishing Co., 1990,
* Patrick R. Harrison: Common Lisp and Artificial Intelligence, Prentice Hall PTR, 1990,
* Timothy Koschmann: The Common Lisp Companion, John Wiley & Sons, 1990,
* W. Richard Stark: LISP, Lore, and Logic, Springer Verlag New York Inc., 1990, , [https://link.springer.com/book/10.1007/978-1-4613-8931-6 PDF]
* Molly M. Miller, Eric Benson: Lisp Style & Design, Digital Press, 1990,
* Guy L. Steele: Common Lisp the Language, 2nd Edition, Digital Press, 1990, , [https://www.cs.cmu.edu/Groups/AI/html/cltl/cltl2.html Web]
* Robin Jones, Clive Maynard, Ian Stewart: The Art of Lisp Programming, Springer Verlag New York Inc., 1990, , [https://link.springer.com/book/10.1007/978-1-4471-1719-3 PDF]
* Steven L. Tanimoto: The Elements of Artificial Intelligence Using Common Lisp, Computer Science Press, 1990,
* Peter Lee: Topics in Advanced Language Implementation, The MIT Press, 1991,
* John H. Riley: A Common Lisp Workbook, Prentice Hall, 1991,
* Peter Norvig: Paradigms of Artificial Intelligence Programming: Case Studies in Common Lisp, Morgan Kaufmann, 1991, , [http://norvig.com/paip.html Web]
* Gregor Kiczales, Jim des Rivieres, Daniel G. Bobrow: The Art of the Metaobject Protocol, The MIT Press, 1991,
* Jo A. Lawless, Molly M. Miller: Understanding CLOS: The Common Lisp Object System, Digital Press, 1991,
* Mark Watson: Common Lisp Modules: Artificial Intelligence in the Era of Neural Networks and Chaos Theory, Springer Verlag New York Inc., 1991, , [https://link.springer.com/book/10.1007/978-1-4612-3186-8 PDF]
* James L. Noyes: Artificial Intelligence with Common Lisp: Fundamentals of Symbolic and Numeric Processing, Jones & Bartlett Pub, 1992,
* Stuart C. Shapiro: COMMON LISP: An Interactive Approach, Computer Science Press, 1992, , [https://archive.today/19981205110924/http://www.cse.buffalo.edu/pub/WWW/faculty/shapiro/Commonlisp/ Web/PDF]
* Kenneth D. Forbus, Johan de Kleer: Building Problem Solvers, The MIT Press, 1993,
* Andreas Paepcke: Object-Oriented Programming: The CLOS Perspective, The MIT Press, 1993,
* Paul Graham: On Lisp, Prentice Hall, 1993, , [http://www.paulgraham.com/onlisp.html Web/PDF]
* Paul Graham: ANSI Common Lisp, Prentice Hall, 1995,
* Otto Mayer: Programmieren in Common Lisp, German, Spektrum Akademischer Verlag, 1995,
* Stephen Slade: Object-Oriented Common Lisp, Prentice Hall, 1997,
* Richard P. Gabriel: Patterns of Software: Tales from the Software Community, Oxford University Press, 1998, , [http://www.dreamsongs.com/Files/PatternsOfSoftware.pdf PDF]
* Taiichi Yuasa, Hiroshi G. Okuno: Advanced Lisp Technology, CRC, 2002,
* David B. Lamkins: Successful Lisp: How to Understand and Use Common Lisp, bookfix.com, 2004. , [https://web.archive.org/web/20100106112300/http://www.psg.com/~dlamkins/sl/contents.html Web]
* Peter Seibel: Practical Common Lisp, Apress, 2005. , [http://www.gigamonkeys.com/book/ Web]
* Doug Hoyte: Let Over Lambda, Lulu.com, 2008, , [http://letoverlambda.com/ Web]
* George F. Luger, William A. Stubblefield: AI Algorithms, Data Structures, and Idioms in Prolog, Lisp and Java, Addison Wesley, 2008, , [https://web.archive.org/web/20110707202029/http://wps.aw.com/wps/media/objects/5771/5909832/PDF/Luger_0136070477_1.pdf PDF]
* Conrad Barski: Land of Lisp: Learn to program in Lisp, one game at a time!, No Starch Press, 2010, , [http://www.lisperati.com/landoflisp/ Web]
* Pavel Penev: Lisp Web Tales, Leanpub, 2013, [https://leanpub.com/lispwebtales Web]
* Edmund Weitz: Common Lisp Recipes, Apress, 2015, , [http://www.apress.com/9781484211779 Web]
* Patrick M. Krusenotto: Funktionale Programmierung und Metaprogrammierung, Interaktiv in Common Lisp'', Springer Fachmedien Wiesbaden 2016, , [https://link.springer.com/book/10.1007%2F978-3-658-13744-1 Web]
External links
* [https://www.quicklisp.org/beta/ Quicklisp] - A very popular and high quality library manager for Common Lisp
* The [https://github.com/CodyReichert/awesome-cl Awesome CL] list, a curated list of Common Lisp frameworks and libraries.
* The [https://lispcookbook.github.io/cl-cookbook/ Common Lisp Cookbook], a collaborative project.
* The [http://www.cliki.net/ CLiki], a Wiki for free and open-source Common Lisp systems running on Unix-like systems.
* One of the main repositories for free Common Lisp for software is [http://www.common-lisp.net/ Common-Lisp.net] .
* [http://lisp-lang.org/ lisp-lang.org] has documentation and a showcase of success stories.
* An overview of the history of Common Lisp:
* [http://clqr.boundp.org Common Lisp Quick Reference] – a compact overview of the Common Lisp standard language.
* [http://planet.lisp.org Planet Lisp] Articles about Common Lisp.
* [http://quickdocs.org/ Quickdocs] summarizes documentation and dependency information for many Quicklisp projects.
Category:Articles with example Lisp (programming language) code
Category:Class-based programming languages
Category:Cross-platform free software
Category:Cross-platform software
Category:Dynamic programming languages
Category:Dynamically typed programming languages
Category:Extensible syntax programming languages
Category:Functional languages
Category:Lisp (programming language)
Category:Lisp programming language family
Category:Multi-paradigm programming languages
Category:Object-oriented programming languages
Category:Procedural programming languages
Category:Programming languages created in 1984
|
https://en.wikipedia.org/wiki/Common_Lisp
|
2025-04-05T18:27:42.768249
|
6069
|
Color code
|
upright|thumb|25-pair color code chart used in certain kinds of wiring
A color code is a system for encoding and representing non-color information with colors to facilitate communication. This information tends to be categorical (representing unordered/qualitative categories) though may also be sequential (representing an ordered/quantitative variable).
History
The earliest examples of color codes in use are for long-distance communication by use of flags, as in semaphore communication. The United Kingdom adopted a color code scheme for such communication wherein red signified danger and white signified safety, with other colors having similar assignments of meaning.
As chemistry and other technologies advanced, it became expedient to use coloration as a signal for telling apart things that would otherwise be confusingly similar, such as wiring in electrical and electronic devices, and pharmaceutical pills.
Encoded Variable
A color code encodes a variable, which may have different representations, where the color code type should match the variable type:
Categorical variable – the variable may represent discrete values of unordered qualitative data (e.g. blood type)
Binary variables are typically treated as a categorical variable (e.g. sex)
Quantitative variable – the variable represents ordered, quantitative data (e.g. age)
Discrete quantitative data (e.g. the 6 sides of a die: 1,2,3,4,5,6) are sometimes treated as a categorical variable, despite the ordered nature.
Types
The types of color code are:
Categorical – the colors are unordered, but are chosen to maximize saliency of the colors, by maximizing color difference between all color pair permutations.
Continuous – the colors are ordered and form a smooth color gradient.
Discrete – only a subset of a continuous color code are used (still ordered), where each is distinguishable from the others.
Categorical
When color is the only varied attribute, the color code is unidimensional. When other attributes are varied (e.g. shape, size), the code is multidimensional, where the dimensions can be independent (each encoding separate variables) or redundant (encoding the same variable). Partial redundancy sees one variable as a subset of another.
The ideal color scheme for a categorical color code depends on whether speed or accuracy is more important. Despite humans being able to distinguish 150 distinct colors along the hue dimension during comparative task, evidence supports that color schemes where colors differ only by hue (equal luminosity and colorfulness) should have a maximum of eight categories with optimized stimulus spacing along the hue dimension, Adding redundant coding of luminosity and colorfulness adds information and increases speed and accuracy of color decoding tasks. so color stimulus of at least 3 mm in diameter or thickness is recommended when the color is on paper or on a screen. Under normal conditions, colored backgrounds do not affect the interpretation of color codes, but chromatic (and/or low) illumination of surface color code can degrade performance.
Color codes are often designed without consideration for accessibility to color blind and blind people, and may even be inaccessible for those with normal color vision, since use of many colors to code many variables can lead to use of confusingly similar colors. Only 15–40% of the colorblind can correctly name surface color codes with 8–10 color categories, most of which test as mildly colorblind. This finding uses ideal illumination; when dimmer illumination is used, performance drops sharply.
In navigation:
Characteristic light
Navigation light
Sea mark
Traffic lights
Other technology:
At point of sale (especially for packaging within a huge range of products: to quickly differentiate variants, brands, categories)
Bottled gases
Fire extinguishers
Kerbside collection
Pipe marking
Queen bee birth year code
Underground utility location
Hospital emergency codes often incorporate colors (such as the widely used "Code Blue" indicating a cardiac arrest),
In military use:
Homeland Security Advisory System
Artillery shells and other munitions, which are color-coded according to their pyrotechnic contents
List of Rainbow Codes
NATO Military Symbols for Land Based Systems
Rainbow Herbicides
In social functions:
Black hat hacking, white hat, grey hat
Blue-collar worker, white-collar worker, pink-collar worker, grey-collar, green-collar worker
Handkerchief code
ISO 22324, Guidelines for color-coded alerts in public warning
Cooper's Color Code of the combat mindset
Rank in judo
Ribbon colors see: :Category:Ribbon symbolism
In religion:
Clerical vestments, frontals and altar hangings in Christian churches
See also
Color coding in data visualization
Secondary notation
References
External links
Category:Encodings
|
https://en.wikipedia.org/wiki/Color_code
|
2025-04-05T18:27:42.777740
|
6080
|
CGI
|
CGI may refer to:
Technology
Computer-generated imagery, computer-graphic effects in films, television programs, and other visual media
Computer Graphics Interface, the low-level interface between the Graphical Kernel System and hardware
Common Gateway Interface, a standard for dynamic generation of web pages by a web server
CGI.pm, a Perl module for implementing Common Gateway Interface programs
Compacted graphite iron, a type of cast iron
Corrugated galvanised iron, a type of molded sheet metal
Cell Global Identity, a standard identifier for mobile phone cells
Organizations
California Graduate Institute, an independent graduate school specializing in psychology
Catholic Guides of Ireland, a Girl Guide association
Chulabhorn Graduate Institute, a private graduate institute in Thailand
CGI Aero or RusAir, a Russian airline
CGI Inc., a multinational information technology and business process services company
Clinton Global Initiative, a forum created by former US President Bill Clinton to discuss global problems
Coast Guard Intelligence, the intelligence branch of the United States Coast Guard
Commission for the Management and Application of Geoscience Information
Compagnie Générale Immobiliere, a Moroccan real-estate development company
Consultative Group on Indonesia, a former consortium of donors to the Indonesian government
Cuerpo Guardia de Infantería, an Argentine police riot control service
General Commissariat of Information, the Comisaría General de Información is an intelligence service within the National Police Corps of Spain.
Other uses
Clinical global impression, a family of scales to assess treatment response associated with mental disorders
Cognitively Guided Instruction, an approach to mathematics teaching and learning
CpG islands, in genetics, genomic regions that contain a high frequency of CG dinucleotides
Cape Girardeau Regional Airport (IATA airport code: CGI), an airport in Missouri, US
See also
|
https://en.wikipedia.org/wiki/CGI
|
2025-04-05T18:27:42.782675
|
6082
|
Cortex
|
Cortex or cortical may refer to:
Biology
Cortex (anatomy), the outermost layer of an organ
Cerebral cortex, the outer layer of the vertebrate cerebrum, part of which is the forebrain
Motor cortex, the regions of the cerebral cortex involved in voluntary motor functions
Prefrontal cortex, the anterior part of the frontal lobes of the brain
Visual cortex, regions of the cerebral cortex involved in visual functions
Cerebellar cortex, the outer layer of the vertebrate cerebellum
Renal cortex, the outer portion of the kidney
Adrenal cortex, a portion of the adrenal gland
Cell cortex, the region of a cell directly underneath the membrane
Cortex (hair), the middle layer of a strand of hair
Cortex (botany), the outer portion of the stem or root of a plant
Entertainment
Cortex (film), a 2008 French film directed by Nicolas Boukhrief
Cortex (podcast), a 2015 podcast
Doctor Neo Cortex, a fictional character in the Crash Bandicoot video game series
Nina Cortex, the niece of Neo Cortex
Cortex (band), a French jazz funk band featuring Alain Mion
Cortex, a Swedish post-punk alternative band featuring Freddie Wadling
Other uses
Cortex (archaeology), the outer layer of rock formed on the exterior of raw materials by chemical and mechanical weathering processes
Cortex (journal), cognitive science journal published by Elsevier
Cortex, a family of the ARM architecture of CPUs
Cortex, a division of Gemini Sound Products
Cortex, a digital lending platform by Think Finance
Cortex Pharmaceuticals, a company of New Jersey, United States
Cortex Innovation Community, a district in St. Louis, Missouri, United States
See also
Cordtex, a type of detonating cord used in mining
Corex (disambiguation)
|
https://en.wikipedia.org/wiki/Cortex
|
2025-04-05T18:27:42.784955
|
6084
|
Collection
|
Collection or Collections may refer to:
Computing
Collection (abstract data type), the abstract concept of collections in computer science
Collection (linking), the act of linkage editing in computing
Garbage collection (computing), automatic memory management method
Mathematics
Set (mathematics)
Class (set theory)
Family of sets
Indexed family
Multiset
Parametric family
Albums
Collection
Collection (Soccer Mommy album), 2017
Collection (2NE1 album), 2012
Collection (Agnes album), 2013
Collection (Arvingarna album), 2002
Collection (Jason Becker album), 2008
Collection (Tracy Chapman album), 2001
Collection (The Charlatans album)
Collection (Dave Grusin album), 1989
Collection (The Jam album)
Collection (Wynonna Judd album)
Collection (Magnus Uggla album), 1985
Collection (Men Without Hats album), 1996
Collection (MFÖ album), 2003
Collection (Mike Oldfield album), 2002
Collection (Praxis album), 1998
Collection (The Rankin Family album), 1996
Collection (Lee Ritenour album), 1991
Collection (Joe Sample album), 1991
Collection (Spyro Gyra album), 1991
Collection (The Stranglers album), 1998
Collection (Suicidal Tendencies album), 1993
Collection (Thee Michelle Gun Elephant album), 2001
Collection (The Warratahs album), 2003
Collection: The Shrapnel Years (Greg Howe album), 2006
Collection: The Shrapnel Years (Tony MacAlpine album), 2006
Collection: The Shrapnel Years (Vinnie Moore album), 2006
Collection I, a 1986 compilation album of songs by the Misfits
Collection II, a 1995 companion album to the Misfits' Collection I
Collections
Collections (Alexia album)
Collections (Rick Astley album), 2006
Collections (Cypress Hill album)
Collections (Terence Trent D'Arby album), 2006
Collections (Delphic album), 2013
Collections (Amanda Marshall album), 2006
Collections (Charlie Major album), 2006
Collections (Red Norvo, Art Pepper, Joe Morello and Gerry Wiggins album), 1957
Collections (Yanni album), 2008
Collections (The Young Rascals album), 1967
Other uses
Cash collection, the function of an accounts receivable department
Collection (church), money donated by the congregation during a church service
Collection agency, agency to collect cash
Collections management (museum)
Collection (museum), objects in a particular field forms the core basis for the museum
Fonds in archives
Private collection, sometimes just called "collection"
Collection (Oxford colleges), a beginning-of-term exam or Principal's Collections
Collection (horse), a horse carrying more weight on his hindquarters than his forehand
Collection (racehorse), an Irish-bred, Hong Kong–based Thoroughbred racehorse
Collection (publishing), a gathering of books under the same title at the same publisher
Scientific collection, any systematic collection of objects for scientific study
Collection (film), a 2021 film starring Alex Petttyfer
Collection #1, a database of sets of email addresses and passwords
Collections care, to prevent or delay the deterioration of cultural heritage
Collection class, in object-oriented programming
Generated collection, a musical scale formed by repeatedly adding a constant interval around the chromatic circle
See also
A Collection (disambiguation)
Aggregate (disambiguation)
Collected (disambiguation)
Collecting
Collector (disambiguation)
|
https://en.wikipedia.org/wiki/Collection
|
2025-04-05T18:27:42.790516
|
6085
|
Cauchy sequence
|
In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given any small positive distance, all excluding a finite number of elements of the sequence are less than that given distance from each other. Cauchy sequences are named after Augustin-Louis Cauchy; they may occasionally be known as fundamental sequences.
It is not sufficient for each term to become arbitrarily close to the term. For instance, in the sequence of square roots of natural numbers:
a_n=\sqrt n,
the consecutive terms become arbitrarily close to each other – their differences
a_{n+1}-a_n \sqrt{n+1}-\sqrt{n} \frac{1}{\sqrt{n+1}+\sqrt{n}}
tend to zero as the index grows. However, with growing values of , the terms a_n become arbitrarily large. So, for any index and distance , there exists an index big enough such that a_m - a_n > d. As a result, no matter how far one goes, the remaining terms of the sequence never get close to ; hence the sequence is not Cauchy.
The utility of Cauchy sequences lies in the fact that in a complete metric space (one where all such sequences are known to converge to a limit), the criterion for convergence depends only on the terms of the sequence itself, as opposed to the definition of convergence, which uses the limit value as well as the terms. This is often exploited in algorithms, both theoretical and applied, where an iterative process can be shown relatively easily to produce a Cauchy sequence, consisting of the iterates, thus fulfilling a logical condition, such as termination.
Generalizations of Cauchy sequences in more abstract uniform spaces exist in the form of Cauchy filters and Cauchy nets.
In real numbers
A sequence
x_1, x_2, x_3, \ldots
of real numbers is called a Cauchy sequence if for every positive real number \varepsilon, there is a positive integer N such that for all natural numbers m, n > N,
|x_m - x_n|
where the vertical bars denote the absolute value. In a similar way one can define Cauchy sequences of rational or complex numbers. Cauchy formulated such a condition by requiring x_m - x_n to be infinitesimal for every pair of infinite m, n.
For any real number r, the sequence of truncated decimal expansions of r forms a Cauchy sequence. For example, when r = \pi, this sequence is (3, 3.1, 3.14, 3.141, ...). The mth and nth terms differ by at most 10^{1-m} when m \varepsilon.
Modulus of Cauchy convergence
If (x_1, x_2, x_3, ...) is a sequence in the set X, then a modulus of Cauchy convergence for the sequence is a function \alpha from the set of natural numbers to itself, such that for all natural numbers k and natural numbers m, n > \alpha(k), |x_m - x_n|
Any sequence with a modulus of Cauchy convergence is a Cauchy sequence. The existence of a modulus for a Cauchy sequence follows from the well-ordering property of the natural numbers (let \alpha(k) be the smallest possible N in the definition of Cauchy sequence, taking \varepsilon to be 1/k). The existence of a modulus also follows from the principle of countable choice. Regular Cauchy sequences are sequences with a given modulus of Cauchy convergence (usually \alpha(k) k or \alpha(k) 2^k). Any Cauchy sequence with a modulus of Cauchy convergence is equivalent to a regular Cauchy sequence; this can be proven without using any form of the axiom of choice.
Moduli of Cauchy convergence are used by constructive mathematicians who do not wish to use any form of choice. Using a modulus of Cauchy convergence can simplify both definitions and theorems in constructive analysis. Regular Cauchy sequences were used by and by in constructive mathematics textbooks.
In a metric space
Since the definition of a Cauchy sequence only involves metric concepts, it is straightforward to generalize it to any metric space X.
To do so, the absolute value \left|x_m - x_n\right| is replaced by the distance d\left(x_m, x_n\right) (where d denotes a metric) between x_m and x_n.
Formally, given a metric space (X, d), a sequence of elements of X
x_1, x_2, x_3, \ldots
is Cauchy, if for every positive real number \varepsilon > 0 there is a positive integer N such that for all positive integers m, n > N, the distance
d\left(x_m, x_n\right)
Roughly speaking, the terms of the sequence are getting closer and closer together in a way that suggests that the sequence ought to have a limit in X.
Nonetheless, such a limit does not always exist within X: the property of a space that every Cauchy sequence converges in the space is called completeness, and is detailed below.
Completeness
A metric space (X, d) in which every Cauchy sequence converges to an element of X is called complete.
Examples
The real numbers are complete under the metric induced by the usual absolute value, and one of the standard constructions of the real numbers involves Cauchy sequences of rational numbers. In this construction, each equivalence class of Cauchy sequences of rational numbers with a certain tail behavior—that is, each class of sequences that get arbitrarily close to one another— is a real number.
A rather different type of example is afforded by a metric space X which has the discrete metric (where any two distinct points are at distance 1 from each other). Any Cauchy sequence of elements of X must be constant beyond some fixed point, and converges to the eventually repeating term.
Non-example: rational numbers
The rational numbers \Q are not complete (for the usual distance):
There are sequences of rationals that converge (in \R) to irrational numbers; these are Cauchy sequences having no limit in \Q. In fact, if a real number x is irrational, then the sequence (xn), whose n-th term is the truncation to n decimal places of the decimal expansion of x, gives a Cauchy sequence of rational numbers with irrational limit x. Irrational numbers certainly exist in \R, for example:
The sequence defined by x_01, x_{n+1}\frac{x_n+2/x_n}{2} consists of rational numbers (1, 3/2, 17/12,...), which is clear from the definition; however it converges to the irrational square root of 2, see Babylonian method of computing square root.
The sequence x_n F_n / F_{n-1} of ratios of consecutive Fibonacci numbers which, if it converges at all, converges to a limit \phi satisfying \phi^2 \phi+1, and no rational number has this property. If one considers this as a sequence of real numbers, however, it converges to the real number \varphi = (1+\sqrt5)/2, the Golden ratio, which is irrational.
The values of the exponential, sine and cosine functions, exp(x), sin(x), cos(x), are known to be irrational for any rational value of x \neq 0, but each can be defined as the limit of a rational Cauchy sequence, using, for instance, the Maclaurin series.
Non-example: open interval
The open interval X (0, 2) in the set of real numbers with an ordinary distance in \R is not a complete space: there is a sequence x_n 1/n in it, which is Cauchy (for arbitrarily small distance bound d > 0 all terms x_n of n > 1/d fit in the (0, d) interval), however does not converge in X — its 'limit', number 0, does not belong to the space X .
Other properties
Every convergent sequence (with limit s, say) is a Cauchy sequence, since, given any real number \varepsilon > 0, beyond some fixed point, every term of the sequence is within distance \varepsilon/2 of s, so any two terms of the sequence are within distance \varepsilon of each other.
In any metric space, a Cauchy sequence x_n is bounded (since for some N, all terms of the sequence from the N-th onwards are within distance 1 of each other, and if M is the largest distance between x_N and any terms up to the N-th, then no term of the sequence has distance greater than M + 1 from x_N).
In any metric space, a Cauchy sequence which has a convergent subsequence with limit s is itself convergent (with the same limit), since, given any real number r > 0, beyond some fixed point in the original sequence, every term of the subsequence is within distance r/2 of s, and any two terms of the original sequence are within distance r/2 of each other, so every term of the original sequence is within distance r of s.
These last two properties, together with the Bolzano–Weierstrass theorem, yield one standard proof of the completeness of the real numbers, closely related to both the Bolzano–Weierstrass theorem and the Heine–Borel theorem. Every Cauchy sequence of real numbers is bounded, hence by Bolzano–Weierstrass has a convergent subsequence, hence is itself convergent. This proof of the completeness of the real numbers implicitly makes use of the least upper bound axiom. The alternative approach, mentioned above, of the real numbers as the completion of the rational numbers, makes the completeness of the real numbers tautological.
One of the standard illustrations of the advantage of being able to work with Cauchy sequences and make use of completeness is provided by consideration of the summation of an infinite series of real numbers
(or, more generally, of elements of any complete normed linear space, or Banach space). Such a series
\sum_{n1}^{\infty} x_n is considered to be convergent if and only if the sequence of partial sums (s_{m}) is convergent, where s_m \sum_{n=1}^{m} x_n. It is a routine matter to determine whether the sequence of partial sums is Cauchy or not, since for positive integers p > q,
s_p - s_q \sum_{nq+1}^p x_n.
If f : M \to N is a uniformly continuous map between the metric spaces M and N and (xn) is a Cauchy sequence in M, then (f(x_n)) is a Cauchy sequence in N. If (x_n) and (y_n) are two Cauchy sequences in the rational, real or complex numbers, then the sum (x_n + y_n) and the product (x_n y_n) are also Cauchy sequences.
Generalizations
In topological vector spaces
There is also a concept of Cauchy sequence for a topological vector space X: Pick a local base B for X about 0; then (x_k) is a Cauchy sequence if for each member V\in B, there is some number N such that whenever
n,m > N, x_n - x_m is an element of V. If the topology of X is compatible with a translation-invariant metric d, the two definitions agree.
In topological groups
Since the topological vector space definition of Cauchy sequence requires only that there be a continuous "subtraction" operation, it can just as well be stated in the context of a topological group: A sequence (x_k) in a topological group G is a Cauchy sequence if for every open neighbourhood U of the identity in G there exists some number N such that whenever m,n>N it follows that x_n x_m^{-1} \in U. As above, it is sufficient to check this for the neighbourhoods in any local base of the identity in G.
As in the construction of the completion of a metric space, one can furthermore define the binary relation on Cauchy sequences in G that (x_k) and (y_k) are equivalent if for every open neighbourhood U of the identity in G there exists some number N such that whenever m,n>N it follows that x_n y_m^{-1} \in U. This relation is an equivalence relation: It is reflexive since the sequences are Cauchy sequences. It is symmetric since y_n x_m^{-1} (x_m y_n^{-1})^{-1} \in U^{-1} which by continuity of the inverse is another open neighbourhood of the identity. It is transitive since x_n z_l^{-1} x_n y_m^{-1} y_m z_l^{-1} \in U' U where U' and U are open neighbourhoods of the identity such that U'U \subseteq U; such pairs exist by the continuity of the group operation.
In groups
There is also a concept of Cauchy sequence in a group G:
Let H=(H_r) be a decreasing sequence of normal subgroups of G of finite index.
Then a sequence (x_n) in G is said to be Cauchy (with respect to H) if and only if for any r there is N such that for all m, n > N, x_n x_m^{-1} \in H_r.
Technically, this is the same thing as a topological group Cauchy sequence for a particular choice of topology on G, namely that for which H is a local base.
The set C of such Cauchy sequences forms a group (for the componentwise product), and the set C_0 of null sequences (sequences such that \forall r, \exists N, \forall n > N, x_n \in H_r) is a normal subgroup of C. The factor group C/C_0 is called the completion of G with respect to H.
One can then show that this completion is isomorphic to the inverse limit of the sequence (G/H_r).
An example of this construction familiar in number theory and algebraic geometry is the construction of the p-adic completion of the integers with respect to a prime p. In this case, G is the integers under addition, and H_r is the additive subgroup consisting of integer multiples of p_r.
If H is a cofinal sequence (that is, any normal subgroup of finite index contains some H_r), then this completion is canonical in the sense that it is isomorphic to the inverse limit of (G/H)_H, where H varies over normal subgroups of finite index. For further details, see Ch. I.10 in Lang's "Algebra".
In a hyperreal continuum
A real sequence \langle u_n : n \in \N \rangle has a natural hyperreal extension, defined for hypernatural values H of the index n in addition to the usual natural n. The sequence is Cauchy if and only if for every infinite H and K, the values u_H and u_K are infinitely close, or adequal, that is,
\mathrm{st}(u_H-u_K)= 0
where "st" is the standard part function.
Cauchy completion of categories
introduced a notion of Cauchy completion of a category. Applied to \Q (the category whose objects are rational numbers, and there is a morphism from x to y'' if and only if x \leq y), this Cauchy completion yields \R\cup\left\{\infty\right\} (again interpreted as a category using its natural ordering).
See also
References
Further reading
(for uses in constructive mathematics)
External links
Category:Augustin-Louis Cauchy
Category:Metric geometry
Category:Topology
Category:Abstract algebra
Category:Sequences and series
Category:Convergence (mathematics)
|
https://en.wikipedia.org/wiki/Cauchy_sequence
|
2025-04-05T18:27:42.812287
|
6088
|
Common Era
|
Common Era (CE) and Before the Common Era (BCE) <!-- This article is about "Common Era". It is not about the abbreviation "CE". Please do not add any other association with that abbreviation as it will be deleted. --> are year notations for the Gregorian calendar (and its predecessor, the Julian calendar), the world's most widely used calendar era. Common Era and Before the Common Era are alternatives to the original Anno Domini (AD) and Before Christ (BC) notations used for the same calendar era. The two notation systems are numerically equivalent: " CE" and "AD " each describe the current year; "400 BCE" and "400 BC" are the same year.
The expression can be traced back to 1615, when it first appears in a book by Johannes Kepler as the (), They have been promoted as more sensitive to non-Christians by not referring to Jesus, the central figure of Christianity, especially via the religious terms "Christ" and ("Lord") used by the other abbreviations. ("in the year of Our Lord Jesus Christ"). Dionysius labeled the column of the table in which he introduced the new era as "Anni Domini Nostri Jesu Christi" (Of the year of our Lord Jesus Christ].}} without a year zero. In 1422, Portugal became the last Western European country to switch to the system begun by Dionysius.]]
The term "Common Era" is traced back in English to its appearance as "Vulgar Era" to distinguish years of the Anno Domini era, which was in popular use, from dates of the regnal year (the year of the reign of a sovereign) typically used in national law.
(The word 'vulgar' originally meant 'of the ordinary people', with no derogatory associations. and again, as , in 1617. A 1635 English edition of that book has the title page in English that may be the earliest-found use of Vulgar Era in English. A 1701 book edited by John Le Clerc includes the phrase "Before Christ according to the Vulgar Æra,6".
The Merriam-Webster Dictionary gives 1716 as the date of first use of the term "vulgar era" (which it defines as Christian era).
The first published use of "Christian Era" may be the Latin phrase on the title page of a 1584 theology book, . In 1649, the Latin phrase appeared in the title of an English almanac. A 1652 ephemeris may be the first instance found so far of the English use of "Christian Era".
The English phrase "Common Era" appears at least as early as 1708,
and in a 1715 book on astronomy it is used interchangeably with "Christian Era" and "Vulgar Era". A 1759 history book uses common æra in a generic sense, to refer to "the common era of the Jews". The first use of the phrase "before the common era" may be that in a 1770 work that also uses common era and vulgar era as synonyms, in a translation of a book originally written in German. The 1797 edition of the Encyclopædia Britannica uses the terms vulgar era and common era synonymously.
In 1835, in his book Living Oracles, Alexander Campbell, wrote: "The vulgar Era, or Anno Domini; the fourth year of Jesus Christ, the first of which was but eight days",
and also refers to the common era as a synonym for vulgar era with "the fact that our Lord was born on the 4th year before the vulgar era, called Anno Domini, thus making (for example) the 42d year from his birth to correspond with the 38th of the common era". The Catholic Encyclopedia (1909) in at least one article reports all three terms (Christian, Vulgar, Common Era) being commonly understood by the early 20th century.
The phrase "common era", in lower case, also appeared in the 19th century in a "generic" sense, not necessarily to refer to the Christian Era, but to any system of dates in common use throughout a civilization. Thus, "the common era of the Jews", "the common era of the Mahometans", "common era of the world", "the common era of the foundation of Rome".
When it did refer to the Christian Era, it was sometimes qualified, e.g., "common era of the Incarnation", "common era of the Nativity", or "common era of the birth of Christ".
An adapted translation of Common Era into Latin as or, with a macron, being an alternative form of ; is the usual form}} was adopted in the 20th century by some followers of Aleister Crowley, and thus the abbreviation "e.v." or "EV" may sometimes be seen as a replacement for AD.
History of the use of the CE/BCE abbreviation
Although Jews have their own Hebrew calendar, they often use the Gregorian calendar without the AD prefix. As early as 1825, the abbreviation VE (for Vulgar Era) was in use among Jews to denote years in the Western calendar. , Common Era notation has also been in use for Hebrew lessons for more than a century.
Contemporary usage
Some academics in the fields of theology, education, archaeology and history have adopted CE and BCE notation despite some disagreement. A study conducted in 2014 found that the BCE/CE notation is not growing at the expense of BC and AD notation in the scholarly literature, and that both notations are used in a relatively stable fashion.
Australia
In 2011, media reports suggested that the BC/AD notation in Australian school textbooks would be replaced by BCE/CE notation. The change drew opposition from some politicians and church leaders. Weeks after the story broke, the Australian Curriculum, Assessment and Reporting Authority denied the rumours and stated that the BC/AD notation would remain, with CE and BCE as an optional suggested learning activity.CanadaIn 2013, the Canadian Museum of Civilization (now the Canadian Museum of History) in Gatineau (opposite Ottawa), which had previously switched to BCE/CE, decided to change back to BC/AD in material intended for the public while retaining BCE/CE in academic content.NepalThe notation is in particularly common use in Nepal in order to disambiguate dates from the local calendar, Bikram or Vikram Sambat. Disambiguation is needed because the era of the local calendar is quite close to the Common Era.United KingdomIn 2002, an advisory panel for the religious education syllabus for England and Wales recommended introducing BCE/CE dates to schools, and by 2018 some local education authorities were using them. English Heritage explains its era policy thus: "It might seem strange to use a Christian calendar system when referring to British prehistory, but the BC/AD labels are widely used and understood." Some parts of the BBC use BCE/CE, but some presenters have said they will not. The style guide for The Guardian says, under the entry for CE/BCE: "some people prefer CE (common era, current era, or Christian era) and BCE (before common era, etc.) to AD and BC, which, however, remain our style".
United States
In the United States, the use of the BCE/CE notation in textbooks was reported in 2005 to be growing. and by the Norton Anthology of English Literature. Others have taken a different approach. The US-based History Channel uses BCE/CE notation in articles on non-Christian religious topics such as Jerusalem and Judaism. The 2006 style guide for the Episcopal Diocese Maryland Church News says that BCE and CE should be used.
In June 2006, in the United States, the Kentucky State School Board reversed its decision to use BCE and CE in the state's new Program of Studies, leaving education of students about these concepts a matter of local discretion.
Rationales
<!-- Please do not add personal opinions or theories in favour or against this notation, as they will be deleted. Wikipedia is an encyclopedia, not an open forum. The article may only reflect the logically argued positions of subject experts, not just anyone with an opinion. -->
Support
The use of CE in Jewish scholarship was historically motivated by the desire to avoid the implicit "Our Lord" in the abbreviation AD. Although other aspects of dating systems are based in Christian origins, AD is a direct reference to Jesus as Lord. Proponents of the Common Era notation assert that the use of BCE/CE shows sensitivity to those who use the same year numbering system as the one that originated with and is currently used by Christians, but who are not themselves Christian.
Adena K. Berkowitz, in her application to argue before the United States Supreme Court, opted to use BCE and CE because, "Given the multicultural society that we live in, the traditional Jewish designationsB.C.E. and C.E. cast a wider net of inclusion." In the World History Encyclopedia, Joshua J. Mark wrote "Non-Christian scholars, especially, embraced [CE and BCE] because they could now communicate more easily with the Christian community. Jewish, Islamic, Hindu and Buddhist scholars could retain their [own] calendar but refer to events using the Gregorian Calendar as BCE and CE without compromising their own beliefs about the divinity of Jesus of Nazareth." In History Today, Michael Ostling wrote: "BC/AD Dating: In the year of whose Lord? The continuing use of AD and BC is not only factually wrong but also offensive to many who are not Christians." Roman Catholic priest and writer on interfaith issues Raimon Panikkar argued that the BCE/CE usage is the less inclusive option since they are still using the Christian calendar numbers and forcing it on other nations. In 1993, the English-language expert Kenneth G. Wilson speculated a slippery slope scenario in his style guide that, "if we do end by casting aside the AD/BC convention, almost certainly some will argue that we ought to cast aside as well the conventional numbering system [that is, the method of numbering years] itself, given its Christian basis." including the Southern Baptist Convention. Thus, the current year is written as in both notations (or, if further clarity is needed, as CE, or as AD ), and the year that Socrates died is represented as 399 BCE (the same year that is represented by 399 BC in the BC/AD notation). The abbreviations are sometimes written with small capital letters, or with periods (e.g., "<span style"font-size:87%;">B.C.E.</span>" or "C.E."). The US-based Society of Biblical Literature style guide for academic texts on religion prefers BCE/CE to BC/AD. Similar conventions in other languages * In Germany, Jews in Berlin seem to have already been using words translating to "(before the) common era" in the 18th century, while others like Moses Mendelssohn opposed this usage as it would hinder the integration of Jews into German society. In 1938 Nazi Germany, the use of this convention was also prescribed by the National Socialist Teachers League. However, it was soon discovered that many German Jews had been using the convention ever since the 18th century, and Time magazine found it ironic to see "Aryans following Jewish example nearly 200 years later".
* In Spanish, common forms used for "BC" are and (for "", "before Christ"), with variations in punctuation and sometimes the use of () instead of . The also acknowledges the use of () and (). In scholarly writing, is the equivalent of the English "BCE", "" or "Before the Common Era".
* In Welsh, OC can be expanded to equivalents of both AD () and CE (); for dates before the Common Era, CC (traditionally, ) is used exclusively, as would abbreviate to a mild obscenity.
* In Russian since the October Revolution (1917) , lit. before our era) and lit. of our era) are used almost universally. Within Christian churches , i.e. before/after the birth of Christ, equivalent to ) remains in use.
* In Polish, "p.n.e." (, lit. before our era) and "n.e." (, lit. of our era) are commonly used in historical and scientific literature. (before Christ) and (after Christ) see sporadic usage, mostly in religious publications.
*In China, upon the foundation of the Republic of China, the Government in Nanking adopted the Republic of China calendar with 1912 designated as year 1, but used the Western calendar for international purposes. The translated term was (, "Western Era"), which is still used in Taiwan in formal documents. In 1949, the People's Republic of China adopted (, "Common Era") for both internal and external affairs in mainland China. This notation was extended to Hong Kong in 1997 and Macau in 1999 (de facto extended in 1966) through Annex III of Hong Kong Basic Law and Macau Basic Law, thus eliminating the ROC calendar in these areas. BCE is translated into Chinese as (, "Before the Common Era").
* In Czech, the "n. l." ( which translates as of our year count) and "př. n. l." or "před n. l." ( meaning before our year count) is used, always after the year number. The direct translation of AD (, abbreviated as L. P.) or BC (, abbreviated as př. Kr.) is seen as archaic.
*In Croatian the common form used for BC and AD are pr. Kr. (prije Krista, "before Christ") and p. Kr. (poslije Krista, after Christ). The abbreviations pr. n. e. (prije nove ere, before new era) and n. e. (nove ere, (of the) new era) have also recently been introduced.
* In Danish, "f.v.t." (, before our time reckoning) and "e.v.t." (, after our time reckoning) are used as BCE/CE are in English. Also commonly used are "f.Kr." (, before Christ) and "e.Kr." (, after Christ), which are both placed after the year number in contrast with BC/AD in English.
* In Macedonian, the terms "п.н.е." (пред нашата ера "before our era") and "н.е." (наша ера "our era") are used in every aspect.
* In Estonian, "e.m.a." (, before our time reckoning) and "m.a.j." (, according to our time reckoning) are used as BCE and CE, respectively. Also in use are terms "eKr" (, before Christ) and "pKr" (, after Christ). In all cases, the abbreviation is written after the year number.
* In Finnish, "eaa." (, before time reckoning) and "jaa." (, after the start of time reckoning) are used as BCE and CE, respectively. Also (decreasingly) in use are terms "eKr", (, before Christ) and "jKr". (, after Christ). In all cases, the abbreviation is written after the year number.
See also
* Astronomical year numbering
* Before Present
* Calendar
* Calendar reform
* Holocene Era
* List of calendars
Explanatory notes
References
External links
*
Category:1610s introductions
Category:1615 beginnings
Category:17th-century neologisms
Category:Calendar eras
Category:Chronology
Category:Gregorian calendar
Category:Linguistic controversies
Category:Secularism and religions
|
https://en.wikipedia.org/wiki/Common_Era
|
2025-04-05T18:27:42.843202
|
6091
|
Charles Robert Malden
|
| death_date
| birth_place = Putney, Surrey
| death_place = Brighton, East Sussex
| placeofburial | placeofburial_label
| placeofburial_coordinates <!-- -->
| nickname | birth_name
| allegiance = United Kingdom
| branch = Royal Navy
| serviceyears | rank First Lieutenant
| servicenumber | unit
| commands | battles Napoleonic Wars<br />War of 1812
| battles_label | awards
| relations | laterwork
| signature | website <!-- -->
}}
Charles Robert Malden (9 August 1797 – 23 May 1855) was a nineteenth-century British naval officer, surveyor and educator. He is the discoverer of Malden Island in the central Pacific, which is named in his honour. He also founded Windlesham House School at Brighton, England.
Biography
Malden was born in Putney, Surrey, son of Jonas Malden, a surgeon. He entered British naval service at the age of 11 on 22 June 1809. He served nine years as a volunteer 1st class, midshipman, and shipmate, including one year in the English Channel and Bay of Biscay (1809), four years at the Cape of Good Hope and in the East Indies (1809–14), two and a half years on the North American and West Indian stations (1814–16), and a year and a half in the Mediterranean (1817–18). He was present at the capture of Mauritius and Java, and at the battles of Baltimore and New Orleans.
He passed the examination in the elements of mathematics and the theory of navigation at the Royal Naval Academy on 2–4 September 1816, and became a 1st Lieutenant on 1 September 1818. In eight years of active service as an officer, he served two and a half years in a surveying ship in the Mediterranean (1818–21), one and a half years in a surveying sloop in the English Channel and off the coast of Ireland (1823–24), and one and a half years as Surveyor of the frigate during a voyage (1824–26) to and from the Hawaiian Islands (then known as the "Sandwich islands").
In Hawaii he surveyed harbours which, he noted, were "said not to exist by Captains Cook and Vancouver." On the return voyage he discovered and explored uninhabited Malden Island in the central Pacific on 30 July 1825. After his return he left active service but remained at half pay. He served for several years as hydrographer to King William IV.
He married Frances Cole, daughter of Rev. William Hodgson Cole, rector of West Clandon and Vicar of Wonersh, near Guildford, Surrey, on 8 April 1828. Malden became the father of seven sons and a daughter.
From 1830 to 1836 he took pupils for the Royal Navy at Ryde, Isle of Wight. He purchased the school of Henry Worsley at Newport, Isle of Wight, in December 1836, reopened it as a preparatory school on 20 February 1837, and moved it to Montpelier Road in Brighton in December 1837. He built the Windlesham House School at Brighton in 1844, and conducted the school until his death there in 1855. He was succeeded as headmaster by his son Henry Charles Malden.
References
Further reading
*
*
Category:1797 births
Category:1855 deaths
Category:Royal Navy officers
Category:People from Putney
Category:17th-century Royal Navy personnel
Category:Military personnel from Surrey
|
https://en.wikipedia.org/wiki/Charles_Robert_Malden
|
2025-04-05T18:27:42.846869
|
6094
|
CPD
|
CPD may refer to:
Organizations
Centre for Policy Development, an Australian think tank
Centre for Policy Dialogue, Bangladesh
Centres of Plant Diversity, an international classification initiative
Commission on Presidential Debates, an American nonprofit
Committee on the Present Danger, an American foreign policy interest group
Police
Cambridge Police Department (Massachusetts)
Camden Police Department (New Jersey), a defunct police department dissolved in 2012
Carmel Police Department (Indiana)
Charleston Police Department (West Virginia)
Chattanooga Police Department, Tennessee
Chicago Police Department, Illinois
Cincinnati Police Department, Ohio
Cleveland Police Department, Ohio
Columbus Police Department, Ohio
Town of Carmel Police Department (New York)
Science and technology
CPD (gene), a human gene encoding the protein Carboxypeptidase D
Canonical polyadic decomposition, in mathematics
Cephalopelvic disproportion, when the capacity of the pelvis is inadequate to allow the fetus to negotiate the birth canal
Chronic pulmonary disease, a pathological condition
Conditional probability distribution, a kind of distribution in statistics
Copy/Paste Detector, software to find duplicate computer code
Cyclobutane pyrimidine dimer, a common UV product
Cyclopentadiene, an organic compound
Cyproterone acetate, a progestin and antiandrogen
Other uses
Camperdown railway station, Australia
Carnet de Passages en Douane, a customs document
Collaborative product development, in business
The Constitutional Practice and Discipline of the Methodist Church of Great Britain
Construction Products Directive, a repealed EU Directive
Continuing professional development
Danio margaritatus (also known as the Celestial Pearl Danio), a fish native to Southeast Asia
Coober Pedy Airport, IATA airport code
Crush protection device (CPD), an alternative to roll bar mandatory on all new Australian ATV's
See also
Congress of People's Deputies (disambiguation)
References
|
https://en.wikipedia.org/wiki/CPD
|
2025-04-05T18:27:42.849098
|
6095
|
Chechnya
|
| coor_pinpoint | subdivision_type2 Federal district
| subdivision_name2 = North Caucasian
| subdivision_type3 = Economic region
| subdivision_name3 = North Caucasus
| leader_title Head
| leader_name Ramzan Kadyrov
| total_type = Total
| area_total_sq_mi | area_total_km2 16,171
| population_rank = 31st
| population_density_km2 | population_as_of 2021 Census
| population_total = 1,510,824
| population_footnotes
| timezone1 MSK
| blank_name = OKTMO ID
| blank_info = 26000000
| native_name = <br/>
| image_shield = Coat of arms of Chechnya.svg
| iso_code = RU-CE
| registration_plate = 95
| utc_offset = +03:00
| anthem <br/><br/>"Shatlak's Song"
| flag_size = 120px
| shield_size = 75px
| flag_link = Flag of Chechnya
| shield_link = Coat of arms of the Chechen Republic
| seat_type = Capital
| seat Grozny
| population_urban = 38.2%
| population_rural = 61.8%
| blank_name_sec1 = Official language(s)
| blank_info_sec1 Chechen
Russian
| area_footnotes | government_type Parliament of the Chechen Republic Following the First Chechen War of 1994–1996 with Russia, Chechnya gained de facto independence as the Chechen Republic of Ichkeria, although de jure it remained a part of Russia. Russian federal control was restored in the Second Chechen War of 1999–2009, with Chechen politics being dominated by the former Ichkerian mufti Akhmad Kadyrov, and later his son Ramzan Kadyrov.
The republic covers an area of , with a population of over 1.5 million residents . It is home to the indigenous Chechens, part of the Nakh peoples, and of primarily Islamic faith. Grozny is the capital and largest city.HistoryOrigin of Chechnya's population
According to Leonti Mroveli, the 11th-century Georgian chronicler, the word "Caucasus" is derived from the Nakh ancestor Kavkas.
According to George Anchabadze of Ilia State University:
American linguist Johanna Nichols "has used language to connect the modern people of the Caucasus region to the ancient farmers of the Fertile Crescent" and her research suggests that "farmers of the region were proto-Nakh-Daghestanians". Nichols stated: "The Nakh–Dagestanian languages are the closest thing we have to a direct continuation of the cultural and linguistic community that gave rise to Western civilisation."PrehistoryTraces of human settlement dating back to 40,000 BC were found near Lake Kezanoi. Cave paintings, artifacts, and other archaeological evidence indicate continuous habitation for some 8,000 years.
The Caucasian Epipaleolithic and early Caucasian Neolithic era saw the introduction of agriculture, irrigation, and the domestication of animals in the region. This period also saw the appearance of the wheel (3000 BC), horseback riding, metal works (copper, gold, silver, iron), dishes, armor, daggers, knives and arrow tips in the region. The artifacts were found near Nasare-Cort, Muzhichi, Ja-E-Bortz (alternatively known as Surkha-khi), Abbey-Gove (also known as Nazran or Nasare).
The 16th century saw the first Russian involvement in the Caucasus. In 1558, Temryuk of Kabarda sent his emissaries to Moscow requesting help from Ivan the Terrible against the Vainakh tribes. Ivan the Terrible married Temryuk's daughter Maria Temryukovna. An alliance was formed to gain the ground in the central Caucasus for the expanding Tsardom of Russia against Vainakh defenders.
In 1667 Mehk-Da Aldaman Gheza defended the borders of Chechnya from invasions of Kabardinians and Avars during the Battle of Khachara. The Chechens converted over the next few centuries to Sunni Islam, as Islam was associated with resistance to Russian encroachment.
Imperial rule
before the commander-in-chief Prince Bariatinsky on 25 August 1859; painting by Theodor Horschelt.]]
Russian Emperor Peter the Great first sought to increase Russia's political influence in the Caucasus and the Caspian Sea at the expense of Safavid Persia when he launched the Russo-Persian War of 1722–1723. Russian forces succeeded in taking much of the Caucasian territories from Persia for several years.
As the Imperial Russian Army took control of the Caspian corridor and moved into Persian-ruled Dagestan, Peter's forces ran into mountain tribes. Peter sent a cavalry force to subdue them, but the Chechens routed them. To increase its influence in the Caucasus and secure communication with Kartli and other Christian-inhabited regions of Transcaucasia, which it considered useful in its wars against Persia and the Ottoman Empire, the Russian Empire began conquering the Northern Caucasus mountains. The Russian Empire used Christianity to justify its conquests. This allowed Islam to spread widely among the Chechens, as it positioned itself as the religion of liberation from the Tsardom of Russia, which viewed Nakh tribes as "bandits".
After Persia was forced to cede the current territories of Dagestan, most of Azerbaijan, and Georgia to Russia following the Russo-Persian War of 1804–1813 and its resultant Treaty of Gulistan, Russia significantly widened its foothold in the Caucasus at Persia's expense. Another successful Caucasus war against Persia several years later, starting in 1826 and ending in 1828 with the Treaty of Turkmenchay, and a successful war against the Ottoman Empire in 1828–1829, enabled Russia to use a much larger portion of its army in subduing the natives of the North Caucasus.
The resistance of the Nakh tribes never ended and was a fertile ground for a new Muslim-Avar commander, Imam Shamil, who fought against the Russians from 1834 to 1859 (see Murid War). In 1859, Shamil was captured by the Russians at aul Gunib. Shamil left Baysangur of Benoa, a Chechen with one arm, one eye, and one leg, in charge of command at Gunib. Baysangur broke through the siege and continued to fight Russia for another two years until he was captured and killed by Russians. The Russian Tsar hoped that by sparing the life of Shamil, the resistance in the North Caucasus would stop, but it did not. Russia began to use a colonization tactic by destroying Nakh settlements and building Cossack defense lines in the lowlands. The Cossacks suffered defeat after defeat and were constantly attacked by mountaineers, who robbed them of food and weaponry.
The Russian Tsarist regime used a different approach at the end of the 1860s. They offered Chechens and Ingush to leave the Caucasus for the Ottoman Empire (see Muhajir (Caucasus)). It is estimated that about 80% of Chechens and Ingush left the Caucasus during the deportation. It weakened the resistance, which went from open warfare to insurgent warfare. One of the notable Chechen resistance fighters at the end of the 19th century was a Chechen abrek Zelimkhan Gushmazukaev and his comrade-in-arms Ingush abrek Sulom-Beck Sagopshinski. Together they built up small units which constantly harassed Russian military convoys, government mints, and the postal service, mainly in Ingushetia and Chechnya. Ingush aul Kek was completely burned when the Ingush refused to hand over Zelimkhan. Zelimkhan was killed at the beginning of the twentieth century. The war between Nakh tribes and Russia resurfaced during the times of the Russian Revolution, which saw the Nakh struggle against Anton Denikin and later against the Soviet Union.
On 21 December 1917, Ingushetia, Chechnya, and Dagestan declared independence from Russia and formed a single state: the United Mountain Dwellers of the North Caucasus, which was recognized by major world powers of the time. The capital of the new state was moved to Temir-Khan-Shura (today in Dagestan). Tapa Tchermoeff, a prominent Chechen statesman, was elected the first prime minister of the state. The second prime minister elected was Vassan-Girey Dzhabagiev, an Ingush statesman, who also was the author of the constitution of the republic in 1917, and in 1920 he was re-elected for the third term. In 1921 the Russians attacked and occupied the country and forcibly absorbed it into the Soviet state. The Caucasian war for independence restarted, and the government went into exile.
Soviet rule
Under the Soviet Union, Chechnya and Ingushetia were combined to form the Checheno-Ingush Autonomous Soviet Socialist Republic. In the 1930s, Chechnya was flooded with many Ukrainians fleeing a famine. As a result, many of the Ukrainians settled in Chechen-Ingush ASSR permanently and survived the famine. Although over 50,000 Chechens and over 12,000 Ingush were fighting against Nazi Germany on the front line (including Heroes of the USSR: Abukhadzhi Idrisov, Khanpasha Nuradilov, Movlid Visaitov), and although Nazi German troops advanced as far as the Ossetian ASSR city of Ordzhonikidze and the Chechen-Ingush ASSR city of Malgobek after capturing half of the Caucasus in less than a month, Chechens and Ingush were falsely accused as Nazi supporters and entire nations were deported during Operation Lentil to the Kazakh SSR (later Kazakhstan) in 1944 near the end of World War II where over 60% of Chechen and Ingush populations perished. American historian Norman Naimark writes:
The deportation was justified by the materials prepared by NKVD officer Bogdan Kobulov accusing Chechens and Ingush in a mass conspiracy preparing rebellion and providing assistance to the German forces. Many of the materials were later proven to be fabricated. Even distinguished Red Army officers who fought bravely against Germans (e.g. the commander of 255th Separate Chechen-Ingush regiment Movlid Visaitov, the first to contact American forces at Elbe river) were deported. There is a theory that the real reason why Chechens and Ingush were deported was the desire of Russia to attack Turkey, an anti-communist country, as Chechens and Ingush could impede such plans. In 2004, the European Parliament recognized the deportation of Chechens and Ingush as an act of genocide.
The territory of the Chechen-Ingush Autonomous Soviet Socialist Republic was divided between Stavropol Krai (where Grozny Okrug was formed), the Dagestan ASSR, the North Ossetian ASSR, and the Georgian SSR.
The Chechens and Ingush were allowed to return to their land after 1956 during de-Stalinisation under Nikita Khrushchev
With the impending dissolution of the Soviet Union in 1991, an independence movement, the Chechen National Congress, was formed, led by ex-Soviet Air Force general and new Chechen President Dzhokhar Dudayev. It campaigned for the recognition of Chechnya as a separate nation. This movement was opposed by Boris Yeltsin's Russian Federation, which argued that Chechnya had not been an independent entity within the Soviet Union—as the Baltic, Central Asian, and other Caucasian states such as Georgia had—but was part of the Russian Soviet Federative Socialist Republic and hence did not have a right under the Soviet constitution to secede. It also argued that other republics of Russia, such as Tatarstan, would consider seceding from the Russian Federation if Chechnya were granted that right. Finally, it argued that Chechnya was a major hub in the oil infrastructure of Russia and hence its secession would hurt the country's economy and energy access.
During the Chechen Revolution, the Soviet Chechen leader Doku Zavgayev was overthrown and Dzhokhar Dudayev seized power. On 1 November 1991, Dudaev's Chechnya issued a unilateral declaration of independence. In the ensuing decade, the territory was locked in an ongoing struggle between various factions, usually fighting unconventionally.
Chechen Wars and brief independence
The First Chechen War, during which Russian forces attempted to regain control over Chechnya, took place from 1994 to 1996. Despite overwhelming numerical superiority in troops, weaponry, and air support, the Russian forces were unable to establish effective permanent control over the mountainous area due to numerous successful full-scale battles and insurgency raids. The Budyonnovsk hospital hostage crisis in 1995 shocked the Russian public. In April 1996, the first democratically elected president of Chechnya, Dzhokhar Dudayev, was killed by Russian forces using a booby trap bomb and a missile fired from a warplane after he was located by triangulating the position of a satellite phone he was using.
The widespread demoralisation of the Russian Army in the area and a successful offensive to retake Grozny by Chechen rebel forces led by Aslan Maskhadov prompted Russian President Boris Yeltsin to declare a ceasefire in 1996, and sign a peace treaty a year later that saw a withdrawal of Russian troops.
After the war, parliamentary and presidential elections took place in January 1997 in Chechnya and brought to power new President Aslan Maskhadov, chief of staff and prime minister in the Chechen coalition government, for a five-year term. Maskhadov sought to maintain Chechen sovereignty while pressing the Russian government to help rebuild the republic, whose formal economy and infrastructure were virtually destroyed. Russia continued to send money for the rehabilitation of the republic; it also provided pensions and funds for schools and hospitals. Nearly half a million people (40% of Chechnya's prewar population) had been internally displaced and lived in refugee camps or overcrowded villages. There was an economic downturn. Two Russian brigades were permanently stationed in Chechnya. although victims were rarely killed. In 1998, 176 people were kidnapped, 90 of whom were released, according to official accounts. President Maskhadov started a major campaign against hostage-takers, and on 25 October 1998, Shadid Bargishev, Chechnya's top anti-kidnapping official, was killed in a remote-controlled car bombing. Bargishev's colleagues then insisted they would not be intimidated by the attack and would go ahead with their offensive. Political violence and religious extremism, blamed on Salafism and Wahhabism, was rife. In 1998, Grozny authorities declared a state of emergency. Tensions led to open clashes between the Chechen National Guard and Islamist militants, such as the July 1998 confrontation in Gudermes.
The War of Dagestan began on 7 August 1999, during which the Islamic International Peacekeeping Brigade (IIPB) began an unsuccessful incursion into the neighboring Russian republic of Dagestan in favor of the Shura of Dagestan, which sought independence from Russia. In September, a series of apartment bombings that killed around 300 people in several Russian cities, including Moscow, were blamed on Chechen separatists. In response to the bombings, a prolonged air campaign of retaliatory strikes against the Ichkerian regime and a ground offensive that began in October 1999 marked the beginning of the Second Chechen War. Much better organized and planned than the First Chechen War, the Russian armed forces took control of most regions. The Russian forces used brutal force, killing 60 Chechen civilians during a mop-up operation in Aldy, Chechnya on 5 February 2000. After the re-capture of Grozny in February 2000, the Ichkerian regime fell apart.
<gallery widths"200px" heights"200px">
File:Evstafiev-chechnya-prayer3.jpg|A Chechen man prays during the Battle of Grozny.
File:Djokhar Doudaïev.jpg|Dzhokhar Dudayev
File:Aslan Maskhadov.jpg|Aslan Maskhadov
File:Cadets of the Ichkeria Chechen national guard 1999.jpg|Cadets of the Ichkeria Chechen national guard, 1999.
File:Evstafiev-chechnya-palace-gunman.jpg|A Chechen fighter stands near the government palace building during a short lull in fighting in Grozny, Chechnya.
</gallery>
Post-war reconstruction and insurgency
issued in 2009 by the Russian Post dedicated to Chechnya]]
Chechen separatists continued to fight Russian troops and conduct terror attacks after the occupation of Grozny. In October 2002, 40–50 Chechen rebels seized a Moscow theater and took about 900 civilians hostage.
In response to these attacks, Russia tightened its grip on Chechnya and expanded its anti-terrorist operations throughout the region. Russia installed a pro-Russian Chechen regime. In 2003, a referendum was held on a constitution that reintegrated Chechnya within Russia but provided limited autonomy. According to the Chechen government, the referendum passed with 95.5% of the votes and almost 80% turnout. The Economist was skeptical of the results, arguing that "few outside the Kremlin regard the referendum as fair".
In September 2004, separatist rebels occupied a school in the town of Beslan, North Ossetia, demanding recognition of the independence of Chechnya and a Russian withdrawal. 1,100 people (including 777 children) were taken hostage. The attack lasted three days, resulting in the deaths of over 331 people, including 186 children. After the 2004 school siege, Russian President Vladimir Putin announced sweeping security and political reforms, sealing borders in the Caucasus region and revealing plans to give the central government more power. He also vowed to take tougher action against domestic terrorism, including preemptive strikes against Chechen separatists. Kadyrov's rule has been characterized by high-level corruption, a poor human rights record, widespread use of torture, and a growing cult of personality. Allegations of anti-gay purges in Chechnya were initially reported on 1 April 2017.
In April 2009, Russia ended its counter-terrorism operations and pulled out the bulk of its army. The insurgency in the North Caucasus continued even after this date. The Caucasus Emirate had fully adopted the tenets of a Salafi-jihadist group through its strict adherence to the Sunni Hanbali obedience to the literal interpretation of the Quran and the Sunnah.
The Chechen government has been outspoken in its support for the 2022 Russian invasion of Ukraine, where a Chechen military force, the Kadyrovtsy, which is under Kadyrov's personal command, has played a leading role, notably in the Siege of Mariupol. Meanwhile, a substantial number of Chechen separatists have allied themselves to the Ukrainian cause and are fighting a mutual Russian enemy in the Donbas.
On March 2025, Chechnya blocked Telegram app due to concerns that it could be used by "enemies".
Geography
]]
Situated in the eastern part of the North Caucasus in Eastern Europe, Chechnya is surrounded on nearly all sides by Russian Federal territory. In the west, it borders North Ossetia and Ingushetia, in the north, Stavropol Krai, in the east, Dagestan, and to the south, Georgia. Its capital is Grozny. Chechnya is well known for being mountainous, but it is in fact split between the more flat areas north of the Terek, and the highlands south of the Terek.
* Area:
* Borders:
** Internal:
*** Dagestan (NE)
*** Ingushetia (W)
*** North Ossetia–Alania (W)
*** Stavropol Krai (NW)
** Foreign:
*** Georgia (Kakheti and Mtskheta-Mtianeti) (S)
Rivers:
* Terek
* Sunzha
* Argun
Climate
Despite a relatively small territory, Chechnya is characterized by a variety of climate conditions. The average temperature in Grozny is .Cities and towns with over 20,000 people
* Grozny (capital)
* Shali
* Urus-Martan
* Gudermes
* Argun
* Kurchaloy
* Achkoy-Martan
Administrative divisions
The Chechen Republic is divided into 15 districts and three cities of republican significance.
Demographics
According to the 2021 Census, the population of the republic is 1,510,824, As of the 2021 Census, Chechens at 1,456,792 make up 96.4% of the republic's population. Other groups include Russians (18,225, or 1.2%), Kumyks (12,184, or 0.8%) and a host of other small groups, each accounting for less than 0.5% of the total population. The birth rate was 25.41 in 2004. (25.7 in Achkhoi Martan, 19.8 in Groznyy, 17.5 in Kurchaloi, 28.3 in Urus Martan and 11.1 in Vedeno).
The languages used in the Republic are Chechen and Russian. Chechen belongs to the Vaynakh or North-central Caucasian language family, which also includes Ingush and Batsb. Some scholars place it in a wider North Caucasian languages.
Life expectancy
veterans in Grozny, during celebrations on the 66th anniversary of victory in the Great Patriotic War.]]
Despite its difficult past, Chechnya has a high life expectancy, one of the highest in Russia. But the pattern of life expectancy is unusual, and in according to numerous statistics, Chechnya stands out from the overall picture. In 2020, Chechnya had the deepest fall in life expectancy, but in 2021 it had the biggest rise. Chechnya has the highest excess of life expectancy in rural areas over cities.
{|style="text-align: center;"
!
! style="width:7em;"|2019
! style="width:7em;"|2021
|-
| style="text-align: left;"|Average:
| 75.9 years
| 73.0 years
|-
| style="text-align: left;"|Male:
| 73.6 years
| 70.5 years
|-
| style="text-align: left;"|Female:
| 78.0 years
| 75.3 years
|}
<gallery mode"packed" heights"180px">
File:Life expectancy in Russian subject -Chechnya.png|Life expectancy at birth in Chechnya
File:Life expectancy in Russian subject -Chechnya -diff.png|Life expectancy with calculated differences
File:Life expectancy in Russia -Chechnya.png|Life expectancy in Chechnya in comparison with neighboring regions of the country
File:Comparison of life expectancy in Russian subjects by sex.svg|Interactive chart of comparison of male and female life expectancy for 2021. Open the [https://upload.wikimedia.org/wikipedia/commons/6/6e/Comparison_of_life_expectancy_in_Russian_subjects_by_sex.svg original svg-file] in a separate window and hover over a bubble to highlight it.
File:Comparison of life expectancy in Russian subjects by type of settlement.svg|Analogious interactive chart of comparison of urban and rural life expectancy.<br>[https://upload.wikimedia.org/wikipedia/commons/4/4b/Comparison_of_life_expectancy_in_Russian_subjects_by_type_of_settlement.svg Original interactive file].
</gallery>
Settlements
Administrative division
| city_1 = Grozny
| div_1 = GroznyCity of republic significance of Grozny
| pop_1 = 328,533
| img_1 = Мечеть "Сердце Чечни".jpg
| city_2 = Gudermes
| div_2 = Gudermessky District
| pop_2 = 64,376
| img_2 = Gudermes City4.jpg
| city_3 = Urus-Martan
| div_3 = Urus-Martanovsky District
| pop_3 = 63,449
| img_3 = Хьалха-Марта къилба агlор.png
| city_4 = Shali, Chechen RepublicShali
| div_4 = Shalinsky District, Chechen RepublicShalinsky District
| pop_4 = 55,054
| img_4 = Pride of Muslims mosque Shali.jpg
| city_5 = Argun, Chechen RepublicArgun
| div_5 = Argun, Chechen RepublicTown of republic significance of Argun
| pop_5 = 41,622
| city_6 = Achkhoy-Martan
| div_6 = Achkhoy-Martanovsky District
| pop_6 = 30,739
| city_7 = Kurchaloy
| div_7 = Kurchaloyevsky District
| pop_7 = 23,425
| city_8 = Oyskhara
| div_8 = Gudermessky District
| pop_8 = 19,415
| city_9 = Goyty
| div_9 = Urus-Martanovsky District
| pop_9 = 19,198
| city_10 = Avtury
| div_10 = Shalinsky District, Chechnya
| pop_10 = 18,446
}}
Vital statistics
]]
{| class"wikitable" style"text-align: right;"
|-
!
! style="width:70pt;" | Average population (x 1000)
! style="width:70pt;" | Live births
! style="width:70pt;" | Deaths
! style="width:70pt;" | Natural change
! style="width:70pt;" | Crude birth rate (per 1000)
! style="width:70pt;" | Crude death rate (per 1000)
! style="width:70pt;" | Natural change (per 1000)
! style="width:70pt;" | Total fertility rate
|-
| 2003
| 1,117
| 27,774 || 7,194 || 20 580
| 24.9 || 6.4 || 18.4
|-
| 2004
| 1,133
| 28,496 || 6,347 || 22,149
| 25.2 || 5.6 || 19.5
|-
| 2005
| 1,150
| 28,652 || 5,857 || 22,795
| 24.9 || 5.1 || 19.8
|-
| 2006
| 1,167
| 27,989 || 5,889 || 22,100
| 24.0 || 5.0 || 18.9
|-
| 2007
| 1,187
| 32,449 || 5,630 || 26,819
| 27.3 || 4.7 || 22.6 || 3.18
|-
| 2008
| 1,210
| 35,897 || 5,447 || 30,450
| 29.7 || 4.5 || 25.2 || 3.44
|-
| 2009
| 1,235
| 36,523 || 6,620 || 29,903
| 29.6 || 5.4 || 24.2 || 3.41
|-
| 2010
| 1,260
| 37,753 || 7,042 || 30,711
| 30.0 || 5.6 || 24.4 || 3.45
|-
| 2011
| 1,289
| 37,335 || 6,810 || 30,525
| 28.9 || 5.3 || 23.6 || 3.36
|-
| 2012
| 1,314
| 34,385 || 7,192 || 27,193
| 26.2 || 5.5 || 20.7 || 3.08
|-
| 2013
| 1,336
| 32,963 || 6,581 || 26,382
| 24.7 || 4.9 || 19.8 || 2.93
|-
| 2014
| 1,358
| 32,949 || 6,864 || 26,085
| 24.3 || 5.1 || 19.2 || 2.91
|-
| 2015
| 1,383
| 32,057 || 6,728 || 25,329
| 23.2 || 4.9 || 18.3 || 2.80
|-
| 2016
| 1,404
| 29,893 || 6,630 || 23,263
| 21.3 || 4.7 || 16.6 || 2.62
|-
| 2017
| 1,425
| 29,890 || 6,586 || 23,304
| 21.0 || 4.6 || 16.4 || 2.73
|-
| 2018
| 1,444
| 29,883 || 6,430 || 23,453
| 20.6 || 4.4 || 16.2 || 2.60
|-
| 2019
| 1,467
| 28,145 || 6,357 || 21,788
| 19.2 || 4.3 || 14.9 || 2.58
|-
| 2020
| 1,488
| 30,111 || 9,188 || 20,923
| 20.2 || 6.2 || 14.0 || 2.57
|-
| 2021
| 1,509
| 30,345 || 8,904 || 21,441
| 20.1 || 5.9 || 14.2 || 2.50
|-
| 2022
|
| 30,821 || 7,370 || 23,451
| 20.2 || 4.8 || 15.4 || 2.74
|-
| 2023
|
| 30,418 || 6,583 || 23,835
| 19.7 || 4.3 || 15.4 || 2.66
|-
| 2024
|
| 31,293 || 7,228 || 24,065
| 20.0 || 4.6 || 15.4 || 2.71
|-
| colspan"9" style"text-align: center;" | Source:
|}
Ethnic groups
(In the territory of modern Chechnya)
{| class"wikitable" style"text-align: right;"
|- style="background:#e0e0e0;"
! rowspan="2" | Ethnic<br />group
! colspan="2" | 1926 Census
! colspan="2" | 1939 Census<sup>2</sup>
! colspan="2" | 1959 Census<sup>2</sup>
! colspan="2" | 1970 Census
! colspan="2" | 1979 Census
! colspan="2" | 1989 Census
! colspan="2" | 2002 Census
! colspan="2" | 2010 Census
! colspan="2" | 2021 Census<sup>1</sup>
|- style="background:#e0e0e0;"
! Number
!%
! Number
!%
! Number
!%
! Number
!%
! Number
!%
! Number
!%
! Number
!%
! Number
!%
! Number
!%
|-
| style="text-align:left;" | Chechens
| 293,298
| 67.3%
| 360,889
| 58.0%
| 238,331
| 39.7%
| 499,962
| 54.7%
| 602,223
| 60.1%
| 715,306
| 66.0%
| 1,031,647
| 93.5%
| 1,206,551
| 95.3%
| 1,456,792
| 96.4%
|-
| style="text-align:left;" | Russians
| 103,271
| 23.5%
| 213,354
| 34.3%
| 296,794
| 49.4%
| 327,701
| 35.8%
| 307,079
| 30.6%
| 269,130
| 24.8%
| 40,645
| 3.7%
| 24,382
| 1.9%
| 18,225
| 1.2%
|-
| style="text-align:left;" | Kumyks
| 2,217
| 0.5%
| 3,575
| 0.6%
|
|
| 6,865
| 0.8%
| 7,808
| 0.8%
| 9,591
| 0.9%
| 8,883
| 0.8%
| 12,221
| 1.0%
| 12,184
| 0.8%
|-
| style="text-align:left;" | Avars
| 830
| 0.2%
| 2,906
| 0.5%
|
|
| 4,196
| 0.5%
| 4,793
| 0.5%
| 6,035
| 0.6%
| 4,133
| 0.4%
| 4,864
| 0.4%
| 4,079
| 0.3%
|-
| style="text-align:left;" | Nogais
| 162
| 0.0%
| 1,302
| 0.2%
|
|
| 5,503
| 0.6%
| 6,079
| 0.6%
| 6,885
| 0.6%
| 3,572
| 0.3%
| 3,444
| 0.3%
| 2,819
| 0.2%
|-
| style="text-align:left;" | Ingush
| 798
| 0.2%
| 4,338
| 0.7%
| 3,639
| 0.6%
| 14,543
| 1.6%
| 20,855
| 2.1%
| 25,136
| 2.3%
| 2,914
| 0.3%
| 1,296
| 0.1%
| 1,100
| 0.1%
|-
| style="text-align:left;" | Ukrainians
| 11,474
| 2.6%
| 8,614
| 1.4%
| 11,947
| 2.0%
| 11,608
| 1.3%
| 11,334
| 1.1%
| 11,884
| 1.1%
| 829
| 0.1%
| rowspan="3" | 13,716
| rowspan="3" | 1.1%
| rowspan="3" | 15,625
| rowspan="3" | 1.0%
|-
| align="left" | Armenians
| 5,978
| 1.4%
| 8,396
| 1.3%
| 12,136
| 2.0%
| 13,948
| 1.5%
| 14,438
| 1.4%
| 14,666
| 1.4%
| 424
| 0.0%
|-
| style="text-align:left;" | Others
| 18,840
| 4.13%
| 18,646
| 3.0%
| 37,550
| 6.3%
| 30,057
| 3.3%
| 27,621
| 2.8%
| 25,800
| 2.4%
| 10,639
| 1.0%
|-
| colspan"19" style"text-align:left;" | <sup>1</sup> <small>2,515 people were registered from administrative databases, and could not declare an ethnicity. It is estimated that the proportion of ethnicities in this group is the same as that of the declared group.</small>
<sup>2</sup> <small>Practically all Chechen and Ingush people were deported to Central Asia in 1944. They were, however, allowed to return to the Northern Caucasus in 1957 by Nikita Khrushchev. See Deportation of the Chechens and Ingush.</small>
|}
Religion
Islam
in Grozny, 2013]]
Salah Mezhiev (right) with Ramzan Kadyrov (left) and Russian President Vladimir Putin (center) at the Prophet Isa Mosque in Grozny, 20 August 2024]]
Sunni Islam is the predominant religion in Chechnya, practiced by 95% of those polled in Grozny in 2010. Most of the population is Sunni and follows either the Shafi'i or the Hanafi schools of Islamic jurisprudence. The Shafi'i school of jurisprudence has a long tradition among the Chechens, and thus it remains the most practiced. Many Chechens are also Sufis, of either the Qadiri or Naqshbandi orders. A supreme Islamic administrative territorial organisation in Chechnya is the Spiritual Administration of the Muslims of the Chechen Republic or the Muftiate of the Chechen Republic. As of 2020, there are eight Eastern Orthodox churches in Chechnya, the largest is the temple of the Archangel Michael in Grozny.
Politics
Since 1990, the Chechen Republic has had many legal, military, and civil conflicts involving separatist movements and pro-Russian authorities. Chechnya has enjoyed a period of relative stability under the Russian-appointed government, although there is still some separatist movement activity. Its regional constitution entered into effect on 2 April 2003, after an all-Chechen referendum was held on 23 March 2003. Some Chechens were controlled by regional teips, or clans, despite the existence of pro- and anti-Russian political structures.
In the 2024 Russian presidential election, which critics called rigged and fraudulent, Russian President Vladimir Putin won 98.99% of the vote in Chechnya.Regional government
, former separatist and head of the Chechen Republic, with Russian President Vladimir Putin, on 8 November 2000]]
The former separatist religious leader (mufti) Akhmad Kadyrov was elected president with 83% of the vote in an internationally monitored election on 5 October 2003. Incidents of ballot stuffing and voter intimidation by Russian soldiers and the exclusion of separatist parties from the polls were subsequently reported by Organization for Security and Co-operation in Europe (OSCE) monitors. On 9 May 2004, Kadyrov was assassinated in Grozny football stadium by a landmine explosion that was planted beneath a VIP stage and detonated during a parade, and Sergey Abramov was appointed acting prime minister after the incident. However, since 2005 Ramzan Kadyrov (son of Akhmad Kadyrov) has been the caretaker prime minister, and in 2007 was appointed as the new president. Many allege he is the wealthiest and most powerful man in the republic, with control over a large private militia (the Kadyrovites). The militia, which began as his father's security force, has been accused of killings and kidnappings by human rights organisations such as Human Rights Watch.Separatist governmentIchkeria was a member of the Unrepresented Nations and Peoples Organisation between 1991 and 2010. Former president of Georgia, Zviad Gamsakhurdia, deposed in a military coup of 1991 and a participant of the Georgian Civil War, recognized the independence of the Chechen Republic of Ichkeria in 1993. Diplomatic relations with Ichkeria were also established by the partially recognised Islamic Emirate of Afghanistan under the Taliban government on 16 January 2000. This recognition ceased with the fall of the Taliban in 2001. However, despite Taliban recognition, there were no friendly relations between the Taliban and Ichkeria—Maskhadov rejected their recognition, stating that the Taliban were illegitimate. Ichkeria also received vocal support from the Baltic countries, a group of Ukrainian nationalists, and Poland; Estonia once voted to recognize, but the act never was followed through due to pressure applied by both Russia and the EU.
, Chechen militant Islamist and a leader of the Chechen rebel movement]]
The president of this government was Aslan Maskhadov, and the foreign minister was Ilyas Akhmadov, who was the spokesman for the president. Maskhadov had been elected for four years in an internationally monitored election in 1997, which took place after signing a peace agreement with Russia. In 2001, he issued a decree prolonging his office for one additional year; he was unable to participate in the 2003 presidential election since separatist parties were barred by the Russian government, and Maskhadov faced accusations of terrorist offenses in Russia. Maskhadov left Grozny and moved to the separatist-controlled areas of the south at the onset of the Second Chechen War. Maskhadov was unable to influence a number of warlords who retain effective control over Chechen territory, and his power was diminished as a result. Russian forces killed Maskhadov on 8 March 2005, and the assassination was widely criticized since it left no legitimate Chechen separatist leader with whom to conduct peace talks. Akhmed Zakayev, deputy prime minister and a foreign minister under Maskhadov, was appointed shortly after the 1997 election and is currently living under asylum in England. He and others chose Abdul Khalim Saidullayev, a relatively unknown Islamic judge who was previously the host of an Islamic program on Chechen television, to replace Maskhadov following his death. On 17 June 2006, it was reported that Russian special forces killed Abdul Khalim Saidullayev in a raid in the Chechen town of Argun. On 10 July 2006, Shamil Basayev, a leader of the Chechen rebel movement, was killed in a truck explosion during an arms deal.
The successor of Saidullayev became Doku Umarov. On 31 October 2007, Umarov abolished the Chechen Republic of Ichkeria and its presidency and in its place proclaimed the Caucasus Emirate with himself as its Emir. This change of status has been rejected by many Chechen politicians and military leaders who continue to support the existence of the republic.
During the 2022 Russian invasion of Ukraine, the Ukrainian parliament voted to recognize the "Chechen Republic of Ichkeria as territory temporarily occupied by the Russian Federation".
Human rights
in 2018]]
Тhe Internal Displacement Monitoring Center reports that after hundreds of thousands of ethnic Russians and Chechens fled their homes following inter-ethnic and separatist conflicts in Chechnya in 1994 and 1999, more than 150,000 people still remain displaced in Russia today.
Нuman rights organizations criticized the conduct of the 2005 parliamentary elections as unfairly influenced by the central Russian government and military. In 2006, Human Rights Watch reported that pro-Russian Chechen forces under the command of Ramzan Kadyrov, as well as Russian federal police personnel, used torture to get information about separatist forces. "If you are detained in Chechnya, you face a real and immediate risk of torture. And there is little chance that your torturer will be held accountable", said Holly Cartner, Director of the Europe and Central Asia division of the Human Rights Watch.
In 2009, the U. S. government-financed American organization Freedom House included Chechnya in the "Worst of the Worst" list of most repressive societies in the world, together with Burma, North Korea, Tibet, and others. Memorial considers Chechnya under Kadyrov to be a totalitarian regime.
On February 1 2009, The New York Times released extensive evidence to support allegations of consistent torture and executions under the Kadyrov government. The accusations were sparked by the assassination in Austria of a former Chechen rebel who had gained access to Kadyrov's inner circle, 27-year-old Umar Israilov.
On July 1 2009, Amnesty International released a detailed report covering the human rights violations committed by the Russian Federation against Chechen citizens. Among the most prominent features was that those abused had no method of redress against assaults, ranging from kidnapping to torture, while those responsible were never held accountable. This led to the conclusion that Chechnya was being ruled without law, being run into further devastating destabilization.
On 10 March 2011, Human Rights Watch reported that since Chechenization, the government has pushed for enforced Islamic dress code. The president Ramzan Kadyrov is quoted as saying "I have the right to criticize my wife. She doesn't [have the right to criticize me]. With us [in Chechen society], a wife is a housewife. A woman should know her place. A woman should give her love to us [men]... She would be [man's] property. And the man is the owner. Here, if a woman does not behave properly, her husband, father, and brother are responsible. According to our tradition, if a woman fools around, her family members kill her... That's how it happens, a brother kills his sister or a husband kills his wife... As a president, I cannot allow for them to kill. So, let women not wear shorts...". He has also openly defended honor killings on several occasions.
On 9 July 2017, Russian newspaper reported that a number of people were extrajudicially executed on the night of 26 January 2017. It published a list of 27 names of the people known to be dead, but stressed that the list is "not all [of those killed]"; the newspaper asserted that 50 people may have been executed. Some of the dead were gay, but not all. The killings appeared to have been precipitated by the death of a policeman;
In December 2021, up to 50 family members of critics of the Kadyrov government were abducted in a wave of mass kidnappings beginning on 22 December. In a case-study published during the same year, Freedom House reported that Kadyrov also conducts a total transnational repression campaign against Chechen exiles outside of Russia, including assassinations of critics and digital intimidation.LGBT rights
demonstration, "Chechen mothers mourn their children", was staged on 1 May 2017 after a purge on Nevsky Prospect in Saint Petersburg, to protest the persecution of gay men in Chechnya.]]
Although homosexuality is officially legal in Chechnya per Russian law, it is de facto illegal. Chechen authorities have reportedly arrested, imprisoned and killed persons based on their perceived sexual orientation.
In 2017, it was reported by and human rights groups that Chechen authorities had set up concentration camps, one of which is in Argun, where gay men are interrogated and subjected to physical violence. On 27 June 2018, the Parliamentary Assembly of the Council of Europe noted "cases of abduction, arbitrary detention, and torture ... with the direct involvement of Chechen law enforcement officials and on the orders of top-level Chechen authorities" and expressed dismay "at the statements of Chechen and Russian public officials denying the existence of LGBTI people in the Chechen Republic". In a 2021 Council of Europe report into anti-LGBTI hate-crimes, rapporteur Foura ben Chikha described the "state-sponsored attacks carried out against LGBTI people in Chechnya in 2017" as "the single most egregious example of violence against LGBTI people in Europe that has occurred in decades".
On 11 January 2019, it was reported that another "gay purge" had begun in the country in December 2018, with several men and women being detained. The Russian LGBT Network believes that around 40 people were detained and two killed.
Economy
During the First Chechen War, the Chechen economy fell apart. In 1994, the separatists planned to introduce a new currency, but the change did not occur due to the re-taking of Chechnya by Russian troops in the Second Chechen War.
Chechnya's unemployment was 67% in 2006 and fell to 21.5% in 2014.
Total revenue of the budget of Chechnya for 2017 was 59.2 billion rubles. Of these, 48.5 billion rubles were grants from the federal budget of the Russian Federation.
In late 1970s, Chechnya produced up to 20 million tons of oil annually, production declined sharply to approximately 3 million tons in the late 1980s, and to below 2 million tons before 1994, first (1994–1996) second Russian invasion of Chechnya (1999) inflicted material damage on the oil-sector infrastructure, oil production decreased to 750,000 tons in 2001 only to increase to 2 million tons in 2006, by 2012 production was 1 million tons.
Culture
The culture of Chechnya is based on the native traditions of Chechen people. Chechen mythology along with art have helped shape the culture for over 1,000 years.
From April 2024, all music must have a tempo between 80 and 116 beats per minute, to comply with Chechen traditions. Borrowing musical culture from other peoples is not allowed.
References
Notes
Sources
*
*
*
*
Further reading
* Anderson, Scott. The Man Who Tried to Save the World.
* Babchenko, Arkady. ''One Soldier's War in Chechnya. Portobello, London
* Baiev, Khassan. The Oath: A Surgeon Under Fire.
* Bennigsen-Broxup, Marie. The North Caucasus Barrier: The Russian Advance Towards the Muslim World.
* Bird, Chris. To Catch a Tartar: Notes from the Caucasus.
* Bornstein, Yvonne and Ribowsky, Mark. Eleven Days of Hell: My True Story of Kidnapping, Terror, Torture and Historic FBI & KGB Rescue. AuthorHouse, 2004. .
* Conrad, Roy. [http://lib.ru/MEMUARY/CHECHNYA/grozny_engl.txt Roy Conrad. Grozny. A few days...]
* Dunlop, John B. Russia Confronts Chechnya: Roots of a Separatist Conflict
* Evangelista, Mathew. The Chechen Wars: Will Russia Go the Way of the Soviet Union?. .
* Gall, Charlotta & de Waal, Thomas. Chechnya: A Small Victorious War.
* Gall, Carlotta, and de Waal, Thomas Chechnya: Calamity in the Caucasus. .
* Goltz, Thomas. Chechnya Diary: A War Correspondent's Story of Surviving the War in Chechnya. M E Sharpe (2003). .
* Hasanov, Zaur. The Man of the Mountains. . Fact-based novel on growing influence of the radical Islam during 1st and 2nd Chechnya wars.
* Khan, Ali. [https://ssrn.com/abstract=940307 "The Chechen Terror: The Play within the Play"].
* Khlebnikov, Paul. Razgovor s varvarom (Interview with a barbarian). .
* Lieven, Anatol. Chechnya: Tombstone of Russian Power. .
* Mironov, Vyacheslav. Ya byl na etoy voyne [I Was in This War]. Biblion – Russkaya Kniga, 2001. Partial translation available online.
* Mironov, Vyacheslav. [http://lib.ru/MEMUARY/CHECHNYA/chechen_war.txt Vyacheslav Mironov. Assault on Grozny Downtown]
* Mironov, Vyacheslav. [https://web.archive.org/web/20160214113121/http://artofwar.ru/a/abramow_o_b/ I was in that war].
* Oliker, Olga Russia's Chechen Wars 1994–2000: Lessons from Urban Combat. . (A strategic and tactical analysis of the Chechen Wars.)
* Pelton, Robert Young. Hunter Hammer and Heaven, Journeys to Three World's Gone Mad ()
* Politkovskaya, Anna. A Small Corner of Hell: Dispatches from Chechnya
* Rasizade, Alec. Chechnya: the Achilles heel of Russia. = Contemporary Review (Oxford) in three parts: 1) [https://web.archive.org/web/20171011195748/https://www.highbeam.com/doc/1G1-133016633.html April 2005 issue, volume 286, number 1671, pages 193–197]; 2) [https://web.archive.org/web/20171011195752/https://www.highbeam.com/doc/1G1-133372881.html May 2005 issue, volume 286, number 1672, pages 277–284]; 3) [https://web.archive.org/web/20170811060052/https://www.highbeam.com/doc/1G1-134103755.html June 2005 issue, volume 286, number 1673, pages 327–332.]
* Seirstad, Asne. The Angel of Grozny.
* Wood, Tony. [https://web.archive.org/web/20110515210953/http://www.independent.co.uk/arts-entertainment/books/reviews/chechnya-the-case-for-independence-by-tony-wood-442076.html "Chechnya: The Case For Independence"]. Book review in The Independent'', 2007.
External links
* of the Republic of Chechnya
*
* (video)
* [https://purl.fdlp.gov/GPO/gpo37759 Islamist Extremism in Chechnya: A Threat to U.S. Homeland?: Joint Hearing before the Subcommittee on Europe, Eurasia, and Emerging Threats and the Subcommittee on Terrorism, Nonproliferation, and Trade of the Committee on Foreign Affairs, House of Representatives, One Hundred Thirteenth Congress, First Session, 26 April 2013]
* [https://www.politicalholidays.com/north-caucasus Chechnya Guide] ()
Category:1993 establishments in Russia
Category:Caucasus
Category:Countries and territories where Chechen is an official language
Category:North Caucasian Federal District
Category:North Caucasus
Category:Regions of Europe with multiple official languages
Category:Republics of Russia
Category:States and territories established in 1993
|
https://en.wikipedia.org/wiki/Chechnya
|
2025-04-05T18:27:42.923196
|
6097
|
Canonization
|
, who urged diligence in the process of canonization]]
Canonization is the declaration of a deceased person as an officially recognized saint, specifically, the official act of a Christian communion declaring a person worthy of public veneration and entering their name in the canon catalogue of saints, or authorized list of that communion's recognized saints.Catholic Church
in 1235. Sándor Liezen-Mayer (1863).]]
Canonization is a papal declaration that the Catholic faithful may venerate a particular deceased member of the church. Popes began making such decrees in the tenth century. Up to that point, the local bishops governed the veneration of holy men and women within their own dioceses; and there may have been, for any particular saint, no formal decree at all. In subsequent centuries, the procedures became increasingly regularized and the Popes began restricting to themselves the right to declare someone a Catholic saint. In contemporary usage, the term is understood to refer to the act by which any Christian church declares that a person who has died is a saint, upon which declaration the person is included in the list of recognized saints, called the "canon". Biblical roots In the Roman Martyrology, the following entry is given for the Penitent Thief: "At Jerusalem, the commemoration of the good Thief, who confessed Christ on the cross, and deserved to hear from Him these words: 'This day thou shalt be with Me in paradise.' Historical development
The Roman Canon, the historical Eucharistic Prayer or Anaphora of Canon of the Roman Rite contains only the names of apostles and martyrs, along with that of the Blessed Virgin Mary and, since 1962, that of Saint Joseph her spouse.
By the fourth century, however, "confessors"—people who had confessed their faith not by dying but by word and life—began to be venerated publicly. Examples of such people are Saint Hilarion and Saint Ephrem the Syrian in the East, and Saint Martin of Tours and Saint Hilary of Poitiers in the West. Their names were inserted in the diptychs, the lists of saints explicitly venerated in the liturgy, and their tombs were honoured in like manner as those of the martyrs. Since the witness of their lives was not as unequivocal as that of the martyrs, they were venerated publicly only with the approval by the local bishop. This process is often referred to as "local canonization".}}
This approval was required even for veneration of a reputed martyr. In his history of the Donatist heresy, Saint Optatus recounts that at Carthage a Catholic matron, named Lucilla, incurred the censures of the Church for having kissed the relics of a reputed martyr whose claims to martyrdom had not been juridically proved. And Saint Cyprian (died 258) recommended that the utmost diligence be observed in investigating the claims of those who were said to have died for the faith. All the circumstances accompanying the martyrdom were to be inquired into; the faith of those who suffered, and the motives that animated them were to be rigorously examined, in order to prevent the recognition of undeserving persons. Evidence was sought from the court records of the trials or from people who had been present at the trials.
Augustine of Hippo (died 430) tells of the procedure which was followed in his day for the recognition of a martyr. The bishop of the diocese in which the martyrdom took place set up a canonical process for conducting the inquiry with the utmost severity. The acts of the process were sent either to the metropolitan or primate, who carefully examined the cause, and, after consultation with the suffragan bishops, declared whether the deceased was worthy of the name of "martyr" and public veneration.
Though not "canonizations" in the narrow sense, acts of formal recognition, such as the erection of an altar over the saint's tomb or transferring the saint's relics to a church, were preceded by formal inquiries into the sanctity of the person's life and the miracles attributed to that person's intercession.
Such acts of recognition of a saint were authoritative, in the strict sense, only for the diocese or ecclesiastical province for which they were issued, but with the spread of the fame of a saint, were often accepted elsewhere also.
Nature
In the Catholic Church, both in the Latin and the constituent Eastern churches, the act of canonization is reserved to the Apostolic See and occurs at the conclusion of a long process requiring extensive proof that the candidate for canonization lived and died in such an exemplary and holy way that they are worthy to be recognized as a saint. The Church's official recognition of sanctity implies that the person is now in Heaven and that they may be publicly invoked and mentioned officially in the liturgy of the Church, including in the Litany of the Saints.
In the Catholic Church, canonization is a decree that allows universal veneration of the saint. For permission to venerate merely locally, only beatification is needed.
Procedure prior to reservation to the Apostolic See
canonizes Catherine of Siena.]]
For several centuries the bishops, or in some places only the primates and patriarchs, could grant martyrs and confessors public ecclesiastical honor; such honor, however, was always decreed only for the local territory of which the grantors had jurisdiction. Only acceptance of the cultus by the Pope made the cultus universal, because he alone can rule the universal Catholic Church. Abuses, however, crept into this discipline, due as well to indiscretions of popular fervor as to the negligence of some bishops in inquiring into the lives of those whom they permitted to be honoured as saints.
In the Medieval West, the Apostolic See was asked to intervene in the question of canonizations so as to ensure more authoritative decisions. The canonization of Saint Udalric, Bishop of Augsburg by Pope John XV in 993 was the first undoubted example of papal canonization of a saint from outside of Rome being declared worthy of liturgical veneration for the entire church.
Thereafter, recourse to the judgment of the Pope occurred more frequently. Toward the end of the 11th century, the Popes began asserting their exclusive right to authorize the veneration of a saint against the older rights of bishops to do so for their dioceses and regions. Popes therefore decreed that the virtues and miracles of persons proposed for public veneration should be examined in councils, more specifically in general councils. Pope Urban II, Pope Calixtus II, and Pope Eugene III conformed to this discipline.
Exclusive reservation to the Apostolic See
Hugh de Boves, Archbishop of Rouen, canonized Walter of Pontoise, or St. Gaultier, in 1153, the final saint in Western Europe to be canonized by an authority other than the Pope: "The last case of canonization by a metropolitan is said to have been that of St. Gaultier, or Gaucher, [A]bbot of Pontoise, by the Archbishop of Rouen. A decree of Pope Alexander III [in] 1170 gave the prerogative to the [P]ope thenceforth, so far as the Western Church was concerned." Theologians disagree as to the full import of the decretal of Pope Alexander III: either a new law was instituted, in which case the Pope then for the first time reserved the right of beatification to himself, or an existing law was confirmed.
However, the procedure initiated by the decretal of Pope Alexander III was confirmed by a bull of Pope Innocent III issued on the occasion of the canonization of Cunigunde of Luxembourg in 1200. The bull of Pope Innocent III resulted in increasingly elaborate inquiries to the Apostolic See concerning canonizations. Because the decretal of Pope Alexander III did not end all controversy and some bishops did not obey it in so far as it regarded beatification, the right of which they had certainly possessed hitherto, Pope Urban VIII issued the Apostolic letter Caelestis Hierusalem cives of 5 July 1634 that exclusively reserved to the Apostolic See both its immemorial right of canonization and that of beatification. He further regulated both of these acts by issuing his Decreta servanda in beatificatione et canonizatione Sanctorum on 12 March 1642.
Procedure from 1734 to 1738 to 1983
In his De Servorum Dei beatificatione et de Beatorum canonizatione of five volumes the eminent canonist Prospero Lambertini (1675–1758), who later became Pope Benedict XIV, elaborated on the procedural norms of Pope Urban VIII's Apostolic letter Caelestis Hierusalem cives of 1634 and Decreta servanda in beatificatione et canonizatione Sanctorum of 1642, and on the conventional practice of the time. His work published from 1734 to 1738 governed the proceedings until 1917. The article "Beatification and canonization process in 1914" describes the procedures followed until the promulgation of the Codex of 1917. The substance of De Servorum Dei beatifιcatione et de Beatorum canonizatione was incorporated into the Codex Iuris Canonici (Code of Canon Law) of 1917, which governed until the promulgation of the revised Codex Iuris Canonici in 1983 by Pope John Paul II. Prior to promulgation of the revised Codex in 1983, Pope Paul VI initiated a simplification of the procedures. Since 1983 The Apostolic constitution Divinus Perfectionis Magister of Pope John Paul II of 25 January 1983 and the norms issued by the Congregation for the Causes of Saints on 7 February 1983 to implement the constitution in dioceses, continued the simplification of the process initiated by Pope Paul VI.
Candidates for canonization undergo the following process:
The satisfaction of the applicable conditions permits beatification, which then bestows on the Venerable the title of "Blessed" (Latin: Beatus or Beata). A feast day will be designated, but its observance is ordinarily only permitted for the Blessed's home diocese, to specific locations associated with them, or to the churches or houses of the Blessed's religious order if they belonged to one. Parishes may not normally be named in honor of beati.
| Saint (Sanctus or Sancta; abbreviated "St." or "S."): To be canonized as a saint, ordinarily at least two miracles must have been performed through the intercession of the Blessed after their death, but for beati confessors, i.e., beati who were not declared martyrs, only one miracle is required, ordinarily being additional to that upon which beatification was premised. Very rarely, a Pope may waive the requirement for a second miracle after beatification if he, the Sacred College of Cardinals, and the Congregation for the Causes of Saints all agree that the Blessed lived a life of great merit proven by certain actions. This extraordinary procedure was used in Pope Francis' canonization of Pope John XXIII, who convoked the first part of the Second Vatican Council.
}}
Canonization is a statement of the Church that the person certainly enjoys the beatific vision of Heaven. The title of "Saint" (Latin: Sanctus or Sancta) is then proper, reflecting that the saint is a refulgence of the holiness (sanctitas) of God himself, which alone comes from God's gift. The saint is assigned a feast day which may be celebrated anywhere in the universal Church, although it is not necessarily added to the General Roman Calendar or local calendars as an "obligatory" feast; parish churches may be erected in their honor; and the faithful may freely celebrate and honor the saint.
Although recognition of sainthood by the Pope does not directly concern a fact of Divine revelation, nonetheless it must be "definitively held" by the faithful as infallible pursuant to, at the least, the Universal Magisterium of the Church, because it is a truth related to revelation by historical necessity.
Equipollent canonization
Popes have several times permitted to the universal Church, without executing the ordinary judicial process of canonization described above, the veneration as a saint, the "cultus" of one long venerated as such locally. This act of a Pope is denominated "equipollent" or "equivalent canonization" and "confirmation of cultus". In such cases, there is no need to have a miracle attributed to the saint to allow their canonization. United Methodist Church The General Conference of the United Methodist Church has formally declared individuals martyrs, including Dietrich Bonhoeffer (in 2008) and Martin Luther King Jr. (in 2012). Eastern Orthodox Church<!--linked from 'Glorification'-->
(1876). On 3 April 2011, Batak massacre victims were canonized as saints.]]
of the Church of Greece unanimously declared saints those Christians who had been tortured and massacred by the Turks in the Great fire of Smyrna in 1922.]]
Various terms are used for canonization by the autocephalous Eastern Orthodox Churches: канонизация ("canonization") or прославление ("glorification", in the Russian Orthodox Church), კანონიზაცია (kanonizats’ia, Georgian Orthodox Church), канонизација (Serbian Orthodox Church), canonizare (Romanian Orthodox Church), and Канонизация (Bulgarian Orthodox Church). Additional terms are used for canonization by other autocephalous Eastern Orthodox Churches: (Katharevousa: ) agiokatataxi/agiokatataxis, "ranking among saints" (Ecumenical Patriarchate of Constantinople, Church of Cyprus, Church of Greece), kanonizim (Albanian Orthodox Church), kanonizacja (Polish Orthodox Church), and kanonizace/kanonizácia (Czech and Slovak Orthodox Church).
The Orthodox Church in America, an Eastern Orthodox Church partly recognized as autocephalous, uses the term "glorification" for the official recognition of a person as a saint.
Oriental Orthodox Church
Within the Armenian Apostolic Church, part of Oriental Orthodoxy, there had been discussions since the 1980s about canonizing the victims of the Armenian genocide. On 23 April 2015, all of the victims of the genocide were canonized. See also
* List of canonizations
* List of saints
* List of early Christian saints
* Decanonization
Notes
References
*
External links
*
** |pages192–193 |noiconx |shortx}}
**
}}
Catholic Church
* [https://www.vatican.va/holy_father/john_paul_ii/apost_constitutions/documents/hf_jp-ii_apc_25011983_divinus-perfectionis-magister_en.html Divinus Perfectionis Magister] – Apostolic Constitution of Pope John Paul II (English)
* [https://www.vatican.va/roman_curia/congregations/csaints/index.htm Congregation for the Causes of Saints] – Vatican Website
* [http://friarsminor.org/xvii4-9.html Historical Sketch of Canonization] – Friarsminor.org
Category:Canon law
Category:Christian practices
Category:Christian saints
Category:Christian terminology
Category:Posthumous recognitions
|
https://en.wikipedia.org/wiki/Canonization
|
2025-04-05T18:27:42.939108
|
6099
|
Carboxylic acid
|
class=skin-invert-image|thumb|150px|Structure of a carboxylic acid
class=skin-invert-image|thumb|150px|Carboxylate anion
thumb|150px|3D structure of a carboxylic acid
In organic chemistry, a carboxylic acid is an organic acid that contains a carboxyl group () attached to an R-group. The general formula of a carboxylic acid is often written as or , sometimes as with R referring to an organyl group (e.g., alkyl, alkenyl, aryl), or hydrogen, or other groups. Carboxylic acids occur widely. Important examples include the amino acids and fatty acids. Deprotonation of a carboxylic acid gives a carboxylate anion.
Examples and nomenclature
Carboxylic acids are commonly identified by their trivial names. They often have the suffix -ic acid. IUPAC-recommended names also exist; in this system, carboxylic acids have an -oic acid suffix. For example, butyric acid () is butanoic acid by IUPAC guidelines. For nomenclature of complex molecules containing a carboxylic acid, the carboxyl can be considered position one of the parent chain even if there are other substituents, such as 3-chloropropanoic acid. Alternately, it can be named as a "carboxy" or "carboxylic acid" substituent on another parent structure, such as 2-carboxyfuran.
The carboxylate anion ( or ) of a carboxylic acid is usually named with the suffix -ate, in keeping with the general pattern of -ic acid and -ate for a conjugate acid and its conjugate base, respectively. For example, the conjugate base of acetic acid is acetate.
Carbonic acid, which occurs in bicarbonate buffer systems in nature, is not generally classed as one of the carboxylic acids, despite that it has a moiety that looks like a COOH group.
+Straight-chain, saturated carboxylic acids (alkanoic acids)CarbonatomsCommon nameIUPAC nameChemical formulaCommon location or use0 Oxygen ? OO Air1 Formic acid Methanoic acid HCOOH Insect stings2 Acetic acid Ethanoic acid Vinegar3 Propionic acid Propanoic acid Preservative for stored grains, body odour, milk, butter, cheese4 Butyric acid Butanoic acid Butter5 Valeric acid Pentanoic acid Valerian plant6 Caproic acid Hexanoic acid Goat fat7 Enanthic acid Heptanoic acid Fragrance8 Caprylic acid Octanoic acid Coconuts9 Pelargonic acid Nonanoic acid Pelargonium plant10 Capric acid Decanoic acid Coconut and Palm kernel oil11 Undecylic acid Undecanoic acid Anti-fungal agent12 Lauric acid Dodecanoic acid Coconut oil and hand wash soaps13 Tridecylic acid Tridecanoic acid Plant metabolite14 Myristic acid Tetradecanoic acid Nutmeg15 Pentadecylic acid Pentadecanoic acid Milk fat16 Palmitic acid Hexadecanoic acid Palm oil17 Margaric acid Heptadecanoic acid Pheromone in various animals18 Stearic acid Octadecanoic acid Chocolate, waxes, soaps, and oils19 Nonadecylic acid Nonadecanoic acid Fats, vegetable oils, pheromone20 Arachidic acid Icosanoic acid Peanut oil
+ Other carboxylic acids Compound class Membersunsaturated monocarboxylic acids acrylic acid (2-propenoic acid) – , used in polymer synthesis Fatty acids medium to long-chain saturated and unsaturated monocarboxylic acids, with even number of carbons; examples: docosahexaenoic acid and eicosapentaenoic acid (nutritional supplements) Amino acids the building-blocks of proteins Keto acids acids of biochemical significance that contain a ketone group; examples: acetoacetic acid and pyruvic acid Aromatic carboxylic acids containing at least one aromatic ring; examples: benzoic acid – the sodium salt of benzoic acid is used as a food preservative; salicylic acid – a beta-hydroxy type found in many skin-care products; phenyl alkanoic acids – the class of compounds where a phenyl group is attached to a carboxylic acid Dicarboxylic acids containing two carboxyl groups; examples: adipic acid the monomer used to produce nylon and aldaric acid – a family of sugar acids Tricarboxylic acids containing three carboxyl groups; examples: citric acid – found in citrus fruits and isocitric acid Alpha hydroxy acids containing a hydroxy group in the first position; examples: glyceric acid, glycolic acid and lactic acid (2-hydroxypropanoic acid) – found in sour milk, tartaric acid – found in wine Beta hydroxy acids containing a hydroxy group in the second position Omega hydroxy acids containing a hydroxy group beyond the first or second position Divinylether fatty acids containing a doubly unsaturated carbon chain attached via an ether bond to a fatty acid, found in some plants
Physical properties
Solubility
Carboxylic acids are polar. Because they are both hydrogen-bond acceptors (the carbonyl ) and hydrogen-bond donors (the hydroxyl ), they also participate in hydrogen bonding. Together, the hydroxyl and carbonyl group form the functional group carboxyl. Carboxylic acids usually exist as dimers in nonpolar media due to their tendency to "self-associate". Smaller carboxylic acids (1 to 5 carbons) are soluble in water, whereas bigger carboxylic acids have limited solubility due to the increasing hydrophobic nature of the alkyl chain. These longer chain acids tend to be soluble in less-polar solvents such as ethers and alcohols. Aqueous sodium hydroxide and carboxylic acids, even hydrophobic ones, react to yield water-soluble sodium salts. For example, enanthic acid has a low solubility in water (0.2 g/L), but its sodium salt is very soluble in water.
class=skin-invert-image|500px
Boiling points
Carboxylic acids tend to have higher boiling points than water, because of their greater surface areas and their tendency to form stabilized dimers through hydrogen bonds. For boiling to occur, either the dimer bonds must be broken or the entire dimer arrangement must be vaporized, increasing the enthalpy of vaporization requirements significantly.
classskin-invert-image|thumb|Carboxylic acid dimers|alt|none
Acidity
Carboxylic acids are Brønsted–Lowry acids because they are proton (H+) donors. They are the most common type of organic acid.
Carboxylic acids are typically weak acids, meaning that they only partially dissociate into cations and anions in neutral aqueous solution. For example, at room temperature, in a 1-molar solution of acetic acid, only 0.001% of the acid are dissociated (i.e. 10−5 moles out of 1 mol). Electron-withdrawing substituents such as trifluoromethyl () give stronger acids (the pKa of acetic acid is 4.76 whereas trifluoroacetic acid, with a trifluoromethyl substituent, has a pKa of 0.23). Electron-donating substituents give weaker acids (the pKa of formic acid is 3.75 whereas acetic acid, with a methyl substituent, has a pKa of 4.76)
Carboxylic acid pKaFormic acid () 3.75Chloroformic acid () 0.27Acetic acid () 4.76Glycine ()2.34Fluoroacetic acid () 2.586Difluoroacetic acid () 1.33Trifluoroacetic acid () 0.23Chloroacetic acid () 2.86Dichloroacetic acid () 1.29Trichloroacetic acid () 0.65Benzoic acid ()4.22-Nitrobenzoic acid (ortho-)2.16Oxalic acid () (first dissociation) 1.27Hydrogen oxalate () (second dissociation of oxalic acid)4.14
Deprotonation of carboxylic acids gives carboxylate anions; these are resonance stabilized, because the negative charge is delocalized over the two oxygen atoms, increasing the stability of the anion. Each of the carbon–oxygen bonds in the carboxylate anion has a partial double-bond character. The carbonyl carbon's partial positive charge is also weakened by the −1/2 negative charges on the 2 oxygen atoms.
Odour
Carboxylic acids often have strong sour odours. Esters of carboxylic acids tend to have fruity, pleasant odours, and many are used in perfume.
Characterization
Carboxylic acids are readily identified as such by infrared spectroscopy. They exhibit a sharp band associated with vibration of the CO carbonyl bond (νCO) between 1680 and 1725 cm−1. A characteristic νO–H band appears as a broad peak in the 2500 to 3000 cm−1 region. By 1H NMR spectrometry, the hydroxyl hydrogen appears in the 10–13 ppm region, although it is often either broadened or not observed owing to exchange with traces of water.
Occurrence and applications
Many carboxylic acids are produced industrially on a large scale. They are also frequently found in nature. Esters of fatty acids are the main components of lipids and polyamides of aminocarboxylic acids are the main components of proteins.
Carboxylic acids are used in the production of polymers, pharmaceuticals, solvents, and food additives. Industrially important carboxylic acids include acetic acid (component of vinegar, precursor to solvents and coatings), acrylic and methacrylic acids (precursors to polymers, adhesives), adipic acid (polymers), citric acid (a flavor and preservative in food and beverages), ethylenediaminetetraacetic acid (chelating agent), fatty acids (coatings), maleic acid (polymers), propionic acid (food preservative), terephthalic acid (polymers). Important carboxylate salts are soaps.
Synthesis
Industrial routes
In general, industrial routes to carboxylic acids differ from those used on a smaller scale because they require specialized equipment.
Carbonylation of alcohols as illustrated by the Cativa process for the production of acetic acid. Formic acid is prepared by a different carbonylation pathway, also starting from methanol.
Oxidation of aldehydes with air using cobalt and manganese catalysts. The required aldehydes are readily obtained from alkenes by hydroformylation.
Oxidation of hydrocarbons using air. For simple alkanes, this method is inexpensive but not selective enough to be useful. Allylic and benzylic compounds undergo more selective oxidations. Alkyl groups on a benzene ring are oxidized to the carboxylic acid, regardless of its chain length. Benzoic acid from toluene, terephthalic acid from para-xylene, and phthalic acid from ortho-xylene are illustrative large-scale conversions. Acrylic acid is generated from propene.
Oxidation of ethene using silicotungstic acid catalyst.
Base-catalyzed dehydrogenation of alcohols.
Carbonylation coupled to the addition of water. This method is effective and versatile for alkenes that generate secondary and tertiary carbocations, e.g. isobutylene to pivalic acid. In the Koch reaction, the addition of water and carbon monoxide to alkenes or alkynes is catalyzed by strong acids. Hydrocarboxylations involve the simultaneous addition of water and CO. Such reactions are sometimes called "Reppe chemistry."
Hydrolysis of triglycerides obtained from plant or animal oils. These methods of synthesizing some long-chain carboxylic acids are related to soap making.
Fermentation of ethanol. This method is used in the production of vinegar.
The Kolbe–Schmitt reaction provides a route to salicylic acid, precursor to aspirin.
Laboratory methods
Preparative methods for small scale reactions for research or for production of fine chemicals often employ expensive consumable reagents.
Oxidation of primary alcohols or aldehydes with strong oxidants such as potassium dichromate, Jones reagent, potassium permanganate, or sodium chlorite. The method is more suitable for laboratory conditions than the industrial use of air, which is "greener" because it yields less inorganic side products such as chromium or manganese oxides.
Oxidative cleavage of olefins by ozonolysis, potassium permanganate, or potassium dichromate.
Hydrolysis of nitriles, esters, or amides, usually with acid- or base-catalysis.
Carbonation of a Grignard reagent and organolithium reagents:
Halogenation followed by hydrolysis of methyl ketones in the haloform reaction
Base-catalyzed cleavage of non-enolizable ketones, especially aryl ketones:
Less-common reactions
Many reactions produce carboxylic acids but are used only in specific cases or are mainly of academic interest.
Disproportionation of an aldehyde in the Cannizzaro reaction
Rearrangement of diketones in the benzilic acid rearrangement
Involving the generation of benzoic acids are the von Richter reaction from nitrobenzenes and the Kolbe–Schmitt reaction from phenols.
Reactions
class=skin-invert-image|thumb|right|400px|Carboxylic acid organic reactions
Acid-base reactions
Carboxylic acids react with bases to form carboxylate salts, in which the hydrogen of the hydroxyl (–OH) group is replaced with a metal cation. For example, acetic acid found in vinegar reacts with sodium bicarbonate (baking soda) to form sodium acetate, carbon dioxide, and water:
Conversion to esters, amides, anhydrides
Widely practiced reactions convert carboxylic acids into esters, amides, carboxylate salts, acid chlorides, and alcohols.
Their conversion to esters is widely used, e.g. in the production of polyesters. Likewise, carboxylic acids are converted into amides, but this conversion typically does not occur by direct reaction of the carboxylic acid and the amine. Instead esters are typical precursors to amides. The conversion of amino acids into peptides is a significant biochemical process that requires ATP.
Converting a carboxylic acid to an amide is possible, but not straightforward. Instead of acting as a nucleophile, an amine will react as a base in the presence of a carboxylic acid to give the ammonium carboxylate salt. Heating the salt to above 100 °C will drive off water and lead to the formation of the amide. This method of synthesizing amides is industrially important, and has laboratory applications as well. In the presence of a strong acid catalyst, carboxylic acids can condense to form acid anhydrides. The condensation produces water, however, which can hydrolyze the anhydride back to the starting carboxylic acids. Thus, the formation of the anhydride via condensation is an equilibrium process.
Under acid-catalyzed conditions, carboxylic acids will react with alcohols to form esters via the Fischer esterification reaction, which is also an equilibrium process. Alternatively, diazomethane can be used to convert an acid to an ester. While esterification reactions with diazomethane often give quantitative yields, diazomethane is only useful for forming methyl esters.
Conversion to acyl halides
The hydroxyl group on carboxylic acids may be replaced with a chlorine atom using thionyl chloride to give acyl chlorides. In nature, carboxylic acids are converted to thioesters. Thionyl chloride can be used to convert carboxylic acids to their corresponding acyl chlorides. First, carboxylic acid 1 attacks thionyl chloride, and chloride ion leaves. The resulting oxonium ion 2 is activated towards nucleophilic attack and has a good leaving group, setting it apart from a normal carboxylic acid. In the next step, 2 is attacked by chloride ion to give tetrahedral intermediate 3, a chlorosulfite. The tetrahedral intermediate collapses with the loss of sulfur dioxide and chloride ion, giving protonated acyl chloride 4. Chloride ion can remove the proton on the carbonyl group, giving the acyl chloride 5 with a loss of HCl.
class=skin-invert-image|Mechanism for the reaction of a carboxylic acid with thionyl chloride to give an acid chloride|700px
Phosphorus(III) chloride (PCl3) and phosphorus(V) chloride (PCl5) will also convert carboxylic acids to acid chlorides, by a similar mechanism. One equivalent of PCl3 can react with three equivalents of acid, producing one equivalent of H3PO3, or phosphorus acid, in addition to the desired acid chloride. PCl5 reacts with carboxylic acids in a 1:1 ratio, and produces phosphorus(V) oxychloride (POCl3) and hydrogen chloride (HCl) as byproducts.
Reactions with carbanion equivalents
Carboxylic acids react with Grignard reagents and organolithiums to form ketones. The first equivalent of nucleophile acts as a base and deprotonates the acid. A second equivalent will attack the carbonyl group to create a geminal alkoxide dianion, which is protonated upon workup to give the hydrate of a ketone. Because most ketone hydrates are unstable relative to their corresponding ketones, the equilibrium between the two is shifted heavily in favor of the ketone. For example, the equilibrium constant for the formation of acetone hydrate from acetone is only 0.002. The carboxylic group is the most acidic in organic compounds.
Specialized reactions
As with all carbonyl compounds, the protons on the α-carbon are labile due to keto–enol tautomerization. Thus, the α-carbon is easily halogenated in the Hell–Volhard–Zelinsky halogenation.
The Schmidt reaction converts carboxylic acids to amines.
Carboxylic acids are decarboxylated in the Hunsdiecker reaction.
The Dakin–West reaction converts an amino acid to the corresponding amino ketone.
In the Barbier–Wieland degradation, a carboxylic acid on an aliphatic chain having a simple methylene bridge at the alpha position can have the chain shortened by one carbon. The inverse procedure is the Arndt–Eistert synthesis, where an acid is converted into acyl halide, which is then reacted with diazomethane to give one additional methylene in the aliphatic chain.
Many acids undergo oxidative decarboxylation. Enzymes that catalyze these reactions are known as carboxylases (EC 6.4.1) and decarboxylases (EC 4.1.1).
Carboxylic acids are reduced to aldehydes via the ester and DIBAL, via the acid chloride in the Rosenmund reduction and via the thioester in the Fukuyama reduction.
In ketonic decarboxylation carboxylic acids are converted to ketones.
Organolithium reagents (>2 equiv) react with carboxylic acids to give a dilithium 1,1-diolate, a stable tetrahedral intermediate which decomposes to give a ketone upon acidic workup.
The Kolbe electrolysis is an electrolytic, decarboxylative dimerization reaction. It gets rid of the carboxyl groups of two acid molecules, and joins the remaining fragments together.
Carboxyl radical
The carboxyl radical, •COOH, only exists briefly. The acid dissociation constant of •COOH has been measured using electron paramagnetic resonance spectroscopy. The carboxyl group tends to dimerise to form oxalic acid.
See also
Acid anhydride
Acid chloride
Amide
Amino acid
Ester
List of carboxylic acids
Dicarboxylic acid
Pseudoacid
Thiocarboxy
Carbon dioxide (CO2)
References
External links
Carboxylic acids pH and titration – freeware for calculations, data analysis, simulation, and distribution diagram generation
PHC.
Category:Functional groups
|
https://en.wikipedia.org/wiki/Carboxylic_acid
|
2025-04-05T18:27:42.990406
|
6100
|
Chernobyl
|
| settlement_type = City
| image_skyline = Administrative center, Radiation Control (11383715816).jpg
| imagesize = 250
| image_caption = Chernobyl's Old City Hall building
| image_shield = Herb Chornobyl.gif
| image_map | map_caption1 Location of Chernobyl in Ukraine
| pushpin_map = Ukraine#Ukraine Kyiv Oblast
| pushpin_label | pushpin_map_caption
| subdivision_type = Country
| subdivision_name =
| subdivision_type1 = Oblast
| subdivision_name1 = Kyiv Oblast
| subdivision_type2 = Raion
| subdivision_name2 = Chernobyl Raion <br />Ivankiv Raion <br />Vyshhorod Raion <br/>Chernobyl Exclusion Zone (de facto)
| parts_type = Control
| parts_style = para
| p1 | leader_title Administration
| leader_name = State Agency of Ukraine on the Exclusion Zone Management
| established_title = First mentioned
| established_date = 1193
| established_title1 = City status
| established_date1 = 1941
| postal_code_type = Postal code
| postal_code = 07270
| area_total_km2 = 25
| area_code = +380-4593
| coordinates
| elevation_m | website
| footnotes | official_name Chornobyl
| population_as_of = 2019
| population_total = 1,054<!-- source->ukwiki -->
| module }}
}}
Chernobyl, , ; , }} also known as Chornobyl,, }} is a partially abandoned city in the Chernobyl Exclusion Zone, situated in the Vyshhorod Raion of northern Kyiv Oblast, Ukraine. Chernobyl is about north of Kyiv, and southwest of the Belarusian city of Gomel. Before its evacuation, the city had about 14,000 residents (considerably less than neighboring Pripyat). While living anywhere within the Chernobyl Exclusion Zone is technically illegal today, authorities tolerate those who choose to live within some of the less irradiated areas, and an estimated 150 people lived in Chernobyl in 2020.
First mentioned as a ducal hunting lodge in 1193, the city has changed hands multiple times over the course of history. Jews moved into the city in the 16th century, and a now-defunct monastery was established in the area in 1626. By the end of the 18th century, Chernobyl was a major centre of Hasidic Judaism under the Twersky Dynasty, which left Chernobyl after the city was subjected to pogroms in the early 20th century. The Jewish community was later murdered during the Holocaust. Chernobyl was chosen as the site of Ukraine's first nuclear power plant in 1972, located north of the city, which opened in 1977. Chernobyl was evacuated on 5 May 1986, nine days after a catastrophic nuclear disaster at the plant, which was the largest nuclear disaster in history. Along with the residents of the nearby city of Pripyat, which was built as a home for the plant's workers, the population was relocated to the newly built city of Slavutych, and most have never returned.
, 1997]]
The city was the administrative centre of Chernobyl Raion (district) from 1923. After the disaster, in 1988, the raion was dissolved and administration was transferred to the neighbouring Ivankiv Raion. The raion was abolished on 18 July 2020 as part of the administrative reform of Ukraine, which reduced the number of raions of Kyiv Oblast to seven. The area of Ivankiv Raion was merged into Vyshhorod Raion.
Although Chernobyl is primarily a ghost town today, a small number of people still live there, in houses marked with signs that read, "Owner of this house lives here", and a small number of animals live there as well. Workers on watch and administrative personnel of the Chernobyl Exclusion Zone are also stationed in the city. The city has two general stores and a hotel.
During the Russian invasion of Ukraine, Chernobyl was temporarily captured and occupied by Russian forces between 24 February and 2 April. After its capture, it was reported that radiation levels temporarily rose, due to human activities, including earthworks, which disturbed the dust.
Name
The city's name is the same as one of the Ukrainian names for Artemisia vulgaris, mugwort or common wormwood: (or more commonly , 'common artemisia'). The name is inherited from or , a compound of + , the parts related to and , 'stalk', so named in distinction to the lighter-stemmed wormwood A. absinthium. or the use of romanized Ukrainian names for Ukrainian places generally.
History
) is the Sea of Azov, "Ponti Euxini pars" marks the Black Sea, and the Carpathians are drawn in the bottom left (southwest) corner as "Carpatus mons".]]
The Polish Geographical Dictionary of the Kingdom of Poland of 1880–1902 states that the time the city was founded is not known.
Identity of Ptolemy's "Azagarium"
Some older geographical dictionaries and descriptions of modern Eastern Europe mention "Czernobol" (Chernobyl) with reference to Ptolemy's world map (2nd century AD). Czernobol is identified as "oppidium Sarmatiae" (Lat., "a city in Sarmatia"), by the 1605 Lexicon geographicum of Filippo Ferrari and the 1677 Lexicon Universale of Johann Jakob Hofmann. According to the Dictionary of Ancient Geography of Alexander Macbean (London, 1773), Azagarium is "a town of Sarmatia Europaea, on the Borysthenes" (Dnieper), 36° East longitude and 50°40' latitude. The city is "now supposed to be Czernobol, a town of Poland, in Red Russia [<nowiki/>Red Ruthenia], in the Palatinate of Kiow [<nowiki/>Kiev Voivodeship], not far from the Borysthenes."
Whether Azagarium is indeed Czernobol is debatable. The question of Azagarium's correct location was raised in 1842 by Habsburg-Slovak historian, Pavel Jozef Šafárik, who published a book titled "Slavic Ancient History" ("Sławiańskie starożytności"), where he claimed Azagarium to be the hill of Zaguryna, which he found on an old Russian map "Bolzoj czertez" (Big drawing) near the city of Pereiaslav, now in central Ukraine.
In 2019, Ukrainian architect Boris Yerofalov-Pylypchak published a book, Roman Kyiv or Castrum Azagarium at Kyiv-Podil.
12th to 18th century
The archaeological excavations that were conducted in 2005–2008 found a cultural layer from the 10–12th centuries AD, which predates the first documentary mention of Chernobyl.
Around the 12th century Chernobyl was part of the land of Kievan Rus′. The first known mention of the settlement as Chernobyl is from an 1193 charter, which describes it as a hunting lodge of Knyaz Rurik Rostislavich. In 1362 it was a crown village of the Grand Duchy of Lithuania. Around that time the town had own castle which was ruined at least on two occasions in 1473 and 1482. Jews were brought to Chernobyl by Filon Kmita, during the Polish campaign of colonization. The first mentioning of Jewish community in Chernobyl is in the 17th century. In 1600 the first Roman Catholic church was built in the town. In 1626, during the Counter-Reformation, a Dominican church and monastery were founded by Lukasz Sapieha. A group of Old Catholics opposed the decrees of the Council of Trent. The Chernobyl residents actively supported the Khmelnytsky Uprising (1648–1657). By the end of the 18th century, the town accounted for 2,865 residents and had 642 buildings. and became part of Radomyshl county (uezd) as a supernumerary town ("zashtatny gorod").
In 1832, following the failed Polish November Uprising, the Dominican monastery was sequestrated. The church of the Old Catholics was disbanded in 1852. The Polish and German community of Chernobyl was deported to Kazakhstan in 1936, during the Frontier Clearances.
World War II and the Holocaust
During World War II, Chernobyl was occupied by the German Army from 25 August 1941 to 17 November 1943. When the Germans arrived, only 400 Jews remained in Chernobyl; they were murdered during the Holocaust.
On 15 August 1972, the Chernobyl Nuclear Power Plant (officially the Vladimir Ilyich Lenin Nuclear Power Plant) began construction about northwest of Chernobyl. The plant was built alongside Pripyat, an "atomograd" city founded on 4 February 1970 that was intended to serve the nuclear power plant. The decision to build the power plant was adopted by the Central Committee of the Communist Party of the Soviet Union and the Council of Ministers of the Soviet Union on recommendations of the State Planning Committee that the Ukrainian SSR be its location. It was the first nuclear power plant to be built in Ukraine.
Nuclear disaster of 26 April 1986
After the nuclear disaster at the Chernobyl Nuclear Power Plant; the worst nuclear disaster in history, the city of Chernobyl was evacuated on 5 May 1986. Along with the residents of the nearby city of Pripyat, built as a home for the plant's workers, the population was relocated to the newly built city of Slavutych. While Pripyat remains completely abandoned with no remaining inhabitants, Chernobyl has since hosted a small population.
Independent Ukraine (1991–present)
With the dissolution of the Soviet Union in 1991, Chernobyl remained part of Ukraine within the Chernobyl Exclusion Zone which Ukraine inherited from the Soviet Union.Russian occupation (February–April 2022)
During the Russian invasion of Ukraine, Russian forces captured the city on 24 February. Following the capture of Chernobyl, the Russian army used the city as a staging point for attacks on Kyiv. Ukrainian officials reported that the radiation levels in the city had started to rise due to recent military activity causing radioactive dust to ascend into the air. Hundreds of Russian soldiers were suffering from radiation poisoning after digging trenches in a contaminated area, and one died. On 31 March it was reported that Russian forces had left the exclusion zone. Ukrainian authorities reasserted control over the area on 2 April.
Geography
Chernobyl is located about north of Kyiv, and southwest of the Belarusian city of Gomel.
Climate
Chernobyl has a humid continental climate (Dfb) with very warm, wet summers with cool nights and long, cold, and snowy winters.
Chernobyl nuclear reactor disaster
'' Memorial Complex]]
<!------
This article describes the city of Chernobyl. Please include information on the Chernobyl accident in Chernobyl disaster.
-------->
On 26 April 1986, one of the reactors at the Chernobyl Nuclear Power Plant exploded after a scheduled test on the reactor was carried out improperly by plant operators. The resulting loss of control was due to design flaws of the RBMK reactor, which made it unstable when operated at low power, and prone to thermal runaway where increases in temperature increase reactor power output.
Chernobyl city was evacuated nine days after the disaster. The level of contamination with caesium-137 was around 555 kBq/m<sup>2</sup> (surface ground deposition in 1986).
Later analyses concluded that, even with very conservative estimates, relocation of the city (or of any area below 1500 kBq/m<sup>2</sup>) could not be justified on the grounds of radiological health.
This however does not account for the uncertainty in the first few days of the accident about further depositions and weather patterns.
Moreover, an earlier short-term evacuation could have averted more significant doses from short-lived isotope radiation (specifically iodine-131, which has a half-life of eight days).
The long-term health effects of the Chernobyl disaster are a subject of some controversy.
In 1998, average caesium-137 doses from the accident (estimated at 1–2 mSv per year) did not exceed those from other sources of exposure. Current effective caesium-137 dose rates as of 2019 are 200–250 nSv/h, or roughly 1.7–2.2 mSv per year,
which is comparable to the worldwide average background radiation from natural sources.
The base of operations for the administration and monitoring of the Chernobyl Exclusion Zone was moved from Pripyat to Chernobyl. Chernobyl currently contains offices for the State Agency of Ukraine on the Exclusion Zone Management and accommodations for visitors. Apartment blocks have been repurposed as accommodations for employees of the State Agency. The length of time that workers may spend within the Chernobyl Exclusion Zone is restricted by regulations that have been implemented to limit radiation exposure. Today, visits are allowed to Chernobyl but limited by strict rules.
In 2003, the United Nations Development Programme launched a project, called the Chernobyl Recovery and Development Programme (CRDP), for the recovery of the affected areas. The main goal of the CRDP's activities is supporting the efforts of the Government of Ukraine to mitigate the long-term social, economic, and ecological consequences of the Chernobyl disaster.
The city has become overgrown and many types of animals live there. According to census information collected over an extended period of time, it is estimated that more mammals live there now than before the disaster.
Notably, Mikhail Gorbachev, the final leader of the Soviet Union, stated in respect to the Chernobyl disaster that, "More than anything else, (Chernobyl) opened the possibility of much greater freedom of expression, to the point that the (Soviet) system as we knew it could no longer continue."
Notable people
* Aaron Twersky of Chernobyl (1784–1871), rabbi
* Aleksander Franciszek Chodkiewicz (1776–1838), Polish politician and lithographer
* Alexander Krasnoshchyokov (1880–1937), politician
* Andriy Smalko (1981–), football player
* Arnold Lakhovsky (1880–1937), artist
* Jan Mikołaj Chodkiewicz (1738–1781), Polish nobleman, father of Rozalia Lubomirska
* Ekaterina Scherbachenko (1977–), opera singer
* Grigory Irmovich Novak (1919–1980), Jewish Soviet weightlifter
* Joshua ben Aaron Zeitlin (1823–1888), scholar and philanthropist
* Markiyan Kamysh (1988–), novelist and son of a liquidator
* Rozalia Lubomirska (1768–1794), Polish noblewoman guillotined during the French Revolution
* Volodymyr Pravyk (1962–1986), firefighter and liquidator
See also
* List of Chernobyl-related articles
Notes
References
External links
* [https://web.archive.org/web/20190729030658/http://dazv.gov.ua/en State Agency of Ukraine on Exclusion Zone Management] – official information on public works, zone status, visits, etc.
* [https://web.archive.org/web/20190720225856/http://dazv.gov.ua/radiatsijnij-stan/informatsiya-pro-radiatsijnij-stan-dovkillya-zoni-vidchuzhennya.html Official radiation measurements] – State Agency of Ukraine on Exclusion Zone Management. [https://web.archive.org/web/20190719223822/http://www.srp.ecocentre.kiev.ua/MEDO-PS/index.php?langENG&online1 Online map].
* [https://web.archive.org/web/20130622165149/http://jewua.org/chernobyl/ Chernobyl] – History of Jewish Communities in Ukraine JewUa.org
* [https://web.archive.org/web/20140307123923/http://chernobylgallery.com/galleries/chernobyl/ The Chernobyl Gallery]
Category:1193 establishments in Europe
Category:12th-century establishments in Ukraine
*
Category:Cities in Kyiv Oblast
Category:Cities of district significance in Ukraine
Category:Environmental disaster ghost towns
Category:Ghost towns in the Chernobyl Exclusion Zone
Category:Holocaust locations in Ukraine
Category:Jewish Ukrainian history
Category:Historic Jewish communities in Ukraine
|
https://en.wikipedia.org/wiki/Chernobyl
|
2025-04-05T18:27:43.014952
|
6102
|
Cyan
|
| caption= Clockwise, from top left: Water Lilies by Claude Monet; American robin's eggs; surgical mask and headscarf of an Iranian woman; shallow water on a sandy beach near Barcelona; a Chinese funerary urn; the planet Uranus
|wavelength=490–520
|frequency=610–575
|symbolism=water
|source=CSS Color Module Level 4000
|cmyk=(100, 0, 0, 0)}}
Cyan () is the color between blue and green on the visible spectrum of light. It is evoked by light with a predominant wavelength between 500 and 520 nm, between the wavelengths of green and blue.
In the subtractive color system, or CMYK color model, which can be overlaid to produce all colors in paint and color printing, cyan is one of the primary colors, along with magenta and yellow. In the additive color system, or RGB color model, used to create all the colors on a computer or television display, cyan is made by mixing equal amounts of green and blue light. Cyan is the complement of red; it can be made by the removal of red from white. Mixing red light and cyan light at the right intensity will make white light. It is commonly seen on a bright, sunny day in the sky.
Shades and variations
Different shades of cyan can vary in terms of hue, chroma (also known as saturation, intensity, or colorfulness), or lightness (or value, tone, or brightness), or any combination of these characteristics. Differences in value can also be referred to as tints and shades, with a tint being a cyan mixed with white, and a shade being mixed with black.
Color nomenclature is subjective. Many shades of cyan with a bluish hue are called blue. Similarly, those with a greenish hue are referred to as green. A cyan with a dark shade is commonly known as teal. A teal blue shade leans toward the blue end of the spectrum. Variations of teal with a greener tint are commonly referred to as teal green.
Turquoise, reminiscent of the stone with the same name, is a shade in the green spectrum of cyan hues. Celeste is a lightly tinted cyan that represents the color of a clear sky. Other colors in the cyan color range are electric blue, aquamarine, and others described as blue-green.History Cyan boasts a rich and diverse history, holding cultural significance for millennia. In ancient civilizations, turquoise, valued for its aesthetic appeal, served as a highly regarded precious gem. Turquoise comes in a variety of shades from green to blue, but cyan hues are particularly prevalent. Approximately 3,700 years ago, an intricately crafted dragon-shaped treasure made from over 2,000 pieces of turquoise and jade was created. This artifact is widely recognized as the oldest Chinese dragon totem by many Chinese scholars.
Turquoise jewelry also held significant importance among the Aztecs, who often featured this precious gemstone in vibrant frescoes for both symbolic and decorative purposes. The Aztecs revered turquoise, associating its color with the heavens and sacredness. Additionally, ancient Egyptians interpreted cyan hues as representing faith and truth, while Tibetans viewed them as a symbol of infinity.
After earlier uses in various contexts, cyan hues found increased use in diverse cultures due to their appealing aesthetic qualities in religious structures and art pieces. For example, the prominent dome of the Goharshad Mosque in Iran, built in 1418, showcases this trend. Additionally, Jacopo da Pontormo's use of a teal shade for Mary's robe in the 1528 painting Carmignano Visitation demonstrates the allure for these hues.
In the 1870s, the French sculptor Frédéric Bartholdi began the construction of what would later become the Statue of Liberty. Over time, exposure to the elements caused the copper structure to develop its distinctive patina, now recognized as iconic cyan. In 1917, the color term teal was introduced to describe deeper shades of cyan.
In the late 19th century, while traditional nomenclature of red, yellow, and blue persisted, the printing industry initiated a shift towards utilizing magenta and cyan inks for red and blue hues, respectively. This transition aimed to establish a more versatile color gamut achievable with only three primary colors. In 1949, a document in the printing industry stated: “The four-color set comprises Yellow, Red (magenta), Blue (cyan), Black”. This practice of labeling magenta, yellow, and cyan as red, yellow, and blue persisted until 1961. As the hues evolved, the printing industry maintained the use of the traditional terms red, yellow, and blue. Consequently, pinpointing the exact date of origin for CMYK, in which cyan serves as a primary color, proves challenging.
In August 1991, the HP Deskwriter 500C became the first Deskwriter to offer color printing as an option. It used interchangeable black and color (cyan, magenta, and yellow) inkjet print cartridges. With the inclusion of cyan ink in printers, the term "cyan" has become widely recognized in both home and office settings. According to TUP/Technology User Profile 2020, approximately 70% of online American adults regularly use a home printer.
Etymology and terminology
Its name is derived from the Ancient Greek word kyanos (κύανος), meaning "dark blue enamel, Lapis lazuli". It was formerly known as "cyan blue" or cyan-blue, and its first recorded use as a color name in English was in 1879. Further origins of the color name can be traced back to a dye produced from the cornflower (Centaurea cyanus).
In most languages, 'cyan' is not a basic color term and it phenomenologically appears as a greenish vibrant hue of blue to most English speakers. Other English terms for this "borderline" hue region include blue green, aqua, turquoise, teal, and grue.
On the web and in printing
Web colors cyan and aqua
The web color cyan shown at right is a secondary color in the RGB color model, which uses combinations of red, green and blue light to create all the colors on computer and television displays. In X11 colors, this color is called both cyan and aqua. In the HTML color list, this same color is called aqua.
The web colors are more vivid than the cyan used in the CMYK color system, and the web colors cannot be accurately reproduced on a printed page. To reproduce the web color cyan in inks, it is necessary to add some white ink to the printer's cyan below, so when it is reproduced in printing, it is not a primary subtractive color. It is called aqua (a name in use since 1598) because it is a color commonly associated with water, such as the appearance of the water at a tropical beach.
Process cyan
|isccname=Brilliant greenish blue}}
Cyan is also one of the common inks used in four-color printing, along with magenta, yellow, and black; this set of colors is referred to as CMYK. In printing, the cyan ink is sometimes known as printer's cyan, process cyan, or process blue.
While both the additive secondary and the subtractive primary are called cyan, they can be substantially different from one another. Cyan printing ink is typically more saturated than the RGB secondary cyan, depending on what RGB color space and ink are considered. That is, process cyan is usually outside the RGB gamut, and there is no fixed conversion from CMYK primaries to RGB. Different formulations are used for printer's ink, so there can be variations in the printed color that is pure cyan ink. This is because real-world subtractive (unlike additive) color mixing does not consistently produce the same result when mixing apparently identical colors, since the specific frequencies filtered out to produce that color affect how it interacts with other colors. Phthalocyanine blue is one such commonly used pigment. A typical formulation of process cyan is shown in the color box on the right.
In science and nature
Color of water
* Pure water is nearly colorless. However, it does absorb slightly more red light than blue, giving significant volumes of water a bluish tint; increased scattering of blue light due to fine particles in the water shifts the blue color toward green, for a typically cyan net color.
Cyan and cyanide
* Cyanide derives its name from Prussian blue, a blue pigment containing the cyanide ion.
Bacteria
* Cyanobacteria (sometimes called blue-green algae) are an important link in the food chain.Astronomy* The planet Uranus is colored cyan because of the abundance of methane in its atmosphere. Methane absorbs red light and reflects the blue-green light which allows observers to see it as cyan.
Energy
* Natural gas (methane), used by many for home cooking on gas stoves, has a cyan colored flame when burned with a mixture of air.
Photography and film
* Cyanotype, or blueprint, a monochrome photographic printing process that predates the use of the word cyan as a color, yields a deep cyan-blue colored print based on the Prussian blue pigment.
* Cinecolor, a bi-pack color process, the photographer would load a standard camera with two films, one orthochromatic, dyed red, and a panchromatic strip behind it. Color light would expose the cyan record on the ortho stock, which also acted as a filter, exposing only red light to the panchromatic film stock.
Medicine
* Cyanosis is an abnormal blueness of the skin, usually a sign of poor oxygen intake; patients are typically described as being "cyanotic".
* Cyanopsia is a color vision defect where vision is tinted blue. This can be a drug-induced side effect or experienced after cataract removal.
Gallery
<gallery>
File:Green and blue make cyan.png|In the RGB color model, used to make colors on computer and TV displays, cyan is created by the combination of green and blue light.
File:RGB color wheel.svg|In the RGB and CMY(K) color wheel, cyan is midway between blue and green.
File:SubtractiveColor.svg|In the CMYK color model, used in color printing, cyan, magenta and yellow combined make black. In practice, since the inks are not perfect, some black ink is added.
File:Refill Ink Kit Color crop.jpg|Color printers today use, magenta, cyan and yellow ink to produce a wide range of colors.
File:Komplementärfarben cyan auf rot.svg|Cyan and red are complementary colors in most color spaces (mixing them in equal amounts produces an achromatic color). They have a strong contrast.
File:Wham-a different corner.jpg|Cyan is the color of shallow water over a sandy beach. The water absorbs the color red from the sunlight, leaving a greenish-blue color.
File:Samarkand05.jpg|The dome of the Tilla Kari Mosque in Samarkand, Uzbekistan (1660) is cyan. The color is widely used in architecture in Turkey and Central Asia.
File:Uranus_Voyager2_color_calibrated.png|The planet Uranus, seen from the Voyager 2 spacecraft. The cyan color comes from a combination of methane gas and atmospheric haze in the planet's atmosphere.
File:Wirbelsäulenoperation OKM.jpg|altA surgical team in Germany. It has been suggested that surgeons and nurses adopted a cyan-colored gown and operating rooms because it is complementary to the color of red blood and thus reduced glare, though the evidence for this claim is limited.|A surgical team in Germany. It has been suggested that surgeons and nurses adopted a cyan-colored gown and operating rooms because it contrasts the color of red blood, thus reducing glare, though the evidence for this claim is limited.
File:Old photo colors degredated into cyan.jpg|The pigments in color photographs may degrade at different rates, potentially resulting in a cyan tint.
</gallery>
See also
* Blue–green distinction in language
* New riddle of induction
* Shades of cyan
* Lists of colors
References
Category:Primary colors
Category:Secondary colors
Category:Optical spectrum
Category:Shades of blue
Category:Shades of green
Category:Rainbow colors
Category:Tertiary colors
|
https://en.wikipedia.org/wiki/Cyan
|
2025-04-05T18:27:43.027246
|
6105
|
Conventional insulin therapy
|
Conventional insulin therapy is a therapeutic regimen for treatment of diabetes mellitus which contrasts with the newer intensive insulin therapy.
This older method (prior to the development of home blood glucose monitoring) is still in use in a proportion of cases.
Characteristics
Conventional insulin therapy is characterized by:
Insulin injections of a mixture of regular (or rapid) and intermediate acting insulin are performed two times a day, or to improve overnight glucose, mixed in the morning to cover breakfast and lunch, but with regular (or rapid) acting insulin alone for dinner and intermediate acting insulin at bedtime (instead of being mixed in at dinner).
Meals are scheduled to match the anticipated peaks in the insulin profiles.
The target range for blood glucose levels is higher than is desired in the intensive regimen.
Frequent measurements of blood glucose levels were not used.
Effects
The down side of this method is that it is difficult to achieve as good results of glycemic control as with intensive insulin therapy. The advantage is that, for diabetics with a regular lifestyle, the regime is less intrusive than the intensive therapy.
References
Category:Insulin delivery
|
https://en.wikipedia.org/wiki/Conventional_insulin_therapy
|
2025-04-05T18:27:43.028973
|
6109
|
Cream
|
thumb|A bottle of unhomogenised milk, with the cream clearly visible, resting on top of the milk
Cream is a dairy product composed of the higher-fat layer skimmed from the top of milk before homogenization. In un-homogenized milk, the fat, which is less dense, eventually rises to the top. In the industrial production of cream, this process is accelerated by using centrifuges called "separators". In many countries, it is sold in several grades depending on the total butterfat content. It can be dried to a powder for shipment to distant markets, and contains high levels of saturated fat.
Cream skimmed from milk may be called "sweet cream" to distinguish it from cream skimmed from whey, a by-product of cheese-making. Whey cream has a lower fat content and tastes more salty, tangy, and "cheesy". In many countries partially fermented cream is also sold: sour cream, crème fraîche, and so on. Both forms have many culinary uses in both sweet and savoury dishes.
Cream produced by cattle (particularly Jersey cattle) grazing on natural pasture often contains some carotenoid pigments derived from the plants they eat; traces of these intensely colored pigments give milk a slightly yellow tone, hence the name of the yellowish-white color: cream. Carotenoids are also the origin of butter's yellow color. Cream from goat's milk, water buffalo milk, or from cows fed indoors on grain or grain-based pellets, is white.
Cuisine
thumb|Christmas cake covered with whipped cream
Cream is used as an ingredient in many foods, including ice cream, many sauces, soups, stews, puddings, and some custard bases, and is also used for cakes. Whipped cream is served as a topping on ice cream sundaes, milkshakes, lassi, eggnog, sweet pies, strawberries, blueberries, or peaches. Cream is also used in Indian curries such as masala dishes. Both single and double cream (see Types for definitions) can be used in cooking. Double cream or full-fat crème fraîche is often used when the cream is added to a hot sauce, to prevent it separating or "splitting". Double cream can be thinned with milk to make an approximation of single cream.
Cream (usually light/single cream or half and half) may be added to coffee.
The French word denotes not only dairy cream but also other thick liquids such as sweet and savory custards, which are normally made with milk, not cream.
Types
thumb|right|Stewed nectarines and heavy cream
Different grades of cream are distinguished by their fat content, whether they have been heat-treated, whipped, and so on. In many jurisdictions, there are regulations for each type.
Australia and New Zealand
The Australia New Zealand Food Standards Code – Standard 2.5.2 – Defines cream as a milk product comparatively rich in fat, in the form of an emulsion of fat-in-skim milk, which can be obtained by separation from milk. Cream sold without further specification must contain no less than 350 g/kg (35%) milk fat.
Manufacturers labels may distinguish between different fat contents, a general guideline is as follows:
Name Fat content Main uses Extra light (or 'lite') 12–12.5% Light (or 'lite') 18–20% Thickened cream 35–36.5% Cream with added gelatine and/or other thickeners to give the cream a thicker texture, also possibly with stabilisers to aid the consistency of whipped cream. Such cream would not typically be used for cooking. Cream >= 35% Recipes calling for cream are usually referring to pure cream with about 35% fat. This is used for cooking as well as for pouring and whipping. It is comparable to whipping cream in some other countries. Double cream 48–60%
Canada
Canadian cream definitions are similar to those used in the United States, except for "light cream", which is very low-fat cream, usually with 5 or 6 percent butterfat. Specific product characteristics are generally uniform throughout Canada, but names vary by both geographic and linguistic area and by manufacturer: "coffee cream" may be 10 or 18 percent cream and "half-and-half" () may be 3, 5, 6 or 10 percent, all depending on location and brand.
Regulations allow cream to contain acidity regulators and stabilizers. For whipping cream, allowed additives include skim milk powder (≤ 0.25%), glucose solids (≤ 0.1%), calcium sulphate (≤ 0.005%), and xanthan gum (≤ 0.02%). The content of milk fat in canned cream must be displayed as a percentage followed by "milk fat", "B.F", or "M.F".
Name Minimum milk fat Additional definition Main uses Manufacturing cream 40%Crème fraîche is also 40–45% but is an acidified cultured product rather than sweet cream. Commercial production. Whipping cream 33–36% Also as cooking or "thick" cream 35% with added stabilizers. Heavy cream must be at least 36%. In Francophone areas: crème à fouetter 35%; and for cooking, crème à cuisson 35%, crème à l'ancienne 35% or crème épaisse 35%. Whips into a creamy and smooth topping that is used for pastries, fresh fruits, desserts, hot cocoa, etc. Cooking version is formulated to resist breaking when heated (as in sauces). Table cream 15–18% Coffee cream. Also as cooking or "thick" cream 15% with added stabilizers. In Francophone areas: crème de table 15% or crème à café 18%; and for cooking, crème champêtre 15%, crème campagnarde (country cream) 15% or crème épaisse 15%. Added as rich whitener to coffee. Ideal for soups, sauces and veloutés. Garnishing fruit and desserts. Cooking version is formulated to resist breaking when heated. Half and half 10% Cereal cream. Product with the most butterfat in the light cream category. In Francophone areas: crème à café 10% and sometimes crème légère 10%. Approximately equal to a 50/50 blend of table cream (at 16–18%) and whole milk (at 3.25%), hence the common name in English. Poured over hot cereal as a garnish. Ideal in sauces for vegetables, fish, meat, poultry, and pasta. Also in cream soups. Light cream 3–10% Light cream 6%. In Francophone areas: mélange de lait et de crème pour café 5%, Crémette™ 5% or crème légère 3% to 10%. A mixture of milk and cream. 5% product is similar to the richest Guernsey or Jersey milk. A lower fat alternative to table cream in coffee.
France
In France, the use of the term "cream" for food products is defined by the decree 80-313 of April 23, 1980. It specifies the minimum rate of milk fat (12%) as well as the rules for pasteurisation or UHT sterilisation. The mention "crème fraîche" (fresh cream) can only be used for pasteurised creams conditioned on production site within 24h after pasteurisation. Even if food additives complying with French and European laws are allowed, usually, none will be found in plain "crèmes" and "crèmes fraîches" apart from lactic ferments (some low cost creams (or close to creams) can contain thickening agents, but rarely). Fat content is commonly shown as "XX% M.G." ("matière grasse").
+NameMilk fatDefinitionMain usesWithout lactic ferments added (liquid texture)Crème fraîche crue30 to 40%Directly from the farm production. Local food circuits. No sterilisation and no pasteurisation.Crème fleurette30%No sterilisation but pasteurised. Liquid and soft the first days, it gets heavier and develops a more pronounced taste with time.Commonly used by cooks in restaurants.Crème entière liquide22 to 40%UHT sterilised (in France, a cream can not legally be called "fraîche" if it has been UHT sterilised).Crème fraîche liquide:30 to 40%
(usually 30%)Pasteurised (can be called "fraîche").Mostly used for fruit desserts and to make crème chantilly or ganaches. Can also be used to make white sauces or added in soups or pastas.Crème fraîche légère liquide12 to 21%
(usually 15%)Pasteurised (can be called "fraîche"). Less fat.Can be used for the same recipes as the non diet one but sometimes considered as less tasty and/or less convenient to cook with.With lactic ferments added (heavy texture)Crème crue maturée30 to 40%Directly from the farm production. Local food circuits. No sterilisation and no pasteurisation.Crème entière épaisse22 to 40%UHT sterilised (in France, a cream can not legally be called "fraîche" if it has been UHT sterilised).Crème fraîche épaisse30 to 40%
(usually 30%)Pasteurised (can be called "fraîche").Suits best for cooking especially reductions and liaisons (used as a binding agent). Also used to cook quiches (such as quiche Lorraine).Crème fraîche légère épaisse12 to 21%
(usually 15%)Pasteurised (can be called "fraîche"). Less fat.Can be used for the same recipes as the non diet one but sometimes considered as less tasty and/or less convenient to cook with.Crème aigre16 to 21%More acidic taste.Same product as the American sour cream or the Canadian crème sure, but rarely used in France.
Russia
Russia, as well as other EAC countries, legally separates cream into two classes: normal (10–34% butterfat) and heavy (35–58%), but the industry has pretty much standardized around the following types:
English Russian Transliteration Milk fat (wt%) Low-fat or drinking cream Нежирные (питьевые) сливки Nezhirnÿe (pityevÿe) slivki 10% (Normal) Cream Сливки Slivki 15% or 20% Whipping cream Сливки для взбивания Slivki dlya vzbivaniya 33% or 35% Double cream Двойные (жирные) сливки Dvoinÿe (Zhirnÿe) slivki 48%
Sweden
In Sweden, cream is usually sold as:
Matlagningsgrädde ("cooking cream"), 10–15%
Kaffegrädde ("Coffee cream"), 10–12%, earlier mostly 12%
Vispgrädde (whipping cream), 36–40%, the 36% variant often has additives.
Mellangrädde (27%) is, nowadays, a less common variant.
Gräddfil (usually 12%) and Creme Fraiche (usually around 35%) are two common sour cream products.
Switzerland
In Switzerland, the types of cream are legally defined as follows:
English German French Italian Typicalmilk fatwt% Minimummilk fatwt% Double cream Doppelrahm double-crème doppia panna 45% 45% Full cream Whipping creamCream VollrahmSchlagrahmRahmSahne crème entièrecrème à fouettercrème panna interapanna da montarepanna 35% 35% Half cream Halbrahm demi-crème mezza panna 25% 15% Coffee cream Kaffeerahm crème à café panna da caffè 15% 15%
Sour cream and crème fraîche (German: Sauerrahm, Crème fraîche; French: crème acidulée, crème fraîche; Italian: panna acidula, crème fraîche) are defined as cream soured by bacterial cultures.
Thick cream (German: ; French: ; Italian: ) is defined as cream thickened using thickening agents.
United Kingdom
In the United Kingdom, these types of cream are produced. Fat content must meet the Food Labelling Regulations 1996.
Name Minimum milk fat Additional definition Main uses Clotted cream
Processing and additives
Cream may have thickening agents and stabilizers added. Thickeners include sodium alginate, carrageenan, gelatine, sodium bicarbonate, tetrasodium pyrophosphate, and alginic acid.
Other processing may be carried out. For example, cream has a tendency to produce oily globules (called "feathering") when added to coffee. The stability of the cream may be increased by increasing the non-fat solids content, which can be done by partial demineralisation and addition of sodium caseinate, although this is expensive. Oreo and Hydrox cookies are a type of sandwich cookie in which two biscuits have a soft, sweet filling between them that is called "crème filling." In some cases, foods can be described as cream although they do not contain predominantly milk fats; for example, in Britain, "ice cream" can contain non-milk fat (declared on the label) in addition to or instead of cream, and salad cream is the customary name for a non-dairy condiment that has been produced since the 1920s.
In other languages, cognates of "cream" are also sometimes used for non-food products, such as fogkrém (Hungarian for toothpaste), or Sonnencreme (German for sunscreen).
Some products are described as "cream alternatives". For example, Elmlea Double, etc. are blends of buttermilk or lentils and vegetable oil with other additives sold by Upfield in the United Kingdom packaged and shelved in the same way as cream, labelled as having "a creamy taste".
See also
Creaming (chemistry)
Buttercream
Condensed milk
Crème, a French culinary term for cream-like preparations
Crème liqueur
Ice cream
Kaymak, which is similar to clotted cream
List of cream soups
Milk skin
Plant cream
References
External links
Virtual Museum Exhibit on Milk, Cream & Butter
Category:Condiments
Category:Dairy products
|
https://en.wikipedia.org/wiki/Cream
|
2025-04-05T18:27:43.069349
|
6111
|
Chemical vapor deposition
|
plasma (violet) enhances the growth of carbon nanotubes in a laboratory-scale PECVD (plasma-enhanced chemical vapor deposition) apparatus]]
Chemical vapor deposition (CVD) is a vacuum deposition method used to produce high-quality, and high-performance, solid materials. The process is often used in the semiconductor industry to produce thin films.
In typical CVD, the wafer (substrate) is exposed to one or more volatile precursors, which react and/or decompose on the substrate surface to produce the desired deposit. Frequently, volatile by-products are also produced, which are removed by gas flow through the reaction chamber.
Microfabrication processes widely use CVD to deposit materials in various forms, including: monocrystalline, polycrystalline, amorphous, and epitaxial. These materials include: silicon (dioxide, carbide, nitride, oxynitride), carbon (fiber, nanofibers, nanotubes, diamond and graphene), fluorocarbons, filaments, tungsten, titanium nitride and various high-κ dielectrics.
The term chemical vapour deposition was coined in 1960 by John M. Blocher, Jr. who intended to differentiate chemical from physical vapour deposition (PVD).
Types
CVD is practiced in a variety of formats. These processes generally differ in the means by which chemical reactions are initiated.
* Classified by operating conditions:
** Atmospheric pressure CVD (APCVD) – CVD at atmospheric pressure.
** Low-pressure CVD (LPCVD) – CVD at sub-atmospheric pressures. Many journal articles and commercial tools use the term reduced pressure CVD (RPCVD) especially for single wafer tools in place of LPCVD which dominates for multi-wafer furnace tube tools. Reduced pressures tend to reduce unwanted gas-phase reactions and improve film uniformity across the wafer.
** Ultrahigh vacuum CVD (UHVCVD) – CVD at very low pressure, typically below 10<sup>−6</sup> Pa (≈ 10<sup>−8</sup> torr). Note that in other fields, a lower division between high and ultra-high vacuum is common, often 10<sup>−7</sup> Pa.
** Sub-atmospheric CVD (SACVD) – CVD at sub-atmospheric pressures. Uses tetraethyl orthosilicate (TEOS) and ozone to fill high aspect ratio Si structures with silicon dioxide (SiO<sub>2</sub>).
Most modern CVD is either LPCVD or UHVCVD.
* Classified by physical characteristics of vapor:
** Aerosol assisted CVD (AACVD) – CVD in which the precursors are transported to the substrate by means of a liquid/gas aerosol, which can be generated ultrasonically. This technique is suitable for use with non-volatile precursors.
** Direct liquid injection CVD (DLICVD) – CVD in which the precursors are in liquid form (liquid or solid dissolved in a convenient solvent). Liquid solutions are injected in a vaporization chamber towards injectors (typically car injectors). The precursor vapors are then transported to the substrate as in classical CVD. This technique is suitable for use on liquid or solid precursors. High growth rates can be reached using this technique.
* Classified by type of substrate heating:
** Hot wall CVD – CVD in which the chamber is heated by an external power source and the substrate is heated by radiation from the heated chamber walls.
** Cold wall CVD – CVD in which only the substrate is directly heated either by induction or by passing current through the substrate itself or a heater in contact with the substrate. The chamber walls are at room temperature.
* Plasma methods (see also Plasma processing):
** Microwave plasma-assisted CVD (MPCVD)
** Plasma-enhanced CVD (PECVD) – CVD that utilizes plasma to enhance chemical reaction rates of the precursors. PECVD processing allows deposition at lower temperatures, which is often critical in the manufacture of semiconductors. The lower temperatures also allow for the deposition of organic coatings, such as plasma polymers, that have been used for nanoparticle surface functionalization.
** Remote plasma-enhanced CVD (RPECVD) – Similar to PECVD except that the wafer substrate is not directly in the plasma discharge region. Removing the wafer from the plasma region allows processing temperatures down to room temperature.
** Low-energy plasma-enhanced chemical vapor deposition (LEPECVD) - CVD employing a high density, low energy plasma to obtain epitaxial deposition of semiconductor materials at high rates and low temperatures.
* Atomic-layer CVD (ALCVD) – Deposits successive layers of different substances to produce layered, crystalline films. See Atomic layer epitaxy.
* Combustion chemical vapor deposition (CCVD) – Combustion Chemical Vapor Deposition or flame pyrolysis is an open-atmosphere, flame-based technique for depositing high-quality thin films and nanomaterials.
* Hot filament CVD (HFCVD) – also known as catalytic CVD (Cat-CVD) or more commonly, initiated CVD, this process uses a hot filament to chemically decompose the source gases. The filament temperature and substrate temperature thus are independently controlled, allowing colder temperatures for better absorption rates at the substrate and higher temperatures necessary for decomposition of precursors to free radicals at the filament.
* Hybrid physical-chemical vapor deposition (HPCVD) – This process involves both chemical decomposition of precursor gas and vaporization of a solid source.
* Metalorganic chemical vapor deposition (MOCVD) – This CVD process is based on metalorganic precursors.
* Rapid thermal CVD (RTCVD) – This CVD process uses heating lamps or other methods to rapidly heat the wafer substrate. Heating only the substrate rather than the gas or chamber walls helps reduce unwanted gas-phase reactions that can lead to particle formation.
* Vapor-phase epitaxy (VPE)
* Photo-initiated CVD (PICVD) – This process uses UV light to stimulate chemical reactions. It is similar to plasma processing, given that plasmas are strong emitters of UV radiation. Under certain conditions, PICVD can be operated at or near atmospheric pressure.
* Laser chemical vapor deposition (LCVD) - This CVD process uses lasers to heat spots or lines on a substrate in semiconductor applications. In MEMS and in fiber production the lasers are used rapidly to break down the precursor gas—process temperature can exceed 2000 °C—to build up a solid structure in much the same way as laser sintering based 3-D printers build up solids from powders.
Uses
CVD is commonly used to deposit conformal films and augment substrate surfaces in ways that more traditional surface modification techniques are not capable of. CVD is extremely useful in the process of atomic layer deposition at depositing extremely thin layers of material. A variety of applications for such films exist. Gallium arsenide is used in some integrated circuits (ICs) and photovoltaic devices. Amorphous polysilicon is used in photovoltaic devices. Certain carbides and nitrides confer wear-resistance. Polymerization by CVD, perhaps the most versatile of all applications, allows for super-thin coatings which possess some very desirable qualities, such as lubricity, hydrophobicity and weather-resistance to name a few. The CVD of metal-organic frameworks, a class of crystalline nanoporous materials, has recently been demonstrated. Recently scaled up as an integrated cleanroom process depositing large-area substrates, the applications for these films are anticipated in gas sensing and low-κ dielectrics. CVD techniques are advantageous for membrane coatings as well, such as those in desalination or water treatment, as these coatings can be sufficiently uniform (conformal) and thin that they do not clog membrane pores.Commercially important materials prepared by CVDPolysilicon
Polycrystalline silicon is deposited from trichlorosilane (SiHCl<sub>3</sub>) or silane (SiH<sub>4</sub>), using the following reactions:
:SiHCl<sub>3</sub> → Si + Cl<sub>2</sub> + HCl
:SiH<sub>4</sub> → Si + 2 H<sub>2</sub>
This reaction is usually performed in LPCVD systems, with either pure silane feedstock, or a solution of silane with 70–80% nitrogen. Temperatures between 600 and 650 °C and pressures between 25 and 150 Pa yield a growth rate between 10 and 20 nm per minute. An alternative process uses a hydrogen-based solution. The hydrogen reduces the growth rate, but the temperature is raised to 850 or even 1050 °C to compensate. Polysilicon may be grown directly with doping, if gases such as phosphine, arsine or diborane are added to the CVD chamber. Diborane increases the growth rate, but arsine and phosphine decrease it.
Silicon dioxide
Silicon dioxide (usually called simply "oxide" in the semiconductor industry) may be deposited by several different processes. Common source gases include silane and oxygen, dichlorosilane (SiCl<sub>2</sub>H<sub>2</sub>) and nitrous oxide (N<sub>2</sub>O), or tetraethylorthosilicate (TEOS; Si(OC<sub>2</sub>H<sub>5</sub>)<sub>4</sub>). The reactions are as follows:
:SiH<sub>4</sub> + O<sub>2</sub> → SiO<sub>2</sub> + 2 H<sub>2</sub>
:SiCl<sub>2</sub>H<sub>2</sub> + 2 N<sub>2</sub>O → SiO<sub>2</sub> + 2 N<sub>2</sub> + 2 HCl
:Si(OC<sub>2</sub>H<sub>5</sub>)<sub>4</sub> → SiO<sub>2</sub> + byproducts
The choice of source gas depends on the thermal stability of the substrate; for instance, aluminium is sensitive to high temperature. Silane deposits between 300 and 500 °C, dichlorosilane at around 900 °C, and TEOS between 650 and 750 °C, resulting in a layer of low- temperature oxide (LTO). However, silane produces a lower-quality oxide than the other methods (lower dielectric strength, for instance), and it deposits nonconformally. Any of these reactions may be used in LPCVD, but the silane reaction is also done in APCVD. CVD oxide invariably has lower quality than thermal oxide, but thermal oxidation can only be used in the earliest stages of IC manufacturing.
Oxide may also be grown with impurities (alloying or "doping"). This may have two purposes. During further process steps that occur at high temperature, the impurities may diffuse from the oxide into adjacent layers (most notably silicon) and dope them. Oxides containing 5–15% impurities by mass are often used for this purpose. In addition, silicon dioxide alloyed with phosphorus pentoxide ("P-glass") can be used to smooth out uneven surfaces. P-glass softens and reflows at temperatures above 1000 °C. This process requires a phosphorus concentration of at least 6%, but concentrations above 8% can corrode aluminium. Phosphorus is deposited from phosphine gas and oxygen:
:4 PH<sub>3</sub> + 5 O<sub>2</sub> → 2 P<sub>2</sub>O<sub>5</sub> + 6 H<sub>2</sub>
Glasses containing both boron and phosphorus (borophosphosilicate glass, BPSG) undergo viscous flow at lower temperatures; around 850 °C is achievable with glasses containing around 5 weight % of both constituents, but stability in air can be difficult to achieve. Phosphorus oxide in high concentrations interacts with ambient moisture to produce phosphoric acid. Crystals of BPO<sub>4</sub> can also precipitate from the flowing glass on cooling; these crystals are not readily etched in the standard reactive plasmas used to pattern oxides, and will result in circuit defects in integrated circuit manufacturing.
Besides these intentional impurities, CVD oxide may contain byproducts of the deposition. TEOS produces a relatively pure oxide, whereas silane introduces hydrogen impurities, and dichlorosilane introduces chlorine.
Lower temperature deposition of silicon dioxide and doped glasses from TEOS using ozone rather than oxygen has also been explored (350 to 500 °C). Ozone glasses have excellent conformality but tend to be hygroscopic – that is, they absorb water from the air due to the incorporation of silanol (Si-OH) in the glass. Infrared spectroscopy and mechanical strain as a function of temperature are valuable diagnostic tools for diagnosing such problems.
Silicon nitride
Silicon nitride is often used as an insulator and chemical barrier in manufacturing ICs. The following two reactions deposit silicon nitride from the gas phase:
:3 SiH<sub>4</sub> + 4 NH<sub>3</sub> → Si<sub>3</sub>N<sub>4</sub> + 12 H<sub>2</sub>
:3 SiCl<sub>2</sub>H<sub>2</sub> + 4 NH<sub>3</sub> → Si<sub>3</sub>N<sub>4</sub> + 6 HCl + 6 H<sub>2</sub>
Silicon nitride deposited by LPCVD contains up to 8% hydrogen. It also experiences strong tensile stress, which may crack films thicker than 200 nm. However, it has higher resistivity and dielectric strength than most insulators commonly available in microfabrication (10<sup>16</sup> Ω·cm and 10 MV/cm, respectively).
Another two reactions may be used in plasma to deposit SiNH:
:2 SiH<sub>4</sub> + N<sub>2</sub> → 2 SiNH + 3 H<sub>2</sub>
:SiH<sub>4</sub> + NH<sub>3</sub> → SiNH + 3 H<sub>2</sub>
These films have much less tensile stress, but worse electrical properties (resistivity 10<sup>6</sup> to 10<sup>15</sup> Ω·cm, and dielectric strength 1 to 5 MV/cm).
Metals
Tungsten CVD, used for forming conductive contacts, vias, and plugs on a semiconductor device, is achieved from tungsten hexafluoride (WF<sub>6</sub>), which may be deposited in two ways:
:WF<sub>6</sub> → W + 3 F<sub>2</sub>
:WF<sub>6</sub> + 3 H<sub>2</sub> → W + 6 HF
Other metals, notably aluminium and copper, can be deposited by CVD. , commercially cost-effective CVD for copper did not exist, although volatile sources exist, such as Cu(hfac)<sub>2</sub>. Copper is typically deposited by electroplating. Aluminium can be deposited from triisobutylaluminium (TIBAL) and related organoaluminium compounds.
CVD for molybdenum, tantalum, titanium, nickel is widely used. These metals can form useful silicides when deposited onto silicon. Mo, Ta and Ti are deposited by LPCVD, from their pentachlorides. Nickel, molybdenum, and tungsten can be deposited at low temperatures from their carbonyl precursors. In general, for an arbitrary metal M'', the chloride deposition reaction is as follows:
:2 MCl<sub>5</sub> + 5 H<sub>2</sub> → 2 M + 10 HCl
whereas the carbonyl decomposition reaction can happen spontaneously under thermal treatment or acoustic cavitation and is as follows:
:M(CO)<sub>n</sub> → M + n CO
the decomposition of metal carbonyls is often violently precipitated by moisture or air, where oxygen reacts with the metal precursor to form metal or metal oxide along with carbon dioxide.
Niobium(V) oxide layers can be produced by the thermal decomposition of niobium(V) ethoxide with the loss of diethyl ether according to the equation:
:2 Nb(OC<sub>2</sub>H<sub>5</sub>)<sub>5</sub> → Nb<sub>2</sub>O<sub>5</sub> + 5 C<sub>2</sub>H<sub>5</sub>OC<sub>2</sub>H<sub>5</sub>
Graphene
Many variations of CVD can be utilized to synthesize graphene. Although many advancements have been made, the processes listed below are not commercially viable yet.
* Carbon source
The most popular carbon source that is used to produce graphene is methane gas. One of the less popular choices is petroleum asphalt, notable for being inexpensive but more difficult to work with.
Although methane is the most popular carbon source, hydrogen is required during the preparation process to promote carbon deposition on the substrate. If the flow ratio of methane and hydrogen are not appropriate, it will cause undesirable results. During the growth of graphene, the role of methane is to provide a carbon source, the role of hydrogen is to provide H atoms to corrode amorphous C, and improve the quality of graphene. But excessive H atoms can also corrode graphene. As a result, the integrity of the crystal lattice is destroyed, and the quality of graphene is deteriorated. Therefore, by optimizing the flow rate of methane and hydrogen gases in the growth process, the quality of graphene can be improved.
* Use of catalyst
The use of catalyst is viable in changing the physical process of graphene production. Notable examples include iron nanoparticles, nickel foam, and gallium vapor. These catalysts can either be used in situ during graphene buildup, or situated at some distance away at the deposition area. Some catalysts require another step to remove them from the sample material. paves the way for synthesizing high-quality graphene for device applications while avoiding the transfer process.
* Physical conditions
Physical conditions such as surrounding pressure, temperature, carrier gas, and chamber material play a big role in production of graphene.
Most systems use LPCVD with pressures ranging from 1 to 1500 Pa. Quartz is chosen because it has a very high melting point and is chemically inert. In other words, quartz does not interfere with any physical or chemical reactions regardless of the conditions.
* Methods of analysis of results
Raman spectroscopy, X-ray spectroscopy, transmission electron microscopy (TEM), and scanning electron microscopy (SEM) are used to examine and characterize the graphene samples.
Graphene nanoribbon
In spite of graphene's exciting electronic and thermal properties, it is unsuitable as a transistor for future digital devices, due to the absence of a bandgap between the conduction and valence bands. This makes it impossible to switch between on and off states with respect to electron flow. Scaling things down, graphene nanoribbons of less than 10 nm in width do exhibit electronic bandgaps and are therefore potential candidates for digital devices. Precise control over their dimensions, and hence electronic properties, however, represents a challenging goal, and the ribbons typically possess rough edges that are detrimental to their performance.
Diamond
CVD can be used to produce a synthetic diamond by creating the circumstances necessary for carbon atoms in a gas to settle on a substrate in crystalline form. CVD of diamonds has received much attention in the materials sciences because it allows many new applications that had previously been considered too expensive. CVD diamond growth typically occurs under low pressure (1–27 kPa; 0.145–3.926 psi; 7.5–203 Torr) and involves feeding varying amounts of gases into a chamber, energizing them and providing conditions for diamond growth on the substrate. The gases always include a carbon source, and typically include hydrogen as well, though the amounts used vary greatly depending on the type of diamond being grown. Energy sources include hot filament, microwave power, and arc discharges, among others. The energy source is intended to generate a plasma in which the gases are broken down and more complex chemistries occur. The actual chemical process for diamond growth is still under study and is complicated by the very wide variety of diamond growth processes used.
Using CVD, films of diamond can be grown over large areas of substrate with control over the properties of the diamond produced. In the past, when high pressure high temperature (HPHT) techniques were used to produce a diamond, the result was typically very small free-standing diamonds of varying sizes. With CVD diamond, growth areas of greater than fifteen centimeters (six inches) in diameter have been achieved, and much larger areas are likely to be successfully coated with diamond in the future. Improving this process is key to enabling several important applications.
The growth of diamond directly on a substrate allows the addition of many of diamond's important qualities to other materials. Since diamond has the highest thermal conductivity of any bulk material, layering diamond onto high heat-producing electronics (such as optics and transistors) allows the diamond to be used as a heat sink. Diamond films are being grown on valve rings, cutting tools, and other objects that benefit from diamond's hardness and exceedingly low wear rate. In each case the diamond growth must be carefully done to achieve the necessary adhesion onto the substrate. Diamond's very high scratch resistance and thermal conductivity, combined with a lower coefficient of thermal expansion than Pyrex glass, a coefficient of friction close to that of Teflon (polytetrafluoroethylene) and strong lipophilicity would make it a nearly ideal non-stick coating for cookware if large substrate areas could be coated economically.
CVD growth allows one to control the properties of the diamond produced. In the area of diamond growth, the word "diamond" is used as a description of any material primarily made up of sp3-bonded carbon, and there are many different types of diamond included in this. By regulating the processing parameters—especially the gases introduced, but also including the pressure the system is operated under, the temperature of the diamond, and the method of generating plasma—many different materials that can be considered diamond can be made. Single-crystal diamond can be made containing various dopants. Polycrystalline diamond consisting of grain sizes from several nanometers to several micrometers can be grown. Some polycrystalline diamond grains are surrounded by thin, non-diamond carbon, while others are not. These different factors affect the diamond's hardness, smoothness, conductivity, optical properties and more.
Chalcogenides
Commercially, mercury cadmium telluride is of continuing interest for detection of infrared radiation. Consisting of an alloy of CdTe and HgTe, this material can be prepared from the dimethyl derivatives of the respective elements.
See also
* Apollo Diamond
* Bubbler cylinder
* Carbonyl metallurgy
* Electrostatic spray assisted vapour deposition
* Element Six
* Gas carbon
* Ion plating
* Metalorganic vapour phase epitaxy
* Virtual metrology
* Lisa McElwee-White
* List of metal-organic chemical vapour deposition precursors
* List of synthetic diamond manufacturers
References
Further reading
*
*
*
* Okada K. (2007). "Plasma-enhanced chemical vapor deposition of nanocrystalline diamond" [https://dx.doi.org/10.1016/j.stam.2007.08.008 Sci. Technol. Adv. Mater. 8, 624] free-download review
* Liu T., Raabe D. and Zaefferer S. (2008). "A 3D tomographic EBSD analysis of a CVD diamond thin film" [https://dx.doi.org/10.1088/1468-6996/9/3/035013 Sci. Technol. Adv. Mater. 9 (2008) 035013] free-download
* Wild, Christoph (2008). "CVD Diamond Properties and Useful Formula" [http://www.diamond-materials.com/downloads/cvd_diamond_booklet.pdf CVD Diamond Booklet PDF] free-download
* Hess, Dennis W. (1988). [https://apps.dtic.mil/sti/pdfs/ADA204709.pdf Chemical vapor deposition of dielectric and metal films] . Free-download from Electronic Materials and Processing: Proceedings of the First Electronic Materials and Processing Congress held in conjunction with the 1988 World Materials Congress Chicago, Illinois, USA, 24–30 September 1988, Edited by Prabjit Singh (Sponsored by the Electronic Materials and Processing Division of ASM International).
Category:Chemical processes
Category:Coatings
Category:Glass coating and surface modification
Category:Industrial processes
Category:Plasma processing
Category:Semiconductor device fabrication
Category:Synthetic diamond
Category:Thin film deposition
Category:Vacuum
Category:Forming processes
|
https://en.wikipedia.org/wiki/Chemical_vapor_deposition
|
2025-04-05T18:27:43.093435
|
6112
|
CN Tower
|
<br />Toronto, Ontario<br />M5V 3L9
| coordinates
| start_date
| highest_next = Burj Khalifa
| building_type = Mixed use:<br /> Observation, telecommunications, attraction, restaurant
| architectural =
| antenna_spire =
| roof =
| elevator_count 9 Completed in 1976, it is located in downtown Toronto, built on the former Railway Lands. Its name "CN" referred to Canadian National, the railway company that built the tower. Following the railway's decision to divest non-core freight railway assets prior to the company's privatization in 1995, it transferred the tower to the Canada Lands Company, a federal Crown corporation responsible for the government's real estate portfolio.
The CN Tower held the record for the world's tallest free-standing structure for 32 years, from 1975 until 2007, when it was surpassed by the Burj Khalifa, and was the world's tallest tower until 2009 when it was surpassed by the Canton Tower. It is currently the tenth-tallest free-standing structure in the world and remains the tallest free-standing structure on land in the Western Hemisphere. In 1995, the CN Tower was declared one of the modern Seven Wonders of the World by the American Society of Civil Engineers. It also belongs to the World Federation of Great Towers.
It is a signature icon of Toronto's skyline and attracts more than two million international visitors annually. It houses several observation decks, a revolving restaurant at some , and an entertainment complex. History
]]
The original concept of the CN Tower was first conceived in 1968 when the Canadian National Railway wanted to build a large television and radio communication platform to serve the Toronto area, and to demonstrate the strength of Canadian industry and CN in particular. These plans evolved over the next few years, and the project became official in 1972.
The tower would have been part of Metro Centre (see CityPlace), a large development south of Front Street on the Railway Lands, a large railway switching yard that was being made redundant after the opening of the MacMillan Yard north of the city in 1965 (then known as Toronto Yard). Key project team members were NCK Engineering as structural engineer; John Andrews Architects; Webb, Zerafa, Menkes, Housden Architects; Foundation Building Construction; and Canron (Eastern Structural Division).
At the time, most data communications took place over point-to-point microwave links, whose dish antennas covered the roofs of large buildings. As each new skyscraper was added to the downtown, former line-of-sight links were no longer possible. CN intended to rent "hub" space for microwave links, visible from almost any building in the Toronto area.
The original plan for the tower envisioned a tripod consisting of three independent cylindrical "pillars" linked at various heights by structural bridges. Had it been built, this design would have been considerably shorter, with the metal antenna located roughly where the concrete section between the main level and the SkyPod lies today. As the design effort continued, it evolved into the current design with a single continuous hexagonal core to the SkyPod, with three support legs blended into the hexagon below the main level, forming a large Y-shape structure at the ground level.
The idea for the main level in its current form evolved around this time, but the Space Deck (later renamed SkyPod) was not part of the plans until later. One engineer in particular felt that visitors would feel the higher observation deck would be worth paying extra for, and the costs in terms of construction were not prohibitive. Also around this time, it was realized that the tower could become the world's tallest free-standing structure to improve signal quality and attract tourists, and plans were changed to incorporate subtle modifications throughout the structure to this end. a subsidiary of Sweden's Skanska, a global project-development and construction group.
Construction began on February 6, 1973, with massive excavations at the tower base for the foundation. By the time the foundation was complete, of earth and shale were removed to a depth of in the centre, and a base incorporating of concrete with of rebar and of steel cable had been built to a thickness of . This portion of the construction was fairly rapid, with only four months needed between the start and the foundation being ready for construction on top. Phases of construction <gallery mode"packed" heights"135px" style"text-align:left">
File:CN Tower footings 1973.jpg|Constructing the base, July 1973
File:Cntower1974.jpg|Brackets being raised, August 1974
File:CN Tower50 construction skycrane March 1975 01d.jpg|Helicopter lifting part of antenna, March 1975
File:CN Tower under construction (April 1975).jpg|Main pod construction, April 1975
File:CN Tower under construction.jpg|Nearing completion, December 1975
File:CN Tower 1976.jpg|Two months after opening, August 1976
</gallery>
Opening
The CN Tower opened on June 26, 1976. The construction costs of approximately ($}} in dollars) were repaid in fifteen years.
From the mid-1970s to the mid-1980s, the CN Tower was practically the only development along Front Street West; it was still possible to see Lake Ontario from the foot of the CN Tower due to the expansive parking lots and lack of development in the area at the time. As the area around the tower was developed, particularly with the completion of the Metro Toronto Convention Centre (north building) in 1984 and SkyDome in 1989 (renamed Rogers Centre in 2005), the former Railway Lands were redeveloped and the tower became the centre of a newly developing entertainment area. Access was greatly improved with the construction of the SkyWalk in 1989, which connected the tower and SkyDome to the nearby Union Station railway and subway station, and, in turn, to the city's Path underground pedestrian system. By the mid-1990s, it was the centre of a thriving tourist district. The entire area continues to be an area of intense building, notably a boom in condominium construction in the first quarter of the 21st century, as well as the 2013 opening of the Ripley's Aquarium by the base of the tower.
The tower would garner worldwide media attention when stuntman Dar Robinson jumped off the CN Tower on two occasions in 1979 and 1980. The first was for a scene from the movie Highpoint, in which Robinson received ($ in dollars) for the stunt. The second was for a personal documentary. The first stunt had him use a parachute which he deployed three seconds before impact with the ground, while the second one used a wire decelerator attached to his back.
On June 26, 1986, the tenth anniversary of the tower's opening, high-rise firefighting and rescue advocate Dan Goodwin, in a sponsored publicity event, used his hands and feet to climb the outside of the tower, a feat he performed twice on the same day. Following both ascents, he used multiple rappels to descend to the ground.
From 1985 to 1992, the CN Tower basement level hosted the world's first flight simulator ride, Tour of the Universe, based on the flight of a Space Shuttle. The ride was replaced in 1992 with a similar attraction entitled "Space Race." It was later dismantled and replaced by two other rides in 1998 and 1999.
The 1990s and 2000s
A glass floor at an elevation of was installed in 1994. though the tower is commonly called the CN Tower.
Further changes were made from 1997 to January 2004: TrizecHahn Corporation managed the tower and instituted several expansion projects including a entertainment expansion, the 1997 addition of two new elevators (to a total of six) and the consequential relocation of the staircase from the north side leg to inside the core of the building, a conversion that also added nine stairs to the climb. TrizecHahn also owned the Willis Tower (Sears Tower at the time) in Chicago approximately at the same time.
In 2007, light-emitting diode (LED) lights replaced the incandescent lights that lit the CN Tower at night. This was done to take advantage of the cost savings of LED lights over incandescent lights. The colour of the LED lights can change, compared to the constant white colour of the incandescent lights. On September 12, 2007, Burj Khalifa in Dubai, then under construction and known as Burj Dubai, surpassed the CN Tower as the world's tallest free-standing structure on land. In 2008, glass panels were installed in one of the CN Tower elevators, which established a world record () for highest glass floor panelled elevator in the world. 2010s: EdgeWalk On August 1, 2011, the CN Tower opened the EdgeWalk, an amusement in which thrill-seekers can walk on and around the roof of the main pod of the tower at , which is directly above the 360 Restaurant. It is the world's highest full-circle, hands-free walk. Visitors are tethered to an overhead rail system and walk around the edge of the CN Tower's main pod above the 360 Restaurant on a metal floor. The attraction is closed throughout the winter and during periods of electrical storms and high winds.
One of the notable guests who visited EdgeWalk was Canadian comedian Rick Mercer, featured as the first episode of the ninth season of his CBC Television news satire show, Rick Mercer Report. There, he was accompanied by Canadian pop singer Jann Arden. The episode first aired on April 10, 2013. 2015 Pan Am Games The tower and surrounding areas were prominent in the 2015 Pan American Games production. In the opening ceremony, a pre-recorded segment featured track-and-field athlete Bruny Surin passing the flame to sprinter Donovan Bailey on the EdgeWalk and parachuting into Rogers Centre. A fireworks display off the tower concluded both the opening and closing ceremonies. Canada 150 On July 1, 2017, as part of the nationwide celebrations for Canada 150, which celebrated the 150th anniversary of Canadian Confederation, fireworks were once again shot from the tower in a five-minute display coordinated with the tower lights and music broadcast on a local radio station. 2020s The CN Tower closed during much of the COVID-19 pandemic. During much of the pandemic, the gift shop was renovated. Closures *The CN Tower was closed on September 11, 2001, following the terrorist attacks on the World Trade Center in New York City.
*The CN Tower was closed during the G20 summit on June 26–27, 2010, for security reasons, given its proximity to the Metro Toronto Convention Centre and ongoing citywide protests and riots.
*The CN Tower was closed from 2020 to 2021 due to COVID-19 pandemic restrictions throughout Ontario.
*The CN Tower was closed on December 16, 2021, due to glass falling off from heavy winds. Structure The CN Tower consists of several substructures. The main portion of the tower is a hollow concrete hexagonal pillar containing the stairwells and power and plumbing connections. The tower's six elevators are located in the three inverted angles created by the Tower's hexagonal shape (two elevators per angle). Each of the three elevator shafts is lined with glass, allowing for views of the city as the glass-windowed elevators make their way through the tower. The stairwell was originally located in one of these angles (the one facing north), but was moved into the central hollow of the tower; the tower's new fifth and sixth elevators were placed in the hexagonal angle that once contained the stairwell. On top of the main concrete portion of the tower is a tall metal broadcast antenna, carrying television and radio signals. There are three visitor areas: the Glass Floor and Outdoor Observation Terrace, which are both located at an elevation of , the Indoor Lookout Level (formerly known as "Indoor Observation Level") located at , and the higher SkyPod (formerly known as "Space Deck") at , just below the metal antenna. The hexagonal shape is visible between the two highest areas; however, below the main deck, three large supporting legs give the tower the appearance of a large tripod.
The main deck level has seven storeys, some of which are open to the public. Below the public areas—at —is a large white donut-shaped radome containing the structure's UHF transmitters. The glass floor and outdoor observation deck are at . The glass floor has an area of and can withstand a pressure of . The floor's thermal glass units are thick, consisting of a pane of laminated glass, airspace and a pane of laminated glass. In 2008, one elevator was upgraded to add a glass floor panel, believed to have the highest vertical rise of any elevator equipped with this feature. The Horizons Cafe and the lookout level are at . The 360 Restaurant, a revolving restaurant that completes a full rotation once every 72 minutes, is at . When the tower first opened, it also featured a discotheque named Sparkles (at the Indoor Observation Level), billed as the highest disco and dance floor in the world.
The SkyPod was once the highest public observation deck in the world until it was surpassed by the Shanghai World Financial Center in 2008.
A metal staircase reaches the main deck level after 1,776 steps, and the SkyPod above after 2,579 steps; it is the tallest metal staircase on Earth. These stairs are intended for emergency use only except for charity stair-climb events two times during the year. The average climber takes approximately 30 minutes to climb to the base of the radome, but the fastest climb on record is 7 minutes and 52 seconds in 1989 by Brendan Keenoy, an Ontario Provincial Police officer.
<gallery mode"packed" heights"135" style="text-align:left">
File:CN Tower, Toronto, Ontario (29969151776).jpg|Inside 360 Restaurant
File:CN Tower Main Observation Level 2023.jpg|Main Observation Level after renovation in 2018
File:CN Tower Turmkorb-Modell-blau.png|Cross-section of Main Pod
File:Inside the skypod of the CN Tower (27287339323).jpg|Skypod
File:CN Tower Terrace Level after renovation in 2023.jpg|Terrace Level glass floor
File:CNTowerNastyFall.jpg|View through glass floor
File:CN Tower Gift Shop after renovation 2023.jpg|Gift shop in 2023
File:CN Tower Ground View Looking Up.png|Ground view looking up at the CN Tower.
</gallery>
Architects
*WZMH Architects
*John Hamilton Andrews
*Webb Zerafa
*Menkes Housden with the help of Edward R. Baldwin
Falling ice danger
in 2010]]
A freezing rain storm on March 2, 2007, resulted in a layer of ice several centimetres thick forming on the side of the tower and other downtown buildings. The sun thawed the ice, then winds of up to blew some of it away from the structure. There were fears that cars and windows of nearby buildings would be smashed by large chunks of ice. In response, police closed some streets surrounding the tower. During morning rush hour on March 5 of the same year, police expanded the area of closed streets to include the Gardiner Expressway away from the tower as increased winds blew the ice farther, as far north as King Street West, away, where a taxicab window was shattered. Subsequently, on March 6, 2007, the Gardiner Expressway reopened after winds abated.
On April 16, 2018, falling ice from the CN Tower punctured the roof of the nearby Rogers Centre stadium, causing the Toronto Blue Jays to postpone the game that day to the following day as a doubleheader; this was the third doubleheader held at the Rogers Centre. On April 20 of the same year, the CN Tower reopened.
Safety features
In August 2000, a fire broke out at the Ostankino Tower in Moscow, killing three people and causing extensive damage. The fire was blamed on poor maintenance and outdated equipment. The failure of the fire-suppression systems and the lack of proper equipment for firefighters allowed the fire to destroy most of the interior and sparked fears the tower might even collapse.
The Ostankino Tower was completed nine years before the CN Tower and is only shorter. The parallels between the towers led to some concern that the CN Tower could be at risk of a similar tragedy. However, Canadian officials subsequently stated that it is "highly unlikely" that a similar disaster could occur at the CN Tower, as it has important safeguards that were not present in the Ostankino Tower. Specifically, officials cited:
* the fireproof building materials used in the tower's construction,
* frequent and stringent safety inspections,
* an extensive sprinkler system,
* a 24-hour emergency monitoring operation,
* two 68,160-litre (15,000-imperial gallon; 18,006-US gallon) water reservoirs at the top, which are automatically replenished,
* a fire hose at the base of the structure capable of sending to any location in the tower,
* a ban on natural gas appliances anywhere in the tower (including the restaurant in the main pod),
* an elevator that can be used during a fire as it runs up the outside of the building and can be powered by three emergency generators at the base of the structure (unlike the elevator at the Ostankino Tower, which malfunctioned).
Officials also noted that the CN Tower has an excellent safety record, although there was an electrical fire in the antennas on August 16, 2017 — the tower's first fire. Moreover, other supertall structures built between 1967 and 1976 — such as the Willis Tower (formerly the Sears Tower), the World Trade Center (until its destruction on September 11, 2001), the Fernsehturm Berlin, the Aon Center, 875 North Michigan Avenue (formerly the John Hancock Center), and First Canadian Place — also have excellent safety records, which suggests that the Ostankino Tower accident was a rare safety failure, and that the likelihood of similar events occurring at other supertall structures is extremely low.
Lighting
following the November 2015 Paris attacks]]
The CN Tower was originally lit at night with incandescent lights, which were removed in 1997 because they were inefficient and expensive to repair. In June 2007, the tower was outfitted with 1,330 super-bright LED lights inside the elevator shafts, shooting over the main pod and upward to the top of the tower's mast to light the tower from dusk until 2 a.m. The official opening ceremony took place on June 28, 2007, before the Canada Day holiday weekend.
The tower changes its lighting scheme on holidays and to commemorate major events. After the 95th Grey Cup in Toronto, the tower was lit in green and white to represent the colours of the Grey Cup champion Saskatchewan Roughriders. From sundown on August 27, 2011, to sunrise the following day, the tower was lit in orange, the official colour of the New Democratic Party (NDP), to commemorate the death of federal NDP leader and leader of the official opposition Jack Layton. When former South African president Nelson Mandela died, the tower was lit in the colours of the South African flag. When former federal finance minister under Stephen Harper's Conservatives Jim Flaherty died, the tower was lit in green to reflect his Irish Canadian heritage. On the night of the attacks on Paris on November 13, 2015, the tower displayed the colours of the French flag. On June 8, 2021, the tower displayed the colours of the Toronto Maple Leafs' archrivals Montreal Canadiens after they advanced to the semifinals of 2021 Stanley Cup playoffs. The CN Tower was lit in the colours of the Ukrainian flag during the beginning of the Russian invasion of Ukraine in late February 2022.
Programmed remotely from a desktop computer with a wireless network interface controller in Burlington, Ontario, the LEDs use less energy to light than the previous incandescent lights (10% less energy than the dimly lit version and 60% less than the brightly lit version). The estimated cost to use the LEDs is $1,000 per month.
During the spring and autumn bird migration seasons, the lights are turned off to comply with the voluntary Fatal Light Awareness Program, which "encourages buildings to dim unnecessary exterior lighting to mitigate bird mortality during spring and summer migration."
{| class="wikitable"
|-
! Date !! Colour !! Occasion
|-
| Ongoing || Red and White || Top of the hour CN Tower light show
|-
| January 26 || Light Blue and Yellow || World Alzheimer Day
|-
| February 4 || Orange and Blue || World Cancer Day
|-
| February 14 || Red || Valentine's Day
|-
| March 17 || Green || Saint Patrick's Day
|-
| March 21–June 20 || Decreased Lighting || Bird Migration - Lighting is decreased during spring bird migration
|-
| September 23–December 20 || Decreased Lighting || Bird Migration - Lighting is decreased during autumn bird migration
|-
| December || Red and Green || Season's Greetings
|-
| December 1 || Red || World AIDS Day
|-
| December 6 || Purple || White Ribbon Day
|-
| December 10 || Yellow || Human Rights Day
|-
| December 21 || Blue and White || First Day of Winter
|-
| December 31 || Countdown to and Light Show || New Year's Eve
|}
Height comparisons
, Dubai<br />• CN Tower, Toronto<br />• Willis Tower, Chicago]]
The CN Tower is the tallest freestanding structure in the Western Hemisphere. As of 2013, there were two other freestanding structures in the Western Hemisphere exceeding in height: the Willis Tower in Chicago, which stands at when measured to its pinnacle, and One World Trade Center in New York City, which has a pinnacle height of , or approximately shorter than the CN Tower. Due to the symbolism of the number 1776 (the year of the signing of the United States Declaration of Independence), the height of One World Trade Center is unlikely to be increased. The proposed Chicago Spire was expected to exceed the height of the CN Tower, but its construction was halted early due to financial difficulties amid the Great Recession, and was eventually cancelled in 2010. Height distinction debate "World's Tallest Tower" title Guinness World Records has called the CN Tower "the world's tallest self-supporting tower" and "the world's tallest free-standing tower". Although Guinness did list this description of the CN Tower under the heading "tallest building" at least once, The issue of what was tallest became moot when Burj Khalifa, then under construction, exceeded the height of the CN Tower in 2007 (see below).
Although the CN Tower contains a restaurant, a gift shop and multiple observation levels, it does not have floors continuously from the ground, and therefore it is not considered a building by the Council on Tall Buildings and Urban Habitat (CTBUH) or Emporis. CTBUH defines a building as "a structure that is designed for residential, business, or manufacturing purposes. An essential characteristic of a building is that it has floors." The tower definition used by Guinness was defined by the Council on Tall Buildings and Urban Habitat as 'a building in which less than 50% of the construction is usable floor space'. Guinness World Records editor-in-chief Craig Glenday announced that Burj Khalifa was not classified as a tower because it has too much usable floor space to be considered to be a tower. CN Tower still held world records for highest above ground wine cellar (in 360 Restaurant) at 351 m, highest above-ground restaurant at 346 m (Horizons Restaurant), and tallest free-standing concrete tower during Guinness's recertification. The CN Tower was surpassed in 2009 by the Canton Tower in Guangzhou, China, which stands at tall, as the world's tallest tower; which in turn was surpassed by the Tokyo Skytree in 2011, which currently is the tallest tower at in height. The CN Tower, as of 2022, stands as the tenth-tallest free-standing structure on land, remains the tallest free-standing structure in the Western Hemisphere, and is the third-tallest tower. The CN Tower is the second-tallest free-standing structure in the Commonwealth of Nations behind Merdeka 118 in Kuala Lumpur, Malaysia.
Height records
]]
Since its construction, the tower has gained the following world height records:
{| class="wikitable"
|-
!Record
!Owner
!Value
!Time period
!Succeeded by
|-
|World's tallest free-standing structure||CN Tower||||March 31, 1975 to September 12, 2007||Burj Khalifa
|-
|World's tallest tower||CN Tower||||1975 to 2009|| rowspan=2 |Canton Tower
|-
|World's highest public observation gallery||SkyPod|||||
|-
|World's highest glass floor panelled elevator||CN Tower||||2008 to present||—
|-
|World's longest metal staircase||CN Tower||2,579 steps||||
|-
|World's highest glass floor||CN Tower||||2008 to July 2, 2009||Willis Tower
|-
|World's highest and largest revolving restaurant||360 Restaurant||||||
|-
|World's highest bar||Horizons Restaurant||||September 21, 2009 to present||—
|-
|World's highest wine cellar||360 Restaurant||||||
|}
Use
The CN Tower has been and continues to be used as a communications tower for a number of different media and by numerous companies. Television broadcasters {| class"wikitable sortable"
|-
<!-- !Frequency -->
!VHF
!UHF
!Virtual
!Callsign
!Affiliation
!Branding
|-
<!-- |186.31 MHz -->
|9
|—
|9.1
|CFTO-DT
|CTV
|CTV Toronto
|-
<!-- |501.31 MHz -->
|—
|19
|19.1
|CICA-DT
|TVO
|TVO
|-
<!-- |507.31 MHz -->
|—
|20
|5.1
|CBLT-DT
|CBC Television
|CBC Toronto
|-
<!-- |537.31 MHz -->
|—
|25
|25.1
|CBLFT-DT
|Ici Radio-Canada Télé
|ICI Ontario
|-
<!-- | *FREQUENCY NEEDED* -->
|—
|40
|40.1
|CJMT-DT
|Omni Television
|Omni.2
|-
<!-- |633.31 MHz -->
|—
|41
|41.1
|CIII-DT-41
|Global
|Global Toronto
|-
<!-- |651.31 MHz -->
|—
|44
|57.1
|CITY-DT
|Citytv
|Citytv Toronto
|-
<!-- |669.31 MHz -->
|—
|47
|47.1
|CFMT-DT
|Omni Television
|Omni.1
|-
| colspan"6" style"text-align: center;" | Source: Vividcomm The FM transmitters are situated in a metal broadcast antenna, on top of the main concrete portion of the tower at an elevation above from the ground.
{| class="wikitable sortable"
!Frequency
!kW
!Callsign
!Affiliation/Owner
!Branding
!Notes
|-
|91.1 MHz
|40
|CJRT
|Independent; Public
|JAZZ.FM91
|Jazz
|-
|94.1 MHz
|38
|CBL
|Canadian Broadcasting Corporation
|CBC Music
|Non-commercial; classical; jazz
|-
|97.3 MHz
|28.9
|CHBM
|Stingray Group
|boom 97.3
|Classic hits
|-
|98.1 MHz
|44
|CHFI
|Rogers Sports & Media
|98.1 CHFI
|Adult contemporary
|-
|99.9 MHz
|40
|CKFM
|Bell Media
|Virgin Radio 99.9FM
|Top 40/Contemporary hits
|-
|100.7 MHz
|4
|CHIN
|CHIN Radio/TV International
|CHIN Radio
|Primarily in Italian and Portuguese
|-
|102.1 MHz
|35
|CFNY
|Corus Entertainment
|102.1 the Edge
|Alternative rock
|-
|104.5 MHz
|40
|CHUM
|Bell Media
|104.5 CHUM FM
|Hot adult contemporary<!--Don't bypass redirect per WP:NOTBROKEN-->
|-
|107.1 MHz
|40
|CILQ
|Corus Entertainment
|Classic Rock Q 107
|Mainstream rock
|-
| colspan"6" style"text-align: center;" | Source: Vividcomm In popular culture The CN Tower has been featured in numerous films, television shows, music recording covers, and video games. The tower also has its own official mascot, which resembles the tower itself.
<!--Before adding a work, please discuss on the talk page; consensus must be reached-->
*Highpoint is a Canadian 1982 action film starring Richard Harris, Christopher Plummer and Beverly D'Angelo. It features a shot of stuntman Dar Robinson jumping off of the CN Tower in 1979. Drake appeared significantly larger than life-size on the cover, and the CN Tower's Twitter<!--Don't replace with X as the tweet was made before Elon Musk purchased the website and rebranded it--> account later confirmed it to be photo edited.
<!--Before adding a work, please discuss on the talk page; consensus must be reached-->
See also
* Architecture of Toronto
* List of tallest buildings in Toronto
* List of tallest structures in Canada
* List of tallest freestanding structures
* List of tallest towers
* List of tallest buildings and structures
* List of tallest structures
References
External links
*
* [https://www.cbc.ca/player/play/video/1.3581406 CBC Archives – CN Tower opens to the public]
* [http://www.edgewalkcntower.ca/ Edgewalk]
* [http://www.pastandfuturehistory.com/ The Design, Engineering and Construction of the CN Tower – 1972 through to 1976]
* [https://www.flickr.com/photos/40744368@N04/sets/72157632200955200/ A visual construction history of the CN Tower – at 40th year anniversaries]
* [https://www.youtube.com/watch?v=K67j5juf-V4 How the CN Tower was Built]—Art of Engineering (YouTube documentary)
Category:1976 establishments in Ontario
Category:Articles containing video clips
Category:Buildings and structures in Toronto
Category:Canadian National Railway facilities
Category:Communication towers in Canada
Category:Former world's tallest buildings
Category:Modernist architecture in Canada
Category:Observation towers in Canada
Category:Railway Lands
Category:Stairways
Category:Tourist attractions in Toronto
Category:Towers completed in 1976
Category:Towers in Ontario
Category:Towers with revolving restaurants
Category:Transmitter sites in Canada
Category:WZMH Architects buildings
|
https://en.wikipedia.org/wiki/CN_Tower
|
2025-04-05T18:27:43.151025
|
6113
|
Chain rule
|
In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions and in terms of the derivatives of and . More precisely, if <math>hf\circ g</math> is the function such that <math>h(x)f(g(x))</math> for every , then the chain rule is, in Lagrange's notation,
<math display"block">h'(x) f'(g(x)) g'(x).</math>
or, equivalently,
<math display"block">h'(f\circ g)'=(f'\circ g)\cdot g'.</math>
The chain rule may also be expressed in Leibniz's notation. If a variable depends on the variable , which itself depends on the variable (that is, and are dependent variables), then depends on as well, via the intermediate variable . In this case, the chain rule is expressed as
<math display"block">\frac{dz}{dx} \frac{dz}{dy} \cdot \frac{dy}{dx},</math>
and
<math display"block"> \left.\frac{dz}{dx}\right|_{x} \left.\frac{dz}{dy}\right|_{y(x)}
\cdot \left. \frac{dy}{dx}\right|_{x} ,</math>
for indicating at which points the derivatives have to be evaluated.
In integration, the counterpart to the chain rule is the substitution rule.
Intuitive explanation
Intuitively, the chain rule states that knowing the instantaneous rate of change of relative to and that of relative to allows one to calculate the instantaneous rate of change of relative to as the product of the two rates of change.
As put by George F. Simmons: "If a car travels twice as fast as a bicycle and the bicycle is four times as fast as a walking man, then the car travels 2 × 4 = 8 times as fast as the man."
The relationship between this example and the chain rule is as follows. Let , and be the (variable) positions of the car, the bicycle, and the walking man, respectively. The rate of change of relative positions of the car and the bicycle is <math DISPLAY inline>\frac {dz}{dy}2.</math> Similarly, <math DISPLAY inline>\frac {dy}{dx}4.</math> So, the rate of change of the relative positions of the car and the walking man is
<math display"block">\frac{dz}{dx}\frac{dz}{dy}\cdot\frac{dy}{dx}2\cdot 48.</math>
The rate of change of positions is the ratio of the speeds, and the speed is the derivative of the position with respect to the time; that is,
<math display"block">\frac{dz}{dx}\frac \frac{dz}{dt}\frac{dx}{dt},</math>
or, equivalently,
<math display"block">\frac{dz}{dt}\frac{dz}{dx}\cdot \frac{dx}{dt},</math>
which is also an application of the chain rule.
History
The chain rule seems to have first been used by Gottfried Wilhelm Leibniz. He used it to calculate the derivative of <math>\sqrt{a + bz + cz^2}</math> as the composite of the square root function and the function <math>a + bz + cz^2\!</math>. He first mentioned it in a 1676 memoir (with a sign error in the calculation). The common notation of the chain rule is due to Leibniz. Guillaume de l'Hôpital used the chain rule implicitly in his Analyse des infiniment petits. The chain rule does not appear in any of Leonhard Euler's analysis books, even though they were written over a hundred years after Leibniz's discovery.. It is believed that the first "modern" version of the chain rule appears in Lagrange's 1797 Théorie des fonctions analytiques; it also appears in Cauchy's 1823 Résumé des Leçons données a L’École Royale Polytechnique sur Le Calcul Infinitesimal.
<math display"block"> (f\circ g)'(c) f'(g(c))\cdot g'(c). </math>
The rule is sometimes abbreviated as
<math display"block">(f\circ g)' (f'\circ g) \cdot g'.</math>
If and , then this abbreviated form is written in Leibniz notation as:
<math display"block">\frac{dy}{dx} \frac{dy}{du} \cdot \frac{du}{dx}.</math>
The points where the derivatives are evaluated may also be stated explicitly:
<math display"block">\left.\frac{dy}{dx}\right|_{xc} \left.\frac{dy}{du}\right|_{u g(c)} \cdot \left.\frac{du}{dx}\right|_{x=c}.</math>
Carrying the same reasoning further, given functions <math>f_1, \ldots, f_n\!</math> with the composite function <math>f_1 \circ ( f_2 \circ \cdots (f_{n-1} \circ f_n) )\!</math>, if each function <math>f_i\!</math> is differentiable at its immediate input, then the composite function is also differentiable by the repeated application of Chain Rule, where the derivative is (in Leibniz's notation):
<math display"block">\frac{df_1}{dx} \frac{df_1}{df_2}\frac{df_2}{df_3}\cdots\frac{df_n}{dx}.</math>
Applications
Composites of more than two functions
The chain rule can be applied to composites of more than two functions. To take the derivative of a composite of more than two functions, notice that the composite of , , and (in that order) is the composite of with . The chain rule states that to compute the derivative of , it is sufficient to compute the derivative of and the derivative of . The derivative of can be calculated directly, and the derivative of can be calculated by applying the chain rule again.
For concreteness, consider the function
<math display"block">y e^{\sin (x^2)}.</math>
This can be decomposed as the composite of three functions:
<math display="block">\begin{align}
y &f(u) e^u, \\
u &g(v) \sin v, \\
v &h(x) x^2.
\end{align}</math>
So that <math> y = f(g(h(x))) </math>.
Their derivatives are:
<math display="block">\begin{align}
\frac{dy}{du} &f'(u) e^u, \\
\frac{du}{dv} &g'(v) \cos v, \\
\frac{dv}{dx} &h'(x) 2x.
\end{align}</math>
The chain rule states that the derivative of their composite at the point is:
<math display="block">\begin{align}
(f \circ g \circ h)'(a) & = f'((g \circ h)(a)) \cdot (g \circ h)'(a) \\
& = f'((g \circ h)(a)) \cdot g'(h(a)) \cdot h'(a) \\
& = (f' \circ g \circ h)(a) \cdot (g' \circ h)(a) \cdot h'(a).
\end{align}</math>
In Leibniz's notation, this is:
<math display"block">\frac{dy}{dx} \left.\frac{dy}{du}\right|_{ug(h(a))}\cdot\left.\frac{du}{dv}\right|_{vh(a)}\cdot\left.\frac{dv}{dx}\right|_{x=a},</math>
or for short,
<math display"block">\frac{dy}{dx} \frac{dy}{du}\cdot\frac{du}{dv}\cdot\frac{dv}{dx}.</math>
The derivative function is therefore:
<math display"block">\frac{dy}{dx} e^{\sin(x^2)}\cdot\cos(x^2)\cdot 2x.</math>
Another way of computing this derivative is to view the composite function as the composite of and h. Applying the chain rule in this manner would yield:
<math display="block">\begin{align}
(f \circ g \circ h)'(a) &= (f \circ g)'(h(a)) \cdot h'(a) \\
&= f'(g(h(a))) \cdot g'(h(a)) \cdot h'(a).
\end{align}</math>
This is the same as what was computed above. This should be expected because .
Sometimes, it is necessary to differentiate an arbitrarily long composition of the form <math>f_1 \circ f_2 \circ \cdots \circ f_{n-1} \circ f_n\!</math>. In this case, define
<math display"block">f_{a\,.\,.\,b} f_{a} \circ f_{a+1} \circ \cdots \circ f_{b-1} \circ f_{b}</math>
where <math>f_{a\,.\,.\,a} f_a</math> and <math>f_{a\,.\,.\,b}(x) x</math> when <math>b < a</math>. Then the chain rule takes the form
<math display="block">\begin{align}
Df_{1\,.\,.\,n}
&= (Df_1 \circ f_{2\,.\,.\,n}) (Df_2 \circ f_{3\,.\,.\,n}) \cdots (Df_{n-1} \circ f_{n\,.\,.\,n}) Df_n \\
&\prod_{k1}^n \left[Df_k \circ f_{(k+1)\,.\,.\,n}\right]
\end{align}</math>
or, in the Lagrange notation,
<math display="block">\begin{align}
f_{1\,.\,.\,n}'(x)
&= f_1' \left( f_{2\,.\,.\,n}(x) \right) \; f_2' \left( f_{3\,.\,.\,n}(x) \right) \cdots f_{n-1}' \left(f_{n\,.\,.\,n}(x)\right) \; f_n'(x) \\[1ex]
&\prod_{k1}^{n} f_k' \left(f_{(k+1\,.\,.\,n)}(x) \right)
\end{align}</math>
Quotient rule
The chain rule can be used to derive some well-known differentiation rules. For example, the quotient rule is a consequence of the chain rule and the product rule. To see this, write the function as the product . First apply the product rule:
<math display="block">\begin{align}
\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)
&= \frac{d}{dx}\left(f(x)\cdot\frac{1}{g(x)}\right) \\
&= f'(x)\cdot\frac{1}{g(x)} + f(x)\cdot\frac{d}{dx}\left(\frac{1}{g(x)}\right).
\end{align}</math>
To compute the derivative of , notice that it is the composite of with the reciprocal function, that is, the function that sends to . The derivative of the reciprocal function is <math>-1/x^2\!</math>. By applying the chain rule, the last expression becomes:
<math display"block">f'(x)\cdot\frac{1}{g(x)} + f(x)\cdot\left(-\frac{1}{g(x)^2}\cdot g'(x)\right) \frac{f'(x) g(x) - f(x) g'(x)}{g(x)^2},</math>
which is the usual formula for the quotient rule.
Derivatives of inverse functions
Suppose that has an inverse function. Call its inverse function so that we have . There is a formula for the derivative of in terms of the derivative of . To see this, note that and satisfy the formula
<math display"block">f(g(x)) x.</math>
And because the functions <math>f(g(x))</math> and are equal, their derivatives must be equal. The derivative of is the constant function with value 1, and the derivative of <math>f(g(x))</math> is determined by the chain rule. Therefore, we have that:
<math display"block">f'(g(x)) g'(x) 1.</math>
To express as a function of an independent variable , we substitute <math>f(y)</math> for wherever it appears. Then we can solve for .
<math display="block">\begin{align}
f'(g(f(y))) g'(f(y)) &= 1 \\
f'(y) g'(f(y)) &= 1 \\
f'(y) = \frac{1}{g'(f(y))}.
\end{align}</math>
For example, consider the function . It has an inverse . Because , the above formula says that
<math display"block">\frac{d}{dy}\ln y \frac{1}{e^{\ln y}} = \frac{1}{y}.</math>
This formula is true whenever is differentiable and its inverse is also differentiable. This formula can fail when one of these conditions is not true. For example, consider . Its inverse is , which is not differentiable at zero. If we attempt to use the above formula to compute the derivative of at zero, then we must evaluate . Since and , we must evaluate 1/0, which is undefined. Therefore, the formula fails in this case. This is not surprising because is not differentiable at zero. Back propagation The chain rule forms the basis of the back propagation algorithm, which is used in gradient descent of neural networks in deep learning (artificial intelligence). Higher derivatives Faà di Bruno's formula generalizes the chain rule to higher derivatives. Assuming that f(u)}} and g(x)}}, then the first few derivatives are:
<math display="block">
\begin{align}
\frac{dy}{dx} & = \frac{dy}{du} \frac{du}{dx} \\
\frac{d^2 y }{d x^2} & =
\frac{d^2 y}{d u^2} \left(\frac{du}{dx}\right)^2
+ \frac{dy}{du} \frac{d^2 u}{dx^2} \\
\frac{d^3 y }{d x^3} & =
\frac{d^3 y}{d u^3} \left(\frac{du}{dx}\right)^3
+ 3 \, \frac{d^2 y}{d u^2} \frac{du}{dx} \frac{d^2 u}{d x^2}
+ \frac{dy}{du} \frac{d^3 u}{d x^3} \\
\frac{d^4 y}{d x^4} & =
\frac{d^4 y}{du^4} \left(\frac{du}{dx}\right)^4
+ 6 \, \frac{d^3 y}{d u^3} \left(\frac{du}{dx}\right)^2 \frac{d^2 u}{d x^2}
+ \frac{d^2 y}{d u^2} \left( 4 \, \frac{du}{dx} \frac{d^3 u}{dx^3}
+ 3 \, \left(\frac{d^2 u}{dx^2}\right)^2\right)
+ \frac{dy}{du} \frac{d^4 u}{dx^4}.
\end{align}</math>
Proofs
First proof
One proof of the chain rule begins by defining the derivative of the composite function , where we take the limit of the difference quotient for as approaches :
<math display"block">(f \circ g)'(a) \lim_{x \to a} \frac{f(g(x)) - f(g(a))}{x - a}.</math>
Assume for the moment that <math>g(x)\!</math> does not equal <math>g(a)</math> for any <math>x</math> near <math>a</math>. Then the previous expression is equal to the product of two factors:
<math display="block">\lim_{x \to a} \frac{f(g(x)) - f(g(a))}{g(x) - g(a)} \cdot \frac{g(x) - g(a)}{x - a}.</math>
If <math>g</math> oscillates near , then it might happen that no matter how close one gets to , there is always an even closer such that . For example, this happens near for the continuous function defined by for and otherwise. Whenever this happens, the above expression is undefined because it involves division by zero. To work around this, introduce a function <math>Q</math> as follows:
<math display"block">Q(y) \begin{cases}
\displaystyle\frac{f(y) - f(g(a))}{y - g(a)}, & y \neq g(a), \\
f'(g(a)), & y = g(a).
\end{cases}</math>
We will show that the difference quotient for is always equal to:
<math display="block">Q(g(x)) \cdot \frac{g(x) - g(a)}{x - a}.</math>
Whenever is not equal to , this is clear because the factors of cancel. When equals , then the difference quotient for is zero because equals , and the above product is zero because it equals times zero. So the above product is always equal to the difference quotient, and to show that the derivative of at exists and to determine its value, we need only show that the limit as goes to of the above product exists and determine its value.
To do this, recall that the limit of a product exists if the limits of its factors exist. When this happens, the limit of the product of these two factors will equal the product of the limits of the factors. The two factors are and . The latter is the difference quotient for at , and because is differentiable at by assumption, its limit as tends to exists and equals .
As for , notice that is defined wherever is. Furthermore, is differentiable at by assumption, so is continuous at , by definition of the derivative. The function is continuous at because it is differentiable at , and therefore is continuous at . So its limit as goes to exists and equals , which is .
This shows that the limits of both factors exist and that they equal and , respectively. Therefore, the derivative of at a exists and equals .
Second proof
Another way of proving the chain rule is to measure the error in the linear approximation determined by the derivative. This proof has the advantage that it generalizes to several variables. It relies on the following equivalent definition of differentiability at a point: A function g is differentiable at a if there exists a real number g′(a) and a function ε(h) that tends to zero as h tends to zero, and furthermore
<math display"block">g(a + h) - g(a) g'(a) h + \varepsilon(h) h.</math>
Here the left-hand side represents the true difference between the value of g at a and at , whereas the right-hand side represents the approximation determined by the derivative plus an error term.
In the situation of the chain rule, such a function ε exists because g is assumed to be differentiable at a. Again by assumption, a similar function also exists for f at g(a). Calling this function η, we have
<math display"block">f(g(a) + k) - f(g(a)) f'(g(a)) k + \eta(k) k.</math>
The above definition imposes no constraints on η(0), even though it is assumed that η(k) tends to zero as k tends to zero. If we set , then η is continuous at 0.
Proving the theorem requires studying the difference as h tends to zero. The first step is to substitute for using the definition of differentiability of g at a:
<math display"block">f(g(a + h)) - f(g(a)) f(g(a) + g'(a) h + \varepsilon(h) h) - f(g(a)).</math>
The next step is to use the definition of differentiability of f at g(a). This requires a term of the form for some k. In the above equation, the correct k varies with h. Set and the right hand side becomes . Applying the definition of the derivative gives:
<math display"block">f(g(a) + k_h) - f(g(a)) f'(g(a)) k_h + \eta(k_h) k_h.</math>
To study the behavior of this expression as h tends to zero, expand k<sub>h</sub>. After regrouping the terms, the right-hand side becomes:
<math display="block">f'(g(a)) g'(a)h + [f'(g(a)) \varepsilon(h) + \eta(k_h) g'(a) + \eta(k_h) \varepsilon(h)] h.</math>
Because ε(h) and η(k<sub>h</sub>) tend to zero as h tends to zero, the first two bracketed terms tend to zero as h tends to zero. Applying the same theorem on products of limits as in the first proof, the third bracketed term also tends zero. Because the above expression is equal to the difference , by the definition of the derivative is differentiable at a and its derivative is
The role of Q in the first proof is played by η in this proof. They are related by the equation:
<math display"block">Q(y) f'(g(a)) + \eta(y - g(a)). </math>
The need to define Q at g(a) is analogous to the need to define η at zero.
Third proof
Constantin Carathéodory's alternative definition of the differentiability of a function can be used to give an elegant proof of the chain rule.
Under this definition, a function is differentiable at a point if and only if there is a function , continuous at and such that . There is at most one such function, and if is differentiable at then .
Given the assumptions of the chain rule and the fact that differentiable functions and compositions of continuous functions are continuous, we have that there exist functions , continuous at , and , continuous at , and such that,
<math display"block">f(g(x))-f(g(a))q(g(x))(g(x)-g(a))</math>
and
<math display"block">g(x)-g(a)r(x)(x-a).</math>
Therefore,
<math display"block">f(g(x))-f(g(a))q(g(x))r(x)(x-a),</math>
but the function given by is continuous at , and we get, for this
<math display"block">(f(g(a)))'q(g(a))r(a)=f'(g(a))g'(a).</math>
A similar approach works for continuously differentiable (vector-)functions of many variables. This method of factoring also allows a unified approach to stronger forms of differentiability, when the derivative is required to be Lipschitz continuous, Hölder continuous, etc. Differentiation itself can be viewed as the polynomial remainder theorem (the little Bézout theorem, or factor theorem), generalized to an appropriate class of functions. Proof via infinitesimals
If <math>yf(x)</math> and <math>xg(t)</math> then choosing infinitesimal <math>\Delta t\not0</math> we compute the corresponding <math>\Delta xg(t+\Delta t)-g(t)</math> and then the corresponding <math>\Delta y=f(x+\Delta x)-f(x)</math>, so that
<math display"block">\frac{\Delta y}{\Delta t} \frac{\Delta y}{\Delta x} \frac{\Delta x}{\Delta t}</math>
and applying the standard part we obtain
<math display"block">\frac{d y}{d t}\frac{d y}{d x} \frac{dx}{dt}</math>
which is the chain rule.
Multivariable case
The full generalization of the chain rule to multi-variable functions (such as <math>f : \mathbb{R}^m \to \mathbb{R}^n</math>) is rather technical. However, it is simpler to write in the case of functions of the form
<math display="block">f(g_1(x), \dots, g_k(x)),</math>
where <math>f : \reals^k \to \reals</math>, and <math>g_i : \mathbb{R} \to \mathbb{R}</math> for each <math>i = 1, 2, \dots, k.</math>
As this case occurs often in the study of functions of a single variable, it is worth describing it separately.
Case of scalar-valued functions with multiple inputs
Let <math>f : \reals^k \to \reals</math>, and <math>g_i : \mathbb{R} \to \mathbb{R}</math> for each <math>i = 1, 2, \dots, k.</math>
To write the chain rule for the composition of functions
<math display="block">x \mapsto f(g_1(x), \dots , g_k(x)),</math>
one needs the partial derivatives of with respect to its arguments. The usual notations for partial derivatives involve names for the arguments of the function. As these arguments are not named in the above formula, it is simpler and clearer to use D-Notation, and to denote by
<math display="block">D_i f</math>
the partial derivative of with respect to its th argument, and by
<math display="block">D_i f(z)</math>
the value of this derivative at .
With this notation, the chain rule is
<math display"block">\frac{d}{dx}f(g_1(x), \dots, g_k (x))\sum_{i1}^k \left(\frac{d}{dx}{g_i}(x)\right) D_i f(g_1(x), \dots, g_k (x)).</math>Example: arithmetic operations
If the function is addition, that is, if
<math display"block">f(u,v)u+v,</math>
then <math display"inline">D_1 f \frac{\partial f}{\partial u} 1</math> and <math display"inline">D_2 f \frac{\partial f}{\partial v} 1</math>. Thus, the chain rule gives
<math display"block">\frac{d}{dx}(g(x)+h(x)) \left( \frac{d}{dx}g(x) \right) D_1 f+\left( \frac{d}{dx}h(x)\right) D_2 f=\frac{d}{dx}g(x) +\frac{d}{dx}h(x).</math>
For multiplication
<math display"block">f(u,v)uv,</math>
the partials are <math>D_1 f v</math> and <math>D_2 f u</math>. Thus,
<math display"block">\frac{d}{dx}(g(x)h(x)) h(x) \frac{d}{dx} g(x) + g(x) \frac{d}{dx} h(x).</math>
The case of exponentiation
<math display"block">f(u,v)u^v</math>
is slightly more complicated, as
<math display"block">D_1 f vu^{v-1},</math>
and, as <math>u^v=e^{v\ln u},</math>
<math display"block">D_2 f u^v\ln u.</math>
It follows that
<math display"block">\frac{d}{dx}\left(g(x)^{h(x)}\right) h(x)g(x)^{h(x)-1} \frac{d}{dx}g(x) + g(x)^{h(x)} \ln g(x) \,\frac{d}{dx}h(x).</math>
General rule: Vector-valued functions with multiple inputs
The simplest way for writing the chain rule in the general case is to use the total derivative, which is a linear transformation that captures all directional derivatives in a single formula. Consider differentiable functions and , and a point in . Let denote the total derivative of at and denote the total derivative of at . These two derivatives are linear transformations and , respectively, so they can be composed. The chain rule for total derivatives is that their composite is the total derivative of at :
<math display"block">D_{\mathbf{a}}(f \circ g) D_{g(\mathbf{a})}f \circ D_{\mathbf{a}}g,</math>
or for short,
<math display"block">D(f \circ g) Df \circ Dg.</math>
The higher-dimensional chain rule can be proved using a technique similar to the second proof given above.
Because the total derivative is a linear transformation, the functions appearing in the formula can be rewritten as matrices. The matrix corresponding to a total derivative is called a Jacobian matrix, and the composite of two derivatives corresponds to the product of their Jacobian matrices. From this perspective the chain rule therefore says:
<math display"block">J_{f \circ g}(\mathbf{a}) J_{f}(g(\mathbf{a})) J_{g}(\mathbf{a}),</math>
or for short,
<math display"block">J_{f \circ g} (J_f \circ g)J_g.</math>
That is, the Jacobian of a composite function is the product of the Jacobians of the composed functions (evaluated at the appropriate points).
The higher-dimensional chain rule is a generalization of the one-dimensional chain rule. If , , and are 1, so that and , then the Jacobian matrices of and are . Specifically, they are:
<math display="block">\begin{align}
J_g(a) &= \begin{pmatrix} g'(a) \end{pmatrix}, \\
J_{f}(g(a)) &= \begin{pmatrix} f'(g(a)) \end{pmatrix}.
\end{align}</math>
The Jacobian of is the product of these matrices, so it is , as expected from the one-dimensional chain rule. In the language of linear transformations, is the function which scales a vector by a factor of and is the function which scales a vector by a factor of . The chain rule says that the composite of these two linear transformations is the linear transformation , and therefore it is the function that scales a vector by .
Another way of writing the chain rule is used when f and g are expressed in terms of their components as and . In this case, the above rule for Jacobian matrices is usually written as:
<math display"block">\frac{\partial(y_1, \ldots, y_k)}{\partial(x_1, \ldots, x_n)} \frac{\partial(y_1, \ldots, y_k)}{\partial(u_1, \ldots, u_m)} \frac{\partial(u_1, \ldots, u_m)}{\partial(x_1, \ldots, x_n)}.</math>
The chain rule for total derivatives implies a chain rule for partial derivatives. Recall that when the total derivative exists, the partial derivative in the -th coordinate direction is found by multiplying the Jacobian matrix by the -th basis vector. By doing this to the formula above, we find:
<math display"block">\frac{\partial(y_1, \ldots, y_k)}{\partial x_i} \frac{\partial(y_1, \ldots, y_k)}{\partial(u_1, \ldots, u_m)} \frac{\partial(u_1, \ldots, u_m)}{\partial x_i}.</math>
Since the entries of the Jacobian matrix are partial derivatives, we may simplify the above formula to get:
<math display"block">\frac{\partial(y_1, \ldots, y_k)}{\partial x_i} \sum_{\ell = 1}^m \frac{\partial(y_1, \ldots, y_k)}{\partial u_\ell} \frac{\partial u_\ell}{\partial x_i}.</math>
More conceptually, this rule expresses the fact that a change in the direction may change all of through , and any of these changes may affect .
In the special case where , so that is a real-valued function, then this formula simplifies even further:
<math display"block">\frac{\partial y}{\partial x_i} \sum_{\ell = 1}^m \frac{\partial y}{\partial u_\ell} \frac{\partial u_\ell}{\partial x_i}.</math>
This can be rewritten as a dot product. Recalling that (g<sub>1</sub>, …, g<sub>m</sub>)}}, the partial derivative is also a vector, and the chain rule says that:
<math display"block">\frac{\partial y}{\partial x_i} \nabla y \cdot \frac{\partial \mathbf{u}}{\partial x_i}.</math>
Example
Given where and , determine the value of and using the chain rule.
<math display"block">\frac{\partial u}{\partial r}\frac{\partial u}{\partial x} \frac{\partial x}{\partial r}+\frac{\partial u}{\partial y} \frac{\partial y}{\partial r} (2x)(\sin(t)) + (2)(0) 2r \sin^2(t),</math>
and
<math display="block">\begin{align}
\frac{\partial u}{\partial t}
&= \frac{\partial u}{\partial x} \frac{\partial x}{\partial t}+\frac{\partial u}{\partial y} \frac{\partial y}{\partial t} \\
&= (2x)(r\cos(t)) + (2)(2\sin(t)\cos(t)) \\
&= (2r\sin(t))(r\cos(t)) + 4\sin(t)\cos(t) \\
&= 2(r^2 + 2) \sin(t)\cos(t) \\
&= (r^2 + 2) \sin(2t).
\end{align}</math>
Higher derivatives of multivariable functions
Faà di Bruno's formula for higher-order derivatives of single-variable functions generalizes to the multivariable case. If is a function of as above, then the second derivative of is:
<math display"block">\frac{\partial^2 y}{\partial x_i \partial x_j} \sum_k \left(\frac{\partial y}{\partial u_k}\frac{\partial^2 u_k}{\partial x_i \partial x_j}\right) + \sum_{k, \ell} \left(\frac{\partial^2 y}{\partial u_k \partial u_\ell}\frac{\partial u_k}{\partial x_i}\frac{\partial u_\ell}{\partial x_j}\right).</math>
Further generalizations
All extensions of calculus have a chain rule. In most of these, the formula remains the same, though the meaning of that formula may be vastly different.
One generalization is to manifolds. In this situation, the chain rule represents the fact that the derivative of is the composite of the derivative of and the derivative of . This theorem is an immediate consequence of the higher dimensional chain rule given above, and it has exactly the same formula.
The chain rule is also valid for Fréchet derivatives in Banach spaces. The same formula holds as before. This case and the previous one admit a simultaneous generalization to Banach manifolds.
In differential algebra, the derivative is interpreted as a morphism of modules of Kähler differentials. A ring homomorphism of commutative rings determines a morphism of Kähler differentials which sends an element to , the exterior differential of . The formula holds in this context as well.
The common feature of these examples is that they are expressions of the idea that the derivative is part of a functor. A functor is an operation on spaces and functions between them. It associates to each space a new space and to each function between two spaces a new function between the corresponding new spaces. In each of the above cases, the functor sends each space to its tangent bundle and it sends each function to its derivative. For example, in the manifold case, the derivative sends a -manifold to a -manifold (its tangent bundle) and a -function to its total derivative. There is one requirement for this to be a functor, namely that the derivative of a composite must be the composite of the derivatives. This is exactly the formula .
There are also chain rules in stochastic calculus. One of these, Itō's lemma, expresses the composite of an Itō process (or more generally a semimartingale) dX<sub>t</sub> with a twice-differentiable function f. In Itō's lemma, the derivative of the composite function depends not only on dX<sub>t</sub> and the derivative of f but also on the second derivative of f. The dependence on the second derivative is a consequence of the non-zero quadratic variation of the stochastic process, which broadly speaking means that the process can move up and down in a very rough way. This variant of the chain rule is not an example of a functor because the two functions being composed are of different types.
See also
* − a computational method that makes heavy use of the chain rule to compute exact numerical derivatives.
*
*
*
*
*
*
References
External links
*
*
Category:Articles containing proofs
Category:Differentiation rules
Category:Theorems in analysis
Category:Theorems in calculus
|
https://en.wikipedia.org/wiki/Chain_rule
|
2025-04-05T18:27:43.195952
|
6115
|
P versus NP problem
|
The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.
Here, "quickly" means an algorithm exists that solves the task and runs in polynomial time (as opposed to, say, exponential time), meaning the task completion time is bounded above by a polynomial function on the size of the input to the algorithm. The general class of questions that some algorithm can answer in polynomial time is "P" or "class P". For some questions, there is no known way to find an answer quickly, but if provided with an answer, it can be verified quickly. The class of questions where an answer can be verified in polynomial time is "NP", standing for "nondeterministic polynomial time".
An answer to the P versus NP question would determine whether problems that can be verified in polynomial time can also be solved in polynomial time. If P ≠ NP, which is widely believed, it would mean that there are problems in NP that are harder to compute than to verify: they could not be solved in polynomial time, but the answer could be verified in polynomial time.
The problem has been called the most important open problem in computer science. Aside from being an important problem in computational theory, a proof either way would have profound implications for mathematics, cryptography, algorithm research, artificial intelligence, game theory, multimedia processing, philosophy, economics and many other fields.
It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute, each of which carries a US$1,000,000 prize for the first correct solution.
Example
Consider the following yes/no problem: given an incomplete Sudoku grid of size n^2 \times n^2, is there at least one legal solution where every row, column, and n \times n square contains the integers 1 through n^2? It is straightforward to verify "yes" instances of this generalized Sudoku problem given a candidate solution. However, it is not known whether there is a polynomial-time algorithm that can correctly answer "yes" or "no" to all instances of this problem. Therefore, generalized Sudoku is in NP (quickly verifiable), but may or may not be in P (quickly solvable). (It is necessary to consider a generalized version of Sudoku, as any fixed size Sudoku has only a finite number of possible grids. In this case the problem is in P, as the answer can be found by table lookup.)
History
The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures" (and independently by Leonid Levin in 1973).
Although the P versus NP problem was formally defined in 1971, there were previous inklings of the problems involved, the difficulty of proof, and the potential consequences. In 1955, mathematician John Nash wrote a letter to the NSA, speculating that cracking a sufficiently complex code would require time exponential in the length of the key. If proved (and Nash was suitably skeptical), this would imply what is now called P ≠ NP, since a proposed key can be verified in polynomial time. Another mention of the underlying problem occurred in a 1956 letter written by Kurt Gödel to John von Neumann. Gödel asked whether theorem-proving (now known to be co-NP-complete) could be solved in quadratic or linear time, and pointed out one of the most important consequences—that if so, then the discovery of mathematical proofs could be automated.
Context
The relation between the complexity classes P and NP is studied in computational complexity theory, the part of the theory of computation dealing with the resources required during computation to solve a given problem. The most common resources are time (how many steps it takes to solve a problem) and space (how much memory it takes to solve a problem).
In such analysis, a model of the computer for which time must be analyzed is required. Typically such models assume that the computer is deterministic (given the computer's present state and any inputs, there is only one possible action that the computer might take) and sequential (it performs actions one after the other).
In this theory, the class P consists of all decision problems (defined below) solvable on a deterministic sequential machine in a duration polynomial in the size of the input; the class NP consists of all decision problems whose positive solutions are verifiable in polynomial time given the right information, or equivalently, whose solution can be found in polynomial time on a non-deterministic machine. Clearly, P ⊆ NP. Arguably, the biggest open question in theoretical computer science concerns the relationship between those two classes:
Is P equal to NP?
Since 2002, William Gasarch has conducted three polls of researchers concerning this and related questions. Confidence that P ≠ NP has been increasing – in 2019, 88% believed P ≠ NP, as opposed to 83% in 2012 and 61% in 2002. When restricted to experts, the 2019 answers became 99% believed P ≠ NP. It is in NP because (given an input) it is simple to check whether M accepts the input by simulating M; it is NP-complete because the verifier for any particular instance of a problem in NP can be encoded as a polynomial-time machine M that takes the solution to be verified as input. Then the question of whether the instance is a yes or no instance is determined by whether a valid input exists.
The first natural problem proven to be NP-complete was the Boolean satisfiability problem, also known as SAT. As noted above, this is the Cook–Levin theorem; its proof that satisfiability is NP-complete contains technical details about Turing machines as they relate to the definition of NP. However, after this problem was proved to be NP-complete, proof by reduction provided a simpler way to show that many other problems are also NP-complete, including the game Sudoku discussed earlier. In this case, the proof shows that a solution of Sudoku in polynomial time could also be used to complete Latin squares in polynomial time. This in turn gives a solution to the problem of partitioning tri-partite graphs into triangles, which could then be used to find solutions for the special case of SAT known as 3-SAT, which then provides a solution for general Boolean satisfiability. So a polynomial-time solution to Sudoku leads, by a series of mechanical transformations, to a polynomial time solution of satisfiability, which in turn can be used to solve any other NP-problem in polynomial time. Using transformations like this, a vast class of seemingly unrelated problems are all reducible to one another, and are in a sense "the same problem".
Harder problems
Although it is unknown whether P = NP, problems outside of P are known. Just as the class P is defined in terms of polynomial running time, the class EXPTIME is the set of all decision problems that have exponential running time. In other words, any problem in EXPTIME is solvable by a deterministic Turing machine in O(2p(n)) time, where p(n) is a polynomial function of n. A decision problem is EXPTIME-complete if it is in EXPTIME, and every problem in EXPTIME has a polynomial-time many-one reduction to it. A number of problems are known to be EXPTIME-complete. Because it can be shown that P ≠ EXPTIME, these problems are outside P, and so require more than polynomial time. In fact, by the time hierarchy theorem, they cannot be solved in significantly less than exponential time. Examples include finding a perfect strategy for chess positions on an N × N board and similar problems for other board games.
The problem of deciding the truth of a statement in Presburger arithmetic requires even more time. Fischer and Rabin proved in 1974 that every algorithm that decides the truth of Presburger statements of length n has a runtime of at least 2^{2^{cn}} for some constant c. Hence, the problem is known to need more than exponential run time. Even more difficult are the undecidable problems, such as the halting problem. They cannot be completely solved by any algorithm, in the sense that for any particular algorithm there is at least one input for which that algorithm will not produce the right answer; it will either produce the wrong answer, finish without giving a conclusive answer, or otherwise run forever without producing any answer at all.
It is also possible to consider questions other than decision problems. One such class, consisting of counting problems, is called #P: whereas an NP problem asks "Are there any solutions?", the corresponding #P problem asks "How many solutions are there?". Clearly, a #P problem must be at least as hard as the corresponding NP problem, since a count of solutions immediately tells if at least one solution exists, if the count is greater than zero. Surprisingly, some #P problems that are believed to be difficult correspond to easy (for example linear-time) P problems. For these problems, it is very easy to tell whether solutions exist, but thought to be very hard to tell how many. Many of these problems are #P-complete, and hence among the hardest problems in #P, since a polynomial time solution to any of them would allow a polynomial time solution to all other #P problems.
Problems in NP not known to be in P or NP-complete
In 1975, Richard E. Ladner showed that if P ≠ NP, then there exist problems in NP that are neither in P nor NP-complete. If graph isomorphism is NP-complete, the polynomial time hierarchy collapses to its second level. Since it is widely believed that the polynomial hierarchy does not collapse to any finite level, it is believed that graph isomorphism is not NP-complete. The best algorithm for this problem, due to László Babai, runs in quasi-polynomial time.
The integer factorization problem is the computational problem of determining the prime factorization of a given integer. Phrased as a decision problem, it is the problem of deciding whether the input has a factor less than k. No efficient integer factorization algorithm is known, and this fact forms the basis of several modern cryptographic systems, such as the RSA algorithm. The integer factorization problem is in NP and in co-NP (and even in UP and co-UP). If the problem is NP-complete, the polynomial time hierarchy will collapse to its first level (i.e., NP = co-NP). The most efficient known algorithm for integer factorization is the general number field sieve, which takes expected time
O\left (\exp \left ( \left (\tfrac{64n}{9} \log(2) \right )^{\frac{1}{3}} \left ( \log(n\log(2)) \right )^{\frac{2}{3}} \right) \right )
to factor an n-bit integer. The best known quantum algorithm for this problem, Shor's algorithm, runs in polynomial time, although this does not indicate where the problem lies with respect to non-quantum complexity classes.
Does P mean "easy"?
thumb|310 px|The graph shows the running time vs. problem size for a knapsack problem of a state-of-the-art, specialized algorithm. The quadratic fit suggests that the algorithmic complexity of the problem is O((log(n))2).
All of the above discussion has assumed that P means "easy" and "not in P" means "difficult", an assumption known as Cobham's thesis. It is a common assumption in complexity theory; but there are caveats.
First, it can be false in practice. A theoretical polynomial algorithm may have extremely large constant factors or exponents, rendering it impractical. For example, the problem of deciding whether a graph G contains H as a minor, where H is fixed, can be solved in a running time of O(n2), where n is the number of vertices in G. However, the big O notation hides a constant that depends superexponentially on H. The constant is greater than 2 \uparrow \uparrow (2 \uparrow \uparrow (2 \uparrow \uparrow (h/2) ) ) (using Knuth's up-arrow notation), and where h is the number of vertices in H.
On the other hand, even if a problem is shown to be NP-complete, and even if P ≠ NP, there may still be effective approaches to the problem in practice. There are algorithms for many NP-complete problems, such as the knapsack problem, the traveling salesman problem, and the Boolean satisfiability problem, that can solve to optimality many real-world instances in reasonable time. The empirical average-case complexity (time vs. problem size) of such algorithms can be surprisingly low. An example is the simplex algorithm in linear programming, which works surprisingly well in practice; despite having exponential worst-case time complexity, it runs on par with the best known polynomial-time algorithms.
Finally, there are types of computations which do not conform to the Turing machine model on which P and NP are defined, such as quantum computation and randomized algorithms.
Reasons to believe P ≠ NP or P = NP
Cook provides a restatement of the problem in The P Versus NP Problem as "Does P NP?" most computer scientists believe that P ≠ NP. A key reason for this belief is that after decades of studying these problems no one has been able to find a polynomial-time algorithm for any of more than 3,000 important known NP-complete problems (see List of NP-complete problems). These algorithms were sought long before the concept of NP-completeness was even defined (Karp's 21 NP-complete problems, among the first found, were all well-known existing problems at the time they were shown to be NP-complete). Furthermore, the result P NP would imply many other startling results that are currently believed to be false, such as NP co-NP and P PH.
It is also intuitively argued that the existence of problems that are hard to solve but whose solutions are easy to verify matches real-world experience.
On the other hand, some researchers believe that it is overconfident to believe P ≠ NP and that researchers should also explore proofs of P = NP. For example, in 2002 these statements were made: that DLIN ≠ NLIN.
Consequences of solution
One of the reasons the problem attracts so much attention is the consequences of the possible answers. Either direction of resolution would advance theory enormously, and perhaps have huge practical consequences as well.
P = NP
A proof that P = NP could have stunning practical consequences if the proof leads to efficient methods for solving some of the important problems in NP. The potential consequences, both positive and negative, arise since various NP-complete problems are fundamental in many fields.
It is also very possible that a proof would not lead to practical algorithms for NP-complete problems. The formulation of the problem does not require that the bounding polynomial be small or even specifically known. A non-constructive proof might show a solution exists without specifying either an algorithm to obtain it or a specific bound. Even if the proof is constructive, showing an explicit bounding polynomial and algorithmic details, if the polynomial is not very low-order the algorithm might not be sufficiently efficient in practice. In this case the initial proof would be mainly of interest to theoreticians, but the knowledge that polynomial time solutions are possible would surely spur research into better (and possibly practical) methods to achieve them.
A solution showing P = NP could upend the field of cryptography, which relies on certain problems being difficult. A constructive and efficient solution to an NP-complete problem such as 3-SAT would break most existing cryptosystems including:
Existing implementations of public-key cryptography, a foundation for many modern security applications such as secure financial transactions over the Internet.
Symmetric ciphers such as AES or 3DES, used for the encryption of communications data.
Cryptographic hashing, which underlies blockchain cryptocurrencies such as Bitcoin, and is used to authenticate software updates. For these applications, finding a pre-image that hashes to a given value must be difficult, ideally taking exponential time. If P = NP, then this can take polynomial time, through reduction to SAT.
These would need modification or replacement with information-theoretically secure solutions that do not assume P ≠ NP.
There are also enormous benefits that would follow from rendering tractable many currently mathematically intractable problems. For instance, many problems in operations research are NP-complete, such as types of integer programming and the travelling salesman problem. Efficient solutions to these problems would have enormous implications for logistics. Many other important problems, such as some problems in protein structure prediction, are also NP-complete; making these problems efficiently solvable could considerably advance life sciences and biotechnology.
These changes could be insignificant compared to the revolution that efficiently solving NP-complete problems would cause in mathematics itself. Gödel, in his early thoughts on computational complexity, noted that a mechanical method that could solve any problem would revolutionize mathematics:
Similarly, Stephen Cook (assuming not only a proof, but a practically efficient algorithm) says:
Research mathematicians spend their careers trying to prove theorems, and some proofs have taken decades or even centuries to find after problems have been stated—for instance, Fermat's Last Theorem took over three centuries to prove. A method guaranteed to find a proof if a "reasonable" size proof exists, would essentially end this struggle.
Donald Knuth has stated that he has come to believe that P = NP, but is reserved about the impact of a possible proof:
thumb|250px|Diagram of complexity classes provided that P ≠ NP. The existence of problems within NP but outside both P and NP-complete, under that assumption, was established by Ladner's theorem.
P ≠ NP
A proof of P ≠ NP would lack the practical computational benefits of a proof that P = NP, but would represent a great advance in computational complexity theory and guide future research. It would demonstrate that many common problems cannot be solved efficiently, so that the attention of researchers can be focused on partial solutions or solutions to other problems. Due to widespread belief in P ≠ NP, much of this focusing of research has already taken place.
P ≠ NP still leaves open the average-case complexity of hard problems in NP. For example, it is possible that SAT requires exponential time in the worst case, but that almost all randomly selected instances of it are efficiently solvable. Russell Impagliazzo has described five hypothetical "worlds" that could result from different possible resolutions to the average-case complexity question. These range from "Algorithmica", where P = NP and problems like SAT can be solved efficiently in all instances, to "Cryptomania", where P ≠ NP and generating hard instances of problems outside P is easy, with three intermediate possibilities reflecting different possible distributions of difficulty over instances of NP-hard problems. The "world" where P ≠ NP but all problems in NP are tractable in the average case is called "Heuristica" in the paper. A Princeton University workshop in 2009 studied the status of the five worlds.
Results about difficulty of proof
Although the P NP problem itself remains open despite a million-dollar prize and a huge amount of dedicated research, efforts to solve the problem have led to several new techniques. In particular, some of the most fruitful research related to the P NP problem has been in showing that existing proof techniques are insufficient for answering the question, suggesting novel technical approaches are required.
As additional evidence for the difficulty of the problem, essentially all known proof techniques in computational complexity theory fall into one of the following classifications, all insufficient to prove P ≠ NP:
ClassificationDefinitionRelativizing proofsImagine a world where every algorithm is allowed to make queries to some fixed subroutine called an oracle (which can answer a fixed set of questions in constant time, such as an oracle that solves any traveling salesman problem in 1 step), and the running time of the oracle is not counted against the running time of the algorithm. Most proofs (especially classical ones) apply uniformly in a world with oracles regardless of what the oracle does. These proofs are called relativizing. In 1975, Baker, Gill, and Solovay showed that P NP with respect to some oracles, while P ≠ NP for other oracles. As relativizing proofs can only prove statements that are true for all possible oracles, these techniques cannot resolve P NP.Natural proofsIn 1993, Alexander Razborov and Steven Rudich defined a general class of proof techniques for circuit complexity lower bounds, called natural proofs. At the time, all previously known circuit lower bounds were natural, and circuit complexity was considered a very promising approach for resolving P NP. However, Razborov and Rudich showed that if one-way functions exist, P and NP are indistinguishable to natural proof methods. Although the existence of one-way functions is unproven, most mathematicians believe that they do, and a proof of their existence would be a much stronger statement than P ≠ NP. Thus it is unlikely that natural proofs alone can resolve P NP.Algebrizing proofsAfter the Baker–Gill–Solovay result, new non-relativizing proof techniques were successfully used to prove that IP PSPACE. However, in 2008, Scott Aaronson and Avi Wigderson showed that the main technical tool used in the IP PSPACE proof, known as arithmetization, was also insufficient to resolve P NP. Arithmetization converts the operations of an algorithm to algebraic and basic arithmetic symbols and then uses those to analyze the workings. In the IP PSPACE proof, they convert the black box and the Boolean circuits to an algebraic problem. However, if the problem is undecidable even with much weaker assumptions extending the Peano axioms for integer arithmetic, then nearly polynomial-time algorithms exist for all NP problems. Therefore, assuming (as most complexity theorists do) some NP problems don't have efficient algorithms, proofs of independence with those techniques are impossible. This also implies proving independence from PA or ZFC with current techniques is no easier than proving all NP problems have efficient algorithms.
Logical characterizations
The P = NP problem can be restated as certain classes of logical statements, as a result of work in descriptive complexity.
Consider all languages of finite structures with a fixed signature including a linear order relation. Then, all such languages in P are expressible in first-order logic with the addition of a suitable least fixed-point combinator. Recursive functions can be defined with this and the order relation. As long as the signature contains at least one predicate or function in addition to the distinguished order relation, so that the amount of space taken to store such finite structures is actually polynomial in the number of elements in the structure, this precisely characterizes P.
Similarly, NP is the set of languages expressible in existential second-order logic—that is, second-order logic restricted to exclude universal quantification over relations, functions, and subsets. The languages in the polynomial hierarchy, PH, correspond to all of second-order logic. Thus, the question "is P a proper subset of NP" can be reformulated as "is existential second-order logic able to describe languages (of finite linearly ordered structures with nontrivial signature) that first-order logic with least fixed point cannot?". The word "existential" can even be dropped from the previous characterization, since P NP if and only if P PH (as the former would establish that NP co-NP, which in turn implies that NP PH).
Polynomial-time algorithms
No known algorithm for a NP-complete problem runs in polynomial time. However, there are algorithms known for NP-complete problems that if P NP, the algorithm runs in polynomial time on accepting instances (although with enormous constants, making the algorithm impractical). However, these algorithms do not qualify as polynomial time because their running time on rejecting instances are not polynomial. The following algorithm, due to Levin (without any citation), is such an example below. It correctly accepts the NP-complete language SUBSET-SUM. It runs in polynomial time on inputs that are in SUBSET-SUM if and only if P NP:
// Algorithm that accepts the NP-complete language SUBSET-SUM.
//
// this is a polynomial-time algorithm if and only if P = NP.
//
// "Polynomial-time" means it returns "yes" in polynomial time when
// the answer should be "yes", and runs forever when it is "no".
//
// Input: S = a finite set of integers
// Output: "yes" if any subset of S adds up to 0.
// Runs forever with no output otherwise.
// Note: "Program number M" is the program obtained by
// writing the integer M in binary, then
// considering that string of bits to be a
// program. Every possible program can be
// generated this way, though most do nothing
// because of syntax errors.
FOR K = 1...∞
FOR M = 1...K
Run program number M for K steps with input S
IF the program outputs a list of distinct integers
AND the integers are all in S
AND the integers sum to 0
THEN
OUTPUT "yes" and HALT
This is a polynomial-time algorithm accepting an NP-complete language only if P = NP. "Accepting" means it gives "yes" answers in polynomial time, but is allowed to run forever when the answer is "no" (also known as a semi-algorithm).
This algorithm is enormously impractical, even if P = NP. If the shortest program that can solve SUBSET-SUM in polynomial time is b bits long, the above algorithm will try at least other programs first.
Formal definitions
P and NP
A decision problem is a problem that takes as input some string w over an alphabet Σ, and outputs "yes" or "no". If there is an algorithm (say a Turing machine, or a computer program with unbounded memory) that produces the correct answer for any input string of length n in at most cnk steps, where k and c are constants independent of the input string, then we say that the problem can be solved in polynomial time and we place it in the class P. Formally, P is the set of languages that can be decided by a deterministic polynomial-time Turing machine. Meaning,
\mathbf{P} \{ L : LL(M) \text{ for some deterministic polynomial-time Turing machine } M \}
where
L(M) = \{ w\in\Sigma^{*}: M \text{ accepts } w \}
and a deterministic polynomial-time Turing machine is a deterministic Turing machine M that satisfies two conditions:
M halts on all inputs w and
there exists k \in N such that T_M(n)\in O(n^k), where O refers to the big O notation and
T_M(n) \max\{ t_M(w) : w\in\Sigma^{*}, |w| n \}
t_M(w) = \text{ number of steps }M\text{ takes to halt on input }w.
NP can be defined similarly using nondeterministic Turing machines (the traditional way). However, a modern approach uses the concept of certificate and verifier. Formally, NP is the set of languages with a finite alphabet and verifier that runs in polynomial time. The following defines a "verifier":
Let L be a language over a finite alphabet, Σ.
L ∈ NP if, and only if, there exists a binary relation R\subset\Sigma^{*}\times\Sigma^{*} and a positive integer k such that the following two conditions are satisfied:
For all x\in\Sigma^{*}, x\in L \Leftrightarrow\exists y\in\Sigma^{*} such that (x, y) ∈ R and |y|\in O(|x|^k); and
the language L_{R} = \{ x\# y:(x,y)\in R\} over \Sigma\cup\{\#\} is decidable by a deterministic Turing machine in polynomial time.
A Turing machine that decides LR is called a verifier for L and a y such that (x, y) ∈ R is called a certificate of membership of x in L.
Not all verifiers must be polynomial-time. However, for L to be in NP, there must be a verifier that runs in polynomial time.
Example
Let
\mathrm{COMPOSITE} \left \{x\in\mathbb{N} \mid xpq \text{ for integers } p, q > 1 \right \}
R = \left \{(x,y)\in\mathbb{N} \times\mathbb{N} \mid 1
Whether a value of x is composite is equivalent to of whether x is a member of COMPOSITE. It can be shown that COMPOSITE ∈ NP by verifying that it satisfies the above definition (if we identify natural numbers with their binary representations).
COMPOSITE also happens to be in P, a fact demonstrated by the invention of the AKS primality test.
NP-completeness
There are many equivalent ways of describing NP-completeness.
Let L be a language over a finite alphabet Σ.
L is NP-complete if, and only if, the following two conditions are satisfied:
L ∈ NP; and
any L''' in NP is polynomial-time-reducible to L (written as L' \leq_{p} L), where L' \leq_{p} L if, and only if, the following two conditions are satisfied:
There exists f : Σ* → Σ* such that for all w in Σ* we have: (w\in L' \Leftrightarrow f(w)\in L); and
there exists a polynomial-time Turing machine that halts with f(w) on its tape on any input w.
Alternatively, if L ∈ NP, and there is another NP-complete problem that can be polynomial-time reduced to L, then L is NP-complete. This is a common way of proving some new problem is NP-complete.
Claimed solutions
While the P versus NP problem is generally considered unsolved, many amateur and some professional researchers have claimed solutions. Gerhard J. Woeginger compiled a list of 116 purported proofs from 1986 to 2016, of which 61 were proofs of P = NP, 49 were proofs of P ≠ NP, and 6 proved other results, e.g. that the problem is undecidable. Some attempts at resolving P versus NP have received brief media attention, though these attempts have been refuted.
Popular culture
The film Travelling Salesman, by director Timothy Lanzone, is the story of four mathematicians hired by the US government to solve the P versus NP problem.
In the sixth episode of The Simpsons seventh season "Treehouse of Horror VI", the equation P = NP is seen shortly after Homer accidentally stumbles into the "third dimension".
In the second episode of season 2 of Elementary, "Solve for X" Sherlock and Watson investigate the murders of mathematicians who were attempting to solve P versus NP.
Similar problems
R vs. RE problem, where R is analog of class P, and RE is analog class NP. These classes are not equal, because undecidable but verifiable problems do exist, for example, Hilbert's tenth problem which is RE-complete.
A similar problem exists in the theory of algebraic complexity: VP vs. VNP problem. Like P vs. NP, the answer is currently unknown.
See also
Game complexity
List of unsolved problems in mathematics
Unique games conjecture
Unsolved problems in computer science
Notes
References
Sources
Further reading
Online drafts
External links
Aviad Rubinstein's Hardness of Approximation Between P and NP, winner of the ACM's 2017 Doctoral Dissertation Award.
Category:1956 in computing
Category:Computer-related introductions in 1956
Category:Conjectures
Category:Mathematical optimization
Category:Millennium Prize Problems
Category:Structural complexity theory
Category:Unsolved problems in computer science
Category:Unsolved problems in mathematics
|
https://en.wikipedia.org/wiki/P_versus_NP_problem
|
2025-04-05T18:27:43.268413
|
6117
|
Charles Sanders Peirce
|
| birth_place = Cambridge, Massachusetts, U.S.
| death_date =
| death_place = Milford, Pennsylvania, U.S.
| relatives = Benjamin Peirce (father)
| institutions = Johns Hopkins University
| alma_mater = Harvard University
| known_for = <!--See -->
| region = Western philosophy
| era = Late modern philosophy
| school_tradition =
| main_interests
| notable_students = ; September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss, Peirce was "the most original and versatile of America's philosophers and America's greatest logician". Bertrand Russell wrote "he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever".
In metaphysics, Peirce was an "objective idealist" in the tradition of German philosopher Immanuel Kant as well as a scholastic realist about universals. He also held a commitment to the ideas of continuity and chance as real features of the universe, views he labeled synechism and tychism respectively. Peirce believed an epistemic fallibilism and anti-skepticism went along with these views.
Biography
Early life
's Graduate School of Arts and Social Sciences.]]
Peirce was born at 3 Phillips Place in Cambridge, Massachusetts. He was the son of Sarah Hunt Mills and Benjamin Peirce, himself a professor of mathematics and astronomy at Harvard University. At age 12, Charles read his older brother's copy of Richard Whately's Elements of Logic, then the leading English-language text on the subject. So began his lifelong fascination with logic and reasoning.
He suffered from his late teens onward from a nervous condition then known as "facial neuralgia", which would today be diagnosed as trigeminal neuralgia. His biographer, Joseph Brent, says that when in the throes of its pain "he was, at first, almost stupefied, and then aloof, cold, depressed, extremely suspicious, impatient of the slightest crossing, and subject to violent outbursts of temper". Its consequences may have led to the social isolation of his later life. Education Peirce went on to earn a Bachelor of Arts degree and a Master of Arts degree (1862) from Harvard. In 1863 the Lawrence Scientific School awarded him a Bachelor of Science degree, Harvard's first summa cum laude chemistry degree. His academic record was otherwise undistinguished. At Harvard, he began lifelong friendships with Francis Ellingwood Abbot, Chauncey Wright, and William James. One of his Harvard instructors, Charles William Eliot, formed an unfavorable opinion of Peirce. This proved fateful, because Eliot, while President of Harvard (1869–1909—a period encompassing nearly all of Peirce's working life), repeatedly vetoed Peirce's employment at the university.
United States Coast Survey
Between 1859 and 1891, Peirce was intermittently employed in various scientific capacities by the United States Coast Survey, which in 1878 was renamed the United States Coast and Geodetic Survey, where he enjoyed his highly influential father's protection until the latter's death in 1880. At the Survey, he worked mainly in geodesy and gravimetry, refining the use of pendulums to determine small local variations in the Earth's gravity. No members of the Peirce family volunteered or enlisted. Peirce grew up in a home where white supremacy was taken for granted, and slavery was considered natural. Peirce's father had described himself as a secessionist until the outbreak of the war, after which he became a Union partisan, providing donations to the Sanitary Commission, the leading Northern war charity.
Peirce liked to use the following syllogism to illustrate the unreliability of traditional forms of logic (for the first premise arguably assumes the conclusion):<poem>
All Men are equal in their political rights.
Negroes are Men.
Therefore, negroes are equal in political rights to whites.</poem>
Travels to Europe
He was elected a resident fellow of the American Academy of Arts and Sciences in January 1867. The Survey sent him to Europe five times, first in 1871 as part of a group sent to observe a solar eclipse. There, he sought out Augustus De Morgan, William Stanley Jevons, and William Kingdon Clifford, British mathematicians and logicians whose turn of mind resembled his own. Harvard observatory From 1869 to 1872, he was employed as an assistant in Harvard's astronomical observatory, doing important work on determining the brightness of stars and the shape of the Milky Way. In 1872 he founded the Metaphysical Club, a conversational philosophical club that Peirce, the future Supreme Court Justice Oliver Wendell Holmes Jr., the philosopher and psychologist William James, amongst others, formed in January 1872 in Cambridge, Massachusetts, and dissolved in December 1872. Other members of the club included Chauncey Wright, John Fiske, Francis Ellingwood Abbot, Nicholas St. John Green, and Joseph Bangs Warner. The discussions eventually birthed Peirce's notion of pragmatism.
National Academy of Sciences
", 1879. Peirce's projection of a sphere onto a square keeps angles true except at four isolated points on the equator, and has less scale variation than the Mercator projection. It can be tessellated; that is, multiple copies can be joined continuously edge-to-edge.]]
On April 20, 1877, he was elected a member of the National Academy of Sciences. Also in 1877, he proposed measuring the meter as so many wavelengths of light of a certain frequency, the kind of definition employed from 1960 to 1983.
In 1879 Peirce developed Peirce quincuncial projection, having been inspired by H. A. Schwarz's 1869 conformal transformation of a circle onto a polygon of n sides (known as the Schwarz–Christoffel mapping).
1880 to 1891
During the 1880s, Peirce's indifference to bureaucratic detail waxed while his Survey work's quality and timeliness waned. Peirce took years to write reports that he should have completed in months. Meanwhile, he wrote entries, ultimately thousands, during 1883–1909 on philosophy, logic, science, and other subjects for the encyclopedic Century Dictionary. In 1885, an investigation by the Allison Commission exonerated Peirce, but led to the dismissal of Superintendent Julius Hilgard and several other Coast Survey employees for misuse of public funds. In 1891, Peirce resigned from the Coast Survey at Superintendent Thomas Corwin Mendenhall's request.
Johns Hopkins University
In 1879, Peirce was appointed lecturer in logic at Johns Hopkins University, which had strong departments in areas that interested him, such as philosophy (Royce and Dewey completed their PhDs at Hopkins), psychology (taught by G. Stanley Hall and studied by Joseph Jastrow, who coauthored a landmark empirical study with Peirce), and mathematics (taught by J. J. Sylvester, who came to admire Peirce's work on mathematics and logic). His Studies in Logic by Members of the Johns Hopkins University (1883) contained works by himself and Allan Marquand, Christine Ladd, Benjamin Ives Gilman, and Oscar Howard Mitchell, several of whom were his graduate students. Peirce's nontenured position at Hopkins was the only academic appointment he ever held.
Brent documents something Peirce never suspected, namely that his efforts to obtain academic employment, grants, and scientific respectability were repeatedly frustrated by the covert opposition of a major Canadian-American scientist of the day, Simon Newcomb. Newcomb had been a favourite student of Peirce's father; although "no doubt quite bright", "like Salieri in Peter Shaffer's Amadeus he also had just enough talent to recognize he was not a genius and just enough pettiness to resent someone who was". Additionally "an intensely devout and literal-minded Christian of rigid moral standards", he was appalled by what he considered Peirce's personal shortcomings. Peirce's efforts may also have been hampered by what Brent characterizes as "his difficult personality". In contrast, Keith Devlin believes that Peirce's work was too far ahead of his time to be appreciated by the academic establishment of the day and that this played a large role in his inability to obtain a tenured position. Personal life Peirce's personal life undoubtedly worked against his professional success. After his first wife, Harriet Melusina Fay ("Zina"), left him in 1875, Peirce, while still legally married, became involved with Juliette, whose last name, given variously as Froissy and Pourtalai, and nationality (she spoke French) remain uncertain. When his divorce from Zina became final in 1883, he married Juliette. That year, Newcomb pointed out to a Johns Hopkins trustee that Peirce, while a Hopkins employee, had lived and traveled with a woman to whom he was not married; the ensuing scandal led to his dismissal in January 1884. Over the years Peirce sought academic employment at various universities without success. He had no children by either marriage.
Later life and poverty
In 1887, Peirce spent part of his inheritance from his parents to buy of rural land near Milford, Pennsylvania, which never yielded an economic return. There he had an 1854 farmhouse remodeled to his design. The Peirces named the property "Arisbe". There they lived with few interruptions for the rest of their lives, Charles writing prolifically, with much of his work remaining unpublished to this day (see Works). Living beyond their means soon led to grave financial and legal difficulties. Charles spent much of his last two decades unable to afford heat in winter and subsisting on old bread donated by the local baker. Unable to afford new stationery, he wrote on the verso side of old manuscripts. An outstanding warrant for assault and unpaid debts led to his being a fugitive in New York City for a while. Several people, including his brother James Mills Peirce and his neighbors, relatives of Gifford Pinchot, settled his debts and paid his property taxes and mortgage.
Peirce did some scientific and engineering consulting and wrote much for meager pay, mainly encyclopedic dictionary entries, and reviews for The Nation (with whose editor, Wendell Phillips Garrison, he became friendly). He did translations for the Smithsonian Institution, at its director Samuel Langley's instigation. Peirce also did substantial mathematical calculations for Langley's research on powered flight. Hoping to make money, Peirce tried inventing. He began but did not complete several books. In 1888, President Grover Cleveland appointed him to the Assay Commission.
From 1890 on, he had a friend and admirer in Judge Francis C. Russell of Chicago, who introduced Peirce to editor Paul Carus and owner Edward C. Hegeler of the pioneering American philosophy journal The Monist, which eventually published at least 14 articles by Peirce. He wrote many texts in James Mark Baldwin's Dictionary of Philosophy and Psychology (1901–1905); half of those credited to him appear to have been written actually by Christine Ladd-Franklin under his supervision. He applied in 1902 to the newly formed Carnegie Institution for a grant to write a systematic book describing his life's work. The application was doomed; his nemesis, Newcomb, served on the Carnegie Institution executive committee, and its president had been president of Johns Hopkins at the time of Peirce's dismissal.
The one who did the most to help Peirce in these desperate times was his old friend William James, dedicating his Will to Believe (1897) to Peirce, and arranging for Peirce to be paid to give two series of lectures at or near Harvard (1898 and 1903). Most important, each year from 1907 until James's death in 1910, James wrote to his friends in the Boston intelligentsia to request financial aid for Peirce; the fund continued even after James died. Peirce reciprocated by designating James's eldest son as his heir should Juliette predecease him. It has been believed that this was also why Peirce used "Santiago" ("St. James" in English) as a middle name, but he appeared in print as early as 1890 as Charles Santiago Peirce. (See Charles Santiago Sanders Peirce for discussion and references).
Death and legacy
Peirce died destitute in Milford, Pennsylvania, twenty years before his widow. Juliette Peirce kept the urn with Peirce's ashes at Arisbe. In 1934, Pennsylvania Governor Gifford Pinchot arranged for Juliette's burial in Milford Cemetery. The urn with Peirce's ashes was interred with Juliette.
Bertrand Russell (1959) wrote "Beyond doubt [...] he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever". Russell and Whitehead's Principia Mathematica, published from 1910 to 1913, does not mention Peirce (Peirce's work was not widely known until later). A. N. Whitehead, while reading some of Peirce's unpublished manuscripts soon after arriving at Harvard in 1924, was struck by how Peirce had anticipated his own "process" thinking. (On Peirce and process metaphysics, see Lowe 1964. Yet Peirce's achievements were not immediately recognized. His imposing contemporaries William James and Josiah Royce admired him and Cassius Jackson Keyser, at Columbia and C. K. Ogden, wrote about Peirce with respect but to no immediate effect.
The first scholar to give Peirce his considered professional attention was Royce's student Morris Raphael Cohen, the editor of an anthology of Peirce's writings entitled Chance, Love, and Logic (1923), and the author of the first bibliography of Peirce's scattered writings. John Dewey studied under Peirce at Johns Hopkins. The publication of the first six volumes of Collected Papers (1931–1935) was the most important event to date in Peirce studies and one that Cohen made possible by raising the needed funds; however it did not prompt an outpouring of secondary studies. The editors of those volumes, Charles Hartshorne and Paul Weiss, did not become Peirce specialists. Early landmarks of the secondary literature include the monographs by Buchler (1939), Feibleman (1946), and Goudge (1950), the 1941 PhD thesis by Arthur W. Burks (who went on to edit volumes 7 and 8), and the studies edited by Wiener and Young (1952). The Charles S. Peirce Society was founded in 1946. Its Transactions, an academic quarterly specializing in Peirce's pragmatism and American philosophy has appeared since 1965. (See Phillips 2014, 62 for discussion of Peirce and Dewey relative to transactionalism.)
By 1943 such was Peirce's reputation, in the US at least, that ''Webster's Biographical Dictionary'' said that Peirce was "now regarded as the most original thinker and greatest logician of his time".
In 1949, while doing unrelated archival work, the historian of mathematics Carolyn Eisele (1902–2000) chanced on an autograph letter by Peirce. So began her forty years of research on Peirce, “the mathematician and scientist,” culminating in Eisele (1976, 1979, 1985). In 1952, the Scottish philosopher W. B. Gallie had his book Peirce and Pragmatism published, which introduced the work of Peirce to an international readership. A.J. Ayer, the English philosopher, provided the Editorial Foreword to Gallie's book. In it he credited Peirce's philosophy as being 'not only of great historical significance, as one of the original sources of American pragmatism, but also extremely important in itself.' Ayer concluded: 'it is clear from Professor Gallie’s exposition of his doctrines that he is a philosopher from whom we still have much to learn.'
Beginning around 1960, Max Fisch (1900-1995), the philosopher and historian of ideas, emerged as an authority on Peirce (Fisch, 1986). He included many of his relevant articles in a survey (Fisch 1986: 422–448) of the impact of Peirce's thought through 1983.
Peirce has gained an international following, marked by university research centers devoted to Peirce studies and pragmatism in Brazil (CeneP/CIEP and Centro de Estudos de Pragmatismo), Finland (HPRC and ), Germany (Wirth's group, Hoffman's and Otte's group, and Deuser's and Härle's group), France (L'I.R.S.C.E.), Spain (GEP), and Italy (CSP). His writings have been translated into several languages, including German, French, Finnish, Spanish, and Swedish. Since 1950, there have been French, Italian, Spanish, British, and Brazilian Peirce scholars of note. For many years, the North American philosophy department most devoted to Peirce was the University of Toronto, thanks in part to the leadership of Thomas Goudge and David Savan. In recent years, U.S. Peirce scholars have clustered at Indiana University – Purdue University Indianapolis, home of the Peirce Edition Project (PEP) –, and Pennsylvania State University.
Peirce's reputation rests largely on academic papers published in American scientific and scholarly journals such as Proceedings of the American Academy of Arts and Sciences, the Journal of Speculative Philosophy, The Monist, Popular Science Monthly, the American Journal of Mathematics, Memoirs of the National Academy of Sciences, The Nation, and others. See Articles by Peirce, published in his lifetime for an extensive list with links to them online. The only full-length book (neither extract nor pamphlet) that Peirce authored and saw published in his lifetime was Photometric Researches (1878), a 181-page monograph on the applications of spectrographic methods to astronomy. While at Johns Hopkins, he edited Studies in Logic (1883), containing chapters by himself and his graduate students. Besides lectures during his years (1879–1884) as lecturer in Logic at Johns Hopkins, he gave at least nine series of lectures, many now published; see Lectures by Peirce.
After Peirce's death, Harvard University obtained from Peirce's widow the papers found in his study, but did not microfilm them until 1964. Only after Richard Robin (1967) catalogued this Nachlass did it become clear that Peirce had left approximately 1,650 unpublished manuscripts, totaling over 100,000 pages, mostly still unpublished except on microfilm. On the vicissitudes of Peirce's papers, see Houser (1989). Reportedly the papers remain in unsatisfactory condition.
The first published anthology of Peirce's articles was the one-volume Chance, Love and Logic: Philosophical Essays, edited by Morris Raphael Cohen, 1923, still in print. Other one-volume anthologies were published in 1940, 1957, 1958, 1972, 1994, and 2009, most still in print. The main posthumous editions of Peirce's works in their long trek to light, often multi-volume, and some still in print, have included:
1931–1958: Collected Papers of Charles Sanders Peirce (CP), 8 volumes, includes many published works, along with a selection of previously unpublished work and a smattering of his correspondence. This long-time standard edition drawn from Peirce's work from the 1860s to 1913 remains the most comprehensive survey of his prolific output from 1893 to 1913. It is organized thematically, but texts (including lecture series) are often split up across volumes, while texts from various stages in Peirce's development are often combined, requiring frequent visits to editors' notes. Edited (1–6) by Charles Hartshorne and Paul Weiss and (7–8) by Arthur Burks, in print and online.
1975–1987: Charles Sanders Peirce: Contributions to The Nation, 4 volumes, includes Peirce's more than 300 reviews and articles published 1869–1908 in The Nation. Edited by Kenneth Laine Ketner and James Edward Cook, online.
1976: The New Elements of Mathematics by Charles S. Peirce, 4 volumes in 5, included many previously unpublished Peirce manuscripts on mathematical subjects, along with Peirce's important published mathematical articles. Edited by Carolyn Eisele, back in print.
1977: Semiotic and Significs: The Correspondence between C. S. Peirce and Victoria Lady Welby (2nd edition 2001), included Peirce's entire correspondence (1903–1912) with Victoria, Lady Welby. Peirce's other published correspondence is largely limited to the 14 letters included in volume 8 of the Collected Papers, and the 20-odd pre-1890 items included so far in the Writings. Edited by Charles S. Hardwick with James Cook, out of print.
1982–now: Writings of Charles S. Peirce, A Chronological Edition (W), Volumes 1–6 & 8, of a projected 30. The limited coverage, and defective editing and organization, of the Collected Papers led Max Fisch and others in the 1970s to found the [http://peirce.iupui.edu/ Peirce Edition Project] (PEP), whose mission is to prepare a more complete critical chronological edition. Only seven volumes have appeared to date, but they cover the period from 1859 to 1892, when Peirce carried out much of his best-known work. Writings of Charles S. Peirce, 8 was published in November 2010; and work continues on Writings of Charles S. Peirce, 7, 9, and 11. In print and online.
1985: ''Historical Perspectives on Peirce's Logic of Science: A History of Science, 2 volumes. Auspitz has said, "The extent of Peirce's immersion in the science of his day is evident in his reviews in the Nation [...] and in his papers, grant applications, and publishers' prospectuses in the history and practice of science", referring latterly to Historical Perspectives. Edited by Carolyn Eisele, back in print.
1992: Reasoning and the Logic of Things collects in one place Peirce's 1898 series of lectures invited by William James. Edited by Kenneth Laine Ketner, with commentary by Hilary Putnam, in print.
1992–1998: The Essential Peirce (EP), 2 volumes, is an important recent sampler of Peirce's philosophical writings. Edited (1) by Nathan Hauser and Christian Kloesel and (2) by Peirce Edition Project editors, in print.
1997: Pragmatism as a Principle and Method of Right Thinking collects Peirce's 1903 Harvard "Lectures on Pragmatism" in a study edition, including drafts, of Peirce's lecture manuscripts, which had been previously published in abridged form; the lectures now also appear in The Essential Peirce, 2. Edited by Patricia Ann Turisi, in print.
2010: Philosophy of Mathematics: Selected Writings collects important writings by Peirce on the subject, many not previously in print. Edited by Matthew E. Moore, in print.
Mathematics
Peirce's most important work in pure mathematics was in logical and foundational areas. He also worked on linear algebra, matrices, various geometries, topology and Listing numbers, Bell numbers, graphs, the four-color problem, and the nature of continuity.
He worked on applied mathematics in economics, engineering, and map projections, and was especially active in probability and statistics.
;Discoveries
<div style"float:right;width:8.5em;text-align:center;margin-right:20px;border:solid 1px #bbb"><div style"margin:2px;background-color:#dddddd;font-size:40pt;height:50pt;line-height:100%">↓</div> <div style="font-size:8pt;line-height:150%">The Peirce arrow, <br>symbol for "(neither) ... nor ...", also called the Quine dagger</div></div>
Peirce made a number of striking discoveries in formal logic and foundational mathematics, nearly all of which came to be appreciated only long after he died:
In 1860, he suggested a cardinal arithmetic for infinite numbers, years before any work by Georg Cantor (who completed his dissertation in 1867) and without access to Bernard Bolzano's 1851 (posthumous) Paradoxien des Unendlichen.
In 1880–1881, he showed how Boolean algebra could be done via a repeated sufficient single binary operation (logical NOR), anticipating Henry M. Sheffer by 33 years. (See also De Morgan's Laws.)
In 1881, he set out the axiomatization of natural number arithmetic, a few years before Richard Dedekind and Giuseppe Peano. In the same paper Peirce gave, years before Dedekind, the first purely cardinal definition of a finite set in the sense now known as "Dedekind-finite", and implied by the same stroke an important formal definition of an infinite set (Dedekind-infinite), as a set that can be put into a one-to-one correspondence with one of its proper subsets.
In 1885, he distinguished between first-order and second-order quantification. In the same paper he set out what can be read as the first (primitive) axiomatic set theory, anticipating Zermelo by about two decades (Brady 2000, pp. 132–133).
s: Alpha graphs]]
In 1886, he saw that Boolean calculations could be carried out via electrical switches, he was devising existential graphs, a diagrammatic notation for the predicate calculus. Based on them are John F. Sowa's conceptual graphs and Sun-Joo Shin's diagrammatic reasoning.
;The New Elements of Mathematics
Peirce wrote drafts for an introductory textbook, with the working title The New Elements of Mathematics, that presented mathematics from an original standpoint. Those drafts and many other of his previously unpublished mathematical manuscripts finally appeared
Mathematics of logic
<div style="padding:5px;width:40%;border: 1px solid #a2a9b1; float:right;">Mathematical logic and foundations, some noted articles
* "On an Improvement in Boole's Calculus of Logic" (1867)
* "Description of a Notation for the Logic of Relatives" (1870)
* "On the Algebra of Logic" (1880)
* "A Boolian Algebra with One Constant" (1880 MS)
* "On the Logic of Number" (1881)
* "Note B: The Logic of Relatives" (1883)
* "On the Algebra of Logic: A Contribution to the Philosophy of Notation" (1884/1885)
* "The Logic of Relatives" (1897)
* "The Simplest Mathematics" (1902 MS)
* "Prolegomena to an Apology for Pragmaticism" (1906, on existential graphs)
</div>
Probability and statistics
Peirce held that science achieves statistical probabilities, not certainties, and that spontaneity ("absolute chance") is real (see Tychism on his view). Most of his statistical writings promote the frequency interpretation of probability (objective ratios of cases), and many of his writings express skepticism about (and criticize the use of) probability when such models are not based on objective randomization. Though Peirce was largely a frequentist, his possible world semantics introduced the "propensity" theory of probability before Karl Popper. Peirce (sometimes with Joseph Jastrow) investigated the probability judgments of experimental subjects, "perhaps the very first" elicitation and estimation of subjective probabilities in experimental psychology and (what came to be called) Bayesian statistics. (Hacking 1990:205) and pragmatism commits one to anti-nominalist belief in the reality of the general (CP 5.453–457).
For Peirce, First Philosophy, which he also called cenoscopy, is less basic than mathematics and more basic than the special sciences (of nature and mind). It studies positive phenomena in general, phenomena available to any person at any waking moment, and does not settle questions by resorting to special experiences. He divided such philosophy into (1) phenomenology (which he also called phaneroscopy or categorics), (2) normative sciences (esthetics, ethics, and logic), and (3) metaphysics; his views on them are discussed in order below.
Peirce did not write extensively in aesthetics and ethics, but came by 1902 to hold that aesthetics, ethics, and logic, in that order, comprise the normative sciences. He characterized aesthetics as the study of the good (grasped as the admirable), and thus of the ends governing all conduct and thought.
Influence and legacy
Umberto Eco described Peirce as "undoubtedly the greatest unpublished writer of our generation" and by Karl Popper as "one of the greatest philosophers of all time". The Internet Encyclopedia of Philosophy says of Peirce that although "long considered an eccentric figure whose contribution to pragmatism was to provide its name and whose importance was as an influence upon James and Dewey, Peirce's significance in his own right is now largely accepted."
Pragmatism
<div style="padding:5px;font-size:94%;max-width:22em; border: 1px solid #a2a9b1; float:right;">Some noted articles and lectures
* Illustrations of the Logic of Science (1877–1878): <br>inquiry, pragmatism, statistics, inference
# The Fixation of Belief (1877)
# How to Make Our Ideas Clear (1878)
# The Doctrine of Chances (1878)
# The Probability of Induction (1878)
# The Order of Nature (1878)
# Deduction, Induction, and Hypothesis (1878)
* The Harvard lectures on pragmatism (1903)
* What Pragmatism Is (1905)
* Issues of Pragmaticism (1905)
* Pragmatism (1907 MS in The Essential Peirce, 2)</div> Peirce's recipe for pragmatic thinking, which he called pragmatism and, later, pragmaticism, is recapitulated in several versions of the so-called pragmatic maxim. Here is one of his more emphatic reiterations of it:
As a movement, pragmatism began in the early 1870s in discussions among Peirce, William James, and others in the Metaphysical Club. James among others regarded some articles by Peirce such as "The Fixation of Belief" (1877) and especially "How to Make Our Ideas Clear" (1878) as foundational to pragmatism. Peirce (CP 5.11–12), like James (Pragmatism: A New Name for Some Old Ways of Thinking, 1907), saw pragmatism as embodying familiar attitudes, in philosophy and elsewhere, elaborated into a new deliberate method for fruitful thinking about problems. Peirce differed from James and the early John Dewey, in some of their tangential enthusiasms, in being decidedly more rationalistic and realistic, in several senses of those terms, throughout the preponderance of his own philosophical moods.
In 1905 Peirce coined the new name pragmaticism "for the precise purpose of expressing the original definition", saying that "all went happily" with James's and F.C.S. Schiller's variant uses of the old name "pragmatism" and that he coined the new name because of the old name's growing use in "literary journals, where it gets abused". Yet he cited as causes, in a 1906 manuscript, his differences with James and Schiller and, in a 1908 publication, his differences with James as well as literary author Giovanni Papini's declaration of pragmatism's indefinability. Peirce in any case regarded his views that truth is immutable and infinity is real, as being opposed by the other pragmatists, but he remained allied with them on other issues.
Pragmatism begins with the idea that belief is that on which one is prepared to act. Peirce's pragmatism is a method of clarification of conceptions of objects. It equates any conception of an object to a conception of that object's effects to a general extent of the effects' conceivable implications for informed practice. It is a method of sorting out conceptual confusions occasioned, for example, by distinctions that make (sometimes needed) formal yet not practical differences. He formulated both pragmatism and statistical principles as aspects of scientific logic, in his "Illustrations of the Logic of Science" series of articles. In the second one, "How to Make Our Ideas Clear", Peirce discussed three grades of clearness of conception:
# Clearness of a conception familiar and readily used, even if unanalyzed and undeveloped.
# Clearness of a conception in virtue of clearness of its parts, in virtue of which logicians called an idea "distinct", that is, clarified by analysis of just what makes it applicable. Elsewhere, echoing Kant, Peirce called a likewise distinct definition "nominal" (CP 5.553).
# Clearness in virtue of clearness of conceivable practical implications of the object's conceived effects, such that fosters fruitful reasoning, especially on difficult problems. Here he introduced that which he later called the pragmatic maxim.
By way of example of how to clarify conceptions, he addressed conceptions about truth and the real as questions of the presuppositions of reasoning in general. In clearness's second grade (the "nominal" grade), he defined truth as a sign's correspondence to its object, and the real as the object of such correspondence, such that truth and the real are independent of that which you or I or any actual, definite community of inquirers think. After that needful but confined step, next in clearness's third grade (the pragmatic, practice-oriented grade) he defined truth as that opinion which would be reached, sooner or later but still inevitably, by research taken far enough, such that the real does depend on that ideal final opinion—a dependence to which he appeals in theoretical arguments elsewhere, for instance for the long-run validity of the rule of induction. Peirce argued that even to argue against the independence and discoverability of truth and the real is to presuppose that there is, about that very question under argument, a truth with just such independence and discoverability.
Peirce said that a conception's meaning consists in "all general modes of rational conduct" implied by "acceptance" of the conception—that is, if one were to accept, first of all, the conception as true, then what could one conceive to be consequent general modes of rational conduct by all who accept the conception as true?—the whole of such consequent general modes is the whole meaning. His pragmatism does not equate a conception's meaning, its intellectual purport, with the conceived benefit or cost of the conception itself, like a meme (or, say, propaganda), outside the perspective of its being true, nor, since a conception is general, is its meaning equated with any definite set of actual consequences or upshots corroborating or undermining the conception or its worth. His pragmatism also bears no resemblance to "vulgar" pragmatism, which misleadingly connotes a ruthless and Machiavellian search for mercenary or political advantage. Instead the pragmatic maxim is the heart of his pragmatism as a method of experimentational mental reflection arriving at conceptions in terms of conceivable confirmatory and disconfirmatory circumstances—a method hospitable to the formation of explanatory hypotheses, and conducive to the use and improvement of verification.
Peirce's pragmatism, as method and theory of definitions and conceptual clearness, is part of his theory of inquiry, which he variously called speculative, general, formal or universal rhetoric or simply methodeutic. He applied his pragmatism as a method throughout his work.Theory of inquiry
In "The Fixation of Belief" (1877), Peirce gives his take on the psychological origin and aim of inquiry. On his view, individuals are motivated to inquiry by desire to escape the feelings of anxiety and unease which Peirce takes to be characteristic of the state of doubt. Doubt is described by Peirce as an "uneasy and dissatisfied state from which we struggle to free ourselves and pass into the state of belief." Peirce uses words like "irritation" to describe the experience of being in doubt and to explain why he thinks we find such experiences to be motivating. The irritating feeling of doubt is appeased, Peirce says, through our efforts to achieve a settled state of satisfaction with what we land on as our answer to the question which led to that doubt in the first place. This settled state, namely, belief, is described by Peirce as "a calm and satisfactory state which we do not wish to avoid." Our efforts to achieve the satisfaction of belief, by whichever methods we may pursue, are what Peirce calls "inquiry". Four methods which Peirce describes as having been actually pursued throughout the history of thought are summarized below in the section after next.
Critical common-sensism
Critical common-sensism, treated by Peirce as a consequence of his pragmatism, is his combination of Thomas Reid's common-sense philosophy with a fallibilism that recognizes that propositions of our more or less vague common sense now indubitable may later come into question, for example because of transformations of our world through science. It includes efforts to raise genuine doubts in tests for a core group of common indubitables that change slowly, if at all.
Rival methods of inquiry
In "The Fixation of Belief" (1877), Peirce described inquiry in general not as the pursuit of truth per se but as the struggle to move from irritating, inhibitory doubt born of surprise, disagreement, and the like, and to reach a secure belief, belief being that on which one is prepared to act. That let Peirce frame scientific inquiry as part of a broader spectrum and as spurred, like inquiry generally, by actual doubt, not mere verbal, quarrelsome, or hyperbolic doubt, which he held to be fruitless. Peirce sketched four methods of settling opinion, ordered from least to most successful:
# The method of (policy of sticking to initial belief) – which brings comforts and decisiveness but leads to trying to ignore contrary information and others' views as if truth were intrinsically private, not public. The method goes against the social impulse and easily falters since one may well notice when another's opinion seems as good as one's own initial opinion. Its successes can be brilliant but tend to be transitory.
# The method of – which overcomes disagreements but sometimes brutally. Its successes can be majestic and long-lasting, but it cannot regulate people thoroughly enough to withstand doubts indefinitely, especially when people learn about other societies present and past.
# The method of the – which promotes conformity less brutally but fosters opinions as something like tastes, arising in conversation and comparisons of perspectives in terms of "what is agreeable to reason". Thereby it depends on fashion in paradigms and goes in circles over time. It is more intellectual and respectable but, like the first two methods, sustains accidental and capricious beliefs, destining some minds to doubt it.
# The method of – wherein inquiry supposes that the real is discoverable but independent of particular opinion, such that, unlike in the other methods, inquiry can, by its own account, go wrong (fallibilism), not only right, and thus purposely tests itself and criticizes, corrects, and improves itself.
Peirce held that, in practical affairs, slow and stumbling ratiocination is often dangerously inferior to instinct and traditional sentiment, and that the scientific method is best suited to theoretical research, which in turn should not be trammeled by the other methods and practical ends; reason's "first rule" is summarized below (except as otherwise noted). There he also reviewed plausibility and inductive precision (issues of critique of arguments).
# Abductive (or retroductive) phase. Guessing, inference to explanatory hypotheses for selection of those best worth trying. From abduction, Peirce distinguishes induction as inferring, on the basis of tests, the proportion of truth in the hypothesis. Every inquiry, whether into ideas, brute facts, or norms and laws, arises from surprising observations in one or more of those realms (and for example at any stage of an inquiry already underway). All explanatory content of theories comes from abduction, which guesses a new or outside idea so as to account in a simple, economical way for a surprising or complicated phenomenon. The modicum of success in our guesses far exceeds that of random luck, and seems born of attunement to nature by developed or inherent instincts, especially insofar as best guesses are optimally plausible and simple in the sense of the "facile and natural", as by Galileo's natural light of reason and as distinct from "logical simplicity". Abduction is the most fertile but least secure mode of inference. Its general rationale is inductive: it succeeds often enough and it has no substitute in expediting us toward new truths. In 1903, Peirce called pragmatism "the logic of abduction". Coordinative method leads from abducting a plausible hypothesis to judging it for its testability and for how its trial would economize inquiry itself. The hypothesis, being insecure, needs to have practical implications leading at least to mental tests and, in science, lending themselves to scientific tests. A simple but unlikely guess, if not costly to test for falsity, may belong first in line for testing. A guess is intrinsically worth testing if it has plausibility or reasoned objective probability, while subjective likelihood, though reasoned, can be misleadingly seductive. Guesses can be selected for trial strategically, for their caution (for which Peirce gave as example the game of Twenty Questions), breadth, or incomplexity. One can discover only that which would be revealed through their sufficient experience anyway, and so the point is to expedite it; economy of research demands the leap, so to speak, of abduction and governs its art. In 1893, Peirce restated most of it for a less advanced audience.
Logic, or semiotic
In 1918, the logician C. I. Lewis wrote, "The contributions of C.S. Peirce to symbolic logic are more numerous and varied than those of any other writer—at least in the nineteenth century."
Relational logic
Beginning with his first paper on the "Logic of Relatives" (1870), Peirce extended the theory of relations pioneered by Augustus De Morgan.
Logic as philosophical
Peirce regarded logic per se as a division of philosophy, as a normative science based on esthetics and ethics, as more basic than metaphysics, and as "the art of devising methods of research". More generally, as inference, "logic is rooted in the social principle", since inference depends on a standpoint that, in a sense, is unlimited. Peirce called (with no sense of deprecation) "mathematics of logic" much of the kind of thing which, in current research and applications, is called simply "logic". He was productive in both (philosophical) logic and logic's mathematics, which were connected deeply in his work and thought.
Peirce argued that logic is formal semiotic: the formal study of signs in the broadest sense, not only signs that are artificial, linguistic, or symbolic, but also signs that are semblances or are indexical such as reactions. Peirce held that "all this universe is perfused with signs, if it is not composed exclusively of signs", along with their representational and inferential relations. He argued that, since all thought takes time, all thought is in signs and sign processes ("semiosis") such as the inquiry process. He divided logic into: (1) speculative grammar, or stechiology, on how signs can be meaningful and, in relation to that, what kinds of signs there are, how they combine, and how some embody or incorporate others; (2) logical critic, or logic proper, on the modes of inference; and (3) speculative or universal rhetoric, or methodeutic,
Four incapacities
<div style="padding:5px;font-size:94%;width:auto; border: 1px solid #a2a9b1; float:right;">The Journal of Speculative Philosophy series (1868–1869), including
* Questions concerning certain Faculties claimed for Man (1868)
* Some Consequences of Four Incapacities (1868)
* Grounds of Validity of the Laws of Logic:<br>Further Consequences of Four Incapacities (1869)</div> In three articles in 1868–1869, Peirce rejected mere verbal or hyperbolic doubt and first or ultimate principles, and argued that we have (as he numbered them Logic as formal semiotic Peirce sought, through his wide-ranging studies through the decades, formal philosophical ways to articulate thought's processes, and also to explain the workings of science. These inextricably entangled questions of a dynamics of inquiry rooted in nature and nurture led him to develop his semiotic with very broadened conceptions of signs and inference, and, as its culmination, a theory of inquiry for the task of saying 'how science works' and devising research methods. This would be logic by the medieval definition taught for centuries: art of arts, science of sciences, having the way to the principles of all methods. As to signs in thought, Peirce emphasized the reverse: "To say, therefore, that thought cannot happen in an instant, but requires a time, is but another way of saying that every thought must be interpreted in another, or that all thought is in signs."—the focus is on sign action in general rather than on psychology, linguistics, or social studies (fields which he also pursued).
Inquiry is a kind of inference process, a manner of thinking and semiosis. Global divisions of ways for phenomena to stand as signs, and the subsumption of inquiry and thinking within inference as a sign process, enable the study of inquiry on semiotics' three levels:
# Conditions for meaningfulness. Study of significatory elements and combinations, their grammar.
# Validity, conditions for true representation. Critique of arguments in their various separate modes.
# Conditions for determining interpretations. Methodology of inquiry in its mutually interacting modes.
Peirce uses examples often from common experience, but defines and discusses such things as assertion and interpretation in terms of philosophical logic. In a formal vein, Peirce said:
Signs
Sign relation
Peirce's theory of signs is known to be one of the most complex semiotic theories due to its generalistic claim. Anything is a sign—not absolutely as itself, but instead in some relation or other. The sign relation is the key. It defines three roles encompassing (1) the sign, (2) the sign's subject matter, called its object, and (3) the sign's meaning or ramification as formed into a kind of effect called its interpretant (a further sign, for example a translation). It is an irreducible triadic relation, according to Peirce. The roles are distinct even when the things that fill those roles are not. The roles are but three; a sign of an object leads to one or more interpretants, and, as signs, they lead to further interpretants.
Extension × intension information. Two traditional approaches to sign relation, necessary though insufficient, are the way of extension (a sign's objects, also called breadth, denotation, or application) and the way of intension (the objects' characteristics, qualities, attributes referenced by the sign, also called depth, comprehension, significance, or connotation). Peirce adds a third, the way of information, including change of information, to integrate the other two approaches into a unified whole. For example, because of the equation above, if a term's total amount of information stays the same, then the more that the term 'intends' or signifies about objects, the fewer are the objects to which the term 'extends' or applies.
Determination. A sign depends on its object in such a way as to represent its object—the object enables and, in a sense, determines the sign. A physically causal sense of this stands out when a sign consists in an indicative reaction. The interpretant depends likewise on both the sign and the object—an object determines a sign to determine an interpretant. But this determination is not a succession of dyadic events, like a row of toppling dominoes; sign determination is triadic. For example, an interpretant does not merely represent something which represented an object; instead an interpretant represents something as a sign representing the object. The object (be it a quality or fact or law or even fictional) determines the sign to an interpretant through one's collateral experience with the object, in which the object is found or from which it is recalled, as when a sign consists in a chance semblance of an absent object. Peirce used the word "determine" not in a strictly deterministic sense, but in a sense of "specializes", bestimmt, involving variable amount, like an influence. Peirce came to define representation and interpretation in terms of (triadic) determination. The object determines the sign to determine another sign—the interpretant—to be related to the object as the sign is related to the object, hence the interpretant, fulfilling its function as sign of the object, determines a further interpretant sign. The process is logically structured to perpetuate itself, and is definitive of sign, object, and interpretant in general. As Peirce sometimes put it (he defined sign at least 76 times All of those are special or partial objects. The object most accurately is the universe of discourse to which the partial or special object belongs.
# An interpretant (or interpretant sign) is a sign's meaning or ramification as formed into a kind of idea or effect, an interpretation, human or otherwise. An interpretant is a sign (a) of the object and (b) of the interpretant's "predecessor" (the interpreted sign) as a sign of the same object. An interpretant either (i) is immediate to a sign and is a kind of quality or possibility such as a word's usual meaning, or (ii) is a dynamic interpretant, such as a state of agitation, or (iii) is a final or normal interpretant, a sum of the lessons which a sufficiently considered sign would have as effects on practice, and with which an actual interpretant may at most coincide.
Some of the understanding needed by the mind depends on familiarity with the object. To know what a given sign denotes, the mind needs some experience of that sign's object, experience outside of, and collateral to, that sign or sign system. In that context Peirce speaks of collateral experience, collateral observation, collateral acquaintance, all in much the same terms. This typology classifies every sign according to the sign's own phenomenological category—the qualisign is a quality, a possibility, a "First"; the sinsign is a reaction or resistance, a singular object, an actual event or fact, a "Second"; and the legisign is a habit, a rule, a representational relation, a "Third".
II. Icon, index, symbol: This typology, the best known one, classifies every sign according to the category of the sign's way of denoting its object—the icon (also called semblance or likeness) by a quality of its own, the index by factual connection to its object, and the symbol by a habit or rule for its interpretant.
III. Rheme, dicisign, argument (also called sumisign, dicisign, suadisign, also seme, pheme, delome, He does this by rearranging the rule (Barbara's major premise), the case (Barbara's minor premise), and the result (Barbara's conclusion):
Deduction.
Rule: All the beans from this bag are white. <br>
Case: These beans are beans from this bag. <br>
<math>\therefore</math> Result: These beans are white.
Induction.
Case: These beans are [randomly selected] from this bag.<br>
Result: These beans are white.<br>
<math>\therefore</math> Rule: All the beans from this bag are white.
Hypothesis (Abduction).
Rule: All the beans from this bag are white.<br>
Result: These beans [oddly] are white.<br>
<math>\therefore</math> Case: These beans are from this bag.
In 1883, in "A Theory of Probable Inference" (Studies in Logic), Peirce equated hypothetical inference with the induction of characters of objects (as he had done in effect before
The logical form does not also cover induction, since induction neither depends on surprise nor proposes a new idea for its conclusion. Induction seeks facts to test a hypothesis; abduction seeks a hypothesis to account for facts. "Deduction proves that something must be; Induction shows that something actually is operative; Abduction merely suggests that something may be." Peirce did not remain quite convinced that one logical form covers all abduction. In his methodeutic or theory of inquiry (see below), he portrayed abduction as an economic initiative to further inference and study, and portrayed all three modes as clarified by their coordination in essential roles in inquiry: hypothetical explanation, deductive prediction, inductive testing
Metaphysics
Peirce divided metaphysics into (1) ontology or general metaphysics, (2) psychical or religious metaphysics, and (3) physical metaphysics.
Ontology
On the issue of universals, Peirce was a scholastic realist, declaring the reality of generals as early as 1868. According to Peirce, his category he called "thirdness", the more general facts about the world, are extra-mental realities. Regarding modalities (possibility, necessity, etc.), he came in later years to regard himself as having wavered earlier as to just how positively real the modalities are. In his 1897 "The Logic of Relatives" he wrote:
Peirce retained, as useful for some purposes, the definitions in terms of information states, but insisted that the pragmaticist is committed to a strong modal realism by conceiving of objects in terms of predictive general conditional propositions about how they would behave under certain circumstances.
Continua
Continuity and synechism are central in Peirce's philosophy: "I did not at first suppose that it was, as I gradually came to find it, the master-Key of philosophy".
From a mathematical point of view, he embraced infinitesimals and worked long on the mathematics of continua. He long held that the real numbers constitute a pseudo-continuum; that a true continuum is the real subject matter of analysis situs (topology); and that a true continuum of instants exceeds—and within any lapse of time has room for—any Aleph number (any infinite multitude as he called it) of instants.
In 1908 Peirce wrote that he found that a true continuum might have or lack such room. Jérôme Havenel (2008): "It is on 26 May 1908, that Peirce finally gave up his idea that in every continuum there is room for whatever collection of any multitude. From now on, there are different kinds of continua, which have different properties."
Psychical or religious metaphysics
Peirce believed in God, and characterized such belief as founded in an instinct explorable in musing over the worlds of ideas, brute facts, and evolving habits—and it is a belief in God not as an actual or existent being (in Peirce's sense of those words), but all the same as a real being. In "A Neglected Argument for the Reality of God" (1908), and (see Synechism) that there is at least an attenuated kind of immortality.
Physical metaphysics
Peirce held the view, which he called objective idealism, that "matter is effete mind, inveterate habits becoming physical laws". Peirce observed that "Berkeley's metaphysical theories have at first sight an air of paradox and levity very unbecoming to a bishop".
Peirce asserted the reality of (1) "absolute chance" or randomness (his tychist view), (2) "mechanical necessity" or physical laws (anancist view), and (3) what he called the "law of love" (agapist view), echoing his categories Firstness, Secondness, and Thirdness, respectively. of the cosmos and its parts. He found his conception of agapasm embodied in Lamarckian evolution; the overall idea in any case is that of evolution tending toward an end or goal, and it could also be the evolution of a mind or a society; it is the kind of evolution which manifests workings of mind in some general sense. He said that overall he was a synechist, holding with reality of continuity, especially of space, time, and law.
Some noted articles
* The Monist Metaphysical Series (1891–1893)
** The Architecture of Theories (1891)
** The Doctrine of Necessity Examined (1892)
** The Law of Mind (1892)
** Man's Glassy Essence (1892)
** Evolutionary Love (1893)
* Immortality in the Light of Synechism (1893 MS)
Philosophy of science
Peirce outlined two fields, "Cenoscopy" and "Science of Review", both of which he called philosophy. Both included philosophy about science. In 1903 he arranged them, from more to less theoretically basic, thus:<ref name="phil"/>
# Science of Discovery.
## Mathematics.
## Cenoscopy (philosophy as discussed earlier in this article – categorial, normative, metaphysical), as First Philosophy, concerns positive phenomena in general, does not rely on findings from special sciences, and includes the general study of inquiry and scientific method.
## Idioscopy, or the Special Sciences (of nature and mind).
# Science of Review, as Ultimate Philosophy, arranges "... the results of discovery, beginning with digests, and going on to endeavor to form a philosophy of science". His examples included Humboldt's Cosmos, Comte's Philosophie positive, and Spencer's Synthetic Philosophy.
# Practical Science, or the Arts.
Peirce placed, within Science of Review, the work and theory of classifying the sciences (including mathematics and philosophy). His classifications, on which he worked for many years, draw on argument and wide knowledge, and are of interest both as a map for navigating his philosophy and as an accomplished polymath's survey of research in his time.
See also
* Howland will forgery trial
* Hypostatic abstraction
*
* Laws of Form
* List of American philosophers
* Logical machine
* Logical matrix
* Mathematical psychology
*
* Peircean realism
* Pragmatics
*
*
* Relation algebra
* Truth table
* Philosophy of science
Contemporaries associated with Peirce
* Oliver Wendell Holmes Jr.
* George Herbert Mead
Notes
References
External links
* [https://arisbe.sitehost.iu.edu/ Arisbe: The Peirce Gateway], Joseph Ransdell, ed. . Includes over 100 annotated writings by Peirce, hundreds of papers on Peirce, and archives of a Peirce email forum.
* [https://web.archive.org/web/20030806032358/http://www.indiana.edu/~sign/ Center for Applied Semiotics (CAS)] (1998–2003), Donald Cunningham & Jean Umiker-Sebeok, Indiana U.
* and previously et al., Pontifical Catholic U. of (PUC-SP), Brazil. In Portuguese, some English.
* [https://www.pragmatismopucsp.com.br/ Centro de Estudos de Pragmatismo] (CEP), Ivo Assad Ibri, Pontifical Catholic U. of São Paulo (PUC-SP), Brazil. In Portuguese.
*"[https://web.archive.org/web/20071011065724/http://revistas.pucsp.br/index.php/cognitiofilosofia/about Cognitio ]". Journal on Pragmatism organized by the Centre for Pragmatism Studies (PPG-Fil, PUC-SP)
* [http://www.commens.org/ Commens Digital Companion to C.S. Peirce], Mats Bergman, Sami Paavola, & , formerly [https://web.archive.org/web/20140121203128/http://www.helsinki.fi/science/commens/index.html Commens at Helsinki U]. Includes Commens Dictionary of Peirce's Terms with Peirce's definitions, often many per term across the decades, and the Digital Encyclopedia of Charles S. Peirce (old edition still at old website).
* [http://www.filosofia.unimi.it/peirce/ Peirce] , Carlo Sini, Rossella Fabbrichesi, et al., U. of Milan, Italy. In Italian and English. Part of [http://www.associazionepragma.com/ Pragma].
* [http://www.peirce-foundation.org/ Charles S. Peirce Foundation]. Co-sponsoring the 2014 Peirce International Centennial Congress (100th anniversary of Peirce's death).
* [http://www.peircesociety.org/ Charles S. Peirce Society]<br>[https://web.archive.org/web/20071011065724/http://peircesociety.org/transactions.html Transactions of the Charles S. Peirce Society]. Quarterly journal of Peirce studies since spring 1965. [https://web.archive.org/web/20091203103238/http://www.peircesociety.org/contents.html Table of Contents] of all issues.
* [http://www.peirce.org/ Charles S. Peirce Studies], Brian Kariger, ed.
*
* [http://translate.google.com/translate?hlen&slde&uhttp://bildakt-verkoerperung.de/forschungsschwerpunkte/ Collegium for the Advanced Study of Picture Act and Embodiment]: The Peirce Archive. Humboldt U, Berlin, Germany. Cataloguing Peirce's innumerable drawings & graphic materials. [https://web.archive.org/web/20110707185056/http://www.audsisselhoel.com/wordpress/?p69 More info] (Prof. Aud Sissel Hoel).
* [http://www.digitalpeirce.fee.unicamp.br/ Digital Encyclopedia of Charles S. Peirce], ([https://ufjf.academia.edu/JoaoQueiroz now at UFJF]) & Ricardo Gudwin ([http://www.dca.fee.unicamp.br/~gudwin/ at Unicamp]), eds., Universidade Estadual de Campinas (Portuguese), Brazil, in English. 84 authors listed, 51 papers online & more listed, as of January 31, 2009. Newer edition now at Commens Digital Companion to C.S. Peirce.
* [https://web.archive.org/web/20050901083355/http://www.existentialgraphs.com/ Existential Graphs], Jay Zeman, ed., U. of Florida. Has 4 Peirce texts.
* , ed., U. of Navarra, Spain. Big study site, Peirce & others in Spanish & English, bibliography, more.
* [http://www.helsinki.fi/peirce/ Helsinki Peirce Research Center] (HPRC), Ahti-Veikko Pietarinen et al., U. of Helsinki.
* [http://www.wyttynys.net/ His Glassy Essence]. Autobiographical Peirce. Kenneth Laine Ketner.
* [http://www.pragmaticism.net/ Institute for Studies in Pragmaticism], Kenneth Laine Ketner, Clyde Hendrick, et al., Texas Tech U. Peirce's life and works.
* [https://web.archive.org/web/*/http://www.rz.uni-frankfurt.de/~wirth International Research Group on Abductive Inference], et al., eds., U., Frankfurt, Germany. Uses frames. Click on link at bottom of its home page for English. Moved to U. of Gießen, Germany, [https://web.archive.org/web/20131103211119/http://www.abduktionsforschung.de/abduktionsforschung.html home page] not in English but see Artikel section there.
* [https://hiphilangsci.net/2024/04/01/podcast-episode-38/ Interview with Dan Everett on C.S. Peirce and Peircean linguistics] (2024) – Dan Everett talks to James McElvenny about Peirce in the History and Philosophy of the Language Sciences podcast series.
* [https://web.archive.org/web/20070717060233/http://webup.univ-perp.fr/lsh/rch/semiotics/irsce/irsce.html L'I.R.S.C.E.] (1974–2003) – , U. of , France.
* [https://web.archive.org/web/20131102231348/http://www.minutesemeiotic.org/?lang=en Minute Semeiotic], , U. of , Brazil. English, Portuguese.
* [https://web.archive.org/web/20120711014221/http://www.signosemio.com/peirce/a_peirce.asp Peirce] at Signo: Theoretical Semiotics on the Web, Louis Hébert, director, supported by U. of Québec. Theory, application, exercises of Peirce's [https://web.archive.org/web/20120711003648/http://www.signosemio.com/peirce/a_semiotique.asp Semiotics] and [https://web.archive.org/web/20120711003340/http://www.signosemio.com/peirce/a_esthetique.asp Esthetics]. English, French.
* [http://www.iupui.edu/~peirce/ Peirce Edition Project (PEP)] , Indiana U.–Purdue U. Indianapolis (IUPUI). André De Tienne, Nathan Houser, et al. Editors of the Writings of Charles S. Peirce (W) and The Essential Peirce (EP) v. 2. Many study aids such as the Robin Catalog of Peirce's manuscripts & letters and:<br>Biographical introductions to [http://www.iupui.edu/~peirce/ep/ep.htm EP 1–2] and [http://www.iupui.edu/~peirce/writings/crit.htm W 1–6] & [http://www.iupui.edu/~peirce/houserintro.html 8]<br>[http://www.iupui.edu/%7Epeirce/writings/v2/toc2.htm Most of Writings of Charles S. Peirce, 2] readable online.<br>[https://web.archive.org/web/20020328213928/http://www.pep.uqam.ca/ PEP's branch at ]. Working on Writings of Charles S. Peirce, 7: Peirce's work on the Century Dictionary. [https://web.archive.org/web/20160304044756/http://www.pep.uqam.ca/definitionoftheweek.pep Definition of the week].
* [http://www.dr-dau.net/eg_readings.shtml Peirce's Existential Graphs], Frithjof Dau, Germany
* [http://peirce.unimi.it/en Peirce Research Group], Department of Philosophy "Piero Martinetti" – University of Milan, Italy.
* [http://www.pragmatism.org/ Pragmatism Cybrary], David Hildebrand & John Shook.
* [https://web.archive.org/web/19970519142208/http://www.uni-bielefeld.de/idm/eng/arbeit/agsem.htm Research Group on Semiotic Epistemology and Mathematics Education] (late 1990s), Germany). See Peirce Project Newsletter v. 3, n. 1, [http://www.iupui.edu/~peirce/news/3_1/3_1pdf/Page13.pdf p. 13].
* [http://perso.numericable.fr/robert.marty/semiotique/anglais.htm Semiotics according to Robert Marty], with [http://perso.numericable.fr/robert.marty/semiotique/access.htm 76 definitions of the sign by C. S. Peirce].
*
*
*
Category:1839 births
Category:1914 deaths
Category:19th-century American mathematicians
Category:19th-century American philosophers
Category:20th-century American mathematicians
Category:20th-century American philosophers
Category:American Episcopalians
Category:American logicians
Category:American semioticians
Category:American statisticians
Category:Analytic philosophers
Category:Anglican philosophers
Category:Communication scholars
Category:Critical theorists
Category:American epistemologists
Category:Fellows of the American Academy of Arts and Sciences
Category:Harvard John A. Paulson School of Engineering and Applied Sciences alumni
Category:Idealists
Category:Johns Hopkins University faculty
Category:Lattice theorists
Category:Mathematicians from Massachusetts
Category:Members of the United States National Academy of Sciences
Category:Modal logicians
Category:The Nation (U.S. magazine) people
Category:Ontologists
Category:Panpsychism
Category:People from Cambridge, Massachusetts
Category:Philosophers from Massachusetts
Category:Philosophers from Pennsylvania
Category:American philosophers of education
Category:American philosophers of language
Category:American philosophers of mathematics
Category:American philosophers of mind
Category:American philosophers of science
Category:Philosophical theists
Category:Pragmatists
Category:Semioticians
Category:United States Coast Survey personnel
Category:United States Coast and Geodetic Survey personnel
|
https://en.wikipedia.org/wiki/Charles_Sanders_Peirce
|
2025-04-05T18:27:43.346058
|
6118
|
Carnot heat engine
|
cross section of Carnot's heat engine. In this diagram, abgh is a cylindrical vessel, cd is a movable piston, and A and B are constant–temperature bodies. The vessel may be placed in contact with either body or removed from both (as it is here). ]]
A Carnot heat engine is a theoretical heat engine that operates on the Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded by Benoît Paul Émile Clapeyron in 1834 and mathematically explored by Rudolf Clausius in 1857, work that led to the fundamental thermodynamic concept of entropy. The Carnot engine is the most efficient heat engine which is theoretically possible. The efficiency depends only upon the absolute temperatures of the hot and cold heat reservoirs between which it operates.
A heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work. The cycle may also be reversed. The system may be worked upon by an external force, and in the process, it can transfer thermal energy from a cooler system to a warmer one, thereby acting as a refrigerator or heat pump rather than a heat engine.
Every thermodynamic system exists in a particular state. A thermodynamic cycle occurs when a system is taken through a series of different states, and finally returned to its initial state. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine.
The Carnot engine is a theoretical construct, useful for exploring the efficiency limits of other heat engines. An actual Carnot engine, however, would be completely impractical to build.
Carnot's diagram
In the adjacent diagram, from Carnot's 1824 work, Reflections on the Motive Power of Fire, there are "two bodies A and B, kept each at a constant temperature, that of A being higher than that of B. These two bodies to which we can give, or from which we can remove the heat without causing their temperatures to vary, exercise the functions of two unlimited reservoirs of caloric. We will call the first the furnace and the second the refrigerator." Carnot then explains how we can obtain motive power, i.e., "work", by carrying a certain quantity of heat from body A to body B.
It also acts as a cooler and hence can also act as a refrigerator.
Modern diagram
W on the surroundings, via cycles of contractions and expansions.]]
The previous image shows the original piston-and-cylinder diagram used by Carnot in discussing his ideal engine. The figure at right shows a block diagram of a generic heat engine, such as the Carnot engine. In the diagram, the "working body" (system), a term introduced by Clausius in 1850, can be any fluid or vapor body through which heat Q can be introduced or transmitted to produce work. Carnot had postulated that the fluid body could be any substance capable of expansion, such as vapor of water, vapor of alcohol, vapor of mercury, a permanent gas, air, etc. Although in those early years, engines came in a number of configurations, typically Q<sub>H</sub> was supplied by a boiler, wherein water was boiled over a furnace; Q<sub>C</sub> was typically removed by a stream of cold flowing water in the form of a condenser located on a separate part of the engine. The output work, W, is transmitted by the movement of the piston as it is used to turn a crank-arm, which in turn was typically used to power a pulley so as to lift water out of flooded salt mines. Carnot defined work as "weight lifted through a height".
<!-- Until this section text gets longer, please leave this space for the right-justified image -->
Carnot cycle
to illustrate the work done.]]
The Carnot cycle when acting as a heat engine consists of the following steps:
# Reversible isothermal expansion of the gas at the "hot" temperature, }} (isothermal heat addition or absorption). During this step ( to ) the gas is allowed to expand and it does work on the surroundings. The temperature of the gas (the system) does not change during the process, and thus the expansion is isothermic. The gas expansion is propelled by absorption of heat energy }} and of entropy / }} from the high temperature reservoir.
# Isentropic (reversible adiabatic) expansion of the gas (isentropic work output). For this step ( to ) the piston and cylinder are assumed to be thermally insulated, thus they neither gain nor lose heat. The gas continues to expand, doing work on the surroundings, and losing an equivalent amount of internal energy. The gas expansion causes it to cool to the "cold" temperature, }}. The entropy remains unchanged.
# Reversible isothermal compression of the gas at the "cold" temperature, }} (isothermal heat rejection) ( to ). Now the gas is exposed to the cold temperature reservoir while the surroundings do work on the gas by compressing it (such as through the return compression of a piston), while causing an amount of waste heat < 0}} (with the standard sign convention for heat) and of entropy / < 0}} to flow out of the gas to the low temperature reservoir. (In magnitude, this is the same amount of entropy absorbed in step 1. The entropy decreases in isothermal compression since the multiplicity of the system decreases with the volume.) In terms of magnitude, the recompression work performed by the surroundings in this step is less than the work performed on the surroundings in step 1 because it occurs at a lower pressure due to the lower temperature (i.e. the resistance to compression is lower under step 3 than the force of expansion under step 1). We can refer to the first law of thermodynamics to explain this behavior: + }}.
# Isentropic compression of the gas (isentropic work input) ( to ). Once again the piston and cylinder are assumed to be thermally insulated and the cold temperature reservoir is removed. During this step, the surroundings continue to do work to further compress the gas and both the temperature and pressure rise now that the heat sink has been removed. This additional work increases the internal energy of the gas, compressing it and causing the temperature to rise to }}. The entropy remains unchanged. At this point the gas is in the same state as at the start of step 1.
Carnot's theorem
. For this figure, the curve indicates a vapor-liquid equilibrium (See Rankine cycle). Irreversible systems and losses of heat (for example, due to friction) prevent the ideal from taking place at every step.]]
'''Carnot's theorem' is a formal statement of this fact: No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.''
<math display"block">\eta_{I}\frac{W}{Q_{\mathrm{H}}}1-\frac{T_{\mathrm{C}}}{T_{\mathrm{H}}}</math>Explanation
This maximum efficiency }} is defined as above:
* is the work done by the system (energy exiting the system as work),
* }} is the heat put into the system (heat energy entering the system),
* }} is the absolute temperature of the cold reservoir, and
* }} is the absolute temperature of the hot reservoir.
A corollary to Carnot's theorem states that: All reversible engines operating between the same heat reservoirs are equally efficient.
It is easily shown that the efficiency is maximum when the entire cyclic process is a reversible process. This means the total entropy of system and surroundings (the entropies of the hot furnace, the "working fluid" of the heat engine, and the cold sink) remains constant when the "working fluid" completes one cycle and returns to its original state. (In the general and more realistic case of an irreversible process, the total entropy of this combined system would increase.)
Since the "working fluid" comes back to the same state after one cycle, and entropy of the system is a state function, the change in entropy of the "working fluid" system is 0. Thus, it implies that the total entropy change of the furnace and sink is zero, for the process to be reversible and the efficiency of the engine to be maximum. This derivation is carried out in the next section.
The coefficient of performance (COP) of the heat engine is the reciprocal of its efficiency.
Efficiency of real heat engines
For a real heat engine, the total thermodynamic process is generally irreversible. The working fluid is brought back to its initial state after one cycle, and thus the change of entropy of the fluid system is 0, but the sum of the entropy changes in the hot and cold reservoir in this one cyclical process is greater than 0.
The internal energy of the fluid is also a state variable, so its total change in one cycle is 0. So the total work done by the system is equal to the net heat put into the system, the sum of <math> Q_\text{H} </math> > 0 taken up and the waste heat <math> Q_\text{C} </math> < 0 given off:
{{NumBlk2|:|<math> WQQ_\text{H}+Q_\text{C} </math> |LnSty=1px dashed |2}}
For real engines, stages 1 and 3 of the Carnot cycle, in which heat is absorbed by the "working fluid" from the hot reservoir, and released by it to the cold reservoir, respectively, no longer remain ideally reversible, and there is a temperature differential between the temperature of the reservoir and the temperature of the fluid while heat exchange takes place.
During heat transfer from the hot reservoir at <math>T_\text{H}</math> to the fluid, the fluid would have a slightly lower temperature than <math>T_\text{H}</math>, and the process for the fluid may not necessarily remain isothermal.
Let <math>\Delta S_\text{H}</math> be the total entropy change of the fluid in the process of intake of heat.
{{NumBlk2|:|<math>\Delta S_\text{H}\int_{Q_\text{in}} \frac{\text{d}Q_\text{H}}{T} </math> |LnSty1px dashed |3}}
where the temperature of the fluid is always slightly lesser than <math>T_\text{H}</math>, in this process.
So, one would get:
{T_\text{H}}\frac{\int \text{d}Q_\text{H}}{T_\text{H}} \leq \Delta S_\text{H} </math> |LnSty1px dashed |4}}
Similarly, at the time of heat injection from the fluid to the cold reservoir one would have, for the magnitude of total entropy change <math> \Delta S_\text{C} </math>< 0 of the fluid in the process of expelling heat:
{{NumBlk2|:|<math> \Delta S_\text{C}\geqslant\frac{Q_\text{C}}{T_\text{C}}< 0 </math> |LnSty=1px dashed |5}}
where, during this process of transfer of heat to the cold reservoir, the temperature of the fluid is always slightly greater than <math>T_\text{C}</math>.
We have only considered the magnitude of the entropy change here. Since the total change of entropy of the fluid system for the cyclic process is 0, we must have
{{NumBlk2|:|<math> \Delta S_\text{H}+\Delta S_\text{C} \Delta S_\text{cycle} 0</math> |LnSty=1px dashed |6}}
The previous three equations, namely (), (), (), substituted into () to give:
{T_\text{C}}\geqslant\frac{Q_\text{H}}{T_\text{H}}</math> |LnSty=1px dashed |7}}
<!--In what follows ≤ and ≥ are treated as operators (binary functions on numbers), but they're relations (propositions about pairs of numbers). It doesn't make sense to add their "results" together, negate them, or compare them to 0. They're also not formatted properly with or <math>-->
For [ΔSh ≥ (Qh/Th)] +[ΔSc ≥ (Qc/Tc)] = 0
[ΔSh ≥ (Qh/Th)] = - [ΔSc ≥ (Qc/Tc)]
<nowiki>=</nowiki> [-ΔSc ≤ (-Qc/Tc)]
it is at least '(Qh/Th) ≤ (-Qc/Tc)
Equations () and () combine to give
{{NumBlk2|:|<math> \frac{W}{Q_\text{H}} \leq 1- \frac{T_\text{C}}{T_\text{H}} </math> |LnSty=1px dashed |8}}
To derive this step needs two adiabatic processes involved to show an isentropic process property for the ratio of the changing volumes of two isothermal processes are equal.
Most importantly, since the two adiabatic processes are volume works without heat lost, and since the ratio of volume changes for this two processes are the same, so the works for these two adiabatic processes are the same with opposite direction to each other, namely, one direction is work done by the system and the other is work done on the system; therefore, heat efficiency only concerns the amount of work done by the heat absorbed comparing to the amount of heat absorbed by the system.
Therefore, (W/Qh) = (Qh - Qc) / Qh
<nowiki>=</nowiki> 1 - (Qc/Qh)
<nowiki>=</nowiki> 1 - (Tc/Th)
And, from ()
(Qh/Th) ≤ (-Qc/Tc) here Qc it is less than 0 (release heat)
(Tc/Th) ≤ (-Qc/Qh)
-(Tc/Th) ≥ (Qc/Qh)
1+[-(Tc/Th)] ≥ 1+(Qc/Qh)
1 - (Tc/Th) ≥ (Qh + Qc)/Qh here Qc<0,
1 - (Tc/Th) ≥ (Qh - Qc)/Qh
1 - (Tc/Th) ≥ W/Qh'
Hence,
{{NumBlk2|:|<math> \eta \leq \eta_\text{I} </math> |LnSty=1px dashed |9}}
where <math>\eta = \frac{W}{Q_\text{H}}</math> is the efficiency of the real engine, and <math>\eta_\text{I}</math> is the efficiency of the Carnot engine working between the same two reservoirs at the temperatures <math>T_\text{H}</math> and <math>T_\text{C}</math>. For the Carnot engine, the entire process is 'reversible', and Equation () is an equality. Hence, the efficiency of the real engine is always less than the ideal Carnot engine.
Equation () signifies that the total entropy of system and surroundings (the fluid and the two reservoirs) increases for the real engine, because (in a surroundings-based analysis) the entropy gain of the cold reservoir as <math>Q_\text{C}</math> flows into it at the fixed temperature <math>T_\text{C}</math>, is greater than the entropy loss of the hot reservoir as <math>Q_\text{H}</math> leaves it at its fixed temperature <math>T_\text{H}</math>. The inequality in Equation () is essentially the statement of the Clausius theorem.
According to the second theorem, "The efficiency of the Carnot engine is independent of the nature of the working substance".
The Carnot engine and Rudolf Diesel
In 1892 Rudolf Diesel patented an internal combustion engine inspired by the Carnot engine. Diesel knew a Carnot engine is an ideal that cannot be built, but he thought he had invented a working approximation. His principle was unsound, but in his struggle to implement it he developed a practical Diesel engine.
The conceptual problem was how to achieve isothermal expansion in an internal combustion engine, since burning fuel at the highest temperature of the cycle would only raise the temperature further. Diesel's patented solution was: having achieved the highest temperature just by compressing the air, to add a small amount of fuel at a controlled rate, such that heating caused by burning the fuel would be counteracted by cooling caused by air expansion as the piston moved. Hence all the heat from the fuel would be transformed into work during the isothermal expansion, as required by Carnot's theorem.
For the idea to work a small mass of fuel would have to be burnt in a huge mass of air. Diesel first proposed a working engine that would compress air to 250 atmospheres at , then cycle to one atmosphere at . However, this was well beyond the technological capabilities of the day, since it implied a compression ratio of 60:1. Such an engine, if it could have been built, would have had an efficiency of 73%. (In contrast, the best steam engines of his day achieved 7%.)
Accordingly, Diesel sought to compromise. He calculated that, were he to reduce the peak pressure to a less ambitious 90 atmospheres, he would sacrifice only 5% of the thermal efficiency. Seeking financial support, he published the "Theory and Construction of a Rational Heat Engine to Take the Place of the Steam Engine and All Presently Known Combustion Engines" (1893). Endorsed by scientific opinion, including Lord Kelvin, he won the backing of Krupp and . He clung to the Carnot cycle as a symbol. But years of practical work failed to achieve an isothermal combustion engine, nor could have done, since it requires such an enormous quantity of air that it cannot develop enough power to compress it. Furthermore, controlled fuel injection turned out to be no easy matter.
Even so, the Diesel engine slowly evolved over 25 years to become a practical high-compression air engine, its fuel injected near the end of the compression stroke and ignited by the heat of compression, capable by 1969 of 40% efficiency. As a macroscopic construct The Carnot heat engine is, ultimately, a theoretical construct based on an idealized thermodynamic system. On a practical human-scale level the Carnot cycle has proven a valuable model, as in advancing the development of the diesel engine. However, on a macroscopic scale limitations placed by the model's assumptions prove it impractical, and, ultimately, incapable of doing any work. As such, per Carnot's theorem, the Carnot engine may be thought as the theoretical limit of macroscopic scale heat engines rather than any practical device that could ever be built.
For example, for the isothermal expansion part of the Carnot cycle, the following
infinitesimal conditions must be satisfied simultaneously at every step in the expansion:
* The hot reservoir temperature T<sub>H</sub> is infinitesimally higher than the system gas temperature T so heat flow (energy transfer) from the hot reservoir to the gas is made without increasing T (via infinitesimal work on the surroundings by the gas as another energy transfer); if T<sub>H</sub> is significantly higher than T, then T may be not uniform through the gas so the system would deviate from thermal equilibrium as well as not being a reversible process (i.e. not a Carnot cycle) or T might increase noticeably so it would not be an isothermal process.
* The force externally applied on the piston (opposite to the internal force on the piston by the gas) needs to be infinitesimally reduced externally. Without this assistance, it would not be possible to follow a gas PV (Pressure-Volume) curve downward at a constant T since following this curve means that the gas-to-piston force decreases (P decreases) as the volume expands (the piston moves outward). If this assistance is so strong that the volume expansion is significant, the system may deviate from thermal equilibrium, and the process fail to be reversible (and thus not a Carnot cycle).
Such "infinitesimal" requirements as these (and others) cause the Carnot cycle to take an infinite amount of time, rendering the production of work impossible.<ref name=hang/>
Other practical requirements that make the Carnot cycle impractical to realize include fine control of the gas, and perfect thermal contact with the surroundings (including high and low temperature reservoirs). Notes External links
References
<!--
Template:Cite book
*
-->
*
* ([https://archive.org/details/bub_gb_QX9iIWF3yOMC First Edition 1824]) and ([https://books.google.com/books?idYcY9AAAAMAAJ Reissued Edition of 1878])
* ([https://books.google.com/books?idtgdJAAAAIAAJ full text of 1897 ed.]) ([https://web.archive.org/web/20120204034518/http://www.history.rochester.edu/steam/carnot/1943/Section2.htm Archived HTML version])
Category:Engines
Category:Thermodynamic cycles
|
https://en.wikipedia.org/wiki/Carnot_heat_engine
|
2025-04-05T18:27:43.359575
|
6119
|
Context-sensitive
|
Context-sensitive is an adjective meaning "depending on context" or "depending on circumstances". It may refer to:
Context-sensitive meaning, where meaning depends on context (language use)
Context-sensitive grammar, a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols
Context-sensitive language, a formal language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar). Context-sensitive is one of the four types of grammars in the Chomsky hierarchy
Context-sensitive help, a kind of online help that is obtained from a specific point in the state of the software, providing help for the situation that is associated with that state
Context-sensitive solutions (also called Context Sensitive Design), a theoretical and practical approach to transportation decision-making and design that takes into consideration the communities and lands through which streets, roads, and highways pass ("the context")
Context-sensitive user interface, in computing
|
https://en.wikipedia.org/wiki/Context-sensitive
|
2025-04-05T18:27:43.360423
|
6121
|
Central America
|
}}
|population 52,700,000 (2023)
|density (2023)
|demonym = Central American}}
|GDP_PPP = $738.8 billion (2023)
|GDP_nominal = $362.62 billion (exchange rate) (2023)
|GDP_per_capita = $6,880 (exchange rate) (2023)<br />$14,019 (PPP) (2023)
|countries =
|
|
|
|
|
|
|
}}
|dependencies = (France)
}}
Malpelo Island (Colombia)
| (Colombia)
}}
Bajo Nuevo Bank
| Serranilla Bank
}}
|languages =
|time = UTC−06:00 to UTC−05:00
|cities = Guatemala City<!--1,104,890-->
| San Salvador <!--2,000,000-->
| Managua<!--2,201,000-->
| Tegucigalpa<!--1,126,534-->
| Panama City<!--880,691--><!--540,898-->
| San Pedro Sula<!--538,101-->
| San José<!--347,281-->
| San Miguelito<!--293,745-->
| Santa Ana<!--245,241-->
| San Miguel<!--221,783-->
}}
|m49 = <code>013</code> – Central America<br /><code>419</code> – Latin America and the Caribbean<br /><code>019</code> – Americas<br /><code>001</code> – World
}}
Central America or }} is a subregion of North America. Its political boundaries are defined as bordering Mexico to the north, Colombia to the southeast, the Caribbean to the east, and the Pacific Ocean to the southwest. Central America is usually defined as consisting of seven countries: Belize, Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and Panama. Within Central America is the Mesoamerican biodiversity hotspot, which extends from southern Mexico to southeastern Panama. Due to the presence of several active geologic faults and the Central America Volcanic Arc, there is a high amount of seismic activity in the region, such as volcanic eruptions and earthquakes, which has resulted in death, injury, and property damage.
Most of Central America falls under the Isthmo-Colombian cultural area. Before the Spanish expedition of Christopher Columbus' voyages to the Americas, hundreds of indigenous peoples made their homes in the area. From the year 1502 onwards, Spain began their colonization. From 1609 to 1821, the majority of Central American territories (except for what would become Belize and Panama and including the modern Mexican state of Chiapas) were governed by the viceroyalty of New Spain from Mexico City as the Captaincy General of Guatemala. On 24 August 1821, Spanish Viceroy Juan de O'Donojú signed the Treaty of Córdoba, which established New Spain's independence and autonomy from mainland Spain. On 15 September, the Act of Independence of Central America was enacted to announce Central America's separation from the Spanish Empire. Some of New Spain's provinces in the Central American region were invaded and annexed to the First Mexican Empire; however in 1823 they seceded from Mexico to form the Federal Republic of Central America until 1838.
In 1838, Costa Rica, Guatemala, Honduras, and Nicaragua became the first of Central America's seven states to become independent countries, followed by El Salvador in 1841, Panama in 1903, and Belize in 1981. Despite the dissolution of the Federal Republic of Central America, the five remaining countries, save for Panama and Belize, all preserved and maintained a Central American identity.
The Spanish-speaking countries officially include both North America and South America as a single continent, , which is split into four subregions: Central America, Insular America (a.k.a. the West Indies), North America (Mexico and Northern America), and South America.
Definitions
, Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and Panama are traditionally the seven Central American countries in political geography.]]
"Central America" may mean different things to various people, based upon different contexts:
* The United Nations geoscheme for the Americas defines Central America as all states of mainland North America south of the United States, hence grouping Mexico as a part of Central America for statistics purposes, but historically and politically Mexico is considered North American.
In 1538, Spain established the Real Audiencia of Panama, which had jurisdiction over all land from the Strait of Magellan to the Gulf of Fonseca. This entity was dissolved in 1543, and most of the territory within Central America then fell under the jurisdiction of the Audiencia Real de Guatemala. This area included the current territories of Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and the Mexican state of Chiapas, but excluded the lands that would become Belize and Panama. The president of the Audiencia, which had its seat in Antigua Guatemala, was the governor of the entire area. In 1609 the area became a captaincy general and the governor was also granted the title of captain general. The Captaincy General of Guatemala encompassed most of Central America, with the exception of present-day Belize and Panama.
The Captaincy General of Guatemala lasted for more than two centuries, but began to fray after a rebellion in 1811 which began in the Intendancy of San Salvador. The Captaincy General formally ended on 15 September 1821, with the signing of the Act of Independence of Central America. Mexican independence was achieved at virtually the same time with the signing of the Treaty of Córdoba and the Declaration of Independence of the Mexican Empire, and the entire region was finally independent from Spanish authority by 28 September 1821.
; decorated Salvadoran General and president of the Federal Republic of Central America from 1825 to 1829]]
volcanic range of El Salvador, visible from the city of Sonsonate, which became the capital of the Federal Republic of Central America in 1834.]]
From its independence from Spain in 1821 until 1823, the former Captaincy General remained intact as part of the short-lived First Mexican Empire. When the Emperor of Mexico abdicated on 19 March 1823, Central America again became independent. On 1 July 1823, the Congress of Central America peacefully seceded from Mexico and declared absolute independence from all foreign nations, and the region formed the Federal Republic of Central America.
The Federal Republic of Central America, initially known as the United Provinces of Central America, was a sovereign state that existed from 1823 to 1840. It was composed of five states: Guatemala, Honduras, El Salvador, Nicaragua, and Costa Rica. The federation was established after these regions declared independence from Spain in 1821 and briefly joined the Mexican Empire before breaking away to form their own union. The republic adopted a constitution in 1824, which was inspired by the federal system of the United States. It provided for a federal capital, initially located in Guatemala City, and a president for each of the five constituent states. The constitution abolished slavery and maintained the privileges of the Roman Catholic Church, while restricting suffrage to the upper classes.
The territory that now makes up Belize was heavily contested in a dispute that continued for decades after Guatemala achieved independence. Spain, and later Guatemala, considered this land a Guatemalan department. In 1862, Britain formally declared it a British colony and named it British Honduras. It became independent as Belize in 1981.
After more than two hundred years of social unrest, violent conflict, and revolution, Central America today remains in a period of political transformation. Poverty, social injustice, and violence are still widespread. The volcano with the most activity in Central America is Santa María. Still experiencing frequent eruptions to this day, with the last one beginning in 2013, and still is going on to this day.
Of the many mountain ranges within Central America, the longest are the Sierra Madre de Chiapas, the Cordillera Isabelia and the Cordillera de Talamanca. At , Volcán Tajumulco is the highest peak in Central America. Other high points of Central America are as listed in the table below:
{| class"wikitable sortable" style"margin: 1em auto;"
|+High points in Central America
|-
! Country
! Name
! Elevation
! Range
|-
|style="text-align:left;"|
|Doyle's Delight
|
|Maya Mountains
|-
|style="text-align:left;"|
|Cerro Chirripó
|
|Cordillera de Talamanca
|-
|style="text-align:left;"|
|Cerro El Pital
|
|Sierra Madre de Chiapas
|-
|style="text-align:left;"|
|Volcán Tajumulco
|
|Sierra Madre de Chiapas
|-
|style="text-align:left;"|
|Cerro Las Minas
|
|Sierra Madre de Chiapas
|-
|style="text-align:left;"|
|Mogotón
|
|Cordillera Isabelia
|-
|style="text-align:left;"|
|Volcán Barú
|
|Cordillera de Talamanca
|}
Between the mountain ranges lie fertile valleys that are suitable for the raising of livestock and for the production of coffee, tobacco, beans and other crops. Most of the population of Honduras, Costa Rica and Guatemala lives in valleys.
Trade winds have a significant effect upon the climate of Central America. Temperatures in Central America are highest just prior to the summer wet season, and are lowest during the winter dry season, when trade winds contribute to a cooler climate. The highest temperatures occur in April, due to higher levels of sunlight, lower cloud cover and a decrease in trade winds. No timeline for implementation was discussed.
Central America already has several supranational institutions such as the Central American Parliament, the Central American Bank for Economic Integration and the Central American Common Market.
On 22 July 2011, President Mauricio Funes of El Salvador became the first president pro tempore to SICA. El Salvador also became the headquarters of SICA with the inauguration of a new building. The President of El Salvador, Nayib Bukele, broke diplomatic relations with Taiwan and established ties with China. On 9 December 2021, Nicaragua resumed relations with the PRC.
Economy
<gallery>
File:Banco deGuatemala.JPG|Central Bank of Guatemala
File:World Trade Center San Salvador.jpg|World Trade Center San Salvador
File:BCH.jpg|Central Bank of Honduras
File:Maqueta del Banco Central de Nicaragua.jpg|Central Bank of Nicaragua
File:Banco Nacional de Panamá, en vía España de la ciudad de Panamá.jpg|National Bank of Panama
File:Belizean Central Bank 2015.jpg|Central Bank of Belize
</gallery>
Signed in 2004, the Central American Free Trade Agreement (CAFTA) is an agreement between the United States, Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and the Dominican Republic. The treaty is aimed at promoting free trade among its members.
Guatemala has the largest economy in the region.
They are also criticised for the working conditions of employees: insults and physical violence, abusive dismissals (especially of pregnant workers), working hours, non-payment of overtime. According to Lucrecia Bautista, coordinator of the maquilas sector of the audit firm Coverco, "labour law regulations are regularly violated in maquilas and there is no political will to enforce their application. In the case of infringements, the labour inspectorate shows remarkable leniency. It is a question of not discouraging investors." Trade unionists are subject to pressure, and sometimes to kidnapping or murder. In some cases, business leaders have used the services of the maras. Finally, black lists containing the names of trade unionists or political activists are circulating in employers' circles.
!GDP<br />(PPP)<br /><small>$ millions</small>
Costa Rica is the most visited nation in Central America.
{| class"wikitable sortable static-row-numbers sort-under" style"text-align:right;"
|- class"static-row-header" style"text-align:center;vertical-align:bottom;"
! rowspan2 style"vertical-align:middle;"|Countries &<br />territories
! colspan=4|2022
! colspan9 style"border-left-width:2px;"|Historical data
! rowspan2 style"border-left-width:2px; text-align:middle;"|<br />COVID-19:<br />2019→2022
|- class"static-row-header" style"text-align:center;vertical-align:bottom;"
! style="vertical-align:middle;width:4em;"|All
! style="vertical-align:middle;"|Male
! style="vertical-align:middle;"|Female
! style="vertical-align:middle; width:3em;"|
! style="border-left-width:2px; vertical-align:middle; width:4em; padding-left:1em;"|2014
! style="text-align:left;"|
! style="vertical-align:middle; width:3em;"|2019
! style="text-align:left;"|2019<br />→2020
! style="vertical-align:middle; width:3em;"|2020
! style="text-align:left;"|2020<br />→2021
! style="vertical-align:middle; width:3em;"|2021
! style="text-align:left;"|2021<br />→2022
! style="vertical-align:middle; width:3em;"|2022
|-
|alignleft| ||style"text-align:center; background:#e0ffd8;"| 77.32 ||style"text-align:center; background:#eaf3ff;"| 74.76 ||style"text-align:center; background:#fee7f6;"| 80.04 ||style"text-align:center; background:#fff8dc;"| 5.27 ||style"text-align:center; border-left-width:2px; padding-left:1em;"| 78.77 ||style"background:#fffae0; color:darkgreen;"| 0.65 ||style"text-align:center;"| 79.43 ||style"background:#fffae0; color:crimson;"| −0.15 ||style"text-align:center;"| 79.28 ||style"background:#fffae0; color:crimson;"| −2.25 ||style"text-align:center;"| 77.02 ||style"background:#fffae0; color:darkgreen;"| 0.30 ||style"text-align:center; background:#e0ffd8;"| 77.32 ||style="background:#fffae0; border-left-width:2px; color:crimson;"| −2.11
|-
|alignleft| ||style"text-align:center; background:#e0ffd8;"| 76.83 ||style"text-align:center; background:#eaf3ff;"| 73.73 ||style"text-align:center; background:#fee7f6;"| 80.09 ||style"text-align:center; background:#fff8dc;"| 6.36 ||style"text-align:center; border-left-width:2px; padding-left:1em;"| 77.25 ||style"background:#fffae0; color:darkgreen;"| 0.56 ||style"text-align:center;"| 77.81 ||style"background:#fffae0; color:crimson;"| −1.15 ||style"text-align:center;"| 76.66 ||style"background:#fffae0; color:crimson;"| −0.43 ||style"text-align:center;"| 76.22 ||style"background:#fffae0; color:darkgreen;"| 0.60 ||style"text-align:center; background:#e0ffd8;"| 76.83 ||style="background:#fffae0; border-left-width:2px; color:crimson;"| −0.98
|-
|alignleft| ||style"text-align:center; background:#e0ffd8;"| 74.61 ||style"text-align:center; background:#eaf3ff;"| 71.61 ||style"text-align:center; background:#fee7f6;"| 77.56 ||style"text-align:center; background:#fff8dc;"| 5.94 ||style"text-align:center; border-left-width:2px; padding-left:1em;"| 72.81 ||style"background:#fffae0; color:darkgreen;"| 1.24 ||style"text-align:center;"| 74.05 ||style"background:#fffae0; color:crimson;"| −2.26 ||style"text-align:center;"| 71.80 ||style"background:#fffae0; color:darkgreen;"| 2.04 ||style"text-align:center;"| 73.84 ||style"background:#fffae0; color:darkgreen;"| 0.78 ||style"text-align:center; background:#e0ffd8;"| 74.61 ||style="background:#fffae0; border-left-width:2px; color:darkgreen;"| 0.56
|-class=static-row-header
|aligncenter| World ||style"text-align:center; background:#e0ffd8;"| 72.00 ||style"text-align:center; background:#eaf3ff;"| 69.60 ||style"text-align:center; background:#fee7f6;"| 74.53 ||style"text-align:center; background:#fff8dc;"| 4.93 ||style"text-align:center; border-left-width:2px; padding-left:1em;"| 71.88 ||style"background:#fffae0; color:darkgreen;"| 1.10 ||style"text-align:center;"| 72.98 ||style"background:#fffae0; color:crimson;"| −0.74 ||style"text-align:center;"| 72.24 ||style"background:#fffae0; color:crimson;"| −0.92 ||style"text-align:center;"| 71.33 ||style"background:#fffae0; color:darkgreen;"| 0.67 ||style"text-align:center; background:#e0ffd8;"| 72.00 ||style="background:#fffae0; border-left-width:2px; color:crimson;"| −0.98
|-
|alignleft| ||style"text-align:center; background:#e0ffd8;"| 71.47 ||style"text-align:center; background:#eaf3ff;"| 66.84 ||style"text-align:center; background:#fee7f6;"| 75.81 ||style"text-align:center; background:#fff8dc;"| 8.98 ||style"text-align:center; border-left-width:2px; padding-left:1em;"| 71.75 ||style"background:#fffae0; color:darkgreen;"| 0.81 ||style"text-align:center;"| 72.56 ||style"background:#fffae0; color:crimson;"| −1.50 ||style"text-align:center;"| 71.06 ||style"background:#fffae0; color:crimson;"| −0.31 ||style"text-align:center;"| 70.75 ||style"background:#fffae0; color:darkgreen;"| 0.73 ||style"text-align:center; background:#e0ffd8;"| 71.47 ||style="background:#fffae0; border-left-width:2px; color:crimson;"| −1.08
|-
|alignleft| ||style"text-align:center; background:#e0ffd8;"| 70.96 ||style"text-align:center; background:#eaf3ff;"| 67.72 ||style"text-align:center; background:#fee7f6;"| 74.69 ||style"text-align:center; background:#fff8dc;"| 6.96 ||style"text-align:center; border-left-width:2px; padding-left:1em;"| 73.31 ||style"background:#fffae0; color:darkgreen;"| 0.62 ||style"text-align:center;"| 73.93 ||style"background:#fffae0; color:crimson;"| −1.08 ||style"text-align:center;"| 72.85 ||style"background:#fffae0; color:crimson;"| −2.38 ||style"text-align:center;"| 70.47 ||style"background:#fffae0; color:darkgreen;"| 0.49 ||style"text-align:center; background:#e0ffd8;"| 70.96 ||style="background:#fffae0; border-left-width:2px; color:crimson;"| −2.97
|-
|alignleft| ||style"text-align:center; background:#e0ffd8;"| 70.73 ||style"text-align:center; background:#eaf3ff;"| 68.46 ||style"text-align:center; background:#fee7f6;"| 73.16 ||style"text-align:center; background:#fff8dc;"| 4.70 ||style"text-align:center; border-left-width:2px; padding-left:1em;"| 72.26 ||style"background:#fffae0; color:darkgreen;"| 0.62 ||style"text-align:center;"| 72.88 ||style"background:#fffae0; color:crimson;"| −1.42 ||style"text-align:center;"| 71.46 ||style"background:#fffae0; color:crimson;"| −1.34 ||style"text-align:center;"| 70.12 ||style"background:#fffae0; color:darkgreen;"| 0.60 ||style"text-align:center; background:#e0ffd8;"| 70.73 ||style="background:#fffae0; border-left-width:2px; color:crimson;"| −2.15
|-
|alignleft| ||style"text-align:center; background:#e0ffd8;"| 68.67 ||style"text-align:center; background:#eaf3ff;"| 65.70 ||style"text-align:center; background:#fee7f6;"| 71.75 ||style"text-align:center; background:#fff8dc;"| 6.06 ||style"text-align:center; border-left-width:2px; padding-left:1em;"| 71.96 ||style"background:#fffae0; color:darkgreen;"| 1.17 ||style"text-align:center;"| 73.13 ||style"background:#fffae0; color:crimson;"| −1.33 ||style"text-align:center;"| 71.80 ||style"background:#fffae0; color:crimson;"| −2.56 ||style"text-align:center;"| 69.24 ||style"background:#fffae0; color:crimson;"| −0.56 ||style"text-align:center; background:#e0ffd8;"| 68.67 ||style="background:#fffae0; border-left-width:2px; color:crimson;"| −4.45
|}
Further reading
* Berger, Mark T. Under Northern Eyes: Latin American Studies and Us Hegemony in the Americas, 1898–1990. (Indiana UP, 1995).
* Biekart, Kees. "Assessing the 'arrival of Democracy' in Central America." (2014): 117–126. [https://repub.eur.nl/pub/51064/Metis_198906.pdf online]
* Bowman, Kirk, Fabrice Lehoucq, and James Mahoney. "Measuring political democracy: Case expertise, data adequacy, and Central America." Comparative Political Studies 38.8 (2005): 939–970. [https://www.academia.edu/download/48163905/BLM_20final_20paper_20for_20web.pdf online]
* Craig, Kern William. "Public Policy in Central America: An Empirical Analysis." Public Administration Research 2.2 (2013): 105+ [http://www.academia.edu/download/38904624/2013-Public_Policy_in_Central_America-corrected_copy.pdf online].
* Dym, Jordana. From Sovereign Villages to National States: City, State, and Federation in Central America, 1759–1839 (UNM Press, 2006).
* von Feigenblatt, Otto Federico. "Costa Rica's Neo-Realist Foreign Policy: Lifting the Veil Hiding the Discursive Co-Optation of Human Rights, Human Security, and Cosmopolitan Official Rhetoric." International Journal of Arts & Sciences Conference, (2009). [https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1308290 online]
* Krenn, Michael L. The Chains of Interdependence: US Policy Toward Central America, 1945–1954 (ME Sharpe, 1996).
* Kruijt, Dirk. Guerrillas: War and Peace in Central America (2013).
* LaFeber, Walter. Inevitable Revolutions: The United States in Central America (WW Norton & Company, 1993).
* Leonard, Thomas M. "Central America and the United States: Overlooked foreign policy objectives." The Americas (1993): 1–30 [https://www.jstor.org/stable/1007262 online].
* Oliva, Karen, and Chad Rector. "Unbalanced Regional Political Integration Is Unstable: Evidence from the Federal Republic of Central America (1823–1838)." Available at SSRN 2429123 (2014) [https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2429123 online].
* Pearcy, Thomas L. We Answer Only to God: Politics and the Military in Panama, 1903–1947 (University of New Mexico Press, 1998).
* Pérez, Orlando J. Historical Dictionary of El Salvador (Rowman & Littlefield, 2016).
* Perez-Brignoli, Hector. A Brief History of Central America (Univ of California Press, 1989).
* Sola, Mauricio. U.S. Intervention and Regime Change in Nicaragua (U of Nebraska Press, 2005).
* Topik, Steven C., and Allen Wells, eds. The Second Conquest of Latin America: Coffee, Henequen, and Oil During the Export Boom, 1850–1930 (U of Texas Press, 2010).
External links
* [https://web.archive.org/web/20070314083919/http://www.bartleby.com/61/8/C0200800.html American Heritage Dictionaries, Central America] (archived 14 March 2007)
* Central America. [http://www.columbiagazetteer.org/The Columbia Gazetteer of the World Online]. 2006. New York: Columbia University Press.
* Hernández, Consuelo (2009). Reconstruyendo a Centroamérica a través de la poesía. Voces y perspectivas en la poesia latinoamericana del siglo XX. Madrid: Visor.
* [http://repository.library.georgetown.edu/handle/10822/552494/search?querygeographic-region%3A%22Mexico%2C+Central+America+and+the+Caribbean%22&rpp20&sort_by0&orderDESC&submit=Go Central America Video Links] from the [https://web.archive.org/web/20160115205405/https://repository.library.georgetown.edu/handle/10822/552494 Dean Peter Krogh Foreign Affairs Digital Archives]
* [http://lanic.utexas.edu/country/central/LANIC Central America country pages]
* [http://www.teachingcentralamerica.org/ Teaching Central America]
|
https://en.wikipedia.org/wiki/Central_America
|
2025-04-05T18:27:43.460316
|
6122
|
Continuous function
|
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is . Until the 19th century, mathematicians largely relied on intuitive notions of continuity and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity.
Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the most general continuous functions, and their definition is the basis of topology.
A stronger form of continuity is uniform continuity. In order theory, especially in domain theory, a related concept of continuity is Scott continuity.
As an example, the function denoting the height of a growing flower at time would be considered continuous. In contrast, the function denoting the amount of money in a bank account at time would be considered discontinuous since it "jumps" at each point in time when money is deposited or withdrawn.
History
A form of the epsilon–delta definition of continuity was first given by Bernard Bolzano in 1817. Augustin-Louis Cauchy defined continuity of <math>y f(x)</math> as follows: an infinitely small increment <math>\alpha</math> of the independent variable x always produces an infinitely small change <math>f(x+\alpha)-f(x)</math> of the dependent variable y (see e.g. ''Cours d'Analyse'', p. 34). Cauchy defined infinitely small quantities in terms of variable quantities, and his definition of continuity closely parallels the infinitesimal definition used today (see microcontinuity). The formal definition and the distinction between pointwise continuity and uniform continuity were first given by Bolzano in the 1830s, but the work wasn't published until the 1930s. Like Bolzano, Karl Weierstrass denied continuity of a function at a point c unless it was defined at and on both sides of c, but Édouard Goursat allowed the function to be defined only at and on one side of c, and Camille Jordan allowed it even if the function was defined only at c. All three of those nonequivalent definitions of pointwise continuity are still in use. Eduard Heine provided the first published definition of uniform continuity in 1872, but based these ideas on lectures given by Peter Gustav Lejeune Dirichlet in 1854.Real functionsDefinitiondefined on the reals.]]
A real function that is a function from real numbers to real numbers can be represented by a graph in the Cartesian plane; such a function is continuous if, roughly speaking, the graph is a single unbroken curve whose domain is the entire real line. A more mathematically rigorous definition is given below.
Continuity of real functions is usually defined in terms of limits. A function with variable is continuous at the real number , if the limit of <math>f(x),</math> as tends to , is equal to <math>f(c).</math>
There are several different definitions of the (global) continuity of a function, which depend on the nature of its domain.
A function is continuous on an open interval if the interval is contained in the function's domain and the function is continuous at every interval point. A function that is continuous on the interval <math>(-\infty, +\infty)</math> (the whole real line) is often called simply a continuous function; one also says that such a function is continuous everywhere. For example, all polynomial functions are continuous everywhere.
A function is continuous on a semi-open or a closed interval; if the interval is contained in the domain of the function, the function is continuous at every interior point of the interval, and the value of the function at each endpoint that belongs to the interval is the limit of the values of the function when the variable tends to the endpoint from the interior of the interval. For example, the function <math>f(x) = \sqrt{x}</math> is continuous on its whole domain, which is the closed interval <math>[0,+\infty).</math>
Many commonly encountered functions are partial functions that have a domain formed by all real numbers, except some isolated points. Examples include the reciprocal function <math display="inline">x \mapsto \frac {1}{x}</math> and the tangent function <math>x\mapsto \tan x.</math> When they are continuous on their domain, one says, in some contexts, that they are continuous, although they are not continuous everywhere. In other contexts, mainly when one is interested in their behavior near the exceptional points, one says they are discontinuous.
A partial function is discontinuous at a point if the point belongs to the topological closure of its domain, and either the point does not belong to the domain of the function or the function is not continuous at the point. For example, the functions <math display"inline">x\mapsto \frac {1}{x}</math> and <math display"inline">x\mapsto \sin(\frac {1}{x})</math> are discontinuous at , and remain discontinuous whichever value is chosen for defining them at . A point where a function is discontinuous is called a discontinuity.
Using mathematical notation, several ways exist to define continuous functions in the three senses mentioned above.
Let <math display="block">f : D \to \R</math> be a function defined on a subset <math>D</math> of the set <math>\R</math> of real numbers.
This subset <math>D</math> is the domain of . Some possible choices include
*<math>D = \R </math>: i.e., <math> D </math> is the whole set of real numbers. or, for and real numbers,
*<math>D [a, b] \{x \in \R \mid a \leq x \leq b \} </math>: <math> D </math> is a closed interval, or
*<math>D (a, b) \{x \in \R \mid a < x < b \} </math>: <math> D </math> is an open interval.
In the case of the domain <math>D</math> being defined as an open interval, <math>a</math> and <math>b</math> do not belong to <math>D</math>, and the values of <math>f(a)</math> and <math>f(b)</math> do not matter for continuity on <math>D</math>.
Definition in terms of limits of functions
The function is continuous at some point of its domain if the limit of <math>f(x),</math> as x approaches c through the domain of f, exists and is equal to <math>f(c).</math> In mathematical notation, this is written as
<math display"block">\lim_{x \to c}{f(x)} f(c).</math>
In detail this means three conditions: first, has to be defined at (guaranteed by the requirement that is in the domain of ). Second, the limit of that equation has to exist. Third, the value of this limit must equal <math>f(c).</math>
(Here, we have assumed that the domain of f does not have any isolated points.)
Definition in terms of neighborhoods
A neighborhood of a point c is a set that contains, at least, all points within some fixed distance of c. Intuitively, a function is continuous at a point c if the range of f over the neighborhood of c shrinks to a single point <math>f(c)</math> as the width of the neighborhood around c shrinks to zero. More precisely, a function f is continuous at a point c of its domain if, for any neighborhood <math>N_1(f(c))</math> there is a neighborhood <math>N_2(c)</math> in its domain such that <math>f(x) \in N_1(f(c))</math> whenever <math>x\in N_2(c).</math>
As neighborhoods are defined in any topological space, this definition of a continuous function applies not only for real functions but also when the domain and the codomain are topological spaces and is thus the most general definition. It follows that a function is automatically continuous at every isolated point of its domain. For example, every real-valued function on the integers is continuous.
Definition in terms of limits of sequences
One can instead require that for any sequence <math>(x_n)_{n \in \N}</math> of points in the domain which converges to c, the corresponding sequence <math>\left(f(x_n)\right)_{n\in \N}</math> converges to <math>f(c).</math> In mathematical notation, <math display"block">\forall (x_n)_{n \in \N} \subset D:\lim_{n\to\infty} x_n c \Rightarrow \lim_{n\to\infty} f(x_n) f(c)\,.</math>Weierstrass and Jordan definitions (epsilon–delta) of continuous functions
Explicitly including the definition of the limit of a function, we obtain a self-contained definition: Given a function <math>f : D \to \mathbb{R}</math> as above and an element <math>x_0</math> of the domain <math>D</math>, <math>f</math> is said to be continuous at the point <math>x_0</math> when the following holds: For any positive real number <math>\varepsilon > 0,</math> however small, there exists some positive real number <math>\delta > 0</math> such that for all <math>x</math> in the domain of <math>f</math> with <math>x_0 - \delta < x < x_0 + \delta,</math> the value of <math>f(x)</math> satisfies
<math display="block">f\left(x_0\right) - \varepsilon < f(x) < f(x_0) + \varepsilon.</math>
Alternatively written, continuity of <math>f : D \to \mathbb{R}</math> at <math>x_0 \in D</math> means that for every <math>\varepsilon > 0,</math> there exists a <math>\delta > 0</math> such that for all <math>x \in D</math>:
<math display="block">\left|x - x_0\right| < \delta ~~\text{ implies }~~ |f(x) - f(x_0)| < \varepsilon.</math>
More intuitively, we can say that if we want to get all the <math>f(x)</math> values to stay in some small neighborhood around <math>f\left(x_0\right),</math> we need to choose a small enough neighborhood for the <math>x</math> values around <math>x_0.</math> If we can do that no matter how small the <math>f(x_0)</math> neighborhood is, then <math>f</math> is continuous at <math>x_0.</math>
In modern terms, this is generalized by the definition of continuity of a function with respect to a basis for the topology, here the metric topology.
Weierstrass had required that the interval <math>x_0 - \delta < x < x_0 + \delta</math> be entirely within the domain <math>D</math>, but Jordan removed that restriction.
Definition in terms of control of the remainder
In proofs and numerical analysis, we often need to know how fast limits are converging, or in other words, control of the remainder. We can formalize this to a definition of continuity.
A function <math>C: [0,\infty) \to [0,\infty]</math> is called a control function if
* C is non-decreasing
*<math>\inf_{\delta > 0} C(\delta) = 0</math>
A function <math>f : D \to R</math> is C-continuous at <math>x_0</math> if there exists such a neighbourhood <math display="inline">N(x_0)</math> that
<math display="block">|f(x) - f(x_0)| \leq C\left(\left|x - x_0\right|\right) \text{ for all } x \in D \cap N(x_0)</math>
A function is continuous in <math>x_0</math> if it is C-continuous for some control function C.
This approach leads naturally to refining the notion of continuity by restricting the set of admissible control functions. For a given set of control functions <math>\mathcal{C}</math> a function is {{nowrap|<math>\mathcal{C}</math>-continuous}} if it is for some <math>C \in \mathcal{C}.</math> For example, the Lipschitz, the Hölder continuous functions of exponent and the uniformly continuous functions below are defined by the set of control functions
<math display"block">\mathcal{C}_{\mathrm{Lipschitz}} \{C : C(\delta) = K|\delta| ,\ K > 0\}</math>
<math display"block">\mathcal{C}_{\text{Hölder}-\alpha} \{C : C(\delta) = K |\delta|^\alpha, \ K > 0\}</math>
<math display"block">\mathcal{C}_{\text{uniform cont.}} \{C : C(0) = 0 \}</math>
respectively.
Definition using oscillation
.]]
Continuity can also be defined in terms of oscillation: a function f is continuous at a point <math>x_0</math> if and only if its oscillation at that point is zero; in symbols, <math>\omega_f(x_0) = 0.</math> A benefit of this definition is that it discontinuity: the oscillation gives how the function is discontinuous at a point.
This definition is helpful in descriptive set theory to study the set of discontinuities and continuous points – the continuous points are the intersection of the sets where the oscillation is less than <math>\varepsilon</math> (hence a <math>G_{\delta}</math> set) – and gives a rapid proof of one direction of the Lebesgue integrability condition.
The oscillation is equivalent to the <math>\varepsilon-\delta</math> definition by a simple re-arrangement and by using a limit (lim sup, lim inf) to define oscillation: if (at a given point) for a given <math>\varepsilon_0</math> there is no <math>\delta</math> that satisfies the <math>\varepsilon-\delta</math> definition, then the oscillation is at least <math>\varepsilon_0,</math> and conversely if for every <math>\varepsilon</math> there is a desired <math>\delta,</math> the oscillation is 0. The oscillation definition can be naturally generalized to maps from a topological space to a metric space.
Definition using the hyperreals
Cauchy defined the continuity of a function in the following intuitive terms: an infinitesimal change in the independent variable corresponds to an infinitesimal change of the dependent variable (see ''Cours d'analyse, page 34). Non-standard analysis is a way of making this mathematically rigorous. The real line is augmented by adding infinite and infinitesimal numbers to form the hyperreal numbers. In nonstandard analysis, continuity can be defined as follows.
is continuous at if its natural extension to the hyperreals has the property that for all infinitesimal , <math>f(x + dx) - f(x)</math> is infinitesimal}}
(see microcontinuity). In other words, an infinitesimal increment of the independent variable always produces an infinitesimal change of the dependent variable, giving a modern expression to Augustin-Louis Cauchy's definition of continuity.
Construction of continuous functions
has no jumps or holes. The function is continuous.]]
Checking the continuity of a given function can be simplified by checking one of the above defining properties for the building blocks of the given function. It is straightforward to show that the sum of two functions, continuous on some domain, is also continuous on this domain. Given
<math display="block">f, g \colon D \to \R,</math>
then the
<math display"block">s f + g</math>
(defined by <math>s(x) = f(x) + g(x)</math> for all <math>x\in D</math>) is continuous in <math>D.</math>
The same holds for the ,
<math display"block">p f \cdot g</math>
(defined by <math>p(x) = f(x) \cdot g(x)</math> for all <math>x \in D</math>)
is continuous in <math>D.</math>
Combining the above preservations of continuity and the continuity of constant functions and of the identity function <math>I(x) = x</math> one arrives at the continuity of all polynomial functions such as
<math display"block">f(x) x^3 + x^2 - 5 x + 3</math>
(pictured on the right).
. The function is not defined for <math>x = -2.</math> The vertical and horizontal lines are asymptotes.]]
In the same way, it can be shown that the
<math display"block">r 1/f</math>
(defined by <math>r(x) = 1/f(x)</math> for all <math>x \in D</math> such that <math>f(x) \neq 0</math>)
is continuous in <math>D\setminus \{x : f(x) = 0\}.</math>
This implies that, excluding the roots of <math>g,</math> the
<math display"block">q f / g</math>
(defined by <math>q(x) = f(x)/g(x)</math> for all <math>x \in D</math>, such that <math>g(x) \neq 0</math>)
is also continuous on <math>D\setminus \{x:g(x) = 0\}</math>.
For example, the function (pictured)
<math display"block">y(x) \frac{2x-1}{x+2}</math>
is defined for all real numbers <math>x \neq -2</math> and is continuous at every such point. Thus, it is a continuous function. The question of continuity at <math>x -2</math> does not arise since <math>x -2</math> is not in the domain of <math>y.</math> There is no continuous function <math>F : \R \to \R</math> that agrees with <math>y(x)</math> for all <math>x \neq -2.</math>
Since the function sine is continuous on all reals, the sinc function <math>G(x) = \sin(x)/x,</math> is defined and continuous for all real <math>x \neq 0.</math> However, unlike the previous example, G be extended to a continuous function on real numbers, by the value <math>G(0)</math> to be 1, which is the limit of <math>G(x),</math> when x approaches 0, i.e.,
<math display"block">G(0) \lim_{x\to 0} \frac{\sin x}{x} = 1.</math>
Thus, by setting
:<math>
G(x) =
\begin{cases}
\frac {\sin (x)}x & \text{ if }x \ne 0\\
1 & \text{ if }x = 0,
\end{cases}
</math>
the sinc-function becomes a continuous function on all real numbers. The term is used in such cases when (re)defining values of a function to coincide with the appropriate limits make a function continuous at specific points.
A more involved construction of continuous functions is the function composition. Given two continuous functions
<math display="block">g : D_g \subseteq \R \to R_g \subseteq \R \quad \text{ and } \quad f : D_f \subseteq \R \to R_f \subseteq D_g,</math>
their composition, denoted as
<math>c g \circ f : D_f \to \R,</math> and defined by <math>c(x) g(f(x)),</math> is continuous.
This construction allows stating, for example, that
<math display="block">e^{\sin(\ln x)}</math>
is continuous for all <math>x > 0.</math>
Examples of discontinuous functions
).]]
An example of a discontinuous function is the Heaviside step function <math>H</math>, defined by
<math display"block">H(x) \begin{cases}
1 & \text{ if } x \ge 0\\
0 & \text{ if } x < 0
\end{cases}
</math>
Pick for instance <math>\varepsilon 1/2</math>. Then there is no around <math>x 0</math>, i.e. no open interval <math>(-\delta,\;\delta)</math> with <math>\delta > 0,</math> that will force all the <math>H(x)</math> values to be within the of <math>H(0)</math>, i.e. within <math>(1/2,\;3/2)</math>. Intuitively, we can think of this type of discontinuity as a sudden jump in function values.
Similarly, the signum or sign function
<math display="block">
\sgn(x) = \begin{cases}
\;\;\ 1 & \text{ if }x > 0\\
\;\;\ 0 & \text{ if }x = 0\\
-1 & \text{ if }x < 0
\end{cases}
</math>
is discontinuous at <math>x = 0</math> but continuous everywhere else. Yet another example: the function
<math display"block">f(x) \begin{cases}
\sin\left(x^{-2}\right)&\text{ if }x \neq 0\\
0&\text{ if }x = 0
\end{cases}</math>
is continuous everywhere apart from <math>x = 0</math>.
Besides plausible continuities and discontinuities like above, there are also functions with a behavior, often coined pathological, for example, Thomae's function,
<math display"block">f(x)\begin{cases}
1 &\text{ if } x=0\\
\frac{1}{q}&\text{ if } x = \frac{p}{q} \text{(in lowest terms) is a rational number}\\
0&\text{ if }x\text{ is irrational}.
\end{cases}</math>
is continuous at all irrational numbers and discontinuous at all rational numbers. In a similar vein, Dirichlet's function, the indicator function for the set of rational numbers,
<math display"block">D(x)\begin{cases}
0&\text{ if }x\text{ is irrational } (\in \R \setminus \Q)\\
1&\text{ if }x\text{ is rational } (\in \Q)
\end{cases}</math>
is nowhere continuous.
Properties
A useful lemma
Let <math>f(x)</math> be a function that is continuous at a point <math>x_0,</math> and <math>y_0</math> be a value such <math>f\left(x_0\right)\neq y_0.</math> Then <math>f(x)\neq y_0</math> throughout some neighbourhood of <math>x_0.</math>
Proof: By the definition of continuity, take <math>\varepsilon =\frac{|y_0-f(x_0)|}{2}>0</math> , then there exists <math>\delta>0</math> such that
<math display="block">\left|f(x)-f(x_0)\right| < \frac{\left|y_0 - f(x_0)\right|}{2} \quad \text{ whenever } \quad |x-x_0| < \delta</math>
Suppose there is a point in the neighbourhood <math>|x-x_0|<\delta</math> for which <math>f(x)=y_0;</math> then we have the contradiction
<math display"block">\left|f(x_0)-y_0\right| < \frac{\left|f(x_0) - y_0\right|}{2}.</math>Intermediate value theorem
The intermediate value theorem is an existence theorem, based on the real number property of completeness, and states:
:If the real-valued function f is continuous on the closed interval <math>[a, b],</math> and k is some number between <math>f(a)</math> and <math>f(b),</math> then there is some number <math>c \in [a, b],</math> such that <math>f(c) = k.</math>
For example, if a child grows from 1 m to 1.5 m between the ages of two and six years, then, at some time between two and six years of age, the child's height must have been 1.25 m.
As a consequence, if f is continuous on <math>[a, b]</math> and <math>f(a)</math> and <math>f(b)</math> differ in sign, then, at some point <math>c \in [a, b],</math> <math>f(c)</math> must equal zero.
Extreme value theorem
The extreme value theorem states that if a function f is defined on a closed interval <math>[a, b]</math> (or any closed and bounded set) and is continuous there, then the function attains its maximum, i.e. there exists <math>c \in [a, b]</math> with <math>f(c) \geq f(x)</math> for all <math>x \in [a, b].</math> The same is true of the minimum of f. These statements are not, in general, true if the function is defined on an open interval <math>(a, b)</math> (or any set that is not both closed and bounded), as, for example, the continuous function <math>f(x) \frac{1}{x},</math> defined on the open interval (0,1), does not attain a maximum, being unbounded above.Relation to differentiability and integrability
Every differentiable function
<math display="block">f : (a, b) \to \R</math>
is continuous, as can be shown. The converse does not hold: for example, the absolute value function
:<math>f(x)|x| \begin{cases}
\;\;\ x & \text{ if }x \geq 0\\
-x & \text{ if }x < 0
\end{cases}</math>
is everywhere continuous. However, it is not differentiable at <math>x = 0</math> (but is so everywhere else). Weierstrass's function is also everywhere continuous but nowhere differentiable.
The derivative f′(x) of a differentiable function f(x) need not be continuous. If f′(x) is continuous, f(x) is said to be continuously differentiable. The set of such functions is denoted <math>C^1((a, b)).</math> More generally, the set of functions
<math display="block">f : \Omega \to \R</math>
(from an open interval (or open subset of <math>\R</math>) <math>\Omega</math> to the reals) such that f is <math>n</math> times differentiable and such that the <math>n</math>-th derivative of f is continuous is denoted <math>C^n(\Omega).</math> See differentiability class. In the field of computer graphics, properties related (but not identical) to <math>C^0, C^1, C^2</math> are sometimes called <math>G^0</math> (continuity of position), <math>G^1</math> (continuity of tangency), and <math>G^2</math> (continuity of curvature); see Smoothness of curves and surfaces.
Every continuous function
<math display="block">f : [a, b] \to \R</math>
is integrable (for example in the sense of the Riemann integral). The converse does not hold, as the (integrable but discontinuous) sign function shows.
Pointwise and uniform limits
Given a sequence
<math display="block">f_1, f_2, \dotsc : I \to \R</math>
of functions such that the limit
<math display"block">f(x) : \lim_{n \to \infty} f_n(x)</math>
exists for all <math>x \in D,</math>, the resulting function <math>f(x)</math> is referred to as the pointwise limit of the sequence of functions <math>\left(f_n\right)_{n \in N}.</math> The pointwise limit function need not be continuous, even if all functions <math>f_n</math> are continuous, as the animation at the right shows. However, f is continuous if all functions <math>f_n</math> are continuous and the sequence converges uniformly, by the uniform convergence theorem. This theorem can be used to show that the exponential functions, logarithms, square root function, and trigonometric functions are continuous.
Directional Continuity
<div style="float:right;">
<gallery>Image:Right-continuous.svg|A right-continuous function
Image:Left-continuous.svg|A left-continuous function</gallery></div>
Discontinuous functions may be discontinuous in a restricted way, giving rise to the concept of directional continuity (or right and left continuous functions) and semi-continuity. Roughly speaking, a function is if no jump occurs when the limit point is approached from the right. Formally, f is said to be right-continuous at the point c if the following holds: For any number <math>\varepsilon > 0</math> however small, there exists some number <math>\delta > 0</math> such that for all x in the domain with <math>c < x < c + \delta,</math> the value of <math>f(x)</math> will satisfy
<math display="block">|f(x) - f(c)| < \varepsilon.</math>
This is the same condition as continuous functions, except it is required to hold for x strictly larger than c only. Requiring it instead for all x with <math>c - \delta < x < c</math> yields the notion of functions. A function is continuous if and only if it is both right-continuous and left-continuous.
Semicontinuity
A function f is if, roughly, any jumps that might occur only go down, but not up. That is, for any <math>\varepsilon > 0,</math> there exists some number <math>\delta > 0</math> such that for all x in the domain with <math>|x - c| < \delta,</math> the value of <math>f(x)</math> satisfies
<math display="block">f(x) \geq f(c) - \epsilon.</math>
The reverse condition is .
Continuous functions between metric spaces <!--This section is linked from F-space-->
The concept of continuous real-valued functions can be generalized to functions between metric spaces. A metric space is a set <math>X</math> equipped with a function (called metric) <math>d_X,</math> that can be thought of as a measurement of the distance of any two elements in X. Formally, the metric is a function
<math display="block">d_X : X \times X \to \R</math>
that satisfies a number of requirements, notably the triangle inequality. Given two metric spaces <math>\left(X, d_X\right)</math> and <math>\left(Y, d_Y\right)</math> and a function
<math display="block">f : X \to Y</math>
then <math>f</math> is continuous at the point <math>c \in X</math> (with respect to the given metrics) if for any positive real number <math>\varepsilon > 0,</math> there exists a positive real number <math>\delta > 0</math> such that all <math>x \in X</math> satisfying <math>d_X(x, c) < \delta</math> will also satisfy <math>d_Y(f(x), f(c)) < \varepsilon.</math> As in the case of real functions above, this is equivalent to the condition that for every sequence <math>\left(x_n\right)</math> in <math>X</math> with limit <math>\lim x_n c,</math> we have <math>\lim f\left(x_n\right) f(c).</math> The latter condition can be weakened as follows: <math>f</math> is continuous at the point <math>c</math> if and only if for every convergent sequence <math>\left(x_n\right)</math> in <math>X</math> with limit <math>c</math>, the sequence <math>\left(f\left(x_n\right)\right)</math> is a Cauchy sequence, and <math>c</math> is in the domain of <math>f</math>.
The set of points at which a function between metric spaces is continuous is a <math>G_{\delta}</math> set – this follows from the <math>\varepsilon-\delta</math> definition of continuity.
This notion of continuity is applied, for example, in functional analysis. A key statement in this area says that a linear operator
<math display="block">T : V \to W</math>
between normed vector spaces <math>V</math> and <math>W</math> (which are vector spaces equipped with a compatible norm, denoted <math>\|x\|</math>) is continuous if and only if it is bounded, that is, there is a constant <math>K</math> such that
<math display="block">\|T(x)\| \leq K \|x\|</math>
for all <math>x \in V.</math>
Uniform, Hölder and Lipschitz continuity
The concept of continuity for functions between metric spaces can be strengthened in various ways by limiting the way <math>\delta</math> depends on <math>\varepsilon</math> and c in the definition above. Intuitively, a function f as above is uniformly continuous if the <math>\delta</math> does
not depend on the point c. More precisely, it is required that for every real number <math>\varepsilon > 0</math> there exists <math>\delta > 0</math> such that for every <math>c, b \in X</math> with <math>d_X(b, c) < \delta,</math> we have that <math>d_Y(f(b), f(c)) < \varepsilon.</math> Thus, any uniformly continuous function is continuous. The converse does not generally hold but holds when the domain space X is compact. Uniformly continuous maps can be defined in the more general situation of uniform spaces.
A function is Hölder continuous with exponent α (a real number) if there is a constant K such that for all <math>b, c \in X,</math> the inequality
<math display="block">d_Y (f(b), f(c)) \leq K \cdot (d_X (b, c))^\alpha</math>
holds. Any Hölder continuous function is uniformly continuous. The particular case <math>\alpha = 1</math> is referred to as Lipschitz continuity. That is, a function is Lipschitz continuous if there is a constant K such that the inequality
<math display="block">d_Y (f(b), f(c)) \leq K \cdot d_X (b, c)</math>
holds for any <math>b, c \in X.</math> The Lipschitz condition occurs, for example, in the Picard–Lindelöf theorem concerning the solutions of ordinary differential equations.
Continuous functions between topological spaces
<!--Linked from Preference (economics) and Continuity (topology)-->
Another, more abstract, notion of continuity is the continuity of functions between topological spaces in which there generally is no formal notion of distance, as there is in the case of metric spaces. A topological space is a set X together with a topology on X, which is a set of subsets of X satisfying a few requirements with respect to their unions and intersections that generalize the properties of the open balls in metric spaces while still allowing one to talk about the neighborhoods of a given point. The elements of a topology are called open subsets of X (with respect to the topology).
A function
<math display="block">f : X \to Y</math>
between two topological spaces X and Y is continuous if for every open set <math>V \subseteq Y,</math> the inverse image
<math display"block">f^{-1}(V) \{x \in X \; | \; f(x) \in V \}</math>
is an open subset of X. That is, f is a function between the sets X and Y (not on the elements of the topology <math>T_X</math>), but the continuity of f depends on the topologies used on X and Y.
This is equivalent to the condition that the preimages of the closed sets (which are the complements of the open subsets) in Y are closed in X.
An extreme example: if a set X is given the discrete topology (in which every subset is open), all functions
<math display="block">f : X \to T</math>
to any topological space T are continuous. On the other hand, if X is equipped with the indiscrete topology (in which the only open subsets are the empty set and X) and the space T set is at least T<sub>0</sub>, then the only continuous functions are the constant functions. Conversely, any function whose codomain is indiscrete is continuous.
Continuity at a point
The translation in the language of neighborhoods of the <math>(\varepsilon, \delta)</math>-definition of continuity leads to the following definition of the continuity at a point:
of <math>f(x)</math> in , there is a neighborhood of <math>x</math> such that <math>f(U) \subseteq V.</math>}}
This definition is equivalent to the same statement with neighborhoods restricted to open neighborhoods and can be restated in several ways by using preimages rather than images.
Also, as every set that contains a neighborhood is also a neighborhood, and <math>f^{-1}(V)</math> is the largest subset of such that <math>f(U) \subseteq V,</math> this definition may be simplified into:
{{Quote frame|A function <math>f : X \to Y</math> is continuous at a point <math>x\in X</math> if and only if <math>f^{-1}(V)</math> is a neighborhood of <math>x</math> for every neighborhood of <math>f(x)</math> in .}}
As an open set is a set that is a neighborhood of all its points, a function <math>f : X \to Y</math> is continuous at every point of if and only if it is a continuous function.
If X and Y are metric spaces, it is equivalent to consider the neighborhood system of open balls centered at x and f(x) instead of all neighborhoods. This gives back the above <math>\varepsilon-\delta</math> definition of continuity in the context of metric spaces. In general topological spaces, there is no notion of nearness or distance. If, however, the target space is a Hausdorff space, it is still true that f is continuous at a if and only if the limit of f as x approaches a is f(a). At an isolated point, every function is continuous.
Given <math>x \in X,</math> a map <math>f : X \to Y</math> is continuous at <math>x</math> if and only if whenever <math>\mathcal{B}</math> is a filter on <math>X</math> that converges to <math>x</math> in <math>X,</math> which is expressed by writing <math>\mathcal{B} \to x,</math> then necessarily <math>f(\mathcal{B}) \to f(x)</math> in <math>Y.</math>
If <math>\mathcal{N}(x)</math> denotes the neighborhood filter at <math>x</math> then <math>f : X \to Y</math> is continuous at <math>x</math> if and only if <math>f(\mathcal{N}(x)) \to f(x)</math> in <math>Y.</math> Moreover, this happens if and only if the prefilter <math>f(\mathcal{N}(x))</math> is a filter base for the neighborhood filter of <math>f(x)</math> in <math>Y.</math>
Alternative definitions
Several equivalent definitions for a topological structure exist; thus, several equivalent ways exist to define a continuous function.
Sequences and nets
In several contexts, the topology of a space is conveniently specified in terms of limit points. This is often accomplished by specifying when a point is the limit of a sequence. Still, for some spaces that are too large in some sense, one specifies also when a point is the limit of more general sets of points indexed by a directed set, known as nets. A function is (Heine-)continuous only if it takes limits of sequences to limits of sequences. In the former case, preservation of limits is also sufficient; in the latter, a function may preserve all limits of sequences yet still fail to be continuous, and preservation of nets is a necessary and sufficient condition.
In detail, a function <math>f : X \to Y</math> is sequentially continuous if whenever a sequence <math>\left(x_n\right)</math> in <math>X</math> converges to a limit <math>x,</math> the sequence <math>\left(f\left(x_n\right)\right)</math> converges to <math>f(x).</math> Thus, sequentially continuous functions "preserve sequential limits." Every continuous function is sequentially continuous. If <math>X</math> is a first-countable space and countable choice holds, then the converse also holds: any function preserving sequential limits is continuous. In particular, if <math>X</math> is a metric space, sequential continuity and continuity are equivalent. For non-first-countable spaces, sequential continuity might be strictly weaker than continuity. (The spaces for which the two properties are equivalent are called sequential spaces.) This motivates the consideration of nets instead of sequences in general topological spaces. Continuous functions preserve the limits of nets, and this property characterizes continuous functions.
For instance, consider the case of real-valued functions of one real variable:
Proof. Assume that <math>f : A \subseteq \R \to \R</math> is continuous at <math>x_0</math> (in the sense of <math>\epsilon-\delta</math> continuity). Let <math>\left(x_n\right)_{n\geq1}</math> be a sequence converging at <math>x_0</math> (such a sequence always exists, for example, <math>x_n = x, \text{ for all } n</math>); since <math>f</math> is continuous at <math>x_0</math>
<math display=block>\forall \epsilon > 0\, \exists \delta_{\epsilon} > 0 : 0 < |x-x_0| < \delta_{\epsilon} \implies |f(x)-f(x_0)| < \epsilon.\quad (*)</math>
For any such <math>\delta_{\epsilon}</math> we can find a natural number <math>\nu_{\epsilon} > 0</math> such that for all <math>n > \nu_{\epsilon},</math>
<math display=block>|x_n-x_0| < \delta_{\epsilon},</math>
since <math>\left(x_n\right)</math> converges at <math>x_0</math>; combining this with <math>(*)</math> we obtain
<math display=block>\forall \epsilon > 0 \,\exists \nu_{\epsilon} > 0 : \forall n > \nu_{\epsilon} \quad |f(x_n)-f(x_0)| < \epsilon.</math>
Assume on the contrary that <math>f</math> is sequentially continuous and proceed by contradiction: suppose <math>f</math> is not continuous at <math>x_0</math>
<math display=block>\exists \epsilon > 0 : \forall \delta_{\epsilon} > 0,\,\exists x_{\delta_{\epsilon}}: 0 < |x_{\delta_{\epsilon}}-x_0| < \delta_\epsilon \implies |f(x_{\delta_{\epsilon}})-f(x_0)| > \epsilon</math>
then we can take <math>\delta_{\epsilon}1/n,\,\forall n > 0</math> and call the corresponding point <math>x_{\delta_{\epsilon}}: x_n</math>: in this way we have defined a sequence <math>(x_n)_{n\geq1}</math> such that
<math display=block>\forall n > 0 \quad |x_n-x_0| < \frac{1}{n},\quad |f(x_n)-f(x_0)| > \epsilon</math>
by construction <math>x_n \to x_0</math> but <math>f(x_n) \not\to f(x_0)</math>, which contradicts the hypothesis of sequential continuity. <math>\blacksquare</math>
Closure operator and interior operator definitions
In terms of the interior operator, a function <math>f : X \to Y</math> between topological spaces is continuous if and only if for every subset <math>B \subseteq Y,</math>
<math display=block>f^{-1}\left(\operatorname{int}_Y B\right) ~\subseteq~ \operatorname{int}_X\left(f^{-1}(B)\right).</math>
In terms of the closure operator, <math>f : X \to Y</math> is continuous if and only if for every subset <math>A \subseteq X,</math>
<math display=block>f\left(\operatorname{cl}_X A\right) ~\subseteq~ \operatorname{cl}_Y (f(A)).</math>
That is to say, given any element <math>x \in X</math> that belongs to the closure of a subset <math>A \subseteq X,</math> <math>f(x)</math> necessarily belongs to the closure of <math>f(A)</math> in <math>Y.</math> If we declare that a point <math>x</math> is a subset <math>A \subseteq X</math> if <math>x \in \operatorname{cl}_X A,</math> then this terminology allows for a plain English description of continuity: <math>f</math> is continuous if and only if for every subset <math>A \subseteq X,</math> <math>f</math> maps points that are close to <math>A</math> to points that are close to <math>f(A).</math> Similarly, <math>f</math> is continuous at a fixed given point <math>x \in X</math> if and only if whenever <math>x</math> is close to a subset <math>A \subseteq X,</math> then <math>f(x)</math> is close to <math>f(A).</math>
Instead of specifying topological spaces by their open subsets, any topology on <math>X</math> can alternatively be determined by a closure operator or by an interior operator.
Specifically, the map that sends a subset <math>A</math> of a topological space <math>X</math> to its topological closure <math>\operatorname{cl}_X A</math> satisfies the Kuratowski closure axioms. Conversely, for any closure operator <math>A \mapsto \operatorname{cl} A</math> there exists a unique topology <math>\tau</math> on <math>X</math> (specifically, <math>\tau := \{ X \setminus \operatorname{cl} A : A \subseteq X \}</math>) such that for every subset <math>A \subseteq X,</math> <math>\operatorname{cl} A</math> is equal to the topological closure <math>\operatorname{cl}_{(X, \tau)} A</math> of <math>A</math> in <math>(X, \tau).</math> If the sets <math>X</math> and <math>Y</math> are each associated with closure operators (both denoted by <math>\operatorname{cl}</math>) then a map <math>f : X \to Y</math> is continuous if and only if <math>f(\operatorname{cl} A) \subseteq \operatorname{cl} (f(A))</math> for every subset <math>A \subseteq X.</math>
Similarly, the map that sends a subset <math>A</math> of <math>X</math> to its topological interior <math>\operatorname{int}_X A</math> defines an interior operator. Conversely, any interior operator <math>A \mapsto \operatorname{int} A</math> induces a unique topology <math>\tau</math> on <math>X</math> (specifically, <math>\tau :\{ \operatorname{int} A : A \subseteq X \}</math>) such that for every <math>A \subseteq X,</math> <math>\operatorname{int} A</math> is equal to the topological interior <math>\operatorname{int}_{(X, \tau)} A</math> of <math>A</math> in <math>(X, \tau).</math> If the sets <math>X</math> and <math>Y</math> are each associated with interior operators (both denoted by <math>\operatorname{int}</math>) then a map <math>f : X \to Y</math> is continuous if and only if <math>f^{-1}(\operatorname{int} B) \subseteq \operatorname{int}\left(f^{-1}(B)\right)</math> for every subset <math>B \subseteq Y.</math>
Filters and prefilters
Continuity can also be characterized in terms of filters. A function <math>f : X \to Y</math> is continuous if and only if whenever a filter <math>\mathcal{B}</math> on <math>X</math> converges in <math>X</math> to a point <math>x \in X,</math> then the prefilter <math>f(\mathcal{B})</math> converges in <math>Y</math> to <math>f(x).</math> This characterization remains true if the word "filter" is replaced by "prefilter."Properties
If <math>f : X \to Y</math> and <math>g : Y \to Z</math> are continuous, then so is the composition <math>g \circ f : X \to Z.</math> If <math>f : X \to Y</math> is continuous and
* X is compact, then f(X) is compact.
* X is connected, then f(X) is connected.
* X is path-connected, then f(X) is path-connected.
* X is Lindelöf, then f(X) is Lindelöf.
* X is separable, then f(X) is separable.
The possible topologies on a fixed set X are partially ordered: a topology <math>\tau_1</math> is said to be coarser than another topology <math>\tau_2</math> (notation: <math>\tau_1 \subseteq \tau_2</math>) if every open subset with respect to <math>\tau_1</math> is also open with respect to <math>\tau_2.</math> Then, the identity map
<math display="block">\operatorname{id}_X : \left(X, \tau_2\right) \to \left(X, \tau_1\right)</math>
is continuous if and only if <math>\tau_1 \subseteq \tau_2</math> (see also comparison of topologies). More generally, a continuous function
<math display="block">\left(X, \tau_X\right) \to \left(Y, \tau_Y\right)</math>
stays continuous if the topology <math>\tau_Y</math> is replaced by a coarser topology and/or <math>\tau_X</math> is replaced by a finer topology.
Homeomorphisms
Symmetric to the concept of a continuous map is an open map, for which of open sets are open. If an open map f has an inverse function, that inverse is continuous, and if a continuous map g has an inverse, that inverse is open. Given a bijective function f between two topological spaces, the inverse function <math>f^{-1}</math> need not be continuous. A bijective continuous function with a continuous inverse function is called a .
If a continuous bijection has as its domain a compact space and its codomain is Hausdorff, then it is a homeomorphism.
Defining topologies via continuous functions
Given a function
<math display="block">f : X \to S,</math>
where X is a topological space and S is a set (without a specified topology), the final topology on S is defined by letting the open sets of S be those subsets A of S for which <math>f^{-1}(A)</math> is open in X. If S has an existing topology, f is continuous with respect to this topology if and only if the existing topology is coarser than the final topology on S. Thus, the final topology is the finest topology on S that makes f continuous. If f is surjective, this topology is canonically identified with the quotient topology under the equivalence relation defined by f.
Dually, for a function f from a set S to a topological space X, the initial topology on S is defined by designating as an open set every subset A of S such that <math>A = f^{-1}(U)</math> for some open subset U of X. If S has an existing topology, f is continuous with respect to this topology if and only if the existing topology is finer than the initial topology on S. Thus, the initial topology is the coarsest topology on S that makes f continuous. If f is injective, this topology is canonically identified with the subspace topology of S, viewed as a subset of X.
A topology on a set S is uniquely determined by the class of all continuous functions <math>S \to X</math> into all topological spaces X. Dually, a similar idea can be applied to maps <math>X \to S.</math>
Related notions
If <math>f : S \to Y</math> is a continuous function from some subset <math>S</math> of a topological space <math>X</math> then a }} of <math>f</math> to <math>X</math> is any continuous function <math>F : X \to Y</math> such that <math>F(s) f(s)</math> for every <math>s \in S,</math> which is a condition that often written as <math>f F\big\vert_S.</math> In words, it is any continuous function <math>F : X \to Y</math> that restricts to <math>f</math> on <math>S.</math> This notion is used, for example, in the Tietze extension theorem and the Hahn–Banach theorem. If <math>f : S \to Y</math> is not continuous, then it could not possibly have a continuous extension. If <math>Y</math> is a Hausdorff space and <math>S</math> is a dense subset of <math>X</math> then a continuous extension of <math>f : S \to Y</math> to <math>X,</math> if one exists, will be unique. The Blumberg theorem states that if <math>f : \R \to \R</math> is an arbitrary function then there exists a dense subset <math>D</math> of <math>\R</math> such that the restriction <math>f\big\vert_D : D \to \R</math> is continuous; in other words, every function <math>\R \to \R</math> can be restricted to some dense subset on which it is continuous.
Various other mathematical domains use the concept of continuity in different but related meanings. For example, in order theory, an order-preserving function <math>f : X \to Y</math> between particular types of partially ordered sets <math>X</math> and <math>Y</math> is continuous if for each directed subset <math>A</math> of <math>X,</math> we have <math>\sup f(A) f(\sup A).</math> Here <math>\,\sup\,</math> is the supremum with respect to the orderings in <math>X</math> and <math>Y,</math> respectively. This notion of continuity is the same as topological continuity when the partially ordered sets are given the Scott topology.
In category theory, a functor
<math display="block">F : \mathcal C \to \mathcal D</math>
between two categories is called if it commutes with small limits. That is to say,
<math display="block">\varprojlim_{i \in I} F(C_i) \cong F \left(\varprojlim_{i \in I} C_i \right)</math>
for any small (that is, indexed by a set <math>I,</math> as opposed to a class) diagram of objects in <math>\mathcal C</math>.
A is a generalization of metric spaces and posets, which uses the concept of quantales, and that can be used to unify the notions of metric spaces and domains.
In measure theory, a function <math>f : E \to \mathbb{R}^k</math> defined on a Lebesgue measurable set <math>E \subseteq \mathbb{R}^n</math> is called approximately continuous at a point <math>x_0 \in E</math> if the approximate limit of <math>f</math> at <math>x_0</math> exists and equals <math>f(x_0)</math>. This generalizes the notion of continuity by replacing the ordinary limit with the approximate limit. A fundamental result known as the Stepanov-Denjoy theorem states that a function is measurable if and only if it is approximately continuous almost everywhere.
See also
* Continuity (mathematics)
* Absolute continuity
* Approximate continuity
* Dini continuity
* Equicontinuity
* Geometric continuity
* Parametric continuity
* Classification of discontinuities
* Coarse function
* Continuous function (set theory)
* Continuous stochastic process
* Normal function
* Open and closed maps
* Piecewise
* Symmetrically continuous function
* Direction-preserving function - an analog of a continuous function in discrete spaces.
References
Bibliography
* <!-- -->
*
Category:Calculus
Category:Types of functions
|
https://en.wikipedia.org/wiki/Continuous_function
|
2025-04-05T18:27:43.496607
|
6123
|
Curl (mathematics)
|
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. which also reveals the relation between curl (rotor), divergence, and gradient operators.
Unlike the gradient and divergence, curl as formulated in vector calculus does not generalize simply to other dimensions; some generalizations are possible, but only in three dimensions is the geometrically defined curl of a vector field again a vector field. This deficiency is a direct consequence of the limitations of vector calculus; on the other hand, when expressed as an antisymmetric tensor field via the wedge operator of geometric calculus, the curl generalizes to all dimensions. The circumstance is similar to that attending the 3-dimensional cross product, and indeed the connection is reflected in the notation <math>\nabla \times</math> for the curl.
The name "curl" was first suggested by James Clerk Maxwell in 1871 but the concept was apparently first used in the construction of an optical field theory by James MacCullagh in 1839.Definition
<!--using multiple image template here to make widths the same-->
at position , normal and tangent to a closed curve in a plane, enclosing a planar vector area {{nowrap|<math>\mathbf{A} A\mathbf{\hat{n}}</math>.}}
}}
</math> and the fingers curl along the orientation of
| align | direction
| alt1 | header Right-hand rule
}}
<!---DEL CROSS F IS NOT A DEFINITION, IT'S AN ALTERNATIVE NOTATION. IT DOESN'T MEAN ANYTHING SO YOU CAN'T BASE A DEFINITION ON IT----->
The curl of a vector field , denoted by , or <math>\nabla \times \mathbf{F}</math>, or , is an operator that maps functions in to functions in , and in particular, it maps continuously differentiable functions to continuous functions . It can be defined in several ways, to be mentioned below:
One way to define the curl of a vector field at a point is implicitly through its components along various axes passing through the point: if <math>\mathbf{\hat{u}}</math> is any unit vector, the component of the curl of along the direction <math>\mathbf{\hat{u}}</math> may be defined to be the limiting value of a closed line integral in a plane perpendicular to <math>\mathbf{\hat{u}}</math> divided by the area enclosed, as the path of integration is contracted indefinitely around the point.
More specifically, the curl is defined at a point as
<math display"block">(\nabla \times \mathbf{F})(p)\cdot \mathbf{\hat{u}} \ \overset{\underset{\mathrm{def}}{}}{{}{}} \lim_{A \to 0}\frac{1}{|A|}\oint_{C(p)} \mathbf{F} \cdot \mathrm{d}\mathbf{r}</math>
where the line integral is calculated along the boundary of the area containing point p, }} being the magnitude of the area. This equation defines the component of the curl of along the direction <math>\mathbf{\hat{u}}</math>. The infinitesimal surfaces bounded by have <math>\mathbf{\hat{u}}</math> as their normal. is oriented via the right-hand rule.
The above formula means that the component of the curl of a vector field along a certain axis is the infinitesimal area density of the circulation of the field in a plane perpendicular to that axis. This formula does not a priori define a legitimate vector field, for the individual circulation densities with respect to various axes a priori need not relate to each other in the same way as the components of a vector do; that they do indeed relate to each other in this precise manner must be proven separately.
To this definition fits naturally the Kelvin–Stokes theorem, as a global formula corresponding to the definition. It equates the surface integral of the curl of a vector field to the above line integral taken around the boundary of the surface.
Another way one can define the curl vector of a function at a point is explicitly as the limiting value of a vector-valued surface integral around a shell enclosing divided by the volume enclosed, as the shell is contracted indefinitely around .
More specifically, the curl may be defined by the vector formula
<math display"block">(\nabla \times \mathbf{F})(p) \overset{\underset{\mathrm{def}}{}}{{}{}} \lim_{V \to 0}\frac{1}{|V|}\oint_S \mathbf{\hat{n}} \times \mathbf{F} \ \mathrm{d}S</math>
where the surface integral is calculated along the boundary of the volume , }} being the magnitude of the volume, and <math>\mathbf{\hat{n}}</math> pointing outward from the surface perpendicularly at every point in .
In this formula, the cross product in the integrand measures the tangential component of at each point on the surface , and points along the surface at right angles to the tangential projection of . Integrating this cross product over the whole surface results in a vector whose magnitude measures the overall circulation of around , and whose direction is at right angles to this circulation. The above formula says that the curl of a vector field at a point is the infinitesimal volume density of this "circulation vector" around the point.
To this definition fits naturally another global formula (similar to the Kelvin-Stokes theorem) which equates the volume integral of the curl of a vector field to the above surface integral taken over the boundary of the volume.
Whereas the above two definitions of the curl are coordinate free, there is another "easy to memorize" definition of the curl in curvilinear orthogonal coordinates, e.g. in Cartesian coordinates, spherical, cylindrical, or even elliptical or parabolic coordinates: <math display="block">\begin{align}
& (\operatorname{curl}\mathbf F)_1=\frac{1}{h_2h_3}\left (\frac{\partial (h_3F_3)}{\partial u_2}-\frac{\partial (h_2F_2)}{\partial u_3}\right ), \\[5pt]
& (\operatorname{curl}\mathbf F)_2=\frac{1}{h_3h_1}\left (\frac{\partial (h_1F_1)}{\partial u_3}-\frac{\partial (h_3F_3)}{\partial u_1}\right ), \\[5pt]
& (\operatorname{curl}\mathbf F)_3=\frac{1}{h_1h_2}\left (\frac{\partial (h_2F_2)}{\partial u_1}-\frac{\partial (h_1F_1)}{\partial u_2}\right ).
\end{align}</math>
The equation for each component can be obtained by exchanging each occurrence of a subscript 1, 2, 3 in cyclic permutation: 1 → 2, 2 → 3, and 3 → 1 (where the subscripts represent the relevant indices).
If are the Cartesian coordinates and are the orthogonal coordinates, then
<math display"block">h_i \sqrt{\left (\frac{\partial x_1}{\partial u_i} \right )^2 + \left (\frac{\partial x_2}{\partial u_i} \right )^2 + \left (\frac{\partial x_3}{\partial u_i} \right )^2}</math>
is the length of the coordinate vector corresponding to . The remaining two components of curl result from cyclic permutation of indices: 3,1,2 → 1,2,3 → 2,3,1.
Usage
In practice, the two coordinate-free definitions described above are rarely used because in virtually all cases, the curl operator can be applied using some set of curvilinear coordinates, for which simpler representations have been derived.
The notation <math>\nabla\times\mathbf{F}</math> has its origins in the similarities to the 3-dimensional cross product, and it is useful as a mnemonic in Cartesian coordinates if <math>\nabla</math> is taken as a vector differential operator del. Such notation involving operators is common in physics and algebra.
Expanded in 3-dimensional Cartesian coordinates (see Del in cylindrical and spherical coordinates for spherical and cylindrical coordinate representations), <math>\nabla\times\mathbf{F}</math> is, for <math>\mathbf{F}</math> composed of <math>[F_x,F_y,F_z]</math> (where the subscripts indicate the components of the vector, not partial derivatives):
<math display="block">
\nabla \times \mathbf{F} =
\begin{vmatrix} \boldsymbol{\hat\imath} & \boldsymbol{\hat\jmath} & \boldsymbol{\hat k} \\[5mu]
{\dfrac{\partial}{\partial x}} & {\dfrac{\partial}{\partial y}} & {\dfrac{\partial}{\partial z}} \\[5mu]
F_x & F_y & F_z \end{vmatrix}
</math>
where , , and are the unit vectors for the -, -, and -axes, respectively. This expands as follows:
<math display="block">
\nabla \times \mathbf{F} =
\left(\frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z}\right) \boldsymbol{\hat\imath} +
\left(\frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \boldsymbol{\hat\jmath} +
\left(\frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \boldsymbol{\hat k}
</math>
Although expressed in terms of coordinates, the result is invariant under proper rotations of the coordinate axes but the result inverts under reflection.
In a general coordinate system, the curl is given by
<math display"block">(\nabla \times \mathbf{F} )^k \frac{1}{\sqrt{g}} \varepsilon^{k\ell m} \nabla_\ell F_m</math>
where denotes the Levi-Civita tensor, the covariant derivative, <math> g</math> is the determinant of the metric tensor and the Einstein summation convention implies that repeated indices are summed over. Due to the symmetry of the Christoffel symbols participating in the covariant derivative, this expression reduces to the partial derivative:
<math display"block">(\nabla \times \mathbf{F} ) \frac{1}{\sqrt{g}} \mathbf{R}_k\varepsilon^{k\ell m} \partial_\ell F_m</math>
where are the local basis vectors. Equivalently, using the exterior derivative, the curl can be expressed as:
<math display"block"> \nabla \times \mathbf{F} \left( \star \big( {\mathrm d} \mathbf{F}^\flat \big) \right)^\sharp </math>
Here and are the musical isomorphisms, and is the Hodge star operator. This formula shows how to calculate the curl of in any coordinate system, and how to extend the curl to any oriented three-dimensional Riemannian manifold. Since this depends on a choice of orientation, curl is a chiral operation. In other words, if the orientation is reversed, then the direction of the curl is also reversed.
Examples
Example 1
Suppose the vector field describes the velocity field of a fluid flow (such as a large tank of liquid or gas) and a small ball is located within the fluid or gas (the center of the ball being fixed at a certain point). If the ball has a rough surface, the fluid flowing past it will make it rotate. The rotation axis (oriented according to the right hand rule) points in the direction of the curl of the field at the center of the ball, and the angular speed of the rotation is half the magnitude of the curl at this point.
The curl of the vector field at any point is given by the rotation of an infinitesimal area in the xy-plane (for z-axis component of the curl), zx-plane (for y-axis component of the curl) and yz-plane (for x-axis component of the curl vector). This can be seen in the examples below.
Example 2
(left) and its curl (right).
}}
The vector field
<math display"block">\mathbf{F}(x,y,z)y\boldsymbol{\hat{\imath}}-x\boldsymbol{\hat{\jmath}}</math>
can be decomposed as
<math display"block">F_xy, F_y -x, F_z0.</math>
Upon visual inspection, the field can be described as "rotating". If the vectors of the field were to represent a linear force acting on objects present at that point, and an object were to be placed inside the field, the object would start to rotate clockwise around itself. This is true regardless of where the object is placed.
Calculating the curl:
<math display"block">\nabla \times \mathbf{F}0\boldsymbol{\hat{\imath}}+0\boldsymbol{\hat{\jmath}}+ \left({\frac{\partial}{\partial x}}(-x) -{\frac{\partial}{\partial y}} y\right)\boldsymbol{\hat{k}}=-2\boldsymbol{\hat{k}}
</math>
The resulting vector field describing the curl would at all points be pointing in the negative direction. The results of this equation align with what could have been predicted using the right-hand rule using a right-handed coordinate system. Being a uniform vector field, the object described before would have the same rotational intensity regardless of where it was placed.
Example 3
(left) and its curl (right).
}}
For the vector field
<math display"block">\mathbf{F}(x,y,z) -x^2\boldsymbol{\hat{\jmath}}</math>
the curl is not as obvious from the graph. However, taking the object in the previous example, and placing it anywhere on the line , the force exerted on the right side would be slightly greater than the force exerted on the left, causing it to rotate clockwise. Using the right-hand rule, it can be predicted that the resulting curl would be straight in the negative direction. Inversely, if placed on , the object would rotate counterclockwise and the right-hand rule would result in a positive direction.
Calculating the curl:
<math display"block">{\nabla} \times \mathbf{F} 0 \boldsymbol{\hat{\imath}} + 0\boldsymbol{\hat{\jmath}} + {\frac{\partial}{\partial x}}\left(-x^2\right) \boldsymbol{\hat{k}} = -2x\boldsymbol{\hat{k}}.</math>
The curl points in the negative direction when is positive and vice versa. In this field, the intensity of rotation would be greater as the object moves away from the plane .
Further examples
* In a vector field describing the linear velocities of each part of a rotating disk in uniform circular motion, the curl has the same value at all points, and this value turns out to be exactly two times the vectorial angular velocity of the disk (oriented as usual by the right-hand rule). More generally, for any flowing mass, the linear velocity vector field at each point of the mass flow has a curl (the vorticity of the flow at that point) equal to exactly two times the local vectorial angular velocity of the mass about the point.
* For any solid object subject to an external physical force (such as gravity or the electromagnetic force), one may consider the vector field representing the infinitesimal force-per-unit-volume contributions acting at each of the points of the object. This force field may create a net torque on the object about its center of mass, and this torque turns out to be directly proportional and vectorially parallel to the (vector-valued) integral of the curl of the force field over the whole volume.
* Of the four Maxwell's equations, two—Faraday's law and Ampère's law—can be compactly expressed using curl. Faraday's law states that the curl of an electric field is equal to the opposite of the time rate of change of the magnetic field, while Ampère's law relates the curl of the magnetic field to the current and the time rate of change of the electric field.
Identities
In general curvilinear coordinates (not only in Cartesian coordinates), the curl of a cross product of vector fields and can be shown to be
<math display"block">\nabla \times \left( \mathbf{v \times F} \right) \Big( \left( \mathbf{ \nabla \cdot F } \right) + \mathbf{F \cdot \nabla} \Big) \mathbf{v}- \Big( \left( \mathbf{ \nabla \cdot v } \right) + \mathbf{v \cdot \nabla} \Big) \mathbf{F} \ . </math>
Interchanging the vector field and operator, we arrive at the cross product of a vector field with curl of a vector field:
<math display"block"> \mathbf{v \ \times } \left( \mathbf{ \nabla \times F} \right)\nabla_\mathbf{F} \left( \mathbf{v \cdot F } \right) - \left( \mathbf{v \cdot \nabla } \right) \mathbf{F} \ , </math>
where is the Feynman subscript notation, which considers only the variation due to the vector field (i.e., in this case, is treated as being constant in space).
Another example is the curl of a curl of a vector field. It can be shown that in general coordinates
<math display"block"> \nabla \times \left( \mathbf{\nabla \times F} \right) \mathbf{\nabla}(\mathbf{\nabla \cdot F}) - \nabla^2 \mathbf{F} \ , </math>
and this identity defines the vector Laplacian of , symbolized as .
The curl of the gradient of any scalar field is always the zero vector field
<math display"block">\nabla \times ( \nabla \varphi ) \boldsymbol{0}</math>
which follows from the antisymmetry in the definition of the curl, and the symmetry of second derivatives.
The divergence of the curl of any vector field is equal to zero:
<math display"block">\nabla\cdot(\nabla\times\mathbf{F}) 0.</math>
If is a scalar valued function and is a vector field, then
<math display"block">\nabla \times ( \varphi \mathbf{F}) \nabla \varphi \times \mathbf{F} + \varphi \nabla \times \mathbf{F} </math>
Generalizations
The vector calculus operations of grad, curl, and div are most easily generalized in the context of differential forms, which involves a number of steps. In short, they correspond to the derivatives of 0-forms, 1-forms, and 2-forms, respectively. The geometric interpretation of curl as rotation corresponds to identifying bivectors (2-vectors) in 3 dimensions with the special orthogonal Lie algebra <math>\mathfrak{so}(3)</math> of infinitesimal rotations (in coordinates, skew-symmetric 3 × 3 matrices), while representing rotations by vectors corresponds to identifying 1-vectors (equivalently, 2-vectors) and {{nowrap|<math>\mathfrak{so}(3)</math>,}} these all being 3-dimensional spaces.
Differential forms
In 3 dimensions, a differential 0-form is a real-valued function <math>f(x,y,z)</math>; a differential 1-form is the following expression, where the coefficients are functions:
<math display="block">a_1\,dx + a_2\,dy + a_3\,dz;</math>
a differential 2-form is the formal sum, again with function coefficients:
<math display="block">a_{12}\,dx\wedge dy + a_{13}\,dx\wedge dz + a_{23}\,dy\wedge dz;</math>
and a differential 3-form is defined by a single term with one function as coefficient:
<math display="block">a_{123}\,dx\wedge dy\wedge dz.</math>
(Here the -coefficients are real functions of three variables; the "wedge products", e.g. <math>\text{d}x\wedge\text{d}y</math>, can be interpreted as some kind of oriented area elements, <math>\text{d}x\wedge\text{d}y=-\text{d}y\wedge\text{d}x</math>, etc.)
The exterior derivative of a -form in is defined as the -form from above—and in if, e.g.,
<math display"block">\omega^{(k)}\sum_{1\leq i_1<i_2<\cdots<i_k\leq n} a_{i_1,\ldots,i_k} \,dx_{i_1}\wedge \cdots\wedge dx_{i_k},</math>
then the exterior derivative leads to
<math display"block"> d\omega^{(k)}\sum_{\scriptstyle{j=1} \atop \scriptstyle{i_1<\cdots<i_k}}^n\frac{\partial a_{i_1,\ldots,i_k}}{\partial x_j}\,dx_j \wedge dx_{i_1}\wedge \cdots \wedge dx_{i_k}.</math>
The exterior derivative of a 1-form is therefore a 2-form, and that of a 2-form is a 3-form. On the other hand, because of the interchangeability of mixed derivatives,
<math display"block">\frac{\partial^2}{\partial x_i\,\partial x_j} \frac{\partial^2}{\partial x_j\,\partial x_i} , </math>
and antisymmetry,
<math display"block">d x_i \wedge d x_j -d x_j \wedge d x_i</math>
the twofold application of the exterior derivative yields <math>0</math> (the zero <math>k+2</math>-form).
Thus, denoting the space of -forms by <math>\Omega^k(\mathbb{R}^3)</math> and the exterior derivative by one gets a sequence:
<math display="block">0 \, \overset{d}{\longrightarrow} \;
\Omega^0\left(\mathbb{R}^3\right) \, \overset{d}{\longrightarrow} \;
\Omega^1\left(\mathbb{R}^3\right) \, \overset{d}{\longrightarrow} \;
\Omega^2\left(\mathbb{R}^3\right) \, \overset{d}{\longrightarrow} \;
\Omega^3\left(\mathbb{R}^3\right) \, \overset{d}{\longrightarrow} \, 0.</math>
Here <math>\Omega^k(\mathbb{R}^n)</math> is the space of sections of the exterior algebra <math>\Lambda^k(\mathbb{R}^n)</math> vector bundle over R<sup>n</sup>, whose dimension is the binomial coefficient <math>\binom{n}{k}</math>; note that <math>\Omega^k(\mathbb{R}^3)=0</math> for <math>k>3</math> or <math>k<0</math>. Writing only dimensions, one obtains a row of Pascal's triangle:
<math display="block">0\rightarrow 1\rightarrow 3\rightarrow 3\rightarrow 1\rightarrow 0;</math>
the 1-dimensional fibers correspond to scalar fields, and the 3-dimensional fibers to vector fields, as described below. Modulo suitable identifications, the three nontrivial occurrences of the exterior derivative correspond to grad, curl, and div.
Differential forms and the differential can be defined on any Euclidean space, or indeed any manifold, without any notion of a Riemannian metric. On a Riemannian manifold, or more generally pseudo-Riemannian manifold, -forms can be identified with -vector fields (-forms are -covector fields, and a pseudo-Riemannian metric gives an isomorphism between vectors and covectors), and on an oriented vector space with a nondegenerate form (an isomorphism between vectors and covectors), there is an isomorphism between -vectors and -vectors; in particular on (the tangent space of) an oriented pseudo-Riemannian manifold. Thus on an oriented pseudo-Riemannian manifold, one can interchange -forms, -vector fields, -forms, and -vector fields; this is known as Hodge duality. Concretely, on this is given by:
* 1-forms and 1-vector fields: the 1-form corresponds to the vector field .
* 1-forms and 2-forms: one replaces by the dual quantity (i.e., omit ), and likewise, taking care of orientation: corresponds to , and corresponds to . Thus the form corresponds to the "dual form" .
Thus, identifying 0-forms and 3-forms with scalar fields, and 1-forms and 2-forms with vector fields:
* grad takes a scalar field (0-form) to a vector field (1-form);
* curl takes a vector field (1-form) to a pseudovector field (2-form);
* div takes a pseudovector field (2-form) to a pseudoscalar field (3-form)
On the other hand, the fact that 0}} corresponds to the identities
<math display"block">\nabla\times(\nabla f) \mathbf 0</math>
for any scalar field , and
<math display"block">\nabla \cdot (\nabla \times\mathbf v)0</math>
for any vector field .
Grad and div generalize to all oriented pseudo-Riemannian manifolds, with the same geometric interpretation, because the spaces of 0-forms and -forms at each point are always 1-dimensional and can be identified with scalar fields, while the spaces of 1-forms and -forms are always fiberwise -dimensional and can be identified with vector fields.
Curl does not generalize in this way to 4 or more dimensions (or down to 2 or fewer dimensions); in 4 dimensions the dimensions are
so the curl of a 1-vector field (fiberwise 4-dimensional) is a 2-vector field, which at each point belongs to 6-dimensional vector space, and so one has
<math display"block">\omega^{(2)}\sum_{i<k=1,2,3,4}a_{i,k}\,dx_i\wedge dx_k,</math>
which yields a sum of six independent terms, and cannot be identified with a 1-vector field. Nor can one meaningfully go from a 1-vector field to a 2-vector field to a 3-vector field (4 → 6 → 4), as taking the differential twice yields zero ( 0}}). Thus there is no curl function from vector fields to vector fields in other dimensions arising in this way.
However, one can define a curl of a vector field as a 2-vector field in general, as described below.
Curl geometrically
2-vectors correspond to the exterior power ; in the presence of an inner product, in coordinates these are the skew-symmetric matrices, which are geometrically considered as the special orthogonal Lie algebra {{math|<math>\mathfrak{so}</math>(V)}} of infinitesimal rotations. This has <big><big>)</big></big> n(n − 1)}} dimensions, and allows one to interpret the differential of a 1-vector field as its infinitesimal rotations. Only in 3 dimensions (or trivially in 0 dimensions) we have n(n − 1)}}, which is the most elegant and common case. In 2 dimensions the curl of a vector field is not a vector field but a function, as 2-dimensional rotations are given by an angle (a scalar – an orientation is required to choose whether one counts clockwise or counterclockwise rotations as positive); this is not the div, but is rather perpendicular to it. In 3 dimensions the curl of a vector field is a vector field as is familiar (in 1 and 0 dimensions the curl of a vector field is 0, because there are no non-trivial 2-vectors), while in 4 dimensions the curl of a vector field is, geometrically, at each point an element of the 6-dimensional Lie algebra {{nowrap|<math>\mathfrak{so}(4)</math>.}}
The curl of a 3-dimensional vector field which only depends on 2 coordinates (say and ) is simply a vertical vector field (in the direction) whose magnitude is the curl of the 2-dimensional vector field, as in the examples on this page.
Considering curl as a 2-vector field (an antisymmetric 2-tensor) has been used to generalize vector calculus and associated physics to higher dimensions.Inverse
In the case where the divergence of a vector field is zero, a vector field exists such that . This is why the magnetic field, characterized by zero divergence, can be expressed as the curl of a magnetic vector potential.
If is a vector field with , then adding any gradient vector field to will result in another vector field such that as well. This can be summarized by saying that the inverse curl of a three-dimensional vector field can be obtained up to an unknown irrotational field with the Biot–Savart law.
See also
*Helmholtz decomposition
*Hiptmair–Xu preconditioner
*Del in cylindrical and spherical coordinates
*Vorticity
References
Further reading
*
* External links *
*
*
Category:Differential operators
Category:Linear operators in calculus
Category:Vector calculus
Category:Analytic geometry
|
https://en.wikipedia.org/wiki/Curl_(mathematics)
|
2025-04-05T18:27:43.516531
|
6125
|
Carl Friedrich Gauss
|
| birth_place = Brunswick, Principality of Brunswick-Wolfenbüttel,
| death_date
| death_place = Göttingen, Kingdom of Hanover,
| fields = Mathematics, Astronomy, Geodesy, Magnetism
| alma_mater =
| workplaces = University of Göttingen
| thesis_title = Demonstratio nova...
| thesis_url = http://www.e-rara.ch/zut/content/titleinfo/1336299
| thesis_year = 1799
| doctoral_advisor = Johann Friedrich Pfaff
| known_for = Full list
| spouse =
*
}}
| children = 6
| awards =
| doctoral_students
| Richard Dedekind
| Christian Ludwig Gerling
| Wilhelm Klinkerfues
| Johann Benedict Listing
| Bernhard Riemann
| August Ritter
| Karl von Staudt
}}
| notable_students
| Gotthold Eisenstein
| Johann Franz Encke
| Carl Wolfgang Benjamin Goldschmidt
| Adolph Theodor Kupffer
| August Ferdinand Möbius
| Moritz Stern
| Georg Frederik Ursin
| Moritz Ludwig Wichmann
}}
| signature = Carl Friedrich Gauß signature.svg
}}
Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855.
While studying at the University of Göttingen, he propounded several mathematical theorems. He completed his masterpieces Disquisitiones Arithmeticae and Theoria motus corporum coelestium'' as a private scholar. Gauss gave the second and third complete proofs of the fundamental theorem of algebra. In number theory, he made numerous contributions, such as formulating his composition law, proving the law of quadratic reciprocity and proving the triangular case of the Fermat polygonal number theorem, and developed the theories of binary and ternary quadratic forms. In geometry, he proved the construction of the heptadecagon. He provided the first systematic treatment of hypergeometric series.
Gauss was instrumental in the identification of Ceres as a dwarf planet. His work on the motion of planetoids disturbed by large planets led to the introduction of the Gaussian gravitational constant and the method of least squares, which he had discovered before Adrien-Marie Legendre published it. Gauss was in charge of the extensive geodetic survey of the Kingdom of Hanover together with an arc measurement project from 1820 to 1844; he was one of the founders of geophysics and formulated the fundamental principles of magnetism. His practical work led to the invention of the heliotrope in 1821, a magnetometer in 1833 and – with Wilhelm Eduard Weber – the first electromagnetic telegraph in 1833.
Gauss was the first to discover and study non-Euclidean geometry, coining the term as well. He developed a fast Fourier transform some 160 years before John Tukey and James Cooley.
Gauss refused to publish incomplete work and left several works to be edited posthumously. He believed that the act of learning, not possession of knowledge, provided the greatest enjoyment. Gauss confessed to disliking teaching, but some of his students became influential mathematicians, such as Richard Dedekind and Bernhard Riemann.
Biography
Youth and education
Gauss was born on 30 April 1777 in Brunswick in the Duchy of Brunswick-Wolfenbüttel (now in the German state of Lower Saxony). His family was of relatively low social status. His father Gebhard Dietrich Gauss (1744–1808) worked variously as a butcher, bricklayer, gardener, and treasurer of a death-benefit fund. Gauss characterized his father as honourable and respected, but rough and dominating at home. He was experienced in writing and calculating, whereas his second wife Dorothea, Carl Friedrich's mother, was nearly illiterate. He had one elder brother from his father's first marriage.
Gauss was a child prodigy in mathematics. When the elementary teachers noticed his intellectual abilities, they brought him to the attention of the Duke of Brunswick who sent him to the local Collegium Carolinum,
}} which he attended from 1792 to 1795 with Eberhard August Wilhelm von Zimmermann as one of his teachers. Thereafter the Duke granted him the resources for studies of mathematics, sciences, and classical languages at the University of Göttingen until 1798. His professor in mathematics was Abraham Gotthelf Kästner, whom Gauss called "the leading mathematician among poets, and the leading poet among mathematicians" because of his epigrams. Fellow students of this time were Johann Friedrich Benzenberg, Farkas Bolyai, and Heinrich Wilhelm Brandes.
He was likely a self-taught student in mathematics since he independently rediscovered several theorems. Gauss had realised that the sum could be rearanged as 50 pairs of 101 (1+100101, 2+99101, etc). Thus, he simply multiplied 50 by 101. Other accounts state that he computed the sum as 100 sets of 101 and divided by 2.
Private scholar
Gauss graduated as a Doctor of Philosophy in 1799, not in Göttingen, as is sometimes stated, Later, the Duke promised him the foundation of an observatory in Brunswick in 1804. Architect Peter Joseph Krahe made preliminary designs, but one of Napoleon's wars cancelled those plans: the Duke was killed in the battle of Jena in 1806. The duchy was abolished in the following year, and Gauss's financial support stopped.
When Gauss was calculating asteroid orbits in the first years of the century, he established contact with the astronomical communities of Bremen and Lilienthal, especially Wilhelm Olbers, Karl Ludwig Harding, and Friedrich Wilhelm Bessel, forming part of the informal group of astronomers known as the Celestial police. One of their aims was the discovery of further planets. They assembled data on asteroids and comets as a basis for Gauss's research on their orbits, which he later published in his astronomical magnum opus Theoria motus corporum coelestium (1809).
Professor in Göttingen
In November 1807, Gauss was hired by the University of Göttingen, then an institution of the newly founded Kingdom of Westphalia under Jérôme Bonaparte, as full professor and director of the astronomical observatory, and kept the chair until his death in 1855. He was soon confronted with the demand for two thousand francs from the Westphalian government as a war contribution, which he could not afford to pay. Both Olbers and Laplace wanted to help him with the payment, but Gauss refused their assistance. Finally, an anonymous person from Frankfurt, later discovered to be Prince-primate Dalberg, paid the sum.
Gauss took on the directorship of the 60-year-old observatory, founded in 1748 by Prince-elector George II and built on a converted fortification tower, with usable, but partly out-of-date instruments. The construction of a new observatory had been approved by Prince-elector George III in principle since 1802, and the Westphalian government continued the planning, but Gauss could not move to his new place of work until September 1816. and only three lectures on subjects of pure mathematics. the physicist Mayer, known for his textbooks, his successor Weber since 1831, and in the observatory Harding, who took the main part of lectures in practical astronomy. When the observatory was completed, Gauss occupied the western wing of the new observatory, while Harding took the eastern.}} Gauss gave another recommendation for an honorary degree for Sophie Germain but only shortly before her death, so she never received it. He also gave successful support to the mathematician Gotthold Eisenstein in Berlin.
Gauss was loyal to the House of Hanover. After King William IV died in 1837, the new Hanoverian King Ernest Augustus annulled the 1833 constitution. Seven professors, later known as the "Göttingen Seven", protested against this, among them his friend and collaborator Wilhelm Weber and Gauss's son-in-law Heinrich Ewald. All of them were dismissed, and three of them were expelled, but Ewald and Weber could stay in Göttingen. Gauss was deeply affected by this quarrel but saw no possibility to help them.
Gauss took part in academic administration: three times he was elected as dean of the Faculty of Philosophy. Being entrusted with the widow's pension fund of the university, he dealt with actuarial science and wrote a report on the strategy for stabilizing the benefits. He was appointed director of the Royal Academy of Sciences in Göttingen for nine years.
Gauss remained mentally active into his old age, even while suffering from gout and general unhappiness. On 23 February 1855, he died of a heart attack in Göttingen; and was interred in the Albani Cemetery there. Heinrich Ewald, Gauss's son-in-law, and Wolfgang Sartorius von Waltershausen, Gauss's close friend and biographer, gave eulogies at his funeral.
Gauss was a successful investor and accumulated considerable wealth with stocks and securities, amounting to a value of more than 150,000 Thaler; after his death, about 18,000 Thaler were found hidden in his rooms. Gauss's brain The day after Gauss's death his brain was removed, preserved, and studied by Rudolf Wagner, who found its mass to be slightly above average, at . Wagner's son Hermann, a geographer, estimated the cerebral area to be in his doctoral thesis. In 2013, a neurobiologist at the Max Planck Institute for Biophysical Chemistry in Göttingen discovered that Gauss's brain had been mixed up soon after the first investigations, due to mislabelling, with that of the physician Conrad Heinrich Fuchs, who died in Göttingen a few months after Gauss. A further investigation showed no remarkable anomalies in the brains of either person. Thus, all investigations of Gauss's brain until 1998, except the first ones of Rudolf and Hermann Wagner, actually refer to the brain of Fuchs. Family Gauss married Johanna Osthoff on 9 October 1805 in St. Catherine's church in Brunswick. They had two sons and one daughter: Joseph (1806–1873), Wilhelmina (1808–1840), and Louis (1809–1810). Johanna died on 11 October 1809, one month after the birth of Louis, who himself died a few months later. Gauss chose the first names of his children in honour of Giuseppe Piazzi, Wilhelm Olbers, and Karl Ludwig Harding, the discoverers of the first asteroids.
On 4 August 1810, Gauss married Wilhelmine (Minna) Waldeck, a friend of his first wife, with whom he had three more children: Eugen (later Eugene) (1811–1896), Wilhelm (later William) (1813–1879), and Therese (1816–1864). Minna Gauss died on 12 September 1831 after being seriously ill for more than a decade. Therese then took over the household and cared for Gauss for the rest of his life; after her father's death, she married actor Constantin Staufenau. Her sister Wilhelmina married the orientalist Heinrich Ewald. Gauss's mother Dorothea lived in his house from 1817 until she died in 1839. }}
Eugen left Göttingen in September 1830 and emigrated to the United States, where he spent five years with the army. He then worked for the American Fur Company in the Midwest. He later moved to Missouri and became a successful businessman. he then moved to Missouri, started as a farmer and became wealthy in the shoe business in St. Louis in later years. Eugene and William have numerous descendants in America, but the Gauss descendants left in Germany all derive from Joseph, as the daughters had no children. his Disquisitiones Arithmeticae was the first mathematical book from Germany to be translated into the French language.
Gauss was "in front of the new development" with documented research since 1799, his wealth of new ideas, and his rigour of demonstration. In contrast to previous mathematicians like Leonhard Euler, who let their readers take part in their reasoning, including certain erroneous deviations from the correct path, Gauss introduced a new style of direct and complete exposition that did not attempt to show the reader the author's train of thought.
}}
But for himself, he propagated a quite different ideal, given in a letter to Farkas Bolyai as follows:
}}
His posthumous papers, his scientific diary, and short glosses in his own textbooks show that he empirically worked to a great extent. He was a lifelong busy and enthusiastic calculator, working extraordinarily quickly and checking his results through estimation. Nevertheless, his calculations were not always free from mistakes. He coped with the enormous workload by using skillful tools. Gauss used numerous mathematical tables, examined their exactness, and constructed new tables on various matters for personal use. He developed new tools for effective calculation, for example the Gaussian elimination. Gauss's calculations and the tables he prepared were often more precise than practically necessary. Very likely, this method gave him additional material for his theoretical work.
with his motto Pauca sed Matura]]
Gauss was only willing to publish work when he considered it complete and above criticism. This perfectionism was in keeping with the motto of his personal seal ("Few, but Ripe"). Many colleagues encouraged him to publicize new ideas and sometimes rebuked him if he hesitated too long, in their opinion. Gauss defended himself by claiming that the initial discovery of ideas was easy, but preparing a presentable elaboration was a demanding matter for him, for either lack of time or "serenity of mind". Nevertheless, he published many short communications of urgent content in various journals, but left a considerable literary estate, too. Gauss referred to mathematics as "the queen of sciences" and arithmetics as "the queen of mathematics", and supposedly once espoused a belief in the necessity of immediately understanding Euler's identity as a benchmark pursuant to becoming a first-class mathematician.
On certain occasions, Gauss claimed that the ideas of another scholar had already been in his possession previously. Thus his concept of priority as "the first to discover, not the first to publish" differed from that of his scientific contemporaries. In contrast to his perfectionism in presenting mathematical ideas, his citations were criticized as negligent. He justified himself with an unusual view of correct citation practice: he would only give complete references, with respect to the previous authors of importance, which no one should ignore, but citing in this way would require knowledge of the history of science and more time than he wished to spend. His second wife and his two daughters suffered from tuberculosis. In a letter to Bessel, dated December 1831, Gauss hinted at his distress, describing himself as "the victim of the worst domestic sufferings". Eugen suddenly left Göttingen under dramatic circumstances in September 1830 and emigrated via Bremen to the United States. He wasted the little money he had taken to start, after which his father refused further financial support.}} His favorite English author was Walter Scott, his favorite German Jean Paul. At the age of 62, he began to teach himself Russian, very likely to understand scientific writings from Russia, among them those of Lobachevsky on non-Euclidean geometry. Gauss liked singing and went to concerts. He was a busy newspaper reader; in his last years, he would visit an academic press salon of the university every noon. Gauss did not care much for philosophy, and mocked the "splitting hairs of the so-called metaphysicians", by which he meant proponents of the contemporary school of Naturphilosophie.
Gauss had an "aristocratic and through and through conservative nature", with little respect for people's intelligence and morals, following the motto "mundus vult decipi". He disliked Napoleon and his system and was horrified by violence and revolution of all kinds. Thus he condemned the methods of the Revolutions of 1848, though he agreed with some of their aims, such as that of a unified Germany. He had a low estimation of the constitutional system and he criticized parliamentarians of his time for their perceived ignorance and logical errors.
Some Gauss biographers have speculated on his religious beliefs. He sometimes said "God arithmetizes" and "I succeeded – not on account of my hard efforts, but by the grace of the Lord." Gauss was a member of the Lutheran church, like most of the population in northern Germany, but it seems that he did not believe all Lutheran dogma or understand the Bible fully literally. According to Sartorius, Gauss' religious tolerance, "insatiable thirst for truth" and sense of justice were motivated by his religious convictions. Mathematics Algebra and number theory Fundamental theorem of algebra
or Gauss plane]]
In his doctoral thesis from 1799, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. Mathematicians including Jean le Rond d'Alembert had produced false proofs before him, and Gauss's dissertation contains a critique of d'Alembert's work. He subsequently produced three other proofs, the last one in 1849 being generally rigorous. His attempts led to considerable clarification of the concept of complex numbers.
Disquisitiones Arithmeticae
In the preface to the Disquisitiones, Gauss dates the beginning of his work on number theory to 1795. By studying the works of previous mathematicians like Fermat, Euler, Lagrange, and Legendre, he realized that these scholars had already found much of what he had independently discovered. The Disquisitiones Arithmeticae, written in 1798 and published in 1801, consolidated number theory as a discipline and covered both elementary and algebraic number theory. Therein he introduces the triple bar symbol () for congruence and uses it for a clean presentation of modular arithmetic. It deals with the unique factorization theorem and primitive roots modulo n. In the main sections, Gauss presents the first two proofs of the law of quadratic reciprocity and develops the theories of binary and ternary quadratic forms.
The Disquisitiones include the Gauss composition law for binary quadratic forms, as well as the enumeration of the number of representations of an integer as the sum of three squares. As an almost immediate corollary of his theorem on three squares, he proves the triangular case of the Fermat polygonal number theorem for n 3. From several analytic results on class numbers that Gauss gives without proof towards the end of the fifth section, it appears that Gauss already knew the class number formula in 1801.
In the last section, Gauss gives proof for the constructibility of a regular heptadecagon (17-sided polygon) with straightedge and compass by reducing this geometrical problem to an algebraic one. He shows that a regular polygon is constructible if the number of its sides is either a power of 2 or the product of a power of 2 and any number of distinct Fermat primes. In the same section, he gives a result on the number of solutions of certain cubic polynomials with coefficients in finite fields, which amounts to counting integral points on an elliptic curve. An unfinished chapter, consisting of work done during 1797–1799, was found among his papers after his death. Further investigations One of Gauss's first results was the empirically found conjecture of 1792 – the later called prime number theorem – giving an estimation of the number of prime numbers by using the integral logarithm.}}
In 1816, Olbers encouraged Gauss to compete for a prize from the French Academy for a proof for Fermat's Last Theorem; he refused, considering the topic uninteresting. However, after his death a short undated paper was found with proofs of the theorem for the cases n 3 and n 5. The particular case of n 3 was proved much earlier by Leonhard Euler, but Gauss developed a more streamlined proof which made use of Eisenstein integers; though more general, the proof was simpler than in the real integers case.
Gauss contributed to solving the Kepler conjecture in 1831 with the proof that a greatest packing density of spheres in the three-dimensional space is given when the centres of the spheres form a cubic face-centred arrangement, when he reviewed a book of Ludwig August Seeber on the theory of reduction of positive ternary quadratic forms. Having noticed some lacks in Seeber's proof, he simplified many of his arguments, proved the central conjecture, and remarked that this theorem is equivalent to the Kepler conjecture for regular arrangements.
In two papers on biquadratic residues (1828, 1832) Gauss introduced the ring of Gaussian integers <math>\mathbb{Z}[i]</math>, showed that it is a unique factorization domain. and generalized some key arithmetic concepts, such as Fermat's little theorem and Gauss's lemma. The main objective of introducing this ring was to formulate the law of biquadratic reciprocity
In the second paper, he stated the general law of biquadratic reciprocity and proved several special cases of it. In an earlier publication from 1818 containing his fifth and sixth proofs of quadratic reciprocity, he claimed the techniques of these proofs (Gauss sums) can be applied to prove higher reciprocity laws. Analysis One of Gauss's first discoveries was the notion of the arithmetic-geometric mean (AGM) of two positive real numbers. He discovered its relation to elliptic integrals in the years 1798–1799 through Landen's transformation, and a diary entry recorded the discovery of the connection of Gauss's constant to lemniscatic elliptic functions, a result that Gauss stated "will surely open an entirely new field of analysis". He also made early inroads into the more formal issues of the foundations of complex analysis, and from a letter to Bessel in 1811 it is clear that he knew the "fundamental theorem of complex analysis" – Cauchy's integral theorem – and understood the notion of complex residues when integrating around poles.
Euler's pentagonal numbers theorem, together with other researches on the AGM and lemniscatic functions, led him to plenty of results on Jacobi theta functions, His works show that he knew modular transformations of order 3, 5, 7 for elliptic functions since 1808.}}
Several mathematical fragments in his Nachlass indicate that he knew parts of the modern theory of modular forms. One of Gauss's sketches of this kind was a drawing of a tessellation of the unit disk by "equilateral" hyperbolic triangles with all angles equal to <math>\pi/4</math>.
An example of Gauss's insight in analysis is the cryptic remark that the principles of circle division by compass and straightedge can also be applied to the division of the lemniscate curve, which inspired Abel's theorem on lemniscate division. Another example is his publication "Summatio quarundam serierum singularium" (1811) on the determination of the sign of quadratic Gauss sums, in which he solved the main problem by introducing q-analogs of binomial coefficients and manipulating them by several original identities that seem to stem from his work on elliptic function theory; however, Gauss cast his argument in a formal way that does not reveal its origin in elliptic function theory, and only the later work of mathematicians such as Jacobi and Hermite has exposed the crux of his argument.
In the "Disquisitiones generales circa series infinitam..." (1813), he provides the first systematic treatment of the general hypergeometric function <math>F(\alpha,\beta,\gamma,x)</math>, and shows that many of the functions known at the time are special cases of the hypergeometric function. This work is the first exact inquiry into convergence of infinite series in the history of mathematics. Furthermore, it deals with infinite continued fractions arising as ratios of hypergeometric functions, which are now called Gauss continued fractions.
In 1823, Gauss won the prize of the Danish Society with an essay on conformal mappings, which contains several developments that pertain to the field of complex analysis. Gauss stated that angle-preserving mappings in the complex plane must be complex analytic functions, and used the later-named Beltrami equation to prove the existence of isothermal coordinates on analytic surfaces. The essay concludes with examples of conformal mappings into a sphere and an ellipsoid of revolution.
Numerical analysis
Gauss often deduced theorems inductively from numerical data he had collected empirically. As such, the use of efficient algorithms to facilitate calculations was vital to his research, and he made many contributions to numerical analysis, such as the method of Gaussian quadrature, published in 1816.
In a private letter to Gerling from 1823, he described a solution of a 4x4 system of linear equations with the Gauss-Seidel method – an "indirect" iterative method for the solution of linear systems, and recommended it over the usual method of "direct elimination" for systems of more than two equations.
Gauss invented an algorithm for calculating what is now called discrete Fourier transforms when calculating the orbits of Pallas and Juno in 1805, 160 years before Cooley and Tukey found their similar Cooley–Tukey algorithm. He developed it as a trigonometric interpolation method, but the paper Theoria Interpolationis Methodo Nova Tractata was published only posthumously in 1876, well after Joseph Fourier's introduction of the subject in 1807.
Geometry
Differential geometry
The geodetic survey of Hanover fuelled Gauss's interest in differential geometry and topology, fields of mathematics dealing with curves and surfaces. This led him in 1828 to the publication of a work that marks the birth of modern differential geometry of surfaces, as it departed from the traditional ways of treating surfaces as cartesian graphs of functions of two variables, and that initiated the exploration of surfaces from the "inner" point of view of a two-dimensional being constrained to move on it. As a result, the Theorema Egregium (remarkable theorem), established a property of the notion of Gaussian curvature. Informally, the theorem says that the curvature of a surface can be determined entirely by measuring angles and distances on the surface, regardless of the embedding of the surface in three-dimensional or two-dimensional space.
The Theorema Egregium leads to the abstraction of surfaces as doubly-extended manifolds; it clarifies the distinction between the intrinsic properties of the manifold (the metric) and its physical realization in ambient space. A consequence is the impossibility of an isometric transformation between surfaces of different Gaussian curvature. This means practically that a sphere or an ellipsoid cannot be transformed to a plane without distortion, which causes a fundamental problem in designing projections for geographical maps. A portion of this essay is dedicated to a profound study of geodesics. In particular, Gauss proves the local Gauss–Bonnet theorem on geodesic triangles, and generalizes Legendre's theorem on spherical triangles to geodesic triangles on arbitrary surfaces with continuous curvature; he found that the angles of a "sufficiently small" geodesic triangle deviate from that of a planar triangle of the same sides in a way that depends only on the values of the surface curvature at the vertices of the triangle, regardless of the behaviour of the surface in the triangle interior.
Gauss's memoir from 1828 lacks the conception of geodesic curvature. However, in a previously unpublished manuscript, very likely written in 1822–1825, he introduced the term "side curvature" (German: "Seitenkrümmung") and proved its invariance under isometric transformations, a result that was later obtained by Ferdinand Minding and published by him in 1830. This Gauss paper contains the core of his lemma on total curvature, but also its generalization, found and proved by Pierre Ossian Bonnet in 1848 and known as the Gauss–Bonnet theorem. Non-Euclidean geometry
(1828)]]
During Gauss' lifetime, the Parallel postulate of Euclidean geometry was heavily discussed. Numerous efforts were made to prove it in the frame of the Euclidean axioms, whereas some mathematicians discussed the possibility of geometrical systems without it. Gauss thought about the basics of geometry from the 1790s on, but only realized in the 1810s that a non-Euclidean geometry without the parallel postulate could solve the problem. In a letter to Franz Taurinus of 1824, he presented a short comprehensible outline of what he named a "non-Euclidean geometry", but he strongly forbade Taurinus to make any use of it. Gauss is credited with having been the one to first discover and study non-Euclidean geometry, even coining the term as well.
The first publications on non-Euclidean geometry in the history of mathematics were authored by Nikolai Lobachevsky in 1829 and Janos Bolyai in 1832. In the following years, Gauss wrote his ideas on the topic but did not publish them, thus avoiding influencing the contemporary scientific discussion. Gauss commended the ideas of Janos Bolyai in a letter to his father and university friend Farkas Bolyai claiming that these were congruent to his own thoughts of some decades. However, it is not quite clear to what extent he preceded Lobachevsky and Bolyai, as his written remarks are vague and obscure.
Sartorius first mentioned Gauss's work on non-Euclidean geometry in 1856, but only the publication of Gauss's Nachlass in Volume VIII of the Collected Works (1900) showed Gauss's ideas on the matter, at a time when non-Euclidean geometry was still an object of some controversy. Early topology Gauss was also an early pioneer of topology or Geometria Situs, as it was called in his lifetime. The first proof of the fundamental theorem of algebra in 1799 contained an essentially topological argument; fifty years later, he further developed the topological argument in his fourth proof of this theorem.
Another encounter with topological notions occurred to him in the course of his astronomical work in 1804, when he determined the limits of the region on the celestial sphere in which comets and asteroids might appear, and which he termed "Zodiacus". He discovered that if the Earth's and comet's orbits are linked, then by topological reasons the Zodiacus is the entire sphere. In 1848, in the context of the discovery of the asteroid 7 Iris, he published a further qualitative discussion of the Zodiacus.
In Gauss's letters of 1820–1830, he thought intensively on topics with close affinity to Geometria Situs, and became gradually conscious of semantic difficulty in this field. Fragments from this period reveal that he tried to classify "tract figures", which are closed plane curves with a finite number of transverse self-intersections, that may also be planar projections of knots. To do so he devised a symbolical scheme, the Gauss code, that in a sense captured the characteristic features of tract figures.
In a fragment from 1833, Gauss defined the linking number of two space curves by a certain double integral, and in doing so provided for the first time an analytical formulation of a topological phenomenon. On the same note, he lamented the little progress made in Geometria Situs, and remarked that one of its central problems will be "to count the intertwinings of two closed or infinite curves". His notebooks from that period reveal that he was also thinking about other topological objects such as braids and tangles. he stated the fundamental theorem of axonometry, which tells how to represent a 3D cube on a 2D plane with complete accuracy, via complex numbers. He described rotations of this sphere as the action of certain linear fractional transformations on the extended complex plane, and gave a proof for the geometric theorem that the altitudes of a triangle always meet in a single orthocenter.
Gauss was concerned with John Napier's "Pentagramma mirificum" – a certain spherical pentagram – for several decades; he approached it from various points of view, and gradually gained a full understanding of its geometric, algebraic, and analytic aspects. In particular, in 1843 he stated and proved several theorems connecting elliptic functions, Napier spherical pentagons, and Poncelet pentagons in the plane.
Furthermore, he contributed a solution to the problem of constructing the largest-area ellipse inside a given quadrilateral, and discovered a surprising result about the computation of area of pentagons. Sciences Astronomy
On 1 January 1801, Italian astronomer Giuseppe Piazzi discovered a new celestial object, presumed it to be the long searched planet between Mars and Jupiter according to the so-called Titius–Bode law, and named it Ceres. He could track it only for a short time until it disappeared behind the glare of the Sun. The mathematical tools of the time were not sufficient to predict the location of its reappearance from the few data available. Gauss tackled the problem and predicted a position for possible rediscovery in December 1801. This turned out to be accurate within a half-degree when Franz Xaver von Zach on 7 and 31 December at Gotha, and independently Heinrich Olbers on 1 and 2 January in Bremen, identified the object near the predicted position.
Gauss's method leads to an equation of the eighth degree, of which one solution, the Earth's orbit, is known. The solution sought is then separated from the remaining six based on physical conditions. In this work, Gauss used comprehensive approximation methods which he created for that purpose.
The discovery of Ceres led Gauss to the theory of the motion of planetoids disturbed by large planets, eventually published in 1809 as Theoria motus corporum coelestium in sectionibus conicis solem ambientum. It introduced the Gaussian gravitational constant.}} After long years of work, he finished it in 1816 without a result that seemed sufficient to him. This marked the end of his activities in theoretical astronomy.
One fruit of Gauss's research on Pallas perturbations was the Determinatio Attractionis... (1818) on a method of theoretical astronomy that later became known as the "elliptic ring method". It introduced an averaging conception in which a planet in orbit is replaced by a fictitious ring with mass density proportional to the time the planet takes to follow the corresponding orbital arcs. Gauss presents the method of evaluating the gravitational attraction of such an elliptic ring, which includes several steps; one of them involves a direct application of the arithmetic-geometric mean (AGM) algorithm to calculate an elliptic integral.
Even after Gauss's contributions to theoretical astronomy came to an end, more practical activities in observational astronomy continued and occupied him during his entire career. As early as 1799, Gauss dealt with the determination of longitude by use of the lunar parallax, for which he developed more convenient formulas than those were in common use. After appointment as director of observatory he attached importance to the fundamental astronomical constants in correspondence with Bessel. Gauss himself provided tables of nutation and aberration, solar coordinates, and refraction. He made many contributions to spherical geometry, and in this context solved some practical problems about navigation by stars. He published a great number of observations, mainly on minor planets and comets; his last observation was the solar eclipse of 28 July 1851.
Chronology
Gauss's first publication following his doctoral thesis dealt with the determination of the date of Easter (1800), an elementary mathematical topic. Gauss aimed to present a convenient algorithm for people without any knowledge of ecclesiastical or even astronomical chronology, and thus avoided the usual terms of golden number, epact, solar cycle, domenical letter, and any religious connotations. This choice of topic likely had historical grounds. The replacement of the Julian calendar by the Gregorian calendar had caused confusion in the Holy Roman Empire since the 16th century and was not finished in Germany until 1700, when the difference of eleven days was deleted. Even after this, Easter fell on different dates in Protestant and Catholic territories, until this difference was abolished by agreement in 1776. In the Protestant states, such as the Duchy of Brunswick, the Easter of 1777, five weeks before Gauss's birth, was the first one calculated in the new manner. In the history of statistics, this disagreement is called the "priority dispute over the discovery of the method of least squares".
In the first paper he proved Gauss's inequality (a Chebyshev-type inequality) for unimodal distributions, and stated without proof another inequality for moments of the fourth order (a special case of the Gauss-Winckler inequality). He derived lower and upper bounds for the variance of the sample variance. In the second paper, Gauss described recursive least squares methods. His work on the theory of errors was extended in several directions by the geodesist Friedrich Robert Helmert to the Gauss-Helmert model.
Gauss also contributed to problems in probability theory that are not directly concerned with the theory of errors. One example appears as a diary note where he tried to describe the asymptotic distribution of entries in the continued fraction expansion of a random number uniformly distributed in (0,1). He derived this distribution, now known as the Gauss-Kuzmin distribution, as a by-product of the discovery of the ergodicity of the Gauss map for continued fractions. Gauss's solution is the first-ever result in the metrical theory of continued fractions. Geodesy
from 9 May 1820 to the triangulation project (with the additional signature of Count Ernst zu Münster below)]]
]]
sextant with additional mirror]]
Gauss was busy with geodetic problems since 1799 when he helped Karl Ludwig von Lecoq with calculations during his survey in Westphalia. Beginning in 1804, he taught himself some practical geodesy in Brunswick and Göttingen.
Since 1816, Gauss's former student Heinrich Christian Schumacher, then professor in Copenhagen, but living in Altona (Holstein) near Hamburg as head of an observatory, carried out a triangulation of the Jutland peninsula from Skagen in the north to Lauenburg in the south. This project was the basis for map production but also aimed at determining the geodetic arc between the terminal sites. Data from geodetic arcs were used to determine the dimensions of the earth geoid, and long arc distances brought more precise results. Schumacher asked Gauss to continue this work further to the south in the Kingdom of Hanover; Gauss agreed after a short time of hesitation. Finally, in May 1820, King George IV gave the order to Gauss.
An arc measurement needs a precise astronomical determination of at least two points in the network. Gauss and Schumacher used the coincidence that both observatories in Göttingen and Altona, in the garden of Schumacher's house, laid nearly in the same longitude. The latitude was measured with both their instruments and a zenith sector of Ramsden that was transported to both observatories.}}
Gauss and Schumacher had already determined some angles between Lüneburg, Hamburg, and Lauenburg for the geodetic connection in October 1818. During the summers of 1821 until 1825 Gauss directed the triangulation work personally, from Thuringia in the south to the river Elbe in the north. The triangle between Hoher Hagen, Großer Inselsberg in the Thuringian Forest, and Brocken in the Harz mountains was the largest one Gauss had ever measured with a maximum size of . In the thinly populated Lüneburg Heath without significant natural summits or artificial buildings, he had difficulties finding suitable triangulation points; sometimes cutting lanes through the vegetation was necessary.
In 1828, when studying differences in latitude, Gauss first defined a physical approximation for the figure of the Earth as the surface everywhere perpendicular to the direction of gravity; later his doctoral student Johann Benedict Listing called this the geoid.
Magnetism and telegraphy
Geomagnetism
Gauss had been interested in magnetism since 1803. After Alexander von Humboldt visited Göttingen in 1826, both scientists began intensive research on geomagnetism, partly independently, partly in productive cooperation. In 1828, Gauss was Humboldt's guest during the conference of the Society of German Natural Scientists and Physicians in Berlin, where he got acquainted with the physicist Wilhelm Weber.
When Weber got the chair for physics in Göttingen as successor of Johann Tobias Mayer by Gauss's recommendation in 1831, both of them started a fruitful collaboration, leading to a new knowledge of magnetism with a representation for the unit of magnetism in terms of mass, charge, and time. They founded the Magnetic Association (German: Magnetischer Verein), an international working group of several observatories, which carried out measurements of Earth's magnetic field in many regions of the world using equivalent methods at arranged dates in the years 1836 to 1841.
In 1836, Humboldt suggested the establishment of a worldwide net of geomagnetic stations in the British dominions with a letter to the Duke of Sussex, then president of the Royal Society; he proposed that magnetic measures should be taken under standardized conditions using his methods. Together with other instigators, this led to a global program known as "Magnetical crusade" under the direction of Edward Sabine. The dates, times, and intervals of observations were determined in advance, the Göttingen mean time was used as the standard. 61 stations on all five continents participated in this global program. Gauss and Weber founded a series for publication of the results, six volumes were edited between 1837 and 1843. Weber's departure to Leipzig in 1843 as late effect of the Göttingen Seven affair marked the end of Magnetic Association activity. and the data allowed to determine their location with rather good precision.
Gauss influenced the beginning of geophysics in Russia, when Adolph Theodor Kupffer, one of his former students, founded a magnetic observatory in St. Petersburg, following the example of the observatory in Göttingen, and similarly, Ivan Simonov in Kazan.
Gauss's main theoretical interests in electromagnetism were reflected in his attempts to formulate quantitive laws governing electromagnetic induction. In notebooks from these years, he recorded several innovative formulations; he discovered the vector potential function, independently rediscovered by Franz Ernst Neumann in 1845, and in January 1835 he wrote down an "induction law" equivalent to Faraday's law, which stated that the electromotive force at a given point in space is equal to the instantaneous rate of change (with respect to time) of this function.
Gauss tried to find a unifying law for long-distance effects of electrostatics, electrodynamics, electromagnetism, and induction, comparable to Newton's law of gravitation, but his attempt ended in a "tragic failure". He characterized optical systems under a paraxial approximation only by its cardinal points, and he derived the Gaussian lens formula, applicable without restrictions in respect to the thickness of the lenses.
Mechanics
Gauss's first work in mechanics concerned the earth's rotation. When his university friend Benzenberg carried out experiments to determine the deviation of falling masses from the perpendicular in 1802, what today is known as the Coriolis force, he asked Gauss for a theory-based calculation of the values for comparison with the experimental ones. Gauss elaborated a system of fundamental equations for the motion, and the results corresponded sufficiently with Benzenberg's data, who added Gauss's considerations as an appendix to his book on falling experiments.
After Foucault had demonstrated the earth's rotation by his pendulum experiment in public in 1851, Gerling questioned Gauss for further explanations. This instigated Gauss to design a new apparatus for demonstration with a much shorter length of pendulum than Foucault's one. The oscillations were observed with a reading telescope, with a vertical scale and a mirror fastened at the pendulum. It is described in the Gauss–Gerling correspondence and Weber made some experiments with this apparatus in 1853, but no data were published.
Gauss's principle of least constraint of 1829 was established as a general concept to overcome the division of mechanics into statics and dynamics, combining D'Alembert's principle with Lagrange's principle of virtual work, and showing analogies to the method of least squares. Metrology In 1828, Gauss was appointed as head of the board for weights and measures of the Kingdom of Hanover. He created standards for length and measure. Gauss himself took care of the time-consuming measures and gave detailed orders for the mechanical construction. In the correspondence with Schumacher, who was also working on this matter, he described new ideas for high-precision scales. He submitted the final reports on the Hanoverian foot and pound to the government in 1841. This work achieved international importance due to an 1836 law that connected the Hanoverian measures with the English ones. the French Academy of Sciences (1804/ 1820), the Royal Society of London (1804), the Royal Prussian Academy in Berlin (1810), the National Academy of Science in Verona (1810), the Royal Society of Edinburgh (1820), the Bavarian Academy of Sciences of Munich (1820), the Royal Danish Academy in Copenhagen (1821), the Royal Astronomical Society in London (1821), the Royal Swedish Academy of Sciences (1821), the American Academy of Arts and Sciences in Boston (1822), the Royal Bohemian Society of Sciences in Prague (1833), the Royal Academy of Science, Letters and Fine Arts of Belgium (1841/1845), the Royal Society of Sciences in Uppsala (1843), the Royal Irish Academy in Dublin (1843), the Royal Institute of the Netherlands (1845/ 1851), the Spanish Royal Academy of Sciences in Madrid (1850), the Russian Geographical Society (1851), the Imperial Academy of Sciences in Vienna (1848), the American Philosophical Society (1853), the Cambridge Philosophical Society, and the Royal Hollandish Society of Sciences in Haarlem.
Both the University of Kazan and the Philosophy Faculty of the University of Prague appointed him honorary member in 1848.
Gauss received the Lalande Prize from the French Academy of Science in 1809 for the theory of planets and the means of determining their orbits from only three observations, the Danish Academy of Science prize in 1823 for his memoir on conformal projection, and the Copley Medal from the Royal Society in 1838 for "his inventions and mathematical researches in magnetism". and became one of the first members of the Prussian Order Pour le Merite (Civil class) when it was established in 1842. He received the Order of the Crown of Westphalia (1810), the Danish Order of the Dannebrog (1817), the Hanoverian Royal Guelphic Order (1815), the Swedish Order of the Polar Star (1844), the Order of Henry the Lion (1849), and the Bavarian Maximilian Order for Science and Art (1853).
The Kings of Hanover appointed him the honorary titles "Hofrath" (1816) and "Geheimer Hofrath" (1845). In 1949, on the occasion of his golden doctor degree jubilee, he received honorary citizenship of both Brunswick and Göttingen. Soon after his death a medal was issued by order of King George V of Hanover with the back inscription dedicated "to the Prince of Mathematicians".
The "Gauss-Gesellschaft Göttingen" ("Göttingen Gauss Society") was founded in 1964 for research on the life and work of Carl Friedrich Gauss and related persons. It publishes the Mitteilungen der Gauss-Gesellschaft (Communications of the Gauss Society). Names and commemorations * List of things named after Carl Friedrich Gauss Selected writings Mathematics and astronomy
(1880), made by Hermann Heinrich Howaldt, designed by Fritz Schaper]]
* 1799: (Doctoral thesis on the fundamental theorem of algebra, University of Helmstedt) [https://edoc.hu-berlin.de/handle/18452/732 Original book]
* 1816: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0003_2NS?tify=%7B%22pages%22%3A%5B268%2C269%5D%2C%22view%22%3A%22info%22%7D Original]
* 1816: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0003_2NS?tify=%7B%22pages%22%3A%5B296%5D%2C%22view%22%3A%22info%22%7D Original]
* 1850: [https://gdz.sub.uni-goettingen.de/id/PPN250442582_0004?tify=%7B%22pages%22%3A%5B287%5D%2C%22view%22%3A%22info%22%7D Original] (Lecture from 1849)
** (German)
* 1800: [https://zs.thulb.uni-jena.de/receive/jportal_jpvolume_00201970 Original]
* 1801:
** (translated from the [https://www.science.org/doi/10.1126/science.154.3749.642.b second German edition, Göttingen 1860])
* 1802: [https://zs.thulb.uni-jena.de/rsc/viewer/jportal_derivate_00237503/Monatlich_Correspondenz_130168688_5_1802_0444%20.tif Original]
* 1804: [https://zs.thulb.uni-jena.de/rsc/viewer/jportal_derivate_00240854/Monatliche_Correspondenz_130168688_10_0175.tif Original] (on the Zodiacus)
* 1808: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0016_1NS?tify=%7B%22pages%22%3A%5B498%2C499%5D%2C%22view%22%3A%22info%22%7D Original] (Introduces Gauss's lemma, uses it in the third proof of quadratic reciprocity)
* 1808:
* 1809: [https://gutenberg.beic.it/webclient/DeliveryManager?pid=12217180 Original book]
**
**
* 1811: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0001_2NS?tify=%7B%22pages%22%3A%5B170%2C171%5D%2C%22view%22%3A%22info%22%7D Original] (from 1810) (Orbit of Pallas)
* 1811: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0001_2NS?tify=%7B%22pages%22%3A%5B194%2C195%5D%2C%22view%22%3A%22info%22%7D Original] (from 1808) (Determination of the sign of the quadratic Gauss sum, uses this to give the fourth proof of quadratic reciprocity)
* 1813: {{cite journal | title Disquisitiones generales circa seriem infinitam <math>1+\frac{\alpha\beta}{\gamma.1}+\mbox{etc.}</math> | journal Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores. Comm. Class. Math. | volume 2 | pages 1–42 | url https://gdz.sub.uni-goettingen.de/id/PPN235999628?tify%7B%22pages%22%3A%5B131%5D%2C%22pan%22%3A%7B%22x%22%3A0.603%2C%22y%22%3A0.4%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.73%7D}} [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0002_2NS?tify=%7B%22pages%22%3A%5B227%5D%2C%22pan%22%3A%7B%22x%22%3A0.559%2C%22y%22%3A0.496%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.456%7D Original] (from 1812, contains the Gauss's continued fraction)
* 1816: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0003_2NS?tify=%7B%22pages%22%3A%5B200%2C201%5D%2C%22view%22%3A%22info%22%7D Original] (from 1814)
* 1818: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0004_2NS?tify=%7B%22pages%22%3A%5B262%2C263%5D%2C%22view%22%3A%22info%22%7D Original] (from 1817) (Fifth and sixth proofs of quadratic reciprocity)
* 1818: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0004_2NS?tify=%7B%22pages%22%3A%5B281%5D%2C%22pan%22%3A%7B%22x%22%3A0.499%2C%22y%22%3A0.677%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.434%7D Original] (Only reference to the – mostly unpublished – work on the algorithm of the arithmetic-geometric mean.)
* 1823: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0005_2NS?tify=%7B%22pages%22%3A%5B276%5D%2C%22view%22%3A%22info%22%7D Original] (from 1821)
* 1823: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0005_2NS?tify=%7B%22pages%22%3A%5B306%5D%2C%22pan%22%3A%7B%22x%22%3A0.413%2C%22y%22%3A0.66%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.413%7D Original]
* 1825: (Prize winning essay from 1822 on conformal mapping)
* 1828: [https://books.google.com/books?idtIg_AAAAcAAJ&pgPA04 Original book]
* 1828: (from 1826)
** (Three essays concerning the calculation of probabilities as the basis of the Gaussian law of error propagation)
* 1828: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0006_2NS?tify=%7B%22pages%22%3A%5B312%2C313%5D%2C%22view%22%3A%22info%22%7D Original] (from 1827)
**
* 1828: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0006_2NS?tify=%7B%22pages%22%3A%5B241%5D%2C%22view%22%3A%22info%22%7D Original] (from 1825)
* 1832: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0007_2NS?tify=%7B%22pages%22%3A%5B273%5D%2C%22view%22%3A%22info%22%7D Original] (from 1831) (Introduces the Gaussian integers, states (without proof) the law of biquadratic reciprocity, proves the supplementary law for 1 + i)
* 1845: [https://gdz.sub.uni-goettingen.de/id/PPN250442582_0002 Original] (from 1843)
* 1847: [https://gdz.sub.uni-goettingen.de/id/PPN250442582_0003 Original] (from 1846)
* 1848: [https://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?journalAN...&year1848&volume..27&letter.&db_keyGEN&page_ind4&plate_selectNO&data_typeGIF&typeSCREEN_GIF&classicYES Original]
* 1903: [https://gdz.sub.uni-goettingen.de/id/PPN236018647?tify%7B%22pages%22%3A%5B516%5D%2C%22pan%22%3A%7B%22x%22%3A0.452%2C%22y%22%3A0.567%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.946%7D Wissenschaftliches Tagebuch] () [https://gdz.sub.uni-goettingen.de/id/DE-611-HS-3382323 Original book] (from 1847, on the Zodiacus)
**
Physics
* 1804: [https://gdz.sub.uni-goettingen.de/id/PPN236006339?tify%7B%22pages%22%3A%5B503%5D%2C%22pan%22%3A%7B%22x%22%3A0.468%2C%22y%22%3A0.479%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.609%7D Fundamentalgleichungen für die Bewegung schwerer Körper auf der Erde] ( in original book: [https://www.digitale-sammlungen.de/de/view/bsb10060427?page392,393 Original])
* 1813: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0002_2NS?tify=%7B%22pages%22%3A%5B318%5D%2C%22pan%22%3A%7B%22x%22%3A0.539%2C%22y%22%3A0.64%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.456%7D Original] (contains Gauss's theorem of vector analysis)
* 1817:
* 1829:
* 1830: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0007_2NS?tify=%7B%22pages%22%3A%5B223%5D%2C%22view%22%3A%22info%22%7D Original] (from 1829)
* 1841: [https://gdz.sub.uni-goettingen.de/id/PPN35283028X_0008_2NS?tify%7B%22pages%22%3A%5B198%5D%2C%22pan%22%3A%7B%22x%22%3A0.569%2C%22y%22%3A0.65%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.449%7D Original] (from 1832)Citations Sources
*
*
*
*
* First edition:
** With a critical view on Dunnington's style and appraisals
*
*
*
*
*
*
*
*
**
*
*
*
*
*
*
Further reading
*
*
*
*
*
Fictional
*
**
External links
*
* [http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?db_keyAST&db_keyPRE&qformAST&arxiv_selastro-ph&arxiv_selcond-mat&arxiv_selcs&arxiv_selgr-qc&arxiv_selhep-ex&arxiv_selhep-lat&arxiv_selhep-ph&arxiv_selhep-th&arxiv_selmath&arxiv_selmath-ph&arxiv_selnlin&arxiv_selnucl-ex&arxiv_selnucl-th&arxiv_selphysics&arxiv_selquant-ph&arxiv_selq-bio&sim_queryYES&ned_queryYES&adsobj_queryYES&aut_logicOR&obj_logicOR&authorGauss%0D%0AGau%C3%9F&object&start_mon&start_year&end_mon12&end_year1965&ttl_logicOR&title&txt_logicOR&text&nr_to_return200&start_nr1&jou_pickALL&ref_stems&data_andALL&group_andALL&start_entry_day&start_entry_mon&start_entry_year&end_entry_day&end_entry_mon&end_entry_year&min_score&sortSCORE&data_typeSHORT&aut_synYES&ttl_synYES&txt_synYES&aut_wt1.0&obj_wt1.0&ttl_wt0.3&txt_wt3.0&aut_wgtYES&obj_wgtYES&ttl_wgtYES&txt_wgtYES&ttl_scoYES&txt_scoYES&version=1 Publications of C. F. Gauss] in Astrophysics Data System
*
*
*
*
*
*
*
* [https://denkmalatlas.niedersachsen.de/viewer/themen/Gauss-Steine/ Carl Friedrich Gauss – Spuren seines Lebens] (Places used as points for triangulation)
Category:1777 births
Category:1855 deaths
Category:18th-century German astronomers
Category:18th-century German mathematicians
Category:18th-century German physicists
Category:19th-century German astronomers
Category:19th-century German mathematicians
Category:19th-century German physicists
Category:University of Göttingen alumni
Category:University of Helmstedt alumni
Category:Academic staff of the University of Göttingen
Category:Ceres (dwarf planet)
Category:Fellows of the American Academy of Arts and Sciences
Category:Fellows of the Royal Society
Category:Corresponding members of the Saint Petersburg Academy of Sciences
Category:Honorary members of the Saint Petersburg Academy of Sciences
Category:Members of the Göttingen Academy of Sciences and Humanities
Category:Members of the Bavarian Academy of Sciences
Category:Members of the Royal Netherlands Academy of Arts and Sciences
Category:Members of the Royal Swedish Academy of Sciences
Category:Mental calculators
Category:German number theorists
Category:Linear algebraists
Category:Differential geometers
Category:Hyperbolic geometers
Category:German optical physicists
Category:19th-century German inventors
Category:Recipients of the Copley Medal
Category:Recipients of the Lalande Prize
Category:Recipients of the Pour le Mérite (civil class)
Category:People from the Duchy of Brunswick
Category:Scientists from Braunschweig
Category:German Lutherans
Category:Members of the American Philosophical Society
|
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss
|
2025-04-05T18:27:43.622365
|
6130
|
Cornish language
|
<br />
| pronunciation =
* )}}
* )}}
* )}}
* )}}
* )}}
* )}}
| image | states United Kingdom
| region = Cornwall
| ethnicity = Cornish
| extinct End of 18th century<!-- NOTE: This date is the result of a talk page discussion. If you wish to change it please take it to the talk page first -->
| revived 20th century (563 L2 users as of the 2021 Census: 557 in 2011)
<!--
5,000 Conversational Speakers
-->| familycolor = Indo-European
| fam2 = Celtic
| fam3 = Insular Celtic
| fam4 = Brittonic
| fam5 = Southwestern Brittonic
| iso1 = kw
| iso2 = cor
| lc1 = cor
| ld1 = Modern Cornish
| lc2 = cnx
| ld2 = Middle Cornish
| lc3 = oco
| ld3 = Old Cornish
| linglist = cnx
| lingname = Middle Cornish
| linglist2 = oco
| lingname2 = Old Cornish
| lingua = 50-ABB-a
| glotto = corn1251
| glottorefname = Cornish
| script = Latin alphabet
| minority = England
* Cornwall
| agency =
| standards = Standard Written Form (Official)<br>Kernewek Kemmyn<br>Unified Cornish<br>Kernowek Standard<br>Modern Cornish
| notice = IPA
| map2 = Lang Status 20-CR.svg
| mapcaption2 = }}
}}
Cornish (Standard Written Form: or , ) is a Southwestern Brittonic language of the Celtic language family. Along with Welsh and Breton, Cornish is descended from the Common Brittonic language spoken throughout much of Great Britain before the English language came to dominate. For centuries, until it was pushed westwards by English, it was the main language of Cornwall, maintaining close links with its sister language Breton, with which it was mutually intelligible, perhaps even as long as Cornish continued to be spoken as a vernacular. Cornish continued to function as a common community language in parts of Cornwall until the mid 18th century, and there is some evidence for traditional speakers of the language persisting into the 19th century.
Cornish became extinct as a living community language in Cornwall by the end of the 18th century<!-- NOTE: This date is the result of a talk page discussion. If you wish to change it please take it to the talk page first -->, although knowledge of Cornish, including speaking ability to a certain extent, persisted within some families and individuals. A revival started in the early 20th century, and in 2010 UNESCO reclassified the language as critically endangered, stating that its former classification of the language as extinct was no longer accurate. The language has a growing number of second-language speakers, and a very small number of families now raise children to speak revived Cornish as a first language.
Cornish is currently recognised under the European Charter for Regional or Minority Languages, and the language is often described as an important part of Cornish identity, culture and heritage. Since the revival of the language, some Cornish textbooks and works of literature have been published, and an increasing number of people are studying the language. independent films, and children's books. A small number of people in Cornwall have been brought up to be bilingual native speakers, and the language is taught in schools and appears on street nameplates. The first Cornish-language day care opened in 2010.
Classification
Cornish is a Southwestern Brittonic language, a branch of the Insular Celtic section of the Celtic language family, which is a sub-family of the Indo-European language family. Brittonic also includes Welsh, Breton, Cumbric and possibly Pictish, the last two of which are extinct. Scottish Gaelic, Irish and Manx are part of the separate Goidelic branch of Insular Celtic.
Joseph Loth viewed Cornish and Breton as being two dialects of the same language, claiming that "Middle Cornish is without doubt closer to Breton as a whole than the modern Breton dialect of Quiberon [] is to that of Saint-Pol-de-Léon []." Also, Kenneth Jackson argued that it is almost certain that Cornish and Breton would have been mutually intelligible as long as Cornish was a living language, and that Cornish and Breton are especially closely related to each other and less closely related to Welsh.
History
Cornish evolved from the Common Brittonic spoken throughout Britain south of the Firth of Forth during the British Iron Age and Roman period. As a result of westward Anglo-Saxon expansion, the Britons of the southwest were separated from those in modern-day Wales and Cumbria, which Jackson links to the defeat of the Britons at the Battle of Deorham in about 577. The western dialects eventually evolved into modern Welsh and the now extinct Cumbric, while Southwestern Brittonic developed into Cornish and Breton, the latter as a result of emigration to parts of the continent, known as Brittany over the following centuries.
Old Cornish
The area controlled by the southwestern Britons was progressively reduced by the expansion of Wessex over the next few centuries. During the Old Cornish () period (800–1200), the Cornish-speaking area was largely coterminous with modern-day Cornwall, after the Saxons had taken over Devon in their south-westward advance, which probably was facilitated by a second migration wave to Brittany that resulted in the partial depopulation of Devon.
The earliest written record of the Cornish language comes from this period: a 9th-century gloss in a Latin manuscript of by Boethius, which used the words . The phrase may mean "it [the mind] hated the gloomy places", or alternatively, as Andrew Breeze suggests, "she hated the land". Other sources from this period include the ''Saints' List'', a list of almost fifty Cornish saints, the Bodmin manumissions, which is a list of manumittors and slaves, the latter with mostly Cornish names, and, more substantially, a Latin–Cornish glossary (the or Cottonian Vocabulary), a Cornish translation of Ælfric of Eynsham's Latin–Old English Glossary, which is thematically arranged into several groups, such as the Genesis creation narrative, anatomy, church hierarchy, the family, names for various kinds of artisans and their tools, flora, fauna, and household items. The manuscript was widely thought to be in Old Welsh until the 18th century when it was identified as Cornish by Edward Lhuyd. Some Brittonic glosses in the 9th-century colloquy were once identified as Old Cornish, but they are more likely Old Welsh, possibly influenced by a Cornish scribe. No single phonological feature distinguishes Cornish from both Welsh and Breton until the beginning of the assibilation of dental stops in Cornish, which is not found before the second half of the eleventh century, and it is not always possible to distinguish Old Cornish, Old Breton, and Old Welsh orthographically. Middle Cornish
}} (the of medieval Cornish literature), written by an unknown monk in the late 14th century]]
}} (The life of St. Meriasek) (f.56v.) Middle Cornish Saint's Play]]
The Cornish language continued to flourish well through the Middle Cornish () period (1200–1600), reaching a peak of about 39,000 speakers in the 13th century, after which the number started to decline. From this period also are the hagiographical dramas (The Life of Meriasek) and (The Life of Ke), both of which feature as an antagonist the villainous and tyrannical King Tewdar (or Teudar), a historical medieval king in Armorica and Cornwall, who, in these plays, has been interpreted as a lampoon of either of the Tudor kings Henry VII or Henry VIII.
Others are the Charter Fragment, the earliest known continuous text in the Cornish language, apparently part of a play about a medieval marriage, and (The Passion of Our Lord), a poem probably intended for personal worship, were written during this period, probably in the second half of the 14th century. Another important text, the , was realized to be Cornish in 1949, having previously been incorrectly classified as Welsh. It is the longest text in the traditional Cornish language, consisting of around 30,000 words of continuous prose. This text is a late 16th century translation of twelve of Bishop Bonner's thirteen homilies by a certain John Tregear, tentatively identified as a vicar of St Allen from Crowan, and has an additional catena, Sacrament an Alter, added later by his fellow priest, Thomas Stephyn. In the reign of Henry VIII, an account was given by Andrew Boorde in his 1542 . He states, ""
When Parliament passed the Act of Uniformity 1549, which established the 1549 edition of the English Book of Common Prayer as the sole legal form of worship in England, including Cornwall, people in many areas of Cornwall did not speak or understand English. The passing of this Act was one of the causes of the Prayer Book Rebellion (which may also have been influenced by government repression after the failed Cornish rebellion of 1497), with "the commoners of Devonshyre and Cornwall" producing a manifesto demanding a return to the old religious services and included an article that concluded, "and so we the Cornyshe men (whereof certen of us understande no Englysh) utterly refuse thys newe Englysh." In response to their articles, the government spokesman (either Philip Nichols or Nicholas Udall) wondered why they did not just ask the king for a version of the liturgy in their own language. Archbishop Thomas Cranmer asked why the Cornishmen should be offended by holding the service in English, when they had before held it in Latin, which even fewer of them could understand. Anthony Fletcher points out that this rebellion was primarily motivated by religious and economic, rather than linguistic, concerns. The rebellion prompted a heavy-handed response from the government, and 5,500 people died during the fighting and the rebellion's aftermath. Government officials then directed troops under the command of Sir Anthony Kingston to carry out pacification operations throughout the West Country. Kingston subsequently ordered the executions of numerous individuals suspected of involvement with the rebellion as part of the post-rebellion reprisals.
The rebellion eventually proved a turning-point for the Cornish language, as the authorities came to associate it with sedition and "backwardness". This proved to be one of the reasons why the Book of Common Prayer was never translated into Cornish (unlike Welsh), as proposals to do so were suppressed in the rebellion's aftermath. The failure to translate the Book of Common Prayer into Cornish led to the language's rapid decline during the 16th and 17th centuries. Peter Berresford Ellis cites the years 1550–1650 as a century of immense damage for the language, and its decline can be traced to this period. In 1680 William Scawen wrote an essay describing 16 reasons for the decline of Cornish, among them the lack of a distinctive Cornish alphabet, the loss of contact between Cornwall and Brittany, the cessation of the miracle plays, loss of records in the Civil War, lack of a Cornish Bible and immigration to Cornwall. Mark Stoyle, however, has argued that the 'glotticide' of the Cornish language was mainly a result of the Cornish gentry adopting English to dissociate themselves from the reputation for disloyalty and rebellion associated with the Cornish language since the 1497 uprising. Late Cornish By the middle of the 17th century, the language had retreated to Penwith and Kerrier, and transmission of the language to new generations had almost entirely ceased. In his Survey of Cornwall, published in 1602, Richard Carew writes:<blockquote>[M]ost of the inhabitants can speak no word of Cornish, but very few are ignorant of the English; and yet some so affect their own, as to a stranger they will not speak it; for if meeting them by chance, you inquire the way, or any such matter, your answer shall be, "," "I [will] speak no Saxonage."</blockquote>
The Late Cornish () period from 1600 to about 1800 has a less substantial body of literature than the Middle Cornish period, but the sources are more varied in nature, including songs, poems about fishing and curing pilchards, and various translations of verses from the Bible, the Ten Commandments, the Lord's Prayer and the Creed. Edward Lhuyd's Archaeologia Britannica, which was mainly recorded in the field from native speakers in the early 1700s, and his unpublished field notebook are seen as important sources of Cornish vocabulary, some of which are not found in any other source. Archaeologia Britannica also features a complete version of a traditional folk tale, John of Chyanhor, a short story about a man from St Levan who goes far to the east seeking work, eventually returning home after three years to find that his wife has borne him a child during his absence.
In 1776, William Bodinar, who describes himself as having learned Cornish from old fishermen when he was a boy, wrote a letter to Daines Barrington in Cornish, with an English translation, which was probably the last prose written in the traditional language. In his letter, he describes the sociolinguistics of the Cornish language at the time, stating that there are no more than four or five old people in his village who can still speak Cornish, concluding with the remark that Cornish is no longer known by young people. However, the last recorded traditional Cornish literature may have been the Cranken Rhyme, a corrupted version of a verse or song published in the late 19th century by John Hobson Matthews, recorded orally by John Davey (or Davy) of Boswednack, of uncertain date but probably originally composed during the last years of the traditional language. Davey had traditional knowledge of at least some Cornish. John Kelynack (1796–1885), a fisherman of Newlyn, was sought by philologists for old Cornish words and technical phrases in the 19th century. Decline of Cornish speakers between 1300 and 1800 (died 1777), said to be the last native speaker of Cornish, in an engraved portrait published in 1781|altA black and white engraving of a woman in 18th century clothing with a bonnet. Fish, a crab, a crustacean and a jug are below]]
It is difficult to state with certainty when Cornish ceased to be spoken, due to the fact that its last speakers were of relatively low social class and that the definition of what constitutes "a living language" is not clear cut. Peter Pool argues that by 1800 nobody was using Cornish as a daily language and no evidence exists of anyone capable of conversing in the language at that date. However, passive speakers, semi-speakers and rememberers, who retain some competence in the language despite not being fluent nor using the language in daily life, generally survive even longer.
The traditional view that Dolly Pentreath (1692–1777) was the last native speaker of Cornish has been challenged, However, although it is clear Davey possessed some traditional knowledge in addition to having read books on Cornish, accounts differ of his competence in the language. Some contemporaries stated he was able to converse on certain topics in Cornish whereas others affirmed they had never heard him claim to be able to do so.
The search for the last speaker is hampered by a lack of transcriptions or audio recordings, so that it is impossible to tell from this distance whether the language these people were reported to be speaking was Cornish, or English with a heavy Cornish substratum, nor what their level of fluency was. Nevertheless, this academic interest, along with the beginning of the Celtic Revival in the late 19th century, provided the groundwork for a Cornish language revival movement.
Notwithstanding the uncertainty over who was the last speaker of Cornish, researchers have posited the following numbers for the prevalence of the language between 1050 and 1800.
{| class="wikitable"
|-
!Year
!Area where<br />Cornish<br />was spoken<br />(in km<sup>2</sup>)
!Total<br />population<br />of Cornwall
!Number of<br />Cornish<br />speakers
|-
|1050
|
|16,000
|15,000
|-
|1110
|
|21,000
|20,000
|-
|1150
|
|28,000
|26,000
|-
|1200
|3,270
|35,000
|30,000
|-
|1250
|
|43,000
|34,000
|-
|1300
|2,780
|52,000
|38,000
|-
|1350
|
|48,000
|32,000
|-
|1400
|2,360
|55,000
|34,000
|-
|1450
|2,360
|62,000
|33,000
|-
|1500
|1,890
|69,000
|33,000
|-
|1550
|
|76,000
|30,000
|-
|1600
|1,400
|84,000
|22,000
|-
|1650
|910
|93,000
|14,000
|-
|1700
|530
|106,000
|5,000
|-
|1750
|160
|140,000
|"Very few"
|-
|1800
|0
|192,000
|0
|}
Revived Cornish
In 1904, the Celtic language scholar and Cornish cultural activist Henry Jenner published A Handbook of the Cornish Language. The publication of this book is often considered to be the point at which the revival movement started. Jenner wrote about the Cornish language in 1905, "one may fairly say that most of what there was of it has been preserved, and that it has been continuously preserved, for there has never been a time when there were not some Cornishmen who knew some Cornish."
The revival focused on reconstructing and standardising the language, including coining new words for modern concepts, and creating educational material in order to teach Cornish to others. In 1929 Robert Morton Nance published his Unified Cornish () system, based on the Middle Cornish literature while extending the attested vocabulary with neologisms and forms based on Celtic roots also found in Breton and Welsh, publishing a dictionary in 1938. Nance's work became the basis of revived Cornish () for most of the 20th century. During the 1970s, criticism of Nance's system, including the inconsistent orthography and unpredictable correspondence between spelling and pronunciation, resulted in the creation of several rival systems. In the 1980s, Ken George published a new system, ('Common Cornish'), based on a reconstruction of the phonological system of Middle Cornish, but with an approximately morphophonemic orthography. It was subsequently adopted by the Cornish Language Board and was the written form used by a reported 54.5% of all Cornish language users according to a survey in 2008, but was heavily criticised for a variety of reasons by Jon Mills and Nicholas Williams, including making phonological distinctions that they state were not made in the traditional language , failing to make distinctions that they believe were made in the traditional language at this time, and the use of an orthography that deviated too far from the traditional texts and Unified Cornish. Also during this period, Richard Gendall created his Modern Cornish system (also known as Revived Late Cornish), which used Late Cornish as a basis, and Nicholas Williams published a revised version of Unified; In 2010 a new milestone was reached when UNESCO altered its classification of Cornish, stating that its previous label of "extinct" was no longer accurate. From before the 1980s to the end of the 20th century there was a sixfold increase in the number of speakers to around 300. One figure for the number of people who know a few basic words, such as knowing that "Kernow" means "Cornwall", was 300,000; the same survey gave the number of people able to have simple conversations as 3,000.
The Cornish Language Strategy project commissioned research to provide quantitative and qualitative evidence for the number of Cornish speakers: due to the success of the revival project it was estimated that 2,000 people were fluent (surveyed in spring 2008), an increase from the estimated 300 people who spoke Cornish fluently suggested in a study by Kenneth MacKinnon in 2000.
Jenefer Lowe of the Cornish Language Partnership said in an interview with the BBC in 2010 that there were around 300 fluent speakers. Bert Biscoe, a councillor and bard, in a statement to the Western Morning News in 2014 said there were "several hundred fluent speakers". Cornwall Council estimated in 2015 that there were 300–400 fluent speakers who used the language regularly, with 5,000 people having a basic conversational ability in the language.
A report on the 2011 Census published in 2013 by the Office for National Statistics placed the number of speakers at somewhere between 325 and 625. In 2017 the ONS released data based on the 2011 Census that placed the number of speakers at 557 people in England and Wales who declared Cornish to be their main language, 464 of whom lived in Cornwall.
A study that appeared in 2018 established the number of people in Cornwall with at least minimal skills in Cornish, such as the use of some words and phrases, to be more than 3,000, including around 500 estimated to be fluent.
The Institute of Cornish Studies at the University of Exeter is working with the Cornish Language Partnership to study the Cornish language revival of the 20th century, including the growth in number of speakers. Legal status and recognition
(), near Crows-an-Wra (), looking towards the village of Treave () with Porthcurno () in the distance.]]
In 2002, Cornish was recognized by the UK government under Part II of the European Charter for Regional or Minority Languages. UNESCO's Atlas of World Languages classifies Cornish as "critically endangered". UNESCO has said that a previous classification of 'extinct' "does not reflect the current situation for Cornish" and is "no longer accurate". This plan has drawn some criticism. In October 2015, the council announced that staff would be encouraged to use "basic words and phrases" in Cornish when dealing with the public. In 2021 Cornwall Council prohibited a marriage ceremony from being conducted in Cornish as the Marriage Act 1949 only allowed for marriage ceremonies in English or Welsh.
In 2014, the Cornish people were recognised by the UK Government as a national minority under the Framework Convention for the Protection of National Minorities. The FCNM provides certain rights and protections to a national minority with regard to their minority language.
In 2016, British government funding for the Cornish language ceased, and responsibility transferred to Cornwall Council.
Orthography
Old Cornish orthography
Until around the middle of the 11th century, Old Cornish scribes used a traditional spelling system shared with Old Breton and Old Welsh, based on the pronunciation of British Latin. By the time of the , usually dated to around 1100, Old English spelling conventions, such as the use of thorn (Þ, þ) and eth (Ð, ð) for dental fricatives, and wynn (Ƿ, ƿ) for /w/, had come into use, allowing documents written at this time to be distinguished from Old Welsh, which rarely uses these characters, and Old Breton, which does not use them at all. Old Cornish features include using initial ⟨ch⟩, ⟨c⟩, or ⟨k⟩ for /k/, and, in internal and final position, ⟨p⟩, ⟨t⟩, ⟨c⟩, ⟨b⟩, ⟨d⟩, and ⟨g⟩ are generally used for the phonemes /b/, /d/, /ɡ/, /β/, /ð/, and /ɣ/ respectively, meaning that the results of Brittonic lenition are not usually apparent from the orthography at this time. Middle Cornish orthography Middle Cornish orthography has a significant level of variation, and shows influence from Middle English spelling practices. Yogh (Ȝ ȝ) is used in certain Middle Cornish texts, where it is used to represent a variety of sounds, including the dental fricatives /θ/ and /ð/, a usage which is unique to Middle Cornish and is never found in Middle English. Middle Cornish scribes tend to use ⟨c⟩ for /k/ before back vowels, and ⟨k⟩ for /k/ before front vowels, though this is not always true, and this rule is less consistent in certain texts. Middle Cornish scribes almost universally use ⟨wh⟩ to represent /ʍ/ (or /hw/), as in Middle English. Middle Cornish, especially towards the end of this period, tends to use orthographic ⟨g⟩ and ⟨b⟩ in word-final position in stressed monosyllables, and ⟨k⟩ and ⟨p⟩ in word-final position in unstressed final syllables, to represent the reflexes of late Brittonic /ɡ/ and /b/, respectively. Late Cornish orthography Written sources from this period are often spelled following English spelling conventions since many of the writers of the time had not been exposed to Middle Cornish texts or the Cornish orthography within them. Around 1700, Edward Lhuyd visited Cornwall, introducing his own partly phonetic orthography that he used in his , which was adopted by some local writers, leading to the use of some Lhuydian features such as the use of circumflexes to denote long vowels, ⟨k⟩ before front vowels, word-final ⟨i⟩, and the use of ⟨dh⟩ to represent the voiced dental fricative /ð/. Nance's system was used by almost all Revived Cornish speakers and writers until the 1970s. Criticism of Nance's system, particularly the relationship of spelling to sounds and the phonological basis of Unified Cornish, resulted in rival orthographies appearing by the early 1980s, including Gendal's Modern Cornish, based on Late Cornish native writers and Lhuyd, and Ken George's Kernewek Kemmyn, a mainly morphophonemic orthography based on George's reconstruction of Middle Cornish , which features a number of orthographic, and phonological, distinctions not found in Unified Cornish. resulted in the creation of Unified Cornish Revised, a modified version of Nance's orthography, featuring: an additional phoneme not distinguished by Nance, "ö in German ", represented in the UCR orthography by ⟨ue⟩; replacement of ⟨y⟩ with ⟨e⟩ in many words; internal ⟨h⟩ rather than ⟨gh⟩; and use of final ⟨b⟩, ⟨g⟩, and ⟨dh⟩ in stressed monosyllables. A Standard Written Form, intended as a compromise orthography for official and educational purposes, was introduced in 2008, although a number of previous orthographic systems remain in use and, in response to the publication of the SWF, another new orthography, Kernowek Standard, was created, mainly by Nicholas Williams and Michael Everson, which is proposed as an amended version of the Standard Written Form. Phonology
The phonological system of Old Cornish, inherited from Proto-Southwestern Brittonic and originally differing little from Old Breton and Old Welsh, underwent various changes during its Middle and Late phases, eventually resulting in several characteristics not found in the other Brittonic languages. The first sound change to distinguish Cornish from both Breton and Welsh, the assibilation of the dental stops and in medial and final position, had begun by the time of the , or earlier. This change, and the subsequent, or perhaps dialectical, palatalization (or occasional rhotacization in a few words) of these sounds, results in orthographic forms such as Middle Cornish 'father', Late Cornish (Welsh ), Middle Cornish 'believe', Late Cornish (Welsh ), and Middle Cornish 'leave', Late Cornish (Welsh ). A further characteristic sound change, pre-occlusion, occurred during the 16th century, resulting in the nasals and being realised as and respectively in stressed syllables, and giving Late Cornish forms such as 'head' (Welsh ) and 'crooked' (Welsh ).
As a revitalised language, the phonology of contemporary spoken Cornish is based on a number of sources, including various reconstructions of the sound system of middle and early modern Cornish based on an analysis of internal evidence such as the orthography and rhyme used in the historical texts, comparison with the other Brittonic languages Breton and Welsh, and the work of the linguist Edward Lhuyd, who visited Cornwall in 1700 and recorded the language in a partly phonetic orthography.
Vocabulary
Cornish is a Celtic language, and the majority of its vocabulary, when usage frequency is taken into account, at every documented stage of its history is inherited from Proto-Celtic, either directly from the ancestral Proto-Indo-European language or through vocabulary borrowed from unknown substrate language(s) at some point in the development of the Celtic proto-language from PIE. Examples of the PIE > PCelt. development are various terms related to kinship and people, including 'mother', 'aunt, mother's sister', 'sister', 'son', 'man', 'person, human', and 'people', and words for parts of the body, including 'hand' and 'tooth'. Inherited adjectives with an Indo-European etymology include 'new', 'broad, wide', 'red', 'old', 'young', and 'alive, living'.
Several Celtic or Brittonic words cannot be reconstructed to Proto-Indo-European, and are suggested to have been borrowed from unknown substrate language(s) at an early stage, such as Proto-Celtic or Proto-Brittonic. Proposed examples in Cornish include 'beer' and 'badger'.
Other words in Cornish inherited direct from Proto-Celtic include a number of toponyms, for example 'hill', 'fort', and 'land', and a variety of animal names such as 'mouse', 'wether', 'pigs', and 'bull'.
During the Roman occupation of Britain a large number (around 800) of Latin loan words entered the vocabulary of Common Brittonic, which subsequently developed in a similar way to the inherited lexicon. These include 'arm' (from British Latin ), 'net' (from ), and 'cheese' (from ).
A substantial number of loan words from English and to a lesser extent French entered the Cornish language throughout its history. Whereas only 5% of the vocabulary of the Old Cornish Vocabularium Cornicum is thought to be borrowed from English, and only 10% of the lexicon of the early modern Cornish writer William Rowe, around 42% of the vocabulary of the whole Cornish corpus is estimated to be English loan words, without taking frequency into account. (However, when frequency is taken into account, this figure for the entire corpus drops to 8%.) The many English loanwords, some of which were sufficiently well assimilated to acquire native Cornish verbal or plural suffixes or be affected by the mutation system, include 'to read', 'to understand', 'way', 'boot' and 'art'.
Many Cornish words, such as mining and fishing terms, are specific to the culture of Cornwall. Examples include 'mine waste' and 'to mend fishing nets'. and are different types of pastries. is a 'traditional Cornish dance get-together' and is a specific kind of ceremonial dance that takes place in Cornwall. Certain Cornish words may have several translation equivalents in English, so for instance may be translated into English as either 'book' or 'volume' and can mean either 'hand' or 'fist'.
Like other Celtic languages, Cornish lacks a number of verbs commonly found in other languages, including modals and psych-verbs; examples are 'have', 'like', 'hate', 'prefer', 'must/have to' and 'make/compel to'. These functions are instead fulfilled by periphrastic constructions involving a verb and various prepositional phrases.
Grammar
The grammar of Cornish shares with other Celtic languages a number of features which, while not unique, are unusual in an Indo-European context. The grammatical features most unfamiliar to English speakers of the language are the initial consonant mutations, the verb–subject–object word order, inflected prepositions, fronting of emphasised syntactic elements and the use of two different forms for 'to be'.
Morphology
Mutations
Cornish has initial consonant mutation: The first sound of a Cornish word may change according to grammatical context. As in Breton, there are four types of mutation in Cornish (compared with three in Welsh, two in Irish and Manx and one in Scottish Gaelic). These changes apply to only certain letters (sounds) in particular grammatical contexts, some of which are given below:
*Lenition or "soft" mutation:
**Feminine singular nouns are lenited after 'the':
*** 'cat' > 'the cat'
*Spirantization or "aspirate" mutation:
**Nouns are spirantized after 'my':
*** 'father' > 'my father'
*Provection or "hard" mutation:
**Verbs are provected after the verbal particle (approximately English "-ing"):
*** 'see' > 'seeing'
*Lenition followed by provection (usually), or "mixed" mutation:
**Type 1 mixed mutation:
***Occurs after the affirmative particle :
**** > 'I see'
**Type 2 mixed mutation:
***Occurs after 2nd person singular infixed pronoun :
**** 'hand' > 'in thy hand'
Articles
Cornish has no indefinite article. can either mean 'harbour' or 'a harbour'. In certain contexts, can be used, with the meaning 'a certain, a particular', e.g. 'a certain harbour'. There is, however, a definite article 'the', which is used for all nouns regardless of their gender or number, e.g. 'the harbour'.
Nouns
Cornish nouns belong to one of two grammatical genders, masculine and feminine, but are not inflected for case. Nouns may be singular or plural. Plurals can be formed in various ways, depending on the noun:
*Vowel change:
** 'hole' > 'holes'
*Addition of a specific plural suffix:
** 'angel' > 'angels'
** 'father' > 'fathers'
** 'peddler' > 'peddlers'
*Suppletion:
** 'man' > 'men, people'
Some nouns are collective or mass nouns. Singulatives can be formed from collective nouns by the addition of the suffix ⫽-enn⫽ (SWF -en):
* 'grass' > 'a blade of grass'
* 'willow-trees' > 'a willow tree'
Verbs
Verbs are conjugated for person, number, tense and mood. For example, the verbal noun 'see' has derived forms such as 1st person singular present indicative 'I see', 3rd person plural imperfect indicative 'they saw', and 2nd person singular imperative 'see!' Grammatical categories can be indicated either by inflection of the main verb, or by the use of auxiliary verbs such as 'be' or 'do'. Prepositions Cornish uses inflected (or conjugated) prepositions: Prepositions are inflected for person and number. For example, (with, by) has derived forms such as 'with me', 'with him', and 'with you (plural)'.
Syntax
Word order in Cornish is somewhat fluid and varies depending on several factors such as the intended element to be emphasised and whether a statement is negative or affirmative. In a study on Cornish word order in the play Bewnans Meriasek (), Ken George has argued that the most common word order in main clauses in Middle Cornish was, in affirmative statements, SVO, with the verb in the third person singular:
}}
When affirmative statements are in the less common VSO order, they usually begin with an adverb or other element, followed by an affirmative particle, with the verb inflected for person and tense:
}}
In negative statements, the order was usually VSO, with an initial negative particle and the verb conjugated for person and tense:
}}
A similar structure is used for questions:
.2PL 2PL|'Did you hear?'}}
Elements can be fronted for emphasis:
}}
Sentences can also be constructed periphrastically using auxiliary verbs such as 'be, exist':
}}
As Cornish lacks verbs such as 'to have', possession can also be indicated in this way:
}}
Enquiring about possession is similar, using a different interrogative form of :
}}
Nouns usually precede the adjective, unlike in English:
}}
Some adjectives usually precede the noun, however:
Culture
() mounted on the north side of Blackheath common, south east London, near the south entrance to Greenwich Park]]
The Celtic Congress and Celtic League are groups that advocate cooperation amongst the Celtic Nations in order to protect and promote Celtic languages and cultures, thus working in the interests of the Cornish language.
There have been films such as , some televised, made entirely, or significantly, in Cornish. Some businesses use Cornish names.
Cornish has significantly and durably affected Cornwall's place-names as well as Cornish surnames and knowledge of the language helps the understanding of these ancient meanings. Cornish names are adopted for children, pets, houses and boats.
There is Cornish literature, including spoken poetry and song, as well as traditional Cornish chants historically performed in marketplaces during religious holidays and public festivals and gatherings.
There are periodicals solely in the language, such as the monthly , and . BBC Radio Cornwall has a news broadcast in Cornish and sometimes has other programmes and features for learners and enthusiasts. Local newspapers such as the Western Morning News have articles in Cornish, and newspapers such as The Packet, The West Briton, and The Cornishman have also been known to have Cornish features. There is an online radio and TV service in Cornish called , publishing a one-hour podcast each week, based on a magazine format. It includes music in Cornish as well as interviews and features.
The language has financial sponsorship from sources including the Millennium Commission. A number of language organisations exist in Cornwall: (Our Language), the Cornish sub-group of the European Bureau for Lesser-Used Languages, , (the Cornish Language Board) and (the Cornish Language Fellowship).
There are ceremonies, some ancient, some modern, that use the language or are entirely in the language.
in several languages, including Cornish]]
Cultural events
Cornwall has had cultural events associated with the language, including the international Celtic Media Festival, hosted in St Ives in 1997. The Old Cornwall Society has promoted the use of the language at events and meetings. Two examples of ceremonies that are performed in both the English and Cornish languages are Crying the Neck and the annual mid-summer bonfires.
Since 1969, there have been three full performances of the Ordinalia, originally written in the Cornish language, the most recent of which took place at the plen-an-gwary in St Just in September 2021. While significantly adapted from the original, as well as using mostly English-speaking actors, the plays used sizable amounts of Cornish, including a character who spoke only in Cornish and another who spoke both English and Cornish. The event drew thousands over two weeks, also serving as a celebration of Celtic culture. The next production, scheduled for 2024, could, in theory, be entirely in Cornish, without English, if assisted by a professional linguist.
Outside of Cornwall, efforts to revive the Cornish language and culture through community events are occurring in Australia. A biennial festival, Kernewek Lowender, takes place in South Australia, where both cultural displays and language lessons are offered. Study and teaching Cornish is taught in some schools; it was previously taught at degree level at the University of Wales, though the only existing course in the language at university level is as part of a course in Cornish studies at the University of Exeter. In March 2008 a course in the language was started as part of the Celtic Studies curriculum at the University of Vienna, Austria.
The University of Cambridge offers courses in Cornish through its John Trim Resources Centre, which is part of the university's Language Centre. In addition, the Department of Anglo-Saxon, Norse and Celtic (which is part of the Faculty of English) also carries out research into the Cornish language.
In 2015 a university-level course aiming at encouraging and supporting practitioners working with young children to introduce the Cornish language into their settings was launched. The Cornish Language Practice Project (Early Years) is a level 4 course approved by Plymouth University and run at Cornwall College. The course is not a Cornish-language course but students will be assessed on their ability to use the Cornish language constructively in their work with young children. The course will cover such topics as Understanding Bilingualism, Creating Resources and Integrating Language and Play, but the focus of the language provision will be on Cornish. A non-accredited specialist Cornish-language course has been developed to run alongside the level 4 course for those who prefer tutor support to learn the language or develop their skills for use with young children.
Cornwall's first Cornish-language crèche, , was established in 2010 at Cornwall College, Camborne. The nursery teaches children aged between two and five years alongside their parents to ensure the language is also spoken in the home.
Classes and conversation groups for adults are available at several locations in Cornwall as well as in London, Cardiff and Bristol. Since the onset of the COVID-19 pandemic a number of conversation groups entitled have been held online, advertised through Facebook and other media. A surge in interest, not just from people in Cornwall but from all over the world, has meant that extra classes have been organised.
Cornish studies
William Scawen produced a manuscript on the declining Cornish language that continually evolved until he died in 1689, aged 89. He was one of the first to realise the language was dying out and wrote detailed manuscripts which he started working on when he was 78. The only version that was ever published was a short first draft but the final version, which he worked on until his death, is a few hundred pages long. At the same time a group of scholars led by John Keigwin (nephew of William Scawen) of Mousehole tried to preserve and further the Cornish language and chose to write in Cornish. One of their number, Nicholas Boson, tells how he had been discouraged from using Cornish to servants by his mother. This group left behind a large number of translations of parts of the Bible, proverbs and songs. They were contacted by the Welsh linguist Edward Lhuyd, who came to Cornwall to study the language.
Early Modern Cornish was the subject of a study published by Lhuyd in 1707, and differs from the medieval language in having a considerably simpler structure and grammar. Such differences included sound changes and more frequent use of auxiliary verbs. The medieval language also possessed two additional tenses for expressing past events and an extended set of possessive suffixes.
John Whitaker, the Manchester-born rector of Ruan Lanihorne, studied the decline of the Cornish language. In his 1804 work the Ancient Cathedral of Cornwall he concluded that: "[T]he English Liturgy, was not desired by the Cornish, but forced upon them by the tyranny of England, at a time when the English language was yet unknown in Cornwall. This act of tyranny was at once gross barbarity to the Cornish people, and a death blow to the Cornish language."
Robert Williams published the first comprehensive Cornish dictionary in 1865, the . As a result of the discovery of additional ancient Cornish manuscripts, 2000 new words were added to the vocabulary by Whitley Stokes in A Cornish Glossary. William C. Borlase published Proverbs and Rhymes in Cornish in 1866 while A Glossary of Cornish Names was produced by John Bannister in the same year. Frederick Jago published his English–Cornish Dictionary in 1882.
In 2002, the Cornish language gained new recognition because of the European Charter for Regional and Minority Languages. Conversely, along with government provision was the governmental basis of "New Public Management", measuring quantifiable results as means of determining effectiveness. This put enormous pressure on finding a single orthography that could be used in unison. The revival of Cornish required extensive rebuilding. The Cornish orthographies that were reconstructed may be considered versions of Cornish because they are not traditional sociolinguistic variations. In the middle-to-late twentieth century, the debate over Cornish orthographies angered more people because several language groups received public funding. This caused other groups to sense favouritism as playing a role in the debate.
A governmental policymaking structure called New Public Management (NPM) has helped the Cornish language by managing public life of the Cornish language and people. In 2007, the Cornish Language Partnership MAGA represents separate divisions of government and their purpose is to further enhance the Cornish Language Developmental Plan. MAGA established an Ad-Hoc Group, which resulted in three orthographies being presented. The relations for the Ad-Hoc Group were to obtain consensus among the three orthographies and then develop a "single written form". The result was creating a new form of Cornish, which had to be natural for both new learners and skilled speakers.
Literature
Recent Modern Cornish literature
In 1981, the Breton library edited (Passion of our lord), a 15th-century Cornish poem. The first complete translation of the Bible into Cornish, translated from English, was published in 2011. Another Bible translation project translating from original languages is underway. The New Testament and Psalms were made available online on YouVersion (Bible.com) and Bibles.org in July 2014 by the Bible Society.
A few small publishers produce books in Cornish which are stocked in some local bookshops, as well as in Cornish branches of Waterstones and WH Smith, although publications are becoming increasingly available on the Internet. Printed copies of these may also be found from Amazon. The Truro Waterstones hosts the annual literary awards, established by to recognise publications relating to Cornwall or in the Cornish language. In recent years, a number of Cornish translations of literature have been published, including ''Alice's Adventures in Wonderland (2009), Around the World in Eighty Days (2009), Treasure Island (2010), The Railway Children (2012), Hound of the Baskervilles (2012), The War of the Worlds (2012), The Wind in the Willows (2013), Three Men in a Boat (2013), Alice in Wonderland and Through the Looking-Glass (2014), and A Christmas Carol (which won the 2012 award for Cornish Language books), as well as original Cornish literature such as (The Lyonesse Stone) by Craig Weatherhill. Literature aimed at children is also available, such as (Where's Spot?), (The Beast of Bodmin Moor), three Topsy and Tim titles, two Tintin'' titles and (Briallen and the Alien), which won the 2015 award for Cornish Language books for children. In 2014 , Nicholas Williams's translation of J. R. R. Tolkien's The Hobbit, was published.
is a monthly magazine published entirely in the Cornish language. Members contribute articles on various subjects. The magazine is produced by Graham Sandercock who has been its editor since 1976.
Media
In 1983 BBC Radio Cornwall started broadcasting around two minutes of Cornish every week. In 1987, however, they gave over 15 minutes of airtime on Sunday mornings for a programme called ('Holdall'), presented by John King, running until the early 1990s. It was eventually replaced with a five-minute news bulletin called ('The News'). The bulletin was presented every Sunday evening for many years by Rod Lyon, then Elizabeth Stewart, and currently a team presents in rotation. Pirate FM ran short bulletins on Saturday lunchtimes from 1998 to 1999. In 2006, Matthew Clarke who had presented the Pirate FM bulletin, launched a web-streamed news bulletin called ('Weekly News'), which in 2008 was merged into a new weekly magazine podcast (RanG).
Cornish television shows have included a 1982 series by Westward Television with each episode containing a three-minute lesson in Cornish. , an eight-episode series produced by Television South West and broadcast between June and July 1984, later on S4C from May to July 1985, and as a schools programme in 1986. Also by Television South West were two bilingual programmes on Cornish Culture called .
In 2016 Kelly's Ice Cream of Bodmin introduced a light hearted television commercial in the Cornish language and this was repeated in 2017.
The first episode from the third season of the US television program Deadwood features a conversation between miners, purportedly in the Cornish language, but really in Irish. One of the miners is then shot by thugs working for businessman George Hearst who justify the murder by saying, "He come at me with his foreign gibberish."
A number of Cornish language films have been made, including Hwerow Hweg, a 2002 drama film written and directed by Hungarian film-maker Antal Kovacs and Trengellick Rising, a short film written and directed by Guy Potter.
Screen Cornwall works with Cornwall Council to commission a short film in the Cornish language each year, with their FilmK competition. Their website states "FylmK is an annual contemporary Cornish language short film competition, producing an imaginative and engaging film, in any genre, from distinctive and exciting filmmakers".
A monthly half-hour online TV show began in 2017 called (The Month). It contained news items about cultural events and more mainstream news stories all through Cornish. It also ran a cookery segment called "" ('Esther's Kitchen'). Music English composer Peter Warlock wrote a Christmas carol in Cornish (setting words by Henry Jenner). The Cornish electronic musician Aphex Twin has used Cornish names for track titles, most notably on his Drukqs album.
Several traditional Cornish folk songs have been collected and can be sung to various tunes. These include "", "", and "".
In 2018, the singer Gwenno Saunders released an album in Cornish, entitled , saying: "I speak Cornish with my son: if you're comfortable expressing yourself in a language, you want to share it."
Place-names and surnames
]]
The Cornish language features in the toponymy of Cornwall, with a significant contrast between English place-names prevalent in eastern Cornwall and Cornish place-names to the west of the Camel-Fowey river valleys, where English place-names are much less common. Hundreds of Cornish family names have an etymology in the Cornish language, the majority of which are derived from Cornish place-names. Long before the agreement of the Standard Written Form of Cornish in the 21st century, Late Cornish orthography in the Early Modern period usually followed Welsh to English transliteration, phonetically rendering C for K, I for Y, U for W, and Z for S. This meant that place names were adopted into English with spellings such as 'Porthcurno' and 'Penzance'; they are written and in the Standard Written Form of Cornish, agreed upon in 2008. Likewise words such as ('island') can be found spelled as as at Ince Castle. These apparent mistransliterations can, however, reveal an insight into how names and places were actually pronounced, explaining, for example, how anglicised is still pronounced [ˈlansǝn] with emphasis on the first element, perhaps from Cornish , though the Concise Oxford Dictionary of English Place-Names considers this unlikely.
The following tables present some examples of Cornish place names and surnames and their anglicised versions:
{| class="wikitable"
! English (anglicised)<br />place-name || Cornish place-name ||Translation
|-
| Truro || ||Three Roads
|-
| || || Mouth [of] Fal
|-
| || || Dunes [of] Pleustri
|-
| || || Head Holy i.e. Holy Headland
|-
| || || Ford Red
|-
| || || Camm (crooked) Hill
|-
| || || Saint Ostel
|-
| || || Abode [of] Monks
|-
| || || Court [of the] Crossroads
|-
| || || Land [of] St Stephen
|}
{| class="wikitable"
|-
! English (anglicised) surname || Cornish surname || Translation
|-
| || || 'The White'
|-
| || || 'The Smith'
|-
| || || Either a dialectal variant of Hilary (from Latin ),<br />or from the parish of , meaning 'swan river'.
|-
| || || 'New house'
|-
| || || 'Easter/Passion'
|-
| || || 'Cornwall'
|-
| || || 'Beautiful'
|-
| || || Possibly 'Homestead of the doctor'
|-
| || || From , literally meaning 'feast-acre'.
|-
| || || 'Mean/Middle town'
|}
Samples
From the Universal Declaration of Human Rights:
{|class="wikitable"
! Cornish
! Translation
|-style="border-bottom-style:hidden;"
|
| All human beings are born free and
|-style="border-bottom-style:hidden;"
|
| equal in dignity and rights. They are
|-style="border-bottom-style:hidden;"
|
| endowed with reason and conscience
|-style="border-bottom-style:hidden;"
|
| and should act towards one another
|-
|
| in a spirit of brotherhood.
|}
From , the Cornish anthem:
{|class="wikitable"
! Cornish
! Translation
|-style="border-bottom-style:hidden;"
|
| Old land of our fathers, your children love you,
|-style="border-bottom-style:hidden;"
|
| Dear country of the west, what land is your equal?
|-style="border-bottom-style:hidden;"
|
| Over all the world, we are spread far and wide,
|-style="border-bottom-style:hidden;"
|
| But our love is for you.
|-style="border-bottom-style:hidden;"
|
| Cornwall, Cornwall, we love Cornwall;
|-style="border-bottom-style:hidden;"
|
|For as long as the sea is a wall around you
|-
|
| We are one and all for Cornwall!
|}
From the wrestler's oath:
{|class="wikitable"
! Cornish
! Translation
|-style="border-bottom-style:hidden;"
|
| On my honour and the honour of my country,
|-style="border-bottom-style:hidden;"
|
| I swear to wrestle without treachery or brutality
|-style="border-bottom-style:hidden;"
|
| And in token of my sincerity I offer my hand to my opponent.
|-style="border-bottom-style:hidden;"
|
| In the words of my forefathers:
|-
|
| "Fair play is sweet play".
|}
See also
* Anglo-Cornish, the Cornish dialect of the English language
* Bible translations into Cornish
* Breton language
* List of Celtic-language media
* The Cornish Language Council ()
* European Charter for Regional or Minority Languages
* Language revival
** Irish language revival
** Manx, another Celtic language subject to revival efforts
* Languages in the United Kingdom
* Cornish literature
* List of topics related to Cornwall
References
Bibliography
* Bruch, Benjamin; Bock, Albert (2008) An Outline of the Standard Written Form of Cornish. Cornish Language Partnership
* Hodge, Pol (2001) Cornish Names. Truro: Dyllansow Fentenwynn
* Jago, F. W. P., A Cornish Dictionary (1887) [https://archive.org/details/EnglishCornishDictionary English Cornish dictionary]
* Jenner, Henry, A Handbook of the Cornish language: Chiefly in its latest stages with some account of its history and literature (1904) [http://www.gutenberg.org/files/26192/26192-h/26192-h.htm] [http://www.gutenberg.org/ebooks/26192]
* Ellis, Peter B. (1971) The Story of the Cornish Language. 32 p. Truro: Tor Mark Press
* Ellis, Peter B. (1974) The Cornish Language and its Literature. ix, 230 p. London: Routledge & Kegan Paul
* Everson, Michael (2007) A Proposed Standard Written Form of Cornish. Cornish Language Partnership Process
* Ferdinand, Siarl (2013). Brief History of the Cornish language, its Revival and its Current Situation. E-Keltoi, Vol. 2, 2 Dec pp. 199–227 [https://www.academia.edu/5323710/A_Brief_History_of_the_Cornish_Language_its_Revival_and_its_Current_Status]
* Jackson, Kenneth (1953) Language and History in Early Britain: A chronological survey of the Brittonic languages, first to twelfth century a.D. Edinburgh Uuniverty Ppress; 2nd ed. Dublin: Four Courts Press (1994) has a new introduction by William Gillies
* Norris, Edwin, [https://archive.org/details/sketchofcornishg00norr Sketch of Cornish grammar (1859)] [https://archive.org/details/sketchofcornishg00norruoft] [https://archive.org/details/sketchcornishgr00norrgoog] [https://archive.org/details/sketchofcornishg00norriala]
* Sandercock, Graham (1996) A Very Brief History of the Cornish Language. Hayle:
* Stokes, Whitley, The Creation of the World: A Cornish Mystery (1863)
* Weatherhill, Craig (1995) Cornish Place Names & Language. Wilmslow: Sigma Press (reissued in 1998, 2000 ; second revised edition 2007 )
* Weatherhill, Craig (2009) Concise Dictionary of Cornish Place-names; edited by Michael Everson. Westport, Co. Mayo: Evertype
* Williams, G. P, [https://archive.org/details/preverbalparticl00willrich The preverbal particle Re in Cornish (1908)]
External links
* [https://www.gutenberg.org/files/26192/26192-h/26192-h.htm A Handbook of the Cornish Language, by Henry Jenner] A Project Gutenberg eBook
* [https://web.archive.org/web/20170112235606/http://www.magakernow.org.uk/ Cornish Language Partnership website]
* [https://www.endangeredlanguages.com/lang/4050 Endangered Languages Project: Cornish]
* [http://radyo.kernewegva.com/ A Cornish Internet radio station in nascent state featuring weekly podcasts in Cornish]
* [http://kernowek.net/mailman/listinfo/spellyans_kernowek.net Spellyans – Standard Written Form Cornish discussion list]
* [http://www.kernowek.net/ UdnFormScrefys' site for the proposed compromise orthography, Kernowek Standard]
* [http://www.kernewegva.com/medhelweyth.html List of localised software in Cornish]
* [https://www.bbc.co.uk/cornwall/connected/stories/new_cornwall_language.shtml – A Taste of Cornish] – basic Cornish lessons hosted by BBC Cornwall
* [https://cornish-language.org/ Cornish Language Fellowship]
* [http://justus.anglican.org/resources/bcp/Cornish/index.htm Lyver Pysadow Kemyn (1980)] Portions of the Book of Common Prayer in Cornish
* [https://www.bbc.co.uk/voices/multilingual/cornish.shtml Cornish today] by Kenneth MacKinnon – from the BBC
* [https://www.bibelkernewek.com/ Bibel Kernewek] Cornish Bible Translation Project
* [http://cornish-place-names.wikidot.com/ An Index to the Historical Place Names of Cornwall]
* [https://qz.com/969597/hebrew-was-the-only-language-ever-to-be-revived-from-extinction-there-may-soon-be-another/ A review of the Cornish revival]
* [https://cornwalldirect.co.uk/cornish-language-sayings-and-phrases/ Cornish language Sayings and Phrases]
Dictionaries
* [https://www.cornishdictionary.org.uk/ Gerlyver kernewek (Cornish dictionary)]
* [https://web.archive.org/web/20151105003722/http://www.magakernow.org.uk/idoc.ashx?docid205a3451-0e49-4216-a825-d4a4ceba9ba2&version-1 An English-Cornish Glossary in the Standard Written Form] – Cornish Language Partnership
* [https://archive.org/details/lexiconcornubrit00willuoft : a Dictionary of the Ancient Celtic Language of Cornwall] by Robert Williams, Llandovery, 1865.
}}
Category:Critically endangered languages
Category:Languages attested from the 9th century
Category:Languages extinct in the 18th century
Category:Southwestern Brittonic languages
*
Category:Languages of England
Category:Languages of the United Kingdom
Category:Cornish nationalism
Category:Endangered Celtic languages
Category:Verb–subject–object languages
Category:Language revival
|
https://en.wikipedia.org/wiki/Cornish_language
|
2025-04-05T18:27:43.702512
|
6132
|
Complexity theory
|
Complexity theory may refer to:
Science and technology
Computational complexity theory, a field in theoretical computer science and mathematics
Complex systems theory, the study of the complexity in context of complex systems
Assembly theory, a way of characterizing extraterrestrial molecular complexity to assess the probability of the presence of life
Other uses
Complexity economics, the application of complexity theory to economics
Complexity theory and organizations, the application of complexity theory to strategy
See also
Computational complexity
Complexity (disambiguation)
Systems theory
Systems thinking
Complex adaptive system, a special case of complex systems
Complex network
|
https://en.wikipedia.org/wiki/Complexity_theory
|
2025-04-05T18:27:43.704385
|
6134
|
Charybdis
|
's painting of Odysseus facing the choice between Scylla and Charybdis, 1794–1796]]
Charybdis (; |Khárybdis}}, ; }}, ) is a sea monster in Greek mythology. Charybdis, along with the sea monster Scylla, appears as a challenge to epic characters such as Odysseus, Jason, and Aeneas. Scholarship locates her in the Strait of Messina.
The idiom "between Scylla and Charybdis" has come to mean being forced to choose between two similarly dangerous situations.
Description
The sea monster Charybdis was believed to live under a small rock on one side of a narrow channel. Opposite her was Scylla, another sea monster, who lived inside a much larger rock. The sides of the strait were within an arrow-shot of each other, and sailors attempting to avoid one of them would come in reach of the other. To be "between Scylla and Charybdis" therefore means to be presented with two opposite dangers, the task being to find a route that avoids both. Three times a day, Charybdis swallowed a huge amount of water, before belching it back out again, creating large whirlpools capable of dragging a ship underwater. In some variations of the story, Charybdis was simply a large whirlpool instead of a sea monster.
Through the descriptions of Greek mythical chroniclers and Greek historians such as Thucydides, modern scholars generally agree that Charybdis was said to have been located in the Strait of Messina, off the coast of Sicily and opposite a rock on the mainland identified with Scylla. A whirlpool does exist there, caused by currents meeting, but it is dangerous only to small craft in extreme conditions. Family Another myth makes Charybdis the daughter of Poseidon and Gaia and living as a loyal servant to her father.Mythology Origin Charybdis aided her father Poseidon in his feud with her paternal uncle Zeus and, as such, helped him engulf lands and islands in water. Zeus, angry over the land she stole from him, sent her to the bottom of the sea with a thunderbolt; from the sea bed, she drank the water from the sea thrice a day, creating whirlpools. She lingered on a rock with Scylla facing her directly on another rock, making a strait.
In some myths, Charybdis was a voracious woman who stole oxen from Heracles, and was hurled by the thunderbolt of Zeus into the sea, where she retained her voracious nature.Jason and the Argonauts
The Argonauts were able to avoid both dangers because Hera ordered the Nereid Thetis to guide them through the perilous passage.
The Aeneid
In the Aeneid, the Trojans are warned by Helenus of Scylla and Charybdis, and are advised to avoid them by sailing around Pachynus point (Cape Passero) rather than risk the strait. Later, however, they find themselves passing Etna, and have to row for their lives to escape Charybdis.
Aesop
Aristotle mentions in his Meteorologica that Aesop once teased a ferryman by telling him a myth concerning Charybdis. With one gulp of the sea, she brought the mountains to view; islands appeared after the next. The third is yet to come and will dry the sea altogether, thus depriving the ferryman of his livelihood.
See also
*Icefalls
Notes
References
*Apollonius Rhodius, Argonautica translated by Robert Cooper Seaton (1853–1915), R. C. Loeb Classical Library Volume 001. London, William Heinemann Ltd, 1912. [https://topostext.org/work/126 Online version at the Topos Text Project.]
*Apollonius Rhodius, Argonautica. George W. Mooney. London. Longmans, Green. 1912. [http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0227 Greek text available at the Perseus Digital Library].
*Homer, The Odyssey with an English Translation by A.T. Murray, Ph.D. in two volumes. Cambridge, MA., Harvard University Press; London, William Heinemann, Ltd. 1919. . [http://www.perseus.tufts.edu/hopper/text?docPerseus:text:1999.01.0136 Online version at the Perseus Digital Library.] [http://www.perseus.tufts.edu/hopper/text?docPerseus:text:1999.01.0135 Greek text available from the same website].
*Maurus Servius Honoratus, In Vergilii carmina comentarii. Servii Grammatici qui feruntur in Vergilii carmina commentarii; recensuerunt Georgius Thilo et Hermannus Hagen. Georgius Thilo. Leipzig. B. G. Teubner. 1881. [http://www.perseus.tufts.edu/hopper/text?docPerseus:text:1999.02.0053 Online version at the Perseus Digital Library].Further reading*Smith, William; Dictionary of Greek and Roman Biography and Mythology'', London (1873). [https://www.perseus.tufts.edu/hopper/text?docPerseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DS%3Aentry+group%3D10%3Aentry%3Dscylla-bio-1 "Scylla" 1.]
External links
*
*
Category:Characters in the Odyssey
Category:Female legendary creatures
Category:Metamorphoses into monsters in Greek mythology
Category:Characters in the Argonautica
Category:Naiads
Category:Children of Gaia
Category:Children of Poseidon
Category:Sea monsters
Category:Whirlpools
Category:Metamorphoses characters
Category:Mount Etna
|
https://en.wikipedia.org/wiki/Charybdis
|
2025-04-05T18:27:43.727463
|
6136
|
Carbon monoxide
|
|PubChem = 281
|ChemSpiderID = 275
|ChemSpiderID_Ref =
|UNII_Ref =
|UNII = 7U1EE4V452
|EINECS = 211-128-3
|UNNumber = 1016
|KEGG_Ref =
|KEGG = D09706
|MeSHName = Carbon+monoxide
|ChEBI_Ref =
|ChEBI = 17245
|ChEMBL = 1231840
|RTECS = FG3500000
|SMILES = [C-]#[O+]
|StdInChI_Ref =
|StdInChI = 1S/CO/c1-2
|StdInChIKey_Ref =
|StdInChIKey = UGFAIRIUMAVXCW-UHFFFAOYSA-N
|Beilstein = 3587264
|Gmelin = 421
}}
|Section2 =
|Solubility = 27.6 mg/L (25 °C)
|SolubleOther = soluble in chloroform, acetic acid, ethyl acetate, ethanol, ammonium hydroxide, benzene
|MeltingPtC = −205.02
|BoilingPtC = −191.5
|Dipole = 0.122 D
|RefractIndex = 1.0003364
|HenryConstant = 1.04 atm·m<sup>3</sup>/mol
|MagSus = −9.8·10<sup>−6</sup> cm<sup>3</sup>/mol
}}
|Section3 =
|Section4 =
|Section5 =
|GHSSignalWord = Danger
|HPhrases =
|PPhrases =
|FlashPtC = −191
|AutoignitionPtC = 609
|ExploLimits = 12.5–74.2%
|NIOSH_ref
|PEL = TWA 50 ppm (55 mg/m<sup>3</sup>)
|REL =
|IDLH = 1200 ppm
|LC50 =
|LCLo =
}}
Carbon monoxide (chemical formula CO) is a poisonous, flammable gas that is colorless, odorless, tasteless, and slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simplest carbon oxide. In coordination complexes, the carbon monoxide ligand is called carbonyl. It is a key ingredient in many processes in industrial chemistry.
The most common source of carbon monoxide is the partial combustion of carbon-containing compounds. Numerous environmental and biological sources generate carbon monoxide. In industry, carbon monoxide is important in the production of many compounds, including drugs, fragrances, and fuels. Upon emission into the atmosphere, carbon monoxide affects several processes that contribute to climate change.
Indoors CO is one of the most acutely toxic contaminants affecting indoor air quality. CO may be emitted from tobacco smoke and generated from malfunctioning fuel burning stoves (wood, kerosene, natural gas, propane) and fuel burning heating systems (wood, oil, natural gas) and from blocked flues connected to these appliances. Carbon monoxide poisoning is the most common type of fatal air poisoning in many countries. This bond length is consistent with a triple bond, as in molecular nitrogen (), which has a similar bond length (109.76 pm) and nearly the same molecular mass. Carbon–oxygen double bonds are significantly longer, 120.8 pm in formaldehyde, for example. The boiling point (82 K) and melting point (68 K) are very similar to those of (77 K and 63 K, respectively). The bond-dissociation energy of 1072 kJ/mol is stronger than that of (942 kJ/mol) and represents the strongest chemical bond known.
The ground electronic state of carbon monoxide is a singlet state since there are no unpaired electrons.
{| class="wikitable mw-collapsible"
|+
Thermal and physical properties of carbon monoxide (CO) at atmospheric pressure
!Temperature (°C) || Temperature (K) || Density (kg/m<sup>3</sup>) || Specific heat (J/g °C) || Dynamic viscosity (cg/m s) || Kinematic viscosity (cm<sup>2</sup>/s) || Thermal conductivity (cW/m °C) || Thermal diffusivity (cm<sup>2</sup>/s) || Prandtl number
|-
| -73.15
|200||1.6888 ||1.045||1.27||0.0752||1.7 ||0.0963||0.781
|-
| -53.15
|220||1.5341 ||1.044||1.37||0.0893||1.9 ||0.119 ||0.753
|-
| -33.15
|240||1.4055 ||1.043||1.47||0.105 ||2.06||0.141 ||0.744
|-
| -13.15
|260||1.2967 ||1.043||1.57||0.121 ||2.21||0.163 ||0.741
|-
|6.85
|280||1.2038 ||1.042||1.66||0.138 ||2.36||0.188 ||0.733
|-
|26.85
|300||1.1233 ||1.043||1.75||0.156 ||2.5 ||0.213 ||0.73
|-
|46.85
|320||1.0529 ||1.043||1.84||0.175 ||2.63||0.239 ||0.73
|-
|66.85
|340||0.9909 ||1.044||1.93||0.195 ||2.78||0.269 ||0.725
|-
|86.85
|360||0.9357 ||1.045||2.02||0.216 ||2.91||0.298 ||0.725
|-
|106.85
|380||0.8864 ||1.047||2.1 ||0.237 ||3.05||0.329 ||0.729
|-
|126.85
|400||0.8421 ||1.049||2.18||0.259 ||3.18||0.36 ||0.719
|-
|176.85
|450||0.7483 ||1.055||2.37||0.317 ||3.5 ||0.443 ||0.714
|-
|226.85
|500||0.67352||1.065||2.54||0.377 ||3.81||0.531 ||0.71
|-
|276.85
|550||0.61226||1.076||2.71||0.443 ||4.11||0.624 ||0.71
|-
|326.85
|600||0.56126||1.088||2.86||0.51 ||4.4 ||0.721 ||0.707
|-
|376.85
|650||0.51806||1.101||3.01||0.581 ||4.7 ||0.824 ||0.705
|-
|426.85
|700||0.48102||1.114||3.15||0.655 ||5 ||0.933 ||0.702
|-
|476.85
|750||0.44899||1.127||3.29||0.733 ||5.28||1.04 ||0.702
|-
|526.85
|800||0.42095||1.14 ||3.43||0.815 ||5.55||1.16 ||0.705
|}
Bonding and dipole moment
The strength of the C-O bond in carbon monoxide is indicated by the high frequency of its vibration, 2143 cm<sup>−1</sup>. For comparison, organic carbonyls such as ketones and esters absorb at around 1700 cm<sup>−1</sup>.
Carbon and oxygen together have a total of 10 electrons in the valence shell. Following the octet rule for both carbon and oxygen, the two atoms form a triple bond, with six shared electrons in three bonding molecular orbitals, rather than the usual double bond found in organic carbonyl compounds. Since four of the shared electrons come from the oxygen atom and only two from carbon, one bonding orbital is occupied by two electrons from oxygen, forming a dative or dipolar bond. This causes a C←O polarization of the molecule, with a small negative charge on carbon and a small positive charge on oxygen. The other two bonding orbitals are each occupied by one electron from carbon and one from oxygen, forming (polar) covalent bonds with a reverse C→O polarization since oxygen is more electronegative than carbon. In the free carbon monoxide molecule, a net negative charge δ<sup>–</sup> remains at the carbon end and the molecule has a small dipole moment of 0.122 D.
The molecule is therefore asymmetric: oxygen is more electron dense than carbon and is also slightly positively charged compared to carbon being negative.
Carbon monoxide has a computed fractional bond order of 2.6, indicating that the "third" bond is important but constitutes somewhat less than a full bond. Thus, in valence bond terms, is the most important structure, while :CO is non-octet, but has a neutral formal charge on each atom and represents the second most important resonance contributor. Because of the lone pair and divalence of carbon in this resonance structure, carbon monoxide is often considered to be an extraordinarily stabilized carbene. Isocyanides are compounds in which the O is replaced by an NR (R alkyl or aryl) group and have a similar bonding scheme.
If carbon monoxide acts as a ligand, the polarity of the dipole may reverse with a net negative charge on the oxygen end, depending on the structure of the coordination complex.
See also the section "Coordination chemistry" below.
Bond polarity and oxidation state
Theoretical and experimental studies show that, despite the greater electronegativity of oxygen, the dipole moment points from the more-negative carbon end to the more-positive oxygen end. The three bonds are in fact polar covalent bonds that are strongly polarized. The calculated polarization toward the oxygen atom is 71% for the σ-bond and 77% for both π-bonds.
The oxidation state of carbon in carbon monoxide is +2 in each of these structures. It is calculated by counting all the bonding electrons as belonging to the more electronegative oxygen. Only the two non-bonding electrons on carbon are assigned to carbon. In this count, carbon then has only two valence electrons in the molecule compared to four in the free atom.
Occurrence
Carbon monoxide occurs in various natural and artificial environments. Photochemical degradation of plant matter for example generates an estimated 60 million tons/year. Typical concentrations in parts per million are as follows:
{| class="wikitable"
|+Composition of dry atmosphere, by volume
|-
! Concentration (ppmv)
! Source
|-
| 0.1
| Natural atmosphere level (MOPITT)
|-
| 0.5–5
| Average level in homes
|-
| 5–15
| Near properly adjusted gas stoves in homes, modern vehicle exhaust emissions
|-
| 17
| Atmosphere of Venus
|-
| 100–200
| Exhaust from automobiles in the Mexico City central area in 1975
|-
| 700
| Atmosphere of Mars
|-
| <1,000
| Car exhaust fumes after passing through catalytic converter
|-
| 5,000
| Exhaust from a home wood fire
|-
| 30,000–100,000
| Undiluted warm car exhaust without a catalytic converter Other natural sources of CO include volcanoes, forest and bushfires, and other miscellaneous forms of combustion such as fossil fuels. Small amounts are also emitted from the ocean, and from geological activity because carbon monoxide occurs dissolved in molten volcanic rock at high pressures in the Earth's mantle. Because natural sources of carbon monoxide vary from year to year, it is difficult to accurately measure natural emissions of the gas.
Carbon monoxide has an indirect effect on radiative forcing by elevating concentrations of direct greenhouse gases, including methane and tropospheric ozone. CO can react chemically with other atmospheric constituents (primarily the hydroxyl radical, <sup>•</sup>OH) that would otherwise destroy methane. Through natural processes in the atmosphere, it is oxidized to carbon dioxide and ozone. Carbon monoxide is short-lived in the atmosphere (with an average lifetime of about one to two months), and spatially variable in concentration.
Due to its long lifetime in the mid-troposphere, carbon monoxide is also used as a tracer for pollutant plumes.
Astronomy
Beyond Earth, carbon monoxide is the second-most common diatomic molecule in the interstellar medium, after molecular hydrogen. Because of its asymmetry, this polar molecule produces far brighter spectral lines than the hydrogen molecule, making CO much easier to detect. Interstellar CO was first detected with radio telescopes in 1970. It is now the most commonly used tracer of molecular gas in general in the interstellar medium of galaxies, as molecular hydrogen can only be detected using ultraviolet light, which requires space telescopes. Carbon monoxide observations provide much of the information about the molecular clouds in which most stars form.
Beta Pictoris, the second brightest star in the constellation Pictor, shows an excess of infrared emission compared to normal stars of its type, which is caused by large quantities of dust and gas (including carbon monoxide) near the star.
In the atmosphere of Venus carbon monoxide occurs as a result of the photodissociation of carbon dioxide by electromagnetic radiation of wavelengths shorter than 169 nm. It has also been identified spectroscopically on the surface of Neptune's moon Triton.
Solid carbon monoxide is a component of comets. The volatile or "ice" component of Halley's Comet is about 15% CO. At room temperature and at atmospheric pressure, carbon monoxide is actually only metastable (see Boudouard reaction) and the same is true at low temperatures where CO and are solid, but nevertheless it can exist for billions of years in comets. There is very little CO in the atmosphere of Pluto, which seems to have been formed from comets. This may be because there is (or was) liquid water inside Pluto.
Carbon monoxide can react with water to form carbon dioxide and hydrogen:
:
This is called the water-gas shift reaction when occurring in the gas phase, but it can also take place (very slowly) in an aqueous solution.
If the hydrogen partial pressure is high enough (for instance in an underground sea), formic acid will be formed:
:
These reactions can take place in a few million years even at temperatures such as found on Pluto.
Pollution and health effects
Urban pollution
Carbon monoxide is a temporary atmospheric pollutant in some urban areas, chiefly from the exhaust of internal combustion engines (including vehicles, portable and back-up generators, lawnmowers, power washers, etc.), but also from incomplete combustion of various other fuels (including wood, coal, charcoal, oil, paraffin, propane, natural gas, and trash).
Large CO pollution events can be observed from space over cities.
Role in ground level ozone formation
Carbon monoxide is, along with aldehydes, part of the series of cycles of chemical reactions that form photochemical smog. It reacts with hydroxyl radical (<sup>•</sup>OH) to produce a radical intermediate <sup>•</sup>HOCO, which rapidly transfers its radical hydrogen to to form peroxy radical (<sup>•</sup>) and carbon dioxide (). Peroxy radical subsequently reacts with nitrogen oxide (NO) to form nitrogen dioxide () and hydroxyl radical. gives O(<sup>3</sup>P) via photolysis, thereby forming following reaction with .
Since hydroxyl radical is formed during the formation of , the balance of the sequence of chemical reactions starting with carbon monoxide and leading to the formation of ozone is:
:
(where hν refers to the photon of light absorbed by the molecule in the sequence)
Although the creation of is the critical step leading to low level ozone formation, it also increases this ozone in another, somewhat mutually exclusive way, by reducing the quantity of NO that is available to react with ozone. Indoor air pollution
Carbon monoxide is one of the most acutely toxic indoor air contaminants. Carbon monoxide may be emitted from tobacco smoke and generated from malfunctioning fuel burning stoves (wood, kerosene, natural gas, propane) and fuel burning heating systems (wood, oil, natural gas) and from blocked flues connected to these appliances. Appliance malfunction may be due to faulty installation or lack of maintenance and proper use. The idiom "Canary in the coal mine" pertained to an early warning of a carbon monoxide presence.
Health effects
<!--Please keep this section short, there is no need to elaborate here. Details will be more useful in the Carbon monoxide poisoning article.-->
Carbon monoxide poisoning is the most common type of fatal air poisoning in many countries. Acute exposure can also lead to long-term neurological effects such as cognitive and behavioural changes. Severe CO poisoning may lead to unconsciousness, coma and death. Chronic exposure to low concentrations of carbon monoxide may lead to lethargy, headaches, nausea, flu-like symptoms and neuropsychological and cardiovascular issues.
Chemistry
Carbon monoxide has a wide range of functions across all disciplines of chemistry. The four premier categories of reactivity involve metal-carbonyl catalysis, radical chemistry, cation and anion chemistries.Coordination chemistry
of CO is a σ MO.]]
of CO is a π* antibonding MO.]]
Most metals form coordination complexes containing covalently attached carbon monoxide. These derivatives, which are called metal carbonyls, tend to be more robust when the metal is in lower oxidation states. For example iron pentacarbonyl () is an air-stable, distillable liquid. Nickel carbonyl is a metal carbonyl complex that forms by the direct combination of carbon monoxide with the metal:
: (1 bar, 55 °C)
These volatile complexes are often highly toxic. Some metal–CO complexes are prepared by decarbonylation of organic solvents, not from CO. For instance, iridium trichloride and triphenylphosphine react in boiling 2-methoxyethanol or DMF to afford .
As a ligand, CO binds through carbon, forming a kind of triple bond. The lone pair on the carbon atom donates electron density to form a M-CO sigma bond. The two π* orbitals on CO bind to filled metal orbitals. The effect is related to the Dewar-Chatt-Duncanson model. The effects of the quasi-triple M-C bond is reflected in the infrared spectrum of these complexes. Whereas free CO vibrates at 2143 cm-1, its complexes tend to absorb near 1950 cm-1.
Organic and main group chemistry
In the presence of strong acids, alkenes react with carboxylic acids. Hydrolysis of this species (an acylium ion) gives the carboxylic acid, a net process known as the Koch–Haaf reaction. In the Gattermann–Koch reaction, arenes are converted to benzaldehyde derivatives in the presence of CO, , and HCl.
A mixture of hydrogen gas and CO reacts with alkenes to give aldehydes. The process requires the presence of metal catalysts.
With main group reagents, CO undergoes several noteworthy reactions. Chlorination of CO is the industrial route to the important compound phosgene. With borane CO forms the adduct , which is isoelectronic with the acylium cation . CO reacts with sodium to give products resulting from C−C coupling such as sodium acetylenediolate . It reacts with molten potassium to give a mixture of an organometallic compound, potassium acetylenediolate , potassium benzenehexolate , and potassium rhodizonate .
The compounds cyclohexanehexone or triquinoyl () and cyclopentanepentone or leuconic acid (), which so far have been obtained only in trace amounts, can be regarded as polymers of carbon monoxide. At pressures exceeding 5 GPa, carbon monoxide converts to polycarbonyl, a solid polymer that is metastable at atmospheric pressure but is explosive. Laboratory preparation Carbon monoxide is conveniently produced in the laboratory by the dehydration of formic acid or oxalic acid, for example with concentrated sulfuric acid. Another method is heating an intimate mixture of powdered zinc metal and calcium carbonate, which releases CO and leaves behind zinc oxide and calcium oxide:
:
Silver nitrate and iodoform also afford carbon monoxide:
:
Finally, metal oxalate salts release CO upon heating, leaving a carbonate as byproduct:
:
Production
Thermal combustion is the most common source for carbon monoxide. Carbon monoxide is produced from the partial oxidation of carbon-containing compounds; it forms when there is not enough oxygen to produce carbon dioxide (), such as when operating a stove or an internal combustion engine in an enclosed space.
A large quantity of CO byproduct is formed during the oxidative processes for the production of chemicals. For this reason, the process off-gases have to be purified.
Many methods have been developed for carbon monoxide production.
Industrial production
A major industrial source of CO is producer gas, a mixture containing mostly carbon monoxide and nitrogen, formed by combustion of carbon in air at high temperature when there is an excess of carbon. In an oven, air is passed through a bed of coke. The initially produced equilibrates with the remaining hot carbon to give CO. The reaction of with carbon to give CO is described as the Boudouard reaction. Above 800 °C, CO is the predominant product:
: (ΔH<sub>r</sub> = 170 kJ/mol)
Another source is "water gas", a mixture of hydrogen and carbon monoxide produced via the endothermic reaction of steam and carbon:
: (ΔH<sub>r</sub> = 131 kJ/mol)
Other similar "synthesis gases" can be obtained from natural gas and other fuels.
Carbon monoxide can also be produced by high-temperature electrolysis of carbon dioxide with solid oxide electrolyzer cells. One method developed at DTU Energy uses a cerium oxide catalyst and does not have any issues of fouling of the catalyst.
:
Carbon monoxide is also a byproduct of the reduction of metal oxide ores with carbon, shown in a simplified form as follows:
:MO + C → M + CO
Carbon monoxide is also produced by the direct oxidation of carbon in a limited supply of oxygen or air.
:
Since CO is a gas, the reduction process can be driven by heating, exploiting the positive (favorable) entropy of reaction. The Ellingham diagram shows that CO formation is favored over in high temperatures.
Use
Chemical industry
Carbon monoxide is an industrial gas that has many applications in bulk chemicals manufacturing. Large quantities of aldehydes are produced by the hydroformylation reaction of alkenes, carbon monoxide, and . Hydroformylation is coupled to the Shell higher olefin process to give precursors to detergents.
Phosgene, useful for preparing isocyanates, polycarbonates, and polyurethanes, is produced by passing purified carbon monoxide and chlorine gas through a bed of porous activated carbon, which serves as a catalyst. World production of this compound was estimated to be 2.74 million tonnes in 1989.
:
Methanol is produced by the hydrogenation of carbon monoxide. In a related reaction, the hydrogenation of carbon monoxide is coupled to C−C bond formation, as in the Fischer–Tropsch process where carbon monoxide is hydrogenated to liquid hydrocarbon fuels. This technology allows coal or biomass to be converted to diesel.
In the Cativa process, carbon monoxide and methanol react in the presence of a homogeneous iridium catalyst and hydroiodic acid to give acetic acid. This process is responsible for most of the industrial production of acetic acid.
Metallurgy
Carbon monoxide is a strong reductive agent and has been used in pyrometallurgy to reduce metals from ores since ancient times. Carbon monoxide strips oxygen off metal oxides, reducing them to pure metal in high temperatures, forming carbon dioxide in the process. Carbon monoxide is not usually supplied as is, in the gaseous phase, in the reactor, but rather it is formed in high temperature in presence of oxygen-carrying ore, or a carboniferous agent such as coke, and high temperature. The blast furnace process is a typical example of a process of reduction of metal from ore with carbon monoxide.
Likewise, blast furnace gas collected at the top of blast furnace, still contains some 10% to 30% of carbon monoxide, and is used as fuel on Cowper stoves and on Siemens-Martin furnaces on open hearth steelmaking.
Proposed use as a rocket fuel
Carbon monoxide has been proposed for use as a fuel on Mars by NASA researcher Geoffrey Landis. Carbon monoxide/oxygen engines have been suggested for early surface transportation use as both carbon monoxide and oxygen can be straightforwardly produced from the carbon dioxide atmosphere of Mars by zirconia electrolysis, without using any Martian water resources to obtain hydrogen, which would be needed to make methane or any hydrogen-based fuel.
Landis also proposed manufacturing the fuel from the similar carbon dioxide atmosphere of Venus for a sample return mission, in combination with solar-powered UAVs and rocket balloon ascent.
Biological and physiological properties
Physiology
Carbon monoxide is a bioactive molecule which acts as a gaseous signaling molecule. It is naturally produced by many enzymatic and non-enzymatic pathways, Following the first report that carbon monoxide is a normal neurotransmitter in 1993, In many tissues, carbon monoxide acts as anti-inflammatory, vasodilatory, and encouragers of neovascular growth. In animal model studies, carbon monoxide reduced the severity of experimentally induced bacterial sepsis, pancreatitis, hepatic ischemia/reperfusion injury, colitis, osteoarthritis, lung injury, lung transplantation rejection, and neuropathic pain while promoting skin wound healing. Therefore, there is significant interest in the therapeutic potential of carbon monoxide becoming pharmaceutical agent and clinical standard of care.Medicine
Studies involving carbon monoxide have been conducted in many laboratories throughout the world for its anti-inflammatory and cytoprotective properties. These properties have the potential to be used to prevent the development of a series of pathological conditions including ischemia reperfusion injury, transplant rejection, atherosclerosis, severe sepsis, severe malaria, or autoimmunity.
Microbiology
Microbiota may also utilize carbon monoxide as a gasotransmitter. Carbon monoxide sensing is a signaling pathway facilitated by proteins such as CooA. The scope of the biological roles for carbon monoxide sensing is still unknown.
The human microbiome produces, consumes, and responds to carbon monoxide. For example, in certain bacteria, carbon monoxide is produced via the reduction of carbon dioxide by the enzyme carbon monoxide dehydrogenase with favorable bioenergetics to power downstream cellular operations.
Carbon monoxide has certain antimicrobial properties which have been studied to treat against infectious diseases. The carbon monoxide combines with myoglobin to form carboxymyoglobin, a bright-cherry-red pigment. Carboxymyoglobin is more stable than the oxygenated form of myoglobin, oxymyoglobin, which can become oxidized to the brown pigment metmyoglobin. This stable red color can persist much longer than in normally packaged meat. Typical levels of carbon monoxide used in the facilities that use this process are between 0.4% and 0.5%. The process is currently unauthorized in many other countries, including Japan, Singapore, and the European Union.
Weaponization
In ancient history, Hannibal executed Roman prisoners with coal fumes during the Second Punic War.History Prehistory Humans have maintained a complex relationship with carbon monoxide since first learning to control fire circa 800,000 BC. Early humans probably discovered the toxicity of carbon monoxide poisoning upon introducing fire into their dwellings. The early development of metallurgy and smelting technologies emerging circa 6,000 BC through the Bronze Age likewise plagued humankind from carbon monoxide exposure. Apart from the toxicity of carbon monoxide, indigenous Native Americans may have experienced the neuroactive properties of carbon monoxide through shamanistic fireside rituals.
Thomas Beddoes and James Watt recognized carbon monoxide (as hydrocarbonate) to brighten venous blood in 1793. Watt suggested coal fumes could act as an antidote to the oxygen in blood, and Beddoes and Watt likewise suggested hydrocarbonate has a greater affinity for animal fiber than oxygen in 1796. In 1854, Adrien Chenot similarly suggested carbon monoxide to remove the oxygen from blood and then be oxidized by the body to carbon dioxide. In a third major process, attributed to researchers at Monsanto, CO combines with methanol to give acetic acid. Most acetic acid is produced by the Cativa process. Hydroformylation and the acetic acid syntheses are two of myriad carbonylation processes.See also
*
*
*
*
*
References
External links
* [https://earth.nullschool.net/#current/chem/surface/level/overlay=cosc/winkel3 Global map of carbon monoxide distribution]
* [https://web.archive.org/web/20110720030754/http://courses.chem.psu.edu/chem210/mol-gallery/co/co.html Explanation of the structure]
* [https://inchem.org/documents/icsc/icsc/eics0023.htm International Chemical Safety Card 0023]
* [https://www.cdc.gov/niosh/npg/npgd0105.html CDC NIOSH Pocket Guide to Chemical Hazards: Carbon monoxide]—National Institute for Occupational Safety and Health (NIOSH), US Centers for Disease Control and Prevention (CDC)
** [https://www.cdc.gov/niosh/topics/co-comp/ Carbon Monoxide—NIOSH Workplace Safety and Health Topic]—CDC
** [https://www.cdc.gov/co/faqs.htm Carbon Monoxide Poisoning—Frequently Asked Questions]—CDC
* [https://web.archive.org/web/20060516154404/http://physchem.ox.ac.uk/MSDS/CA/carbon_monoxide.html External MSDS data sheet]
* [https://web.archive.org/web/20081218075252/http://www.homesafe.com/coalert/detect.htm Carbon Monoxide Detector Placement]
* [http://mattson.creighton.edu/CO/index.html Microscale Gas Chemistry Experiments with Carbon Monoxide]
*
Category:Airborne pollutants
Category:Articles containing video clips
Category:Gaseous signaling molecules
Category:Industrial gases
Category:Oxocarbons
Category:Smog
Category:Toxicology
Category:Diatomic molecules
|
https://en.wikipedia.org/wiki/Carbon_monoxide
|
2025-04-05T18:27:43.773370
|
6138
|
Conjecture
|
, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.]]
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.Resolution of conjecturesProof
Formal mathematics is based on provable truth. In mathematics, any number of cases supporting a universally quantified conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample could immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 10<sup>12</sup> (1.2 trillion). However, the failure to find a counterexample after extensive search does not constitute a proof that the conjecture is true—because the conjecture might be false but with a very large minimal counterexample.
Nevertheless, mathematicians often regard a conjecture as strongly supported by evidence even though not yet proved. That evidence may be of various kinds, such as verification of consequences of it or strong interconnections with known results.
A conjecture is considered proven only when it has been shown that it is logically impossible for it to be false. There are various methods of doing so; see methods of mathematical proof for more details.
One method of proof, applicable when there are only a finite number of cases that could lead to counterexamples, is known as "brute force": in this approach, all possible cases are considered and shown not to give counterexamples. In some occasions, the number of cases is quite large, in which case a brute-force proof may require as a practical matter the use of a computer algorithm to check all the cases. For example, the validity of the 1976 and 1997 brute-force proofs of the four color theorem by computer was initially doubted, but was eventually confirmed in 2005 by theorem-proving software.
When a conjecture has been proven, it is no longer a conjecture but a theorem. Many important theorems were once conjectures, such as the Geometrization theorem (which resolved the Poincaré conjecture), Fermat's Last Theorem, and others.
Disproof
Conjectures disproven through counterexample are sometimes referred to as false conjectures (cf. the Pólya conjecture and Euler's sum of powers conjecture). In the case of the latter, the first counterexample found for the n4 case involved numbers in the millions, although it has been subsequently found that the minimal counterexample is actually smaller.Independent conjectures
Not every conjecture ends up being proven true or false. The continuum hypothesis, which tries to ascertain the relative cardinality of certain infinite sets, was eventually shown to be independent from the generally accepted set of Zermelo–Fraenkel axioms of set theory. It is therefore possible to adopt this statement, or its negation, as a new axiom in a consistent manner (much as Euclid's parallel postulate can be taken either as true or false in an axiomatic system for geometry).
In this case, if a proof uses this statement, researchers will often look for a new proof that does not require the hypothesis (in the same way that it is desirable that statements in Euclidean geometry be proved using only the axioms of neutral geometry, i.e. without the parallel postulate). The one major exception to this in practice is the axiom of choice, as the majority of researchers usually do not worry whether a result requires it—unless they are studying this axiom in particular.
Conditional proofs
Sometimes, a conjecture is called a hypothesis when it is used frequently and repeatedly as an assumption in proofs of other results. For example, the Riemann hypothesis is a conjecture from number theory that — amongst other things — makes predictions about the distribution of prime numbers. Few number theorists doubt that the Riemann hypothesis is true. In fact, in anticipation of its eventual proof, some have even proceeded to develop further proofs which are contingent on the truth of this conjecture. These are called conditional proofs: the conjectures assumed appear in the hypotheses of the theorem, for the time being.
These "proofs", however, would fall apart if it turned out that the hypothesis was false, so there is considerable interest in verifying the truth or falsity of conjectures of this type.
Important examples
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called '''Fermat's conjecture', especially in older texts) states that no three positive integers <math>a</math>, <math>b</math>, and <math>c</math> can satisfy the equation <math>a^n + b^n = c^n</math> for any integer value of <math>n</math> greater than two.
This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica, where he claimed that he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century, and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics, and prior to its proof it was in the Guinness Book of World Records for "most difficult mathematical problems".Four color theorem
In mathematics, the four color theorem, or the four color map theorem, states that given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map—so that no two adjacent regions have the same color. Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions. For example, in the map of the United States of America, Utah and Arizona are adjacent, but Utah and New Mexico, which only share a point that also belongs to Arizona and Colorado, are not.
Möbius mentioned the problem in his lectures as early as 1840. The conjecture was first proposed on October 23, 1852 when Francis Guthrie, while trying to color the map of counties of England, noticed that only four different colors were needed. The five color theorem, which has a short elementary proof, states that five colors suffice to color a map and was proven in the late 19th century; however, proving that four colors suffice turned out to be significantly harder. A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.
The four color theorem was ultimately proven in 1976 by Kenneth Appel and Wolfgang Haken. It was the first major theorem to be proved using a computer. Appel and Haken's approach started by showing that there is a particular set of 1,936 maps, each of which cannot be part of a smallest-sized counterexample to the four color theorem (i.e., if they did appear, one could make a smaller counter-example). Appel and Haken used a special-purpose computer program to confirm that each of these maps had this property. Additionally, any map that could potentially be a counterexample must have a portion that looks like one of these 1,936 maps. Showing this with hundreds of pages of hand analysis, Appel and Haken concluded that no smallest counterexample exists because any must contain, yet do not contain, one of these 1,936 maps. This contradiction means there are no counterexamples at all and that the theorem is therefore true. Initially, their proof was not accepted by mathematicians at all because the computer-assisted proof was infeasible for a human to check by hand. However, the proof has since then gained wider acceptance, although doubts still remain.Hauptvermutung
The Hauptvermutung (German for main conjecture) of geometric topology is the conjecture that any two triangulations of a triangulable space have a common refinement, a single triangulation that is a subdivision of both of them. It was originally formulated in 1908, by Steinitz and Tietze.
This conjecture is now known to be false. The non-manifold version was disproved by John Milnor in 1961 using Reidemeister torsion.
The manifold version is true in dimensions . The cases were proved by Tibor Radó and Edwin E. Moise in the 1920s and 1950s, respectively.
Weil conjectures
In mathematics, the Weil conjectures were some highly influential proposals by on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields.
A variety V over a finite field with q elements has a finite number of rational points, as well as points over every finite field with q<sup>k</sup> elements containing that field. The generating function has coefficients derived from the numbers N<sub>k</sub> of points over the (essentially unique) field with q<sup>k</sup> elements.
Weil conjectured that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places. The last two parts were quite consciously modeled on the Riemann zeta function and Riemann hypothesis. The rationality was proved by , the functional equation by , and the analogue of the Riemann hypothesis was proved by .
Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. The conjecture states that: An equivalent form of the conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence: if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it.
Originally conjectured by Henri Poincaré in 1904, the theorem concerns a space that locally looks like ordinary three-dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere. An analogous result has been known in higher dimensions for some time.
After nearly a century of effort by mathematicians, Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv. The proof followed on from the program of Richard S. Hamilton to use the Ricci flow to attempt to solve the problem. Hamilton later introduced a modification of the standard Ricci flow, called Ricci flow with surgery to systematically excise singular regions as they develop, in a controlled way, but was unable to prove this method "converged" in three dimensions. Perelman completed this portion of the proof. Several teams of mathematicians have verified that Perelman's proof is correct.
The Poincaré conjecture, before being proven, was one of the most important open questions in topology.
Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by , is a conjecture that the non-trivial zeros of the Riemann zeta function all have real part 1/2. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.
The Riemann hypothesis implies results about the distribution of prime numbers. Along with suitable generalizations, some mathematicians consider it the most important unresolved problem in pure mathematics. The Riemann hypothesis, along with the Goldbach conjecture, is part of Hilbert's eighth problem in David Hilbert's list of 23 unsolved problems; it is also one of the Clay Mathematics Institute Millennium Prize Problems.
P versus NP problem
The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer; it is widely conjectured that the answer is no. It was essentially first mentioned in a 1956 letter written by Kurt Gödel to John von Neumann. Gödel asked whether a certain NP-complete problem could be solved in quadratic or linear time. The precise statement of the PNP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures" and is considered by many to be the most important open problem in the field. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US$1,000,000 prize for the first correct solution.Other conjectures
* Goldbach's conjecture
* The twin prime conjecture
* The Collatz conjecture
* The Manin conjecture
* The Maldacena conjecture
* The Euler conjecture, proposed by Euler in the 18th century but for which counterexamples for a number of exponents (starting with n=4) were found beginning in the mid 20th century
* The Hardy-Littlewood conjectures are a pair of conjectures concerning the distribution of prime numbers, the first of which expands upon the aforementioned twin prime conjecture. Neither one has either been proven or disproven, but it has been proven that both cannot simultaneously be true (i.e., at least one must be false). It has not been proven which one is false, but it is widely believed that the first conjecture is true and the second one is false.
* The Langlands program is a far-reaching web of these ideas of 'unifying conjectures' that link different subfields of mathematics (e.g. between number theory and representation theory of Lie groups). Some of these conjectures have since been proved.In other sciencesKarl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is related to hypothesis, which in science refers to a testable conjecture.
See also
* Bold hypothesis
* Futures studies
* Hypotheticals
* List of conjectures
* Ramanujan machine
References
Works cited
*
*
*}}External links
*
*[http://garden.irmacs.sfu.ca/ Open Problem Garden]
*[https://web.archive.org/web/20191107190855/http://www.unsolvedproblems.org/ Unsolved Problems web site]
Category:Concepts in the philosophy of science
Category:Statements
Category:Mathematical terminology
|
https://en.wikipedia.org/wiki/Conjecture
|
2025-04-05T18:27:43.793959
|
6139
|
Christoph Ludwig Agricola
|
| death_place = Regensburg, Holy Roman Empire
| resting_place | resting_place_coordinates <!-- -->
| nationality | residence
| education | alma_mater
| known_for = Painting, etching
| notable_works | style
| movement | spouse
| partner | awards
| elected | patrons
| memorials | website
| module =
}}
Christoph Ludwig Agricola (5 November 1665 – 8 August 1724) was a German landscape painter and etcher. He was born and died in Regensburg (Ratisbon).
Life and career
Christoph Ludwig Agricola was born on 5 November 1665 in Regensburg in Germany. He trained, as many painters of the period did, by studying nature.
He spent a great part of his life in travel visiting England, the Netherlands and France, and residing for a considerable period in Naples, where he may have been influenced by Nicolas Poussin. He also stayed in Venice for several years around 1712, where he painted many works for Zaccaria Sagredo.
He died in Regensburg in 1724.
Work
Although he primarily worked in gouache and oils, documentary sources show that he also produced a small number of etchings. He was a good draughtsman, used warm lighting and exhibited a warm, masterly brushstroke.
His numerous landscapes, chiefly cabinet pictures, are remarkable for their fidelity to nature, and especially for their skilful representation of varied phases of climate, especially nocturnal scenes and weather phenomena like thunderstorms. In composition, his style shows the influence of Nicolas Poussin: Agricola's work often displays idealistic scenes like Poussin's work. In light and colour Agricola's work resembles that of Claude Lorrain. His compositions often include ruins of ancient buildings in the foreground, but his favourite foreground figures were men dressed in Oriental attire.
His pictures can be found in Dresden, Braunschweig, Vienna, Florence, Naples and many other locations in Germany and Italy.
Legacy
He probably tutored the artist Johann Theile and had a strong influence on him. Art historians have also noted that the work of the landscape painter Christian Johann Bendeler (1699–1728) was influenced by Agricola.<ref name"PDF Online"/>Gallery<gallery modepacked heights=180>
File:Christoph Ludwig Agricola (zugeschr.) - Eine Flusslandschaft mit Anglern.jpg|River landscape
File:Christoph Ludwig Agricola - Großer Hänfling und Schopfmeise.jpg|Greater Redpole and crested titmous; Bluethroat
File:Christoph Ludwig Agricola (Umkreis) - Räuber schießen auf Reisende.jpg|Bandits Shooting at Travellers
File:Christoph Ludwig Agricola - Trappe un Elster in exotischer Landschaft.jpg|A bustard and a magpie in an exotic landscape
File:Christoph Ludwig Agricola - Ein Vogel auf einem Ast.jpg|A bird seated on a branch
File:Wintergezicht met ijsvermaak, RP-T-1898-A-3549.jpg|Winter face with ice entertainment
File:Christoph Ludwig Agricola - Singvogel auf einem Nadelbaum.jpg|Songbird in an Evergreen
</gallery>
References
Further reading
*
Category:1665 births
Category:1724 deaths
Category:17th-century German painters
Category:18th-century German painters
Category:18th-century German male artists
Category:German male painters
Category:German landscape painters
|
https://en.wikipedia.org/wiki/Christoph_Ludwig_Agricola
|
2025-04-05T18:27:43.797283
|
6140
|
Claudius
|
}}
| issue-link = #Marriages and personal life
| issue-pipe =
| full name Tiberius Claudius Nero Germanicus Simpson and Hurley suggest that he added the 'Germanicus' in 9 BC by senatorial decree and switched 'Drusus' for 'Nero' when he became head of the family Claudii Nerones in AD 4. Stuart and Levick somewhat ignore Suetonius and propose that his name was always Ti. Claudius Nero, and that he added Germanicus only in AD 4.}}
| regnal name = Tiberius Claudius Caesar Augustus Germanicus<!--Not a repository; full name as Roman emperor, no dates.-->
| dynasty = Julio-Claudian
| father = Nero Claudius Drusus
| mother = Antonia the Younger
}}
}}
Tiberius Claudius Caesar Augustus Germanicus ( ; ; 1 August 10 BC – 13 October AD 54), or Claudius, was a Roman emperor, ruling from AD 41 to 54. A member of the Julio-Claudian dynasty, Claudius was born to Drusus and Antonia Minor at Lugdunum in Roman Gaul, where his father was stationed as a military legate. He was the first Roman emperor to be born outside Italy.
As he had a limp and slight deafness due to an illness he suffered when young, he was ostracized by his family and was excluded from public office until his consulship (which was shared with his nephew, Caligula, in 37). Claudius's infirmity probably saved him from the fate of many other nobles during the purges throughout the reigns of Tiberius and Caligula, as potential enemies did not see him as a serious threat. His survival led to him being declared emperor by the Praetorian Guard after Caligula's assassination, at which point he was the last adult male of his family.
Despite his lack of experience, Claudius was an able and efficient administrator. He expanded the imperial bureaucracy to include freedmen, and helped restore the empire's finances after the excesses of Caligula's reign. He was also an ambitious builder, constructing new roads, aqueducts, and canals across the Empire. During his reign, the Empire started its successful conquest of Britain. Having a personal interest in law, he presided at public trials, and issued edicts daily. He was seen as vulnerable throughout his reign, particularly by elements of the nobility. Claudius was constantly forced to shore up his position, which resulted in the deaths of many senators. Those events damaged his reputation among the ancient writers, though more recent historians have revised that opinion. Many authors contend that he was murdered by his own wife, Agrippina the Younger. After his death at the age of 63, his grandnephew and legally adopted step-son, Nero, succeeded him as emperor.
Name
As a consequence of Roman customs, society, and personal preference, Claudius' full name varied throughout his life:
*Tiberius Claudius D. f. Ti. n. Drusus, the cognomen Drusus being inherited from his father as his brother Germanicus, as the eldest son, inherited the cognomen Nero when their uncle the future Emperor Tiberius was adopted by Augustus into the Julii Caesares and the victory name (agnomen) Germanicus from their father.
*Tiberius Claudius D. f. Ti. n. Nero, the cognomen Nero devolved to Claudius as the head of the Claudii Nerones after his elder brother was adopted by Tiberius as required by Augustus into the Julii Caesares in AD 9. Germanicus kept the victory title Germanicus as a praenomen, becoming Germanicus Julius Caesar. His son, Caligula, was known as Gaius Julius Caesar Germanicus, keeping the victory title, and later was known as Gaius Caesar Augustus Germanicus. Some authorities consider that his full name may have been Tiberius Claudius Drusus Nero Germanicus. and Hurley suggest that he added the 'Germanicus' in 9 BC by senatorial decree and switched 'Drusus' for 'Nero' when he became head of the family Claudii Nerones in AD 4. Stuart and Levick somewhat ignore Suetonius and propose that his name was always Ti. Claudius Nero, and that he added Germanicus only in AD 4.}}
*Tiberius Claudius Caesar Augustus Germanicus While Claudius had never been formally adopted either by Augustus or his successors, he was nevertheless the grandson of Augustus's sister Octavia, and so he felt that he had the right of family. He also adopted the name "Augustus" as the two previous emperors had done at their accessions. He kept the honorific "Germanicus" to display the connection with his heroic brother and father. He deified his paternal grandmother Livia to highlight her position as wife of the divine Augustus. Claudius frequently used the term "filius Drusi" (son of Drusus) in his titles, to remind the people of his legendary father and lay claim to his reputation. Family and youth Early life
]]
Claudius was born on 1 August 10 BC at Lugdunum (modern Lyon, France). He had two older siblings, Germanicus and Livilla. His mother, Antonia Minor, may have had two other children who died young. Claudius's maternal grandparents were Mark Antony and Octavia Minor, Augustus's sister, and he was therefore the great-great-grandnephew of Gaius Julius Caesar. His paternal grandparents were Livia, Augustus's third wife, and Tiberius Claudius Nero. During his reign, Claudius revived the rumour that his father Nero Claudius Drusus was actually the illegitimate son of Augustus, to give the appearance that Augustus was Claudius's paternal grandfather.
In 9 BC, Claudius's father Drusus died on campaign in Germania from a fall from a horse. Claudius was then raised by his mother, who never remarried. When his disability became evident, the relationship with his family turned sour. Antonia referred to him as a monster, and used him as a standard for stupidity. She seems to have passed her son off to his grandmother Livia for a number of years.
Livia was a little kinder, but nevertheless sent Claudius short, angry letters of reproof. He was put under the care of a former mule-driver to keep him disciplined, under the logic that his condition was due to laziness and a lack of willpower. However, by the time he reached his teenage years, his symptoms apparently waned and his family began to take some notice of his scholarly interests. In AD 7, Livy was hired to tutor Claudius in history, with the assistance of Sulpicius Flavus. He spent a lot of his time with the latter, as well as the philosopher Athenodorus. Augustus, according to a letter, was surprised at the clarity of Claudius's oratory.
Public life
Claudius' work as a historian damaged his prospects for advancement in public life. According to Vincent Scramuzza and others, he began work on a history of the Civil Wars that was either too truthful or too critical of Octavian, then reigning as Caesar Augustus. In either case, it was far too early for such an account, and may have only served to remind Augustus that Claudius was Antony's descendant. His mother and grandmother quickly put a stop to it, and this may have convinced them that Claudius was not fit for public office, since he could not be trusted to toe the existing party line.
When Claudius returned to the narrative later in life, he skipped over the wars of the Second Triumvirate altogether; but the damage was done, and his family pushed him into the background. When the Arch of Pavia was erected to honour the Imperial clan in AD 8, Claudius's name (now Tiberius Claudius Nero Germanicus after his elevation to pater familias of the Claudii Nerones on the adoption of his brother) was inscribed on the edge, past the deceased princes, Gaius and Lucius, and Germanicus's children. There is some speculation that the inscription was added by Claudius himself decades later, and that he originally did not appear at all.
When Augustus died in AD 14, Claudius – then aged 23 – appealed to his uncle Tiberius to allow him to begin the cursus honorum. Tiberius, the new Emperor, responded by granting Claudius consular ornaments. Claudius requested office once more and was snubbed. Since the new emperor was no more generous than the old, Claudius gave up hope of public office and retired to a scholarly, private life.
Despite the disdain of the Imperial family, it seems that from very early on the general public respected Claudius. At Augustus's death, the equites, or knights, chose Claudius to head their delegation. When his house burned down, the Senate demanded it be rebuilt at public expense. They also requested that Claudius be allowed to debate in the Senate. Tiberius turned down both motions, but the sentiment remained.
During the period immediately after the death of Tiberius's son, Drusus, Claudius was pushed by some quarters as a potential heir to the throne. This again suggests the political nature of his exclusion from public life. However, as this was also the period during which the power and terror of the commander of the Praetorian Guard, Sejanus, was at its peak, Claudius chose to downplay this possibility. After the death of Tiberius, the new emperor Caligula (the son of Claudius's brother Germanicus) recognized Claudius to be of some use. He appointed Claudius his co-consul in 37 to emphasize the memory of Caligula's deceased father Germanicus.
Despite this, Caligula tormented his uncle: playing practical jokes, charging him enormous sums of money, humiliating him before the Senate, and the like. According to Cassius Dio, Claudius became sickly and thin by the end of Caligula's reign, most likely due to stress. A possible surviving portrait of Claudius from this period may support this.Assassination of Caligula (AD 41)
, showing him with his brother Agrippa of Judaea crowning Claudius, AD 43.]]
On 24 January 41, Caligula was assassinated in a conspiracy involving Cassius Chaerea – a military tribune in the Praetorian Guard – and several senators. There is no evidence that Claudius had a direct hand in the assassination, although it has been argued that he knew about the plot – particularly since he left the scene of the crime shortly before his nephew was murdered. However, after the deaths of Caligula's wife and daughter, it became apparent that Cassius intended to go beyond the terms of the conspiracy and wipe out the Imperial family.
.
| footer = Two drastically different oil paintings by Lawrence Alma-Tadema of Claudius being proclaimed emperor by Gratus.
}}
In the chaos following the murder, Claudius witnessed the German guard cut down several uninvolved noblemen, including many of his friends. He fled to the palace to hide. According to tradition, a Praetorian named Gratus found him hiding behind a curtain and suddenly declared him princeps. so it remains uncertain. Eventually the Senate was forced to give in. In return, Claudius granted a general amnesty, although he executed a few junior officers involved in the conspiracy. The actual assassins, including Cassius Chaerea and Julius Lupus, the murderer of Caligula's wife and daughter, were put to death to ensure Claudius's own safety and as a future deterrent.
Emperor
Claudius took several steps to legitimize his rule against potential usurpers, most of them emphasizing his place within the Julio-Claudian family. He adopted the name "Caesar" as a cognomen, as the name still carried great weight with the populace. To do so, he dropped the cognomen "Nero", which he had adopted as pater familias of the Claudii Nerones when his brother Germanicus was adopted. As Pharaoh of Egypt, Claudius adopted the royal titulary Tiberios Klaudios, Autokrator Heqaheqau Meryasetptah, Kanakht Djediakhshuemakhet ("Tiberius Claudius, Emperor and ruler of rulers, beloved of Isis and Ptah, the strong bull of the stable moon on the horizon").
While Claudius had never been formally adopted either by Augustus or his successors, he was nevertheless the grandson of Augustus's sister Octavia, and so he felt that he had the right of family. He also adopted the name "Augustus" as the two previous emperors had done at their accessions. He kept the honorific "Germanicus" to display the connection with his heroic brother. He deified his paternal grandmother Livia to highlight her position as wife of the divine Augustus. Claudius frequently used the term "filius Drusi" (son of Drusus) in his titles, to remind the people of his legendary father and lay claim to his reputation.
Since Claudius was the first emperor proclaimed on the initiative of the Praetorian Guard instead of the Senate, his repute suffered at the hands of commentators (such as Seneca). Moreover, he was the first emperor who resorted to bribery as a means to secure army loyalty and rewarded the soldiers of the Praetorian Guard that had elevated him with 15,000 sesterces. Tiberius and Augustus had both left gifts to the army and guard in their wills, and upon Caligula's death the same would have been expected, even if no will existed. Claudius remained grateful to the guard, issuing coins with tributes to the Praetorians in the early part of his reign.
Pliny the Elder noted, according to the 1938 Loeb Classical Library translation by Harris Rackham, "... many people do not allow any gems in a signet-ring, and seal with the gold itself; this was a fashion invented when Claudius Cæsar was emperor."
Claudius restored the status of the peaceful Imperial Roman provinces of Macedonia and Achaea as senatorial provinces.
Expansion of the Empire
at Rendham, near Saxmundham, Suffolk (British Museum). Potentially taken from the Temple of Claudius in Colonia Victricensis (now Colchester) during the Boudican revolt.]]
Under Claudius, the Empire underwent its first major expansion since the reign of Augustus. The provinces of Thrace, Noricum, Lycia, and Judea were annexed (or put under direct rule) under various circumstances during his term. The annexation of Mauretania, begun under Caligula, was completed after the defeat of rebel forces, as well as the official division of the former client kingdom into two Imperial provinces. The most far-reaching conquest was that of Britannia.
In 43, Claudius sent Aulus Plautius with four legions to Britain (Britannia) after an appeal from an ousted tribal ally. Britain was an attractive target for Rome because of its material wealth: mines and the potential of slave labor, as well as being a haven for Gallic rebels. Claudius himself traveled to the island after the completion of initial offensives, bringing with him reinforcements and elephants. The Roman colonia of Colonia Claudia Victricensis was established as the provincial capital of the newly established province of Britannia at Camulodunum, where a large temple was dedicated in his honour.
He left Britain after 16 days, but remained in the provinces for some time. The Senate granted him a triumph for his efforts. Only members of the Imperial family were allowed such honours, but Claudius subsequently lifted this restriction for some of his conquering generals. He was granted the honorific "Britannicus" but only accepted it on behalf of his son, never using the title himself. When the British general Caractacus was captured in 50, Claudius granted him clemency. Caractacus lived out his days on land provided by the Roman state, an unusual end for an enemy commander.
Claudius conducted a census in 48 that found 5,984,072 (adult male) Roman citizens (women, children, slaves, and free adult males without Roman citizenship were not counted), an increase of around a million since the census conducted at Augustus's death. He had helped increase this number through the foundation of Roman colonies that were granted blanket citizenship. These colonies were often made out of existing communities, especially those with elites who could rally the populace to the Roman cause. Several colonies were placed in new provinces or on the border of the Empire to secure Roman holdings as quickly as possible.Judicial and legislative affairsClaudius personally judged many of the legal cases tried during his reign. Ancient historians have many complaints about this, stating that his judgments were variable and sometimes did not follow the law. He was also easily swayed. Nevertheless, Claudius paid detailed attention to the operation of the judicial system. He extended the summer court session, as well as the winter term, by shortening the traditional breaks. Claudius also made a law requiring plaintiffs to remain in the city while their cases were pending, as defendants had previously been required to do. These measures had the effect of clearing out the docket. The minimum age for jurors was also raised to 25 to ensure a more experienced jury pool.
Claudius also settled disputes in the provinces. He freed the island of Rhodes from Roman rule for their good faith and exempted Ilium (Troy) from taxes. Early in his reign, the Greeks and Jews of Alexandria each sent him embassies after riots broke out between the two communities. This resulted in the famous "Letter to the Alexandrians", which reaffirmed Jewish rights in the city but forbade them to move in more families en masse. According to Josephus, he then reaffirmed the rights and freedoms of all the Jews in the Empire. However, Claudius also expelled Jews from the city of Rome, following disturbances allegedly instigated by Christians. This expulsion is attested to in Acts of the Apostles (18:2), and by Roman historians Suetonius and Cassius Dio along with the fifth-century Christian author Paulus Orosius.
One of Claudius's investigators discovered that many old Roman citizens based in the city of Tridentum (modern Trento) were not in fact citizens. The Emperor issued a declaration, contained in the Tabula clesiana, that they would be allowed to hold citizenship from then on, since to strip them of their status would cause major problems. However, in individual cases, Claudius punished the false assumption of citizenship harshly, making it a capital offense. Similarly, any freedmen found to be laying false claim to membership of the Roman equestrian order were to have their property confiscated and selling into slavery, in the words of Suetonius, "such as were ungrateful and a cause of complaint to their patrons".
Numerous edicts were issued throughout Claudius's reign. These were on a number of topics, everything from medical advice to moral judgments. A famous medical example is one promoting yew juice as a cure for snakebite. Suetonius wrote that he is even said to have thought of an edict allowing public flatulence for good health. One of the more famous edicts concerned the status of sick slaves. Masters had been abandoning ailing slaves at the temple of Aesculapius on Tiber Island to die instead of providing them with medical assistance and care, and then reclaiming them if they lived. Claudius ruled that slaves who were thus abandoned and recovered after such treatment would be free. Furthermore, masters who chose to kill slaves rather than take care of them were liable to be charged with murder.Public works
in Rome: remains of aqueducts Aqua Claudia and Aqua Anio Novus]]
Claudius embarked on many public works throughout his reign, both in the capital and in the provinces. He built or finished two aqueducts, the Aqua Claudia, begun by Caligula, and the Aqua Anio Novus. These entered the city in 52 and met at the Porta Maggiore. He also restored a third, the Aqua Virgo.
He paid special attention to transportation. Throughout Italy and the provinces he built roads and canals. Among these was a large canal leading from the Rhine to the sea, as well as a road from Italy to Germany – both begun by his father, Drusus. Closer to Rome, he built a navigable canal on the Tiber, leading to Portus, his new port just north of Ostia. This port was constructed in a semicircle with two moles and a lighthouse at its mouth, reducing flooding in Rome.
The port at Ostia was part of Claudius's solution to the constant grain shortages that occurred in winter, after the Roman shipping season. The other part of his solution was to insure the ships of grain merchants who were willing to risk travelling to Egypt in the off-season. He also granted their sailors special privileges, including citizenship and exemption from the Lex Papia Poppaea, a law that regulated marriage. In addition, he repealed the taxes that Caligula had instituted on food, and further reduced taxes on communities suffering drought or famine.
The last part of Claudius's plan to avoid famine was to increase the amount of arable land in Italy. This was to be achieved by draining the Fucine lake, also making the nearby river navigable year-round. A serious famine is mentioned in the book of Acts as taking place during Claudius' reign, and had been prophesied by a Christian called Agabus while visiting Antioch.
A tunnel was dug through the lake bed, but the plan was a failure. The tunnel was crooked and not large enough to carry the water, which caused it to back up when opened. The resultant flood washed out a large gladiatorial exhibition held to commemorate the opening, causing Claudius to run for his life along with the other spectators. The draining of the lake continued to present a problem well into the Middle Ages. It was finally achieved by the Prince Torlonia in the 19th century, producing over of new arable land. He expanded the Claudian tunnel to three times its original size.Senate
Because of the circumstances of his accession, Claudius took great pains to please the Senate. During regular sessions, the Emperor sat among the Senate body, speaking in turn. When introducing a law, he sat on a bench between the consuls in his position as holder of the power of Tribune, (the Emperor could not officially serve as a Tribune of the Plebes since he was a patrician, but this was a power taken by previous rulers, which he continued). He refused to accept all his predecessors' titles (including Imperator) at the beginning of his reign, preferring to earn them in due course. He allowed the Senate to issue its own bronze coinage for the first time since Augustus. He also put the Imperial provinces of Macedonia and Achaea back under Senate control.
Claudius set about remodeling the Senate into a more efficient, representative body. He chided the senators about their reluctance to debate bills introduced by himself, as noted in the fragments of a surviving speech:
In 47, he assumed the office of censor with Lucius Vitellius, which had been allowed to lapse for some time. He struck out the names of many senators and equites who no longer met qualifications, but showed respect by allowing them to resign in advance. At the same time, he sought to admit to the senate eligible men from the provinces. The Lyon Tablet preserves his speech on the admittance of Gallic senators, in which he addresses the Senate with reverence but also with criticism for their disdain of these men. He even joked about how the Senate had admitted members from beyond Gallia Narbonensis (Lyons), i.e. himself. He also increased the number of patricians by adding new families to the dwindling number of noble lines. Here he followed the precedent of Lucius Junius Brutus and Julius Caesar.
Nevertheless, many in the Senate remained hostile to Claudius, and many plots were made on his life. This hostility carried over into the historical accounts. As a result, Claudius reduced the Senate's power for the sake of efficiency. The administration of Ostia was turned over to an Imperial procurator after construction of the port. Administration of many of the empire's financial concerns was turned over to Imperial appointees and freedmen. This led to further resentment and suggestions that these same freedmen were ruling the Emperor.
Plots and coup attempts
Several coup attempts were made during Claudius's reign, resulting in the deaths of many senators. Appius Silanus was executed early in Claudius's reign under questionable circumstances. Shortly after this, a large rebellion was undertaken by the Senator Vinicianus and Scribonianus - governor of Dalmatia - and gained quite a few senatorial supporters. It ultimately failed because of the reluctance of Scribonianus' troops, which led to the suicide of the main conspirators.
Many other senators tried different conspiracies and were condemned. Claudius's son-in-law Pompeius Magnus was executed for his part in a conspiracy with his father Crassus Frugi. Another plot involved the consulars Lusius Saturninus, Cornelius Lupus, and Pompeius Pedo.
In 46, Asinius Gallus, grandson of Asinius Pollio, and Titus Statilius Taurus Corvinus were exiled for a plot hatched with several of Claudius's own freedmen. Valerius Asiaticus was executed without public trial for unknown reasons. Ancient sources say the charge was adultery, and that Claudius was tricked into issuing the punishment. However, Claudius singles out Asiaticus for special damnation in his speech on the Gauls, which dates over a year later, suggesting that the charge must have been much more serious.
Asiaticus had been a claimant to the throne in the chaos following Caligula's death and a co-consul with Titus Statilius Taurus Corvinus. Most of these conspiracies took place before Claudius's term as Censor, and may have induced him to review the Senatorial rolls. The conspiracy of Gaius Silius in the year after his Censorship, 48, is detailed in book 11 of Tacitus' Annals. This section of Tacitus' history narrates the alleged conspiracy of Claudius's third wife, Messalina. Suetonius states that a total of 35 senators and 300 knights were executed for offenses during Claudius's reign. Needless to say, the responses to these conspiracies could not have helped Senate–emperor relations.Secretariat and centralization of powers
Claudius was hardly the first emperor to use freedmen to help with the day-to-day running of the Empire. He was, however, forced to increase their role as the powers of the princeps became more centralized and the burden of running the government became larger. Claudius did not want free-born magistrates to serve under him as if they were not peers.
The secretariat was divided into bureaus, with each being placed under the leadership of one freedman. Narcissus was the secretary of correspondence. Pallas became the secretary of the treasury. Callistus became secretary of justice. There was a fourth bureau for miscellaneous issues, which was put under Polybius until his execution for treason. The freedmen could also officially speak for the Emperor, as when Narcissus addressed the troops in Claudius's stead before the conquest of Britain.
Since these were important positions, the senators were aghast at their being placed in the hands of former slaves and "well-known eunuchs". If freedmen had total control of money, letters and law, it seemed it would not be hard for them to manipulate the Emperor. This is exactly the accusation put forth by ancient sources. However, these same sources admit that the freedmen were loyal to Claudius.and manipulated his policies to amass wealth. In 48, Messalina married her lover Gaius Silius in a public ceremony while Claudius was at Ostia.
Sources disagree as to whether or not she divorced the Emperor first, and whether the intention was to usurp the throne. Under Roman law, the spouse needed to be informed that he or she had been divorced before a new marriage could take place; the sources state that Claudius was in total ignorance until after the marriage. Scramuzza, in his biography, suggests that Silius may have convinced Messalina that Claudius was doomed, and the union was her only hope of retaining her rank and protecting her children. The historian Tacitus suggests that Claudius's ongoing term as Censor may have prevented him from noticing the affair before it reached such a critical point, after which she was executed.Agrippina the YoungerClaudius married once more. Ancient sources tell that his freedmen put forward three candidates, Caligula's third wife Lollia Paulina, Claudius's divorced second wife Aelia Paetina and Claudius's niece Agrippina the Younger. According to Suetonius, Agrippina won out through her feminine wiles. She gradually seized power from Claudius and successfully conspired to eliminate his son's rivals, opening the way for her son to become emperor.
The truth is probably more political. The attempted coup d'état by Silius and Messalina probably made Claudius realize the weakness of his position as a member of the Claudian (but not the Julian) family. This weakness was compounded by the fact that he did not yet have an obvious adult heir, Britannicus being just a boy. Agrippina was one of the few remaining descendants of Augustus, and her son Lucius Domitius Ahenobarbus (the future Nero) was one of the last males of the Imperial family. Coup attempts might rally around the pair and Agrippina was already showing such ambition. It has been suggested that the Senate may have pushed for the marriage, an attempt to end the feud between the Julian and Claudian branches. This feud dated back to Agrippina's mother's actions against Tiberius after the death of her husband Germanicus (Claudius's brother), actions that Tiberius had punished.
Another reason was to bring in Lucius Domitius Ahenobarbus as a candidate for the succession. His prestige as the descendent of Augustus and Germanicus made him popular, and marking him as an heir would have helped the survival of Claudius' regime. In any case, Claudius accepted Agrippina and later adopted the mature Ahenobarbus as his son, renaming him as 'Nero Claudius Caesar'.
Nero was married to Claudius's daughter Octavia, made joint heir with the underage Britannicus, and promoted; Augustus had similarly named his grandson Postumus Agrippa and his stepson Tiberius as joint heirs, and Tiberius had named Caligula as his joint heir with his grandson Tiberius Gemellus. Adoption of adults or near adults was an old tradition in Rome when a suitable natural adult heir was unavailable, as was the case during Britannicus's minority. Claudius may have previously looked to adopt one of his sons-in-law to protect his own reign.
Faustus Cornelius Sulla Felix, who was married to Claudius's daughter Claudia Antonia, was only descended from Octavia and Antony on one side – not close enough to the Imperial family to ensure his right to be Emperor (although that did not stop others from making him the object of a coup attempt against Nero a few years later), besides being the half-brother of Valeria Messalina, which told against him. Nero was more popular with the general public as both the grandson of Germanicus and the direct descendant of Augustus.
Affliction<!-- ! check for tone --> and personality
The historian Suetonius describes the physical manifestations of Claudius's condition. His knees were weak and gave way under him and his head shook. He stammered and his speech was confused. He slobbered and his nose ran when he was excited. The Stoic Seneca states in his Apocolocyntosis that Claudius's voice belonged to no land animal, and that his hands were weak as well.
]]
However, he showed no physical deformity, as Suetonius notes that when calm and seated he was a tall, well-built figure of dignitas. When angered or stressed, his symptoms became worse. Historians agree that this condition improved upon his accession to the throne. Claudius himself claimed that he had exaggerated his ailments to save his life.
Modern assessments of his health have changed several times in the past century. Prior to World War II, infantile paralysis (or polio) was widely accepted as the cause. This is the diagnosis used in Robert Graves's Claudius novels, first published in the 1930s. The New York Times wrote in 1934 that Claudius suffered from infantile paralysis (which led to his limp state) and measles (which made him deaf) at seven months of age, among several other ailments. Polio does not explain many of the described symptoms, however, and a more recent theory implicates cerebral palsy as the cause. Tourette syndrome has also been considered a possibility.
As a person, ancient historians described Claudius as generous and lowbrow, a man who sometimes lunched with the plebeians. They also paint him as bloodthirsty and cruel, over-fond of gladiatorial combat and executions, and very quick to anger; Claudius himself acknowledged the latter trait, and apologized publicly for his temper. According to the ancient historians he was also excessively trusting, and easily manipulated by his wives and freedmen, but at the same time they portray him as paranoid and apathetic, dull and easily confused.
Scholarly works and their impact
Claudius wrote copiously throughout his life. Arnaldo Momigliano states that during the reign of Tiberius, which covers the peak of Claudius's literary career, it became impolitic to speak of republican Rome. The trend among the young historians was either to write about the new empire or about obscure antiquarian topics. Claudius was the rare scholar who covered both.
Besides his history of Augustus' reign that caused him so much grief, his major works included Tyrrhenika, a twenty-book Etruscan history, and Carchedonica, an eight-volume history of Carthage, as well as an Etruscan dictionary. He also wrote a book on dice-playing. Despite the general avoidance of the topic of the Republican era, he penned a defense of Cicero against the charges of Asinius Gallus. Modern historians have used this to determine the nature of his politics and of the aborted chapters of his civil war history.
]]
He proposed a reform of the Latin alphabet by the addition of three new letters; he officially instituted the change during his censorship but they did not survive his reign. Claudius also tried to revive the old custom of putting dots between successive words (Classical Latin was written with no spacing). Finally, he wrote an eight-volume autobiography that Suetonius describes as lacking in taste. Claudius (like most of the members of his dynasty) harshly criticized his predecessors and relatives in surviving speeches.
None of the works survived, but other sources' reference to him provide material for the surviving histories of the Julio-Claudian dynasty. Suetonius quotes Claudius's autobiography once and must have used it as a source numerous times. Tacitus uses Claudius's arguments for the orthographical innovations mentioned above and may have used him for some of the more antiquarian passages in his annals. Claudius is the source for numerous passages of Pliny's Natural History.
The influence of historical study on Claudius is obvious. In his speech on Gallic senators, he uses a version of the founding of Rome identical to that of Livy, his tutor in adolescence. Many of the public works instituted in his reign were based on plans first suggested by Julius Caesar. Levick believes this emulation of Caesar may have spread to all aspects of his policies.
His censorship seems to have been based on those of his ancestors, particularly Appius Claudius Caecus, and he used the office to put into place many policies based on those of Republican times. This is when many of his religious reforms took effect; also, his building efforts greatly increased during his tenure. In fact, his assumption of the office of Censor may have been motivated by a desire to see his academic labors bear fruit. For example, he believed (as most Romans did) that Caecus had used the power of the censorship office to introduce the letter "R" and so used his own term to introduce his new letters.
Death
, Malta]]
Ancient historians agree that Claudius was murdered by poison – possibly contained in mushrooms or on a feather (ostensibly put down his throat to induce vomiting) – and died in the early hours of 13 October 54.
Nearly all implicate his final and powerful wife, Agrippina, as the instigator. Agrippina and Claudius had become more combative in the months leading up to his death. This carried on to the point where Claudius openly lamented his bad wives, and began to comment on Britannicus' approaching manhood with an eye towards restoring his status within the imperial family. Agrippina had motive in ensuring the succession of Nero before Britannicus could gain power.
Some implicate either his taster Halotus, his doctor Xenophon, or the infamous poisoner Locusta as the administrator of the fatal substance. Some say he died after prolonged suffering following a single dose at dinner, and some have him recovering only to be poisoned again. Among his contemporary sources, Seneca the Younger ascribed the emperor's death to natural causes, while Josephus only spoke of rumors of his poisoning.
Some historians have cast doubt on whether Claudius was murdered or merely died from illness or old age. says that tradition makes every emperor the victim of foul play, so we can't know if Claudius was truly murdered. The Emperor appears to have been seriously ill since at least 53. raises the possibility that Claudius was killed by the stress of fighting with Agrippina over the succession, but concludes that the timing makes murder the most likely cause.}} Evidence against his murder include his serious illnesses in his last years, his unhealthy lifestyle and the fact that his taster Halotus continued to serve in the same position under Nero. Claudius had been so ill the year before that Nero vowed games for his recovery and the year of 54 seems to have been such an unhealthy year that one sitting member of each magistracy died within the span of a few months. He may even have died by eating a naturally poisonous mushroom, possibly Amanita muscaria. On the other hand, some modern scholars claim the near universality of the accusations in ancient texts lends credence to the crime. Claudius's ashes were interred in the Mausoleum of Augustus on 24 October 54, after a funeral similar to that of his great-uncle Augustus 40 years earlier.LegacyDivine honoursAlready, while alive, he received the widespread private worship of a living princeps and was worshipped in Britannia in his own temple in Camulodunum.
Claudius was deified by Nero and the Senate almost immediately.Views of the new regime
Agrippina had sent Narcissus away shortly before Claudius's death, and now had the freedman murdered.
The last act of this secretary of letters was to burn all of Claudius's correspondence – most likely so it could not be used against him and others in an already hostile new regime. Thus Claudius's private words about his own policies and motives were lost to history. Just as Claudius had criticized his predecessors in official edicts, Nero often criticized the deceased Emperor, and many Claudian laws and edicts were disregarded under the reasoning that he was too stupid and senile to have meant them.
Seneca's Apocolocyntosis mocks the deification of Claudius and reinforces the view of Claudius as an unpleasant fool; this remained the official view for the duration of Nero's reign. Eventually Nero stopped referring to his deified adoptive father at all. Claudius's temple was left unfinished after only some of the foundation had been laid down. Eventually the site was overtaken by Nero's Golden House.
Flavian and later perspectives
The Flavians, who had risen to prominence under Claudius, took a different tack. They needed to shore up their legitimacy, but also justify the fall of the Julio-Claudians. They reached back to Claudius in contrast with Nero, to show that they were associated with a good regime. Commemorative coins were issued of Claudius and his son Britannicus, who had been a friend of Emperor Titus (Titus was born in 39, Britannicus was born in 41). When Nero's Golden House was burned, the Temple of Claudius was finally completed on the Caelian Hill.
However, as the Flavians became established, they needed to emphasize their own credentials more, and their references to Claudius ceased. Instead, he was lumped with the other emperors of the fallen dynasty. His state-cult in Rome probably continued until the abolition of all cults of dead Emperors by Maximinus Thrax in 237–238. The Feriale Duranum, probably identical to the festival calendars of every regular army unit, assigns him a sacrifice of a steer on his birthday, the Kalends of August. And such commemoration (and consequent feasting) probably continued until the Christianization and disintegration of the army in the late 4th century.
** Graves's two books were the basis for a British television adaptation I, Claudius, produced by the BBC. The series starred Derek Jacobi as Claudius and was broadcast in 1976 on BBC2. It was a substantial critical success, and won several BAFTA awards. The series was later broadcast in the United States on Masterpiece Theatre in 1977. The 1996 7-VHS release and the later DVD release of the television series, include The Epic That Never Was documentary.
** A radio adaptation of the Graves novels by Robin Brooks and directed by Jonquil Panting, was broadcast in six one-hour episodes on BBC Radio 4 beginning 4 December 2010. The cast featured Tom Goodman-Hill as Claudius, Derek Jacobi as Augustus, Harriet Walter as Livia, Tim McInnerny as Tiberius and Samuel Barnett as Caligula.
** In 2011, it was announced rights for a miniseries adaptation passed to HBO and BBC Two. Anne Thomopoulos and Jane Tranter, producers of the popular HBO–BBC2 Rome miniseries, were attached to the I, Claudius project. However, as of 2018, it has yet to be produced, and no release date is pending.
* The 1954 film Demetrius and the Gladiators also portrayed him sympathetically, played by Barry Jones.
* In the 1960 film Messalina, Claudius is portrayed by Mino Doro.
* On television, Freddie Jones portrayed Claudius in the 1968 British television series The Caesars.
* The 1975 TV Special Further Up Pompeii! (based on the Frankie Howerd sit-com Up Pompeii!) featured Cyril Appleton as Claudius.
* In the 1979 motion picture Caligula, where the role was performed by Giancarlo Badessi, Claudius is depicted as an idiot, in contrast to Robert Graves' portrait of Claudius as a cunning and deeply intelligent man, who is perceived by others to be an idiot.
* In the 1981 Franco-Italian film Caligula and Messalina, he was portrayed by Gino Turini (as John Turner).
* The 1985 made-for-television miniseries A.D. features actor Richard Kiley as Claudius. Kiley portrays him as thoughtful, but willing to cater to public opinion as well as being under the influence of Agrippina.
* In the 2004 TV film Imperium: Nero, Claudius is portrayed by Massimo Dapporto.
* He is portrayed in Season 3 of the Netflix documentary series Roman Empire, which focused on the reign of Caligula, by Kelson Henderson. The series concludes with Claudius's accession.
* There is also a reference to Claudius's suppression of a coup in the movie Gladiator, though that incident is entirely fictional.
* In the series Britannia (2018), Claudius visits Britannia, played by Steve Pemberton as a fool who is drugged by Aulus Plautius.
* He is portrayed by Derek Jacobi in the 2019 BBC film Horrible Histories: The Movie - Rotten Romans
In literature, Claudius and his contemporaries appear in the historical novel The Roman by Mika Waltari. Canadian-born science fiction writer A. E. van Vogt reimagined Robert Graves's Claudius story, in his two novels, Empire of the Atom and The Wizard of Linn.
The historical novel Chariot of the Soul by Linda Proud features Claudius as host and mentor of the young Togidubnus, son of King Verica of the Atrebates, during his ten-year stay in Rome. When Togidubnus returns to Britain in advance of the Roman army, it is with a mission given to him by Claudius.
See also
* Julio-Claudian family tree
* List of Roman emperors
* Temple of Claudius
Notes
References
Bibliography
Ancient sources
*|orig-date=1st century}}
*|orig-date= 77 AD}}
*|orig-date 96 AD|chapter-url=https://en.wikisource.org/wiki/The_Antiquities_of_the_Jews/Book_XIX}}
*|orig-date AD 110|chapterBooks 11–11|chapter-urlhttps://en.wikisource.org/wiki/The_Annals_(Tacitus)/Book_11}}
*|orig-date AD 121}}
*|orig-date= 230}}
Modern sources
*
*
*
* |ref= }}
*
* |author-linkBarbara Levick }}
*
*
*
*
*
*
*
* }}
* }}
*
*
External links
* Works by Claudius
** [http://www.csun.edu/~hcfll004/claualex.html Claudius' Letter to the Alexandrians]
** Lyon Tablet
*** [http://www.fordham.edu/halsall/ancient/48claudius.html Second half of the Lyons Tablet]
*** [http://www.fordham.edu/halsall/ancient/tacitus-ann11a.html Tacitus' version of the Lyons Tablet speech]
** Edict confirming the rights of the people of Trent. Full Latin text here.
* [http://www.roman-emperors.org/claudius.htm Biography from De Imperatoribus Romanis]
* [https://web.archive.org/web/20091019213016/http://geocities.com/Athens/Parthenon/7094/claudius.html Claudius Page]
* [https://www.bbc.co.uk/history/historic_figures/claudius.shtml Claudius I] at [https://www.bbc.co.uk/history/ BBC History]
Category:10 BC births
Category:54 deaths
Category:1st-century Gallo-Roman people
Category:1st-century historians
Category:1st-century murdered monarchs
Category:1st-century Roman consuls
Category:1st-century Roman emperors
Category:Ancient Romans in Britain
Category:Claudii Nerones
Category:Creators of writing systems
Category:Etruscologists
Category:Deified Roman emperors
Category:Husbands of Agrippina the Younger
Category:Julio-Claudian dynasty
Category:Latin historians
Category:Murdered Roman emperors
Category:People from Lugdunum
Category:People with cerebral palsy
Category:Poisoned ancient Romans
Category:Royalty and nobility with disabilities
Category:Roman pharaohs
Category:Incest
|
https://en.wikipedia.org/wiki/Claudius
|
2025-04-05T18:27:43.829732
|
6141
|
Cardinal
|
Cardinal or The Cardinal most commonly refers to
Cardinalidae, a family of North and South American birds
Cardinalis, genus of three species in the family Cardinalidae
Northern cardinal, Cardinalis cardinalis, the common cardinal of eastern North America
Pyrrhuloxia or desert cardinal, Cardinalis sinuatus, found in southwest North America
Vermilion cardinal, Cardinalis phoeniceus, found in Colombia and Venezuela
Cardinal (Catholic Church), a senior official of the Catholic Church
Member of the College of Cardinals
Cardinal Health, a health care services company
Cardinal number
Large cardinal
Cardinal direction, one of the four primary directions: north, south, east, and west
Cardinal (TV series), a 2017 Canadian television series
Arizona Cardinals, an American professional football team
St. Louis Cardinals, an American professional baseball team
Cardinal or The Cardinal may also refer to:
Animals
Birds
In addition to the aforementioned cardinalids:
Paroaria, a South American genus of birds in the family Thraupidae commonly called red-headed cardinals or cardinal-tanagers
Yellow cardinal, Gubernatrix cristata a South American bird in the family Thraupidae
Other animals
Argynnis pandora, a species of butterfly
Cardinal tetra, a freshwater fish
Businesses
Cardinal Brewery, a brewery founded in 1788 by François Piller, located in Fribourg, Switzerland
Cardinal Technologies, a defunct modem manufacturer (1987–1997)
Christianity
Cardinal (Church of England), either of two members of the College of Minor Canons of St. Paul's Cathedral
Cardinal (Catholic Church) a senior member of the Catholic Church.
Entertainment
Films
Cardinals, a 2017 Canadian film
The Cardinal, a 1936 British historical drama
The Cardinal, a 1963 American film
Games
Cardinal (chess), a fairy chess piece, also known as the archbishop
Cardinal, a participant in the army drinking game Cardinal Puff
Music
Groups
Cardinal (band), indie pop duo formed in 1992
The Cardinals (rock band), a group formed in 2003
The Cardinals, a 1950s R&B group
Albums
Cardinal (Cardinal album), 1994
Cardinal (Pinegrove album), 2016
Television
"Cardinal" (The Americans), the second episode of the second season of the television series The Americans
Other arts, entertainment, and media
Cardinal (comics), a supervillain appearing in Marvel Comics
The Cardinal (1641 play), a Caroline era tragedy by James Shirley
The Cardinal (1901 play), a historical play by the British writer Louis N. Parker
The Cardinal System, a system appearing in the Sword Art Online series
Cardinal, a stormtrooper officer featured in Star Wars: Phasma, a novel by Delilah S. Dawson
Linguistics
Cardinal numeral, a part of speech for expressing numbers by name
Cardinal vowel, a concept in phonetics
Mathematics
Cardinal voting
Navigation
Cardinal mark, a sea mark used in navigation
Places
Cardinal, Manitoba, Canada
Cardinal, Ontario, Canada
Cardinal High School (Middlefield, Ohio), a public high school in Middlefield, Ohio, Geauga County, United States
Cardinal Mountain, a summit in California
Cardinal Power Plant, a power plant in Jefferson County, Ohio
Cardinal, Virginia, United States
C/2008 T2 (Cardinal), a comet
Plants
Cardinal (grape), a table grape first produced in California in 1939
Lobelia cardinalis, also known as "cardinal flower"
Sports
Assindia Cardinals, an American football club from Essen, Germany
Ball State Cardinals, the athletic teams of Ball State University
Cardenales de Lara, a Venezuelan baseball team
Catholic University Cardinals, the athletic teams of the Catholic University of America
Front Royal Cardinals, an American baseball team
Incarnate Word Cardinals, the athletic teams of the University of the Incarnate Word
Lamar Cardinals, the athletic teams of Lamar University in Beaumont, Texas, USA
Louisville Cardinals, the athletic teams of University of Louisville
Mapúa Cardinals, the athletic teams of Mapúa University
North Central Cardinals, the athletic teams of North Central College
St. John Fisher Cardinals, the athletic teams of St. John Fisher College in Rochester, NY
Stanford Cardinal, the athletic teams of Stanford University; named for the color but not the bird
Wesleyan Cardinals, the athletic teams of Wesleyan University
West Perth Football Club, an Australian rules football club in Western Australia
Woking F.C., an English football team
Transport
Aircraft
Cessna 177 Cardinal, a single engine aircraft
St. Louis Cardinal C-2-110, a light aircraft built in 1928
NCSIST Cardinal, a family of small UAVs
Trains
Cardinal (train)
The Cardinal (railcar)
Other uses
Cardinal (color), a vivid red
Cardinal (name), a surname
Cardinal, a Ruby programming language implementation using for the Parrot virtual machine
See also
Cardenal, a surname
Cardinal sin or cardinal syn
Cardinale, a surname
|
https://en.wikipedia.org/wiki/Cardinal
|
2025-04-05T18:27:43.835522
|
6172
|
Cantor set
|
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and mentioned by German mathematician Georg Cantor in 1883.
Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. The most common construction is the Cantor ternary set, built by removing the middle third of a line segment and then repeating the process with the remaining shorter segments. Cantor mentioned this ternary construction only in passing, as an example of a perfect set that is nowhere dense.
center|thumb|600px|400px|class=skin-invert
Expansion of a Cantor set. Each point in the set is represented here by a vertical line.
Construction and formula of the ternary set
The Cantor ternary set \mathcal{C} is created by iteratively deleting the open middle third from a set of line segments. One starts by deleting the open middle third \left(\frac{1}{3}, \frac{2}{3}\right) from the interval \textstyle\left[0, 1\right], leaving two line segments: \left[0, \frac{1}{3}\right]\cup\left[\frac{2}{3}, 1\right]. Next, the open middle third of each of these remaining segments is deleted, leaving four line segments: \left[0, \frac{1}{9}\right]\cup\left[\frac{2}{9}, \frac{1}{3}\right]\cup\left[\frac{2}{3}, \frac{7}{9}\right]\cup\left[\frac{8}{9}, 1\right].
The Cantor ternary set contains all points in the interval [0,1] that are not deleted at any step in this infinite process. The same construction can be described recursively by setting
C_0 := [0,1]
and
C_n :\frac{C_{n-1}} 3 \cup \left(\frac 2 {3} +\frac{C_{n-1}} 3 \right) \frac13 \bigl(C_{n-1} \cup \left(2 + C_{n-1} \right)\bigr)
for n \ge 1, so that
\mathcal{C} :{\color{Blue}\lim_{n\to\infty}C_n} \bigcap_{n0}^\infty C_n \bigcap_{n=m}^\infty C_n for any m \ge 0.
The first six steps of this process are illustrated below.
729px|class=skin-invert|
Cantor ternary set, in seven iterations
Using the idea of self-similar transformations, T_L(x)x/3, T_R(x)(2+x)/3 and C_n =T_L(C_{n-1})\cup T_R(C_{n-1}), the explicit closed formulas for the Cantor set are
\mathcal{C}[0,1] \,\setminus\, \bigcup_{n0}^\infty \bigcup_{k=0}^{3^n-1} \left(\frac{3k+1}{3^{n+1}},\frac{3k+2}{3^{n+1}} \right)\!,
where every middle third is removed as the open interval \left(\frac{3k+1}{3^{n+1}},\frac{3k+2}{3^{n+1}}\right) from the closed interval \left[\frac{3k+0}{3^{n+1}},\frac{3k+3}{3^{n+1}}\right] = \left[\frac{k+0}{3^n},\frac{k+1}{3^n}\right] surrounding it, or
\mathcal{C}\bigcap_{n1}^\infty \bigcup_{k=0}^{3^{n-1}-1} \left( \left[\frac{3k+0}{3^n},\frac{3k+1}{3^n}\right] \cup \left[\frac{3k+2}{3^n},\frac{3k+3}{3^n}\right] \right)\!,
where the middle third \left(\frac{3k+1}{3^n},\frac{3k+2}{3^n}\right) of the foregoing closed interval \left[\frac{k+0}{3^{n-1}},\frac{k+1}{3^{n-1}}\right] = \left[\frac{3k+0}{3^n},\frac{3k+3}{3^n}\right] is removed by intersecting with \left[\frac{3k+0}{3^n},\frac{3k+1}{3^n}\right] \cup \left[\frac{3k+2}{3^n},\frac{3k+3}{3^n}\right]\!.
This process of removing middle thirds is a simple example of a finite subdivision rule. The complement of the Cantor ternary set is an example of a fractal string.
400px
In arithmetical terms, the Cantor set consists of all real numbers of the unit interval [0,1] that do not require the digit 1 in order to be expressed as a ternary (base 3) fraction. As the above diagram illustrates, each point in the Cantor set is uniquely located by a path through an infinitely deep binary tree, where the path turns left or right at each level according to which side of a deleted segment the point lies on. Representing each left turn with 0 and each right turn with 2 yields the ternary fraction for a point.
Mandelbrot's construction by "curdling"
In The Fractal Geometry of Nature, mathematician Benoit Mandelbrot provides a whimsical thought experiment to assist non-mathematical readers in imagining the construction of \mathcal{C}. His narrative begins with imagining a bar, perhaps of lightweight metal, in which the bar's matter "curdles" by iteratively shifting towards its extremities. As the bar's segments become smaller, they become thin, dense slugs that eventually grow too small and faint to see.CURDLING: The construction of the Cantor bar results from the process I call curdling. It begins with a round bar. It is best to think of it as having a very low density. Then matter "curdles" out of this bar's middle third into the end thirds, so that the positions of the latter remain unchanged. Next matter curdles out of the middle third of each end third into its end thirds, and so on ad infinitum until one is left with an infinitely large number of infinitely thin slugs of infinitely high density. These slugs are spaced along the line in the very specific fashion induced by the generating process. In this illustration, curdling (which eventually requires hammering!) stops when both the printer's press and our eye cease to follow; the last line is indistinguishable from the last but one: each of its ultimate parts is seen as a gray slug rather than two parallel black slugs.
All endpoints of segments are terminating ternary fractions and are contained in the set
\left\{x \in [0,1] \mid \exists i \in \N_0: x \, 3^i \in \Z \right\} \qquad \Bigl(\subset \N_0 \, 3^{-\N_0} \Bigr)
which is a countably infinite set.
As to cardinality, almost all elements of the Cantor set are not endpoints of intervals, nor rational points like 1/4. The whole Cantor set is in fact not countable.
Properties
Cardinality
It can be shown that there are as many points left behind in this process as there were to begin with, and that therefore, the Cantor set is uncountable. To see this, we show that there is a function f from the Cantor set \mathcal{C} to the closed interval [0,1] that is surjective (i.e. f maps from \mathcal{C} onto [0,1]) so that the cardinality of \mathcal{C} is no less than that of [0,1]. Since \mathcal{C} is a subset of [0,1], its cardinality is also no greater, so the two cardinalities must in fact be equal, by the Cantor–Bernstein–Schröder theorem.
To construct this function, consider the points in the [0, 1] interval in terms of base 3 (or ternary) notation. Recall that the proper ternary fractions, more precisely: the elements of \bigl(\Z \setminus \{0\}\bigr) \cdot 3^{-\N_0}, admit more than one representation in this notation, as for example , that can be written as 0.13 3, but also as 0.0222...3 3, and , that can be written as 0.23 3 but also as 0.1222...3 3.
When we remove the middle third, this contains the numbers with ternary numerals of the form 0.1xxxxx...3 where xxxxx...3 is strictly between 00000...3 and 22222...3. So the numbers remaining after the first step consist of
Numbers of the form 0.0xxxxx...3 (including 0.022222...3 = 1/3)
Numbers of the form 0.2xxxxx...3 (including 0.222222...3 = 1)
This can be summarized by saying that those numbers with a ternary representation such that the first digit after the radix point is not 1 are the ones remaining after the first step.
The second step removes numbers of the form 0.01xxxx...3 and 0.21xxxx...3, and (with appropriate care for the endpoints) it can be concluded that the remaining numbers are those with a ternary numeral where neither of the first two digits is 1.
Continuing in this way, for a number not to be excluded at step n, it must have a ternary representation whose nth digit is not 1. For a number to be in the Cantor set, it must not be excluded at any step, it must admit a numeral representation consisting entirely of 0s and 2s.
It is worth emphasizing that numbers like 1, 0.13 and 0.213 are in the Cantor set, as they have ternary numerals consisting entirely of 0s and 2s: 1 0.222...3 3, 0.0222...3 3 and 0.20222...3 3.
All the latter numbers are "endpoints", and these examples are right limit points of \mathcal{C}. The same is true for the left limit points of \mathcal{C}, e.g. 0.1222...3 3 3 and 0.21222...3 3 3. All these endpoints are proper ternary fractions (elements of \Z \cdot 3^{-\N_0}) of the form , where denominator q is a power of 3 when the fraction is in its irreducible form. Since this construction provides an injection from [-1,1] to \mathcal{C}\times\mathcal{C}, we have |\mathcal{C}\times\mathcal{C}|\geq|[-1,1]|\mathfrak{c} as an immediate corollary. Assuming that |A\times A||A| for any infinite set A (a statement shown to be equivalent to the axiom of choice by Tarski), this provides another demonstration that |\mathcal{C}|=\mathfrak{c}.
The Cantor set contains as many points as the interval from which it is taken, yet itself contains no interval of nonzero length. The irrational numbers have the same property, but the Cantor set has the additional property of being closed, so it is not even dense in any interval, unlike the irrational numbers which are dense in every interval.
It has been conjectured that all algebraic irrational numbers are normal. Since members of the Cantor set are not normal in base 3, this would imply that all members of the Cantor set are either rational or transcendental.
Self-similarity
The Cantor set is the prototype of a fractal. It is self-similar, because it is equal to two copies of itself, if each copy is shrunk by a factor of 3 and translated. More precisely, the Cantor set is equal to the union of two functions, the left and right self-similarity transformations of itself, T_L(x)x/3 and T_R(x)(2+x)/3, which leave the Cantor set invariant up to homeomorphism: T_L(\mathcal{C})\cong T_R(\mathcal{C})\cong \mathcal{C}=T_L(\mathcal{C})\cup T_R(\mathcal{C}).
Repeated iteration of T_L and T_R can be visualized as an infinite binary tree. That is, at each node of the tree, one may consider the subtree to the left or to the right. Taking the set \{T_L, T_R\} together with function composition forms a monoid, the dyadic monoid.
The automorphisms of the binary tree are its hyperbolic rotations, and are given by the modular group. Thus, the Cantor set is a homogeneous space in the sense that for any two points x and y in the Cantor set \mathcal{C}, there exists a homeomorphism h:\mathcal{C}\to \mathcal{C} with h(x)y. An explicit construction of h can be described more easily if we see the Cantor set as a product space of countably many copies of the discrete space \{0,1\}. Then the map h:\{0,1\}^\N\to\{0,1\}^\N defined by h_n(u):u_n+x_n+y_n \mod 2 is an involutive homeomorphism exchanging x and y.
Conservation law
It has been found that some form of conservation law is always responsible behind scaling and self-similarity. In the case of Cantor set it can be seen that the d_fth moment (where d_f=\ln(2)/\ln(3) is the fractal dimension) of all the surviving intervals at any stage of the construction process is equal to a constant which is one in the case of the Cantor set.
We know that there are N2^n intervals of size 1/3^n present in the system at the nth step of its construction. Then if we label the surviving intervals as x_1, x_2, \ldots, x_{2^n} then the d_fth moment is x_1^{d_f}+x_2^{d_f}+\cdots+x_{2^n}^{d_f}1 since x_1x_2 \cdots x_{2^n}1/3^n.
The Hausdorff dimension of the Cantor set is equal to ln(2)/ln(3) ≈ 0.631.
Topological and analytical properties
Although "the" Cantor set typically refers to the original, middle-thirds Cantor set described above, topologists often talk about "a" Cantor set, which means any topological space that is homeomorphic (topologically equivalent) to it.
As the above summation argument shows, the Cantor set is uncountable but has Lebesgue measure 0. Since the Cantor set is the complement of a union of open sets, it itself is a closed subset of the reals, and therefore a complete metric space. Since it is also totally bounded, the Heine–Borel theorem says that it must be compact.
For any point in the Cantor set and any arbitrarily small neighborhood of the point, there is some other number with a ternary numeral of only 0s and 2s, as well as numbers whose ternary numerals contain 1s. Hence, every point in the Cantor set is an accumulation point (also called a cluster point or limit point) of the Cantor set, but none is an interior point. A closed set in which every point is an accumulation point is also called a perfect set in topology, while a closed subset of the interval with no interior points is nowhere dense in the interval.
Every point of the Cantor set is also an accumulation point of the complement of the Cantor set.
For any two points in the Cantor set, there will be some ternary digit where they differ — one will have 0 and the other 2. By splitting the Cantor set into "halves" depending on the value of this digit, one obtains a partition of the Cantor set into two closed sets that separate the original two points. In the relative topology on the Cantor set, the points have been separated by a clopen set. Consequently, the Cantor set is totally disconnected. As a compact totally disconnected Hausdorff space, the Cantor set is an example of a Stone space.
As a topological space, the Cantor set is naturally homeomorphic to the product of countably many copies of the space \{0, 1\}, where each copy carries the discrete topology. This is the space of all sequences in two digits
2^\mathbb{N} = \{(x_n) \mid x_n \in \{0,1\} \text{ for } n \in \mathbb{N}\},
which can also be identified with the set of 2-adic integers. The basis for the open sets of the product topology are cylinder sets; the homeomorphism maps these to the subspace topology that the Cantor set inherits from the natural topology on the real line. This characterization of the Cantor space as a product of compact spaces gives a second proof that Cantor space is compact, via Tychonoff's theorem.
From the above characterization, the Cantor set is homeomorphic to the p-adic integers, and, if one point is removed from it, to the p-adic numbers.
The Cantor set is a subset of the reals, which are a metric space with respect to the ordinary distance metric; therefore the Cantor set itself is a metric space, by using that same metric. Alternatively, one can use the p-adic metric on 2^\mathbb{N}: given two sequences (x_n),(y_n)\in 2^\mathbb{N}, the distance between them is d((x_n),(y_n)) = 2^{-k}, where k is the smallest index such that x_k \ne y_k; if there is no such index, then the two sequences are the same, and one defines the distance to be zero. These two metrics generate the same topology on the Cantor set.
We have seen above that the Cantor set is a totally disconnected perfect compact metric space. Indeed, in a sense it is the only one: every nonempty totally disconnected perfect compact metric space is homeomorphic to the Cantor set. See Cantor space for more on spaces homeomorphic to the Cantor set.
The Cantor set is sometimes regarded as "universal" in the category of compact metric spaces, since any compact metric space is a continuous image of the Cantor set; however this construction is not unique and so the Cantor set is not universal in the precise categorical sense. The "universal" property has important applications in functional analysis, where it is sometimes known as the representation theorem for compact metric spaces.
For any integer q ≥ 2, the topology on the group G Zqω (the countable direct sum) is discrete. Although the Pontrjagin dual Γ is also Zqω, the topology of Γ is compact. One can see that Γ is totally disconnected and perfect - thus it is homeomorphic to the Cantor set. It is easiest to write out the homeomorphism explicitly in the case q 2. (See Rudin 1962 p 40.)
Measure and probability
The Cantor set can be seen as the compact group of binary sequences, and as such, it is endowed with a natural Haar measure. When normalized so that the measure of the set is 1, it is a model of an infinite sequence of coin tosses. Furthermore, one can show that the usual Lebesgue measure on the interval is an image of the Haar measure on the Cantor set, while the natural injection into the ternary set is a canonical example of a singular measure. It can also be shown that the Haar measure is an image of any probability, making the Cantor set a universal probability space in some ways.
In Lebesgue measure theory, the Cantor set is an example of a set which is uncountable and has zero measure. In contrast, the set has a Hausdorff measure of 1 in its dimension of log 2 / log 3.
Cantor numbers
If we define a Cantor number as a member of the Cantor set, then
Every real number in [0, 2] is the sum of two Cantor numbers.
Between any two Cantor numbers there is a number that is not a Cantor number.
Descriptive set theory
The Cantor set is a meagre set (or a set of first category) as a subset of [0,1] (although not as a subset of itself, since it is a Baire space). The Cantor set thus demonstrates that notions of "size" in terms of cardinality, measure, and (Baire) category need not coincide. Like the set \mathbb{Q}\cap[0,1], the Cantor set \mathcal{C} is "small" in the sense that it is a null set (a set of measure zero) and it is a meagre subset of [0,1]. However, unlike \mathbb{Q}\cap[0,1], which is countable and has a "small" cardinality, \aleph_0, the cardinality of \mathcal{C} is the same as that of [0,1], the continuum \mathfrak{c}, and is "large" in the sense of cardinality. In fact, it is also possible to construct a subset of [0,1] that is meagre but of positive measure and a subset that is non-meagre but of measure zero: By taking the countable union of "fat" Cantor sets \mathcal{C}^{(n)} of measure \lambda (n-1)/n (see Smith–Volterra–Cantor set below for the construction), we obtain a set \mathcal{A} : \bigcup_{n1}^{\infty}\mathcal{C}^{(n)}which has a positive measure (equal to 1) but is meagre in [0,1], since each \mathcal{C}^{(n)} is nowhere dense. Then consider the set \mathcal{A}^{\mathrm{c}} [0,1] \setminus\bigcup_{n1}^\infty \mathcal{C}^{(n)}. Since \mathcal{A}\cup\mathcal{A}^{\mathrm{c}} [0,1], \mathcal{A}^{\mathrm{c}} cannot be meagre, but since \mu(\mathcal{A})=1, \mathcal{A}^{\mathrm{c}} must have measure zero.
Variants
thumb|Radial plot of the first ten steps
Smith–Volterra–Cantor set
Instead of repeatedly removing the middle third of every piece as in the Cantor set, we could also keep removing any other fixed percentage (other than 0% and 100%) from the middle. In the case where the middle of the interval is removed, we get a remarkably accessible case — the set consists of all numbers in [0,1] that can be written as a decimal consisting entirely of 0s and 9s. If a fixed percentage is removed at each stage, then the limiting set will have measure zero, since the length of the remainder (1-f)^n\to 0 as n\to\infty for any f such that 0.
On the other hand, "fat Cantor sets" of positive measure can be generated by removal of smaller fractions of the middle of the segment in each iteration. Thus, one can construct sets homeomorphic to the Cantor set that have positive Lebesgue measure while still being nowhere dense. If an interval of length r^n (r\leq 1/3) is removed from the middle of each segment at the nth iteration, then the total length removed is \sum_{n1}^\infty 2^{n-1}r^nr/(1-2r), and the limiting set will have a Lebesgue measure of \lambda(1-3r)/(1-2r). Thus, in a sense, the middle-thirds Cantor set is a limiting case with r1/3. If 0, then the remainder will have positive measure with 0. The case r=1/4 is known as the Smith–Volterra–Cantor set, which has a Lebesgue measure of 1/2.
Stochastic Cantor set
One can modify the construction of the Cantor set by dividing randomly instead of equally. Besides, to incorporate time we can divide only one of the available intervals at each step instead of dividing all the available intervals. In the case of stochastic triadic Cantor set the resulting process can be described by the following rate equation
{{\partial c(x,t)}\over{\partial t}}=-xc(x,t)+(1+p)\int_x^\infty c(y,t) \, dy,
where c(x,t)dx is the number of intervals of size between x and x+dx. In the case of triadic Cantor set the fractal dimension is 0.5616 which is
less than its deterministic counterpart 0.6309. In the case of stochastic dyadic Cantor set
the fractal dimension is p which is again less than that of its deterministic counterpart \ln (1+p)/\ln 2. In the case of stochastic dyadic Cantor set the solution for c(x,t) exhibits dynamic scaling as its solution in the long-time limit is t^{-(1+d_f)}e^{-xt} where the fractal dimension of the stochastic dyadic Cantor set d_fp. In either case, like triadic Cantor set, the d_fth moment (\int x^{d_f} c(x,t) \, dx \text{constant}) of stochastic triadic and dyadic Cantor set too are conserved quantities.
Cantor dust
Cantor dust is a multi-dimensional version of the Cantor set. It can be formed by taking a finite Cartesian product of the Cantor set with itself, making it a Cantor space. Like the Cantor set, Cantor dust has zero measure.
thumb|right|250px|Cantor cubes recursion progression towards Cantor dust
thumb|Cantor dust (2D)thumb|Cantor dust (3D)
A different 2D analogue of the Cantor set is the Sierpinski carpet, where a square is divided up into nine smaller squares, and the middle one removed. The remaining squares are then further divided into nine each and the middle removed, and so on ad infinitum. One 3D analogue of this is the Menger sponge.
Historical remarks
thumb|an image of the 2nd iteration of Cantor dust in two dimensionsalt=an image of the 4th iteration of Cantor dust in two dimensions|thumb|an image of the 4th iteration of Cantor dust in two dimensions
Cantor introduced what we call today the Cantor ternary set \mathcal C as an example "of a perfect point-set, which is not everywhere-dense in any interval, however small." Cantor described \mathcal C in terms of ternary expansions, as "the set of all real numbers given by the formula: z=c_1/3 +c_2/3^2 + \cdots + c_\nu/3^\nu +\cdots where the coefficients c_\nu arbitrarily take the two values 0 and 2, and the series can consist of a finite number or an infinite number of elements." He further reflected on the puzzling or even upsetting nature of such structures to those in the mathematics and physics community. In The Fractal geometry of Nature, he described how "When I started on this topic in 1962, everyone was agreeing that Cantor dusts are at least as monstrous as the Koch and Peano curves," and added that "every self-respecting physicist was automatically turned off by a mention of Cantor, ready to run a mile from anyone claiming \mathcal C to be interesting in science."
See also
alt=an image of the 6th iteration of Cantor dust in two dimensions|thumb|an image of the 6th iteration of Cantor dust in two dimensions
The indicator function of the Cantor set
Smith–Volterra–Cantor set
Cantor function
Cantor cube
Antoine's necklace
Koch snowflake
Knaster–Kuratowski fan
List of fractals by Hausdorff dimension
Moser–de Bruijn sequencethumb|Column capital with pattern evocative of the Cantor set, but expressed in binary rather than ternary. Engraving of Île de Philae from Description d'Égypte by Jean-Baptiste Prosper Jollois and Édouard Devilliers, Imprimerie Impériale, Paris, 1809-1828
Notes
References
.
External links
Cantor Sets and Cantor Set and Function at cut-the-knot
Cantor Set at Platonic Realms
Category:Measure theory
Category:Topological spaces
Category:Sets of real numbers
Category:Georg Cantor
Category:L-systems
|
https://en.wikipedia.org/wiki/Cantor_set
|
2025-04-05T18:27:43.915469
|
6173
|
Cardinal number
|
thumb|200px|A bijective function, f: X → Y, from set X to set Y demonstrates that the sets have the same cardinality, in this case equal to the cardinal number 4.
thumb|right|150px|Aleph-null, the smallest infinite cardinal
In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the case of infinite sets, the infinite cardinal numbers have been introduced, which are often denoted with the Hebrew letter \aleph (aleph) marked with subscript indicating their rank among the infinite cardinals.
Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets. In the case of finite sets, this agrees with the intuitive notion of number of elements. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for a proper subset of an infinite set to have the same cardinality as the original set—something that cannot happen with proper subsets of finite sets.
There is a transfinite sequence of cardinal numbers:
0, 1, 2, 3, \ldots, n, \ldots ; \aleph_0, \aleph_1, \aleph_2, \ldots, \aleph_{\alpha}, \ldots.\
This sequence starts with the natural numbers including zero (finite cardinals), which are followed by the aleph numbers. The aleph numbers are indexed by ordinal numbers. If the axiom of choice is true, this transfinite sequence includes every cardinal number. If the axiom of choice is not true (see ), there are infinite cardinals that are not aleph numbers.
Cardinality is studied for its own sake as part of set theory. It is also a tool used in branches of mathematics including model theory, combinatorics, abstract algebra and mathematical analysis. In category theory, the cardinal numbers form a skeleton of the category of sets.
History
The notion of cardinality, as now understood, was formulated by Georg Cantor, the originator of set theory, in 1874–1884. Cardinality can be used to compare an aspect of finite sets. For example, the sets {1,2,3} and {4,5,6} are not equal, but have the same cardinality, namely three. This is established by the existence of a bijection (i.e., a one-to-one correspondence) between the two sets, such as the correspondence {1→4, 2→5, 3→6}.
Cantor applied his concept of bijection to infinite sets (for example the set of natural numbers N = {0, 1, 2, 3, ...}). Thus, he called all sets having a bijection with N denumerable (countably infinite) sets, which all share the same cardinal number. This cardinal number is called \aleph_0, aleph-null. He called the cardinal numbers of infinite sets transfinite cardinal numbers.
Cantor proved that any unbounded subset of N has the same cardinality as N, even though this might appear to run contrary to intuition. He also proved that the set of all ordered pairs of natural numbers is denumerable; this implies that the set of all rational numbers is also denumerable, since every rational can be represented by a pair of integers. He later proved that the set of all real algebraic numbers is also denumerable. Each real algebraic number z may be encoded as a finite sequence of integers, which are the coefficients in the polynomial equation of which it is a solution, i.e. the ordered n-tuple (a0, a1, ..., an), ai ∈ Z together with a pair of rationals (b0, b1) such that z is the unique root of the polynomial with coefficients (a0, a1, ..., an) that lies in the interval (b0, b1).
In his 1874 paper "On a Property of the Collection of All Real Algebraic Numbers", Cantor proved that there exist higher-order cardinal numbers, by showing that the set of real numbers has cardinality greater than that of N. His proof used an argument with nested intervals, but in an 1891 paper, he proved the same result using his ingenious and much simpler diagonal argument. The new cardinal number of the set of real numbers is called the cardinality of the continuum and Cantor used the symbol \mathfrak{c} for it.
Cantor also developed a large portion of the general theory of cardinal numbers; he proved that there is a smallest transfinite cardinal number (\aleph_0, aleph-null), and that for every cardinal number there is a next-larger cardinal
(\aleph_1, \aleph_2, \aleph_3, \ldots).
His continuum hypothesis is the proposition that the cardinality \mathfrak{c} of the set of real numbers is the same as \aleph_1. This hypothesis is independent of the standard axioms of mathematical set theory, that is, it can neither be proved nor disproved from them. This was shown in 1963 by Paul Cohen, complementing earlier work by Kurt Gödel in 1940.
Motivation
In informal use, a cardinal number is what is normally referred to as a counting number, provided that 0 is included: 0, 1, 2, .... They may be identified with the natural numbers beginning with 0. The counting numbers are exactly what can be defined formally as the finite cardinal numbers. Infinite cardinals only occur in higher-level mathematics and logic.
More formally, a non-zero number can be used for two purposes: to describe the size of a set, or to describe the position of an element in a sequence. For finite sets and sequences it is easy to see that these two notions coincide, since for every number describing a position in a sequence we can construct a set that has exactly the right size. For example, 3 describes the position of 'c' in the sequence , and we can construct the set {a,b,c}, which has 3 elements.
However, when dealing with infinite sets, it is essential to distinguish between the two, since the two notions are in fact different for infinite sets. Considering the position aspect leads to ordinal numbers, while the size aspect is generalized by the cardinal numbers described here.
The intuition behind the formal definition of cardinal is the construction of a notion of the relative size or "bigness" of a set, without reference to the kind of members which it has. For finite sets this is easy; one simply counts the number of elements a set has. In order to compare the sizes of larger sets, it is necessary to appeal to more refined notions.
A set Y is at least as big as a set X if there is an injective mapping from the elements of X to the elements of Y. An injective mapping identifies each element of the set X with a unique element of the set Y. This is most easily understood by an example; suppose we have the sets X {1,2,3} and Y {a,b,c,d}, then using this notion of size, we would observe that there is a mapping:
1 → a
2 → b
3 → c
which is injective, and hence conclude that Y has cardinality greater than or equal to X. The element d has no element mapping to it, but this is permitted as we only require an injective mapping, and not necessarily a bijective mapping. The advantage of this notion is that it can be extended to infinite sets.
We can then extend this to an equality-style relation. Two sets X and Y are said to have the same cardinality if there exists a bijection between X and Y. By the Schroeder–Bernstein theorem, this is equivalent to there being both an injective mapping from X to Y, and an injective mapping from Y to X. We then write |X| |Y|. The cardinal number of X itself is often defined as the least ordinal a with |a| |X|. This is called the von Neumann cardinal assignment; for this definition to make sense, it must be proved that every set has the same cardinality as some ordinal; this statement is the well-ordering principle. It is however possible to discuss the relative cardinality of sets without explicitly assigning names to objects.
The classic example used is that of the infinite hotel paradox, also called Hilbert's paradox of the Grand Hotel. Supposing there is an innkeeper at a hotel with an infinite number of rooms. The hotel is full, and then a new guest arrives. It is possible to fit the extra guest in by asking the guest who was in room 1 to move to room 2, the guest in room 2 to move to room 3, and so on, leaving room 1 vacant. We can explicitly write a segment of this mapping:
1 → 2
2 → 3
3 → 4
...
n → n + 1
...
With this assignment, we can see that the set {1,2,3,...} has the same cardinality as the set {2,3,4,...}, since a bijection between the first and the second has been shown. This motivates the definition of an infinite set being any set that has a proper subset of the same cardinality (i.e., a Dedekind-infinite set); in this case {2,3,4,...} is a proper subset of {1,2,3,...}.
When considering these large objects, one might also want to see if the notion of counting order coincides with that of cardinal defined above for these infinite sets. It happens that it does not; by considering the above example we can see that if some object "one greater than infinity" exists, then it must have the same cardinality as the infinite set we started out with. It is possible to use a different formal notion for number, called ordinals, based on the ideas of counting and considering each number in turn, and we discover that the notions of cardinality and ordinality are divergent once we move out of the finite numbers.
It can be proved that the cardinality of the real numbers is greater than that of the natural numbers just described. This can be visualized using Cantor's diagonal argument; classic questions of cardinality (for instance the continuum hypothesis) are concerned with discovering whether there is some cardinal between some pair of other infinite cardinals. In more recent times, mathematicians have been describing the properties of larger and larger cardinals.
Since cardinality is such a common concept in mathematics, a variety of names are in use. Sameness of cardinality is sometimes referred to as equipotence, equipollence, or equinumerosity. It is thus said that two sets with the same cardinality are, respectively, equipotent, equipollent, or equinumerous.
Formal definition
Formally, assuming the axiom of choice, the cardinality of a set X is the least ordinal number α such that there is a bijection between X and α. This definition is known as the von Neumann cardinal assignment. If the axiom of choice is not assumed, then a different approach is needed. The oldest definition of the cardinality of a set X (implicit in Cantor and explicit in Frege and Principia Mathematica) is as the class [X] of all sets that are equinumerous with X. This does not work in ZFC or other related systems of axiomatic set theory because if X is non-empty, this collection is too large to be a set. In fact, for X ≠ ∅ there is an injection from the universe into [X] by mapping a set m to {m} × X, and so by the axiom of limitation of size, [X] is a proper class. The definition does work however in type theory and in New Foundations and related systems. However, if we restrict from this class to those equinumerous with X that have the least rank, then it will work (this is a trick due to Dana Scott: it works because the collection of objects with any given rank is a set).
Von Neumann cardinal assignment implies that the cardinal number of a finite set is the common ordinal number of all possible well-orderings of that set, and cardinal and ordinal arithmetic (addition, multiplication, power, proper subtraction) then give the same answers for finite numbers. However, they differ for infinite numbers. For example, 2^\omega\omega in ordinal arithmetic while 2^{\aleph_0}>\aleph_0\aleph_0^2 in cardinal arithmetic, although the von Neumann assignment puts \aleph_0=\omega. On the other hand, Scott's trick implies that the cardinal number 0 is \{\emptyset\}, which is also the ordinal number 1, and this may be confusing. A possible compromise (to take advantage of the alignment in finite arithmetic while avoiding reliance on the axiom of choice and confusion in infinite arithmetic) is to apply von Neumann assignment to the cardinal numbers of finite sets (those which can be well ordered and are not equipotent to proper subsets) and to use Scott's trick for the cardinal numbers of other sets.
Formally, the order among cardinal numbers is defined as follows: |X| ≤ |Y| means that there exists an injective function from X to Y. The Cantor–Bernstein–Schroeder theorem states that if |X| ≤ |Y| and |Y| ≤ |X| then |X| = |Y|. The axiom of choice is equivalent to the statement that given two sets X and Y, either |X| ≤ |Y| or |Y| ≤ |X|.
A set X is Dedekind-infinite if there exists a proper subset Y of X with |X| |Y|, and Dedekind-finite if such a subset does not exist. The finite cardinals are just the natural numbers, in the sense that a set X is finite if and only if |X| |n| = n for some natural number n. Any other set is infinite.
Assuming the axiom of choice, it can be proved that the Dedekind notions correspond to the standard ones. It can also be proved that the cardinal \aleph_0 (aleph null or aleph-0, where aleph is the first letter in the Hebrew alphabet, represented \aleph) of the set of natural numbers is the smallest infinite cardinal (i.e., any infinite set has a subset of cardinality \aleph_0). The next larger cardinal is denoted by \aleph_1, and so on. For every ordinal α, there is a cardinal number \aleph_{\alpha}, and this list exhausts all infinite cardinal numbers.
Cardinal arithmetic
We can define arithmetic operations on cardinal numbers that generalize the ordinary operations for natural numbers. It can be shown that for finite cardinals, these operations coincide with the usual operations for natural numbers. Furthermore, these operations share many properties with ordinary arithmetic.
Successor cardinal
If the axiom of choice holds, then every cardinal κ has a successor, denoted κ+, where κ+ > κ and there are no cardinals between κ and its successor. (Without the axiom of choice, using Hartogs' theorem, it can be shown that for any cardinal number κ, there is a minimal cardinal κ+ such that + ࣞ κ.-->\kappa^+\nleq\kappa. ) For finite cardinals, the successor is simply κ + 1. For infinite cardinals, the successor cardinal differs from the successor ordinal.
Cardinal addition
If X and Y are disjoint, addition is given by the union of X and Y. If the two sets are not already disjoint, then they can be replaced by disjoint sets of the same cardinality (e.g., replace X by X×{0} and Y by Y×{1}).
|X| + |Y| = | X \cup Y|.
Zero is an additive identity κ + 0 0 + κ κ.
Addition is associative (κ + μ) + ν = κ + (μ + ν).
Addition is commutative κ + μ = μ + κ.
Addition is non-decreasing in both arguments:
(\kappa \le \mu) \rightarrow ((\kappa + \nu \le \mu + \nu) \mbox{ and } (\nu + \kappa \le \nu + \mu)).
Assuming the axiom of choice, addition of infinite cardinal numbers is easy. If either κ or μ is infinite, then
\kappa + \mu = \max\{\kappa, \mu\}\,.
Subtraction
Assuming the axiom of choice and, given an infinite cardinal σ and a cardinal μ, there exists a cardinal κ such that μ + κ σ if and only if μ ≤ σ. It will be unique (and equal to σ) if and only if μ |X|\cdot|Y| |X \times Y|
The continuum hypothesis
The continuum hypothesis (CH) states that there are no cardinals strictly between \aleph_0 and 2^{\aleph_0}. The latter cardinal number is also often denoted by \mathfrak{c}; it is the cardinality of the continuum (the set of real numbers). In this case 2^{\aleph_0} = \aleph_1.
Similarly, the generalized continuum hypothesis (GCH) states that for every infinite cardinal \kappa, there are no cardinals strictly between \kappa and 2^\kappa. Both the continuum hypothesis and the generalized continuum hypothesis have been proved to be independent of the usual axioms of set theory, the Zermelo–Fraenkel axioms together with the axiom of choice (ZFC).
Indeed, Easton's theorem shows that, for regular cardinals \kappa, the only restrictions ZFC places on the cardinality of 2^\kappa are that \kappa , and that the exponential function is non-decreasing.
See also
Aleph number
Beth number
The paradox of the greatest cardinal
Cardinal number (linguistics)
Counting
Inclusion–exclusion principle
Large cardinal
Names of numbers in English
Nominal number
Ordinal number
Regular cardinal
References
Notes
Bibliography
Hahn, Hans, Infinity, Part IX, Chapter 2, Volume 3 of The World of Mathematics. New York: Simon and Schuster, 1956.
Halmos, Paul, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. (Springer-Verlag edition).
External links
|
https://en.wikipedia.org/wiki/Cardinal_number
|
2025-04-05T18:27:43.948067
|
6174
|
Cardinality
|
has 5 elements. Thus the cardinality of <math>S</math> is 5 or, written symbolically, <math>|S|=5</math>.]]
In mathematics, the cardinality of a set is the number of its elements. The cardinality of a set may also be called its size, when no confusion with other notions of size is possible. Beginning in the late 19th century, this concept of size was generalized to infinite sets, allowing one to distinguish between different types of infinity and to perform arithmetic on them. Nowadays, infinite sets are encountered in almost all parts of mathematics, even those that may seem to be unrelated. Familiar examples are provided by most number systems and algebraic structures (natural numbers, rational numbers, real numbers, vector spaces, etc.), as well as, in geometry, by lines, line segments and curves, which are considered as the sets of their points.
There are two approaches to describing cardinality: one which uses cardinal numbers and another which compares sets directly using functions between them, either bijections or injections.
The former states the size as a number; the latter compares their relative size and led to the discovery of different sizes of infinity. For example, the sets <math>A \{1, 2, 3\}</math> and <math>B \{2,4,6\}</math> are the same size as they each contain 3 elements (the first approach) and there is a bijection between them (the second approach). Notation and terminology The cardinality, or cardinal number, of a set <math>A</math> is generally denoted by <math>|A|</math>, with a vertical bar on each side. (This is the same notation as for absolute value; the meaning depends on context.) The notation <math>|A| |B|</math> means that the two sets and have the same cardinality. The cardinal number of a set <math>A</math> may also be denoted by <math>n(A)</math>, <span style"border-top: 3px double black;"><math>A</math></span>, <math>\operatorname{card}(A)</math>, <math>\#A</math>, etc.
It is conventional to recognize three kinds of cardinality:
*Any set X with cardinality less than that of the natural numbers, or | X | < | N |, is said to be a finite set.
*Any set X that has the same cardinality as the set of the natural numbers, or | X | | N | <math>\aleph_0</math>, is said to be a countably infinite set. Human expression of cardinality is seen as early as years ago, with equating the size of a group with a group of recorded notches, or a representative collection of other things, such as sticks and shells. The abstraction of cardinality as a number is evident by 3000 BCE, in Sumerian mathematics and the manipulation of numbers without reference to a specific group of things or events. Ancient History One of the earliest explicit uses of a one-to-one correspondence is recorded in Aristotle's Mechanics, known as Aristotle's wheel paradox. The paradox can be briefly described as follows: A wheel is depicted as two concentric circles. The larger, outer circle is tangent to a horizontal line (e.g. a road that it rolls on), while the smaller, inner circle is rigidly affixed to the larger. Assuming the larger circle rolls along the line without slipping (or skidding) for one full revolution, the distances moved by both circles are the same: the circumference of the larger circle. Further, the lines traced by the bottom-most point of each is the same length. Since the smaller wheel does not skip any points, and no point on the smaller wheel is used more than once, there is a one-to-one correspondence between the two circles.
From the 6th century BCE, the writings of Greek philosophers show hints of the cardinality of infinite sets. While they considered the notion of infinity as an endless series of actions, such as adding 1 to a number repeatedly, they did not consider the size of an infinite set of numbers to be a thing. The ancient Greek notion of infinity also considered the division of things into parts repeated without limit. In Euclid's Elements, commensurability was described as the ability to compare the length of two line segments, a and b, as a ratio, as long as there were a third segment, no matter how small, that could be laid end-to-end a whole number of times into both a and b. But with the discovery of irrational numbers, it was seen that even the infinite set of all rational numbers was not enough to describe the length of every possible line segment. Still, there was no concept of infinite sets as something that had cardinality. Pre-Cantorian Set theory Galileo Galilei presented what was later coined Galileo's paradox in his book Two New Sciences (1638), where he attempts to show that infinite quantities cannot be called greater or less than one another. He presents the paradox roughly as follows: a square number is one which is the product of another number with itself, such as 4 and 9, which are the squares of 2 and 3 respectively. Then the square root of a square number is that multiplicand. He then notes that there are as many square numbers as there are square roots, since every square has its own root and every root its own square, while no square has more than one root and no root more than one square. But there are as many square roots as there are numbers, since every number is the square root of some square. He, however, concluded that this meant we could not compare the sizes of infinite sets, missing the opportunity to discover cardinality.
Early Set theory
To better understand infinite sets, a notion of cardinality was formulated by Georg Cantor, the originator of set theory. He examined the process of equating two sets with a bijection, a one-to-one correspondence between the elements of two sets. In 1891, with the publication of his diagonal argument, he demonstrated that there are sets of numbers that cannot be placed in one-to-one correspondence with the set of natural numbers, i.e., there are "uncountable sets" that contain more elements than there are in the infinite set of natural numbers.Comparing sets
s. Although E is a proper subset of N, both sets have the same cardinality.]]
P(N): For every function f from N to P(N), the set T = {n∈N: n∉f(n)} disagrees with every set in the range of f, hence f cannot be surjective. The picture shows an example f and the corresponding T; : n∈f(n)\T, :n∈T\f(n).]]
While the cardinality of a finite set is simply its number of elements, extending that notion to infinite sets usually starts with defining comparison of sizes of arbitrary sets (some of which are possibly infinite).
Definition 1: Two sets have the same cardinality if there exists a one-to-one correspondence between the elements of and those (that is, a bijection from to ). Such sets are said to be equipotent, equipollent, or equinumerous.
For example, the set <math>E \{0, 2, 4, 6, \text{...}\}</math> of non-negative even numbers has the same cardinality as the set <math>\N \{0, 1, 2, 3, \text{...}\}</math> of natural numbers, since the function <math>f(n) = 2n</math> is a bijection from to (see picture).
For finite sets and , if some bijection exists from to , then each injective or surjective function from to is a bijection. This is no longer true for infinite and . For example, the function from to , defined by <math>g(n) 4n</math> is injective, but not surjective since 2, for instance, is not mapped to, and from to , defined by <math>h(n) n - (n \text{ mod } 2)</math> (see: modulo operation) is surjective, but not injective, since 0 and 1 for instance both map to 0. Neither nor can challenge <math>|E| |\N|</math>, which was established by the existence of .Definition 2: ≤
has cardinality less than or equal to the cardinality of , if there exists an injective function from into .
If <math>|A| \leq |B|</math> and <math>|B| \leq |A|</math>, then <math>|A| |B|</math> (a fact known as the Schröder–Bernstein theorem). The axiom of choice is equivalent to the statement that <math>|A| \leq |B|</math> or <math>|B| \leq |A|</math> for every and .
Definition 3: <
has cardinality strictly less than the cardinality of , if there is an injective function, but no bijective function, from to .
For example, the set of all natural numbers has cardinality strictly less than its power set , because <math>g(n) \{n\}</math> is an injective function from to , and it can be shown that no function from to can be bijective (see picture). By a similar argument, has cardinality strictly less than the cardinality of the set of all real numbers. For proofs, see Cantor's diagonal argument or Cantor's first uncountability proof.Cardinal numbers
In the above section, "cardinality" of a set was defined functionally. In other words, it was not defined as a specific object itself. However, such an object can be defined as follows.
The relation of having the same cardinality is called equinumerosity, and this is an equivalence relation on the class of all sets. The equivalence class of a set A under this relation, then, consists of all those sets which have the same cardinality as A. There are two ways to define the "cardinality of a set":
#The cardinality of a set A is defined as its equivalence class under equinumerosity.
#A representative set is designated for each equivalence class. The most common choice is the initial ordinal in that class. This is usually taken as the definition of cardinal number in axiomatic set theory.
Assuming the axiom of choice, the cardinalities of the infinite sets are denoted
:<math>\aleph_0 < \aleph_1 < \aleph_2 < \ldots . </math>
For each ordinal <math>\alpha</math>, <math>\aleph_{\alpha + 1}</math> is the least cardinal number greater than <math>\aleph_\alpha</math>.
The cardinality of the natural numbers is denoted aleph-null (<math>\aleph_0</math>), while the cardinality of the real numbers is denoted by "<math>\mathfrak c</math>" (a lowercase fraktur script "c"), and is also referred to as the cardinality of the continuum. Cantor showed, using the diagonal argument, that <math>{\mathfrak c} >\aleph_0</math>. We can show that <math>\mathfrak c = 2^{\aleph_0}</math>, this also being the cardinality of the set of all subsets of the natural numbers.
The continuum hypothesis says that <math>\aleph_1 = 2^{\aleph_0}</math>, i.e. <math>2^{\aleph_0}</math> is the smallest cardinal number bigger than <math>\aleph_0</math>, i.e. there is no set whose cardinality is strictly between that of the integers and that of the real numbers. The continuum hypothesis is independent of ZFC, a standard axiomatization of set theory; that is, it is impossible to prove the continuum hypothesis or its negation from ZFC—provided that ZFC is consistent. For more detail, see § Cardinality of the continuum below.Infinite setsOur intuition gained from finite sets breaks down when dealing with infinite sets. In the late 19th century Georg Cantor, Gottlob Frege, Richard Dedekind and others rejected the view that the whole cannot be the same size as the part. One example of this is Hilbert's paradox of the Grand Hotel.
Indeed, Dedekind defined an infinite set as one that can be placed into a one-to-one correspondence with a strict subset (that is, having the same size in Cantor's sense); this notion of infinity is called Dedekind infinite. Cantor introduced the cardinal numbers, and showed—according to his bijection-based definition of size—that some infinite sets are greater than others. The smallest infinite cardinality is that of the natural numbers (<math>\aleph_0</math>).
Cardinality of the continuum
One of Cantor's most important results was that the cardinality of the continuum (<math>\mathfrak{c}</math>) is greater than that of the natural numbers (<math>\aleph_0</math>); that is, there are more real numbers R than natural numbers N. Namely, Cantor showed that <math>\mathfrak{c} 2^{\aleph_0} \beth_1</math> (see Beth one) satisfies:
:<math>2^{\aleph_0} > \aleph_0</math>
:(see Cantor's diagonal argument or Cantor's first uncountability proof).
The continuum hypothesis states that there is no cardinal number between the cardinality of the reals and the cardinality of the natural numbers, that is,
:<math>2^{\aleph_0} = \aleph_1</math>
However, this hypothesis can neither be proved nor disproved within the widely accepted ZFC axiomatic set theory, if ZFC is consistent.
Cardinal arithmetic can be used to show not only that the number of points in a real number line is equal to the number of points in any segment of that line, but that this is equal to the number of points on a plane and, indeed, in any finite-dimensional space. These results are highly counterintuitive, because they imply that there exist proper subsets and proper supersets of an infinite set S that have the same size as S, although S contains elements that do not belong to its subsets, and the supersets of S contain elements that are not included in it.
The first of these results is apparent by considering, for instance, the tangent function, which provides a one-to-one correspondence between the interval (−½π, ½π) and R (see also Hilbert's paradox of the Grand Hotel).
The second result was first demonstrated by Cantor in 1878, but it became more apparent in 1890, when Giuseppe Peano introduced the space-filling curves, curved lines that twist and turn enough to fill the whole of any square, or cube, or hypercube, or finite-dimensional space. These curves are not a direct proof that a line has the same number of points as a finite-dimensional space, but they can be used to obtain such a proof.
Cantor also showed that sets with cardinality strictly greater than <math>\mathfrak c</math> exist (see his generalized diagonal argument and theorem). They include, for instance:
:* the set of all subsets of R, i.e., the power set of R, written P(R) or 2<sup>R</sup>
:* the set R<sup>R</sup> of all functions from R to R
Both have cardinality
:<math>2^\mathfrak {c} = \beth_2 > \mathfrak c </math>
:(see Beth two).
The cardinal equalities <math>\mathfrak{c}^2 \mathfrak{c},</math> <math>\mathfrak c^{\aleph_0} \mathfrak c,</math> and <math>\mathfrak c ^{\mathfrak c} = 2^{\mathfrak c}</math> can be demonstrated using cardinal arithmetic:
:<math>\mathfrak{c}^2 \left(2^{\aleph_0}\right)^2 2^{2\times{\aleph_0}} 2^{\aleph_0} \mathfrak{c},</math>
:<math>\mathfrak c^{\aleph_0} \left(2^{\aleph_0}\right)^{\aleph_0} 2^{{\aleph_0}\times{\aleph_0}} 2^{\aleph_0} \mathfrak{c},</math>
:<math> \mathfrak c ^{\mathfrak c} \left(2^{\aleph_0}\right)^{\mathfrak c} 2^{\mathfrak c\times\aleph_0} 2^{\mathfrak c}.</math>Examples and properties* If X {a, b, c} and Y {apples, oranges, peaches}, where a, b, and c are distinct, then | X | | Y | because { (a, apples), (b, oranges), (c, peaches)} is a bijection between the sets X and Y. The cardinality of each of X and Y is 3.
* If | X | ≤ | Y |, then there exists Z such that | X | = | Z | and Z ⊆ Y.
*If | X | ≤ | Y | and | Y | ≤ | X |, then | X | = | Y |. This holds even for infinite cardinals, and is known as Cantor–Bernstein–Schroeder theorem.
* Sets with cardinality of the continuum include the set of all real numbers, the set of all irrational numbers and the interval <math>[0, 1]</math>.
Union and intersection
If A and B are disjoint sets, then
:<math>\left\vert A \cup B \right\vert = \left\vert A \right\vert + \left\vert B \right\vert.</math>
From this, one can show that in general, the cardinalities of unions and intersections are related by the following equation:
:<math> \left\vert C \cup D \right\vert + \left\vert C \cap D \right\vert \left\vert C \right\vert + \left\vert D \right\vert.</math>Definition of cardinality in class theory (NBG or MK)
Here <math>V</math> denote a class of all sets, and <math>\mbox{Ord}</math> denotes the class of all ordinal numbers.
:<math>|A|:=\mbox{Ord}\cap\bigcap \{\alpha\in\mbox{Ord}|\exists (f:A\to\alpha):(f\mbox{ injective})\}</math>
We use the intersection of a class which is defined by <math>(x\in\bigcap Q)\iff(\forall q\in Q:x\in q)</math>, therefore <math>\bigcap\emptyset = V</math>.
In this case
:<math>(x\mapsto|x|):V\to\mbox{Ord}</math>.
This definition allows also obtain a cardinality of any proper class <math>P</math>, in particular
:<math>|P|=\mbox{Ord}</math>
This definition is natural since it agrees with the axiom of limitation of size which implies bijection between <math>V</math> and any proper class.
See also
* Aleph number
* Beth number
* Cantor's paradox
* Cantor's theorem
* Countable set
* Counting
* Ordinality
* Pigeonhole principle
References
Category:Basic concepts in infinite set theory
|
https://en.wikipedia.org/wiki/Cardinality
|
2025-04-05T18:27:43.963186
|
6176
|
Cecil B. DeMille
|
| birth_name = Cecil Blount DeMille
| birth_date
| birth_place = Ashfield, Massachusetts, U.S.
| death_date
| death_place = Los Angeles, California, U.S.
| resting_place = Hollywood Forever Cemetery
| other_names | alma_mater Pennsylvania Military College<br />American Academy of Dramatic Arts
| occupation =
| years_active = 1899–1958
| known_for | party Republican
| children = 4, including Katherine DeMille (adopted) and Richard de Mille (adopted)
| parents = Henry Churchill de Mille<br />Matilda Beatrice deMille
| relatives = William C. deMille (brother)<br />Agnes de Mille (niece)<br />Peggy George (niece)
| awards | website
| spouse =
}}
Cecil Blount DeMille (; August 12, 1881January 21, 1959) was an American filmmaker and actor. Between 1914 and 1958, he made 70 features, both silent and sound films. He is acknowledged as a founding father of American cinema and the most commercially successful producer-director in film history, with many films dominating the box office three or four at a time. His films were distinguished by their epic scale and by his cinematic showmanship. His silent films included social dramas, comedies, Westerns, farces, morality plays, and historical pageants. He was an active Freemason and member of Prince of Orange Lodge #16 in New York City.
DeMille was born in Ashfield, Massachusetts, where his parents were vacationing for the summer. He grew up in New York City. He began his career as a stage actor in 1900. He later began to write and direct stage plays, a few with his older brother William de Mille, and some with Jesse L. Lasky, who was then a vaudeville producer.
DeMille's first film, The Squaw Man (1914), was the first full-length feature film shot in Hollywood. Its interracial love story was commercially successful, and the film marked Hollywood as the new home of the U.S. film industry. It had previously been based in New York and New Jersey. Based on continued film successes, DeMille founded Famous Players Lasky which was later reverse merged into Paramount Pictures with Lasky and Adolph Zukor. His first biblical epic, The Ten Commandments (1923), was both a critical and commercial success; it held the Paramount revenue record for 25 years.
DeMille directed The King of Kings (1927), a biography of Jesus, which gained approval for its sensitivity and reached more than 800 million viewers. The Sign of the Cross (1932) is said to be the first sound film to integrate all aspects of cinematic technique. Cleopatra (1934) was his first film to be nominated for the Academy Award for Best Picture.
After more than 30 years in film production, DeMille reached a pinnacle in his career with Samson and Delilah (1949), a biblical epic that became the highest-grossing film of 1950. Along with biblical and historical narratives, he also directed films oriented toward "neo-naturalism", which tried to portray the laws of man fighting the forces of nature.
DeMille received his first nomination for the Academy Award for Best Director for his circus drama The Greatest Show on Earth (1952), which won both the Academy Award for Best Picture and the Golden Globe Award for Best Motion Picture – Drama. His last and best-known film, The Ten Commandments (1956), also a Best Picture Academy Award nominee, and it is<!--as of date --> the eighth-highest-grossing film of all time, adjusted for inflation.
In addition to his Best Picture Awards, DeMille received an Academy Honorary Award for his film contributions, the Palme d'Or (posthumously) for Union Pacific (1939), a DGA Award for Lifetime Achievement, and the Irving G. Thalberg Memorial Award. He was the first recipient of the Golden Globe Cecil B. DeMille Award, which was named in his honor. DeMille's reputation had a renaissance in the 2010s, and his work has influenced numerous other films and directors.
Biography
1881–1899: early years
Cecil Blount DeMille was of paternal Dutch ancestry. His surname was spelled de Mil before his grandfather William added an "le" for "visual symmetry".
As an adult, Cecil De Mille adopted the spelling DeMille because he believed it would look better on a marquee, but continued to use de Mille in private life. The family name de Mille was used by his children Cecilia, John, Richard, and Katherine. Cecil's brother, William, and his daughters, Margaret and Agnes, as well as DeMille's granddaughter, Cecilia de Mille Presley, also used the de Mille spelling.
DeMille was born on August 12, 1881, in a boarding house on Main Street in Ashfield, Massachusetts, where his parents had been vacationing for the summer. On September 1, 1881, the family returned with the newborn DeMille to their flat in New York. DeMille was named after his grandmothers Cecelia Wolff and Margarete Blount. He was the second of three children of Henry Churchill de Mille (September 4, 1853 – February 10, 1893) and his wife, Matilda Beatrice deMille (née Samuel; January 30, 1853 – October 8, 1923), known as Beatrice. His older brother, William C. deMille, was born on July 25, 1878.
Henry de Mille, whose ancestors were of English and Dutch-Belgian descent, was a North Carolina-born dramatist, actor, and lay reader in the Episcopal Church. In New York, Henry also taught English at Columbia College (now Columbia University). He worked as a playwright, administrator, and faculty member during the early years of the American Academy of Dramatic Arts, established in New York City in 1884. Henry de Mille frequently collaborated with David Belasco in playwriting; their best-known collaborations included "The Wife", "Lord Chumley", "The Charity Ball", and "Men and Women".
Cecil B. DeMille's mother, Beatrice, a literary agent and scriptwriter, was the daughter of German Jews. She had emigrated from England with her parents in 1871 when she was 18; the newly arrived family settled in Brooklyn, New York, where they maintained a middle-class, English-speaking household.
DeMille's parents met as members of a music and literary society in New York. Henry was a tall, red-headed student. Beatrice was intelligent, educated, forthright, and strong-willed. They married on July 1, 1876, despite Beatrice's parents' objections because of the young couple's differing religions; Beatrice converted to Episcopalianism. until Henry built a three-story Victorian-style house for his family in Pompton Lakes, New Jersey<!-- When was this? -->; they named this estate "Pamlico". John Philip Sousa was a friend of the family, and DeMille recalled throwing mud balls in the air so neighbor Annie Oakley <!-- North Carolina or New Jersey? -->could practice her shooting. DeMille's sister, Agnes, was born on April 23, 1891; his mother nearly did not survive the birth. Agnes died on February 11, 1894, from spinal meningitis.
DeMille's parents operated a private school in Pompton Lakes and attended Christ Episcopal Church. DeMille recalled that this church was the place where he visualized the story of his 1923 version of The Ten Commandments.
On January 8, 1893, at age 40, Henry de Mille died suddenly from typhoid fever, leaving Beatrice with three children. To provide for her family, she opened the Henry C. de Mille School for Girls in her home in February 1893. The aim of the school was to teach young women to properly understand and fulfill the women's duty to themselves, their home, and their country. Beatrice had "enthusiastically supported" Henry's theatrical aspirations. She later became the second female play broker on Broadway. On Henry's deathbed, he told his wife that he did not want his sons to become playwrights. DeMille's mother sent him to Pennsylvania Military College (now Widener University) in Chester, Pennsylvania, at age 15. He fled the school to join the Spanish–American War, but failed to meet the age requirement. At the military college, even though his grades were average, he reportedly excelled in personal conduct.
DeMille attended the American Academy of Dramatic Arts (tuition-free due to his father's service to the academy). He graduated in 1900, and for graduation, his performance was the play The Arcady Trail. In the audience was Charles Frohman, who cast DeMille in his play Hearts are Trumps, DeMille's Broadway debut.
1900–1912: theater
Charles Frohman, Constance Adams, and David Belasco
Cecil B. DeMille began his career as an actor on stage in 1900 in the theatrical company of Charles Frohman. He debuted on February 21, 1900, in the play Hearts Are Trumps at New York's Garden Theater. In 1901, DeMille starred in productions of A Repentance, To Have and to Hold, and Are You a Mason? At age 21, he married Constance Adams on August 16, 1902, at Adams's father's home in East Orange, New Jersey. The wedding party was small. Beatrice DeMille's family did not attend. Simon Louvish suggests that this was to conceal DeMille's partial Jewish heritage. Adams was 29 years old at the time of the marriage. They had met in a theater in Washington D.C. while they were both acting in Hearts Are Trumps.
They were sexually incompatible; according to DeMille, Adams was too "pure" to "feel such violent and evil passions" as he. DeMille had more violent sexual preferences and fetishes than his wife. Adams allowed DeMille to have several long-term mistresses during their marriage as an outlet while maintaining an appearance of a faithful marriage. One of DeMille's affairs was with his screenwriter Jeanie MacPherson. Despite his reputation for extramarital affairs, DeMille did not like to have affairs with his stars, as he believed it would cause him to lose control as a director. He once said he maintained his self-control when Gloria Swanson sat on his lap, and refused to touch her.
In 1902, he played a small part in Hamlet. Publicists wrote that he became an actor in order to learn how to direct and produce, but DeMille admitted that he became an actor in order to pay the bills. From 1904 to 1905, he attempted to make a living as a stock theater actor with his wife, Constance. DeMille made a 1905 reprise in Hamlet as Osric. In the summer of 1905, DeMille joined the stock cast at the Elitch Theatre in Denver, Colorado. He appeared in 11 of the 15 plays presented that season, all in minor roles. Maude Fealy was the featured actress in several productions that summer and developed a lasting friendship with DeMille. (He later cast her in The Ten Commandments.)
His brother, William, was establishing himself as a playwright and sometimes invited DeMille to collaborate. DeMille and William collaborated on The Genius, The Royal Mounted, and After Five. None of these was very successful. William de Mille was most successful when he worked alone.
DeMille and his brother at times worked with the legendary impresario David Belasco, who had been a friend and collaborator of their father. DeMille later adapted Belasco's The Girl of the Golden West, Rose of the Rancho, and The Warrens of Virginia into films. He was credited with the conception of Belasco's The Return of Peter Grimm. The Return of Peter Grimm sparked controversy, because Belasco had taken DeMille's unnamed screenplay, changed the characters, and named it The Return of Peter Grimm, producing and presenting it as his own work. DeMille was credited in small print as "based on an idea by Cecil DeMille". The play was successful, and DeMille was distraught that his childhood idol had plagiarized his work.
Losing interest in theater
DeMille performed on stage with actors he later directed in films: Charlotte Walker, Mary Pickford, and Pedro de Cordoba. He also produced and directed plays. His 1905 performance in The Prince Chap as the Earl of Huntington was well received by audiences.
DeMille wrote a few of his own plays in between stage performances, but his playwriting was less successful. His first play was The Pretender-A Play in a Prologue and 4 Acts set in 17th-century Russia. Another unperformed play he wrote was Son of the Winds, a mythological Native American story. Life was difficult for DeMille and his wife as traveling actors, but travel allowed him to experience parts of the United States he had not yet seen. DeMille sometimes worked with the director E. H. Sothern, who influenced DeMille's later perfectionism. In 1907, due to a scandal with one of Beatrice's students, Evelyn Nesbit, the Henry de Mille School lost students. The school closed, and Beatrice filed for bankruptcy. DeMille wrote another play originally called Sergeant Devil May Care and renamed The Royal Mounted. He also toured with the Standard Opera Company, but there are few records of his singing ability.
On November 5, 1908, Constance and DeMille had a daughter, Cecilia, their only biological child. In the 1910s, DeMille began directing and producing other writers' plays.
DeMille was poor and struggled to find work. Consequently, his mother hired him for her agency, The DeMille Play Company, and taught him how to be an agent and a playwright. He became the agency's manager and later a junior partner with his mother. In 1911, DeMille became acquainted with vaudeville producer Jesse Lasky when Lasky was searching for a writer for his new musical. He initially sought out William deMille. William had been a successful playwright, but DeMille was suffering from the failure of his plays The Royal Mounted and The Genius.
Beatrice introduced Lasky to Cecil DeMille instead. The collaboration of DeMille and Lasky produced a successful musical, California, which opened in New York in January 1912. Another DeMille-Lasky production that opened in January 1912 was The Antique Girl. In the spring of 1913, DeMille found success producing Reckless Age by Lee Wilson, a play about a high-society girl wrongly accused of manslaughter, starring Frederick Burton and Sydney Shields. But changes in the theater rendered DeMille's melodramas obsolete before they were produced, and true theatrical success eluded him. He produced many flops. Having become uninterested in working in theater, DeMille became ignited by passion for film when he watched the 1912 French film Les Amours de la reine Élisabeth.
1913–1914: entering films
'' (1914) full film]]
Desiring a change of scene, DeMille, Lasky, Sam Goldfish (later Samuel Goldwyn), and a group of East Coast businessmen created the Jesse L. Lasky Feature Play Company in 1913, of which DeMille became director-general. Lasky and DeMille were said to have sketched out the organization of the company on the back of a restaurant menu. As director-general, DeMille's job was to make the films. In addition to directing, he was the supervisor and consultant for the first year of films the company made. Sometimes, he directed scenes for other directors at the company in order to release films on time. Moreover, he co-authored other Lasky Company scripts and created screen adaptations that others directed.
The Lasky Play Company tried to recruit William de Mille, but he rejected the offer because he did not believe there was any promise in a film career. When William found out that DeMille had begun working in the motion picture industry, he wrote his brother a letter, saying that he was disappointed that Cecil was willing "to throw away [his] future" when he was "born and raised in the finest traditions of the theater".
The Lasky Company wanted to attract high-class audiences to their films, so it began producing films from literary works. The company bought the rights to Edwin Milton Royle's play The Squaw Man and cast Dustin Farnum in the lead role. It offered Farnum a choice between a quarter stock in the company or $250 in weekly salary. Farnum chose the salary. Already $15,000 in debt to Royle for the screenplay of The Squaw Man, Lasky's relatives bought the $5,000 stock to save the Lasky Company from bankruptcy. With no knowledge of filmmaking, DeMille was introduced to observe the process at film studios. He was eventually introduced to Oscar Apfel, a stage director who had been a director with the Edison Company.
On December 12, 1913, DeMille, his cast, and crew boarded a Southern Pacific train bound for Flagstaff via New Orleans. His tentative plan was to shoot a film in Arizona, but he felt that Arizona lacked the Western look they were searching for. They also learned that other filmmakers were successfully shooting in Los Angeles, even in winter. He continued to Los Angeles. Once there, he chose not to shoot in Edendale, where many studios were, but in Hollywood. DeMille rented a barn to function as their film studio. Filming began on December 29, 1913, and lasted three weeks. Apfel filmed most of The Squaw Man due to DeMille's inexperience, but DeMille learned quickly and was particularly adept at impromptu screenwriting as necessary. He made his first film run 60 minutes, as long as a short play. The Squaw Man (1914), co-directed by Apfel, was a sensation, and it established the Lasky Company. It was the first feature-length film made in Hollywood. There were problems with the perforation of the film stock, and it was discovered the DeMille had brought a cheap British film perforator that had punched in 65 holes per foot instead of the industry standard of 64. Lasky and DeMille convinced film pioneer Siegmund Lubin of the Lubin Manufacturing Company to have his experienced technicians reperforate the film.
This was the first American feature film, according to its release date. D. W. Griffith's Judith of Bethulia was filmed earlier than The Squaw Man, but released later. This as the only film in which DeMille shared director's credit with Apfel.
The Squaw Man was a success, which led to the eventual founding of Paramount Pictures and Hollywood becoming the "film capital of the world". The film grossed more than ten times its budget after its New York premiere in February 1914. DeMille's next project was to aid Apfel in directing ''Brewster's Millions'', which was wildly successful. In December 1914, Constance Adams brought home John DeMille, a 15-month-old boy, whom the couple legally adopted three years later. Biographer Scott Eyman suggested that she may have decided to adopt after recently having had a miscarriage.}}
1915–1928: silent era
Westerns, Paradise, and World War I
Cecil B. DeMille's second film, credited exclusively to him, was The Virginian. It is the earliest of DeMille's films available in a quality, color-tinted video format, but that version is actually a 1918 rerelease. The Lasky Company's first few years were spent making films nonstop. DeMille directed 20 films by 1915. The most successful films during this period were ''Brewster's Millions (co-directed by DeMille), Rose of the Rancho, and The Ghost Breaker''. DeMille adapted Belasco's dramatic lighting techniques to film technology, mimicking moonlight with U.S. cinema's first attempts at "motivated lighting" in The Warrens of Virginia. This was the first of a few film collaborations with his brother William. They struggled to adapt the play from the stage to the set. After the film was shown, viewers complained that the shadows and lighting prevented the audience from seeing the actors' full faces and said they would pay only half price. Sam Goldwyn suggested that if they called it "Rembrandt" lighting, the audience would pay double the price. Additionally, because of DeMille's cordiality after the Peter Grimm incident, DeMille was able to rekindle his partnership with Belasco. He adapted several of Belasco's screenplays into film.
DeMille's most successful film was The Cheat; his direction in the film was acclaimed. In 1916, exhausted from three years of nonstop filmmaking, DeMille purchased land in the Angeles National Forest for a ranch that would become his getaway. He called this place "Paradise", declaring it a wildlife sanctuary; no shooting of animals besides snakes was allowed. His wife did not like Paradise, so DeMille often brought his mistresses there with him, including actress Julia Faye. In 1921, DeMille purchased a yacht he called The Seaward.}}
While filming The Captive in 1915, an extra, Charles Chandler, died on set when another extra failed to heed DeMille's orders to unload all guns for rehearsal. DeMille instructed the guilty man to leave town and never revealed his name. Lasky and DeMille maintained Chandler's widow on the payroll and, according to leading actor House Peters Sr., DeMille refused to stop production for Chandler's funeral. Peters said that he encouraged the cast to attend the funeral with him anyway since DeMille would not be able to shoot the film without him. On July 19, 1916, the Jesse Lasky Feature Play Company merged with Adolph Zukor's Famous Players Film Company, becoming Famous Players–Lasky. Zukor became president, Lasky vice president, DeMille director-general, and Goldwyn chairman of the board. Famous Players–Lasky later fired Goldwyn for frequent clashes with Lasky, DeMille, and Zukor. While on a European vacation in 1921, DeMille contracted rheumatic fever in Paris. He was confined to bed and unable to eat. His poor physical condition upon his return home affected the production of his 1922 film Manslaughter. According to Richard Birchard, DeMille's weakened state during production may have led to the film being received as uncharacteristically substandard.
During World War I, the Famous Players–Lasky organized a military company underneath the National Guard, the Home Guard, made up of film studio employees, with DeMille as captain. Eventually, the Guard was enlarged to a battalion and recruited soldiers from other film studios. They took time off weekly to practice military drills. Additionally, during the war, DeMille volunteered for the Justice Department's Intelligence Office, investigating friends, neighbors, and others he came in contact with in connection with the Famous Players–Lasky. He also volunteered for the Intelligence Office during World War II. DeMille considered enlisting in World War I, but stayed in the U.S. and made films. He did take a few months to set up a movie theater for the French front. Famous Players–Lasky donated the films. DeMille and Adams adopted Katherine Lester in 1920, whom Adams had found in the orphanage she directed. In 1922, the couple adopted Richard deMille. DeMille became a notable psychiatrist, filmmaker and writer.}}
Scandalous dramas, Biblical epics, and departure from Paramount
Film started becoming more sophisticated and the Lasky company's subsequent films were criticized for primitive and unrealistic set design. Consequently, Beatrice deMille introduced the Famous Players–Lasky to Wilfred Buckland, whom DeMille knew from his time at the American Academy of Dramatic Arts, and he became DeMille's art director. William deMille reluctantly became a story editor. William later converted from theater to Hollywood and spent the rest of his career as a film director. DeMille frequently remade his own films. In 1917, he remade The Squaw Man (1918), only four years after the original. Despite its quick turnaround, the film was fairly successful. DeMille's second remake at MGM in 1931 was a failure.
After five years and 30 hit films, DeMille became the American film industry's most successful director. In the silent era, he was renowned for Male and Female (1919), Manslaughter (1922), The Volga Boatman (1926), and The Godless Girl (1928). His trademark scenes included bathtubs, lion attacks, and Roman orgies. Many of his films featured scenes in two-color Technicolor. In 1923, DeMille released the modern melodrama The Ten Commandments, a significant change from his previous irreligious films. The film was produced on a budget of $600,000, Paramount's most expensive production. This concerned Paramount executives, but the film was the studio's highest-grossing film. It held the Paramount record for 25 years until DeMille broke the record again.
In the early 1920s, scandal surrounded Paramount; religious groups and the media opposed portrayals of immorality in films. A censorship board called the Hays Code was established. DeMille's film The Affairs of Anatol came under fire. Furthermore, DeMille argued with Zukor over his extravagant and over-budget production costs. Consequently, DeMille left Paramount in 1924 despite having helped establish it. He joined the Producers Distributing Corporation. His first film in the new production company, DeMille Pictures Corporation, was The Road to Yesterday in 1925. He directed and produced four films on his own, working with Producers Distributing Corporation because he found front office supervision too restricting. Aside from The King of Kings, none of DeMille's films away from Paramount were successful. The King of Kings established DeMille as "master of the grandiose and of biblical sagas". Considered at the time the most successful Christian film of the silent era, DeMille calculated that it had been viewed over 800 million times around the world. After the release of DeMille's The Godless Girl, silent films in America became obsolete, and DeMille was forced to shoot a shoddy final reel with the new sound production technique. Although this final reel looked so different from the first 11 reels that it appeared to be from another movie, according to Simon Louvish, the film is one of DeMille's strangest and most "DeMillean" film.
The immense popularity of DeMille's silent films enabled him to branch out into other areas. The Roaring Twenties were the boom years and DeMille took full advantage, opening the Mercury Aviation Company, one of America's first commercial airlines. He was also a real estate speculator, and vice president of the Commercial National Trust and Savings Bank in Los Angeles, where he approved loans for other filmmakers. In 1916, DeMille purchased a mansion in Hollywood. Charlie Chaplin lived next door for a time, and after he moved, DeMille purchased the other house and combined the estates.
1929–1956: sound era
MGM and return to Paramount
When "talking pictures" were invented in 1928, DeMille made a successful transition, offering his own innovations to the painful process; he devised a microphone boom and a soundproof camera blimp. He also popularized the camera crane. His first three sound films, Dynamite, Madame Satan, and his 1931 remake of The Squaw Man, were produced at Metro-Goldwyn-Mayer. These films were critically and financially unsuccessful. He had completely adapted to the production of sound film despite the film's poor dialogue. After his contract ended at MGM, he left, but no production studios would hire him. He attempted to create a guild of a half a dozen directors with the same creative desires called the Director's Guild, but the idea failed due to lack of funding and commitment. Moreover, the Internal Revenue Service audited DeMille due to issues with his production company. This was, according to DeMille, the lowest point of his career. He traveled abroad to find employment until he was offered a deal at Paramount.
In 1932, DeMille returned to Paramount at Lasky's request, bringing with him his own production unit. His first film back at Paramount, The Sign of the Cross, was also his first success since leaving Paramount besides The King of Kings. Zukor approved DeMille's return on the condition that DeMille not exceed his production budget of $650,000 for The Sign of the Cross. Produced in eight weeks without exceeding budget, the film was financially successful. The Sign of the Cross was the first film to integrate all cinematic techniques. The film was considered a "masterpiece" and surpassed the quality of other sound films of the time. DeMille followed this epic with two dramas released in 1933 and 1934, This Day and Age and Four Frightened People. These were box-office disappointments, though Four Frightened People received good reviews. DeMille stuck to large-budget spectaculars for the rest of his career.Politics and Lux Radio TheatreDeMille was outspoken about his Episcopalian integrity, but his private life included mistresses and adultery. He was a conservative Republican activist, becoming more conservative as he aged. He was known as anti-union and worked to prevent the unionization of film production studios. But according to DeMille himself, he was not anti-union and belonged to a few unions. He said he was rather against union leaders such as Walter Reuther and Harry Bridges, whom he compared to dictators. He supported Herbert Hoover and in 1928 made his largest campaign donation to Hoover. But DeMille also liked Franklin D. Roosevelt, finding him charismatic, tenacious, and intelligent, and agreeing with Roosevelt's abhorrence of Prohibition. DeMille lent Roosevelt a car for his 1932 United States presidential election campaign and voted for him. He never again voted for a Democratic candidate in a presidential election.
From June 1, 1936, until January 22, 1945, DeMille hosted and directed Lux Radio Theatre, a weekly digest of current feature films. Broadcast on the Columbia Broadcasting System (CBS) from 1935 to 1954, Lux Radio was one of the most popular weekly shows in radio history. While DeMille was host, the show had 40 million weekly listeners and DeMille had an annual salary of $100,000. From 1936 to 1945, he produced, hosted, and directed every show, with the occasional exception of a guest director. He resigned from Lux Radio because he refused to pay a dollar to the American Federation of Radio Artists (AFRA), on the principle that no organization had the right to "levy a compulsory assessment upon any member".
DeMille sued the union for reinstatement but lost. He appealed to the California Supreme Court and lost again. When the AFRA expanded to television, DeMille was banned from television appearances. Consequently, he formed the DeMille Foundation for Political Freedom to campaign for the right to work. He gave speeches across the nation for the next few years. DeMille's primary criticism was of closed shops, but later included criticism of communism and unions in general. The U.S. Supreme Court declined to review his case, but DeMille lobbied for the Taft–Hartley Act, which passed. It prohibited denying anyone the right to work if they refuse to pay a political assessment. But the law did not apply retroactively, so DeMille's television and radio appearance ban lasted the rest of his life, though he was permitted to appear on radio or television to publicize a movie. William Keighley replaced him. DeMille never worked in radio again.}}
Adventure films and dramatic spectacles
In 1939, DeMille's Union Pacific was successful through DeMille's collaboration with the Union Pacific Railroad. The Union Pacific gave DeMille access to historical data, early period trains, and expert crews, adding to the film's authenticity. During pre-production, DeMille was dealing with his first serious health issue. In March 1938, he underwent a major emergency prostatectomy. He had a post-surgery infection from which he nearly did not recover, citing streptomycin as his saving grace. The surgery caused him to suffer from sexual dysfunction for the rest of his life, according to some family members. After his surgery and the success of Union Pacific, DeMille first used three-strip Technicolor in 1940, in North West Mounted Police. DeMille wanted to film in Canada, but due to budget constraints, the film was instead shot in Oregon and Hollywood. Critics were impressed with the visuals but found the scripts dull, calling it DeMille's "poorest Western". Despite the criticism, it was Paramount's highest-grossing film of the year. Audiences liked its highly saturated color, so DeMille made no further black-and-white features. DeMille was anti-communist and abandoned a project in 1940 to film Ernest Hemingway's For Whom the Bell Tolls due to its communist themes, even though he had already paid $100,000 for the rights to the novel. He was so eager to produce the film that he hadn't yet read it. He claimed he abandoned the project in order to complete a different project, but it was actually to preserve his reputation and avoid appearing reactionary.}} While concurrently filmmaking, he served during World War II at age 60 as his neighborhood air-raid warden.
In 1942, DeMille worked with Jeanie MacPherson and William deMille to produce a film, Queen of Queens, that was intended to be about Mary, mother of Jesus. After reading the screenplay, Daniel A. Lord warned DeMille that Catholics would find the film too irreverent while non-Catholics would consider it Catholic propaganda. Consequently, the film was never made. MacPherson worked as a scriptwriter on many of DeMille's films.}} In 1938, DeMille supervised the film compilation Land of Liberty as the American film industry's contribution to the 1939 New York World's Fair. He used clips from his own films in it. Land of Liberty was not high-grossing, but it was well-received, and DeMille was asked to shorten its running time to allow for more showings per day. MGM distributed the film in 1941 and donated profits to World War II relief charities.
'' (1952), the film for which he won the Academy Award for Best Picture|alt=Closeup of DeMille leaning on a setpiece]]
In 1942, DeMille released Paramount's most successful film, Reap the Wild Wind. It had a large budget and many special effects, including an electronically operated giant squid. After working on it, DeMille was the master of ceremonies at a rally organized by David O. Selznick in the Los Angeles Coliseum in support of the Dewey–Bricker presidential ticket as well as Governor Earl Warren of California.}} DeMille's 1947 film Unconquered had the longest running time (146 minutes), longest filming schedule (102 days), and largest budget ($5 million). Its sets and effects were so realistic that 30 extras needed to be hospitalized due to a scene with fireballs and flaming arrows. It was commercially very successful.
DeMille's next film, Samson and Delilah (1949), was Paramount's highest-grossing film up to that time. A Biblical epic with sex, it was a characteristically DeMille film. 1952's The Greatest Show on Earth became Paramount's highest-grossing film to that point and won the Academy Award for Best Picture and the Academy Award for Best Story. It began production in 1949. Ringling Brothers-Barnum and Bailey were paid $250,000 for use of the title and facilities. DeMille toured with the circus while helping write the script. Noisy and bright, the film was not well-liked by critics but was an audience favorite. In 1953, DeMille signed a contract with Prentice Hall to publish an autobiography. He reminisced into a voice recorder, the recording was transcribed, and the information was organized by topic. Art Arthur also interviewed people for the autobiography. DeMille did not like the biography's first draft, saying he thought the person portrayed in it was an egotistical "SOB". In the early 1950s, Allen Dulles and Frank Wisner recruited DeMille to serve on the board of the anti-communist National Committee for a Free Europe, the public face of the organization that oversaw Radio Free Europe. In 1954, Secretary of the Air Force Harold E. Talbott asked DeMille for help designing the cadet uniforms at the newly established United States Air Force Academy. DeMille's designs, most notably that of the cadet parade uniform, were praised by Air Force and Academy leadership, adopted, and still worn.Final works and unrealized projects |source – Alfred Zukor responding to DeMille's proposal of The Ten Commandments remake |width25% |align=right}}
In 1952, DeMille sought approval for a lavish remake of his 1923 silent film The Ten Commandments. He went before the Paramount board of directors, which was mostly Jewish-American. The board rejected his proposal, even though his last two films, Samson and Delilah and The Greatest Show on Earth, had been record-breaking hits. Adolph Zukor convinced the board to change its mind on the grounds of morality. DeMille did not have an exact budget proposal for the project, and it promised to be the most costly in U.S. film history. Still, the board unanimously approved it. The Ten Commandments, released in 1956, was DeMille's final film. It was the longest (3 hours, 39 minutes) and most expensive ($13 million) film in Paramount history. Production began in October 1954. The Exodus scene was filmed on-site in Egypt with four Technicolor-VistaVision cameras filming 12,000 people. Filming continued in 1955 in Paris and Hollywood on 30 different sound stages. They even expanded to RKO sound studios for filming. Post-production lasted a year, and the film premiered in Salt Lake City. Nominated for an Academy Award for Best Picture, it grossed over $80 million, which surpassed the gross of The Greatest Show on Earth and every other film in history except Gone with the Wind. DeMille offered ten percent of his profit to the crew, a unique practice at the time.
On November 7, 1954, while in Egypt filming the Exodus sequence for The Ten Commandments, DeMille (who was 73) climbed a ladder to the top of the set and had a serious heart attack. Despite the urging of his associate producer, DeMille wanted to return to the set right away. He developed a plan with his doctor to allow him to continue directing while reducing his physical stress. DeMille completed the film, but his health was diminished by several more heart attacks. His daughter Cecilia took over as director as DeMille sat behind the camera with Loyal Griggs as the cinematographer. This film was his last.}}
Due to his frequent heart attacks, DeMille asked his son-in-law, actor Anthony Quinn, to direct a remake of his 1938 film The Buccaneer. DeMille served as executive producer, overseeing producer Henry Wilcoxon. Despite a cast led by Charlton Heston and Yul Brynner, the 1958 film The Buccaneer was a disappointment. DeMille attended its Santa Barbara premiere in December 1958. He was unable to attend its Los Angeles premiere. In the months before his death, DeMille was researching a film biography of Robert Baden-Powell, the founder of the Scout Movement. DeMille asked David Niven to star in the film, but it was never made. DeMille also was planning a film about the space race and a biblical epic based on the Book of Revelation. His autobiography was mostly complete when he died, and was published in November 1959.DeathDeMille suffered a series of heart attacks from June 1958 to January 1959, and died on January 21, 1959, following an attack. After his death, news outlets such as The New York Times, the Los Angeles Times, and The Guardian called DeMille a "pioneer of movies", "the greatest creator and showman of our industry", and "the founder of Hollywood". DeMille left his multi-million dollar estate in Los Feliz, Los Angeles, in Laughlin Park to his daughter Cecilia because his wife had dementia and was unable to care for an estate. She died a year later. The house was auctioned by his granddaughter Cecilia DeMille Presley, who also lived there in the late 1980s.FilmmakingInfluencesDeMille believed his first influences to be his parents, Henry and Beatrice DeMille. His playwright father introduced him to the theater at a young age. Henry was heavily influenced by the work of Charles Kingsley, whose ideas trickled down to DeMille. DeMille noted that his mother had a "high sense of the dramatic" and was determined to continue the artistic legacy of her husband after he died. Beatrice became a play broker and author's agent, influencing DeMille's early life and career. DeMille's father worked with David Belasco who was a theatrical producer, impresario, and playwright. Belasco was known for adding realistic elements in his plays such as real flowers, food, and aromas that could transport his audiences into the scenes. While working in theatre, DeMille used real fruit trees in his play California, as influenced by Belasco. Similar to Belasco, DeMille's theatre revolved around entertainment rather than artistry. Generally, Belasco's influence of DeMille's career can be seen in DeMille's showmanship and narration. E. H. Sothern's early influence on DeMille's work can be seen in DeMille's perfectionism. train wrecks in The Road to Yesterday, Union Pacific and The Greatest Show on Earth; the destruction of an airship in Madam Satan; and the parting of the Red Sea in both versions of The Ten Commandments.
'' (1949)|alt=Large pagan temple film set with a large idol in the middle, and surrounded by hieroglyphics and red drapery]]
In his early films, DeMille experimented with photographic light and shade, which created dramatic shadows instead of glare. His specific use of lighting, influenced by his mentor David Belasco, was for the purpose of creating "striking images" and heightening "dramatic situations". DeMille was unique in using this technique. In addition to his use of volatile and abrupt film editing, his lighting and composition were innovative for the time period as filmmakers were primarily concerned with a clear, realistic image. Another important aspect of DeMille's editing technique was to put the film away for a week or two after an initial edit in order to re-edit the picture with a fresh mind. This allowed for the rapid production of his films in the early years of the Lasky Company. The cuts were sometimes rough, but the movies were always interesting.
DeMille often edited in a manner that favored psychological space rather than physical space through his cuts. In this way, the characters' thoughts and desires are the visual focus rather than the circumstances regarding the physical scene. As DeMille's career progressed, he increasingly relied on artist Dan Sayre Groesbeck's concept, costume, and storyboard art. Groesbeck's art was circulated on set to give actors and crew members a better understanding of DeMille's vision. His art was even shown at Paramount meetings when pitching new films. DeMille adored the art of Groesbeck, even hanging it above his fireplace, but film staff found it difficult to convert his art into three-dimensional sets. As DeMille continued to rely on Groesbeck, the nervous energy of his early films transformed into more steady compositions of his later films. While visually appealing, this made the films appear more old-fashioned.
Composer Elmer Bernstein described DeMille as "sparing no effort" when filmmaking. Bernstein recalled that DeMille would scream, yell, or flatter—whatever it took to achieve the perfection he required in his films. DeMille was painstakingly attentive to details on set and was as critical of himself as he was of his crew. Costume designer Dorothy Jeakins, who worked with DeMille on The Ten Commandments (1956), said that he was skilled in humiliating people. Jeakins admitted that she received quality training from him, but that it was necessary to become a perfectionist on a DeMille set to avoid being fired. DeMille had an authoritarian persona on set; he required absolute attention from the cast and crew. He had a band of assistants who catered to his needs. He would speak to the entire set, sometimes enormous with countless numbers of crew members and extras, via a microphone to maintain control of the set. He was disliked by many inside and outside of the film industry for his cold and controlling reputation.}}
DeMille was known for autocratic behavior on the set, singling out and berating extras who were not paying attention. Many of these displays were thought to be staged, however, as an exercise in discipline. He despised actors who were unwilling to take physical risks, especially when he had first demonstrated that the required stunt would not harm them. This occurred with Victor Mature in Samson and Delilah. Mature refused to wrestle Jackie the Lion, even though DeMille had just tussled with the lion, proving that he was tame. DeMille told the actor that he was "one hundred percent yellow". Paulette Goddard's refusal to risk personal injury in a scene involving fire in Unconquered cost her DeMille's favor and a role in The Greatest Show on Earth. DeMille did receive help in his films, notably from Alvin Wyckoff, who shot forty-three of DeMille's films; brother William deMille who would occasionally serve as his screenwriter; and Jeanie Macpherson, who served as DeMille's exclusive screenwriter for fifteen years; and Eddie Salven, DeMille's favorite assistant director.
DeMille made stars of unknown actors: Gloria Swanson, Bebe Daniels, Rod La Rocque, William Boyd, Claudette Colbert, and Charlton Heston. He also cast established stars such as Gary Cooper, Robert Preston, Paulette Goddard and Fredric March in multiple pictures. DeMille cast some of his performers repeatedly, including Henry Wilcoxon, Julia Faye, Joseph Schildkraut, Ian Keith, Charles Bickford, Theodore Roberts, Akim Tamiroff, and William Boyd. DeMille was credited by actor Edward G. Robinson with saving his career following his eclipse in the Hollywood blacklist.
Style and themes
Cecil B. DeMille's film production career evolved from critically significant silent films to financially significant sound films. He began his career with reserved yet brilliant melodramas; from there, his style developed into marital comedies with outrageously melodramatic plots. In order to attract a high-class audience, DeMille based many of his early films on stage melodramas, novels, and short stories. He began the production of epics earlier in his career until they began to solidify his career in the 1920s. By 1930, DeMille had perfected his film style of mass-interest spectacle films with Western, Roman, or Biblical themes. DeMille was often criticized for making his spectacles too colorful and for being too occupied with entertaining the audience rather than accessing the artistic and auteur possibilities that film could provide. However, others interpreted DeMille's work as visually impressive, thrilling, and nostalgic. Along the same lines, critics of DeMille often qualify him by his later spectacles and fail to consider several decades of ingenuity and energy that defined him during his generation. Throughout his career, he did not alter his films to better adhere to contemporary or popular styles. Actor Charlton Heston admitted DeMille was, "terribly unfashionable" and Sidney Lumet called DeMille, "the cheap version of D. W. Griffith", adding that DeMille, "[didn't have]...an original thought in his head", though Heston added that DeMille was much more than that.
According to Scott Eyman, DeMille's films were at the same time masculine and feminine due to his thematic adventurousness and his eye for the extravagant. DeMille's distinctive style can be seen through camera and lighting effects as early as The Squaw Man with the use of daydream images; moonlight and sunset on a mountain; and side-lighting through a tent flap. In the early age of cinema, DeMille differentiated the Lasky Company from other production companies due to the use of dramatic, low-key lighting they called "Lasky lighting" and marketed as "Rembrandt lighting" to appeal to the public. DeMille achieved international recognition for his unique use of lighting and color tint in his film The Cheat. DeMille's 1956 version of The Ten Commandments, according to director Martin Scorsese, is renowned for its level of production and the care and detail that went into creating the film. He stated that The Ten Commandments was the final culmination of DeMille's style.
DeMille was interested in art and his favorite artist was Gustave Doré; DeMille based some of his most well-known scenes on the work of Doré. DeMille was the first director to connect art to filmmaking; he created the title of "art director" on the film set. DeMille was also known for his use of special effects without the use of digital technology. Notably, DeMille had cinematographer John P. Fulton create the parting of the Red Sea scene in his 1956 film The Ten Commandments, which was one of the most expensive special effects in film history, and has been called by Steven Spielberg "the greatest special effect in film history". The actual parting of the sea was created by releasing 360,000 gallons of water into a huge water tank split by a U-shaped trough, overlaying it with a film of a giant waterfall that was built on the Paramount backlot, and playing the clip backward.
Aside from his Biblical and historical epics, which are concerned with how man relates to God, some of DeMille's films contained themes of "neo-naturalism", which portray the conflict between the laws of man and the laws of nature. Although he is known for his later "spectacular" films, his early films are held in high regard by critics and film historians. DeMille discovered the possibilities of the "bathroom" or "boudoir" in the film without being "vulgar" or "cheap". DeMille's films Male and Female, Why Change Your Wife?, and The Affairs of Anatol can be retrospectively described as high camp and are categorized as "early DeMille films" due to their particular style of production and costume and set design. However, his earlier films The Captive, Kindling, Carmen, and The Whispering Chorus are more serious films. It is difficult to typify DeMille's films into one specific genre. His first three films were Westerns, and he filmed many Westerns throughout his career. However, throughout his career, he filmed comedies, periodic and contemporary romances, dramas, fantasies, propaganda, Biblical spectacles, musical comedies, suspense, and war films. At least one DeMille film can represent each film genre. DeMille produced the majority of his films before the 1930s, and by the time sound films were invented, film critics saw DeMille as antiquated, with his best filmmaking years behind him.
DeMille's films contained many similar themes throughout his career. However, the films of his silent era were often thematically different from the films of his sound era. His silent-era films often included the "battle of the sexes" theme due to the era of women's suffrage and the enlarging role of women in society. Moreover, before his religious-themed films, many of his silent era films revolved around "husband-and-wife-divorce-and-remarry satires", considerably more adult-themed. According to Simon Louvish, these films reflected DeMille's inner thoughts and opinions about marriage and human sexuality. Religion was a theme that DeMille returned to throughout his career. Of his seventy films, five revolved around stories of the Bible and the New Testament; however many others, while not direct retellings of Biblical stories, had themes of faith and religious fanaticism in films such as The Crusades and The Road to Yesterday. Western and frontier American were also themes that DeMille returned to throughout his career. His first several films were Westerns, and he produced a chain of westerns during the sound era. Instead of portraying the danger and anarchy of the West, he portrayed the opportunity and redemption found in Western America. Another common theme in DeMille's films is the reversal of fortune and the portrayal of the rich and the poor, including the war of the classes and man versus society conflicts such as in The Golden Chance and The Cheat. In relation to his own interests and sexual preferences, sadomasochism was a minor theme present in some of his films. Another minor characteristic of DeMille's films include train crashes, which can be found in several of his films.LegacyKnown as the father of the Hollywood motion picture industry, Cecil B. DeMille made 70 films including several box-office hits. DeMille is one of the more commercially successful film directors in history, with his films before the release of The Ten Commandments estimated to have grossed $650 million worldwide. Adjusted for inflation, DeMille's remake of The Ten Commandments is the eighth highest-grossing film in the world.
According to Sam Goldwyn, critics did not like DeMille's films, but the audiences did, and "they have the final word". Similarly, scholar David Blanke, argued that DeMille had lost the respect of his colleagues and film critics by his late film career. However, his final films maintained that DeMille was still respected by his audiences. Five of DeMille's films were the highest-grossing films at the year of their release, with only Spielberg topping him with six of his films as the highest-grossing films of the year. DeMille's highest-grossing films include: The Sign of the Cross (1932), Unconquered (1947), Samson and Delilah (1949), The Greatest Show on Earth (1952), and The Ten Commandments (1956). Director Ridley Scott has been called "the Cecil B. DeMille of the digital era" due to his classical and medieval epics.
Despite his box-office success, awards, and artistic achievements, DeMille has been dismissed and ignored by critics both during his life and posthumously. He was consistently criticized for producing shallow films without talent or artistic care. Compared to other directors, few film scholars have taken the time to academically analyze his films and style. During the French New Wave, critics began to categorize certain filmmakers as auteurs such as Howard Hawks, John Ford, and Raoul Walsh. DeMille was omitted from the list, thought to be too unsophisticated and antiquated to be considered an auteur. However, Simon Louvish wrote "he was the complete master and auteur of his films", and Anton Kozlovic called him the "unsung American auteur".
DeMille was one of the first directors to become a celebrity in his own right. He cultivated the image of the omnipotent director, complete with megaphone, riding crop, and jodhpurs. He was known for his unique working wardrobe, which included riding boots, riding pants, and soft, open necked shirts. Joseph Henabery recalled that DeMille looked like "a king on a throne surrounded by his court" while directing films on a camera platform.
DeMille was liked by some of his fellow directors and disliked by others, though his actual films were usually dismissed by his peers as a vapid spectacle. Director John Huston intensely disliked both DeMille and his films. "He was a thoroughly bad director", Huston said. "A dreadful showoff. Terrible. To diseased proportions." Said fellow director William Wellman: "Directorially, I think his pictures were the most horrible things I've ever seen in my life. But he put on pictures that made a fortune. In that respect, he was better than any of us." Producer David O. Selznick wrote: "There has appeared only one Cecil B. DeMille. He is one of the most extraordinarily able showmen of modern times. However much I may dislike some of his pictures, it would be very silly of me, as a producer of commercial motion pictures, to demean for an instant his unparalleled skill as a maker of mass entertainment." Salvador Dalí wrote that DeMille, Walt Disney, and the Marx Brothers were "the three great American Surrealists". DeMille appeared as himself in numerous films, including the MGM comedy Free and Easy. He often appeared in his coming-attraction trailers and narrated many of his later films, even stepping on screen to introduce The Ten Commandments''. DeMille was immortalized in Billy Wilder's Sunset Boulevard when Gloria Swanson spoke the line: "All right, Mr. DeMille. I'm ready for my close-up." DeMille plays himself in the film. DeMille's reputation had a renaissance in the 2010s.
As a filmmaker, DeMille was the aesthetic inspiration of many directors and films due to his early influence during the crucial development of the film industry. DeMille's early silent comedies influenced the comedies of Ernst Lubitsch and Charlie Chaplin's A Woman of Paris. Additionally, DeMille's epics such as The Crusades influenced Sergei Eisenstein's Alexander Nevsky. Moreover, DeMille's epics inspired directors such as Howard Hawks, Nicholas Ray, Joseph L. Mankiewicz, and George Stevens to try producing epics. Cecil B. DeMille has influenced the work of several well-known directors. Alfred Hitchcock cited DeMille's 1921 film Forbidden Fruit as an influence of his work and one of his top ten favorite films. DeMille has influenced the careers of many modern directors. Martin Scorsese cited Unconquered, Samson and Delilah, and The Greatest Show on Earth as DeMille films that have imparted lasting memories on him. Scorsese said he had viewed The Ten Commandments forty or fifty times. Famed director Steven Spielberg stated that DeMille's The Greatest Show on Earth was one of the films that influenced him to become a filmmaker. Furthermore, DeMille influenced about half of Spielberg's films, including War of the Worlds. The Ten Commandments inspired DreamWorks Animation's later film about Moses, The Prince of Egypt. As one of the establishing members of Paramount Pictures and co-founder of Hollywood, DeMille had a role in the development of the film industry. Consequently, the name "DeMille" has become synonymous with filmmaking. DeMille received more than a dozen awards from Christian and Jewish religious and cultural groups, including B'nai B'rith. However, not everyone received DeMille's religious films favorably. DeMille was accused of antisemitism after the release of The King of Kings, and director John Ford despised DeMille for what he saw as "hollow" biblical epics meant to promote DeMille's reputation during the politically turbulent 1950s. In response to the claims, DeMille donated some of the profits from The King of Kings to charity. In the 2012 Sight & Sound poll, both DeMille's Samson and Delilah and 1923 version of The Ten Commandments received votes, but did not make the top 100 films. Although many of DeMille's films are available on DVD and Blu-ray release, only 20 of his silent films are commercially available on DVD.Commemoration and tributeswas the place of origin of Paramount Pictures and the location in which The Squaw Man (1913) was filmed. It became the Hollywood Heritage Museum in 1985.|altYellow, house-like barn with a large white museum sign]]
The original Lasky-DeMille Barn in which The Squaw Man was filmed was converted into a museum named the "Hollywood Heritage Museum". It opened on December 13, 1985, and features some of DeMille's personal artifacts. The Lasky-DeMille Barn was dedicated as a California historical landmark in a ceremony on December 27, 1956; DeMille was the keynote speaker. It was listed on the National Register of Historic Places in 2014. The Dunes Center in Guadalupe, California, contains an exhibition of artifacts uncovered in the desert near Guadalupe from DeMille's set of his 1923 version of The Ten Commandments, known as the "Lost City of Cecil B. DeMille". Donated by the Cecil B. DeMille Foundation in 2004, the moving image collection of Cecil B. DeMille is held at the Academy Film Archive and includes home movies, outtakes, and never-before-seen test footage.
In summer 2019, The Friends of the Pompton Lakes Library hosted a Cecil B DeMille film festival to celebrate DeMille's achievements and connection to Pompton Lakes. They screened four of his films at Christ Church, where DeMille and his family attended church when they lived there. Two schools have been named after him: Cecil B. DeMille Middle School, in Long Beach, California, which was closed and demolished in 2010 to make way for a new high school; and Cecil B. DeMille Elementary School in Midway City, California. The former film building at Chapman University in Orange, California, is named in honor of DeMille. During the Apollo 11 mission, Buzz Aldrin referred to himself in one instance as "Cecil B. DeAldrin", as a humorous nod to DeMille. The title of the 2000 John Waters film Cecil B. Demented alludes to DeMille.
DeMille's legacy is maintained by his granddaughter Cecilia DeMille Presley who serves as the president of the Cecil B. DeMille Foundation, which strives to support higher education, child welfare, and film in Southern California. In 1963, the Cecil B. DeMille Foundation donated the "Paradise" ranch to the Hathaway Foundation, which cares for emotionally disturbed and abused children.Awards and recognition
Cecil B. DeMille received many awards and honors, especially later in his career.
.]]
In August 1941, DeMille was honored with a block in the forecourt of Grauman's Chinese Theatre.
The American Academy of Dramatic Arts honored DeMille with an Alumni Achievement Award in 1958.
In 1957, DeMille gave the commencement address for the graduation ceremony of Brigham Young University, wherein he received an honorary Doctorate of Letter degree. Additionally, in 1958, he received an honorary Doctorate of Law degree from Temple University.
From the film industry, DeMille received the Irving G. Thalberg Memorial Award at the Academy Awards in 1953, and a Lifetime Achievement Award from the Directors Guild of America Award the same year. In the same ceremony, DeMille received a nomination from Directors Guild of America Award for Outstanding Directorial Achievement in Motion Pictures for The Greatest Show on Earth. In 1952, DeMille was awarded the first Cecil B. DeMille Award at the Golden Globes. An annual award, the Golden Globe's Cecil B. DeMille Award recognizes lifetime achievement in the film industry. For his contribution to the motion picture and radio industry, DeMille has two stars on the Hollywood Walk of Fame. The first, for radio contributions, is located at 6240 Hollywood Blvd. The second star is located at 1725 Vine Street.
DeMille received two Academy Awards: an Honorary Award for "37 years of brilliant showmanship" in 1950 and a Best Picture award in 1953 for The Greatest Show on Earth. DeMille received a Golden Globe Award for Best Director and was additionally nominated for the Best Director category at the 1953 Academy Awards for the same film. He was further nominated in the Best Picture category for The Ten Commandments at the 1957 Academy Awards. DeMille's Union Pacific received a Palme d'Or in retrospect at the 2002 Cannes Film Festival.
Two of DeMille's films have been selected for preservation in the National Film Registry by the United States Library of Congress: The Cheat (1915) and The Ten Commandments (1956).FilmographyDeMille made 70 features, 52 of which are silent. The first 24 of his silents were produced during the first three years of his career (1913–1916). Eight of his films were "epics" with five classified as "Biblical". Six of DeMille's films — The Arab, The Wild Goose Chase, The Dream Girl, The Devil-Stone, ''We Can't Have Everything, and The Squaw Man (1918) — were destroyed by nitrate decomposition, and are considered lost. The Ten Commandments'' is broadcast every Saturday at Passover in the United States on the ABC Television Network.
Directed features
Filmography obtained from Fifty Hollywood Directors.
Silent films
* The Arab (1915, Lost)
* Chimmie Fadden (1915)
* Kindling (1915)
* Carmen (1915)
* Chimmie Fadden Out West (1915)
* The Cheat (1915)
* Temptation (1915, Lost)
* The Golden Chance (1915)
* The Trail of the Lonesome Pine (1916)
* The Heart of Nora Flynn (1916)
* Maria Rosa (1916)
* The Dream Girl (1916, Lost)
* Joan the Woman (1916)
* A Romance of the Redwoods (1917)
* The Little American (1917)
* The Woman God Forgot (1917)
* The Devil-Stone (1917) incomplete: 2/6 reels survive
* The Whispering Chorus (1918)
* Old Wives for New (1918)
* We Can't Have Everything (1918, Lost)
* Till I Come Back to You (1918)
* The Squaw Man (1918, Lost)
* Don't Change Your Husband (1919)
* For Better, for Worse (1919)
* Male and Female (1919)
* Why Change Your Wife? (1920)
* Something to Think About (1920)
* Forbidden Fruit (1921)
* The Affairs of Anatol (1921)
* Fool's Paradise (1921)
* Saturday Night (1922)
* Manslaughter (1922)
* Adam's Rib (1923)
* The Ten Commandments (1923)
* Triumph (1924)
* Feet of Clay (1924, Lost)
* The Golden Bed (1925)
* The Road to Yesterday (1925)
* The Volga Boatman (1926)
* The King of Kings (1927)
* The Godless Girl (1928)
}}
Sound films
Directing or producing credit
These films represent those which DeMille produced or assisted in directing, credited or uncredited.
* Brewster's Millions (1914, lost)
* The Master Mind (1914)
* The Only Son (1914, lost)
* The Man on the Box (1914)
* The Ghost Breaker (1914, lost)
* After Five (1915)
* Nan of Music Mountain (1917)
* Chicago (1927, Producer, uncredited)
* When Worlds Collide (1951, executive producer)
* The War of the Worlds (1953, executive producer)
* The Buccaneer (1958, producer)Acting and cameosDeMille frequently made cameos as himself in other Paramount films. Additionally, he often starred in prologues and special trailers that he created for his films, having an opportunity to personally address the audience.
* Hollywood (1923) as Himself
* Free and Easy (1930) as Himself
* Estrellados (1930) as Himself (Guest Appearance)
* Madam Satan (1930) as Radio Newscaster (voice, uncredited)
* The Last Train from Madrid (1937) as Crowd Member (uncredited)
* North West Mounted Police (1940) as Narrator (voice, uncredited)
* Glamour Boy (1941) as Movie Director (uncredited)
* Reap the Wild Wind (1942) as Prologue Speaker (voice, uncredited)
* Star Spangled Rhythm (1942) as Himself
* The Story of Dr. Wassell (1944) as Narrator (uncredited)
* Variety Girl (1947) as Himself
* Unconquered (1947) as Narrator (uncredited)
* Jens Mansson in America (1947) as Himself
* Samson and Delilah (1949) as Narrator (uncredited)
* Sunset Boulevard (1950) as Himself
* The Greatest Show on Earth (1952) as Narrator (voice, uncredited)
* Son of Paleface (1952) as Photographer (uncredited)
* The Ten Commandments (1956) as Himself (film introduction) and Narrator (uncredited)
* The Buster Keaton Story (1957) as Himself
* The Buccaneer (1958) as Himself - Prologue (uncredited) (final film role)
}}
Explanatory notes
CitationsGeneral sources
*
*
*
*
*
*
*
*
*
*
*
*
*
*
* Orrison, Katherine. Written in Stone: Making Cecil B. DeMille's Epic, The Ten Commandments''. New York: Vestal Press, 1990. .
*
*
*
*
*
External links
* by the Cecil B. DeMille Foundation
*
*
*
*
* [http://film.virtual-history.com/person.php?personid=2378 Cecil B. DeMille at Virtual History]
* [https://web.archive.org/web/20110927190052/http://www.cinemaweb.com/silentfilm/bookshelf/10_dwp_3.htm Cecil B. DeMille's Early Films' Costs and Grosses by David Pierce]
*[https://web.archive.org/web/20110927190052/http://www.cinemaweb.com/silentfilm/bookshelf/index.htm Silent Film Bookshelf]
Archival materials
* [http://archives.lib.byu.edu/repositories/ltpsc/resources/upb_mss1400 Cecil B. DeMille papers], Vault MSS 1400, L. Tom Perry Special Collections, Harold B. Lee Library, Brigham Young University, DeMille's personal and business papers including correspondence, audio, and video recordings, financial ledgers, and memorabilia
* [http://archives.lib.byu.edu/agents/people/2596 Other collections related to DeMille] at the L. Tom Perry Special Collections, Harold B. Lee Library, Brigham Young University
* [https://archive.today/20140602193934/http://digital.library.pitt.edu/cgi-bin/f/findaid/findaid-idx?cascead;ccascead;q11958.03;rgnmain;viewtext;didnoUS-PPiU-sc195803 The Mary Roberts Rinehart Papers], Vault SC.1958.03, ULS Special Collections, University of Pittsburgh Library, includes conversations with DeMille about her plays
}}
Category:1881 births
Category:1959 deaths
Category:20th-century American dramatists and playwrights
Category:20th-century American male actors
Category:20th-century American male writers
Category:20th-century American memoirists
Category:20th-century American screenwriters
Category:Academy Honorary Award recipients
Category:American Academy of Dramatic Arts alumni
Category:American anti-communists
Category:American Episcopalians
Category:American film editors
Category:American Freemasons
Category:American male dramatists and playwrights
Category:Members of The Lambs Club
Category:American male film actors
Category:American male screenwriters
Category:American male stage actors
Category:American people of Belgian descent
Category:American people of British-Jewish descent
Category:American people of Dutch descent
Category:American people of English descent
Category:American people of German-Jewish descent
Category:American radio directors
Category:American radio personalities
Category:American radio producers
Category:American silent film directors
Category:American theatre directors
Category:American theatre managers and producers
Category:Articles containing video clips
Category:Best Director Golden Globe winners
Category:Burials at Hollywood Forever Cemetery
Category:California Republicans
Category:Cecil B. DeMille Award Golden Globe winners
Cecil B.
Category:Directors of Best Picture Academy Award winners
Category:Directors of Palme d'Or winners
Category:Episcopalians from Massachusetts
Category:Film directors from Massachusetts
Category:Film directors from New Jersey
Category:Film directors from North Carolina
Category:Film producers from Massachusetts
Category:Film producers from New Jersey
Category:Golden Globe Award–winning producers
Category:People from Ashfield, Massachusetts
Category:People from Los Feliz, Los Angeles
Category:People from Pompton Lakes, New Jersey
Category:People from Washington, North Carolina
Category:Producers who won the Best Picture Academy Award
Category:Screenwriters from Massachusetts
Category:Screenwriters from New Jersey
Category:Screenwriters from North Carolina
Category:American special effects people
Category:Western (genre) film directors
Category:Widener University alumni
Category:Writers from Passaic County, New Jersey
|
https://en.wikipedia.org/wiki/Cecil_B._DeMille
|
2025-04-05T18:27:44.038840
|
6181
|
Chinese Islamic cuisine
|
Chinese Islamic cuisine consists of variations of regionally popular foods that are typical of Han Chinese cuisine, in particular to make them halal. Dishes borrow ingredients from Middle Eastern, Turkic, Iranian and South Asian cuisines, notably mutton and spices. Much like other northern Chinese cuisines, Chinese Islamic cuisine uses wheat noodles as the staple, rather than rice. Chinese Islamic dishes include clear-broth beef noodle soup and chuanr.
The Hui (ethnic Chinese Muslims), Bonan, Dongxiang, Salar and Uyghurs of China, as well as the Dungans of Central Asia and the Panthays of Burma, collectively contribute to Chinese Islamic cuisine.
History
Due to the large Muslim population in Western China, many Chinese restaurants cater to or are run by Muslims. Northern Chinese Islamic cuisine originated in China proper. It is heavily influenced by Beijing cuisine, with nearly all cooking methods identical and differs only in material due to religious restrictions. As a result, northern Islamic cuisine is often included in home Beijing cuisine though seldom in east coast restaurants.
During the Yuan dynasty, halal and kosher methods of slaughtering animals and preparing food was banned and forbidden by the Mongol emperors, starting with Genghis Khan who banned Muslims and Jews from slaughtering their animals their own way and made them follow the Mongol method.
Among all the [subject] alien peoples only the Hui-hui say "we do not eat Mongol food." [Cinggis Qa'an replied:] "By the aid of heaven we have pacified you; you are our slaves. Yet you do not eat our food or drink. How can this be right?" He thereupon made them eat. "If you slaughter sheep, you will be considered guilty of a crime." He issued a regulation to that effect ... [In 1279/1280 under Qubilai] all the Muslims say: “if someone else slaughters [the animal] we do not eat." Because the poor people are upset by this, from now on, Musuluman [Muslim] Huihui and Zhuhu [Jewish] Huihui, no matter who kills [the animal] will eat [it] and must cease slaughtering sheep themselves, and cease the rite of circumcision.
thumb|left|A halal meat store in Hankou, 1934 to 1935
Traditionally, there is a distinction between Northern and Southern Chinese Islamic cuisine despite both using lamb and mutton. Northern Chinese Islamic cuisine relies heavily on beef, but rarely ducks, geese, shrimp or seafood, while southern Islamic cuisine is the reverse. The reason for this difference is due to availability of the ingredients. Oxen have been long used for farming and Chinese governments have frequently strictly prohibited the slaughter of oxen for food. However, due to the geographic proximity of the northern part of China to minority-dominated regions that were not subjected to such restrictions, beef could be easily purchased and transported to Northern China. At the same time, ducks, geese and shrimp are rare in comparison to Southern China due to the arid climate of Northern China.
thumb|left|An Islamic fast food restaurant at Shanghai Expo
A Chinese Islamic restaurant () can be similar to a Mandarin restaurant with the exception that there is no pork on the menu and the dishes are primarily noodle/soup based.
In most major eastern cities in China, there are very limited Islamic/Halal restaurants, which are typically run by migrants from Western China (e.g., Uyghurs). They primarily offer inexpensive noodle soups only. These restaurants are typically decorated with Islamic motifs such as Islamic writing.
Another difference is that lamb and mutton dishes are more commonly available than in other Chinese restaurants, due to the greater prevalence of these meats in the cuisine of Western Chinese regions. (Refer to image 1.)
Other Muslim ethnic minorities like the Bonan, Dongxiang, Salar and Tibetan Muslims have their own cuisines as well. Dongxiang people operate their own restaurants serving their cuisine.
Many cafeterias (canteens) at Chinese universities have separate sections or dining areas for Muslim students (Hui or Western Chinese minorities), typically labeled "qingzhen". Student ID cards sometimes indicate whether a student is Muslim and will allow access to these dining areas or will allow access on special occasions such as the Eid feast following Ramadan.
Several Hui restaurants serving Chinese Islamic cuisine exist in Los Angeles. San Francisco, despite its huge number of Chinese restaurants, appears to have only one whose cuisine would qualify as halal.
Many Chinese Hui Muslims who moved from Yunnan to Burma (Myanmar) are known as Panthays operate restaurants and stalls serving Chinese Islamic cuisine such as noodles. Chinese Hui Muslims from Yunnan who moved to Thailand are known as Chin Haw and they also own restaurants and stalls serving Chinese Islamic food.
thumb|right|Restaurant in Bishkek, Kyrgyzstan, advertising Dungan cuisine.
In Central Asia, Dungan people, descendants of Hui, operate restaurants serving Chinese Islamic cuisine, which is respectively referred to as Dungan cuisine there. They cater to Chinese businessmen. Chopsticks are used by Dungans. The cuisine of the Dungan resembles northwestern Chinese cuisine.
Most Chinese regard Hui halal food as cleaner than food made by non-Muslims so their restaurants are popular in China. Hui who migrated to Northeast China (Manchuria) after the Chuang Guandong opened many new inns and restaurants to cater to travelers, which were regarded as clean.
The Hui who migrated to Taiwan operate Qingzhen restaurants and stalls serving Chinese Islamic cuisine in Taipei and other big cities.
The Thai Department of Export Promotion claims that "China's halal food producers are small-scale entrepreneurs whose products have little value added and lack branding and technology to push their goods to international standards" to encourage Thai private sector halal producers to market their products in China.
A 1903-started franchise serving Muslim food is Dong Lai Shun in Hankou.
400 meters have to be kept as a distance from each restaurant serving beef noodles to another of its type if they belong to Hui Muslims, since Hui have a pact between each other in Ningxia, Gansu and Shaanxi.
Halal restaurants are checked up upon by clerics from mosques.
Halal food manufacture has been sanctioned by the government of the Ningxia Autonomous Region.
Famous dishes
thumb|Chinese halal restaurant in Taipei, Taiwan
thumb|Chinese Islamic restaurant in Melaka, Malaysia
Lamian
Lamian (, Dungan: Ламян) is a Chinese dish of hand-made noodles, usually served in a beef or mutton-flavored soup (湯麪, даңмян, tāngmiàn), but sometimes stir-fried (炒麪, Чаомян, chǎomiàn) and served with a tomato-based sauce. Literally, 拉, ла (lā) means to pull or stretch, while 麪, мян (miàn) means noodle. The hand-making process involves taking a lump of dough and repeatedly stretching it to produce a single very long noodle. There exists a local variant in Lanzhou, the Lanzhou beef noodles, also known as Lanzhou lamian.
Words that begin with L are not native to Turkic — läghmän is a loanword as stated by Uyghur linguist Abdlikim: It is of Chinese derivation and not originally Uyghur.
Beef noodle soup
Beef noodle soup is a noodle soup dish composed of stewed beef, beef broth, vegetables and wheat noodles. It exists in various forms throughout East and Southeast Asia. It was created by the Hui people during the Qing dynasty of China.
In the west, this food may be served in a small portion as a soup. In China, a large bowl of it is often taken as a whole meal with or without any side dish.
Chuanr
Chuanr (Chinese: 串儿, Dungan: Чўанр, Pinyin: chuànr (shortened from "chuan er"), "kebab"), originating in the Xinjiang (新疆) province of China and in recent years has been disseminated throughout the rest of that country, most notably in Beijing. It is a product of the Chinese Islamic cuisine of the Uyghur (维吾尔) people and other Chinese Muslims. Yang rou chuan or lamb kebabs, is particularly popular.
Suan cai
Suan cai is a traditional fermented vegetable dish, similar to Korean kimchi and German sauerkraut, used in a variety of ways. It consists of pickled Chinese cabbage. Suan cai is a unique form of pao cai due to the material used and the method of production. Although suan cai is not exclusive to Chinese Islamic cuisine, it is used in Chinese Islamic cuisine to top off noodle soups, especially beef noodle soup.
Nang
Nang (Chinese: 馕, Dungan: Нәң) is a type of round unleavened bread, topped with sesame. It is similar to South and Central Asia naan.
Image gallery
File:Beef noodle.JPG|Beef noodle served
File:Peking Duck.jpg|Peking duck served at a halal restaurant in Beijing
File:5658-Linxia-City-niang-pi.jpg|Niang pi (酿皮, Няң пы), a popular vegetarian noodle cold dish in Linxia
See also
Chinese cuisine
Islam in China
Uyghur cuisine
Dali City
Gansu
Kunming
Lanzhou
Ningxia
Qinghai
Shaanxi
Xi'an
Yunnan
References
External links
article on a Chinese Islamic restaurant in the San Francisco Bay area, San Francisco Chronicle.
chinaheritagequarterly.org
The Famous Dungan Noodles or Lyu Mian with Eight Seasoning Dishes!
More pictures of the Dungan Cuisine
Category:Regional cuisines of China
Category:Islamic culture
Category:Xinjiang
Category:Multiculturalism and Islam
|
https://en.wikipedia.org/wiki/Chinese_Islamic_cuisine
|
2025-04-05T18:27:44.076604
|
6182
|
Cantonese cuisine
|
|p=Guǎngdōngcài
|tp=Guǎngdong-cài
|w=
|mi=
|bpmf=ㄍㄨㄤˇ ㄉㄨㄥ ㄘㄞˋ
|altname=Yue cuisine
|s2=粤菜
|t2=粵菜
|j2=Jyut6 coi3
|y2=Yuht choi
|ci2=
|p2=Yuècài
|tp2=Yuè-cài
|w2=
|mi2=
|bpmf2=ㄩㄝˋ ㄘㄞˋ
|showflag=jy
}}
Cantonese or Guangdong cuisine, also known as Yue cuisine ( or ), is the cuisine of Cantonese people, associated with the Guangdong province of China, particularly the provincial capital Guangzhou, and the surrounding regions in the Pearl River Delta including Hong Kong and Macau. Strictly speaking, Cantonese cuisine is the cuisine of Guangzhou or of Cantonese speakers, but it often includes the cooking styles of all the speakers of Yue Chinese languages in Guangdong.
The Teochew cuisine and Hakka cuisine of Guangdong are considered their own styles. However, scholars may categorize Guangdong cuisine into three major groups based on the region's dialect: Cantonese, Hakka and Chaozhou cuisines. Neighboring Guangxi's cuisine is also considered separate despite eastern Guangxi being considered culturally Cantonese due to the presence of ethnic Zhuang influences in the rest of the province.
Cantonese cuisine is one of the Eight Great Traditions of Chinese cuisine. Its prominence outside China is due to the large number of Cantonese emigrants. Chefs trained in Cantonese cuisine are highly sought after throughout China. Until the late 20th century, most Chinese restaurants in the West served largely Cantonese dishes.
Background
Guangzhou (Canton) City, the provincial capital of Guangdong and the centre of Cantonese culture, has long been a trading hub and many imported foods and ingredients are used in Cantonese cuisine. Besides pork, beef and chicken, Cantonese cuisine incorporates almost all edible meats, including offal, chicken feet, duck's tongue, frog legs, snakes and snails. However, lamb and goat are less commonly used than in the cuisines of northern or western China. Many cooking methods are used, with steaming and stir-frying being the most favoured due to their convenience and rapidity. Other techniques include shallow frying, double steaming, braising and deep frying.
Compared to other Chinese regional cuisines, the flavours of most traditional Cantonese dishes should be well-balanced and not greasy. Apart from that, spices should be used in modest amounts to avoid overwhelming the flavours of the primary ingredients, and these ingredients in turn should be at the peak of their freshness and quality. There is no widespread use of fresh herbs in Cantonese cooking, in contrast with their liberal use in other cuisines such as Sichuanese, Vietnamese, Lao, Thai and European. Garlic chives and coriander leaves are notable exceptions, although the former are often used as a vegetable and the latter are usually used as mere garnish in most dishes.
Foods
Sauces and condiments
In Cantonese cuisine, ingredients such as sugar, salt, soy sauce, rice wine, corn starch, vinegar, scallion and sesame oil suffice to enhance flavour, although garlic is heavily used in some dishes, especially those in which internal organs, such as entrails, may emit unpleasant odours. Ginger, chili peppers, five-spice powder, powdered black pepper, star anise and a few other spices are also used, but often sparingly.
{| class="wikitable"
! English !! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| Black bean sauce || || || syun3 jung4 dau6 si6 zoeng3 || suànróng dòuchǐjiàng
|-
| Char siu sauce || || || caa1 siu1 zoeng3 || chāshāojiàng
|-
| Chu hau paste|| || || cyu5 hau4 zoeng3 || zhùhóujiàng
|-
| Hoisin sauce || || || hoi2 sin1 zoeng3 || hǎixiānjiàng
|-
| Master stock || || || lou5 seoi2 || lǔshuǐ
|-
| Oyster sauce || || || hou4 jau4 || háoyóu
|-
| Plum sauce || || || syun1 mui4 zoeng3 || sūméijiàng
|-
| Red vinegar || || || daai6 hung4 zit3 cou3 || dàhóngzhècù
|-
| Shrimp paste || || || haam4 haa1 zoeng3 || xiánxiājiàng
|-
|Shrimp paste block
|蝦膏
|虾膏
|haa1 gou1
|Xiāgāo
|-
| Sweet and sour sauce || || || tong4 cou3 zoeng3 || tángcùjiàng
|-
|}
<gallery widths"175" arrow"6">
File:Macharsiew by daxiang stef.jpg|Char siu is often marinated with plum sauce and honey for sweet flavour
File:Steamed Oysters.jpg|Oysters steamed in two ways: with ginger and garlic, and in black bean sauce
</gallery>
Dried and preserved ingredients
Although Cantonese cooks pay much attention to the freshness of their primary ingredients, Cantonese cuisine also uses a long list of preserved food items to add flavour to a dish. This may be influenced by Hakka cuisine, since the Hakkas were once a dominant group occupying imperial Hong Kong and other southern territories.
Some items gain very intense flavours during the drying/preservation/oxidation process and some foods are preserved to increase their shelf life. Some chefs combine both dried and fresh varieties of the same items in a dish. Dried items are usually soaked in water to rehydrate before cooking. These ingredients are generally not served a la carte, but rather with vegetables or other Cantonese dishes.
{| class="wikitable"
! Image !! English !! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin !! Notes
|-
| || Century egg ||colspan"2" style"text-align:center"| || pei4 daan2 || pídàn ||Can be found served with roasted dishes, in congee with lean pork, and in a sweet pastry with lotus paste.
|-
| || Chinese sausage || || || laap6 coeng2 || làcháng || Usually added to rice together with preserved-salted duck and pork.
|-
|
|Dried sea snail
|螺頭 / 螺片
|螺头 / 螺片
|lo4 tau4 / lo2 pin2
|Luótóu/ luópiàn
|Usually added to clear soup.
|-
|||Dried bok choy|| || || coi3 gon1 || càigān ||
|-
|rowspan2| ||rowspan2|Dried scallops ||colspan"2" style"text-align:center"| || rowspan2| gong1 jiu4 cyu5 || rowspan2| jiāngyáozhù || rowspan=2| Usually added to clear soup.
|-
| ||
|-
| || Dried shrimp|| || || haa1 gon1 || xiāgān || Usually de-shelled, sliced into half and added to vegetable dishes.
|-
| || Dried small<!-- Maybe "baby" as in, "baby shrimp", an ingredient --> shrimp || || || haa1 mai5 || xiāmǐ || Usually mixed with stir-fried vegetables.
|-
||| Fermented tofu ||colspan"2" style"text-align:center"| || fu6 jyu5 || fǔrǔ ||
|-
| || Fermented black beans ||colspan"2" style"text-align:center"| || dau6 si6 || dòuchǐ || Usually added to pork and tofu dishes.
|-
| ||Mei cai|| colspan"2" style"text-align:center" | || mui4 coi3 || méicài || Usually cooked with pork or stir-fried with rice.
|-
|||Chai poh / Dried preserved radish || colspan"2" style"text-align:center" | || coi3 pou2 || càifǔ || A key ingredient for making chai poh omelette.
|-
|||Preserved-salted duck || || || laap6 aap2 || làyā || Usually eaten with rice in a family meal.
|-
|||Preserved-salted pork || || || laap6 juk6 || làròu || Usually eaten with rice in a family meal.
|-
| ||Salted duck egg || || || haam4 daan2 || xiándàn || May be eaten as it is or mixed with stir-fried vegetables and steam dishes or cooked with diced pork in congee.
|-
||| Salted fish || || || haam4 jyu2 || xiányú || Usually paired with steamed pork or added to fried rice together with diced chicken.
|-
||| Suan cai || || || haam4 syun1 coi3 || xiánsuāncài || The key ingredient for making Haam Coi Pepper Hog Maw Soup (咸菜胡椒豬肚湯).
|-
|
|Jinhua ham
|金華火腿
|金华火腿
|gam1 waa4 fo2 teoi2
|Jīnhuáhuǒtuǐ
|Usually added to clear soup.
|-
|||Tofu skin ||colspan"2" style"text-align:center"| || fu6 pei4 || fǔpí || Usually used as wrapping for ground pork dishes. It is fried in a similar manner as spring rolls.
|-
|}
Traditional dishes
A number of dishes have been part of Cantonese cuisine since the earliest territorial establishments of Guangdong. While many of these are on the menus of typical Cantonese restaurants, some simpler ones are more commonly found in Cantonese homes. Home-made Cantonese dishes are usually served with plain white rice.
{| class="wikitable"
|-
! Name !! Image !! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| Cantonese style fried rice || || || || gwong2 sik1 cau2 faan6 || guǎng shì chǎofàn
|-
| Choy sum in oyster sauce || || || || hou4 jau4 coi3 sam1 || háoyóu càixīn
|-
|Sampan congee
|
| colspan"2" style"text-align:center" |艇仔粥
|teng5 zai2 zuk1
|Tǐngzǐzhōu
|-
| Congee with lean pork and century egg || ||colspan"2" style"text-align:center"| || pei4 daan2 sau3 juk6 zuk1 || pídàn shòuròuzhōu
|-
| Steamed egg || ||colspan"2" style"text-align:center"| || zing1 seoi2 daan2 || zhēngshuǐdàn
|-
| Steamed frog legs on lotus leaf |||| || || ho4 jip6 zing1 tin4 gai1 || héyè zhēng tiánjī
|-
| Steamed ground pork with salted duck egg || || || || haam4 daan2 zing1 juk6 beng2 || xiándàn zhēng ròubǐng
|-
| Steamed spare ribs with fermented black beans and chilli pepper || ||colspan"2" style"text-align:center"| || si6 ziu1 paai4 gwat1 || chǐjiāo páigǔ
|-
| Stewed beef brisket || ||colspan"2" style"text-align:center"| || cyu5 hau4 ngau4 naam5 || zhùhóu niú nǎn
|-
| Stir-fried hairy gourd with dried shrimp and cellophane noodles |||| || || daai6 ji4 maa1 gaa3 neoi5 || dàyímā jiànǚ
|-
| Stir-fried water spinach with shredded chilli and fermented tofu || || || || ziu1 si1 fu6 jyu5 tung1 coi3 || jiāosī fǔrǔ tōngcài
|-
| Sweet and sour pork || || || || gu1 lou1 juk6 || gūlūròu
|-
| Shunde-style fish slices || || || || seon6 dak1 jyu4 saang1 || shùndé yú shēng
|}
Deep fried dishes
There are a small number of deep-fried dishes in Cantonese cuisine, which can often be found as street food. They have been extensively documented in colonial Hong Kong records of the 19th and 20th centuries. A few are synonymous with Cantonese breakfast and lunch, even though these are also part of other cuisines.
{| class="wikitable"
|-
! English !! Image !!Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| Dace fish balls |||| || || leng4 jyu4 kau4 ||
|-
| Chinese Donut ||||colspan"2" style"text-align:center"| || jau4 zaa3 gwai2 ||
|-
|Ox-tongue pastry
|
| colspan"2" style"text-align:center"|牛脷酥
|ngau4 lei6 sou1
|niúlìsū
|-
| Zaa Leung |||| || || zaa3 loeng5 ||
|-
|}
Soups
Old fire soup, or lou fo tong (), is a clear broth prepared by simmering meat and other ingredients over a low heat for several hours. Chinese herbs are often used as ingredients. There are basically two ways to make old fire soup – put ingredients and water in the pot and heat it directly on fire, which is called bou tong (); or put the ingredients in a small stew pot, and put it in a bigger pot filled with water, then heat the bigger pot on fire directly, which is called dun tong (). The latter way can keep the most original taste of the soup.
Soup chain stores or delivery outlets in cities with significant Cantonese populations, such as Hong Kong, serve this dish due to the long preparation time required of slow-simmered soup.
{| class="wikitable"
|-
! English !! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| Cantonese seafood soup ||colspan"2" style"text-align:center"| || hoi2 wong4 gang1 || hǎihuáng gēng
|-
| Night-blooming cereus soup || || || baa3 wong4 faa1 bou1 tong1 || bàwánghuā bāotāng
|-
| Snow fungus soup || || || ngan4 ji5 tong1 || yín'ěr tāng
|-
| Spare ribs soup with watercress and apricot kernels || || || naam4 bak1 hang6 sai1 joeng4 coi3 zyu1 gwat1 tong1 || nánběixìng xīyángcài zhūgǔ tāng
|-
| Winter melon soup || || || dung1 gwaa1 tong1 || dōngguā tāng
|-
|}
Seafood
Due to Guangdong's location along the South China Sea coast, fresh seafood is prominent in Cantonese cuisine, and many Cantonese restaurants keep aquariums or seafood tanks on the premises. In Cantonese cuisine, as in cuisines from other parts of Asia, if seafood has a repugnant odour, strong spices and marinating juices are added; the freshest seafood is odourless and, in Cantonese culinary arts, is best cooked by steaming. For instance, in some recipes, only a small amount of soy sauce, ginger and spring onion is added to steamed fish. In Cantonese cuisine, the light seasoning is used only to bring out the natural sweetness of the seafood. As a rule of thumb, the spiciness of a dish is usually negatively correlated to the freshness of the ingredients.
{| class="wikitable"
|-
! Image !! English !! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
|||Lobster with ginger and scallions || || || goeng1 cung1 lung4 haa1 || jiāngcōng lóngxiā
|-
|
|Lobster with e-fu noodles in soup /
Cheese lobster with e-fu noodles
|上湯龍蝦伊麵 / 芝士龍蝦伊麵
|上汤龙虾伊面 / 芝士龙虾伊面
|soeng6 tong1 lung4 haa1 ji1 min6 / zi1 si2 lung4 haa1 ji1 min6
|Shàngtāng lóngxiā yīmiàn / Zhīshì lóngxiā yīmiàn
|-
|||Mantis shrimp || || || laai6 niu6 haa1 || làniàoxiā
|-
| || Orange cuttlefish || || || lou5 seoi2 mak6 jyu4 || lǔshuǐ mòyú ||
|-
||| Steamed fish || || || zing1 yu4 || zhēngyú
|-
|||Steamed scallops with ginger and garlic || || || syun3 jung4 zing1 sin3 bui3 || suànróng zhēng shànbèi
|-
|||White boiled shrimp || || || baak6 zoek3 haa1 || báizhuóxiā
|-
|}
<gallery caption"" widths"175px" arrow="6">
File:HK Hotpot foods Dec-2013 Ingredients 蟶子 Solenidae 蟹 Crabs 蝦 Prawn 雞肉腸仔 Sausage n 魚旦 Fishballs.jpg|Typical ingredients for Cantonese style hotpot are razor shell (), crab (), prawn (), chicken sausage () and dace fishball ()
</gallery>
Noodle dishes
Noodles are served either in soup broth or fried. These are available as home-cooked meals, on dim sum side menus, or as street food at dai pai dongs, where they can be served with a variety of toppings such as fish balls, beef balls, or fish slices.
{| class="wikitable"
|-
! English !! Image !! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin !! Notes
|-
| Beef brisket noodles || || || || ngau4 laam5 min6 || niú nǎn miàn || May be served dry or in soup.
|-
| Beef chow fun|| || || || gon1 caau2 ngau4 ho2 || gān chǎo niú hé || Fried beef noodles made with hor-fun, typically chilli oil is also added.
|-
| Chow mein|| || || || caau2 min6 || chǎo miàn || A generic term for various stir-fried noodle dishes. Hong Kong-style chow mein is made from pan-fried thin crispy noodles.
|-
| Jook-sing noodles|| || || || zuk1 sing1 min6 || zhúshēngmiàn || Bamboo log pressed noodles.
|-
| Lo mein|| || || || lou1 min6 || lāo miàn || Boiled wheat noodles mixed with a sauce, or served with a sauce alongside. Traditionally not stir-fried.
|-
| Rice noodle roll|| || || || coeng2 fan2 || chángfěn || Also known as chee cheong fun.
|-
| Shahe fen|| ||colspan"2" style"text-align:center"| || ho4 fun2 || héfěn || Also known as hor-fun.
|-
|Rice noodles
|
| colspan="2" |米粉
|mai5 fan2
|mǐfěn
|Also known as rice vermicelli
|-
| Silver needle noodles|| || || || ngan4 zam1 fun2 || yín zhēn fěn || Also known as rat noodles ().
|-
| Yi mein|| || || || ji1 min6 || yī miàn || Also known as e-fu noodles.
|-
| Wonton noodles|| || || || wan4 tan1 min6 || yúntūn miàn || Sometimes spelled as wanton noodles.
|}
Siu mei
Siu mei () is essentially the Chinese rotisserie style of cooking. Unlike most other Cantonese dishes, siu mei solely consists of meat, with no vegetables.
All Cantonese-style cooked meats, including siu mei, lou mei and preserved meat can be classified as siu laap ().
]]
{| class="wikitable"
|-
! English !!Image!! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| Char siu || || || || caa1 siu1 || chāshāo
|-
| Poached duck in master stock |||| || || lou5 seoi2 aap3 || lǔ shuǐ yā ||
|-
| Roast duck || || || || siu1 aap3 || shāoyā
|-
| Roast goose || || || || siu1 ngo4 || shāo'é
|-
| Roast pigeon || || || || siu1 jyu5 gap3 || shāorǔgē
|-
| Siu laap platter || || || || siu1 laap6 ping6 pun4 || shāolà pīnpán
|-
| Siu mei platter || || || || siu1 mei6 ping6 poon4 || shāowèi pīnpán
|-
| Siu yuk || || || || siu1 yuk1 || shāoròu
|-
| Soy sauce chicken || || || || si6 jau4 gai1 || chǐ yóu jī ||Typically found in traditional Chinese restaurants.
|-
| White cut chicken || || || || baak6 cit3 gai1 || bái qiè jī || Also known as white chopped chicken () in some places.
|-
|}
Lou mei
Lou mei () is the name given to dishes made from internal organs, entrails and other left-over parts of animals. It is widely available in southern Chinese regions.
{| class="wikitable"
|-
!Image !!English !! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| ||Beef entrails || || || ngau4 zaap6 || niú zá
|-
| ||Beef brisket ||colspan"2" style"text-align:center"| || ngau4 laam5 || niú nǎn
|-
| ||Chicken scraps || || || gai1 zaap6 || jī zá
|-
| ||Duck gizzard || || || aap3 san6 || yā shèn
|-
|||Pig's tongue || || || zyu1 lei6 || zhū lì
|}
Meat and rice plates
A portion of meat, such as char siu, served on a bed of steamed white rice. A typical variant consists of half-and-half portions of two types of siu mei and lou mei (or sometimes more than two). A steamed vegetable (such as choy sum) is frequently, but not always included.
{| class="wikitable"
|-
! English !! Image !! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| Rice with char siu and siu yuk || || || || caa1 siu1 siu1 juk6 faan6 || chāshāo shāo ròu fàn
|-
| Rice with Chinese sausage and char siu || || || || laap6 ceung4 caa1 siu1 faan6 || làcháng chāshāo fàn
|-
| Rice with roast goose and goose intestines || || || || siu1 ngo4 ngo4 coeng4 faan6 || shāo é é cháng fàn
|-
|}
Little pot rice
]]
Little pot rice () are dishes cooked and served in a flat-bottomed pot (as opposed to a round-bottomed wok). Usually this is a saucepan or braising pan (see clay pot cooking). Such dishes are cooked by covering and steaming, making the rice and ingredients very hot and soft. Usually the ingredients are layered on top of the rice with little or no mixing in between. Many standard combinations exist.
{| class="wikitable"
|-
! English !! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| Rice with Chinese sausage and preserved meat || || || laap6 coeng2 bou1 zai2 faan6 || làwèi bāozǎifàn
|-
| Rice with layered egg and beef || || || wo1 daan2 ngaw4 juk6 faan6 || wōdàn niúròu fàn
|-
| Rice with minced beef patty || || || juk6 beng2 bou1 zai2 faan6 || ròubǐng bāozǎifàn
|-
| Rice with spare ribs || || || paai4 gwat1 bou1 zai2 faan6 || páigǔ bāozǎifàn
|-
| Rice with steamed chicken || || || zing1 gai1 juk6 bou1 zai2 faan6 || zhēng jīròu bāozǎifàn
|-
|}
Banquet/dinner dishes
A number of dishes are traditionally served in Cantonese restaurants only at dinner time. Dim sum restaurants stop serving bamboo-basket dishes after the yum cha period (equivalent to afternoon tea) and begin offering an entirely different menu in the evening. Some dishes are standard while others are regional. Some are customised for special purposes such as Chinese marriages or banquets. Salt and pepper dishes are one of the few spicy dishes.
{| class="wikitable"
|-
! English !!Image!! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| Crispy fried chicken || || || || zaa3 zi2 gai1 || zhá zǐ jī
|-
| Duck with taro || || || || can4 pei4 wu6 tau4 aap3 || chén pí yùtóu yā
|-
| Fried tofu with shrimp || || || || haa1 joeng4 caau2 dau4 fu6 || xiārén chǎo dòufǔ
|-
| Pork chop with salt and pepper || || || || ziu1 jim4 zyu1 paa2 || jiāo yán zhū pà
|-
| Roast pigeon || || || || jyu5 gap3 || rǔ gē
|-
| Roast suckling pig || || || || siu1 jyu5 zyu1 || shāo rǔ zhū
|-
| Seafood with bird's nest || || || || hoi2 sin1 zoek3 caau4 || hǎixiān quècháo
|-
| Shrimp with salt and pepper || || || || ziu1 jim4 haa1 || jiāo yán xiā
|-
| Sour spare ribs || || || || saang1 cau2 paai4 gwat1 || shēng chǎo páigǔ
|-
| Spare ribs with salt and pepper || || || || ziu1 jim4 paai4 gwat1 || jiāo yán gǔ
|-
| Squid with salt and pepper || || || || ziu1 jim4 jau4 jyu2 || jiāo yán yóuyú
|-
| Yangzhou fried rice || || || || Joeng4 zau1 cau2 faan6 || Yángzhōu chǎofàn
|}
Dessert
After the evening meal, most Cantonese restaurants offer tong sui (), a sweet soup. Many varieties of tong sui are also found in other Chinese cuisines. Some desserts are traditional, while others are recent innovations. The more expensive restaurants usually offer their specialty desserts. Sugar water is the general name of dessert in Guangdong province. It is cooked by adding water and sugar to some other cooking ingredients.
{| class="wikitable"
|-
! English !! Image !! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| Black sesame soup || ||colspan"2" style"text-align:center"| || zi1 maa4 wu2 || zhīmahú
|-
| Coconut pudding || ||colspan"2" style"text-align:center"| || je4 zap1 gou1 || yēzhīgāo
|-
| Double skin milk || || || || soeng1 pei4 naai5 || shuāngpínǎi
|-
| Mung bean soup || || || || luk6 dau6 saa1 || lǜdòushā
|-
| Red bean soup || || || || hong4 dau6 saa1 || hóngdòushā
|-
| Sago soup || ||colspan"2" style"text-align:center"| || sai1 mei5 lou6 || xīmǐlù
|-
| Shaved ice || ||colspan"2" style"text-align:center"| || paau4 bing1 || bǎobīng
|-
| Steamed egg custard || || || || dan6 daan2 || dùndàn
|-
| Steamed milk custard || || || || dan6 naai5 || dùnnǎi
|-
| Sweet Chinese pastry || || || || gou1 dim2 || gāodiǎn
|-
| Sweet potato soup || ||colspan"2" style"text-align:center"| || faan1 syu4 tong4 seoi2 || fānshǔ tángshuǐ
|-
| Tofu flower pudding || ||colspan"2" style"text-align:center"| || dau6 fu6 faa1 || dòufǔhuā
|-
| Tortoise Jelly|| || || || gwai1 ling4 gou1 || guīlínggāo
|-
|}
Delicacies
Certain Cantonese delicacies consist of parts taken from rare or endangered animals, which raises controversy over animal rights and environmental issues. This is often due to alleged health benefits of certain animal products. For example, the continued spreading of the idea that shark cartilage can cure cancer has led to decreased shark populations even though scientific research has found no evidence to support the credibility of shark cartilage as a cancer cure.
{| class="wikitable"
|-
! English !!Image!! Traditional Chinese !! Simplified Chinese !! Jyutping !! Pinyin
|-
| Bird's nest soup || ||colspan"2" style"text-align:center"| || jin1 wo1 || yànwō
|-
| Braised abalone || || || || mun6 baau1 jyu4 || mèn bàoyú
|-
| Jellyfish || ||colspan"2" style"text-align:center"| || hoi2 zit3 || hǎizhé
|-
| Sea cucumber || ||colspan"2" style"text-align:center"| || hoi2 saam1 || hǎishēn
|-
| Shark fin soup || || || || jyu4 ci3 tong1 || yúchì tāng
|-
|}
See also
* Cantonese culture
* Chinese food therapy
* Dim sum
* Hong Kong cuisine
* List of Chinese dishes
* Macanese cuisine
* Restaurant industry in Guangzhou
References
Further reading
*''Eight Immortal Flavors: Secrets of Cantonese Cookery from San Francisco's Chinatown'', Johnny Kan and Charles L. Leong. Berkeley, California: Howell-North Books, 1963
Category:Cantonese culture
Category:Hong Kong cuisine
Category:Macanese cuisine
Category:Regional cuisines of China
|
https://en.wikipedia.org/wiki/Cantonese_cuisine
|
2025-04-05T18:27:44.126580
|
6183
|
Teochew cuisine
|
|p=Cháozhōu cài
|teo=diê<sup>5</sup> ziu<sup>1</sup> cai<sup>3</sup>
|j=ciu<sup>4</sup> zau<sup>1</sup> coi<sup>3</sup>
|altname=Chaoshan cuisine
|c2=
|p2=Cháoshàn cài
|teo2=diê<sup>5</sup> suan<sup>1</sup> cai<sup>3</sup>
|j2=ciu<sup>4</sup> saan<sup>3</sup> coi<sup>3</sup>}}
Teochew cuisine, also known as Chiuchow cuisine, Chaozhou cuisine or Teo-swa cuisine, originated from the Chaoshan region in the eastern part of China's Guangdong Province, which includes the cities of Chaozhou, Shantou and Jieyang. Teochew cuisine bears more similarities to that of Fujian cuisine, particularly Southern Min cuisine, due to the similarity of Teochew's and Fujian's culture, language, and their geographic proximity to each other. However, Teochew cuisine is also influenced by Cantonese cuisine in its style and technique. Other notable Teochew diaspora communities are in Vietnam, Cambodia and France. A popular noodle soup in both Vietnam and Cambodia, known as hu tieu, originated from the Teochew . There is also a large diaspora of Teochew people (most were from Southeast Asia) in the United States - particularly in California. There is a Teochew Chinese Association in Paris called L'Amicale des Teochews en France.
Notable dishes
{| class="wikitable"
|-
! English !! Traditional Chinese !! Simplified Chinese !! Pinyin !! Peng'im !! Description
|-
| Bak chor mee
|
|
|
| /
| Boiled noodles, dried and mixed with variety sauce such as soy sauce, chilli sauce and lard topped with vegetables, sliced onion, minced pork, mushrooms and fish balls or fishcakes.
|-
| Bak kut teh
|
|
|
| /
| A hearty soup that, at its simplest, consists of meaty pork ribs in a complex broth of herbs and spices (including star anise, cinnamon, cloves, danggui, fennel seeds and garlic), boiled together with pork bones for hours. Dark and light soy sauce may also be added to the soup during the cooking stages. Some Teochew families like to add extra Chinese herbs such as yuzhu (rhizome of Solomon's seal) and juzhi (buckthorn fruit) for a sweeter, slightly stronger flavoured soup. The dish is usually eaten with rice or noodles (sometimes as a noodle soup), and often served with fried dough fritters. Garnish includes chopped coriander or green onions and a sprinkling of fried shallots. A variation of bak kut uses chicken instead of pork, which then becomes chik kut teh. Bak kut is particularly popular in Southeast Asian countries such as Singapore and Malaysia.
|-
| Braised varieties
|
|
|
|
| Teochew cuisine is noted for its variety of braised dishes, which includes geese, duck, pork, bean curd and offal.
|-
| Chai tau kueh
|
|
|
|
| A savoury fried cake, made of white radish and rice flour. It is commonly stir-fried with soy sauce, eggs, garlic, spring onion and occasionally dried shrimp.
|-
| Chwee kueh
|
|
|
|
| Cup-shaped steamed rice cakes topped with chopped preserved/salted radish.
|-
| Crystal balls
|
|
|
|
| A steamed dessert with a variety of fillings such as yellow milk (; ni ng, ni7 ng5), yam paste (; or ni, ou7 ni5) or bean paste made from mung beans or azuki beans (red beans). They are similar to mochi.
|-
| Deep-Fried tofu
|
|
|
|
| A simple deep fried tofu dish, and was later adopted by Guangzhou's residents. First, deep-fry slices of fresh firm tofu until they are golden, and then serve with salted water dip (ingredients are boiling water, salt, and chopped Chinese chives). In modern times, some Teochew people now use the air fryer to prepare them for convenience and reduction of the amount of fat and calories in the food.
|-
| Fish balls / fishcakes / fish dumplings
|
|
|
| (her ee) / (her kueh) / (her kiaw)
| This fish paste made into balls, cakes and dumplings can be cooked in many ways but are often served in Teochew-style noodle and soups.
|-
| Fish ball noodle soup
|
|
|
| (her ee mee)
| Any of several kinds of egg and rice noodles may be served either in a light fish-flavoured broth or dry, along with fishballs, fishcakes, beansprouts and lettuce.
|-
| Flavored-potted goose
|
|
|
|
| A well-known braised goose dish, often accompanised by tofu.
|-
| Fried beef balls
|
|
|
| (za ghu bak ee)
| A simple deep-fired beef ball dish serves with dipping sauce such as shacha sauce or salted water dip (ingredients are boiling water, salt, and chopped Chinese chives). In modern times, some Teochew people now use the air fryer to prepare them for convenience and reduction of the amount of fat and calories in the food.
|-
| Fun guo
|
|
|
|
| A type of steamed dumplings. This is usually filled with dried radish, garlic chives, ground pork, dried shrimp, shiitake mushrooms and peanuts. The dumpling wrapper is made from a mixture of flour or plant starches mixed together with water. In Cantonese, these are called chiu chow fun guo (), in which the Chinese character is replaced by .
|-
| Head of mustard greens with mushrooms
|
|
|
|
| A dish of Brassica juncea (Chinese mustard) and shiitake (Chinese black mushrooms) in a soup. Originally a vegetarian soup, it often added with diced pork belly and other ingredients.
|-
| Kway chap
|
|
|
| (kueh chap)
| A dish of flat, broad rice sheets in a soup made from dark soy sauce served with pig offal, braised duck meat, various kinds of bean curd, preserved salted vegetables and braised hard-boiled eggs.
|-
| Marinating pork head / Braised pig head
|
|
|
|
| Clean and braise pork head in soy sauce and rock sugar. Cilantro, garlic, ginger, chilies, star anise and other spices may also added.
|-
| Mee pok
|
|
|
| (mee pok)
| A popular noodle dish served with minced pork, braised mushrooms, fishballs, dumplings, sauce and other garnish.
|-
| Oolong tea
|
|
|
| (Ou-leeng )
| Tieguanyin is one of the most popular Teochew teas. However, the Teochew people prefer their own brand of Oolong tea, which is the hong wang dan cong teh ().
|-
| Oyster omelette
|
|
|
| (or lua)
| A dish of omelette cooked with fresh raw oysters, tapioca starch and eggs. Teochew-style oyster omelette is usually deep fried and very crisp. Dip condiments are fish sauce and pepper or chili sauce.
|-
| Pan-fried marinated fish
|
|
|
|
| A pan-fried dish of marinated fish, typically using Larimichthys crocea as the main ingredient but can use other alternatives such as a white croaker, Japanese sea bass or other types of bass, or tilefish.
|-
| Patriotic soup (Protect the Country Dish)
|
|
|
|
| Developed during the Mongol conquest of the Song dynasty and named by Song's last emperor Zhao Bing. A simple soup boiled with stir-fried leaf vegetable (commonly sweet potato leaves since the Ming dynasty but also can use amaranth, spinach, Ipomoea aquatica or other leafy greens as alternatives) and edible mushrooms (preferably straw mushrooms) and broth (vegetable, chicken, or beef).
|-
| Pig's organ soup (Pork offal soup)
|
|
|
| (ter zap terng)
|
|-
| Popiah
|
|
|
| (薄饼) (po piah)
| A fresh (non-fried) spring roll usually eaten during the Qingming Festival. The skin is a soft, thin paper-like crepe made from wheat flour. The filling is mainly finely grated and steamed or stir-fried turnip, yam bean (jicama), which has been cooked with a combination of other ingredients such as bean sprouts, French beans, and lettuce leaves, depending on the individual vendor, along with grated carrots, slices of Chinese sausage, thinly sliced fried tofu, chopped peanuts or peanut powder, fried shallots and shredded omelette. Other common variations of popiah include pork (lightly seasoned and stir-fried), shrimp or crab meat. It is eaten in accompaniment with a sweet sauce (often a bean sauce, a blended soy sauce or hoisin sauce or a shrimp paste sauce).
|-
| Pork jelly
|
|
|
| (ter ka dang)
| Braised pig's leg made into jelly form, sliced and served cold.
|-
| Prawns sautéed with olive vegetables ||
|
|
|
| A dish of deep-fried prawns
|-
| Raw Pickled Seafood
|
|
|
|
| There are various kinds of Chaoshan fresh seafoods pickles, such as raw pickled crab, raw pickled blood clams, raw pickled shrimp, raw pickled prawns, raw pickled mantis shrimp. Seafoods are steeped in a pickling bath made of vinegar, salt, soy sauce, wine, cilantro, garlic, ginger, chilies and other spices.
|-
| Red peach cake
|
|
|
| (ang tao kueh, ung toh kway)
| Pink hue rice flour skin wrapped with flavorful glutinous rice. Pressed on a nicely designed peach shaped wooden mould, and then steam the dumpling to perfection. You can eat it freshly steamed, or pan-fried.
|-
| Salted vegetable duck soup
|
|
|
| (kiam cai ak terng)
| A soup boiled with duck, preserved salted vegetable, tomatoes and preserved sour plum.
|-
| Scalding (hot water dipping) blood clams
|
|
|
|
| Wash the blood clams and then soak them in cold salted water to let them release sands inside their body. Boil a pot of water, add some coriander, carefully pour the blood clams into the boiling water, dip them in hot water for 10 seconds and they are ready to eat.
|-
| Sichuan pepper chicken
|
|
|
|
| A traditionally deep-fried chicken dish, usually accompanied with leafy green from Lysimachia clethroides, known as pearl vegetable (). However, Lysimachia clethroides's leaves are unavailable to use in culinary outside of China, but basil, spinach, or other leafy green vegetables can be substitutes to them in preparation of the dish.
|-
| Sliced Cuttlefish on Ice with Wasabi Sauce
|
|
|
|
| Clean the cuttlefish, remove the skin, internal organs and head and boil it in 80<sup>o</sup>C salty water for 10 minutes. Soak it in ice water for 5 minutes after cook. Pat dry with kitchen towel and slice it. Place the slices on top of a dish with a thick layer of ice. When eating, pick up the cuttlefish slices with chopsticks and dip them in mustard and soy sauce.
|-
| Spring rolls with prawn or minced meat fillings
|
|
|
| (heh gerng) / , (sio gerng) / (ngo hiang)
| Mixed pork and prawn paste (sometimes fish), seasoned with five-spice powder, wrapped and rolled in a bean curd skin and deep-fried or pan-fried. It is sometimes referred to as Teochew-style spring roll in restaurant menus.
|-
| Steamed chives dumplings
|
|
|
|
| They are sometimes sautéed to give them a crispy texture.
|-
| Steamed goose
|
|
|
|
|
|-
| Taro paste
|
|
|
| (orh ni / orh nee)
| A traditional Teochew dessert made primarily from taro. The taro is steamed and then mashed into a thick paste, which forms the base of the dessert. Pumpkin is also added for sweetness and to create a smoother consistency. Lard or fried onion oil is then added for fragrance. The dessert is traditionally sweetened with water chestnut syrup, and served with ginkgo nuts. Modern versions of the dessert include the addition of coconut cream and sweet corn. The dessert is commonly served at traditional Teochew wedding banquet dinners as the last course, marking the end of the banquet.
|-
| Teochew chicken
|
|
|
| (Teochew koi)
| A dish of sliced chicken
|-
| Teochew cold crab
|
|
|
| (Teochew ngang hoi)
| The whole crab is first steamed then served chilled. The species of crab most commonly used is Charybdis cruciata.
|-
| Teochew cold fish
|
|
|
| (Teochew he bung)
| Steam fish with ginger slices, let it cool down to room temperature, then remove the ginger slices and keep it in refrigerator for at least 2 hours.
|-
| Teochew hot pot / Teochew steamboat
|
|
|
| (Teochew zuang lou)
| A dish where fresh, thinly sliced ingredients are placed into a simmering flavourful broth to cook and then dipped into various mixed sauces, usually with Shacha and soy sauce as its main components. Ingredients often include leafy vegetables, yam, tofu, pomfret and other seafood, beef balls, fish balls, pork balls, mushrooms and Chinese noodles, among others. Teochew hot pot, like other Chinese hot pots, is served in a large communal metal pot at the center of the dining table.
|-
| Teochew Oyster Congee
|
|
|
|
| Teochew congee with oysters and minced pork
|-
| Teochew rice noodle soup
|
|
|
| (Teochew kuay teow)
| A quintessential Teochew-style noodle soup that is also particularly popular in Vietnam and Cambodia (known respectively as hủ tiếu /hủ tíu and គុយទាវ kuyteav), through the influx of Teochew immigrants. It is a dish of yellow egg noodles and thin rice noodles served in a delicate, fragrant soup with meatballs, other various meats, seafood (such as shrimp), fried fishcake slices, quail eggs, blanched Chinese cabbage and sometimes offal. The soup base is typically made of pork or chicken bones and dried squid. Just before serving, the noodle soup is garnished with fried minced garlic, fried shallots, thinly sliced scallions and fresh cilantro (coriander) sprigs. For those who enjoy their noodle soup with added depth, the solid ingredients may be dipped into Shacha sauce or Teochew chilli oil.
|-
| Teochew-style congee
|
|
|
| (Teochew mue)
| A rice soup that has a more watery texture as compared to the Cantonese congee. It is commonly served with various salty accompaniments such as salted vegetables (kiam chai), preserved radish (chai por), black Chinese olives (烏橄欖), olive grits (橄欖糝), boiled salted duck eggs, fried salted fish and fried peanuts.
|-
| Teochew-style steamed pomfret
|
|
|
| (Teochew chue chioh her)
| Silvery pomfret steamed with preserved salted vegetables, lard and sour plums.
|-
| Yusheng
|
|
|
| (her sae)
| A raw fish salad (similar to ceviche or sashimi) whose typical ingredients include fresh salmon, white radish, carrot, red pepper (capsicum), ginger, kaffir lime leaves, Chinese parsley, chopped peanuts, toasted sesame seeds, Chinese shrimp crackers or fried dried shrimp, and five-spice powder, with the dressing primarily made from plum sauce. It is customarily served as an appetiser to bring good luck for the new year and is usually eaten on the seventh day of the Lunar New Year.
|-
|}
Gallery
<gallery class"center" widths"200">
File:HK Wan Chai 春園街 Spring Garden Lane night Chiu Chow food shop window.jpg|"Flavor potted" goose ()
File:Teochew Sweet Yam Paste - After Stirring.jpg|Taro paste ()
File:Shui jing bao zz.JPG|Crystal balls ()
File:Teochew pomfret.jpg|Steamed fish ()
File:Oyster omelette.jpg|Oyster omelette ()
File:Khanom kuichai.jpg|Fried chive dumplings ()
File:Song dynasty's 'patriotic soup' (prepared in Clovis California) 宋朝的“護國菜”（在加利福尼亞克洛維斯市製備）。.jpg|Patriotic Soup (Protect the Country Dish ())
File:Fried Tofu (炸豆腐).jpg|A dish of fried tofu () with dipping sauce.
File:Teochew rice noodle soup (潮州粿條).jpg|Teochew rice noodle soup ().
File:Sautéed Prawns with Olive Vegetables (欖菜焗蝦).jpg|Sautéed prawns with olive vegetables () .
File:Teochew Hotpot (prepared in Clovis California) 潮州火鍋（在加利福尼亞克洛維斯市製備）.jpg|Teochew hotpot ()
File:Sichuan pepper chicken - air-fried version (川椒雞 - 氣炸版).jpg|Sichuan pepper chicken ()
File:Mixed Bak Kut Teh - Teochew Bak Kut Teh (4590434658).jpg|Bak Kut Teh (肉骨茶)
</gallery>
See also
*List of Chinese dishes
*Teochew porridge
*Teochew people
References
External links
*[http://www.sfgate.com/cgi-bin/article.cgi?f=/chronicle/archive/2007/09/19/FD2SRSDKH.DTL Yeo's Teochew Popiah Recipe]
*[http://www.jenius.com.au/2011/02/teochew_peach-shaped_kueh.php Jenius' Teochew peach shaped kueh Recipe]
Category:Chaozhou
Category:Regional cuisines of China
|
https://en.wikipedia.org/wiki/Teochew_cuisine
|
2025-04-05T18:27:44.148196
|
6184
|
Co-NP
|
{{unsolved|computer science|{{tmath|1\textsf{NP}\ \overset{?}{}\ \textsf{co-NP} }} }}
In computational complexity theory, co-NP is a complexity class. A decision problem X is a member of co-NP if and only if its complement is in the complexity class NP. The class can be defined as follows: a decision problem is in co-NP if and only if for every no-instance we have a polynomial-length "certificate" and there is a polynomial-time algorithm that can be used to verify any purported certificate.
That is, co-NP is the set of decision problems where there exists a polynomial and a polynomial-time bounded Turing machine M such that for every instance x, x is a no-instance if and only if: for some possible certificate c of length bounded by , the Turing machine M accepts the pair .Complementary problems
While an NP problem asks whether a given instance is a yes-instance, its complement asks whether an instance is a no-instance, which means the complement is in co-NP. Any yes-instance for the original NP problem becomes a no-instance for its complement, and vice versa.
Unsatisfiability
An example of an NP-complete problem is the Boolean satisfiability problem: given a Boolean formula, is it satisfiable (is there a possible input for which the formula outputs true)? The complementary problem asks: "given a Boolean formula, is it unsatisfiable (do all possible inputs to the formula output false)?". Since this is the complement of the satisfiability problem, a certificate for a no-instance is the same as for a yes-instance from the original NP problem: a set of Boolean variable assignments which make the formula true. On the other hand, a certificate of a yes-instance for the complementary problem (whatever form it might take) would be equally as complex as for the no-instance of the original NP satisfiability problem.
co-NP-completeness
A problem L is co-NP-complete if and only if L is in co-NP and for any problem in co-NP, there exists a polynomial-time reduction from that problem to L.
Tautology reduction
Determining if a formula in propositional logic is a tautology is co-NP-complete: that is, if the formula evaluates to true under every possible assignment to its variables.
NP and co-NP are also thought to be unequal. If so, then no NP-complete problem can be in co-NP and no co-NP-complete problem can be in NP. This can be shown as follows. Suppose for the sake of contradiction there exists an NP-complete problem that is in co-NP. Since all problems in NP can be reduced to , it follows that for every problem in NP, we can construct a non-deterministic Turing machine that decides its complement in polynomial time; i.e., {{tmath|\textsf{NP} \subseteq \textsf{co-NP} }}. From this, it follows that the set of complements of the problems in NP is a subset of the set of complements of the problems in co-NP; i.e., {{tmath|\textsf{co-NP} \subseteq \textsf{NP} }}. Thus {{tmath|1\textsf{co-NP} \textsf{NP} }}. The proof that no co-NP-complete problem can be in NP if {{tmath|\textsf{NP} \neq \textsf{co-NP} }} is symmetrical.
co-NP is a subset of PH, which itself is a subset of PSPACE.
Integer factorization
An example of a problem that is known to belong to both NP and co-NP (but not known to be in P) is Integer factorization: given positive integers m and n, determine if m has a factor less than n and greater than one. Membership in NP is clear; if m does have such a factor, then the factor itself is a certificate. Membership in co-NP is also straightforward: one can just list the prime factors of m, all greater or equal to n, which the verifier can confirm to be valid by multiplication and the AKS primality test. It is presently not known whether there is a polynomial-time algorithm for factorization, equivalently that integer factorization is in P, and hence this example is interesting as one of the most natural problems known to be in NP and co-NP but not known to be in P. References External links
*
Category:Complexity classes
|
https://en.wikipedia.org/wiki/Co-NP
|
2025-04-05T18:27:44.153086
|
6185
|
Chuck Yeager
|
| birth_place = Myra, West Virginia, U.S.
| death_date =
| death_place = Los Angeles, California,<!--Links not needed per MOS:OVERLINK--> U.S.
| placeofburial | allegiance
| branch = United States Army Air Forces|}}
| serviceyears =
| rank = Brigadier general
| battles =
| awards =
| spouse =
*
}}
| children = 4
| relations = Steve Yeager (cousin)
| laterwork =
| website =
| signature = Chuck Yeager signature.SVG
| signature_size = 150px
}}
Brigadier General Charles Elwood Yeager ( , February 13, 1923December 7, 2020) was a United States Air Force officer, flying ace, and record-setting test pilot who in October 1947 became the first pilot in history confirmed to have exceeded the speed of sound in level flight.
Yeager was raised in Hamlin, West Virginia. His career began in World War II as a private in the United States Army, assigned to the Army Air Forces in 1941. After serving as an aircraft mechanic, in September 1942, he entered enlisted pilot training and upon graduation was promoted to the rank of flight officer (the World War II Army Air Force version of the Army's warrant officer), later achieving most of his aerial victories as a P-51 Mustang fighter pilot on the Western Front, where he was credited with shooting down 11.5 enemy aircraft. The half credit is from a second pilot assisting him in a single shootdown. On October 12, 1944, he attained "ace in a day" status, shooting down five enemy aircraft in one mission.
After the war, Yeager became a test pilot and flew many types of aircraft, including experimental rocket-powered aircraft for the National Advisory Committee for Aeronautics (NACA). Through the NACA program, he became the first human to officially break the sound barrier on October 14, 1947, when he flew the experimental Bell X-1 at Mach 1.05 at an altitude of , for which he won both the Collier and Mackay trophies in 1948. He broke several other speed and altitude records in the following years. In 1962, he became the first commandant of the USAF Aerospace Research Pilot School, which trained and produced astronauts for NASA and the Air Force.
Yeager later commanded fighter squadrons and wings in Germany, as well as in Southeast Asia during the Vietnam War. In recognition of his achievements and the outstanding performance ratings of those units, he was promoted to brigadier general in 1969 and inducted into the National Aviation Hall of Fame in 1973, retiring on March 1, 1975, for its colloquial similarity to "Mach 1". His three-war active-duty flying career spanned more than 30 years and took him to many parts of the world, including the Korean War zone and the Soviet Union during the height of the Cold War.
Yeager is referred to by many as one of the greatest pilots of all time, and was ranked fifth on Flying list of the 51 Heroes of Aviation in 2013. He flew more than 360 different types of aircraft over a 70-year period, and continued to fly for two decades after retirement as a consultant pilot for the United States Air Force. In 2020 at the age of 97, Yeager died in a Los Angeles-area hospital.
Early life and education
Yeager was born February 13, 1923, in Myra, West Virginia, to farming parents Albert Hal Yeager (1896–1963) and Susie Mae Yeager (; 1898–1987). When he was five years old, his family moved to Hamlin, West Virginia. Yeager had two brothers, Roy and Hal Jr., and two sisters, Doris Ann (accidentally killed at age two by four-year-old Roy playing with a firearm) and Pansy Lee.
He attended Hamlin High School, where he played basketball and football, receiving his best grades in geometry and typing. He graduated from high school in June 1941.
His first experience with the military was as a teen at the Citizens Military Training Camp at Fort Benjamin Harrison, Indianapolis, Indiana, during the summers of 1939 and 1940. On February 26, 1945, Yeager married Glennis Dickhouse. The couple had four children. Glennis Yeager died in 1990, predeceasing her husband by 30 years.
His cousin, Steve Yeager, was a professional baseball catcher.
Career
World War II
On September 12, 1941, Yeager enlisted as a private in the U.S. Army Air Forces (USAAF), and became an aircraft mechanic at George Air Force Base, Victorville, California. At enlistment, Yeager was not eligible for flight training because of his age and educational background, but the entry of the U.S. into World War II less than three months later prompted the USAAF to alter its recruiting standards. Yeager had unusually sharp vision, a visual acuity rated 20/10, which once enabled him to shoot a deer at .
At the time of his flight training acceptance, he was a crew chief on an AT-11. He received his pilot wings and a promotion to flight officer at Luke Field, Arizona, where he graduated from Class 43C on March 10, 1943. Assigned to the 357th Fighter Group at Tonopah, Nevada, he initially trained as a fighter pilot, flying Bell P-39 Airacobras (being grounded for seven days for clipping a farmer's tree during a training flight), and shipped overseas with the group on November 23, 1943.
in the United States Army Air Forces.]]
Stationed in the United Kingdom at RAF Leiston, Yeager flew P-51 Mustangs in combat with the 363d Fighter Squadron. He named his aircraft Glamorous Glen after his girlfriend, Glennis Faye Dickhouse, who became his wife in February 1945. Yeager had gained one victory before he was shot down over France in his first aircraft (P-51B-5-NA s/n 43-6763) on March 5, 1944, on his eighth mission. He escaped to Spain on March 30, 1944, with the help of the Maquis (French Resistance) and returned to England on May 15, 1944. During his stay with the Maquis, Yeager assisted the guerrillas in duties that did not involve direct combat; he helped construct bombs for the group, a skill that he had learned from his father. He was awarded the Bronze Star for helping a navigator, Omar M. "Pat" Patterson Jr., to cross the Pyrenees.
Despite a regulation prohibiting "evaders" (escaped pilots) from flying over enemy territory again, the purpose of which was to prevent resistance groups from being compromised by giving the enemy a second chance to possibly capture him, Yeager was reinstated to flying combat. He had joined another evader, fellow P-51 pilot 1st Lt Fred Glover, in speaking directly to the Supreme Allied Commander, General Dwight D. Eisenhower, on June 12, 1944. "I raised so much hell that General Eisenhower finally let me go back to my squadron" Yeager said. "He cleared me for combat after D Day, because all the free Frenchmen – Maquis and people like that – had surfaced". Eisenhower, after gaining permission from the War Department to decide the requests, concurred with Yeager and Glover.
, Glamorous Glen III, is the aircraft in which Yeager achieved most of his aerial victories.]]
Yeager demonstrated outstanding flying skills and combat leadership. On October 12, 1944, he became the first pilot in his group to make "ace in a day," downing five enemy aircraft in a single mission. Two of these victories were scored without firing a single shot: when he flew into firing position against a Messerschmitt Bf 109, the pilot of the aircraft panicked, breaking to port and colliding with his wingman. Yeager said both pilots bailed out. He finished the war with 11.5 official victories, including one of the first air-to-air victories over a jet fighter, a German Messerschmitt Me 262 that he shot down as it was on final approach for landing.
Yeager's official statement of the 12 October mission states:
In his 1986 memoirs, Yeager recalled with disgust that "atrocities were committed by both sides", and said he went on a mission with orders from the Eighth Air Force to "strafe anything that moved". During the mission briefing, he whispered to Major Donald H. Bochkay, "If we are going to do things like this, we sure as hell better make sure we are on the winning side". He also expressed bitterness at his treatment in England during World War II, describing the British as "arrogant" and "nasty" on Twitter.
Yeager was commissioned a second lieutenant while at Leiston, and was promoted to captain before the end of his tour. He flew his 61st and final mission on January 15, 1945, and returned to the United States in early February 1945. As an evader, he received his choice of assignments and, because his new wife was pregnant, chose Wright Field to be near his home in West Virginia. His high number of flight hours and maintenance experience qualified him to become a functional test pilot of repaired aircraft, which brought him under the command of Colonel Albert Boyd, head of the Aeronautical Systems Flight Test Division. Post-World War II Test pilot – breaking the sound barrier After the war, Yeager remained in the U.S. Army Air Forces. Upon graduating from Air Materiel Command Flight Performance School (Class 46C), Yeager became a test pilot at Muroc Army Air Field (now Edwards Air Force Base). After Bell Aircraft test pilot Chalmers "Slick" Goodlin demanded <!--over US$1.7 million in 2020 dollars--> to break the sound "barrier", the USAAF selected the 24-year-old Yeager to fly the rocket-powered Bell XS-1 in a NACA program to research high-speed flight. Under the National Security Act of 1947, the USAAF became the United States Air Force (USAF) on September 18.
named Glamorous Glennis. He named all of his assigned aircraft in some variation after his wife.]]
Yeager's flight was scheduled for October 14. Two nights before his flight, Yeager went horseback riding with his wife, fell, and broke two ribs under his right arm. Worried the injury would remove him from the mission, Yeager had civilian doctor in nearby Rosamond tape his ribs. over the Rogers Dry Lake of the Mojave Desert in California. The success of the mission was not announced to the public for nearly eight months, until June 10, 1948. Yeager was awarded the Mackay Trophy and the Collier Trophy in 1948 for his mach-transcending flight, and the Harmon International Trophy in 1954. The X-1 he flew that day was later put on permanent display at the Smithsonian Institution's National Air and Space Museum. During 1952, he attended the Air Command and Staff College.
Yeager continued to break many speed and altitude records. He was one of the first American pilots to fly a Mikoyan-Gurevich MiG-15, after its pilot, No Kum-sok, defected to South Korea. Returning to Muroc, during the latter half of 1953, Yeager was involved with the USAF team that was working on the X-1A, an aircraft designed to surpass Mach 2 in level flight. That year, he flew a chase aircraft for the civilian pilot Jackie Cochran as she became the first woman to fly faster than sound.
The new record flight, however, did not entirely go to plan, since shortly after reaching Mach 2.44, Yeager lost control of the X-1A at about due to inertia coupling, a phenomenon largely unknown at the time. With the aircraft simultaneously rolling, pitching, and yawing out of control, Yeager dropped in less than a minute before regaining control at around . He then managed to land without further incident.
Military command
, 1959.]]
Yeager was foremost a fighter pilot and held several squadron and wing commands. From 1954 to 1957, he commanded the F-86H Sabre-equipped 417th Fighter-Bomber Squadron (50th Fighter-Bomber Wing) at Hahn AB, West Germany, and Toul-Rosieres Air Base, France; and from 1957 to 1960 the F-100D Super Sabre-equipped 1st Fighter Day Squadron <!-- (later, while still under Yeager's command, re-designated the 306th Tactical Fighter Squadron) -->at George Air Force Base, California, and Morón Air Base, Spain.
He was a full colonel in 1962, after completion of a year's studies and final thesis on STOL aircraft at the Air War College. He became the first commandant of the USAF Aerospace Research Pilot School, which produced astronauts for NASA and the USAF, after its redesignation from the USAF Flight Test Pilot School. He had only a high school education, so he was not eligible to become an astronaut like those he trained. In April 1962, Yeager made his only flight with Neil Armstrong. Their job, flying a T-33, was to evaluate Smith Ranch Dry Lake in Nevada for use as an emergency landing site for the North American X-15. In his autobiography, Dwight details how Yeager's leadership led to discriminatory treatment throughout his training at Edwards Air Force Base.
Between December 1963 and January 1964, Yeager completed five flights in the NASA M2-F1 lifting body. An accident during a December 1963 test flight in one of the school's NF-104s resulted in serious injuries. After climbing to a near-record altitude, the plane's controls became ineffective, and it entered a flat spin. After several turns, and an altitude loss of approximately 95,000 feet, Yeager ejected from the plane. During the ejection, the seat straps released normally, but the seat base slammed into Yeager, with the still-hot rocket motor breaking his helmet's plastic faceplate and causing his emergency oxygen supply to catch fire. The resulting burns to his face required extensive and agonizing medical care. This was Yeager's last attempt at setting test-flying records.
In 1966, Yeager took command of the 405th Tactical Fighter Wing at Clark Air Base, the Philippines, whose squadrons were deployed on rotational temporary duty (TDY) in South Vietnam and elsewhere in Southeast Asia. There he flew 127 missions. In February 1968, Yeager was assigned command of the 4th Tactical Fighter Wing at Seymour Johnson Air Force Base, North Carolina, and led the McDonnell Douglas F-4 Phantom II wing in South Korea during the Pueblo crisis.
From 1971 to 1973, at the behest of Ambassador Joseph Farland, Yeager was assigned as the Air Attache in Pakistan to advise the Pakistan Air Force which was led by Abdur Rahim Khan (the first Pakistani to break the sound barrier). He arrived in Pakistan at a time when tensions with India were at a high level. One of Yeager's jobs during this time was to assist Pakistani technicians in installing AIM-9 Sidewinders on PAF's Shenyang F-6 fighters. He also had a keen interest in interacting with PAF personnel from various Pakistani Squadrons and helping them develop combat tactics. After hostilities broke out in 1971, he decided to stay in West Pakistan and continued overseeing the PAF's operations.
During the war, he flew around the western front in a helicopter documenting wreckages of Indian aircraft of Soviet origin, which included Sukhoi Su-7s and MiG-21s. These aircraft were transported to the United States after the war for analysis. Yeager also flew around in his Beechcraft Queen Air, a small passenger aircraft that was assigned to him by the Pentagon, picking up shot-down Indian fighter pilots. The Beechcraft was later destroyed during an air raid by the IAF at a Pakistani airbase when Yeager was not present. Edward C. Ingraham, a U.S. diplomat who had served as political counselor to Ambassador Farland in Islamabad, recalled this incident in the Washington Monthly of October 1985: "After Yeager's Beechcraft was destroyed during an Indian air raid, he raged to his cowering colleagues that the Indian pilot had been specifically instructed by Indira Gandhi to blast his plane. 'It was', he later wrote, 'the Indian way of giving Uncle Sam the finger'". Yeager was incensed over the incident and demanded U.S. retaliation. Post-retirement and in popular culture On March 1, 1975, Yeager retired from the Air Force at Norton Air Force Base, California.
Yeager made a cameo appearance in the movie The Right Stuff (1983). He played "Fred", a bartender at "Pancho's Place", which was most appropriate, because he said, "if all the hours were ever totaled, I reckon I spent more time at her place than in a cockpit over those years". Sam Shepard portrayed Yeager in the film, which chronicles in part his famous 1947 record-breaking flight.
Yeager has been referenced several times in the shared Star Trek universe, including having a namesake fictional type of starship, a dangerous starship formation-maneuver named after him called the "Yeager Loop" (most notably mentioned in the Star Trek: The Next Generation episode "The First Duty"), and appearing in archival footage within the opening title sequence for the series Star Trek: Enterprise (2001–2005). For Enterprise, executive producer Rick Berman said that he envisaged the lead character, Captain Jonathan Archer, as being "halfway between Chuck Yeager and Han Solo".
For several years in the 1980s, Yeager was connected to General Motors, publicizing ACDelco, the company's automotive parts division. In 1986, he was invited to drive the Chevrolet Corvette pace car for the 70th running of the Indianapolis 500. In 1988, Yeager was again invited to drive the pace car, this time at the wheel of an Oldsmobile Cutlass Supreme. In 1986, President Reagan appointed Yeager to the Rogers Commission that investigated the explosion of the Space Shuttle Challenger.
During this time, Yeager also served as a technical adviser for three Electronic Arts flight simulator video games. The games include ''Chuck Yeager's Advanced Flight Trainer, Chuck Yeager's Advanced Flight Trainer 2.0, and Chuck Yeager's Air Combat''. The game manuals feature quotes and anecdotes from Yeager and were well received by players. Missions feature several of Yeager's accomplishments and let players challenge his records. ''Chuck Yeager's Advanced Flight Trainer'' was Electronic Art's top-selling game for 1987.
In 2009, Yeager participated in the documentary The Legend of Pancho Barnes and the Happy Bottom Riding Club, a profile of his friend Pancho Barnes. The documentary was screened at film festivals, aired on public television in the United States, and won an Emmy Award.
On October 14, 1997, on the 50th anniversary of his historic flight past Mach 1, he flew a new Glamorous Glennis III'', an F-15D Eagle, past Mach 1. The chase plane for the flight was an F-16 Fighting Falcon piloted by Bob Hoover, a longtime test, fighter, and aerobatic pilot who had been Yeager's wingman for the first supersonic flight. At the end of his speech to the crowd in 1997, Yeager concluded, "All that I am ... I owe to the Air Force". Later that month, he was the recipient of the Tony Jannus Award for his achievements.
On October 14, 2012, on the 65th anniversary of breaking the sound barrier, Yeager did it again at the age of 89, flying as co-pilot in a McDonnell Douglas F-15 Eagle piloted by Captain David Vincent out of Nellis Air Force Base.
In October 2016, Yeager reached international headlines when a Twitter argument he was having with an Irish teenager led to him lashing out at the British and Irish, namely calling Irish people British, and labeling all British people as "nasty" and "arrogant". No stranger to controversy in his life, this was one of Yeager's last major public faux-pas.
Awards and decorations
<!-- Deleted image removed: -->
In 1973, Yeager was inducted into the National Aviation Hall of Fame, arguably aviation's highest honor. In 1974, Yeager received the Golden Plate Award of the American Academy of Achievement. In December 1975, the U.S. Congress awarded Yeager a silver medal "equivalent to a noncombat Medal of Honor ... for contributing immeasurably to aerospace science by risking his life in piloting the X-1 research airplane faster than the speed of sound on October 14, 1947". President Gerald Ford presented the medal to Yeager in a ceremony at the White House on December 8, 1976.
Yeager never attended college and was often modest about his background, but is considered by many, including Flying Magazine, the California Hall of Fame, the State of West Virginia, National Aviation Hall of Fame, a few U.S. presidents, and the United States Army Air Force, to be one of the greatest pilots of all time. Air & Space/Smithsonian magazine ranked him the fifth greatest pilot of all time in 2003. Regardless of his lack of higher education, West Virginia's Marshall University named its highest academic scholarship the Society of Yeager Scholars in his honor. He was the chairman of Experimental Aircraft Association (EAA)'s Young Eagle Program from 1994 to 2004, and was named the program's chairman emeritus.
In 1966, Yeager was inducted into the International Air & Space Hall of Fame. He was inducted into the International Space Hall of Fame in 1981. He was inducted into the Aerospace Walk of Honor 1990 inaugural class.
Yeager Airport in Charleston, West Virginia, is named in his honor. The Interstate 64/Interstate 77 bridge over the Kanawha River in Charleston is named in his honor. He also flew directly under the Kanawha Bridge and West Virginia named it the Chuck E. Yeager Bridge. On October 19, 2006, the state of West Virginia also honored Yeager with a marker along Corridor G (part of U.S. Highway 119) in his home Lincoln County, and also renamed part of it the Yeager Highway.
Yeager was an honorary board member of the humanitarian organization Wings of Hope. On August 25, 2009, Governor Arnold Schwarzenegger and Maria Shriver announced that Yeager would be one of 13 California Hall of Fame inductees in The California Museum's yearlong exhibit. The induction ceremony was on December 1, 2009, in Sacramento, California. Flying Magazine ranked Yeager number 5 on its 2013 list of The 51 Heroes of Aviation; for many years, he was the highest-ranked living person on the list.
The Civil Air Patrol, the volunteer auxiliary of the USAF, awards the Charles E. "Chuck" Yeager Award to its senior members as part of its Aerospace Education program.
{| class="wikitable"
|- style="background:#ccf; text-align:center;"
| colspan=2 |Badges, patches and tabs
|-
|
|U.S. Air Force Command Pilot Badge
|- style="background:#ccf; text-align:center;"
| colspan=2 |Personal decorations
|-
|
|Air Force Distinguished Service Medal (retirement award in 1975)
|-
|
|Distinguished Service Medal (Army design awarded in 1954)
|-
|
|Silver Star with bronze oak leaf cluster (for shooting down five Messerschmitt Bf 109s in one day)
|-
|
|Legion of Merit with bronze oak leaf cluster
|-
|
|Distinguished Flying Cross with two bronze oak leaf clusters (for a Messerschmitt Me 262 kill and first to break the sound barrier)
|-
|
|Bronze Star Medal with bronze valor device (for helping rescue a fellow airman from Occupied France
|-
|
|Republic of Vietnam Gallantry Cross Unit Citation
|-
|
|Republic of Vietnam Campaign Medal
|}
Other achievements
)]]
* 1940–1949 – Harmon Trophy: Citation of Honorable Mention
* 1947 – Collier Trophy and Mackay Trophy, for breaking the sound barrier for the first time.
* 1953 – Harmon Trophy
* 1976 – Congressional Silver Medal Dates of rank {|class"wikitable plainrowheaders" style="background:white"
! scope="col" | Insignia
! scope="col" | Rank
! scope="col" | Service and Component
! scope="col" | Date
|-
|align="center" |no insignia at the time
!scope="row" | Private
| United States Army
Regular Army<br/>(Army Air Corps)
| September 12, 1941Aerial victory credits{| class"wikitable" style="margin:auto; width:600px;"
|- style="color:blue;"
! style"background:#39f;"|Date !! style"background:#39f;"|# !! style"background:#39f;"|Type !! style"background:#39f;"|Location !! style"background:#39f;"|Aircraft flown !! style"background:#39f;"|Unit Assigned
|-
|-style="background: #eeeeee;"
|March 4, 1944||aligncenter|1 ||aligncenter|Messerschmitt Bf 109||aligncenter|Kassel, Germany||aligncenter|P-51||align=center|363 FS, 357 FG
|-
|September 13, 1944||aligncenter|0.5 ||aligncenter|Bf 109||aligncenter|Kassel, Germany||aligncenter|P-51||align=center|363 FS, 357 FG
|-
|-style="background: #eeeeee;"
|October 12, 1944||aligncenter|5 ||aligncenter|Bf 109||aligncenter|Hanover, Germany||aligncenter|P-51||align=center|363 FS, 357 FG
|-
|November 6, 1944||aligncenter|1 ||aligncenter|Messerschmitt Me 262||aligncenter|Assen, Germany||aligncenter|P-51||align=center|363 FS, 357 FG
|-style="background: #eeeeee;"
|November 27, 1944||aligncenter|4 ||aligncenter|Focke-Wulf Fw 190||aligncenter|Magdeburg, Germany||aligncenter|P-51||align=center|363 FS, 357 FG
|}
Personal life
to commemorate the 65th anniversary of his historic flight.]]
Yeager named his plane after his wife, Glennis, as a good-luck charm: "You're my good-luck charm, hon. Any airplane I name after you always brings me home." Yeager and Glennis moved to Grass Valley, California, after his retirement from the Air Force in 1975. The couple prospered as a result of Yeager's best-selling autobiography, speaking engagements, and commercial ventures. Glennis Yeager died of ovarian cancer in 1990. They had four children (Susan, Don, Mickey, and Sharon). Yeager's son Mickey (Michael) died unexpectedly in Oregon, on March 26, 2011.
Yeager appeared in a Texas advertisement for George H. W. Bush's 1988 presidential campaign.
In 2000, Yeager met actress Victoria Scott D'Angelo on a hiking trail in Nevada County. The pair started dating shortly thereafter, and married in August 2003. A bitter dispute arose between Yeager, his children, and D'Angelo. The children contended that she, at least 35 years Yeager's junior, had married him for his fortune. Yeager and D'Angelo both denied the charge. Litigation ensued, in which his children accused D'Angelo of "undue influence" on Yeager, and Yeager accused his children of diverting millions of dollars from his assets. In August 2008, the California Court of Appeal ruled for Yeager, finding that his daughter Susan had breached her duty as trustee.
Yeager lived in Grass Valley, Northern California and died in the afternoon of December 7, 2020 (National Pearl Harbor Remembrance Day), at age 97, in a Los Angeles hospital. Following his death, President Donald Trump issued a statement of condolences stating Yeager "was one of the greatest pilots in history, a proud West Virginian, and an American original who relentlessly pushed the boundaries of human achievement". See also
* History of aviation
* List of firsts in aviation
* Society of Experimental Test Pilots
Notes
References Further reading
*
*
* Wolfe, Tom The Right Stuff New York: Farrar-Straus-Giroux, 1979
* Yeager, Chuck, Bob Cardenas, Bob Hoover, Jack Russell and James Young The Quest for Mach One: A First-Person Account of Breaking the Sound Barrier New York: Penguin Studio, 1997
* Yeager, Chuck and Leo Janos, Yeager: An Autobiography New York: Bantam, 1985
External links
*
* [http://www.chuckyeager.org/history/background/ Biography from ChuckYeager.org]
* [https://www.af.mil/About-Us/Biographies/Display/Article/105165/charles-e-chuck-yeager/ U.S. Air Force: Chuck Yeager biography]
* [https://www.biography.com/political-figure/chuck-yeager Yeager in Biography.com]
* [http://www.nationalaviation.org/our-enshrinees/yeager-charles-chuck/ Biography in the National Aviation Hall of Fame]
* [https://achievement.org/achiever/general-chuck-yeager/#interview General Chuck Yeager, USAF, Biography and Interview] with the American Academy of Achievement
*
* [http://airportjournals.com/chuck-yeager-booming-and-zooming-part-1/ Airport Journals' "Chuck Yeager: Booming And Zooming" Part 1] and [http://airportjournals.com/chuck-yeager-booming-and-zooming-part-2/ Part 2]
* [http://www.aerospaceweb.org/question/history/q0011a.shtml "Chuck Yeager & the Sound Barrier" in Aerospaceweb.org]
* [https://web.archive.org/web/20060502161501/http://www.edwards.af.mil/history/docs_html/people/yeager_biography.html Space.com: Chuck Yeager]
*
*
* [https://www.nytimes.com/2020/12/07/us/chuck-yeager-dead.html Yeager obituary] via The New York Times
Category:1923 births
Category:2020 deaths
Category:American aviation record holders
Category:American expatriates in Pakistan
Category:American people of German descent
Category:American test pilots
Category:American Vietnam War pilots
Category:American World War II flying aces
Category:Articles containing video clips
Category:Aviation history of the United States
Category:American aviation pioneers
Category:Aviators from West Virginia
Category:Collier Trophy recipients
Category:Experimental Aircraft Association
Category:Harmon Trophy winners
Category:Knights of the Legion of Honour
Category:Mackay Trophy winners
Category:Military personnel from West Virginia
Category:National Aviation Hall of Fame inductees
Category:Order of National Security Merit members
Category:People from Hamlin, West Virginia
Category:People from Lincoln County, West Virginia
Category:Presidential Medal of Freedom recipients
Category:Recipients of the Air Force Distinguished Service Medal
Category:Recipients of the Air Medal
Category:Recipients of the Distinguished Flying Cross (United States)
Category:Recipients of the Distinguished Service Medal (US Army)
Category:Recipients of the Legion of Merit
Category:Recipients of the Silver Star
Category:Shot-down aviators
Category:Survivors of aviation accidents or incidents
Category:U.S. Air Force Test Pilot School alumni
Category:United States Air Force generals
Category:United States Air Force personnel of the Vietnam War
Category:United States Army Air Forces officers
Category:United States Army Air Forces pilots of World War II
|
https://en.wikipedia.org/wiki/Chuck_Yeager
|
2025-04-05T18:27:44.219836
|
6186
|
Cajun cuisine
|
, the state dish of Louisiana, prepared with seafood in a Cajun style.]]
Cajun cuisine ( , ) is a subset of Louisiana cooking developed by the Cajuns, itself a Louisianan development incorporating elements of Native American, West African, French, and Spanish cuisine.
Cajun cuisine is often referred to as a "rustic" cuisine, meaning that it is based on locally available ingredients and that preparation is simple. Cajuns historically cooked their dishes, gumbo for example, in one pot.
Crawfish, shrimp, and andouille sausage are staple meats used in a variety of dishes. The aromatic vegetables green bell pepper (), onion, and celery are called "the trinity" by chefs in Cajun and Louisiana Creole cuisines. Roughly diced and combined in cooking, the method is similar to the use of the mirepoix in traditional French cuisine which blends roughly diced carrot, onion, and celery. Additional characteristic aromatics for both the Creole and Cajun versions may include parsley, bay leaf, thyme, green onions, ground cayenne pepper, and ground black pepper. Cayenne and Louisiana-style hot sauce are the primary sources of spice in Cajun cuisine, which usually tends towards a moderate, well-balanced heat, despite the national "Cajun hot" craze of the 1980s and 1990s.
History
The Acadians were a group of French colonists who lived in Acadia, what is today Eastern Canada. In the mid-18th century, they were deported from Acadia by the British during the French and Indian War in what they termed le Grand Dérangement, and many of them ended up settling in southern Louisiana.
is a staple Cajun starch.]]
Due to the extreme change in climate from that of Acadia, Acadians were unable to cook their original dishes. Soon, their former culinary traditions were adapted and, in time, incorporated not only Native American traditions, but also African-American traditions—as is exemplified in the classic Cajun dish "gumbo", which takes its name from the word for its principal ingredient, okra, in the West African Bambara language. In Louisiana, the Acadian settlers replaced the whole wheat bread they were accustomed to with cornbread, which by the beginning of the 19th century they were eating with cane syrup. Between 1790 and 1810 most Louisiana Acadians bought one to three enslaved black persons, many of whom who had come from the West Indies, from whom they learned the use of new ingredients, including okra, to incorporate in their cuisine. The ragu sauces that the Cajuns developed are very similar to sauces used in French West Africa, possibly introduced by enslaved cooks.
Many other meals developed along these lines, adapted in no small part from Haiti, to become what is now considered classic Cajun cuisine traditions (not to be confused with the more modern concept associated with Prudhomme's style).
Up through the 20th century, the meals were not elaborate but instead, rather basic. The public's false perception of "Cajun" cuisine was based on Prudhomme's style of Cajun cooking, which was spicy, flavorful, and not true to the classic form of the cuisine.
Cajun and Creole cuisine have mistakenly been considered the same, but the origins of Creole cooking are in New Orleans, and Cajun cooking arose 40 years after its establishment. Today, most restaurants serve dishes that consist of Cajun styles, which Paul Prudhomme dubbed "Louisiana cooking". In Cajun home-cooking, these individual styles are still kept separate. However, there are fewer and fewer people cooking the classic Cajun dishes that would have been eaten by the original settlers.
Cultural aspects
According to political scientist Kevin V. Mulcahy writing on cultural identity, Cajun cuisine today is different from that of the 19th and early 20th centuries, but still defines Cajun culture for many people within and outside Acadiana. Its heritage reflects French, Spanish, American Indian, German, and Afro-Caribbean influences. Cajun food is the result of this assimilation or "cultural blending". Rural Cajun cuisine is distinct from the urban Creole cuisine, having arisen by economic necessity among the Acadian immmigrants who came to Louisiana in the 18th century. These settlers lived off the land and survived on foods they could obtain by hunting, fishing, ranching, foraging, or growing crops.
Although there is a large variety of dishes within the regions that make up Cajun country in Louisiana, rural Cajuns generally prefer strong dark roast coffee, highly seasoned foods, hot peppers, vegetables smothered in brown gravy, and one-pot dishes served with rice. Each region has its own specialties, such as andouille sausage on the west bank of the Mississippi River above New Orleans, formerly known as the German Coast; barbecued shrimp in Terrebonne Parish; tasso ham made from hog's shoulder in the area around Opelousas; and crawfish all across the parishes of southern Louisiana, where they are abundant in the fresh water wetlands and waterways.
Many Cajun recipes are based on rice and the "holy trinity" of onions, celery, and green pepper, and use locally caught shell fish such as shrimp and crawfish. Much of Cajun cookery starts with a roux made of wheat flour cooked and slowly stirred with a fat such as oil, butter or lard, known especially as the base for étouffée, gumbo and sauce piquante.
There was continuity in cuisines between the southern Bayou Teche area and the northern boundary of Cajun country in Avoyelles Parish. Fresh sausage, pork, and the use of salt and pepper as the main seasonings were universal in the region's foodway traditions, north and south. The role of seafood in the cuisine of the southern parishes distinguished it from that of the prairies, where more wild game was consumed instead. Modern conveniences influenced Louisiana's culinary traditions: with the introduction of electricity and refrigerators, consuming freshly butchered meat immediately was not imperative as in the past, thus community events such as hog-killings (boucheries) occurred less frequently. Improved transportation and increased incomes made food stores more accessible and buying produce became more affordable for working families. Cajuns now bought their bread at a grocery store rather than baking their own. According to Gutierrez, when the economy of southern Louisiana boomed with the expansion of oil industry operations in the 1970s, Cajuns gained a renewed pride in their ethnicity. Shrimping, crabbing, fishing, frog-gigging, and gardening have been practiced in Terrebonne and Lafourche Parishes as subsistence and commercial pursuits for many generations. Before the introduction of modern transportation and refrigeration, Cajuns who lived in the southwestern prairie parishes away from the coast had little opportunity to incorporate seafood into their diets. Today, fresh seafood is available all across Acadiana, so that now it is regarded as a regional food rather than one available only to coastal residents. In the Ville Platte area, a unique sauce is made from dried onions reconstituted in water and vegetable oil thick with ketchup, mustard, Worcestershire sauce, and seasonings. The flavorful oil that rises to the top is applied directly to meats being cooked as a baste. Two popular brands are Jack Miller's and Pig Stand, which are available online and in grocery stores across the state. This sauce is also commonly used on hamburgers, hot dogs, pork chops, chicken, and other grilled items.
* Baking—direct and indirect dry heat in a furnace or oven, faster than smoking but slower than grilling
* Grilling—direct heat on a shallow surface, fastest of all variants; sub-variants include:
** Charbroiling—direct dry heat on a solid surface with wide raised ridges
** Gridironing—direct dry heat on a solid or hollow surface with narrow raised ridges
** Griddling—direct dry or moist heat along with the use of oils and butter on a flat surface
* Braising—combining a direct dry heat charbroil-grill or gridiron-grill with a pot filled with broth for direct moist heat, faster than smoking but slower than regular grilling and baking; time starts fast, slows down, then speeds up again to finish
* Boiling—as in boiling of blue crabs, crawfish, or shrimp, in seasoned liquid, often with side items like corn on the cob, whole new potatoes, and mushrooms cooked in the same boiling pot. A seafood boil is often a large outdoor social event.
* Deep frying—lightly breaded and fried seafood including various fish, shrimp, oysters, and soft-shell crab is universally popular in Cajun cuisine, often on French bread po-boys in the New Orleans style, along with traditional Southern favorites like fried chicken, fried okra, and pork chops.
* Smothering—cooking a vegetable or meat over low heat with the sauteed "trinity," plus small amounts of water or stock, similar to braising. This forms a pan sauce or gravy, and the finished product is served over rice. Étouffée is a popular variant done with crawfish or shrimp. A meatless version might feature mushrooms and eggplant. Two commonly smothered meats are pork chops and round steak]; these heartier meats may sometimes have a bit of roux added to the gravy.
* Pan-broiling or pan-frying
* Injecting—using a large syringe-type setup to place seasoning deep inside large cuts of meat; this technique is much newer than the others on this list, but very common in Cajun cuisine
* Stewing, also known as ; a whole chicken cut into pieces is a popular choice for this method, particularly an older hen.
Deep frying of turkeys or oven-roasted turduckens entered southern Louisiana cuisine more recently. Also, blackening of fish or chicken and barbecuing of shrimp in the shell are excluded because they were not prepared in traditional Cajun cuisine. Blackening was actually an invention by chef Paul Prudhomme in the 1970s, becoming associated with Cajun cooking, and presented as such by him, but is not a true historical or traditional Cajun cooking process.
Ingredients
In the late 18th century, about the same time that Acadian musicians embraced the Spanish guitar, spices from the Iberian Peninsula were adopted in the Acadian cuisine. With the cross-cultural borrowing that took place between them and their neighbors in southern Louisiana, Acadians were eating African okra and American Indian corn by the time of the Louisiana Purchase (1803) in such dishes as gumbo, pain de maïs, and soupe de maïs, which did not closely resemble the African and Indian versions.
The following is a partial list of ingredients used in Cajun cuisine and some of the staple ingredients of the Acadian food culture.
Meat and seafood
Cajun foodways include many ways of preserving meat, some of which are waning due to the availability of refrigeration and mass-produced meat at the grocer. Smoking of meats remains a fairly common practice, but once-common preparations such as turkey or duck confit (preserved in poultry fat, with spices) are now seen even by Acadians as quaint rarities.
Game (and hunting) are still uniformly popular in Acadiana.
The recent increase of catfish farming in the Mississippi Delta has brought about an increase in its usage in Cajun cuisine in place of the more traditional wild-caught speckled trout.
* Andouille—a spicy smoked pork sausage, characterized by a coarse-ground texture and large-diameter casing.
* Boudin—a cooked sausage made with green onions, pork, and rice, and usually a large amount of ground pork or chicken livers. Boudin may be thought of as "dirty rice in a casing." Some locals prefer to eat the sausage with the casing on, while others squeeze the contents out. Boudin filling is completely cooked before being stuffed into casings and may be consumed immediately after purchase, although it is also popularly grilled at cookouts. Pork blood is sometimes added to produce boudin rouge. Other versions can contain seafood, such as crawfish.
* Chaurice, a sausage similar to Spanish chorizo
* Chaudin or ponce—a pig's stomach, stuffed with spiced pork & smoked.
* Ham hocks
* Wild boar or feral hog
* Head cheese
* Gratons—hog cracklings or pork rinds; fried, seasoned pork fat & skin, sometimes with small bits of meat attached. Similar to Spanish chicharrones.
* New Orleans hot sausage—<nowiki/>a spiced pork or beef sausage characterized by a reddish color.
* Pork sausage (fresh)—distinctively seasoned and usually smoked, this sausage is often used in gumbos as is andouille, but it may also be grilled or pan-cooked to produce a rice and gravy dish. The sausage itself does not include rice, separating it from boudin. In Cajun country, a distinction exists between this sausage, which is simply called "pork sausage," is finer ground, and uses smaller pork casings, and the similar andouille, which has a coarser grind and larger beef casings.
* Salt pork
* Tasso—a highly seasoned, smoked pork shoulder
Beef and dairy<br>
Though parts of Acadiana are well suited to cattle or dairy farming, beef is not often used in a pre-processed or uniquely Cajun form. It is usually prepared fairly simply as chops, stews, or steaks, taking a cue from Texas to the west. Ground beef is used as is traditional throughout the US, although seasoned differently.
Dairy farming is not as prevalent as in the past, but there are still some farms in the business. There are no unique dairy items prepared in Cajun cuisine. Traditional Cajun and New Orleans Creole-influenced desserts are common.
, 1938.]]
Seasonings
* Onion (bell pepper, onion, and celery used together are known as the "holy trinity" of Cajun cuisine)
Thyme, sage, mint, marjoram, savory, and basil are considered sweet herbs. In colonial times a herbes de Provence would be several sweet herbs tied up in a muslin.Blended* "Creole/Cajun spice" blends such as Tony Chachere's are sometimes used in Cajun kitchens, but do not suit every cook's style because Creole- and Cajun-style seasoning is often achieved from scratch, even by taste.<div style="line-height: 0.22em;"></div>
:Cajun seasonings consist of a blend of salt with a variety of spices, most common being cayenne pepper and garlic. The spicy heat comes from the cayenne pepper, while other flavors come from bell pepper, paprika, green onions, parsley and more.
Cooking bases
* Dark roux—Cajuns inherited roux from the French. However, unlike the French, theirs is made with oil or bacon fat and more lately with olive oil, and not normally with butter. It is used as a thickening agent, especially in gumbo and étouffée.<div style="line-height: 0.22em;"></div>
:Preparation of a dark roux is probably the most involved or complicated procedure in Cajun cuisine, involving heating fat and flour very carefully, constantly stirring for about 15–45 minutes (depending on the color of the desired product), until the mixture has darkened in color and developed a nutty flavor. The temperature should not be too high, as a burnt roux renders a dish unpalatable.
* Light roux—The secret to making a good gumbo is pairing the roux with the protein. A dark roux, with its strong (dense) nutty flavor will completely overpower a simple seafood gumbo, but is the perfect complement to a gumbo using chicken, sausage, crawfish or alligator.<div style="line-height: 0.22em;"></div>
:A light roux, on the other hand, is better suited for strictly seafood dishes and unsuitable for meat gumbos for the reason that it does not support the heavier meat flavor as well. Pairing roux with protein follows the same orthodox philosophy as pairing wine with protein.
* Stocks: Cajun stocks are more heavily seasoned than Continental counterparts, and the shellfish stock sometimes made with shrimp and crawfish heads is unique to Cajun cuisine.
Cajun dishes
Primary favorites
]]
Boudin—a type of sausage made from pork, pork liver, rice, garlic, green onions and other spices. It is widely available by the link or pound from butcher shops. Boudin is typically stuffed in a natural casing and has a softer consistency than other, better-known sausage varieties. It is usually served with side dishes such as rice dressing, maque choux or bread. Boudin balls are commonly served in southern Louisiana restaurants and are made by taking the boudin out of the case and frying it in spherical form.
Gumbo—High on the list of favorites of Cajun cooking are the soups called gumbos. Contrary to non-Cajun or Continental beliefs, gumbo does not mean simply "everything in the pot". Gumbo exemplifies the influence of French, Spanish, African and Native American food cultures on Cajun cuisine.
The origins of the word gumbo are in West Africa. Kellersberger Vass lists kingumbo and tshingombo as the Bantu words for okra, while John Laudon of the University of Louisiana says the word gombo is a French word that came to the Western Hemisphere from West Africa, where okra was known as (ki) ngombo along much of the region's coast.
Both filé and okra can be used as thickening agents in gumbo. Historically, large amounts of filé were added directly to the pot when okra was out of season. While a distinction between filé gumbo and okra gumbo is still held by some, many people enjoy putting filé in okra gumbo simply as a flavoring. Regardless of which is the dominant thickener, filé is also provided at the table and added to taste.
Many claim that gumbo is a Cajun dish, but gumbo was established long before the Acadian arrival.
Its early existence came via the early French Creole culture in New Orleans, Louisiana, where French, Spanish and Africans frequented and also influenced by later waves of Italian, German and Irish settlers.
The backbone of a gumbo is roux, as described above. Cajun gumbo typically favors darker roux, often approaching the color of chocolate or coffee beans. Since the starches in the flour break down more with longer cooking time, a dark roux has less thickening power than a lighter one. While the stovetop method is traditional, flour may also be dry-toasted in an oven for a fat-free roux, or a regular roux may be prepared in a microwave oven for a hands-off method. If the roux is for immediate use, the "trinity" may be sauteed in it, which stops the cooking process.
A classic gumbo is made with chicken and andouille, especially in the colder months, but the ingredients vary according to what is available. Seafood gumbos are also very popular in Cajun country.
Jambalaya—The only certain thing that can be said about jambalaya is that it contains rice, some sort of meat (often chicken, ham, sausage, or a combination), seafood (such as shrimp or crawfish), plus other items that may be available. Usually, it will include green peppers, onions, celery, tomatoes and hot chili peppers. This is also a great pre-Acadian dish, established by the Spanish in Louisiana. Jambalaya may be a tomato-rich New Orleans-style "red" jambalaya of Spanish Creole roots, or a Cajun-style "brown" jambalaya which draws its color and flavor from browned meat and caramelized onions. Historically, tomatoes were not as widely available in Acadiana as the area around New Orleans, but in modern times, both styles are popular across the state. Brown is the style served at the annual World Jambalaya Festival in Gonzales.
Rice and gravy—Rice and gravy dishes are a staple of Cajun cuisine and is usually a brown gravy based on pan drippings, which are deglazed and simmered with extra seasonings and served over steamed or boiled rice.
The dish is traditionally made from cheaper cuts of meat and cooked in a cast-iron pot, typically for an extended time period to let the tough cuts of meat become tender. Beef, pork, chicken or any of a large variety of game meats are used for its preparation. Popular local varieties include hamburger steak, smothered rabbit, turkey necks, and chicken fricassee.Food as an eventCrawfish boil
The crawfish boil is a celebratory event where Cajuns boil crawfish, potatoes, onions and corn in large pots over propane cookers. Lemons and small muslin bags containing a mixture of bay leaves, mustard seeds, cayenne pepper, and other spices, commonly known as "crab boil" or "crawfish boil" are added to the water for seasoning.
The results are then dumped onto large, newspaper-draped tables and in some areas covered in Creole/Cajun spice blends, such as REX, Zatarain's, Louisiana Fish Fry, or Tony Chachere's. Also, cocktail sauce, mayonnaise, and hot sauce are sometimes used. The seafood is scooped onto large trays or plates and eaten by hand.
During times when crawfish are not abundant, shrimp and crabs are prepared and served in the same manner.
Attendees are encouraged to "suck the head" of a crawfish by separating the head from the abdomen of the crustacean and sucking out the fat and juices from the head.
Often, newcomers to the crawfish boil or those unfamiliar with the traditions are jokingly warned "not to eat the dead ones." This comes from the common belief that when live crawfish are boiled, their tails curl beneath themselves, but when dead crawfish are boiled, their tails are straight and limp.
Seafood boils with crabs and shrimp are also popular.
Family
]]
The traditional Cajun outdoor food event is hosted by a farmer in the rural areas of Acadiana. Family and friends of the farmer gather to socialize, play games, dance, drink, and have a copious meal consisting of hog and other dishes. Men have the task of slaughtering a hog, cutting it into usable parts, and cooking the main pork dishes while women have the task of making boudin.
Similar to a family , the is a food event that revolves around pork but does not need to be hosted by a farmer. Traditionally, a suckling pig was purchased for the event, but in modern , adult pigs are used.
Unlike the family , a hog is not butchered by the hosts and there are generally not as many guests or activities. The host and male guests have the task of roasting the pig (see pig roast) while female guests bring side dishes.Rural Mardi GrasThe traditional Cajun Mardi Gras (see: Courir de Mardi Gras) is a Mardi Gras celebration in rural Cajun Parishes. The tradition originated in the 18th century with the Cajuns of Louisiana, but it was abandoned in the early 20th century because of unwelcome violence associated with the event. In the early 1950s the tradition was revived in Mamou in Evangeline Parish.
The event revolves around male maskers on horseback who ride into the countryside to collect food ingredients for the party later on. They entertain householders with Cajun music, dancing, and festive antics in return for the ingredients. The preferred ingredient is fresh chicken: the householder throws a live chicken to the maskers, allowing them to chase it down (symbolizing a hunt); other ingredients include rice, sausage, vegetables, or a frozen chicken if a live one is not available.
Unlike other Cajun events, men take no part in cooking the main course for the party, and women prepare the chicken and ingredients for the gumbo. Once the festivities begin, the Cajun community members eat and dance to Cajun music until midnight after which is the beginning of Lent.
List of Cajun-influenced chefs
* Frank Joseph Davis
* John Folse
* Emeril Lagasse
* Paul Prudhomme
* Justin Wilson
See also
* Cuisine of New Orleans
* Cuisine of the United States
* List of festivals in Louisiana
* Louisiana Creole cuisine
* Acadian cuisine
References
External links
Category:American cuisine by ethnic group
|
https://en.wikipedia.org/wiki/Cajun_cuisine
|
2025-04-05T18:27:44.237209
|
6187
|
Cologne
|
<br />
|type = City
| image_skyline =
|image_coa = DEU Koeln COA.svg
|image_flag = Flagge Köln.svg
|image_plan = North rhine w K.svg
|plantext = Cologne within North Rhine-Westphalia
|coordinates
|state = Nordrhein-Westfalen
|region = Cologne
|district = urban
|elevation = 37
|area = 405.15
|pop_metro = 8,711,712 (Rhineland)
|pop_urban = 3500000 (Cologne Bonn)
|postal_code = 50441–51149
|area_code = 0221, 02203 (Porz)
|licence = K
|Gemeindeschlüssel = 05 3 15 000
|mayor Henriette Reker
|leader_term = 2020–25
|Bürgermeistertitel = Lord Mayor
|party = Independent
|website =
|year = 38 BC
}}
Cologne ( ; ; ) is the largest city of the German state of North Rhine-Westphalia and the fourth-most populous city of Germany with nearly 1.1 million inhabitants in the city proper and over 3.1 million people in the Cologne Bonn urban region. Cologne is also part of the Rhine-Ruhr metropolitan region, the second biggest metropolitan region by GDP in the European Union. Centered on the left (west) bank of the Rhine, Cologne is located on the River Rhine (Lower Rhine), about southeast of the North Rhine-Westphalia state capital Düsseldorf and northwest of Bonn, the former capital of West Germany.
The city's medieval Cologne Cathedral () was the world's tallest building 1880–1890 and is today the third-tallest church and tallest cathedral in the world. It was constructed to house the Shrine of the Three Kings and is a globally recognized landmark and one of the most visited sights and pilgrimage destinations in Europe. The cityscape is further shaped by the Twelve Romanesque churches of Cologne. Cologne is famous for Eau de Cologne, which has been produced in the city since 1709; "cologne" has since come to be a generic term.
Cologne was founded and established in Germanic Ubii territory in the 1st century CE as the Roman , hence its name. was later dropped (except in Latin), and became the name of the city in its own right, which developed into modern German as . , the French version of the city's name, has become standard in English as well. Cologne functioned as the capital of the Roman province of and as the headquarters of the Roman military in the region until occupied by the Franks in 462. During the Middle Ages the city flourished as being located on one of the most important major trade routes between eastern and western Europe (including the Brabant Road, Via Regia and Publica). Cologne was a free imperial city of the Holy Roman Empire and one of the major members of the trade union Hanseatic League. It was one of the largest European cities in medieval and renaissance times.
Prior to World War II, the city had undergone occupations by the French (1794–1815) and the British (1918–1926), and was part of Prussia beginning in 1815. Cologne was one of the most heavily bombed cities in Germany during World War II. The bombing reduced the population by 93% mainly due to evacuation, and destroyed around 80% of the millennia-old city center. The post-war rebuilding has resulted in a mixed cityscape, restoring most major historic landmarks like city gates and churches (31 of them being Romanesque). The city nowadays consists of around 25% pre World War II buildings and boasts around 9,000 historic buildings.
Cologne is a major cultural center for the Rhineland; it hosts more than 30 museums and hundreds of galleries. There are many institutions of higher education, most notably the University of Cologne, one of Europe's oldest and largest universities; the Technical University of Cologne, Germany's largest university of applied sciences; and the German Sport University Cologne. It hosts three Max Planck science institutes and is a major research hub for the aerospace industry, with the German Aerospace Center and the European Astronaut Centre headquarters. Lufthansa, Europe's largest airline, have their main corporate headquarters in Cologne. It also has a significant chemical and automobile industry. Cologne Bonn Airport is a regional hub, the main airport for the region being Düsseldorf Airport. The Cologne Trade Fair hosts a number of trade shows.
History
Roman Cologne
from a Roman villa of Cologne, Germany (site of the ancient city Colonia Claudia Ara Agrippinensium), 3rd century CE, Romano-Germanic Museum]]
The first urban settlement on the grounds of modern-day Cologne was Oppidum Ubiorum, founded in 38 BCE by the Ubii, a Cisrhenian Germanic tribe. In 50 CE, the Romans founded Colonia Claudia Ara Agrippinensium (Cologne) on the river Rhine, It was also known as . Considerable Roman remains can be found in present-day Cologne, especially near the wharf area, where a 1,900-year-old Roman boat was discovered in late 2007. From 260 to 271, Cologne was the capital of the Gallic Empire under Postumus, Marius, and Victorinus. In 310, under emperor Constantine I, a bridge was built over the Rhine at Cologne. Roman imperial governors resided in the city and it became one of the most important trade and production centers in the Roman Empire north of the Alps.
Middle Ages
Early medieval Cologne was part of Austrasia within the Frankish Empire. Cunibert, made bishop of Cologne in 623, was an important advisor to the Merovingian King Dagobert I and served with domesticus Pepin of Landen as tutor to the king's son and heir Siegebert III, the future king of Austrasia. In 716, Charles Martel commanded an army for the first time and suffered the only defeat of his life when Chilperic II, King of Neustria, invaded Austrasia and the city fell to him in the Battle of Cologne. Charles fled to the Eifel mountains, rallied supporters and took the city back that same year after defeating Chilperic in the Battle of Amblève. Cologne had been the seat of a bishop since the Roman period; under Charlemagne, in 795, bishop Hildebold was promoted to archbishop. In order to weaken the secular nobility, who threatened his power, Otto endowed Bruno and his archiepiscopal successors with the prerogatives of secular princes, thus establishing the Electorate of Cologne, formed by the temporal possessions of the archbishopric and included in the end a strip of territory along the left Bank of the Rhine east of Jülich, as well as the Duchy of Westphalia on the other side of the Rhine, beyond Berg and Mark. By the end of the 12th century, the Archbishop of Cologne was one of the seven electors of the Holy Roman Emperor. Besides being prince elector, he was Archchancellor of Italy as well, technically from 1238 and permanently from 1263 until 1803.
Following the Battle of Worringen in 1288, Cologne gained its independence from the archbishops and became a Free City. Archbishop Sigfried II von Westerburg was forced to reside in Bonn. The archbishop nevertheless preserved the right of capital punishment. Thus the municipal council (though in strict political opposition towards the archbishop) depended upon him in all matters concerning criminal justice. This included torture, the sentence for which was only allowed to be handed down by the episcopal judge known as the greve. This legal situation lasted until the French conquest of Cologne.
Besides its economic and political significance Cologne also became an important centre of medieval pilgrimage, when Cologne's archbishop, Rainald of Dassel, gave the relics of the Three Wise Men to Cologne's cathedral in 1164 (after they had been taken from Milan). Besides the three magi Cologne preserves the relics of Saint Ursula and Albertus Magnus.
Cologne's location on the river Rhine placed it at the intersection of the major trade routes between east and west as well as the main south–north Western Europe trade route, Venice to Netherlands; even by the mid-10th century, merchants in the town were already known for their prosperity and luxurious standard of living due to the availability of trade opportunities. Cologne was a member of the Hanseatic League in 1475, when Frederick III confirmed the city's imperial immediacy.
The Free Imperial City of Cologne must not be confused with the Electorate of Cologne, which was a state of its own within the Holy Roman Empire. Since the second half of the 16th century the majority of archbishops were drawn from the Bavarian Wittelsbach dynasty. Due to the free status of Cologne, the archbishops were usually not allowed to enter the city. Thus they took up residence in Bonn and later in Brühl on the Rhine. As members of an influential and powerful family, and supported by their outstanding status as electors, the archbishops of Cologne repeatedly challenged and threatened the free status of Cologne during the 17th and 18th centuries, resulting in complicated affairs, which were handled by diplomatic means and propaganda as well as by the supreme courts of the Holy Roman Empire.
From the 19th century until World War I
Cologne lost its status as a free city during the French period. According to the Treaty of Lunéville (1801) all the territories of the Holy Roman Empire on the left bank of the Rhine were officially incorporated into the French Republic (which had already occupied Cologne in 1794). Thus this region later became part of Napoleon's Empire. Cologne was part of the French Département Roer (named after the river Roer, German: Rur) with Aachen (French: Aix-la-Chapelle) as its capital. The French modernised public life, for example by introducing the Napoleonic code and removing the old elites from power. The Napoleonic code remained in use on the left bank of the Rhine until 1900, when a unified civil code (the Bürgerliches Gesetzbuch) was introduced in the German Empire. In 1815 at the Congress of Vienna, Cologne was made part of the Kingdom of Prussia, first in the Province of Jülich-Cleves-Berg and then the Rhine Province.
The permanent tensions between the Catholic Rhineland and the overwhelmingly Protestant Prussian state repeatedly escalated with Cologne being in the focus of the conflict. In 1837 the archbishop of Cologne, Clemens August von Droste-Vischering, was arrested and imprisoned for two years after a dispute over the legal status of marriages between Catholics and Protestants (Mischehenstreit). In 1874, during the Kulturkampf, Archbishop Paul Melchers was imprisoned before taking asylum in the Netherlands. These conflicts alienated the Catholic population from Berlin and contributed to a deeply felt anti-Prussian resentment, which was still significant after World War II, when the former mayor of Cologne, Konrad Adenauer, became the first West German chancellor.
During the 19th and 20th centuries, Cologne absorbed numerous surrounding towns, and by World War I had already grown to 700,000 inhabitants. Industrialisation changed the city and spurred its growth. Vehicle and engine manufacturing was especially successful, though the heavy industry was less ubiquitous than in the Ruhr area. The cathedral, started in 1248 but abandoned around 1560, was eventually finished in 1880 not just as a place of worship but also as a German national monument celebrating the newly founded German empire and the continuity of the German nation since the Middle Ages. Some of this urban growth occurred at the expense of the city's historic heritage with much being demolished (for example, the city walls or the area around the cathedral) and sometimes replaced by contemporary buildings.
Cologne was designated as one of the Fortresses of the German Confederation. It was turned into a heavily armed fortress (opposing the French and Belgian fortresses of Verdun and Liège) with two fortified belts surrounding the city, the remains of which can be seen to this day. The military demands on what became Germany's largest fortress presented a significant obstacle to urban development, with forts, bunkers, and wide defensive dugouts completely encircling the city and preventing expansion; this resulted in a very densely built-up area within the city itself.
During World War I Cologne was the target of several minor air raids but suffered no significant damage. Cologne was occupied by the British Army of the Rhine until 1926, under the terms of the Armistice and the subsequent Versailles Peace Treaty. In contrast with the harsh behaviour of the French occupation troops in Germany, the British forces were more lenient to the local population. Konrad Adenauer, the mayor of Cologne from 1917 until 1933 and later a West German chancellor, acknowledged the political impact of this approach, especially since Britain had opposed French demands for a permanent Allied occupation of the entire Rhineland.
As part of the demilitarisation of the Rhineland, the city's fortifications had to be dismantled. This was an opportunity to create two green belts (Grüngürtel) around the city by converting the fortifications and their fields of fire into large public parks. This was not completed until 1933. In 1919 the University of Cologne, closed by the French in 1798, was reopened. This was considered to be a replacement for the loss of the University of Strasbourg on the west bank of the Rhine, which reverted to France with the rest of Alsace. Cologne prospered during the Weimar Republic (1919–33), and progress was made especially in public governance, city planning, housing and social affairs. Social housing projects were considered exemplary and were copied by other German cities. Cologne competed to host the Olympics, and a modern sports stadium was erected at Müngersdorf. When the British occupation ended, the prohibition of civil aviation was lifted and Cologne Butzweilerhof Airport soon became a hub for national and international air traffic, second in Germany only to Berlin Tempelhof Airport.
The democratic parties lost the local elections in Cologne in March 1933 to the Nazi Party and other extreme-right parties. The Nazis then arrested the Communist and Social Democrats members of the city assembly, and Mayor Adenauer was dismissed. Compared to some other major cities, however, the Nazis never gained decisive support in Cologne. (Significantly, the number of votes cast for the Nazi Party in Reichstag elections had always been the national average.) By 1939, the population had risen to 772,221 inhabitants.
World War II
During World War II, Cologne was a Military Area Command Headquarters () for Wehrkreis VI (headquartered at Münster). Cologne was under the command of Lieutenant-General Freiherr Roeder von Diersburg, who was responsible for military operations in Bonn, Siegburg, Aachen, Jülich, Düren, and Monschau. Cologne was home to the 211th Infantry Regiment and the 26th Artillery Regiment.
The Allies dropped 44,923.2 tons of bombs on the city during World War II, destroying 61% of its built up area. During the Bombing of Cologne in World War II, Cologne endured 262 air raids by the Western Allies, which caused approximately 20,000 civilian casualties and almost completely wiped out the central part of the city. During the night of 31 May 1942, Cologne was the target of "Operation Millennium", the first 1,000 bomber raid by the Royal Air Force in World War II. 1,046 heavy bombers attacked their target with 1,455 tons of explosives, approximately two-thirds of which were incendiary. This raid lasted about 75 minutes, destroyed of built-up area (61%), killed 486 civilians and made 59,000 people homeless. The devastation was recorded by Hermann Claasen from 1942 until the end of the war, and presented in his exhibition and book of 1947 Singing in the furnace. Cologne – Remains of an old city''.
Cologne was taken by the American First Army in early March 1945 during the Invasion of Germany after a battle. By the end of the war, the population of Cologne had been reduced by 95%. This loss was mainly caused by a massive evacuation of the people to more rural areas. The same happened in many other German cities in the last two years of war. By the end of 1945, however, the population had already recovered to approximately 450,000. By the end of the war, essentially all of Cologne's pre-war Jewish population of 11,000 had been deported or killed by the Nazis. The six synagogues of the city were destroyed. The synagogue on Roonstraße was rebuilt in 1959.
Post-war and Cold War eras
Despite Cologne's status as the largest city in the region, nearby Düsseldorf was chosen as the political capital of the federated state of North Rhine-Westphalia. With Bonn being chosen as the provisional federal capital (provisorische Bundeshauptstadt) and seat of the government of the Federal Republic of Germany (then informally West Germany), Cologne benefited by being sandwiched between two important political centres. The city became–and still is–home to a number of federal agencies and organizations. After reunification in 1990, Berlin was made the capital of Germany.
In 1945 architect and urban planner Rudolf Schwarz called Cologne the "world's greatest heap of rubble". Schwarz designed the master plan for reconstruction in 1947, which included the construction of several new thoroughfares through the city centre, especially the Nord-Süd-Fahrt ("North-South-Drive"). The master plan took into consideration the fact that even shortly after the war a large increase in automobile traffic could be anticipated. Plans for new roads had already, to a certain degree, evolved under the Nazi administration, but the actual construction became easier when most of the city centre was in ruins.
The destruction of 95% of the city centre, including the famous Twelve Romanesque churches such as St. Gereon, Great St. Martin, St. Maria im Kapitol and several other monuments in World War II, meant a tremendous loss of cultural treasures. The rebuilding of those churches and other landmarks such as the Gürzenich event hall was not undisputed among leading architects and art historians at that time, but in most cases, civil intention prevailed. The reconstruction lasted until the 1990s, when the Romanesque church of St. Kunibert was finished.
In 1959, the city's population reached pre-war numbers again. It then grew steadily, exceeding 1 million for about one year from 1975. It remained just below that until mid-2010, when it exceeded 1 million again.
Post-reunification
In the 1980s and 1990s Cologne's economy prospered for two main reasons. The first was the growth in the number of media companies, both in the private and public sectors; they are especially catered for in the newly developed Media Park, which creates a strong visual focal point in Cologne's city centre and includes the KölnTurm, one of Cologne's most prominent high-rise buildings. The second was the permanent improvement of the diverse traffic infrastructure, which made Cologne one of the most easily accessible metropolitan areas in Central Europe.
Due to the economic success of the Cologne Trade Fair, the city arranged a large extension to the fair site in 2005. At the same time the original buildings, which date back to the 1920s, were rented out to RTL, Germany's largest private broadcaster, as their new corporate headquarters.
Cologne was the focus of the 2015-16 New Year's Eve sexual assaults in Germany, with over 500 women reporting that they were sexually assaulted by persons of African and Arab appearance.GeographyThe metropolitan area encompasses over , extending around a central point that lies at 50° 56' 33 latitude and 6° 57' 32 longitude. The city's highest point is above sea level (the Monte Troodelöh) and its lowest point is above sea level (the Worringer Bruch). The city of Cologne lies within the larger area of the Cologne Lowland, a cone-shaped area of the central Rhineland that lies between Bonn, Aachen and Düsseldorf.
Districts
Cologne is divided into 9 boroughs (Stadtbezirke) and 85 districts (Stadtteile):
{| class"toccolours" style"margin:0 auto;"
| style="padding-right:1em;" |
; Innenstadt (Stadtbezirk 1)
: Altstadt-Nord, Altstadt-Süd, Neustadt-Nord, Neustadt-Süd, Deutz
; Rodenkirchen (Stadtbezirk 2)
: Bayenthal, Godorf, Hahnwald, Immendorf, Marienburg, Meschenich, Raderberg, Raderthal, Rodenkirchen, Rondorf, Sürth, Weiß, Zollstock
; Lindenthal (Stadtbezirk 3)
: Braunsfeld, Junkersdorf, Klettenberg, Lindenthal, Lövenich, Müngersdorf, Sülz, Weiden, Widdersdorf
; Ehrenfeld (Stadtbezirk 4)
: Bickendorf, Bocklemünd/Mengenich, Ehrenfeld, Neuehrenfeld, Ossendorf, Vogelsang
; Nippes (Stadtbezirk 5)
: Bilderstöckchen, Longerich, Mauenheim, Niehl, Nippes, Riehl, Weidenpesch
|
|
; Chorweiler (Stadtbezirk 6)
: Blumenberg, Chorweiler, Esch/Auweiler, Fühlingen, Heimersdorf, Lindweiler, Merkenich, Pesch, Roggendorf/Thenhoven, Seeberg, Volkhoven/Weiler, Worringen
; Porz (Stadtbezirk 7)
: Eil, Elsdorf, Ensen, Finkenberg, Gremberghoven, Grengel, Langel, Libur, Lind, Poll, Porz, Urbach, Wahn, Wahnheide, Westhoven, Zündorf
; Kalk (Stadtbezirk 8)
: Brück, Höhenberg, Humboldt/Gremberg, Kalk, Merheim, Neubrück, Ostheim, Rath/Heumar, Vingst
; Mülheim (Stadtbezirk 9)
: Buchforst, Buchheim, Dellbrück, Dünnwald, Flittard, Höhenhaus, Holweide, Mülheim, Stammheim
|}
Climate
Located in the Rhine-Ruhr area, Cologne is one of the warmest cities in Germany. It has a temperate–oceanic climate (Köppen: Cfb) with cool winters and warm summers. It is also one of the cloudiest cities in Germany, with just 1,567.5 hours of sun a year. Its average annual temperature is : during the day and at night. In January, the mean temperature is , while the mean temperature in July is . The record high temperature of happened on 25 July 2019 during the July 2019 European heat wave in which Cologne saw three consecutive days over . Especially the inner urban neighbourhoods experience a greater number of hot days, as well as significantly higher temperatures during nighttime compared to the surrounding area (including the airport, where temperatures are classified). Still temperatures can vary noticeably over the course of a month with warmer and colder weather. Precipitation is spread evenly throughout the year with a light peak in summer due to showers and thunderstorms.
The progressing climate change can be seen by looking at the climate data of the previous decade with lower mean temperatures.
Flood protection
Cologne is regularly affected by flooding from the Rhine and is considered the most flood-prone European city. A city agency (Stadtentwässerungsbetriebe Köln, "Cologne Urban Drainage Operations") manages an extensive flood control system which includes both permanent and mobile flood walls, protection from rising waters for buildings close to the river banks, monitoring and forecasting systems, pumping stations and programmes to create or protect floodplains, and river embankments. The system was redesigned after a 1993 flood, which resulted in heavy damage.
|-
! From country || Population (2022)
|-
| ||57,135
|-
| ||21,351
|-
| ||12,634
|-
| ||9,766
|-
| ||8,631
|-
| ||8,074
|-
| ||7,916
|-
| ||5,841
|-
| ||4,910
|-
| ||4,837
|-
| ||4,786
|-
| ||4,651
|-
| ||3,954
|-
| ||3,830
|-
| ||3,539
|-
| ||3,263
|-
| ||3,043
|-
| ||2,586
|-
| ||2,523
|-
| ||2,418
|-
| ||2,394
|-
| ||2,328
|-
| ||2,287
|}
In the Roman Empire, the city was large and rich with a population of 40,000 in 100–200 AD. The city was home to around 20,000 people in 1000 AD, growing to 50,000 in 1200 AD. The Rhineland metropolis still had 50,000 residents in 1300 AD.
Cologne is the fourth-largest city by population in Germany after Berlin, Hamburg and Munich. As of 31 December 2021, there were 1,079,301 people registered as living in Cologne in an area of , which makes Cologne the third largest city by area. The population density was . Cologne first reached the population of 1,000,000 in 1975 due to the incorporation of Wesseling, however this was reversed after public opposition. In 2009 Cologne's population again reached 1,000,000 and it became one of the four cities in Germany with a population exceeding 1 Million. The metropolitan area of the Cologne Bonn Region is home to 3,573,500 living on . It is part of the polycentric megacity region Rhine-Ruhr with a population of over 11,000,000 people.
There were 551,528 women and 527,773 men in Cologne. In 2021, there were 11,127 births in Cologne; 5,844 marriages and 1,808 divorces, and 10,536 deaths. In the city, the population was spread out, with 16.3% under the age of 18, and 17.8% were 65 years of age or older. 203 people in Cologne were over the age of 100. Irenaeus of Lyons claimed that Christianity was brought to Cologne by Roman soldiers and traders at an unknown early date. It is known that in the early second century it was a bishop's seat. The first historical Bishop of Cologne was Saint Maternus. Thomas Aquinas studied in Cologne in 1244 under Albertus Magnus. Cologne is the seat of the Archdiocese of Cologne.
According to the 2011 census, 2.1% of the population was Eastern Orthodox, 0.5% belonged of an Evangelical Free Church and 4.2% belonged to further religious communities officially recognized by the state of North Rhine-Westphalia (such as Jehovah's Witnesses).
There are several mosques, including the Cologne Central Mosque run by the Turkish-Islamic Union for Religious Affairs. In 2011, about 11.2% of the population was Muslim.
Cologne also has one of the oldest and largest Jewish communities in Germany. In 2011, 0.3% of Cologne's population was Jewish.
Government and politics
The city's administration is headed by the mayor and the three deputy mayors.
Political traditions and developments
The long tradition of a free imperial city, which long dominated an exclusively Catholic population and the age-old conflict between the church and the bourgeoisie (and within it between the patricians and craftsmen) have created its own political climate in Cologne. Various interest groups often form networks beyond party boundaries. The resulting web of relationships, with political, economic, and cultural links with each other in a system of mutual favours, obligations and dependencies, is called the 'Cologne coterie'. This has often led to an unusual proportional distribution in the city government and degenerated at times into corruption: in 1999, a "waste scandal" over kickbacks and illegal campaign contributions came to light, which led not only to the imprisonment of the entrepreneur Hellmut Trienekens, but also to the downfall of almost the entire leadership of the ruling Social Democrats.
Mayor
The incumbent Lord Mayor of Cologne is Henriette Reker. She received 52.66% of the vote at the municipal election on 17 October 2015, running as an independent with the support of the CDU, FDP, and Greens. She took office on 15 December 2015. Reker was re-elected to a second term in a runoff election on 27 September 2020, in which she received 59.27% of the vote.
The most recent mayoral election was held on 13 September 2020, with a runoff held on 27 September, and the results were as follows:
! rowspan2 colspan2| Candidate
! rowspan=2| Party
! colspan=2| First round
! colspan=2| Second round
|-
! Votes
! %
! Votes
! %
|-
| bgcolor=|
| align=left| Henriette Reker
| align=left| Independent (Green/CDU)
| 187,389
| 45.1
| 174,263
| 59.3
|-
| bgcolor=|
| align=left| Andreas Kossiski
| align=left| Social Democratic Party
| 111,353
| 26.8
| 119,753
| 40.7
|-
| bgcolor=|
| align=left| Jörg Detjen
| align=left| The Left
| 29,810
| 7.2
|-
| bgcolor=|
| align=left| Olivier Fuchs
| align=left| Volt Germany
| 18,520
| 4.5
|-
| bgcolor=|
| align=left| Christer Cremer
| align=left| Alternative for Germany
| 17,441
| 4.2
|-
|
| align=left| Nicolin Gabrysch
| align=left| Climate Friends
| 14,370
| 3.5
|-
| bgcolor=|
| align=left| Roberto Campione
| align=left| Independent
| 14,122
| 3.4
|-
|
| align=left| Thor Zimmermann
| align=left| Good Cologne
| 8,613
| 2.1
|-
|
| align=left| Dagmar Langel
| align=left| We Are Cologne
| 4,464
| 1.1
|-
| bgcolor=|
| align=left| Robert Nussholz
| align=left| Independent
| 4,044
| 1.0
|-
| bgcolor=|
| align=left| Sabine Neumeyer
| align=left| Independent
| 2,547
| 0.6
|-
| bgcolor=|
| align=left| Rüdiger-René Keune
| align=left| Ecological Democratic Party
| 2,336
| 0.6
|-
| bgcolor=|
| align=left| Martin Przybylski
| align=left| Independent
| 924
| 0.2
|-
! colspan=3| Valid votes
! 415,933
! 98.7
! 294,016
! 99.1
|-
! colspan=3| Invalid votes
! 5,633
! 1.3
! 2,727
! 0.9
|-
! colspan=3| Total
! 421,566
! 100.0
! 296,743
! 100.0
|-
! colspan=3| Electorate/voter turnout
! 820,527
! 51.4
! 818,731
! 36.2
|-
| colspan7| Source: City of Cologne ([https://wahlen.stadt-koeln.de/prod/KW2020/05315000/html5/Buergermeisterwahl_NRW_44_Gemeinde_Stadt_Koeln.html 1st round] , [https://www.stadt-koeln.de/wahlen/kommunalwahl/09-2020/Buergermeisterstichwahl_NRW_46_Gemeinde_Stadt_Koeln.html 2nd round])
|}
City council
The Cologne city council (Kölner Stadtrat) governs the city alongside the Mayor. It serves a term of five years. The most recent city council election was held on 13 September 2020, and the results were as follows:
! colspan=2| Party
! Votes
! %
! +/-
! Seats
! +/-
|-
| bgcolor=|
| align=left| Alliance 90/The Greens (Grüne)
| 118,997
| 28.5
| 9.0
| 26
| 8
|-
| bgcolor=|
| align=left| Social Democratic Party (SPD)
| 90,040
| 21.6
| 7.8
| 19
| 7
|-
| bgcolor=|
| align=left| Christian Democratic Union (CDU)
| 89,659
| 21.5
| 5.7
| 19
| 6
|-
| bgcolor=|
| align=left| The Left (Die Linke)
| 27,044
| 6.5
| 0.4
| 6
| ±0
|-
| bgcolor=|
| align=left| Free Democratic Party (FDP)
| 21,965
| 5.3
| 0.2
| 5
| ±0
|-
| bgcolor=|
| align=left| Volt Germany (Volt)
| 20,783
| 5.0
| New
| 4
| New
|-
| bgcolor=|
| align=left| Alternative for Germany (AfD)
| 18,272
| 4.4
| 0.8
| 4
| 1
|-
| bgcolor=|
| align=left| Die PARTEI (PARTEI)
| 10,261
| 2.5
| 2.4
| 2
| 2
|-
|
| align=left| Climate Friends (Klima Freunde)
| 8,383
| 2.0
| 0.0
| 2
| ±0
|-
|
| align=left| Good Cologne (GUT)
| 8,298
| 2.0
| 0.6
| 2
| ±0
|-
| bgcolor=|
| align=left| Free Voters Cologne (FWK)
| 2,501
| 0.6
| 0.2
| 1
| ±0
|-
| colspan7 bgcolorlightgrey|
|-
| bgcolor=|
| align=left| Ecological Democratic Party (ÖDP)
| 374
| 0.1
| New
| 0
| New
|-
|
| align=left| We Are Cologne 2020 (Wir Sind Köln)
| 265
| 0.1
| New
| 0
| New
|-
|
| align=left| Independent A. Krause
| 107
| 0.0
| New
| 0
| New
|-
|
| align=left| Independent Neumeyer
| 72
| 0.0
| New
| 0
| New
|-
|
| align=left| Independent Weber
| 72
| 0.0
| New
| 0
| New
|-
|
| align=left| Independent R. Krause
| 71
| 0.0
| New
| 0
| New
|-
|
| align=left| Independent Schidlowsky
| 32
| 0.0
| New
| 0
| New
|-
|
| align=left| Party of Progress (PdF)
| 31
| 0.0
| New
| 0
| New
|-
! colspan=2| Valid votes
! 417,227
! 98.9
!
!
!
|-
! colspan=2| Invalid votes
! 4,596
! 1.1
!
!
!
|-
! colspan=2| Total
! 421,823
! 100.0
!
! 90
! ±0
|-
! colspan=2| Electorate/voter turnout
! 820,526
! 51.4
! 1.8
!
!
|-
| colspan=7| Source: [https://www.stadt-koeln.de/wahlen/kommunalwahl/09-2020/Ratswahl_NRW_42_Gemeinde_Stadt_Koeln.html City of Cologne]
|}
State Landtag
in Cologne]]
In the Landtag of North Rhine-Westphalia, Cologne is divided among seven constituencies. After the 2022 North Rhine-Westphalia state election, the composition and representation of each was as follows:
{| class"wikitable" style"text-align:center"
! Constituency
! Area
! colspan=2| Party
! Member
|-
| 13 Köln I
| Rodenkirchen and part of Innenstadt
| bgcolor=|
| Grüne
| Eileen Woestmann
|-
| 14 Köln II
| Lindenthal
| bgcolor=|
| Grüne
| Frank Jablonski
|-
| 15 Köln III
| Ehrenfeld and part of Nippes
| bgcolor=|
| Grüne
| Arndt Klocke
|-
| 16 Köln IV
| Chorweiler and most of Nippes
| bgcolor=|
| SPD
| Lena Teschlade
|-
| 17 Köln V
| Porz and the east of Kalk
| bgcolor=|
| CDU
| Florian Braun
|-
| 18 Köln VI
| Most of Innenstadt and the west of Kalk
| bgcolor=|
| Grüne
| Berivan Aymaz
|-
| 19 Köln VII
| Mülheim
| bgcolor=|
| SPD
| Carolin Kirsch
|}
Federal parliament
In the Bundestag, Cologne is divided among four constituencies. In the 20th Bundestag, elected 26 September 2021, the composition and representation of each was as follows:
{| class"wikitable" style"text-align:center"
! Constituency
! Area
! colspan=2| Party
! Member
|-
| 93 Cologne I
| Porz, Kalk, and part of Innenstadt
| bgcolor=|
| SPD
| Sanae Abdi
|-
| 94 Cologne II
| Rodenkirchen, Lindenthal, and part of Innenstadt
| bgcolor=|
| Grüne
| Sven Lehmann
|-
| 95 Cologne III
| Ehrenfeld, Nippes, and Chorweiler
| bgcolor=|
| SPD
| Rolf Mützenich
|-
| 101 Leverkusen – Cologne IV
| Mülheim (and the city of Leverkusen)
| bgcolor=|
| SPD
| Karl Lauterbach
|}
Cityscape
The inner city of Cologne was largely destroyed during World War II. The reconstruction of the city followed the style of the 1950s, while respecting the old layout and naming of the streets. Thus, the city centre today is characterized by modern architecture, with a few interspersed pre-war buildings which were reconstructed due to their historical importance. Some buildings of the "Wiederaufbauzeit" (era of reconstruction), for example, the opera house by Wilhelm Riphahn, are nowadays regarded as classics of modern architecture. Nevertheless, the uncompromising style of the Cologne Opera house and other modern buildings has remained controversial.
The districts outside the city center consist mostly of 19th and 20th century buildings.
<gallery>
File:Kemmerlingshof, Köln-Junkersdorf Dürener Str 437.jpg|Junkersdorf old town
File:Köln Bayenthalgürtel 9.jpg|upright|Art Nouveau villa on Bayenthal-gürtel, part of the Cologne Ring
File:Neptunbad, Köln-Ehrenfeld-8466.jpg|Gründerzeit building in Ehrenfeld, Cologne
File:Hansahochhaus Köln - Gesamtansicht (0308-10).jpg|Hansahochhaus, a building in the style of Brick Expressionism
</gallery>
Wildlife
The dominant wildlife of Cologne is insects, small rodents, and several species of birds. Pigeons are the most often seen animals in Cologne, although the number of birds is augmented each year by a growing population of feral exotics, most visibly parrots such as the rose-ringed parakeet. The sheltered climate in southeast Northrhine-Westphalia allows these birds to survive through the winter, and in some cases, they are displacing native species. The plumage of Cologne's green parrots is highly visible even from a distance, and contrasts starkly with the otherwise muted colours of the cityscape.
Hedgehogs, rabbits and squirrels are common in parks and the greener parts of town. In the outer suburbs foxes and wild boar can be seen, even during the day.
Tourism
Cologne had 5.8 million overnight stays booked and 3.35 million arrivals in 2016.
Landmarks
Churches
* Cologne Cathedral (German: Kölner Dom) is the city's most famous monument and the Cologne residents' most loved landmark. It is a Gothic church, started in 1248, and completed in 1880. In 1996, it was designated a World Heritage Site; it houses the Shrine of the Three Kings, which supposedly contains the relics of the Three Magi (see also). Residents of Cologne sometimes refer to the cathedral as "the eternal construction site" (die ewige Baustelle).
* Twelve Romanesque churches: These buildings are outstanding examples of early medieval church architecture. The origins of some of these churches go back as far as Roman times, for example St. Gereon, which was originally a huge mausoleum in a Roman graveyard, or St. Maria im Kapitol, built on the substructure of a Roman temple. Great St. Martin Church stands on the site of Roman warehouses and previously a sports field with a swimming pool, the walls of which can be seen in the basement of the church. With the exception of St. Maria Lyskirchen all of these churches were very badly damaged during World War II. Reconstructions of the last ones were only finished in the 1990s.
<gallery heights"80" perrow"6">
Kdom.jpg|Cologne Cathedral
Cologne, Germany. Basilica of St. Gereon.jpg|St. Gereon's Basilica
Köln st maria im kapitol dreikonchenanlage 251204.jpg|St. Maria im Kapitol
Köln - Groß St. Martin vom Dom.jpg|Great St. Martin Church
Severeinskirche aus Severinstorburg 2009.jpg|Basilica of St. Severin
Koeln mariae himmelfahrt 001.jpg|Church of the Assumption
Trinitatiskirche Koeln2007.jpg|Trinity Church
</gallery>
Medieval houses
The Cologne City Hall (Kölner Rathaus), founded in the 12th century, is the oldest city hall in Germany still in use. The Renaissance-style loggia and tower were added in the 15th century. Other famous buildings include the Gürzenich, Haus Saaleck and the Overstolzenhaus.
<gallery heights"80" perrow"6">
File:Keoln Maerz 2009 PD 20090327 028.JPG|Cologne City Hall
File:Köln gürzenich.jpg|Gürzenich
File:Overstolzenhaus-Rheingasse-Köln.JPG|Overstolzenhaus
</gallery>
Medieval city gates
Of the twelve medieval city gates that once existed, only the Eigelsteintorburg at Ebertplatz, the Hahnentor at Rudolfplatz and the Severinstorburg at Chlodwigplatz still stand today.
<gallery heights"80" perrow"6">
File:Köln eigelsteintorburg.jpg|Eigelsteintor
File:Hahnentorburg.jpg|Hahnentor
File:Severinstorburg Köln-0410.jpg|Severinstor
</gallery>
Streets
* The Cologne Ring boulevards (such as Hohenzollernring, Kaiser-Wilhelm-Ring, Hansaring) with their medieval city gates (such as Hahnentorburg on Rudolfplatz) are also known for their night life.
* Hohe Straße (literally: High Street) is one of the main shopping areas and extends past the cathedral in an approximately southerly direction. The street contains many gift shops, clothing stores, fast food restaurants and electronic goods dealers.
* Schildergasse – connects Neumarkt square at its western end to the Hohe Strasse shopping street at its eastern end and has been named the busiest shopping street in Europe with 13,000 people passing through every hour, according to a 2008 study by GfK.
* Ehrenstraße – the shopping area around Apostelnstrasse, Ehrenstrasse, and Rudolfplatz is a little more on the quirky and stylish side.
Bridges
Several bridges cross the Rhine in Cologne. They are (from south to north): the Rodenkirchen Bridge, South Bridge (railway), , Deutz Bridge, Hohenzollern Bridge (railway), (Zoobrücke) and Mülheim Bridge. In particular the iron tied arch Hohenzollern Bridge (Hohenzollernbrücke) is a dominant landmark along the river embankment. A Rhine crossing of a special kind is provided by the Cologne Cable Car (German: Kölner Seilbahn), a cableway that runs across the river between the Cologne Zoological Garden in Riehl and the Rheinpark in Deutz.
High-rise structures
Cologne's tallest structure is the Colonius telecommunication tower at . The observation deck has been closed since 1992. A selection of the tallest buildings in Cologne is listed below. Other tall structures include the Hansahochhaus (designed by architect Jacob Koerfer and completed in 1925 – it was at one time Europe's tallest office building), the Kranhaus buildings at Rheinauhafen, and the Messeturm Köln ("trade fair tower").
{| class"wikitable sortable" style"text-align:center; background:#fefef6; width:80%;"
|-
! Skyscraper
!class="unsortable"| Image
! Height in metres
! Floors
! Year
! Address
!class="unsortable"| Notes
|-
| align=left| KölnTurm
|
| 148.5
| 43
| 2001
| align=left| MediaPark 8, Neustadt-Nord
| align=left| (literally: Cologne Tower), Cologne's second tallest building at in height, second only to the Colonius telecommunication tower. The 30th floor of the building has a restaurant and a terrace with 360° views of the city.
|-
| align=left| Colonia-Hochhaus
|
| 147
| 45
| 1973
| align=left| An der Schanz 2, Riehl
| align=left| tallest building in Germany from 1973 to 1976. Today, it is still the country's second tallest residential building.
|-
| align=left|Rheintower
|
| 138
| 34
| 1980
| align=left| Raderberggürtel, Marienburg
| align=left| former headquarters of Deutsche Welle, since 2007 under renovation with the new name Rheintower Köln-Marienburg.
|-
| alignleft| Uni-Center
|
| 133
| 45
| 1973
| align=left| Luxemburger Straße, Sülz
| align=left|
|-
| align=left| TÜV Rheinland
|
| 112
| 22
| 1974
| align=left| Am Grauen Stein, Poll
| align=left|
|-
| align=left| Ringturm
|
| 109
| 26
| 1973
| align=left| Ebertplatz, Neustadt-Nord
| align=left|
|-
| align=left| Justizzentrum Köln
|
| 105
| 25
| 1981
| align=left| Luxemburger Straße, Sülz
| align=left|
|-
| align=left| KölnTriangle
|
| 103
| 29
| 2006
| align=left| Ottoplatz 1, Deutz
| alignleft| opposite to the cathedral with a high viewing platform and a view of the cathedral over the Rhine.
|-
| align=left| Herkules-Hochhaus
|
| 102
| 31
| 1969
| align=left| Graeffstraße 1, Ehrenfeld
| align=left|
|-
| align=left| Deutschlandfunk-Turm
|
| 102
| 19
| 1975
| align=left| Raderberggürtel, Marienburg
| align=left|
|}
Culture
museum in 2007, designed by Peter Zumthor]]
'', a limestone sculpture by Nikolaus Friedrich, 1911]]
Cologne has numerous museums. The famous Roman-Germanic Museum features art and architecture from the city's distant past; the Museum Ludwig houses one of the most important collections of modern art in Europe, including a Picasso collection matched only by the museums in Barcelona and Paris. The Museum Schnütgen of religious art is partly housed in St. Cecilia, one of Cologne's Twelve Romanesque churches. Many art galleries in Cologne enjoy a worldwide reputation like e.g. Galerie Karsten Greve, one of the leading galleries for postwar and contemporary art.
Cologne has more than 60 music venues and the third-highest density of music venues of Germany's four largest cities, after Munich and Hamburg and ahead of Berlin.
Several orchestras are active in the city, among them the Gürzenich Orchestra, which is also the orchestra of the Cologne Opera and the WDR Symphony Orchestra Cologne (German State Radio Orchestra), both based at the Cologne Philharmonic Orchestra Building (Kölner Philharmonie). Other orchestras are the Musica Antiqua Köln, the WDR Rundfunkorchester Köln and WDR Big Band, and several choirs, including the WDR Rundfunkchor Köln. Cologne was also an important hotbed for electronic music in the 1950s (Studio für elektronische Musik, Karlheinz Stockhausen) and again from the 1990s onward. The public radio and TV station WDR was involved in promoting musical movements such as Krautrock in the 1970s; the influential Can was formed there in 1968. There are several centres of nightlife, among them the Kwartier Latäng (the student quarter around the Zülpicher Straße) and the nightclub-studded areas around Hohenzollernring, Friesenplatz and Rudolfplatz.
The large annual literary festival with its features regional and international authors. The main literary figure connected with Cologne is the writer Heinrich Böll, winner of the Nobel Prize for Literature. Since 2012, there is also an annual international festival of philosophy called .
The city also has the most pubs per capita in Germany. Cologne is well known for its beer, called Kölsch. Kölsch is also the name of the local dialect. This has led to the common joke of Kölsch being the only language one can drink.
Cologne is also famous for Eau de Cologne (German: Kölnisch Wasser; lit: "Water of Cologne"), a perfume created by Italian expatriate Johann Maria Farina at the beginning of the 18th century. During the 18th century, this perfume became increasingly popular, was exported all over Europe by the Farina family and Farina became a household name for Eau de Cologne. In 1803 Wilhelm Mülhens entered into a contract with an unrelated person from Italy named Carlo Francesco Farina who granted him the right to use his family name and Mühlens opened a small factory at Cologne's Glockengasse. In later years, and after various court battles, his grandson Ferdinand Mülhens was forced to abandon the name Farina for the company and their product. He decided to use the house number given to the factory at Glockengasse during the French occupation in the early 19th century, 4711. Today, original Eau de Cologne is still produced in Cologne by both the Farina family, in the eighth generation, and by Mäurer & Wirtz who bought the 4711 brand in 2006.
Carnival
The Cologne carnival is one of the largest street festivals in Europe. In Cologne, the carnival season officially starts on 11 November at 11 minutes past 11 a.m. with the proclamation of the new Carnival Season, and continues until Ash Wednesday. However, the so-called "Tolle Tage" (crazy days) do not start until Weiberfastnacht (Women's Carnival) or, in dialect, Wieverfastelovend, the Thursday before Ash Wednesday, which is the beginning of the street carnival. Zülpicher Strasse and its surroundings, Neumarkt square, Heumarkt and all bars and pubs in the city are crowded with people in costumes dancing and drinking in the streets. Hundreds of thousands of visitors flock to Cologne during this time. Generally, around a million people celebrate in the streets on the Thursday before Ash Wednesday.
Rivalry with Düsseldorf
Cologne and Düsseldorf have a "fierce regional rivalry", which includes carnival parades, ice hockey, football, and beer.
Museums
.]]
in Cologne: Dionysus Mosaic on display at Römisch-Germanisches Museum]]
* Farina Fragrance Museum – birthplace of Eau de Cologne
* Römisch-Germanisches Museum (Roman-Germanic Museum) – ancient Roman and Germanic culture
* Wallraf-Richartz Museum – European painting from the 13th to the early 20th century
* Museum Ludwig – modern art
* Museum Schnütgen – medieval art
* Museum für Angewandte Kunst – applied art
* Kolumba Kunstmuseum des Erzbistums Köln (art museum of the Archbishopric of Cologne) – modern art museum built around medieval ruins of St. Kolumba, Cologne, completed 2007
* Cathedral Treasury "Domschatzkammer" – historic underground vaults of the Cathedral
* EL-DE Haus – former local headquarters of the Gestapo houses a museum documenting Nazi rule in Cologne with a special focus on the persecution of political dissenters and minorities
* German Sports and Olympic Museum – exhibitions about sports from antiquity until the present
* Imhoff-Schokoladenmuseum – Chocolate Museum
* Geomuseum of the University of Cologne – the exhibition includes fossils (such as dinosaur bones and the skeleton of an Eryops), stones and minerals
* Forum for Internet Technology in Contemporary Art – collections of Internet-based art, corporate part of (NewMediaArtProjectNetwork):cologne, the experimental platform for art and New Media
* Flora und Botanischer Garten Köln – the city's formal park and main botanical garden
* Forstbotanischer Garten Köln – an arboretum and woodland botanical garden
Music fairs and festivals
The city was home to the internationally famous Ringfest, and now to the C/o pop festival.
In addition, Cologne enjoys a thriving Christmas Market (Weihnachtsmarkt) presence with several locations in the city.
Economy
, 2008]]
, EA Games headquarters]]
As the largest city in the Rhine-Ruhr metropolitan region, Cologne benefits from a large market structure. In competition with Düsseldorf, the economy of Cologne is primarily based on insurance and media industries, while the city is also an important cultural and research centre and home to a number of corporate headquarters.
Among the largest media companies based in Cologne are Westdeutscher Rundfunk, RTL Television (with subsidiaries), n-tv, Deutschlandradio, Brainpool TV and publishing houses like J. P. Bachem, Taschen, Tandem Verlag, and M. DuMont Schauberg. Several clusters of media, arts and communications agencies, TV production studios, and state agencies work partly with private and government-funded cultural institutions. Among the insurance companies based in Cologne are Central, DEVK, DKV, Generali Deutschland, Gen Re, Gothaer, HDI Gerling and national headquarters of Axa Insurance, Mitsui Sumitomo Insurance Group and Zurich Financial Services.
The German flag carrier Lufthansa and its subsidiary Lufthansa CityLine have their main corporate headquarters in Cologne. The largest employer in Cologne is Ford Europe, which has its European headquarters and a factory in Niehl (Ford-Werke GmbH). Toyota Motorsport GmbH (TMG), Toyota's official motorsports team, responsible for Toyota rally cars, and then Formula One cars, has its headquarters and workshops in Cologne. Other large companies based in Cologne include the REWE Group, TÜV Rheinland, Deutz AG and a number of Kölsch breweries. The largest three Kölsch breweries of Cologne are Reissdorf, Gaffel, and Früh.
{| class="wikitable"
! style="text-align:left;"| Brewery
! valign=bottom | Established
! valign=bottom | Annual output in hectoliters
|-
| Heinrich Reissdorf
| 1894
| 650,000
|-
| Gaffel Becker & Co
| 1908
| 500,000
|-
| Cölner Hofbräu Früh
| 1904
| 440,000
|}
Historically, Cologne has always been an important trade city, with land, air, and sea connections.
Cologne has also become the first German city with a population of more than a million people to declare climate emergency.
Transport
Roads
]]
Road building had been a major issue in the 1920s under the leadership of mayor Konrad Adenauer. The first German limited-access road was constructed after 1929 between Cologne and Bonn. Today, this is the Bundesautobahn 555. In 1965, Cologne became the first German city to be fully encircled by a motorway ring road. Roughly at the same time, a city centre bypass (Stadtautobahn) was planned, but only partially put into effect, due to opposition by environmental groups. The completed section became Bundesstraße ("Federal Road") B 55a, which begins at the Zoobrücke ("Zoo Bridge") and meets with A 4 and A 3 at the interchange Cologne East. Nevertheless, it is referred to as Stadtautobahn by most locals. In contrast to this, the Nord-Süd-Fahrt ("North-South-Drive") was actually completed, a new four/six-lane city centre through-route, which had already been anticipated by planners such as Fritz Schumacher in the 1920s. The last section south of Ebertplatz was completed in 1972.
In 2005, the first stretch of an eight-lane motorway in North Rhine-Westphalia was opened to traffic on Bundesautobahn 3, part of the eastern section of the Cologne Beltway between the interchanges Cologne East and Heumar.
Cycling
Compared to other German cities, Cologne has a traffic layout that is not very bicycle-friendly. It has repeatedly ranked among the worst in an independent evaluation conducted by the Allgemeiner Deutscher Fahrrad-Club. In 2014, it ranked 36th out of 39 German cities with a population greater than 200,000.
Railway
]]
Cologne has a railway service with InterCity and ICE-trains stopping at Köln Hauptbahnhof (Cologne Main Station), Köln Messe/Deutz and Cologne/Bonn Airport. ICE and TGV Thalys high-speed trains link Cologne with Amsterdam, Brussels (in 1h47, 9 departures/day) and Paris (in 3h14, 6 departures/day). There are frequent ICE trains to other German cities, including Frankfurt am Main and Berlin. ICE trains to London via the Channel Tunnel were planned for 2013.
The Cologne Stadtbahn operated by Kölner Verkehrsbetriebe (KVB) is an extensive light rail system that is partially underground and serves Cologne and a number of neighbouring cities. It evolved from the tram system. Nearby Bonn is linked by both the Stadtbahn and main line railway trains, with occasional recreational boats on the Rhine. Düsseldorf is also linked by S-Bahn trains, which are operated by .
The Rhine-Ruhr S-Bahn has 5 lines which cross Cologne. The S13/S19 runs 24/7 between Cologne Hbf and Cologne/Bonn airport.
Buses
There are frequent buses covering most of the city and surrounding suburbs, and Eurolines coaches to London via Brussels.
Water
Häfen und Güterverkehr Köln (Ports and Goods traffic Cologne, HGK) is one of the largest operators of inland ports in Germany. Ports include Köln-Deutz, Köln-Godorf and Köln-Niehl I and II.AirCologne's international airport is Cologne/Bonn Airport (CGN). It is also called Konrad Adenauer Airport after Germany's first post-war Chancellor Konrad Adenauer, who was born in the city and was mayor of Cologne from 1917 until 1933. The airport is shared with the neighbouring city of Bonn. Cologne is headquarters to the European Aviation Safety Agency (EASA).EducationCologne is home to numerous universities and colleges, and host to some 72,000 students. Foreigners can have German lessons in the VHS (Adult Education Centre).
{|
|-
|valign=top|
* Public and state universities:
** University of Cologne (Universität zu Köln);
** German Sport University Cologne (Deutsche Sporthochschule Köln).
* Public and state colleges:
** Cologne University of Applied Sciences ("Technology, Arts, Sciences TH KöLN" Technische Hochschule Köln);
** Köln International School of Design;
** Cologne University of Music and Dance ();
** Academy of Media Arts Cologne (Kunsthochschule für Medien Köln);
* Private colleges:
** Catholic University of Applied Sciences (Katholische Hochschule Nordrhein-Westfalen);
** Cologne Business School;
** international filmschool cologne (internationale filmschule köln);
** Rhenish University of Applied Sciences (Rheinische Fachhochschule Köln)
** University of Applied Sciences Fresenius (Hochschule Fresenius)
|valign=top|
* Research institutes:
** German Aerospace Centre (Deutsches Zentrum für Luft- und Raumfahrt);
** European Astronaut Centre (EAC) of the European Space Agency;
** European College of Sport Science (ECSS);
** Max Planck Institute for the Biology of Ageing (Max-Planck-Institut für die Biologie des Alterns);
** Max Planck Institute for the Study of Societies (Max-Planck-Institut für Gesellschaftsforschung);
** Max Planck Institute for Neurological Research (Max-Planck-Institut für neurologische Forschung);
** Max Planck Institute for Plant Breeding Research (Max-Planck-Institut für Züchtungsforschung).
** CologneAMS – Centre for Accelerator Mass Spectrometry, Institute for Nuclear Physics, University of Cologne
Former colleges include:
* The Cologne Art and Crafts Schools (Kölner Werkschulen);
* The Cologne Institute for Religious Art (Kölner Institut für religiöse Kunst)
|}
Lauder Morijah School (), a Jewish school in Cologne, previously closed. After Russian immigration increased the Jewish population, the school reopened in 2002.MediaWithin Germany, Cologne is known as an important media centre. Several radio and television stations, including Westdeutscher Rundfunk (WDR), RTL and VOX, have their headquarters in the city. Film and TV production is also important. The city is "Germany's capital of TV crime stories". A third of all German TV productions are made in the Cologne region.
Sports
Cologne hosts the football club 1. FC Köln, who play currently in the 2. Bundesliga (second division). They play their home matches in RheinEnergieStadion which also hosted five matches of the 2006 FIFA World Cup. The International Olympic Committee and the International Association of Sports and Leisure Facilities gave RheinEnergieStadion a bronze medal for "being one of the best sporting venues in the world".
* Barcelona, Spain (1984)
* Beijing, China (1987)
* Bethlehem, Palestine (1996)
* Cluj-Napoca, Romania (1976)
* Corinto, Nicaragua (1988)
* Cork, Ireland (1988)
* Dnipro, Ukraine (2024)
* Esch-sur-Alzette, Luxembourg (1958)
* Indianapolis, United States (1988)
* Istanbul, Turkey (1997)
* Katowice, Poland (1991)
* Kyoto, Japan (1963)
* Liège, Belgium (1958)
* Lille, France (1958)
* Liverpool, England, United Kingdom (1952)
* Neukölln (Berlin), Germany (1967)
* El Realejo, Nicaragua (1988)
* Rio de Janeiro, Brazil (2011)
* Rotterdam, Netherlands (1958)
* Tel Aviv, Israel (1979)
* Thessaloniki, Greece (1988)
* Treptow-Köpenick (Berlin), Germany (1990)
* Tunis, Tunisia (1964)
* Turin, Italy (1958)
* Turku, Finland (1967)
Former twin towns* Volgograd, Russia (1988) - suspended in 2022See also
* Stadtwerke Köln, the municipal infrastructure company, operator of the city's railways, ports, and other utilities
* New Year's Eve sexual assaults in Germany
* Hänneschen-Theater
References
External links
*
<!--Empty space per standard-->
Category:Cities in North Rhine-Westphalia
Category:Urban districts of North Rhine-Westphalia
Category:Cologne (region)
Category:Populated places on the Rhine
Category:Rhineland
Category:Catholic pilgrimage sites
Category:Holy cities
Category:Members of the Hanseatic League
Category:Coloniae (Roman)
Category:Roman towns and cities in Germany
Category:Germania Inferior
Category:Free imperial cities
Category:Populated places established in the 1st century BC
Category:30s BC establishments
Category:38 BC
Category:Burial sites of the Pippinids
Category:Holocaust locations in Germany
|
https://en.wikipedia.org/wiki/Cologne
|
2025-04-05T18:27:44.302560
|
6188
|
Buddhist cuisine
|
|pojche-chhài
|kanji精進料理|kanaしょうじんりょうり|revhepshōjin ryōri|kunreisyôzin ryôri
|hangul사찰음식|hanja寺刹飮食|rrsachal eumsik |mrsach'al ŭmsik
|qn=đồ chay
|chunom=塗齋
|c|mi|ci|altname|Myanmar nameဆွမ်း (Swan)|khmម្ហូបព្រះពុទ្ធសាសនា|tgl=Lutuing Budista}}
Buddhist cuisine is an Asian cuisine that is followed by monks and many believers from areas historically influenced by Mahayana Buddhism. It is vegetarian or vegan, and it is based on the Dharmic concept of ahimsa (non-violence). Vegetarianism is common in other Dharmic faiths such as Hinduism, Jainism and Sikhism, as well as East Asian religions like Taoism. While monks, nuns and a minority of believers are vegetarian year-round, many believers follow the Buddhist vegetarian diet for celebrations.
Buddhists believe that cooking is seen as a spiritual practice that produces the nourishment which the body needs to work hard and meditate. The origin of "Buddhist food" as a distinct sub-style of cuisine is tied to monasteries, where one member of the community would have the duty of being the head cook and supplying meals that paid respect to the strictures of Buddhist precepts. Temples that were open to visitors from the general public might also serve meals to them and a few temples effectively run functioning restaurants on the premises. In Japan, this culinary custom, recognized as shōjin ryōri (精進料理) or devotion cuisine, is commonly offered at numerous temples, notably in Kyoto. This centuries-old culinary tradition, primarily associated with religious contexts, is seldom encountered beyond places like temples, religious festivals, and funerals. Vegetarian eating is primarily associated with the East and Southeast Asian tradition in China, Vietnam, Japan, and Korea where it is commonly practiced by clergy and may be observed by laity on holidays or as a devotional practice. The exception to this alms rule is when monks and nuns have seen, heard or known that animal(s) have been specifically killed to feed the alms-seeker, in which case consumption of such meat would be karmically negative, as well as meat from certain animals, such as dogs and snakes, that were regarded as impure in ancient India. The same restriction is also followed by some lay Buddhists and is known as the consumption of "triply clean meat" (三净肉). The Pāli Scriptures also indicated that Lord Buddha refusing a proposal by his traitor disciple Devadatta to mandate vegetarianism in the monastic precepts.
Tibetan Buddhism has long accepted that the practical difficulties in obtaining vegetables and grains within most of Tibet make it impossible to insist upon vegetarianism; however, many leading Tibetan Buddhist teachers agree upon the great worth of practicing vegetarianism whenever and wherever possible, such as Chatral Rinpoche, a lifelong advocate of vegetarianism who famously released large numbers of fish caught for food back into the ocean once a year, and who wrote about the practice of saving lives.
Both Mahayana and Theravada Buddhists consider that one may practice vegetarianism as part of cultivating Bodhisattvas's paramita.
Other restrictions
, Japan]]
In addition to the ban on garlic, practically all Mahayana monastics in China, Korea, Vietnam and Japan specifically avoid eating strong-smelling plants, traditionally asafoetida, shallot, mountain leek and Chinese onion, which together with garlic are referred to as wǔ hūn (五葷, or 'Five Acrid and Strong-smelling Vegetables') or wǔ xīn (五辛 or 'Five Spices') as they tend to excite senses. This is based on teachings found in the Brahmajala Sutra, the Surangama Sutra and the Lankavatara Sutra. In modern times this rule is often interpreted to include other vegetables of the onion genus, as well as coriander. The origin of this additional restriction is from the Indic region and can still be found among some believers of Hinduism and Jainism.
The consumption of non-vegetarian food by strict Buddhists is also subject to various restrictions. As well as the aforementioned "triply clean meat" rule followed by Theravada monks, nuns, and some lay Buddhists, many Chinese Buddhists avoid the consumption of beef, large animals, and exotic species. Some Buddhists abstain from eating offal (organ meat), known as xiàshui (下水).
Alcohol and other drugs are also avoided by many Buddhists because of their effects on the mind and "mindfulness". It is part of the Five Precepts which dictate that one is not to "not to take any substance that will cloud the mind." Caffeinated drinks may sometimes be included under this restriction.
Simple and natural
In theory and practice, many regional styles of cooking may be adapted to be "Buddhist" as long as the cook, with the above restrictions in mind, prepares the food, generally in simple preparations, with expert attention to its quality, wholesomeness and flavor. Often working on a tight budget, the monastery cook would have to make the most of whatever ingredients were available.
In Tenzo kyokun ("Instructions for the Zen Cook"), Soto Zen founder Eihei Dogen wrote:
<blockquote>In preparing food, it is essential to be sincere and to respect each ingredient regardless of how coarse or fine it is. (...) A rich buttery soup is not better as such than a broth of wild herbs. In handling and preparing wild herbs, do so as you would the ingredients for a rich feast, wholeheartedly, sincerely, clearly. When you serve the monastic assembly, they and you should taste only the flavour of the Ocean of Reality, the Ocean of unobscured Awake Awareness, not whether or not the soup is creamy or made only of wild herbs. In nourishing the seeds of living in the Way, rich food and wild grass are not separate.</blockquote> Ingredients Following its dominant status in most parts of East Asia where Buddhism is most practiced, rice features heavily as a staple in the Buddhist meal, especially in the form of rice porridge or congee as the usual morning meal. Noodles and other grains may often be served as well. Vegetables of all sorts are generally either stir-fried or cooked in vegetarian broth with seasonings and may be eaten with various sauces. Onions and garlic are usually avoided as consumption of these is thought to increase undesirable emotions such as anger or sexual desire. Traditionally, eggs and dairy are not permitted. Seasonings will be informed by whatever is common in the local region; for example, soy sauce and vegan dashi figure strongly in Japanese monastery food while Thai curry and tương (as a vegetarian replacement for fish sauce) may be prominent in Southeast Asia. Sweets and desserts are not often consumed, but are permitted in moderation and may be served at special occasions, such as in the context of a tea ceremony in the Zen tradition.
Buddhist vegetarian chefs have become extremely creative in imitating meat using prepared wheat gluten, also known as seitan, kao fu (烤麸) or wheat meat, soy (such as tofu or tempeh), agar, konnyaku and other plant products. Some of their recipes are the oldest and most-refined meat analogues in the world. Soy and wheat gluten are very versatile materials, because they can be manufactured into various shapes and textures, and they absorb flavorings (including, but not limited to, meat-like flavorings), while having very little flavor of their own. With the proper seasonings, they can mimic various kinds of meat quite closely.
Some of these Buddhist vegetarian chefs are in the many monasteries and temples which serve allium-free and mock-meat (also known as 'meat analogues') dishes to the monks and visitors (including non-Buddhists who often stay for a few hours or days, to Buddhists who are not monks, but staying overnight for anywhere up to weeks or months). Many Buddhist restaurants also serve vegetarian, vegan, non-alcoholic or allium-free dishes.
Some Buddhists eat vegetarian on the 1st and 15th of the lunar calendar (lenten days), on Chinese New Year eve, and on saint and ancestral holy days. To cater to this type of customer, as well as full-time vegetarians, the menu of a Buddhist vegetarian restaurant usually shows no difference from a typical Chinese or East Asian restaurant, except that in recipes originally made to contain meat, a soy chicken substitute might be served instead.
Variations by sect or region
According to cookbooks published in English, formal monastery meals in the Zen tradition generally follow a pattern of "three bowls" in descending size. The first and largest bowl is a grain-based dish such as rice, noodles or congee; the second contains the protein dish which is often some form of stew or soup; the third and smallest bowl is a vegetable dish or a salad. History
The earliest surviving written accounts of Buddhism are the Edicts written by King Ashoka, a well-known Buddhist king who propagated Buddhism throughout Asia, and is honored by both Theravada and Mahayana schools of Buddhism. The authority of the Edicts of Ashoka as a historical record is suggested by the mention of numerous topics omitted as well as corroboration of numerous accounts found in the Theravada and Mahayana Tripitakas written down centuries later.
Asoka Rock Edict 1, dated to c. 257 BCE, mentions the prohibition of animal sacrifices in Ashoka's Maurya Empire as well as his commitment to vegetarianism; however, whether the Sangha was vegetarian in part or in whole is unclear from these edicts. However, Ashoka's personal commitment to, and advocating of, vegetarianism suggests Early Buddhism (at the very least for the layperson) most likely already had a vegetarian tradition (the details of what that entailed besides not killing animals and eating their flesh were not mentioned, and therefore are unknown).
See also
* Buddha's delight
<!--* Buddhist dietitian-->
* Buddhist ethics
* Buddhist vegetarianism
* Cultural elements of Buddhism
* Index of Buddhism-related articles
* List of diets
* Secular Buddhism
* Vegetarian cuisine
* Vegetarianism and religion
* Korean temple cuisine
* Kaiseki
References
External links
* [http://www.shabkar.org Shabkar.org: Vegetarianism as a way of life for Buddhists]
* [http://www.shabkar.org/download/pdf/Shojin_Ryori_Culinary_Fundamentals_in_Zen.pdf Shojin Ryori: Vegetarian Cooking]
* [http://www.shabkar.org/scripture/tantras/index.htm Tantras on Buddhist food]
* [http://www.shabkar.org/scripture/sutras/index.htm Sutras on vegetarianism]
* [http://www.headcity.com/uptown/bigmouth/hungry/chinese/middle.html Return To The Middle Kingdom: Chinese Vegetarian Eating in East Asia]
* [http://zecoow.com Toshio Tanahashi]
*
* [https://tastetrip.cc/#/pc/supplier?id=35 Daigo: a MICHELIN Guide Restaurant]
Category:Food and drink in Buddhism
Category:Buddhism in China
Buddhist
|
https://en.wikipedia.org/wiki/Buddhist_cuisine
|
2025-04-05T18:27:44.311101
|
6191
|
Charles V
|
Charles V may refer to:
Charles V, Holy Roman Emperor (1500–1558)
Charles V of Naples (1661–1700), better known as Charles II of Spain
Charles V of France (1338–1380), called the Wise
Charles V, Duke of Lorraine (1643–1690)
Charles Egon V, Prince of Fürstenberg (1891–1973)
Infante Carlos of Spain, Count of Molina (1788–1855), first Carlist pretender to the throne of Spain (as Charles V)
See also
Karl V. (opera)
Carlos V (chocolate bar)
King Charles (disambiguation)
Charles
eo:Karolo (regantoj)#Karolo la 5-a
|
https://en.wikipedia.org/wiki/Charles_V
|
2025-04-05T18:27:44.311894
|
6193
|
Constantin von Tischendorf
|
| birth_place = Lengenfeld, Kingdom of Saxony
| death_date
| death_place = Leipzig, Saxony, German Empire
| nationality = German
| discipline = theology
| birth_name = Lobegott Friedrich Constantin (von) Tischendorf
| signature = Signatur Konstantin von Tischendorf.PNG
| honorific_prefix = Doctor
}}
Lobegott Friedrich Constantin (von) Tischendorf (18 January 18157 December 1874) was a German biblical scholar. In 1844, he discovered the world's oldest and most complete Bible dated to around the mid-4th century and called Codex Sinaiticus after Saint Catherine's Monastery at Mount Sinai.
Tischendorf was made an honorary doctor by the University of Oxford on 16 March 1865, and by the University of Cambridge on 9 March 1865 following his discovery. While a student gaining his academic degree in the 1840s, he earned international recognition when he deciphered the Codex Ephraemi Rescriptus, a 5th-century Greek manuscript of the New Testament.Early life and education
, published in 1862]]
Tischendorf was born in Lengenfeld, Saxony, the son of a forensic physician. After attending primary school in Lengenfield, he went to grammar school in nearby Plauen. Despite his father's death in 1835 and his mother's just a year later, he was still able to achieve his doctorate in 1838,
A great triumph of these laborious months was the decipherment of the palimpsest Codex Ephraemi Syri Rescriptus, of which the New Testament part was printed before he left Paris, and the Old Testament in 1845. His success in dealing with a manuscript that, having been over-written with other works of Ephrem the Syrian, had been mostly illegible to earlier collators, made him more well known, and gained support for more extended critical expeditions. He now became professor extraordinarius at Leipzig, where he was married in 1845. He also began to publish Reise in den Orient, an account of his travels in the east (in 2 volumes, 1845–46, translated as Travels in the East in 1847). Even though he was an expert in reading the text of a palimpsest (this is a document where the original writing has been removed and new writing added), he was not able to identify the value or meaning of the Archimedes Palimpsest, a torn leaf of which he held and after his death was sold to the Cambridge University Library.
Tischendorf briefly visited the Netherlands in 1841 and England in 1842. In 1843 he visited Italy for thirteen months, before continuing on to Egypt, Sinai, and the Levant, returning via Vienna and Munich.
Discovery of the Codex Sinaiticus Bible manuscripts
In 1844 Tischendorf travelled the first time to Saint Catherine's Monastery at the foot of Mount Sinai in Egypt, where he found a portion of what would later be hailed as the oldest complete known New Testament.
Of the many pages which were contained in an old wicker basket (the kind that the monastery hauled in its visitors as customary in unsafe territories) he was given 43 pages containing a part of the Old Testament as a present. He donated those 43 pages to King Frederick Augustus II of Saxony (reigned 1836–1854), to honour him and to recognise his patronage as the funder of Tischendorf's journey. (Tischendorf held a position as Theological Professor at Leipzig University, also under the patronage of Frederick Augustus II.) Leipzig University put two of the leaves on display in 2011.
Tischendorf reported in his 1865 book Wann Wurden Unsere Evangelen Verfasst, translated to English in 1866 as When Were Our Gospels Written in the section "The Discovery of the Sinaitic Manuscript" that he found, in a trash basket, forty-three sheets of parchment of an ancient copy of the Greek Old Testament, reporting that the monks were using the trash to start fires. And Tischendorf, horrified, asked if he could have them. He deposited them at the University of Leipzig, under the title of the Codex Friderico-Augustanus, a name given in honour of his patron, Frederick Augustus II of Saxony, king of Saxony. The fragments were published in 1846, although Tischendorf kept the place of discovery a secret.
Many have expressed skepticism at the historical accuracy of this report of saving a 1500-year-old parchment from the flames. J. Rendel Harris referred to the story as a myth. The Tischendorf Lesebuch (see References) quotes that the Librarian Kyrillos mentioned to Tischendorf that the contents of the basket had already twice been submitted to the fire. The contents of the baskets were damaged scriptures, the third filling apparently, so cited by Tischendorf himself.[see Tischendorf Lesebuch, Tischendorf's own account].
In 1853 Tischendorf made a second trip to the Syrian monastery but made no new discoveries. He returned a third time in January 1859 under the patronage of Tsar Alexander II of Russia with the active aid of the Russian government to find more of the Codex Frederico-Augustanus or similar ancient Biblical texts. On 4 February, the last day of his visit, he was shown a text which he recognized as significant – the Codex Sinaiticus – a Greek manuscript of the complete New Testament and parts of the Old Testament dating to the 4th century.
Tischendorf persuaded the monks to present the manuscript to Tsar Alexander II of Russia, at the cost of the Tsar it was published in 1862 (in four folio volumes). Those ignorant of the details of his discovery of the Codex Sinaiticus accused Tischendorf of buying manuscripts from ignorant monastery librarians at low prices. Indeed, he was never rich, but he staunchly defended the rights of the monks at Saint Catherine's Monastery when he persuaded them eventually to send the manuscript to the Tsar. This took approximately 10 years because the abbot of St Catherines had to be re-elected and confirmed in office in Cairo and in Jerusalem, and during those 10 years no one in the monastery had the authority to hand over any documents. However the documents were handed over in due course following a signed and sealed letter to the Tsar Alexander II (Schenkungsurkunde). Even so, the monks of Mt. Sinai still display a receipt-letter from Tischendorf promising to return the manuscript to them in the case that the donation can not be done. This token-letter had to be destroyed, following the late issue of a "Schenkungsurkunde". This donation act regulated the Codex exchange with the Tsar, against 9000 Rubels and Rumanian estate protection. The Tsar was seen as the protector of Greek-Orthodox Christians. Thought lost since the Russian revolution, the document (Schenkungsurkunde) has now resurfaced in St Petersburg 2003, and has also been long before commented upon by other scholars like Kurt Aland. The monastery has disputed the existence of the gift certificate (Schenkungsurkunde) since the British Library was named as the new owner of the Codex. Now following the late find of the gift certificate by the National Russian Library the existence cannot be disputed in earnest.
In 1869 the Tsar awarded Tischendorf the style of "von" Tischendorf as a Russian noble. 327 facsimile editions of the Codex were printed in Leipzig for the Tsar (instead of a salary for the three-year work of Tischendorf the Tsar gave him 100 copies for reselling) in order to celebrate the 1000th anniversary of the traditional foundation of the Rus' state in 862 with the publication of this most amazing find. Supporting the production of the facsimile, all made with special print characters for each of the 4 scribes of the Codex Sinaiticus, was shift work and contributed to Tischendorf's early demise due to exhausting work for months also during nights. Thus the Codex found its way to the Imperial Library at St. Petersburg. and of the Septuagint version of the Old Testament (7th edition, 1887); in 1852, amongst other works, his edition of the Codex Claromontanus. In 1859, he was named professor ordinarius of theology and of Biblical paleography, this latter professorship being specially created for him; and another book of travel, Aus dem heiligen Lande, appeared in 1862. Tischendorf's Eastern journeys were rich enough in other discoveries to merit the highest praise.
Besides his fame as a scholar, he was a friend of both Robert Schumann, with whom he corresponded, and Felix Mendelssohn, who dedicated a song to him. His colleague Samuel Prideaux Tregelles wrote warmly of their mutual interest in textual scholarship. His personal library, purchased after his death, eventually came to the University of Glasgow, where a commemorative exhibition of books from his library was held in 1974 and can be accessed by the public.DeathLobegott Friedrich Constantin (von) Tischendorf died in Leipzig on 7 December 1874, aged 59.
Codex Sinaiticus
The Codex Sinaiticus contains a 4th-century manuscript of New Testament texts. Two other Bibles of similar age exist, though they are less complete: Codex Vaticanus in the Vatican Library and Codex Alexandrinus, currently owned by the British Library. The Codex Sinaiticus is deemed by some to be the most important surviving New Testament manuscript, as no older manuscript is as nearly complete as the Codex. The codex can be viewed in the British Library in London, or as a digitized version on the Internet.
Tischendorf's motivation
Throughout his life, Tischendorf sought old biblical manuscripts, as he saw it as his task to give theology a Greek New Testament that was based on the oldest possible manuscripts. He intended to be as close as possible to the sources. Tischendorf's greatest discovery was in the monastery of Saint Catherine on the Sinai Peninsula, which he visited in May 1844, and again in 1853 and 1859 (as Russian envoy).
In 1862, Tischendorf published the text of the Codex Sinaiticus for the 1000th Anniversary of the Russian Monarchy in both an illustrious four-volume facsimile edition and a less costly text edition, the latter to enable as many scholars as possible to have access to the contents of the Codex.
Tischendorf pursued a constant course of editorial labors, mainly on the New Testament, until he was broken down by overwork in 1873. Prof. (Leipzig University, Prof. of Theology) explained in a publication on Tischendorf's Letter that he was motivated to prove scientifically that the words of the Bible were trustworthily transmitted over the centuries.Works
His magnum opus was the "Critical Edition of the New Testament."
The great edition, of which the text and apparatus appeared in 1869 and 1872, was called by himself editio viii; but this number is raised to twenty or twenty-one, if mere reprints from stereotype plates and the minor editions of his great critical texts are included; posthumous prints bring the total to forty-one. Four main recensions of Tischendorf's text may be distinguished, dating respectively from his editions of 1841, 1849, 1859 (ed. vii), and 1869–72 (ed. viii). The edition of 1849 may be regarded as historically the most important, from the mass of new critical material it used; that of 1859 is distinguished from Tischendorf's other editions by coming nearer to the received text; in the eighth edition, the testimony of the Sinaitic manuscript received great (probably too great) weight. The readings of the Vatican manuscript were given with more exactness and certainty than had been possible in the earlier editions, and the editor had also the advantage of using the published labours of his colleague and friend Samuel Prideaux Tregelles.
Of relatively lesser importance was Tischendorf's work on the Greek Old Testament. His edition of the Roman text, with the variants of the Alexandrian manuscript, the Codex Ephraemi, and the Friderico-Augustanus, was of service when it appeared in 1850, but, being stereotyped, was not greatly improved in subsequent issues. Its imperfections, even within the limited field it covers, may be judged by the aid of Eberhard Nestle's appendix to the 6th issue (1880).
Besides this may be mentioned editions of the New Testament apocrypha, De Evangeliorum apocryphorum origine et usu (1851); Acta Apostolorum apocrypha (1851); Evangelia apocrypha (1853; 2nd edition, 1876); Apocalypses apocryphae (1866), and various minor writings, partly of an apologetic character, such as Wann wurden unsere Evangelien verfasst? (When Were Our Gospels Written?; 1865; 4th edition, 1866, digitized by Google and available for e-readers), Haben wir den echten Schrifttext der Evangelisten und Apostel? (1873), and Synopsis evangelica (7th edition, 1898).
Facsimile of manuscripts
* [https://books.google.com/books?id=wWFAAAAAcAAJ Codex Ephraemi Syri rescriptus, sive Fragmenta Novi Testamenti], Lipsiae 1843
* [https://archive.org/stream/Tischendorf.V.Various/01.CodexEphraemiSyriRescriptus.FragUtriusqTest.1845.#page/n9/mode/2up Codex Ephraemi Syri rescriptus, sive Fragmenta Veteris Testamenti], Lipsiae 1845
* [https://books.google.com/books?id=1CFMAAAAYAAJ Notitia editionis codicis Bibliorum Sinaitici] (Leipzig 1860)
* [https://archive.org/stream/Tischendorf.V.Various/04.AnecdotaSacraProfanaOrientOccidentNotitiaCodex..v1.Tischendorf.1861.#page/n7/mode/2up Anecdota sacra et profana] (Leipzig 1861)
Editions of Novum Testamentum Graece
* [https://archive.org/stream/hkaindiathknovu00tiscgoog#page/n5/mode/2up Novum Testamentum Graece. Editio stereotypa secunda, (Lipsiae 1862)]
* [https://archive.org/stream/novumtestamentu01tiscgoog#page/n5/mode/2up Novum Testamentum Graece. Editio Quinta, Lipsiae 1878]
* [https://archive.org/stream/novumtestamentu00tiscgoog#page/n6/mode/2up Novum Testamentum Graece. Editio Septima, Lipsiae 1859]
Editio Octava
* Gospels: [https://archive.org/stream/novumtestamentu01greggoog#page/n4/mode/2up Novum Testamentum Graece: ad antiquissimos testes denuo recensuit, apparatum criticum omni studio perfectum, vol. I (1869)]
* Acts–Revelation: [https://archive.org/stream/novumtestamentu02abbogoog#page/n4/mode/2up Novum Testamentum Graece. Editio Octava Critica Maior, vol. II (1872)]
* Prolegomena I–VI: [https://archive.org/stream/p1novumtestamentum03tiscuoft#page/n5/mode/2up Novum Testamentum Graece. Editio Octava Critica Maior, vol. III, Part 1 (1884)]
* Prolegomena VII–VIII: [https://archive.org/stream/novumtestamentu00abbogoog#page/n6/mode/2up Novum Testamentum Graece. Editio Octava Critica Maior, vol. III, Part 2 (1890)]
* Prolegomena IX–XIII: [https://archive.org/stream/novumtestamentu01abbogoog#page/n11/mode/2up Novum Testamentum Graece. Editio Octava Critica Maior, vol. III, Part 3 (1894)]
* [https://archive.org/stream/novumtestamentu00hortgoog#page/n6/mode/2up Novum Testamentum graece: recensionis Tischendorfianae ultimae textum. Lipsiae 1881]
LXX
* [https://archive.org/stream/vetustestamentu01tiscgoog#page/n7/mode/2up Vetus Testamentum Graece iuxta LXX interpretes: Vetus Testamentum Graece iuxta LXX (Volume 1)]
*[https://books.google.com/books?ideNM7AAAAcAAJ Vetus Testamentum Graece iuxta LXX interpretes: Vetus Testamentum Graece iuxta LXX (Volume 2)]His publications continued
* Doctrina Pauli apostoli de vi mortis Christi satisfactoria. Leipzig, 1837 Google
* Fritz der junge Mystiker, oder die drei letzten Festzeiten aus seinem Leben...: eine biographische Skizze. Leipzig, [1839]
* Disputatio de Christo, pane vitae, sive de loco Evang. Ioann. c. VI. vv. 5159 Leipzig, 1839
* Die Geissler: namentlich die große Geißelfahrt nach Straßburg im Jahre 1349. Leipzig, 1840
* De ev. Matth. c. 19. v. 16 et 39. Leipzig, 1840
* De recensionibus quas dicunt textus Novi Testamenti ratione potissimum habita Scholzii: dissertatio historica exegetica critica. Leipzig, 1840 [Hochschulschrift]
* Novum Testamentum Graece / Ad Antiquos Testes Recensuit Lectionesque Variantes Elzeviriorum Stephani Griesbachii Notavit Constantinus Tischendorf. Paris, 1842
* Hē Kainē Diathēkē / In Antiquis Testibus Textum Versionis Vulgatae Latinae Indagavit Lectionesque Variantes Stephani Et Griesbachii Notavit V. S. Venerabili Jager in Consilium Adhibito Constantinus Tischendorf. Paris, 1842
* Codex Ephraemi Syri rescriptus sive fragmenta utriusque testamenti. T.1. Fragmenta Veteris testamenti, T. 2. Fragmenta Novi testamenti. Leipzig, 1843
* Weihnachtspredigt ... in Lengefeld. Leipzig, 1845
* Monumenta sacra inedita sive reliquiae antiquissimae textus Novi testamenti Graeci: ex novum plus mille annorum codicibus per Europam dispersis. Leipzig, 1846
* Codex Friderico-Augustanus sive fragmenta Veteris Testamenti: e codice Graeco, omnium qui in Europa supersunt facile antiquissimo; in Oriente detexit, in patriam attulit. Leipzig, 1846
* De Israelitarum per mare rubrum transitu: cum tabula. Leipzig, 1847
* Evangelium Palatinum ineditum sive reliquiae textus Evangeliorum Latini ante Hieronymum versi: ex Codice Palatino Purpureo quarti vel quinti p. Chr. saeculi. Leipzig, 1847
* Der Geist der Wahrheit: Zeitpredigt am Sonntag Cantate den 6. Mai 1849 in der Universitätskirche zu Leipzig gehalten. Leipzig, 1849
* Novum Testamentum: Latine interprete Hieronymo; ex celeberrimo codice Amiatino omnium et antiquissimo et praestantissimo. Leipzig, 1850
* Acta apostolorum apocrypha. Leipzig, 1851 Google
* Synopsis evangelica: ex quattuor evangeliis ordine chronologico concinnavit. Leipzig, 1851 Google-USA* (5. Aufl. 1884)
* De evangeliorum apocryphorum origine et usu. In: Verhandelingen / uitg. door het Haagsche Genootschap tot Verdediging van de christelijke Godsdienst, Bd. 12, Den Haag, 1851
* Codex Claromontanus sive Epistulae Pauli omnes Graece et Latine: ex Codice Parisiensi celeberrimo nomine Claromontani plerumque dicto sexti ut videtur post Christum saeculi. Leipzig, 1852
* Evangelia apocrypha: adhibitis plurimis codicibus graecis et latinis maximam partem nunc primum consultis atque ineditorum copia insignibus. Leipzig, 1853 Google Editio Altera 1874: Google-USA*
* Novum Testamentum Triglottum: graece, latine, germanice; graecum textum addito lectionum variarum delectu recensuit, latinum Hieronymi notata Clementina lectione ex auctoritate codicum restituit, germanicum ad pristinam lutheranae editionis veritatem revocavit. Leipzig, 1854
* Anecdota sacra et profana ex oriente et occidente allata sive notitia codicum Graecorum, Arabicorum, Syriacorum, Copticorum, Hebraicorum, Aethiopicorum, Latinorum: cum excerptis multis maximam partem Graecis et 35 scripturarum antiquissimarum speciminibus. Leipzig, 1855 Google Editio repetita 1861: Michigan, Google, Google
* Pastor: Graece; ex fragmentis Lipsiensibus. Leipzig, 1856
* Novum Testamentum Graece et Latine: Graecum textum addito lectionum variarum delectu rec.; Latinum Hieronymi notata Clementina lectione ex auct. codicum. Leipzig, 1858
* Notitia editionis Codicis Bibliorum Sinaitici auspiciis imperatoris Alexandri II. susceptae. Leipzig, 1860
* Aus dem heiligen Lande: nebst fünf Abbildungen in Holzschnitt und einer lithographirten Tafel. Leipzig, 1862
* Vorworte zur sinaitischen Bibelhandschrift zu St. Petersburg : unter den Auspicien seiner Kaiserlichen Maiestät Alexander II. dem Dunkel entzogen, nach Europa überbracht, zur Hebung und Verherrlichung christlicher Wissenschaft. Leipzig, 1862
* Novum Testamentum Sinaiticum sive Novum Testamentum cum Epistola Barnabae et Fragmentis Pastoris : ex codice Sinaitico ... Leipzig, 1863
* Die Anfechtungen der Sinai-Bibel. Leipzig, 1865 Google
* Aus Dem Heiligen Lande. Leipzig, 1865 Google
* Wann wurden unsere Evangelien verfasst? Leipzig, 1865 Google, 2. Expl. Google
* Novum Testamentum Graece: ex sinaitico codice omnium antiquissimo vaticana itemque Elzeviriana lectione notata. Leipzig, 1865
* Apocalypses apocryphae Mosis, Esdrae, Pauli, Johannis, item Mariae Dormitio: additis Evangeliorum et actuum Apocryphorum supplementis. Leipzig, 1866 Internet Archive Internet Archive
* Appendix Codicum celeberrimorum Sinaitici, Vaticani, Alexandrini cum imitatione ipsorum antiqua manu scriptorum. Leipzig, 1867
* Philonea: inedita altera, altera nunc demum recte ex vetere scriptura eruta. Leipzig, 1868 Internet Archive
* Responsa ad calumnias romanas: item supplementum novi testamenti ex sinaitico codice anno 1865 editi. Leipzig, 1870
* Novum Testamentum graece: ad antiquissimos testes denuo recensuit, apparatum. Leipzig, 1869–1872. 1. Band 1869 Google-USA*, 2. Band 1872 Google-USA*
* Die Sinaibibel, ihre Entdeckung, Herausgabe und Erwerbung. Leipzig, 1871 Google-USA*
* Die evangelische Alliance-Deputation an Kaiser Alexander zu Friedrichshafen: zur Abwehr der groben Entstellungen und Verleumdungen des Herrn von Wurstemberger (zu Bach bei Bern). Leipzig, 1872
* Clementis Romani epistulae. Ad ipsius codicis alexandrini fidem ac modum repetitis curis edidit Constantinus de Tischendorf. Leipzig, 1873. Internet Archive
* Haben wir den ächten Schrifttext der Evangelisten und Apostel? Leipzig, 1873 Google-USA* (2. Aufl.)
* Liber Psalmorum: hebraicus atque latinus ab Hieronymo ex hebraeo conversus. Leipzig, 1874
Cooperation
* Textum ... recensuit, brevem apparatum criticum una cum variis lectionibus Elzevirorum, Knapii, Scholzii, Lachmanni subjunxit, argumenta et locos parallelos indicavit, commentationem ... edd. Stephanicae tertiae atque Millianae, Matthaeianae, Griesbachianae praemisit Aenoth. Frid. Const. Tischendorf. Leipzig, 1841
* Clementinorum Epitomae duae: altera edita correctior, inedita altera nunc primum integra ex codicibus Romanis et excerptis Tischendorfianis, cura Alberti Rud. Max. Dressel. Accedunt Friderici Wieseleri Adnotationes criticae ad Clementis Romani quae feruntur homilias. Leipzig, 1859 Internet Archive
* Ad Vetus Testamentum Graecum ex auctoritate Sixti V. Pont. Max. a. 1587 editum a Leandro van Ess quoad textum accuratissime recusum trecentis annis post editionem originalem novis curis iteratum prolegomena et epilegomena. Bredt, 1887
* Novum Testamentum : Constantin Tischendorf: griechisch, lateinisch, englisch, Ostervald: französisch, Martin Luther, DeWette, Richard Nagel: deutsch ... Hrsg. Eugen Niethe Berlin, 1891
Second Author
* Ezra Abbot: The late Professor Tischendorf. Aus: The Unitarian Review and Religious Magazine. März 1875 (Festschrift Konstantin von Tischendorf)
* Caspar René Gregory: Tischendorf, Lobegott Friedrich Constantin. In: Allgemeine Deutsche Biographie. Band 38. Duncker & Humblot, Leipzig 1894, S. 371–373
See also
* List of New Testament papyri
* List of New Testament uncials
* Agnes and Margaret Smith
* Editio Octava Critica Maior
Footnotes
References
* Black, Matthew, and Robert Davidson, Constantin von Tischendorf and the Greek New Testament Glasgow: University of Glasgow Press, 1981.
*
* Christfried Böttrich: "One Story – Different Perspectives. The Case of the Codex Sinaiticus", in: Codex Sinaiticus - New Perspectives on the Ancient Biblical Manuscript, Scot McKendrick, David Parker, Amy David Myshrall, Cillian O'Hogan (Hg.), London 2015 (Papers from the Sinaticus-Conference July 2009 in the British Library London).
*
*
* In addition to the handbooks on New Testament criticism, Carl Bertheau's article on Tischendorf in Herzog-Hauck, Realencyklopädie (3rd edition, 1907)
*
* [https://web.archive.org/web/20140718022435/http://www.nlr.ru/eng/exib/CodexSinaiticus/zah/ THE HISTORY OF THE ACQUISITION OF THE SINAI BIBLE BY THE RUSSIAN GOVERNMENT IN THE CONTEXT OF RECENT FINDINGS IN RUSSIAN ARCHIVES1, A.V. Zakharova]
* Bibliographie Konstantin von Tischendorf (1815–1874), Christfried Bőttrich
* Tischendorf Lesebuch, Christfried Bőttrich, 1999
* Tischendorf Erinnerungen, Ludwig Schneller, Verlag der St-Johannis Druckerei, Schweickhardt, Lahr-Dinglingen, 1991
* [https://web.archive.org/web/20140727034304/http://www.theologie.uni-greifswald.de/nt/prof-dr-christfried-boettrich/forschungsprojekte.html Various Tischendorf publications from Christfried Bőttrich]
External links
* [https://archive.org/details/Tischendorf.V.Various Tischendorf. V. Various Works. Codices, Synoptics, Testaments, Anecdotes, Criticism. 12 vols. 1845–1880]
* [https://archive.org/details/Tischendorf.iv.monumentaSacraInedita.newcollection.subscript.6vols.1857-1870 Monumenta sacra inedita. Nova Collectio, 1–6 volumes (1857–1870)] at the Internert Archive
*[https://archive.org/search.php?querycreator%3A%22Tischendorf%2C+Constantin+von%2C+1815-1874%22 Tischendorf] Internet Archive Sortable articles
* [http://www.ccel.org/t/tischendorf/ Works by Von Tischendorf] in English at CCEL
* [https://web.archive.org/web/20070702052740/http://morphgnt.org/projects/tischendorf Tischendorf's eighth Greek New Testament with morphological tags and lemmas]
* [https://web.archive.org/web/20090306060614/http://openscriptures.org/prototypes/manuscript-comparator/ Comparison of Tischendorf's 8th GNT text with other manuscript editions] on the Manuscript Comparator
* [http://www.documentacatholicaomnia.eu/04z/z_sine-data__AA_VV__Evangelia_Apocrypha_%5BTischendorf_Von._Constantin%5D__LT_GR.pdf.html A digital edition of the Evangelia Apocrypha document written in Latin and Greek], in pdf format.
* [https://archive.org/details/novumtestamentu00goog Novum Testamentum graece (1859)]
* [http://www.biblestudyaids.net/nt/tiscapp/main.htm Complete Apparatus, 8th Version in pdf – ]
Category:1815 births
Category:1874 deaths
Category:People from Lengenfeld
Category:People from the Kingdom of Saxony
Category:German untitled nobility
Category:19th-century German Christian theologians
Category:19th-century German theologians
Category:German biblical scholars
Category:New Testament scholars
Category:Textual scholarship
Category:German male non-fiction writers
Category:19th-century German male writers
Category:Leipzig University alumni
Category:Academic staff of Leipzig University
Category:Commanders of the Order of Franz Joseph
Category:Order of the Polar Star
Category:Recipients of the Order of St. Anna
Category:Knights of the Legion of Honour
|
https://en.wikipedia.org/wiki/Constantin_von_Tischendorf
|
2025-04-05T18:27:44.323952
|
6195
|
Calvin Coolidge
|
*
}}
| predecessor = Warren G. Harding
| successor = Herbert Hoover
| order2 = 29th
| office2 = Vice President of the United States
| term_start2 = March 4, 1921
| term_end2 = August 2, 1923
| president2 = Warren G. Harding
| predecessor2 = Thomas R. Marshall
| successor2 = Charles G. Dawes
| order3 = 48th
| office3 = Governor of Massachusetts
| lieutenant3 = Channing H. Cox
| term_start3 = January 2, 1919
| term_end3 = January 6, 1921
| predecessor3 = Samuel W. McCall
| successor3 = Channing H. Cox
| order4 = 46th
| office4 = Lieutenant Governor of Massachusetts
| governor4 = Samuel W. McCall
| term_start4 = January 6, 1916
| term_end4 = January 2, 1919
| predecessor4 = Grafton D. Cushing
| successor4 = Channing H. Cox
| office5 = President of the Massachusetts Senate
| term_start5 = January 7, 1914
| term_end5 = January 6, 1915
| predecessor5 = Levi H. Greenwood
| successor5 = Henry Gordon Wells
| office6 = Member of the Massachusetts Senate
| term_start6 = January 3, 1912
| term_end6 = January 6, 1915
| predecessor6 = Allen T. Treadway
| successor6 = John B. Hull
| constituency6 = Berkshire, Hampden, and Hampshire counties
| office7 = 16th Mayor of Northampton
| term_start7 = January 3, 1910
| term_end7 = January 1, 1912
| predecessor7 = James W. O'Brien
| successor7 = William Feiker
| state_house8 = Massachusetts
| district8 = 1st Hampshire
| term_start8 = January 2, 1907
| term_end8 = January 6, 1909
| predecessor8 = Moses M. Bassett
| successor8 = Charles A. Montgomery
| birth_name = John Calvin Coolidge Jr.
| birth_date =
| birth_place = Plymouth Notch, Vermont, U.S.
| death_date =
| death_place = Northampton, Massachusetts, U.S.
| resting_place = Plymouth Notch Cemetery
| party = Republican
| parents =
| spouse =
| children = 2, including John
| relatives =
| education = Amherst College (AB)
| occupation =
| signature = C Coolidge signature.svg
| signature_alt = Cursive signature in ink
| module
}}
Calvin Coolidge (born John Calvin Coolidge Jr.; ; July 4, 1872January 5, 1933) was the 30th president of the United States, serving from 1923 to 1929. A Republican lawyer from Massachusetts, he previously served as the 29th vice president from 1921 to 1923 under President Warren G. Harding, and as the 48th governor of Massachusetts from 1919 to 1921. Coolidge gained a reputation as a small-government conservative with a taciturn personality and dry sense of humor that earned him the nickname "Silent Cal".
Coolidge began his career as a member of the Massachusetts State House. He rose up the ranks of Massachusetts politics and was elected governor in 1918. As governor, Coolidge ran on the record of fiscal conservatism, strong support for women's suffrage, and vague opposition to Prohibition. His prompt and effective response to the Boston police strike of 1919 thrust him into the national spotlight as a man of decisive action. The following year, the Republican Party nominated Coolidge as the running mate to Senator Warren G. Harding in the 1920 presidential election, which they won in a landslide. Coolidge served as vice president until Harding's death in 1923, after which he assumed the presidency.
During his presidency, Coolidge restored public confidence in the White House after the Harding administration's many scandals. He signed into law the Indian Citizenship Act of 1924, which granted U.S. citizenship to all Native Americans, and oversaw a period of rapid and expansive economic growth known as the "Roaring Twenties", leaving office with considerable popularity. Coolidge was known for his hands-off governing approach and pro-business stance; biographer Claude Fuess wrote: "He embodied the spirit and hopes of the middle class, could interpret their longings and express their opinions. That he did represent the genius of the average is the most convincing proof of his strength." Coolidge chose not to run again in 1928, remarking that ten years as president would be "longer than any other man has had it—too long!"
Coolidge is widely admired for his stalwart support of racial equality during a period of heightened racial tension, and is highly regarded by advocates of smaller government and laissez-faire economics; supporters of an active central government generally view him far less favorably. His critics argue that he failed to use the country's economic boom to help struggling farmers and workers in other flailing industries, and there is still much debate among historians about the extent to which Coolidge's economic policies contributed to the onset of the Great Depression, which began shortly after he left office. Scholars have ranked Coolidge in the lower half of U.S. presidents.Early life and family historyJohn Calvin Coolidge Jr. was born on July 4, 1872, in Plymouth Notch, Vermont—the only U.S. president to be born on Independence Day. He was the elder of the two children of John Calvin Coolidge Sr. (1845–1926) and Victoria Josephine Moor (1846–1885). Although named for his father, from early childhood Coolidge was addressed by his middle name. The name Calvin was used in multiple generations of the Coolidge family, apparently selected in honor of John Calvin, the Protestant Reformer.
Coolidge Senior engaged in many occupations and developed a statewide reputation as a prosperous farmer, storekeeper, and public servant. He held various local offices, including justice of the peace and tax collector and served in both houses of the Vermont General Assembly. When Coolidge was 12 years old, his chronically ill mother died at the age of 39, perhaps from tuberculosis. His younger sister, Abigail Grace Coolidge (1875–1890), died at the age of 15, probably of appendicitis, when Coolidge was 18. Coolidge's father married a Plymouth schoolteacher in 1891, and lived to the age of 80.
Coolidge's earliest American ancestor, John Coolidge, emigrated from Cottenham, Cambridgeshire, England, around 1630 and settled in Watertown, Massachusetts. Coolidge also descended from Samuel Appleton, who settled in Ipswich and led the Massachusetts Bay Colony during King Philip's War. Coolidge's great-great-grandfather, another John Coolidge, was an American military officer in the Revolutionary War and one of the first selectmen of the town of Plymouth.
His grandfather Calvin Galusha Coolidge served in the Vermont House of Representatives. His cousin Park Pollard was a businessman in Cavendish, Vermont, and the longtime chair of the Vermont Democratic Party. Coolidge's mother was the daughter of Hiram Dunlap Moor, a Plymouth Notch farmer, and Abigail Franklin.<gallery mode"packed" heights="150px">
File:PlymouthVT_CalvinCoolidgeHouse.jpg|The Coolidge Homestead in Plymouth Notch, Vermont
File:CoolidgeAmherst.png|Coolidge as an Amherst College undergraduate
</gallery>
Early career and marriage
Education and law practice
Coolidge attended the Black River Academy and then St. Johnsbury Academy before enrolling at Amherst College, where he distinguished himself in the debating class. As a senior, he joined the Phi Gamma Delta fraternity and graduated cum laude. While at Amherst, Coolidge was profoundly influenced by philosophy professor Charles Edward Garman, a Congregational mystic who had a neo-Hegelian philosophy. Coolidge explained Garman's ethics forty years later:}}
At his father's urging after graduation, Coolidge moved to Northampton, Massachusetts, to become a lawyer. Coolidge followed the common practice of apprenticing with a local law firm, Hammond & Field, and reading law with them. John C. Hammond and Henry P. Field, both Amherst graduates, introduced Coolidge to practicing law in the county seat of Hampshire County, Massachusetts. In 1897, Coolidge was admitted to the Massachusetts bar, becoming a country lawyer. With his savings and a small inheritance from his grandfather, Coolidge opened his own law office in Northampton in 1898. He practiced commercial law, believing that he served his clients best by staying out of court. As his reputation as a hard-working and diligent attorney grew, local banks and other businesses began to retain his services.Marriage and familyIn 1903, Coolidge met Grace Goodhue, a graduate of the University of Vermont and a teacher at Northampton's Clarke School for the Deaf. They married on October 4, 1905, at 2:30 p.m. in a small ceremony which took place in the parlor of Grace's family's house, having overcome her mother's objections to the marriage. The newlyweds went on a honeymoon trip to Montreal, originally planned for two weeks but cut short by a week at Coolidge's request. After 25 years he wrote of Grace, "for almost a quarter of a century she has borne with my infirmities and I have rejoiced in her graces".
The Coolidges had two sons: John (1906–2000) and Calvin Jr. (1908–1924). On June 30, 1924, Calvin Jr. had played tennis with his brother on the White House tennis courts without putting on socks and developed a blister on one of his toes. The blister subsequently degenerated into sepsis. Calvin Jr. died a little over a week later at the age of 16.
Coolidge never forgave himself for Calvin Jr's death. His eldest son John said it "hurt [Coolidge] terribly", and psychiatric biographer Robert E. Gilbert, author of The Tormented President: Calvin Coolidge, Death, and Clinical Depression, said that Coolidge "ceased to function as President after the death of his sixteen-year-old son". Gilbert writes that after Calvin Jr.'s death Coolidge displayed all ten of the symptoms the American Psychiatric Association lists as evidence of major depressive disorder. John later became a railroad executive, helped start the Coolidge Foundation, and was instrumental in creating the President Calvin Coolidge State Historic Site.
Coolidge was frugal, and when it came to securing a home, he insisted upon renting. He and his wife attended Northampton's Edwards Congregational Church before and after his presidency.
Local political office (1898−1915)
City offices
The Republican Party was dominant in New England at the time, and Coolidge followed the example of Hammond and Field by becoming active in local politics. In 1896, Coolidge campaigned for Republican presidential candidate William McKinley, and was selected to be a member of the Republican City Committee the next year. In 1898, he won election to the City Council of Northampton, placing second in a ward where the top three candidates were elected. The position offered no salary but provided Coolidge with valuable political experience.
In 1899, the city council made Coolidge city solicitor. He was elected to a one-year term in 1900 and reelected in 1901. This position gave Coolidge more experience as a lawyer and paid a salary of $600 (). In 1902, the city council selected a Democrat for city solicitor, and Coolidge returned to private practice. Soon thereafter, the clerk of courts for the county died, and Coolidge was chosen to replace him. The position paid well, but it barred him from practicing law, so he remained at the job for only a year.
In 1904, Coolidge suffered his sole defeat at the ballot box, losing an election to the Northampton school board. When told that some of his neighbors voted against him because he had no children in the schools he would govern, the recently married Coolidge replied, "Might give me time!"Massachusetts state legislator and mayor
In 1906, the local Republican committee nominated Coolidge for election to the Massachusetts House of Representatives. He won a close victory over the incumbent Democrat, and reported to Boston for the 1907 session of the Massachusetts General Court. In his freshman term, Coolidge served on minor committees and, although he usually voted with the party, was known as a Progressive Republican, voting in favor of such measures as women's suffrage and the direct election of Senators.
While in Boston, Coolidge became an ally, and then a liegeman, of then U.S. Senator Winthrop Murray Crane, who controlled the Massachusetts Republican Party's western faction; Crane's party rival in eastern Massachusetts was U.S. Senator Henry Cabot Lodge. Coolidge forged another key strategic alliance with Guy Currier, who had served in both state houses and had the social distinction, wealth, personal charm, and broad circle of friends Coolidge lacked, and which had a lasting impact on his political career. In 1907, Coolidge was reelected. In the 1908 session he was more outspoken, though not in a leadership position.
Instead of vying for another term in the State House, Coolidge returned home to his growing family and ran for mayor of Northampton when the incumbent Democrat retired. He was well liked in the town, and defeated his challenger by a vote of 1,597 to 1,409. During his first term from 1910 to 1911, he increased teachers' salaries and retired some of the city's debt while still managing to effect a slight tax decrease. In 1911, he was renominated and defeated the same opponent by a slightly larger margin.
In 1911, the State Senator for the Hampshire County area retired and successfully encouraged Coolidge to run for his seat for the 1912 session. Coolidge defeated his Democratic opponent by a large margin. At the start of that term, he became chairman of a committee to arbitrate the "Bread and Roses" strike by the workers of the American Woolen Company in Lawrence, Massachusetts. After two tense months, the company agreed to the workers' demands, in a settlement proposed by the committee.
A major issue affecting Massachusetts Republicans in 1912 was the party split between the progressive wing, which favored Theodore Roosevelt, and the conservative wing, which favored William Howard Taft. Although he favored some progressive measures, Coolidge refused to leave the Republican party. When the new Progressive Party declined to run a candidate in his state senate district, Coolidge won reelection against his Democratic opponent by an increased margin.
{| class"toccolours" style"float: right; margin-left: 1em; margin-right: 2em; font-size: 85%; background:#c6dbf7; color:black; width:30em; max-width: 40%;" cellspacing="5"
| style="text-align: left;" |"Do the day's work. If it be to protect the rights of the weak, whoever objects, do it. If it be to help a powerful corporation better to serve the people, whatever the opposition, do that. Expect to be called a stand-patter, but don't be a stand-patter. Expect to be called a demagogue, but don't be a demagogue. Don't hesitate to be as revolutionary as science. Don't hesitate to be as reactionary as the multiplication table. Don't expect to build up the weak by pulling down the strong. Don't hurry to legislate. Give administration a chance to catch up with legislation."
|-
| style"text-align: left;" | "Have Faith in Massachusetts" as delivered by Calvin Coolidge to the Massachusetts State Senate, 1914
|}
In the 1913 session, Coolidge enjoyed renowned success in arduously navigating to passage the Western Trolley Act, which connected Northampton with a dozen similar industrial communities in Western Massachusetts.
Coolidge intended to retire after his second term, as was customary, but when the president of the state senate, Levi H. Greenwood, considered running for lieutenant governor, Coolidge decided to run for the Senate again in hopes of being elected its presiding officer. Greenwood later decided to run for reelection to the Senate, and was defeated primarily due to his opposition to women's suffrage.
Coolidge was in favor of the women's vote, and was reelected. With Crane's help, Coolidge assumed the presidency of a closely divided Senate. After his election in January 1914, Coolidge delivered a published and frequently quoted speech, Have Faith in Massachusetts, which summarized his philosophy of government.
Coolidge's speech was well received, and he attracted some admirers on its account. Towards the end of the term, many of them were proposing Coolidge's name for nomination to lieutenant governor. After winning reelection to the Senate by an increased margin in the 1914 elections, Coolidge was reelected unanimously to be President of the Senate. Coolidge's supporters, led by fellow Amherst alumnus Frank Stearns, encouraged him again to run for lieutenant governor. Stearns, an executive with the Boston department store R. H. Stearns, became another key ally, and began a publicity campaign on Coolidge's behalf before he announced his candidacy at the end of the 1915 legislative session.
Lieutenant Governor and Governor of Massachusetts (1916−1921)
Coolidge entered the primary election for lieutenant governor and was nominated to run alongside gubernatorial candidate Samuel W. McCall. Coolidge was the leading vote-getter in the Republican primary, and balanced the Republican ticket by adding a western presence to McCall's eastern base of support. McCall and Coolidge won the 1915 election to their respective one-year terms, with Coolidge defeating his opponent by more than 50,000 votes.
In Massachusetts, the lieutenant governor does not preside over the state Senate, as is the case in many other states; nevertheless, as lieutenant governor, Coolidge was a deputy governor functioning as an administrative inspector and was a member of the governor's council. He was also chairman of the finance committee and the pardons committee. As a full-time elected official, Coolidge discontinued his law practice in 1916, though his family continued to live in Northampton. McCall and Coolidge were both reelected in 1916 and in 1917. When McCall decided that he would not stand for a fourth term, Coolidge announced his intention to run for governor.1918 electionCoolidge was unopposed for the Republican nomination for Governor of Massachusetts in 1918. He and his running mate, Channing Cox, a Boston lawyer and Speaker of the Massachusetts House of Representatives, ran on the previous administration's record: fiscal conservatism, a vague opposition to Prohibition, support for women's suffrage, and support for American involvement in World War I. The issue of the war proved divisive, especially among Irish and German Americans. Coolidge was elected by a margin of 16,773 votes over his opponent, Richard H. Long, in the smallest margin of victory of any of his statewide campaigns.
Boston police strike
]]
In 1919, in reaction to a plan of the policemen of the Boston Police Department to register with a union, Police Commissioner Edwin U. Curtis announced that such an act would not be tolerated. In August of that year, the American Federation of Labor issued a charter to the Boston Police Union. Curtis declared the union's leaders were guilty of insubordination and would be relieved of duty, but indicated he would cancel their suspension if the union was dissolved by September 4. The mayor of Boston, Andrew Peters, convinced Curtis to delay his action for a few days, but with no results, and Curtis suspended the union leaders on September 8. The following day, about three-quarters of the policemen in Boston went on strike.}}
Tacitly but fully in support of Curtis's position, Coolidge closely monitored the situation but initially deferred to the local authorities. He anticipated that only a resulting measure of lawlessness could sufficiently prompt the public to understand and appreciate the controlling principle: that a policeman does not strike. That night and the next, there was sporadic violence and rioting in the city. Concerned about sympathy strikes by the firemen and others, Peters called up some units of the Massachusetts National Guard stationed in the Boston area pursuant to an old and obscure legal authority and relieved Curtis of duty.
Coolidge, sensing the severity of circumstances were then in need of his intervention, conferred with Crane's operative, William Butler, and then acted. He called up more units of the National Guard, restored Curtis to office, and took personal control of the police force. Curtis proclaimed that all of the strikers were fired from their jobs, and Coolidge called for a new police force to be recruited.
That night Coolidge received a telegram from AFL leader Samuel Gompers. "Whatever disorder has occurred", Gompers wrote, "is due to Curtis's order in which the right of the policemen has been denied".
Coolidge publicly answered Gompers's telegram, denying any justification whatsoever for the strike—and his response launched him into the national consciousness. Newspapers nationwide picked up on Coolidge's statement and he became the strike's opponents' newest hero. Amid the First Red Scare, many Americans were terrified of the spread of communist revolutions like those in Russia, Hungary, and Germany. Coolidge had lost some friends among organized labor, but conservatives saw a rising star. Although he usually acted with deliberation, the Boston police strike gave Coolidge a national reputation as a decisive leader and strict enforcer of law and order.
{| class"toccolours" style"float: right; margin-left: 1em; margin-right: 2em; font-size: 85%; background:#c6dbf7; color:black; width:30em; max-width: 40%;" cellspacing="5"
| style="text-align: left;" |"Your assertion that the Commissioner was wrong cannot justify the wrong of leaving the city unguarded. That furnished the opportunity; the criminal element furnished the action. There is no right to strike against the public safety by anyone, anywhere, any time. ... I am equally determined to defend the sovereignty of Massachusetts and to maintain the authority and jurisdiction over her public officers where it has been placed by the Constitution and laws of her people."
|-
| style"text-align: left;" | "Telegram from Governor Calvin Coolidge to Samuel Gompers", September 14, 1919
|}
1919 election
In 1919, Coolidge and Cox were renominated for their respective offices in 1919. By this time Coolidge's supporters, especially Stearns, had publicized his actions in the Police Strike around the state and the nation, and some of Coolidge's speeches were published in book form. He faced the same opponent as in 1918, Richard Long, but this time Coolidge defeated him by 125,101 votes, more than seven times his margin of victory from a year earlier.}} His actions in the police strike, combined with the massive electoral victory, led to suggestions that Coolidge run for president in 1920.
Legislation and vetoes as governor
By the time Coolidge was inaugurated on January 2, 1919, the First World War had ended, and Coolidge pushed the legislature to give a $100 bonus () to Massachusetts veterans. He signed a bill reducing the work week for women and children from 54 hours to 48, saying, "We must humanize the industry, or the system will break down." He passed a budget that kept the tax rates the same, while trimming $4 million from expenditures, allowing the state to retire some of its debt.
Coolidge wielded the veto pen as governor. His most publicized veto prevented an increase in legislators' pay by 50%. Although he was personally opposed to Prohibition, he vetoed a bill in May 1920 that would have allowed the sale of beer or wine of 2.75% alcohol or less, in Massachusetts in violation of the Eighteenth Amendment to the United States Constitution. "Opinions and instructions do not outmatch the Constitution," he said in his veto message. "Against it, they are void."Vice presidency (1921–1923)1920 election
At the 1920 Republican National Convention, most of the delegates were selected by state party caucuses, not primaries. As such, the field was divided among many local favorites. Coolidge was one such candidate, and while he placed as high as sixth in the voting, the powerful party bosses running the convention, primarily the party's U.S. Senators, never considered him seriously. After ten ballots, the bosses and then the delegates settled on Senator Warren G. Harding of Ohio as their nominee for president.
When the time came to select a vice-presidential nominee, the bosses also announced their choice, Senator Irvine Lenroot of Wisconsin, and then departed after his name was put forth, relying on the rank and file to confirm their decision. A delegate from Oregon, Wallace McCamant, had read Have Faith in Massachusetts and proposed Coolidge for vice president instead. The suggestion caught on quickly, with the masses craving an act of independence from the absent bosses, and Coolidge was unexpectedly nominated.
The Democrats nominated another Ohioan, James M. Cox, for president and the Assistant Secretary of the Navy, Franklin D. Roosevelt, for vice president. The question of the United States joining the League of Nations was a major issue in the campaign, as was the unfinished legacy of Progressivism. Harding ran a "front-porch" campaign from his home in Marion, Ohio, but Coolidge took to the campaign trail in the Upper South, New York, and New Englandhis audiences carefully limited to those familiar with Coolidge and those placing a premium upon concise and short speeches. On November 2, 1920, Harding and Coolidge were victorious in a landslide, winning more than 60 percent of the popular vote, including every state outside the South. They won in Tennessee, the first time a Republican ticket had won a Southern state since Reconstruction.
"Silent Cal"
The vice presidency did not carry many official duties, but Harding invited Coolidge to attend cabinet meetings, making him the first vice president to do so. He gave a number of unremarkable speeches around the country.
As vice president, Coolidge and his vivacious wife Grace were invited to quite a few parties, where the legend of "Silent Cal" was born. It is from this time that most of the jokes and anecdotes involving Coolidge originate, such as Coolidge being "silent in five languages". Although Coolidge was known to be a skilled and effective public speaker, in private he was a man of few words and was commonly referred to as "Silent Cal".
An apocryphal story has it that a person seated next to Coolidge at a dinner told him, "I made a bet today that I could get more than two words out of you", to which Coolidge replied, "You lose". On April 22, 1924, Coolidge said that the "You lose" incident never occurred. The story was related by Frank B. Noyes, President of the Associated Press, to its membership at its annual luncheon at the Waldorf Astoria Hotel, when toasting and introducing Coolidge, the invited speaker. After the introduction and before his prepared remarks, Coolidge told the membership, "Your President [Noyes] has given you a perfect example of one of those rumors now current in Washington which is without any foundation."
Coolidge often seemed uncomfortable among fashionable Washington society. When asked why he continued to attend so many of their dinner parties, he replied, "Got to eat somewhere." Alice Roosevelt Longworth, a leading Republican wit, underscored Coolidge's silence and his dour personality: "When he wished he were elsewhere, he pursed his lips, folded his arms, and said nothing. He looked then precisely as though he had been weaned on a pickle." Coolidge and his wife, Grace, who was a great baseball fan, once attended a Washington Senators game and sat through all nine innings without saying a word, except once when he asked her the time.
As president, Coolidge's reputation as a quiet man continued. "The words of a President have an enormous weight," he later wrote, "and ought not to be used indiscriminately." Coolidge was aware of his stiff reputation, and cultivated it. "I think the American people want a solemn ass as a President," he once told Ethel Barrymore, "and I think I will go along with them." Some historians suggest that Coolidge's image was created deliberately as a campaign tactic. Others believe his withdrawn and quiet behavior was natural, deepening after the death of his son in 1924.}} Dorothy Parker, upon learning that Coolidge had died, reportedly remarked, "How can they tell?"
Presidency (1923–1929)
On August 2, 1923, President Harding died unexpectedly from a heart attack in San Francisco while on a speaking tour of the western United States. Vice President Coolidge was in Vermont visiting his family home, which had neither electricity nor a telephone, when he received word by messenger of Harding's death. Coolidge dressed, said a prayer, and came downstairs to greet the reporters who had assembled. His father, a notary public and justice of the peace, administered the oath of office in the family's parlor by the light of a kerosene lamp at 2:47 a.m. on August 3, 1923, whereupon the new President of the United States returned to bed.
Coolidge returned to Washington the next day, and was sworn in again by Justice Adolph A. Hoehling Jr. of the Supreme Court of the District of Columbia, to forestall any questions about the authority of a state official to administer a federal oath. This second oath-taking remained a secret until it was revealed by Harry M. Daugherty in 1932, and confirmed by Hoehling. When Hoehling confirmed Daugherty's story, he indicated that Daugherty, then serving as United States Attorney General, asked him to administer the oath without fanfare at the Willard Hotel. According to Hoehling, he did not question Daugherty's reason for requesting a second oath-taking but assumed it was to resolve any doubt about whether the first swearing-in was valid.
The nation initially did not know what to make of Coolidge, who had maintained a low profile in the Harding administration. Many had even expected him to be replaced on the ballot in 1924. Coolidge believed that those of Harding's men under suspicion were entitled to every presumption of innocence, taking a methodical approach to the scandals, principally the Teapot Dome scandal, while others clamored for rapid punishment of those they presumed guilty.
Coolidge thought the Senate investigations of the scandals would suffice. The resulting resignations of those involved affirmed this. He personally intervened in demanding the resignation of Attorney General Harry M. Daugherty after Daugherty refused to cooperate with the investigations. He then set about to confirm that no loose ends remained in the administration, arranging for a full briefing on the wrongdoing. Harry A. Slattery reviewed the facts with him, Harlan F. Stone analyzed the legal aspects for him, and Senator William E. Borah assessed and presented the political factors.
On December 6, 1923, Coolidge addressed Congress when it reconvened, giving a speech that supported many of Harding's policies, including Harding's formal budgeting process, the enforcement of immigration restrictions, and the arbitration of coal strikes ongoing in Pennsylvania.
The address to Congress was the first presidential speech to be broadcast over the radio. The Washington Naval Treaty was proclaimed one month into Coolidge's term, and was generally well received nationally. In May 1924, Congress passed the World War I veterans' World War Adjusted Compensation Act ("Bonus Bill"), overriding Coolidge's veto. Later that year, Coolidge signed the Immigration Act, which was aimed at restricting southern and eastern European immigration, but appended a signing statement expressing his unhappiness with the bill's specific exclusion of Japanese immigrants.
Just before the Republican Convention began, Coolidge signed into law the Revenue Act of 1924, which reduced the top marginal tax rate from 58% to 46%, cut personal income tax rates across the board, increased the estate tax, and bolstered it with a new gift tax.
On June 2, 1924, Coolidge signed the act granting citizenship to all Native Americans born in the United States. By that time, two-thirds of them were already citizens, having gained it through marriage, military service (veterans of World War I were granted citizenship in 1919), or land allotments.1924 election
The Republican Convention was held from June 10 to 12, 1924, in Cleveland, Ohio. Coolidge was nominated on the first ballot. The convention nominated Frank Lowden of Illinois for vice president on the second ballot, but he declined. Former Brigadier General Charles G. Dawes was nominated on the third ballot and accepted.
The Democrats held their convention the next month in New York City. The convention soon deadlocked, and after 103 ballots, the delegates agreed upon a compromise candidate, John W. Davis, with Charles W. Bryan nominated for vice president. The Democrats' hopes were buoyed when Robert M. La Follette, a Republican senator from Wisconsin, split from the GOP to form a new Progressive Party. Many believed that the split in the Republican Party, like the one in 1912, would allow a Democrat to win the presidency.
After the conventions and the death of his younger son Calvin, Coolidge became withdrawn. He later said that "when he [the son] died, the power and glory of the Presidency went with him." Even as he mourned, Coolidge ran his standard campaign, not mentioning his opponents by name or maligning them, and delivering speeches on his theory of government, including several that were broadcast over the radio.
It was the most subdued campaign since 1896, partly because of Coolidge's grief, but also because of his naturally non-confrontational style. The other candidates campaigned in a more modern fashion, but despite the split in the Republican party, the results were similar to those of 1920. Coolidge won every state outside the South except Wisconsin, La Follette's home state. He won the election with 382 electoral votes and the popular vote by 2.5 million votes.
Industry and trade
{| class"toccolours" style"float: right; margin-left: 1em; margin-right: 2em; font-size: 85%; background:#c6dbf7; color:black; width:30em; max-width: 40%;" cellspacing="5"
| style="text-align: left;" |"[I]t is probable that a press which maintains an intimate touch with the business currents of the nation is likely to be more reliable than it would be if it were a stranger to these influences. After all, the chief business of the American people is business. They are profoundly concerned with buying, selling, investing and prospering in the world."
|-
| style"text-align: left;" | "President Calvin Coolidge's address to the American Society of Newspaper Editors", Washington D.C., January 25, 1925
|}
During Coolidge's presidency, the United States experienced a period of rapid economic growth known as the "Roaring Twenties". He left the administration's industrial policy in the hands of his activist Secretary of Commerce, Herbert Hoover, who energetically used government auspices to promote business efficiency and develop airlines and radio.
Coolidge disdained regulation and appointed men to the Federal Trade Commission and the Interstate Commerce Commission, who did little to restrict the activities of businesses under their jurisdiction. The regulatory state under Coolidge was, as one biographer called it, "thin to the point of invisibility".
Historian Robert Sobel offers some context for Coolidge's laissez-faire ideology, based on the prevailing understanding of federalism during his presidency: "As Governor of Massachusetts, Coolidge supported wages and hours legislation, opposed child labor, imposed economic controls during World War I, favored safety measures in factories, and even worker representation on corporate boards. Did he support these measures while president? No, because in the 1920s, such matters were considered the responsibilities of state and local governments."
Coolidge signed the Radio Act of 1927, which established the Federal Radio Commission and the equal-time rule for radio broadcasters and restricted radio broadcasting licenses to stations that demonstrated they served "the public interest, convenience, or necessity".Taxation and government spendingCoolidge adopted the taxation policies of his Secretary of the Treasury, Andrew Mellon, who advocated "scientific taxation"—the notion that lowering taxes will increase, rather than decrease, government receipts. Congress agreed, and tax rates were reduced in Coolidge's term.
In addition to federal tax cuts, Coolidge proposed reductions in federal expenditures and retiring the federal debt. His ideas were shared by the Republicans in Congress, and in 1924, Congress passed the Revenue Act of 1924, which reduced income tax rates and eliminated all income taxation for two million people. It reduced taxes again by passing the Revenue Acts of 1926 and 1928, while keeping spending down to reduce the overall federal debt. By 1927, only the wealthiest 2% of taxpayers paid federal income tax. Federal spending remained flat during Coolidge's administration, allowing one-fourth of the federal debt to be retired.
State and local governments saw considerable growth, surpassing the federal budget in 1927. In 1929, after Coolidge's series of tax rate reductions had cut the tax rate to 24% on those making over $100,000, the federal government collected more than $1 billion in income taxes, of which 65% was from those making over $100,000. In 1921, when the tax rate on those making over $100,000 a year was 73%, the federal government collected a little over $700 million in income taxes, of which 30% was from those making over $100,000.Opposition to farm subsidies
]]
Perhaps the most contentious issue of Coolidge's presidency was relief for farmers. Some in Congress proposed a bill designed to fight falling agricultural prices by allowing the federal government to purchase crops to sell abroad at lower prices. Agriculture Secretary Henry C. Wallace and other administration officials favored the bill when it was introduced in 1924, but rising prices convinced many in Congress that the bill was unnecessary, and it was defeated just before the 1924 elections.
In 1926, with farm prices falling once more, Senator Charles L. McNary and Representative Gilbert N. Haugen—both Republicans—proposed the McNary–Haugen Farm Relief Bill. The bill proposed a federal farm board that would purchase surplus production in high-yield years, and hold it, when feasible, for later sale or sell it abroad.
Coolidge opposed McNary-Haugen, saying that agriculture must stand "on an independent business basis" and that "government control cannot be divorced from political control". Instead of manipulating prices, he favored Herbert Hoover's proposal to increase profitability by modernizing agriculture. Secretary Mellon wrote a letter denouncing McNary-Haugen as unsound and likely to cause inflation, and it was defeated.
After McNary-Haugen's defeat, Coolidge supported a less radical measure, the Curtis-Crisp Act, which would have created a federal board to lend money to farm cooperatives in times of surplus. The bill did not pass. In February 1927, Congress took up McNary-Haugen again, this time narrowly passing it, and Coolidge vetoed it.
In his veto message, he expressed the belief that the bill would do nothing to help farmers, benefiting only exporters and expanding the federal bureaucracy. Congress did not override the veto. In May 1928, Congress passed the bill again by an increased majority, and Coolidge vetoed it again. "Farmers never have made much money" he said. "I do not believe we can do much about it."
Flood control
Coolidge has often been criticized for his actions during the Great Mississippi Flood of 1927, the worst natural disaster to hit the Gulf Coast until Hurricane Katrina in 2005. Although he eventually named Hoover to a commission in charge of flood relief, scholars argue that, overall, Coolidge showed lack of interest in federal flood control.
Coolidge believed that visiting the region after the floods would accomplish nothing and be seen as political grandstanding. He also did not want to incur the federal spending that flood control would require. He believed that property owners should bear much of the cost. Congress wanted a bill that would place the federal government completely in charge of flood mitigation. When Congress passed a compromise measure in 1928, Coolidge declined to take credit for it and signed the bill in private on May 15.Civil rights
men with Coolidge after he signed the bill granting Native Americans U.S. citizenship]]
According to one biographer, Coolidge was "devoid of racial prejudice", but he rarely took the lead on civil rights. Coolidge disliked the Ku Klux Klan and no Klansman is known to have received an appointment from him. In the 1924 presidential election, his opponents, Robert La Follette and John Davis, and his running mate, Charles Dawes, often attacked the Klan, but Coolidge avoided the subject.
Due to Coolidge's failure to condemn the Klan, some African-American leaders such as former assistant attorney general William Henry Lewis endorsed Davis. Davis got little of the black vote outside Indiana, where Klan control of the Indiana Republican Party caused many blacks to vote Democratic. It is estimated that over 90% of non-Indiana blacks voted for Coolidge.
Secretary of Commerce Herbert Hoover was accused of running forced labor camps for African Americans during the Great Mississippi Flood of 1927, which led more African Americans to vote Democratic when Hoover was the Republican presidential nominee in 1928 and 1932. During Coolidge's administration, lynchings of African-Americans decreased and millions of people left the Ku Klux Klan.
Coolidge spoke in favor of African Americans' civil rights, saying in his first State of the Union address that their rights were "just as sacred as those of any other citizen" under the U.S. Constitution and that it was a "public and a private duty to protect those rights".
Coolidge repeatedly called for laws to make lynching a federal crime. It was already a state crime, though not always enforced. Congress refused to pass any such legislation. On June 2, 1924, Coolidge signed the Indian Citizenship Act, which granted U.S. citizenship to all Native Americans living on reservations. Those off reservations had long been citizens.
On June 6, 1924, Coolidge delivered a commencement address at historically black, non-segregated Howard University, in which he thanked and commended African Americans for their rapid advances in education and contributions to U.S. society over the years, as well as their eagerness to render their services as soldiers in the World War, all while faced with discrimination and prejudice at home.
In an October 1924 speech, Coolidge stressed tolerance of differences as an American value and thanked immigrants for their contributions to U.S. society, saying that they had "contributed much to making our country what it is". He said that although the diversity of peoples was a source of conflict and tension in Europe, it was a peculiarly "harmonious" benefit for the U.S. Coolidge added that the U.S. should assist and help immigrants and urged immigrants to reject "race hatreds" and "prejudices".Foreign policy
, February 1927. Left to right: Secretary of the Treasury, Andrew Mellon; Secretary of State, Frank B. Kellogg; President Calvin Coolidge; former president and Chief Justice William Howard Taft, Secretary of the Smithsonian, Charles D. Walcott among others.]]
Coolidge was neither well versed nor very interested in world affairs. His focus was mainly on U.S. business, especially pertaining to trade, and "Maintaining the Status Quo". Although not an isolationist, he was reluctant to enter into European involvements. Coolidge believed strongly in a non-interventionist foreign policy and supported American exceptionalism. He considered the 1920 Republican victory a rejection of the Wilsonian position that the U.S. should join the League of Nations.
Coolidge did not believe the League served U.S. interests. But he spoke in favor of joining the Permanent Court of International Justice (World Court), provided that the nation would not be bound by advisory decisions. In 1926, the Senate approved joining the Court, with reservations. The League of Nations accepted the reservations, but suggested some modifications of its own. The Senate failed to act, and so the U.S. did not join the World Court.
In 1924, the Coolidge administration nominated Charles Dawes to head the multinational committee that produced the Dawes Plan. It set fixed annual amounts for Germany's World War I reparations payments and authorized a large loan, mostly from U.S. banks, to help stabilize and stimulate the German economy. Coolidge attempted to pursue further curbs on naval strength after the successes of Harding's Washington Naval Conference, by sponsoring the Geneva Naval Conference in 1927, which failed owing to a French and Italian boycott and the failure of Great Britain and the U.S. to agree on cruiser tonnages. As a result, the conference was a failure and Congress eventually authorized for increased American naval spending in 1928.
The Kellogg–Briand Pact of 1928, named for U.S. Secretary of State Frank B. Kellogg and French Foreign Minister Aristide Briand, was a key peacekeeping initiative. Ratified in 1929, the treaty committed signatories—the U.S., the United Kingdom, France, Italy, Germany, and Japan—to "renounce war, as an instrument of national policy in their relations with one another". The treaty did not achieve its intended result—to outlaw war—but it did provide the founding principle for international law after World War II. Coolidge continued the Harding administration's policy of withholding recognition of the Soviet Union.
Efforts were made to normalize ties with post-Revolution Mexico. Coolidge recognized Mexico's new governments under Álvaro Obregón and Plutarco Elías Calles, and continued U.S. support for the elected Mexican government against the National League for the Defense of Religious Liberty during the Cristero War, lifting the arms embargo on Mexico. He appointed Dwight Morrow as Ambassador to Mexico with the successful objective to avoid further conflict with Mexico.
Cabinet
.<br/>Front row, left to right: Harry Stewart New, John W. Weeks, Charles Evans Hughes, Coolidge, Andrew Mellon, Harlan F. Stone, Curtis D. Wilbur.<br/>Back row, left to right: James J. Davis, Henry C. Wallace, Herbert Hoover, Hubert Work.|271x271px]]
Although some of Harding's cabinet appointees were scandal-tarred, Coolidge initially retained all of them out of conviction that as successor to a deceased elected president, he was obligated to retain Harding's counselors and policies until the next election. He kept Harding's speechwriter Judson T. Welliver. Stuart Crawford replaced Welliver in November 1925. Coolidge appointed C. Bascom Slemp, a Virginia Congressman and experienced federal politician, to work jointly with Edward T. Clark, a Massachusetts Republican organizer whom he retained from his vice-presidential staff, as Secretaries to the President, a position equivalent to the modern White House Chief of Staff.
Perhaps the most powerful person in Coolidge's cabinet was Secretary of the Treasury Andrew Mellon, who controlled the administration's financial policies and was regarded by many, including House Minority Leader John Nance Garner, as more powerful than Coolidge himself. Commerce Secretary Herbert Hoover also held a prominent place in the cabinet, in part because Coolidge found value in Hoover's ability to win positive publicity with his pro-business proposals.
Secretary of State Charles Evans Hughes directed Coolidge's foreign policy until he resigned in 1925 following Coolidge's reelection. He was replaced by Frank B. Kellogg, who had previously served as a senator and ambassador to Great Britain. Coolidge made two other appointments after his reelection: William M. Jardine as Secretary of Agriculture and John G. Sargent as Attorney General. Coolidge had no vice president during his first term. Charles Dawes became vice president during Coolidge's second term, and Dawes and Coolidge clashed over farm policy and other issues.
{| class"toccolours" align"left"
!bgcolor"#000000" colspan"3"|
|-
|align"center"|OFFICE||align"left"|NAME||align="left"|TERM
|-
!bgcolor"#000000" colspan"3"|
|-
| align"center" |President||align"left" |Calvin Coolidge||align="left"|1923–1929
|-
| align"center" |Vice President||align"left"|None||align="left"|1923–1925
|-
|align"left"| ||align"left"|Charles G. Dawes||align="left"|1925–1929
|-
!bgcolor"#000000" colspan"3"|
|-
| align"center" |Secretary of State||align"left"|Charles Evans Hughes||align="left"|1923–1925
|-
|align"left"| ||align"left"|Frank B. Kellogg||align="left"|1925–1929
|-
| align"center" |Secretary of the Treasury||align"left"|Andrew Mellon||align="left"|1923–1929
|-
| align"center" |Secretary of War||align"left"|John W. Weeks||align="left"|1923–1925
|-
|align"left"| ||align"left"|Dwight F. Davis||align="left"|1925–1929
|-
| align"center" |Attorney General||align"left"|Harry M. Daugherty||align="left"|1923–1924
|-
|align"left"| ||align"left"|Harlan F. Stone||align="left"|1924–1925
|-
|align"left"| ||align"left"|John G. Sargent||align="left"|1925–1929
|-
| align"center" |Postmaster General||align"left"|Harry S. New||align="left"|1923–1929
|-
| align"center" |Secretary of the Navy||align"left"|Edwin C. Denby||align="left"|1923–1924
|-
|align"left"| ||align"left"|Curtis D. Wilbur||align="left"|1924–1929
|-
| align"center" |Secretary of the Interior||align"left"|Hubert Work||align="left"|1923–1928
|-
|align"left"| ||align"left"|Roy O. West||align="left"|1928–1929
|-
| align"center" |Secretary of Agriculture||align"left"|Henry C. Wallace||align="left"|1923–1924
|-
|align"left"| ||align"left"|Howard M. Gore||align="left"|1924–1925
|-
|align"left"| ||align"left"|William M. Jardine||align="left"|1925–1929
|-
| align"center" |Secretary of Commerce||align"left"|Herbert Hoover||align="left"|1923–1928
|-
|align"left"| ||align"left"|William F. Whiting||align="left"|1928–1929
|-
| align"center" |Secretary of Labor||align"left"|James J. Davis||align="left"|1923–1929
|}
Judicial appointments
first as attorney general and then as a Supreme Court justice.]]
In 1925, Coolidge appointed one justice to the Supreme Court of the United States, Harlan F. Stone. Stone was Coolidge's fellow Amherst alumnus, a Wall Street lawyer and conservative Republican. In 1924, Stone was serving as the dean of Columbia Law School when Coolidge appointed him to be attorney general to restore the reputation tarnished by Harding's attorney general, Harry M. Daugherty.
It does not appear that Coolidge considered appointing anyone other than Stone, although Stone urged him to appoint Benjamin N. Cardozo. Stone proved to be a firm believer in judicial restraint and was regarded as one of the court's three liberal justices who often voted to uphold New Deal legislation. President Franklin D. Roosevelt later appointed Stone chief justice.
Coolidge nominated 17 judges to the United States Courts of Appeals and 61 to the United States district courts. He appointed judges to various specialty courts, including Genevieve R. Cline, who became the first woman named to the federal judiciary when Coolidge placed her on the United States Customs Court in 1928. Coolidge signed the Judiciary Act of 1925 into law, allowing the Supreme Court more discretion over its workload.1928 election
In the summer of 1927, Coolidge vacationed in the Black Hills of South Dakota. While on vacation, he issued a terse statement that he would not seek a second full term as president: "I do not choose to run for President in 1928." After allowing the reporters to take that in, Coolidge elaborated. "If I take another term, I will be in the White House till 1933 … Ten years in Washington is longer than any other man has had it—too long!"
In his memoirs, Coolidge explained his decision not to run: "The Presidential office takes a heavy toll of those who occupy it and those who are dear to them. While we should not refuse to spend and be spent in the service of our country, it is hazardous to attempt what we feel is beyond our strength to accomplish."
After leaving office, he and Grace returned to Northampton, where he wrote his memoirs. The Republicans retained the White House in 1928 when Herbert Hoover was elected in a landslide. Coolidge was reluctant to endorse Hoover. On one occasion he remarked, "for six years that man has given me unsolicited advice—all of it bad." But Coolidge had no desire to split the party by publicly opposing Hoover's nomination.}}Post-presidency (1929–1933)After his presidency, Coolidge retired to a spacious home in Northampton, "The Beeches". He kept a Hacker runabout boat on the Connecticut River, and local boating enthusiasts often observed him on the water. During this time, he chaired the Non-Partisan Railroad Commission, an entity several banks and corporations created to survey the country's long-term transportation needs and make recommendations for improvements. He was an honorary president of the American Foundation for the Blind, a director of New York Life Insurance Company, president of the American Antiquarian Society, and a trustee of Amherst College.
Coolidge published his autobiography in 1929 and wrote a syndicated newspaper column, "Calvin Coolidge Says", from 1930 to 1931. Faced with looming defeat in 1932, some Republicans spoke of rejecting Herbert Hoover as their party's nominee, and instead drafting Coolidge to run, but the former President made it clear that he was not interested in running again, and that he would publicly repudiate any effort to draft him, should it come about. Hoover was renominated, and Coolidge made several radio addresses in support of him. Hoover lost the general election to Franklin D. Roosevelt in a landslide.DeathCoolidge died suddenly of coronary thrombosis at The Beeches on January 5, 1933, at 12:45 p.m., aged 60. Shortly before his death, he told an old friend, "I feel I no longer fit in with these times." Coolidge is buried in Plymouth Notch Cemetery in Plymouth Notch, Vermont. The nearby family home is maintained as one of the original buildings on the Calvin Coolidge Homestead District site. In July 1972, the State of Vermont dedicated a new visitors' center nearby to mark Coolidge's 100th birthday.Legacy
in the White House Cabinet Room with a portrait of Coolidge in the background.]]
Despite being one of the most popular U.S. presidents while in office, Coolidge is generally rated below average by modern historians. David Greenberg, a scholar from Rutgers University, said, "although the public liked and admired Calvin Coolidge during his tenure, the Great Depression that began in 1929 seriously eroded his reputation and changed public opinion about his policies".
Historians have criticized Coolidge for his lack of assertiveness and have called him a "do nothing president" who enjoyed high public approval only because he was in office when things were going well around the world. Some historians have scrutinized Coolidge for signing laws that broadened federal regulatory authority and say it paved the way for corruption in future presidential administrations.
In a 1982 Chicago Tribune survey of 49 historians, Coolidge was ranked the eighth-worst U.S. president. In 2006, British journalist William Shawcross said he believed Coolidge was the worst president of the 20th century. In a 2021 C-SPAN survey, historians ranked Coolidge 24th out of 44 presidents. They gave him high ratings for "moral authority" and "administrative skills" but poor ratings for "setting an agenda" and "pursuing equal justice".
Although historians generally view Coolidge unfavorably, his hands-off government approach continues to resonate with modern conservatives and Republican politicians. In 1981, President Ronald Reagan publicly praised Coolidge's laissez-faire policy.Radio, film, and commemorationsDespite his reputation as a quiet and even reclusive politician, Coolidge made use of the new medium of radio and made radio history several times while president. He made himself available to reporters, giving 520 press conferences, meeting with reporters more regularly than any president before or since. Coolidge's second inauguration was the first presidential inauguration broadcast on radio. On December 6, 1923, his speech to Congress was broadcast on radio, the first presidential radio address.
Coolidge signed the Radio Act of 1927, which assigned regulation of radio to the newly created Federal Radio Commission. On August 11, 1924, Theodore W. Case, using the Phonofilm sound-on-film process he developed for Lee de Forest, filmed Coolidge on the White House lawn, making him the first president to appear in a sound film, President Coolidge, Taken on the White House Grounds. When Charles Lindbergh arrived in Washington on a U.S. Navy ship after his celebrated 1927 trans-Atlantic flight, Coolidge welcomed him back to the U.S. and presented him with the Medal of Honor, and the event was filmed.
<gallery class="center">
File:Ccoolidge.jpeg|Official presidential portrait of Coolidge, 1932
File:Sesquicentennial american independence half dollar commemorative obverse.jpg|The Sesquicentennial of American Independence Half Dollar, minted in 1926
File:Calvin Coolidge 1938 Issue-$5.jpg|Coolidge on a 1938 postage stamp
File:Coolidge with press.jpg|Coolidge with reporters and cameramen, 1924
File:Calvin Coolidge video montage.ogg|Collection of video clips of President Coolidge
</gallery>
See also
* Coolidge, Arizona
* Coolidge Dam
* List of things named after Calvin Coolidge
* Presidency of Calvin Coolidge
*
General:
* List of presidents of the United States
* List of presidents of the United States by previous experience
Notes
References
Works cited
About Coolidge and his era
* }}
*
*
*
*
*
*
*
*
*
*
* }}
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
By Coolidge
*
* }}
*
* }}
Further reading
*
*
*
*
* Postell, Joseph W. "Roaring Against Progressivism: The Principled Conservatism of Calvin Coolidge," in Joseph W. Postell and Johnathan O'Neill, eds. Toward an American Conservatism: Constitutional Conservatism during the Progressive Era (2013) pp. 181–208.
* Russell, Francis. "Coolidge and the Boston Police Strike." Antioch Review 16#4 (1956), pp. 403–15. [https://doi.org/10.2307/4609899 online]
* Tacoma, Thomas J. The Political Thought of Calvin Coolidge: Burkean Americanist (Lexington Books, 2020).
* Tacoma, Thomas. "Calvin Coolidge and the Great Depression: A New Assessment." Independent Review 24.3 (2019): 361–380. [https://www.jstor.org/stable/45238861 online]
* Zibel, Howard J. "The Role of Calvin Coolidge in the Boston Police Strike of 1919," Industrial and Labor Relations Forum 6, no. 3 (November 1969): 299–318
Primary sources
*
*
External links
Biographical information
* [https://bidenwhitehouse.archives.gov/about-the-white-house/presidents/calvin-coolidge/ White House biography]
*
Digital collections
*
*
*
* [http://millercenter.org/president/speeches#coolidge Text of a number of Coolidge speeches], Miller Center of Public Affairs
Physical collections
* [https://forbeslibrary.org/coolidge/ Calvin Coolidge Presidential Library & Museum]
* [https://www.coolidgefoundation.org/ Calvin Coolidge Presidential Foundation]
* [https://www.loc.gov/rr/program/bib/presidents/coolidge/index.html Calvin Coolidge: A Resource Guide], Library of Congress
* [http://www.shapell.org/Collection/Presidents/Coolidge-Calvin Calvin Coolidge Personal Manuscripts]
Other
*
* [https://archive.org/details/coolidge_1924 President Coolidge, Taken on the White House Ground], the first presidential film with sound recording
* [http://www.c-span.org/video/?151626-1/life-portrait-calvin-coolidge "Life Portrait of Calvin Coolidge"], from C-SPAN's American Presidents: Life Portraits, September 27, 1999
*
*
*
}}
}}
}}
*
Category:1872 births
Category:1933 deaths
Category:19th-century Congregationalists
Category:20th-century American male writers
Category:20th-century American non-fiction writers
Category:20th-century Congregationalists
Category:20th-century members of the Massachusetts General Court
Category:20th-century presidents of the United States
Category:20th-century vice presidents of the United States
Category:1920 United States vice-presidential candidates
Category:Activists for Native American rights
Category:American anti-lynching activists
Category:American autobiographers
Category:American Congregationalists
Category:American lawyers admitted to the practice of law by reading law
Category:American people of English descent
Category:Amherst College alumni
Category:Appleton family
Category:Articles containing video clips
Category:Candidates in the 1920 United States presidential election
Category:Candidates in the 1924 United States presidential election
Category:College Republicans
Calvin
Category:Deaths from coronary thrombosis
Category:Governors of Massachusetts
Category:Harding administration cabinet members
Category:Lieutenant governors of Massachusetts
Category:Massachusetts city council members
Category:Massachusetts lawyers
Category:Massachusetts Republicans
Category:Massachusetts state senators
Category:Mayors of places in Massachusetts
Category:Members of the Massachusetts House of Representatives
Category:Members of the Sons of the American Revolution
Category:People from Plymouth, Vermont
Category:Politicians from Northampton, Massachusetts
Category:Presidents of the United States
Category:Republican Party (United States) presidential nominees
Category:Republican Party (United States) vice presidential nominees
Category:Republican Party governors of Massachusetts
Category:Republican Party presidents of the United States
Category:Republican Party vice presidents of the United States
Category:St. Johnsbury Academy alumni
Category:Vice presidents of the United States
Category:Writers from Northampton, Massachusetts
Category:Writers from Vermont
|
https://en.wikipedia.org/wiki/Calvin_Coolidge
|
2025-04-05T18:27:44.401011
|
6198
|
Convention on Biological Diversity
|
| date_signed = 5 June 1992 – 4 June 1993
| location_signed = Rio de Janeiro, Brazil <br /> New York, United States
| date_effective
| condition_effective = Ratification by 30 States
| parties = All UN Member States except
|
|
|
|
|
}}
| depositor = Secretary-General of the United Nations
| languages =
| wikisource = United Nations Convention on Biological Diversity
| footnotes =
}}
The Convention on Biological Diversity (CBD), known informally as the Biodiversity Convention, is a multilateral treaty. The Convention has three main goals: the conservation of biological diversity (or biodiversity); the sustainable use of its components; and the fair and equitable sharing of benefits arising from genetic resources. Its objective is to develop national strategies for the conservation and sustainable use of biological diversity, and it is often seen as the key document regarding sustainable development.
The Convention was opened for signature at the Earth Summit in Rio de Janeiro on 5 June 1992 and entered into force on 29 December 1993. The United States is the only UN member state which has not ratified the Convention. It has two supplementary agreements, the Cartagena Protocol and Nagoya Protocol.
The Cartagena Protocol on Biosafety to the Convention on Biological Diversity is an international treaty governing the movements of living modified organisms (LMOs) resulting from modern biotechnology from one country to another. It was adopted on 29 January 2000 as a supplementary agreement to the CBD and entered into force on 11 September 2003.
The Nagoya Protocol on Access to Genetic Resources and the Fair and Equitable Sharing of Benefits Arising from their Utilization (ABS) to the Convention on Biological Diversity is another supplementary agreement to the CBD. It provides a transparent legal framework for the effective implementation of one of the three objectives of the CBD: the fair and equitable sharing of benefits arising out of the utilization of genetic resources. The Nagoya Protocol was adopted on 29 October 2010 in Nagoya, Japan, and entered into force on 12 October 2014.
2010 was also the International Year of Biodiversity, and the Secretariat of the CBD was its focal point. Following a recommendation of CBD signatories at Nagoya, the UN declared 2011 to 2020 as the United Nations Decade on Biodiversity in December 2010. The Convention's Strategic Plan for Biodiversity 2011–2020, created in 2010, include the Aichi Biodiversity Targets.
The meetings of the Parties to the Convention are known as Conferences of the Parties (COP), with the first one (COP 1) held in Nassau, Bahamas, in 1994 and the most recent one (COP 16) in 2024 in Cali, Colombia.
In the area of marine and coastal biodiversity CBD's focus at present is to identify Ecologically or Biologically Significant Marine Areas (EBSAs) in specific ocean locations based on scientific criteria. The aim is to create an international legally binding instrument (ILBI) involving area-based planning and decision-making under UNCLOS to support the conservation and sustainable use of marine biological diversity beyond areas of national jurisdiction (BBNJ treaty or High Seas Treaty).Origin and scopeThe notion of an international convention on biodiversity was conceived at a United Nations Environment Programme (UNEP) Ad Hoc Working Group of Experts on Biological Diversity in November 1988. The subsequent year, the Ad Hoc Working Group of Technical and Legal Experts was established for the drafting of a legal text which addressed the conservation and sustainable use of biological diversity, as well as the sharing of benefits arising from their utilization with sovereign states and local communities. In 1991, an intergovernmental negotiating committee was established, tasked with finalizing the Convention's text.
A Conference for the Adoption of the Agreed Text of the Convention on Biological Diversity was held in Nairobi, Kenya, in 1992, and its conclusions were distilled in the Nairobi Final Act. The Convention's text was opened for signature on 5 June 1992 at the United Nations Conference on Environment and Development (the Rio "Earth Summit"). By its closing date, 4 June 1993, the Convention had received 168 signatures. It entered into force on 29 December 1993. It also covers the rapidly expanding field of biotechnology through its Cartagena Protocol on Biosafety, addressing technology development and transfer, benefit-sharing and biosafety issues. Importantly, the Convention is legally binding; countries that join it ('Parties') are obliged to implement its provisions.
The Convention reminds decision-makers of the finite status of natural resources and sets out a philosophy of sustainable use. While past conservation efforts were aimed at protecting particular species and habitats, the Convention recognizes that ecosystems, species and genes must be used for the benefit of humans. However, this should be done in a way and at a rate that does not lead to the long-term decline of biological diversity.
The Convention also offers decision-makers guidance based on the precautionary principle which demands that where there is a threat of significant reduction or loss of biological diversity, lack of full scientific certainty should not be used as a reason for postponing measures to avoid or minimize such a threat. The Convention acknowledges that substantial investments are required to conserve biological diversity. It argues, however, that conservation will bring us significant environmental, economic and social benefits in return.
The Convention on Biological Diversity of 2010 banned some forms of geoengineering.
Executive secretary
As of April 2024, the acting executive secretary is Astrid Schomaker.
The previous executive secretaries were: David Cooper (2023–2024), Elizabeth Maruma Mrema (2020–2023), :pl:Cristiana Pașca Palmer (2017–2019), Braulio Ferreira de Souza Dias (2012–2017), Ahmed Djoghlaf (2006–2012), Hamdallah Zedan (1998–2005), Calestous Juma (1995–1998), and Angela Cropper (1993–1995).
Issues
Some of the many issues dealt with under the Convention include:
* Measures the incentives for the conservation and sustainable use of biological diversity.
* Regulated access to genetic resources and traditional knowledge, including Prior Informed Consent of the party providing resources.
* Sharing, in a fair and equitable way, the results of research and development and the benefits arising from the commercial and other utilization of genetic resources with the Contracting Party providing such resources (governments and/or local communities that provided the traditional knowledge or biodiversity resources utilized).
* Access to and transfer of technology, including biotechnology, to the governments and/or local communities that provided traditional knowledge and/or biodiversity resources.
* Technical and scientific cooperation.
* Coordination of a global directory of taxonomic expertise (Global Taxonomy Initiative).
* Impact assessment.
* Education and public awareness.
* Provision of financial resources.
* National reporting on efforts to implement treaty commitments.
International bodies established
Conference of the Parties (COP)
The Convention's governing body is the Conference of the Parties (COP), consisting of all governments (and regional economic integration organizations) that have ratified the treaty. This ultimate authority reviews progress under the Convention, identifies new priorities, and sets work plans for members. The COP can also make amendments to the Convention, create expert advisory bodies, review progress reports by member nations, and collaborate with other international organizations and agreements.
The Conference of the Parties uses expertise and support from several other bodies that are established by the Convention. In addition to committees or mechanisms established on an ad hoc basis, the main organs are:
CBD Secretariat
The CBD Secretariat, based in Montreal, Quebec, Canada, operates under UNEP, the United Nations Environment Programme. Its main functions are to organize meetings, draft documents, assist member governments in the implementation of the programme of work, coordinate with other international organizations, and collect and disseminate information.
Subsidiary Body for Scientific, Technical and Technological Advice (SBSTTA)
The SBSTTA is a committee composed of experts from member governments competent in relevant fields. It plays a key role in making recommendations to the COP on scientific and technical issues. It provides assessments of the status of biological diversity and of various measures taken in accordance with Convention, and also gives recommendations to the Conference of the Parties, which may be endorsed in whole, in part or in modified form by the COPs. SBSTTA had met 26 times, with a 26th meeting taking place in Nairobi, Kenya in 2024.Subsidiary Body on ImplementationIn 2014, the Conference of the Parties to the Convention on Biological Diversity established the Subsidiary Body on Implementation (SBI) to replace the Ad Hoc Open-ended Working Group on Review of Implementation of the Convention. The four functions and core areas of work of SBI are: (a) review of progress in implementation; (b) strategic actions to enhance implementation; (c) strengthening means of implementation; and (d) operations of the Convention and the Protocols. The first meeting of the SBI was held on 2–6 May 2016 and the second meeting was held on 9–13 July 2018, both in Montreal, Canada. The latest (fifth) meeting of the SBI was held in October 2024 in Cali, Colombia. The Bureau of the Conference of the Parties serves as the Bureau of the SBI. The current chair of the SBI is Ms. Clarissa Souza Della Nina of Brazil.
Parties
thumb|right|
As of 2016, the Convention has 196 Parties, which includes 195 states and the European Union. All UN member states—with the exception of the United States—have ratified the treaty. Non-UN member states that have ratified are the Cook Islands, Niue, and the State of Palestine. The Holy See and the states with limited recognition are non-Parties. The US has signed but not ratified the treaty, because ratification requires a two-thirds majority in the Senate and is blocked by Republican Party senators.
Implementation by the Parties to the Convention is achieved using two means:
National Biodiversity Strategies and Action Plans (NBSAP)
National Biodiversity Strategies and Action Plans (NBSAP) are the principal instruments for implementing the Convention at the national level. The Convention requires that countries prepare a national biodiversity strategy and to ensure that this strategy is included in planning for activities in all sectors where diversity may be impacted. As of early 2012, 173 Parties had developed NBSAPs.
The United Kingdom, New Zealand and Tanzania carried out elaborate responses to conserve individual species and specific habitats. The United States of America, a signatory who had not yet ratified the treaty by 2010, produced one of the most thorough implementation programs through species recovery programs and other mechanisms long in place in the US for species conservation.
Singapore established a detailed National Biodiversity Strategy and Action Plan. The National Biodiversity Centre of Singapore represents Singapore in the Convention for Biological Diversity.National ReportsIn accordance with Article 26 of the Convention, Parties prepare national reports on the status of implementation of the Convention.Protocols and plans developed by CBDCartagena Protocol (2000)
The Cartagena Protocol on Biosafety, also known as the Biosafety Protocol, was adopted in January 2000, after a CBD Open-ended Ad Hoc Working Group on Biosafety had met six times between July 1996 and February 1999. The Working Group submitted a draft text of the Protocol for consideration by Conference of the Parties at its first extraordinary meeting, which was convened for the express purpose of adopting a protocol on biosafety to the Convention on Biological Diversity. After a few delays, the Cartagena Protocol was eventually adopted on 29 January 2000. The Biosafety Protocol seeks to protect biological diversity from the potential risks posed by living modified organisms resulting from modern biotechnology.
The Biosafety Protocol makes clear that products from new technologies must be based on the precautionary principle and allow developing nations to balance public health against economic benefits. It will, for example, let countries ban imports of a genetically modified organism if they feel there is not enough scientific evidence the product is safe and requires exporters to label shipments containing genetically modified commodities such as corn or cotton. Global Strategy for Plant Conservation (2002)
In April 2002, the Parties of the UN CBD adopted the recommendations of the Gran Canaria Declaration Calling for a Global Plant Conservation Strategy, and adopted a 16-point plan aiming to slow the rate of plant extinctions around the world by 2010.
Nagoya Protocol (2010)
The Nagoya Protocol on Access to Genetic Resources and the Fair and Equitable Sharing of Benefits Arising from their Utilization to the Convention on Biological Diversity was adopted on 29 October 2010 in Nagoya, Aichi Prefecture, Japan, at the tenth meeting of the Conference of the Parties, The protocol is a supplementary agreement to the Convention on Biological Diversity, and provides a transparent legal framework for the effective implementation of one of the three objectives of the CBD: the fair and equitable sharing of benefits arising out of the utilization of genetic resources. It thereby contributes to the conservation and sustainable use of biodiversity.
Strategic Plan for Biodiversity 2011–2020
Also, at the tenth meeting of the Conference of the Parties, held from 18 to 29 October 2010 in Nagoya, a revised and updated "Strategic Plan for Biodiversity, 2011–2020" was agreed and published. This document included the "Aichi Biodiversity Targets", comprising 20 targets that address each of five strategic goals defined in the plan. The strategic plan includes the following strategic goals: This helps to understand the contributions of biodiversity to achieving the SDGs.
Post-2020 Global Biodiversity Framework
A new plan, known as the post-2020 Global Biodiversity Framework (GBF) was developed to guide action through 2030. A first draft of this framework was released in July 2021, and its final content was discussed and negotiated as part of the COP 15 meetings. Reducing agricultural pollution and sharing the benefits of digital sequence information arose as key points of contention among Parties during development of the framework. A final version was adopted by the Convention on 19 December 2022. The framework includes a number of ambitious goals, including a commitment to designate at least 30 percent of global land and sea as protected areas (known as the "30 by 30" initiative). A series of expert workshops have been held (2018–2022) to identify options for modifying the description of Ecologically or Biologically Significant Marine Areas (EBSAs) and describing new areas. These have focused on the North-East, North-West and South-Eastern Atlantic Ocean, Baltic Sea, Caspian Sea, Black Sea, Seas of East Asia, North-West Indian Ocean and Adjacent Gulf Areas, Southern and North-East Indian Ocean, Mediterranean Sea, North and South Pacific, Eastern Tropical and Temperate Pacific, Wider Caribbean and Western Mid-Atlantic. The workshop meetings have followed the EBSA process based on internationally agreed scientific criteria. This is aimed at creating an international legally binding instrument (ILBI) under UNCLOS to support the conservation and sustainable use of marine biological diversity beyond areas of national jurisdiction (BBNJ or High Seas Treaty). The central mechanism is area-based planning and decision-making. It integrates EBSAs, Vulnerable Marine Ecosystems (VMEs) and High Seas (Marine Protected Areas) with Blue Growth scenarios. There is also linkage with the EU Marine Strategy Framework Directive.
Criticism
There have been criticisms against CBD that its implementation has been weakened due to resistance of Western countries to the implementation of pro-South provisions of the Convention. CBD is also regarded as a case of a hard treaty gone soft in the implementation trajectory. The argument to enforce the treaty as a legally binding multilateral instrument with the Conference of Parties reviewing the infractions and non-compliance is also gaining strength.
Although the Convention explicitly states that all forms of life are covered by its provisions, examination of reports and of national biodiversity strategies and action plans submitted by participating countries shows that in practice this is not happening. The fifth report of the European Union, for example, makes frequent reference to animals (particularly fish) and plants, but does not mention bacteria, fungi or protists at all. The International Society for Fungal Conservation has assessed more than 100 of these CBD documents for their coverage of fungi using defined criteria to place each in one of six categories. No documents were assessed as good or adequate, less than 10% as nearly adequate or poor, and the rest as deficient, seriously deficient or totally deficient.
Scientists working with biodiversity and medical research are expressing fears that the Nagoya Protocol is counterproductive, and will hamper disease prevention and conservation efforts, and that the threat of imprisonment of scientists will have a chilling effect on research. Non-commercial researchers and institutions such as natural history museums fear maintaining biological reference collections and exchanging material between institutions will become difficult, and medical researchers have expressed alarm at plans to expand the protocol to make it illegal to publicly share genetic information, e.g. via GenBank.
William Yancey Brown, when with the Brookings Institution, suggested that the Convention on Biological Diversity should include the preservation of intact genomes and viable cells for every known species and for new species as they are discovered.Meetings of the Parties
A Conference of the Parties (COP) was held annually for three years after 1994, and thence biennially on even-numbered years.
:{| class="wikitable sortable"
|-
! style="text-align:center" | COP
! style="text-align:center" | Year
! style="text-align:left" | Country
! style="text-align:center" | Begin
! style="text-align:center" | End
! style="text-align:center" | Days
! style="text-align:left" | City
! style="text-align:left" | Link
|-
| style"text-align:center"| 1 || style"text-align:center"| 1994 || || style"text-align:center"| 28.11.1994 || style"text-align:center"| 09.12.1994 || style="text-align:center"| 12 || Nassau || [https://www.cbd.int/meetings/COP-01 COP 1]
|-
| style"text-align:center"| 2 || style"text-align:center"| 1995 || || style"text-align:center"| 06.11.1995 || style"text-align:center"| 17.11.1995 || style="text-align:center"| 12 || Jakarta || [https://www.cbd.int/meetings/COP-02 COP 2]
|-
| style"text-align:center"| 3 || style"text-align:center"| 1996 || || style"text-align:center"| 04.11.1996 || style"text-align:center"| 15.11.1996 || style="text-align:center"| 12 || Buenos Aires || [https://www.cbd.int/meetings/COP-03 COP 3]
|-
| style"text-align:center"| 4 || style"text-align:center"| 1998 || || style"text-align:center"| 04.05.1998 || style"text-align:center"| 15.05.1998 || style="text-align:center"| 12 || Bratislava || [https://www.cbd.int/meetings/COP-04 COP 4]
|-
| style"text-align:center"| 5 || style"text-align:center"| 2000 || || style"text-align:center"| 15.05.2000 || style"text-align:center"| 26.05.2000 || style="text-align:center"| 12 || Nairobi || [https://www.cbd.int/meetings/COP-05 COP 5]
|-
| style"text-align:center"| 6 || style"text-align:center"| 2002 || || style"text-align:center"| 07.04.2002 || style"text-align:center"| 19.04.2002 || style="text-align:center"| 13 || The Hague || [https://www.cbd.int/meetings/COP-06 COP 6]
|-
| style"text-align:center"| 7 || style"text-align:center"| 2004 || || style"text-align:center"| 09.02.2004 || style"text-align:center"| 20.02.2004 || style="text-align:center"| 12 || Kuala Lumpur || [https://www.cbd.int/meetings/COP-07 COP 7]
|-
| style"text-align:center"| 8 || style"text-align:center"| 2006 || || style"text-align:center"| 20.03.2006 || style"text-align:center"| 31.03.2006 || style="text-align:center"| 12 || Curitiba || [https://www.cbd.int/meetings/COP-08 COP 8]
|-
| style"text-align:center"| 9 || style"text-align:center"| 2008 || || style"text-align:center"| 19.05.2008 || style"text-align:center"| 30.05.2008 || style="text-align:center"| 12 || Bonn || [https://www.cbd.int/cop9 COP 9]
|-
| style"text-align:center"| 10 || style"text-align:center"| 2010 || || style"text-align:center"| 18.10.2010 || style"text-align:center"| 29.10.2010 || style="text-align:center"| 12 || Nagoya || [https://www.cbd.int/cop10 COP 10]
|-
| style"text-align:center"| 11 || style"text-align:center"| 2012 || || style"text-align:center"| 08.10.2012 || style"text-align:center"| 19.10.2012 || style="text-align:center"| 12 || Hyderabad || [https://www.cbd.int/cop11 COP 11]
|-
| style"text-align:center"| 12 || style"text-align:center"| 2014 || || style"text-align:center"| 06.10.2014 || style"text-align:center"| 17.10.2014 || style="text-align:center"| 12 || Pyeongchang || [https://www.cbd.int/cop12 COP 12]
|-
| style"text-align:center"| 13 || style"text-align:center"| 2016 || || style"text-align:center"| 04.12.2016 || style"text-align:center"| 17.12.2016 || style="text-align:center"| 14 || Cancun || [https://www.cbd.int/conferences/2016 COP 13]
|-
| style"text-align:center"| 14 || style"text-align:center"| 2018 || || style"text-align:center"| 13.11.2018 || style"text-align:center"| 29.11.2018 || style="text-align:center"| 17 || Sharm El Sheik || [https://www.cbd.int/conferences/2018 COP 14]
|-
| style"text-align:center"| 15 || style"text-align:center"| 2022 || || style"text-align:center"| 07.12.2022 || style"text-align:center"| 19.12.2022 || style="text-align:center"| 13 || Montreal || [https://www.cbd.int/conferences/2021-2022 COP 15]
|-
| style"text-align:center"| 16 || style"text-align:center"| 2024 || || style"text-align:center"| 21.10.2024 || style"text-align:center"| 01.11.2024 || style="text-align:center"| 12 || Cali || [https://www.cbd.int/conferences/2024 COP 16]
|}
1994 COP 1
The first ordinary meeting of the Parties to the Convention took place in November and December 1994, in Nassau, Bahamas. The International Coral Reef Initiative (ICRI) was launched at this first COP for the Convention on Biological Diversity.
1995 COP 2
The second ordinary meeting of the Parties to the Convention took place in November 1995, in Jakarta, Indonesia.
1996 COP 3
The third ordinary meeting of the Parties to the Convention took place in November 1996, in Buenos Aires, Argentina.
1998 COP 4
The fourth ordinary meeting of the Parties to the Convention took place in May 1998, in Bratislava, Slovakia.
1999 EX-COP 1 (Cartagena)
The First Extraordinary Meeting of the Conference of the Parties took place in February 1999, in Cartagena, Colombia. A series of meetings led to the adoption of the Cartagena Protocol on Biosafety in January 2000, effective from 2003.2002 COP 6The sixth ordinary meeting of the Parties to the Convention took place in April 2002, in The Hague, Netherlands.2004 COP 7The seventh ordinary meeting of the Parties to the Convention took place in February 2004, in Kuala Lumpur, Malaysia.2006 COP 8The eighth ordinary meeting of the Parties to the Convention took place in March 2006, in Curitiba, Brazil.2008 COP 9The ninth ordinary meeting of the Parties to the Convention took place in May 2008, in Bonn, Germany.
2010 COP 10 (Nagoya)
The tenth ordinary meeting of the Parties to the Convention took place in October 2010, in Nagoya, Japan. It was at this meeting that the Nagoya Protocol was ratified.
2010 was the International Year of Biodiversity, which resulted in 110 reports on the loss of biodiversity in different countries, but little or no progress toward the goal of "significant reduction" in the problem. Following a recommendation of CBD signatories, the UN declared 2011 to 2020 as the United Nations Decade on Biodiversity.
2012 COP 11
Leading up to the Conference of the Parties (COP 11) meeting on biodiversity in Hyderabad, India, 2012, preparations for a World Wide Views on Biodiversity has begun, involving old and new partners and building on the experiences from the World Wide Views on Global Warming.
2014 COP 12
Under the theme, "Biodiversity for Sustainable Development", thousands of representatives of governments, NGOs, indigenous peoples, scientists and the private sector gathered in Pyeongchang, Republic of Korea in October 2014 for the 12th meeting of the Conference of the Parties to the Convention on Biological Diversity (COP 12).
From 6–17 October 2014, Parties discussed the implementation of the Strategic Plan for Biodiversity 2011–2020 and its Aichi Biodiversity Targets, which are to be achieved by the end of this decade. The results of Global Biodiversity Outlook 4, the flagship assessment report of the CBD informed the discussions.
The conference gave a mid-term evaluation to the UN Decade on Biodiversity (2011–2020) initiative, which aims to promote the conservation and sustainable use of nature. The meeting achieved a total of 35 decisions, including a decision on "Mainstreaming gender considerations", to incorporate gender perspective to the analysis of biodiversity.
At the end of the meeting, the meeting adopted the "Pyeongchang Road Map", which addresses ways to achieve biodiversity through technology cooperation, funding and strengthening the capacity of developing countries.
2016 COP 13
The thirteenth ordinary meeting of the Parties to the Convention took place between 2 and 17 December 2016 in Cancún, Mexico.
2018 COP 14
The 14th ordinary meeting of the Parties to the Convention took place on 17–29 November 2018, in Sharm El-Sheikh, Egypt. The 2018 UN Biodiversity Conference closed on 29 November 2018 with broad international agreement on reversing the global destruction of nature and biodiversity loss threatening all forms of life on Earth. Parties adopted the Voluntary Guidelines for the design and effective implementation of ecosystem-based approaches to climate change adaptation and disaster risk reduction. Governments also agreed to accelerate action to achieve the Aichi Biodiversity Targets, agreed in 2010, until 2020. Work to achieve these targets would take place at the global, regional, national and subnational levels.2021/2022 COP 15
The 15th meeting of the Parties was originally scheduled to take place in Kunming, China in 2020, but was postponed several times due to the COVID-19 pandemic. After the start date was delayed for a third time, the Convention was split into two sessions. A mostly online event took place in October 2021, where over 100 nations signed the Kunming declaration on biodiversity. The theme of the declaration was "Ecological Civilization: Building a Shared Future for All Life on Earth". Twenty-one action-oriented draft targets were provisionally agreed in the October meeting, to be further discussed in the second session: an in-person event that was originally scheduled to start in April 2022, but was rescheduled to occur later in 2022. The second part of COP 15 ultimately took place in Montreal, Canada, from 5–17 December 2022. At the meeting, the Parties to the Convention adopted a new action plan, the Kunming-Montreal Global Biodiversity Framework.2024 COP 16The 16th meeting of the Parties is scheduled to be held in Cali, Colombia in 2024. Originally, Turkey was going to host it but after a series of earthquakes in February 2023 they had to withdraw.See also
* 2010 Biodiversity Indicators Partnership
* 2010 Biodiversity Target
* 30 by 30
* Agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPs)
* Biodiversity banking
* Biological Diversity Act, 2002
* Biopiracy
* Bioprospecting
* Biosphere Reserve
* Convention on the Conservation of Migratory Species of Wild Animals
* Convention on the International Trade in Endangered Species of Wild Flora and Fauna
* Convention on Wetlands of International Importance, especially as Waterfowl Habitat
* Ecotourism
* Endangered species
* Endangered Species Recovery Plan
* Environmental agreements
* Environmental Modification Convention, another ban on weather modification / climate engineering.
* Globally Important Agricultural Heritage Systems (GIAHS)
* Green Development Initiative (GDI)
* Holocene extinction
* Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services
* International Cooperative Biodiversity Groups
* International Organization for Biological Control
* International Treaty on Plant Genetic Resources for Food and Agriculture
* International Day for Biological Diversity
* International Year of Biodiversity
* Kunming-Montreal Global Biodiversity Framework
* Migratory Bird Treaty Act of 1918
* Red Data Book of Singapore
* Red Data Book of the Russian Federation
* Satoyama
* Sustainable forest management
* United Nations Convention to Combat Desertification
* United Nations Decade on Biodiversity
* United Nations Framework Convention on Climate Change
* World Conservation Monitoring Centre
References
* Further reading* Davis, K. 2008. A CBD manual for botanic gardens [http://www.bgci.org/files/cbd_manual.pdf English version], [http://www.bgci.org/files/cbd_manual_italian.pdf Italian version] Botanic Gardens Conservation International (BGCI)External links
* [https://www.cbd.int/ The Convention on Biological Diversity (CBD)] website
* [https://www.cbd.int/convention/text/ Text of the Convention] from CBD website
* [https://treaties.un.org/Pages/ViewDetails.aspx?srcIND&mtdsg_noXXVII-8&chapter27&clang_en Ratifications] at depositary
* [https://web.archive.org/web/20101231072643/http://www.bgci.org/ourwork/1414/ Case studies on the implementation of the Convention] from BGCI website with links to relevant articles
* [http://legal.un.org/avl/ha/cpbcbd/cpbcbd.html Introductory note by Laurence Boisson de Chazournes, procedural history note and audiovisual material] on the Convention on Biological Diversity in the [http://legal.un.org/avl/historicarchives.html Historic Archives of the United Nations Audiovisual Library of International Law]
<!--article's eponymous cat always placed first-->
C
Convention
Category:United Nations treaties
Category:Treaties concluded in 1992
Category:Treaties entered into force in 1993
.Convention on Biodiversity
.Convention on Biodiversity
Convention on Biodiversity
Convention on Biodiversity
Convention on Biodiversity
Convention on Biodiversity
Category:Animal treaties
Convention
Convention
Convention
Convention on Biodiversity
Convention on Biodiversity
Category:Treaties entered into by the European Union
Category:Treaties of the Afghan Transitional Administration
Category:Treaties of Albania
Category:Treaties of Algeria
Category:Treaties of Andorra
Category:Treaties of Angola
Category:Treaties of Antigua and Barbuda
Category:Treaties of Argentina
Category:Treaties of Armenia
Category:Treaties of Australia
Category:Treaties of Austria
Category:Treaties of Azerbaijan
Category:Treaties of the Bahamas
Category:Treaties of Bahrain
Category:Treaties of Bangladesh
Category:Treaties of Barbados
Category:Treaties of Belarus
Category:Treaties of Belgium
Category:Treaties of Belize
Category:Treaties of Benin
Category:Treaties of Bhutan
Category:Treaties of Bolivia
Category:Treaties of Bosnia and Herzegovina
Category:Treaties of Botswana
Category:Treaties of Brazil
Convention on Biodiversity
Category:Treaties of Brunei
Category:Treaties of Bulgaria
Category:Treaties of Burkina Faso
Category:Treaties of Burundi
Category:Treaties of Cambodia
Category:Treaties of Cameroon
Category:Treaties of Canada
Category:Treaties of Cape Verde
Category:Treaties of the Central African Republic
Category:Treaties of Chad
Category:Treaties of Chile
Category:Treaties of the People's Republic of China
Category:Treaties of Colombia
Category:Treaties of the Comoros
Category:Treaties of the Republic of the Congo
Category:Treaties of the Cook Islands
Category:Treaties of Costa Rica
Category:Treaties of Ivory Coast
Category:Treaties of Croatia
Category:Treaties of Cuba
Category:Treaties of Cyprus
Category:Treaties of the Czech Republic
Category:Treaties of North Korea
Category:Treaties of Zaire
Category:Treaties of Denmark
Category:Treaties of Djibouti
Category:Treaties of Dominica
Category:Treaties of the Dominican Republic
Category:Treaties of Ecuador
Category:Treaties of Egypt
Category:Treaties of El Salvador
Category:Treaties of Equatorial Guinea
Category:Treaties of Eritrea
Category:Treaties of Estonia
Category:Treaties of Eswatini
Category:Treaties of the Transitional Government of Ethiopia
Category:Treaties of Fiji
Category:Treaties of Finland
Category:Treaties of France
Category:Treaties of Gabon
Category:Treaties of the Gambia
Category:Treaties of Georgia (country)
Category:Treaties of Germany
Category:Treaties of Ghana
Category:Treaties of Greece
Category:Treaties of Grenada
Category:Treaties of Guatemala
Category:Treaties of Guinea
Category:Treaties of Guinea-Bissau
Category:Treaties of Guyana
Category:Treaties of Haiti
Category:Treaties of Honduras
Category:Treaties of Hungary
Category:Treaties of Iceland
Category:Treaties of India
Category:Treaties of Indonesia
Category:Treaties of Iran
Category:Treaties of Iraq
Category:Treaties of Ireland
Category:Treaties of Israel
Category:Treaties of Italy
Category:Treaties of Jamaica
Category:Treaties of Japan
Category:Treaties of Jordan
Category:Treaties of Kazakhstan
Category:Treaties of Kenya
Category:Treaties of Kiribati
Category:Treaties of Kuwait
Category:Treaties of Kyrgyzstan
Category:Treaties of Laos
Category:Treaties of Latvia
Category:Treaties of Lebanon
Category:Treaties of Lesotho
Category:Treaties of Liberia
Category:Treaties of the Libyan Arab Jamahiriya
Category:Treaties of Liechtenstein
Category:Treaties of Lithuania
Category:Treaties of Luxembourg
Category:Treaties of Madagascar
Category:Treaties of Malawi
Category:Treaties of Malaysia
Category:Treaties of the Maldives
Category:Treaties of Mali
Category:Treaties of Malta
Category:Treaties of the Marshall Islands
Category:Treaties of Mauritania
Category:Treaties of Mauritius
Category:Treaties of Mexico
Category:Treaties of the Federated States of Micronesia
Category:Treaties of Moldova
Category:Treaties of Monaco
Category:Treaties of Mongolia
Category:Treaties of Montenegro
Category:Treaties of Morocco
Category:Treaties of Mozambique
Category:Treaties of Myanmar
Category:Treaties of Namibia
Category:Treaties of Nauru
Category:Treaties of Nepal
Category:Treaties of the Netherlands
Category:Treaties of New Zealand
Category:Treaties of Nicaragua
Category:Treaties of Niger
Category:Treaties of Nigeria
Category:Treaties of Niue
Category:Treaties of North Macedonia
Category:Treaties of Norway
Category:Treaties of Oman
Category:Treaties of Pakistan
Category:Treaties of Palau
Category:Treaties of Palestine
Category:Treaties of Panama
Category:Treaties of Papua New Guinea
Category:Treaties of Paraguay
Category:Treaties of Peru
Category:Treaties of the Philippines
Category:Treaties of Poland
Category:Treaties of Portugal
Category:Treaties of Qatar
Category:Treaties of Romania
Category:Treaties of Russia
Category:Treaties of Rwanda
Category:Treaties of Saint Kitts and Nevis
Category:Treaties of Saint Lucia
Category:Treaties of Saint Vincent and the Grenadines
Category:Treaties of Samoa
Category:Treaties of San Marino
Category:Treaties of São Tomé and Príncipe
Category:Treaties of Saudi Arabia
Category:Treaties of Senegal
Category:Treaties of Serbia and Montenegro
Category:Treaties of Seychelles
Category:Treaties of Sierra Leone
Category:Treaties of Singapore
Category:Treaties of Slovakia
Category:Treaties of Slovenia
Category:Treaties of the Solomon Islands
Category:Treaties of the Transitional Federal Government of Somalia
Category:Treaties of South Africa
Category:Treaties of South Korea
Category:Treaties of South Sudan
Category:Treaties of Spain
Category:Treaties of Sri Lanka
Category:Treaties of the Republic of the Sudan (1985–2011)
Category:Treaties of Suriname
Category:Treaties of Sweden
Category:Treaties of Switzerland
Category:Treaties of Syria
Category:Treaties of Tajikistan
Category:Treaties of Thailand
Category:Treaties of Timor-Leste
Category:Treaties of Togo
Category:Treaties of Tonga
Category:Treaties of Trinidad and Tobago
Category:Treaties of Tunisia
Category:Treaties of Turkey
Category:Treaties of Turkmenistan
Category:Treaties of Tuvalu
Category:Treaties of Uganda
Category:Treaties of Ukraine
Category:Treaties of the United Arab Emirates
Category:Treaties of the United Kingdom
Category:Treaties of the United States
Category:Treaties of Tanzania
Category:Treaties of Uruguay
Category:Treaties of Uzbekistan
Category:Treaties of Vanuatu
Category:Treaties of Venezuela
Category:Treaties of Vietnam
Category:Treaties of Yemen
Category:Treaties of Zambia
Category:Treaties of Zimbabwe
Category:Treaties extended to Aruba
Category:Treaties extended to the Netherlands Antilles
Category:Treaties extended to Jersey
Category:Treaties extended to the British Virgin Islands
Category:Treaties extended to the Cayman Islands
Category:Treaties extended to Gibraltar
Category:Treaties extended to Saint Helena, Ascension and Tristan da Cunha
Category:Treaties extended to the Isle of Man
Category:Treaties extended to Greenland
Category:Treaties extended to the Faroe Islands
Category:Treaties extended to Portuguese Macau
Category:Treaties extended to Hong Kong
Category:Treaties extended to the Falkland Islands
Category:Treaties extended to South Georgia and the South Sandwich Islands
Category:Anti-biopiracy treaties
Category:Biopiracy
|
https://en.wikipedia.org/wiki/Convention_on_Biological_Diversity
|
2025-04-05T18:27:44.434434
|
6199
|
Convention on Fishing and Conservation of the Living Resources of the High Seas
|
The Convention on Fishing and Conservation of Living Resources of the High Seas is an agreement that was designed to solve through international cooperation the problems involved in the conservation of living resources of the high seas, considering that because of the development of modern technology some of these resources are in danger of being overexploited. The convention opened for signature on 29 April 1958 and entered into force on 20 March 1966.
Participation
Parties – (39): Australia, Belgium, Bosnia and Herzegovina, Burkina Faso, Cambodia, Colombia, Republic of the Congo, Denmark, Dominican Republic, Fiji, Finland, France, Haiti, Jamaica, Kenya, Lesotho, Madagascar, Malawi, Malaysia, Mauritius, Mexico, Montenegro, Netherlands, Nigeria, Portugal, Senegal, Serbia, Sierra Leone, Solomon Islands, South Africa, Spain, Switzerland, Thailand, Tonga, Trinidad and Tobago, Uganda, United Kingdom, United States, Venezuela.
Countries that have signed, but not yet ratified – (21): Afghanistan, Argentina, Bolivia, Canada, Costa Rica, Cuba, Ghana, Iceland, Indonesia, Iran, Ireland, Israel, Lebanon, Liberia, Nepal, New Zealand, Pakistan, Panama, Sri Lanka, Tunisia, Uruguay.
See also
Environmental effects of fishing
United Nations Convention on the Law of the Sea
Convention on the High Seas
References
CIA World Factbook, edition
Indonesian Law #19/1961
External links
Indonesian Law #19/1961
Convention of the High Seas (1958)
Convention on Fishing and Conservation of Living Resources of the High Seas (1958)
Category:Environmental treaties
Category:Fisheries law
Category:Treaties concluded in 1958
Category:Treaties entered into force in 1966
Category:1966 in the environment
Category:Treaties of Australia
Category:Treaties of Belgium
Category:Treaties of Bosnia and Herzegovina
Category:Treaties of Burkina Faso
Category:Treaties of the Kingdom of Cambodia (1953–1970)
Category:Treaties of Colombia
Category:Treaties of the Republic of the Congo
Category:Treaties of Denmark
Category:Treaties of the Dominican Republic
Category:Treaties of Fiji
Category:Treaties of Finland
Category:Treaties of France
Category:Treaties of Haiti
Category:Treaties of Indonesia
Category:Treaties of Jamaica
Category:Treaties of Kenya
Category:Treaties of Lesotho
Category:Treaties of Madagascar
Category:Treaties of Malawi
Category:Treaties of Malaysia
Category:Treaties of Mauritius
Category:Treaties of Mexico
Category:Treaties of the Netherlands
Category:Treaties of Nigeria
Category:Treaties of the Estado Novo (Portugal)
Category:Treaties of Senegal
Category:Treaties of Serbia and Montenegro
Category:Treaties of Sierra Leone
Category:Treaties of the Solomon Islands
Category:Treaties of South Africa
Category:Treaties of Francoist Spain
Category:Treaties of Switzerland
Category:Treaties of Thailand
Category:Treaties of Tonga
Category:Treaties of Trinidad and Tobago
Category:Treaties of Uganda
Category:Treaties of the United Kingdom
Category:Treaties of the United States
Category:Treaties of Venezuela
Category:Treaties of Yugoslavia
Category:Fisheries treaties
Category:Fish conservation
Category:Treaties extended to the Netherlands Antilles
Category:Treaties extended to Aruba
Category:Treaties extended to Saint Christopher-Nevis-Anguilla
Category:Treaties extended to Bermuda
Category:Treaties extended to the British Virgin Islands
Category:Treaties extended to the Cayman Islands
Category:Treaties extended to the Falkland Islands
Category:Treaties extended to Gibraltar
Category:Treaties extended to Montserrat
Category:Treaties extended to the Pitcairn Islands
Category:Treaties extended to Saint Helena, Ascension and Tristan da Cunha
Category:Treaties extended to South Georgia and the South Sandwich Islands
Category:Treaties extended to the Turks and Caicos Islands
Category:Treaties extended to Surinam (Dutch colony)
Category:Treaties extended to the Faroe Islands
Category:Treaties extended to Greenland
Category:United Nations treaties
|
https://en.wikipedia.org/wiki/Convention_on_Fishing_and_Conservation_of_the_Living_Resources_of_the_High_Seas
|
2025-04-05T18:27:44.439101
|
6200
|
Convention on Long-Range Transboundary Air Pollution
|
thumb|400px|Map showing Convention on Long-Range Transboundary Air Pollution signatories (green) and ratifications (dark green) as of July 2007
The Convention on Long-Range Transboundary Air Pollution, often abbreviated as Air Convention or CLRTAP, is intended to protect the human environment against air pollution and to gradually reduce and prevent air pollution, including long-range transboundary air pollution. It is implemented by the European Monitoring and Evaluation Programme (EMEP), directed by the United Nations Economic Commission for Europe (UNECE).
The convention opened for signature on , and entered into force on .
Secretariat
The Convention, which now has 51 Parties, identifies the Executive Secretary of the United Nations Economic Commission for Europe (UNECE) as its secretariat. The current parties to the Convention are shown on the map.
The Convention is implemented by the European Monitoring and Evaluation Programme (EMEP) (short for Co-operative Programme for Monitoring and Evaluation of the Long-range Transmission of Air Pollutants in Europe). Results of the EMEP programme are published on the EMEP website, www.emep.int.
Procedure
The aim of the Convention is that Parties shall endeavour to limit and, as far as possible, gradually reduce and prevent air pollution including long-range transboundary air pollution. Parties develop policies and strategies to combat the discharge of air pollutants through exchanges of information, consultation, research and monitoring.
The Parties meet annually at sessions of the Executive Body to review ongoing work and plan future activities including a workplan for the coming year. The three main subsidiary bodies – the Working Group on Effects, the Steering Body to EMEP and the Working Group on Strategies and Review – as well as the Convention's Implementation Committee, report to the Executive Body each year.
Currently, the Convention's priority activities include review and possible revision of its most recent protocols, implementation of the Convention and its protocols across the entire UNECE region (with special focus on Eastern Europe, the Caucasus and Central Asia and South-East Europe) and sharing its knowledge and information with other regions of the world.
Protocols
Since 1979 the Convention on Long-range Transboundary Air Pollution has addressed some of the major environmental problems of the UNECE region through scientific collaboration and policy negotiation. The Convention has been extended by eight protocols that identify specific measures to be taken by Parties to cut their emissions of air pollutants:
Protocol on Long-Term Financing of the Cooperative Programme for Monitoring and Evaluation of the Long-range Transmission of Air Pollutants in Europe (EMEP) (1984)
1985 Helsinki Protocol on the Reduction of Sulphur Emissions
Nitrogen Oxide Protocol (1988)
Volatile Organic Compounds Protocol (1991)
1994 Oslo Protocol on Further Reduction of Sulphur Emissions
Protocol on Heavy Metals (1998)
Aarhus Protocol on Persistent Organic Pollutants (1998)
1999 Gothenburg Protocol to Abate Acidification, Eutrophication and Ground-level Ozone (1999)
See also
Aarhus Protocol on Persistent Organic Pollutants
Protocol on Heavy Metals
Critical load
International environmental agreements
Gothenburg (Multi-effect) Protocol
1985 Helsinki Protocol on the Reduction of Sulphur Emissions
1994 Oslo Protocol on Further Reduction of Sulphur Emissions
Volatile Organic Compounds Protocol
CIA World Factbook, edition
References
External links
Convention on Long-Range Transboundary Air Pollution
Ratifications, at depositary
Category:Climate change treaties
Category:Environmental treaties
Category:Treaties concluded in 1979
Category:Treaties entered into force in 1983
Category:Air pollution
Category:1983 in the environment
Category:Treaties of Albania
Category:Treaties of Armenia
Category:Treaties of Austria
Category:Treaties of Azerbaijan
Category:Treaties of the Byelorussian Soviet Socialist Republic
Category:Treaties of Belgium
Category:Treaties of Bosnia and Herzegovina
Category:Treaties of the People's Republic of Bulgaria
Category:Treaties of Canada
Category:Treaties of Croatia
Category:Treaties of Cyprus
Category:Treaties of the Czech Republic
Category:Treaties of Czechoslovakia
Category:Treaties of Denmark
Category:Treaties of Estonia
Category:Treaties entered into by the European Union
Category:Treaties of Finland
Category:Treaties of France
Category:Treaties of Georgia (country)
Category:Treaties of West Germany
Category:Treaties of East Germany
Category:Treaties of Greece
Category:Treaties of the Hungarian People's Republic
Category:Treaties of Iceland
Category:Treaties of Ireland
Category:Treaties of Italy
Category:Treaties of Kazakhstan
Category:Treaties of Kyrgyzstan
Category:Treaties of Latvia
Category:Treaties of Liechtenstein
Category:Treaties of Lithuania
Category:Treaties of Luxembourg
Category:Treaties of Malta
Category:Treaties of Monaco
Category:Treaties of Montenegro
Category:Treaties of the Netherlands
Category:Treaties of Norway
Category:Treaties of the Polish People's Republic
Category:Treaties of Portugal
Category:Treaties of Moldova
Category:Treaties of Romania
Category:Treaties of the Soviet Union
Category:Treaties of Serbia and Montenegro
Category:Treaties of Slovakia
Category:Treaties of Slovenia
Category:Treaties of Spain
Category:Treaties of Sweden
Category:Treaties of Switzerland
Category:Treaties of North Macedonia
Category:Treaties of Turkey
Category:Treaties of the Ukrainian Soviet Socialist Republic
Category:Treaties of the United Kingdom
Category:Treaties of the United States
Category:United Nations Economic Commission for Europe treaties
Category:Treaties extended to Jersey
Category:Treaties extended to Guernsey
Category:Treaties extended to the Isle of Man
Category:Treaties extended to Gibraltar
Category:Treaties extended to Akrotiri and Dhekelia
Category:Treaties extended to the Faroe Islands
Category:Treaties extended to Greenland
Category:Treaties extended to West Berlin
|
https://en.wikipedia.org/wiki/Convention_on_Long-Range_Transboundary_Air_Pollution
|
2025-04-05T18:27:44.442116
|
6201
|
CITES
|
CITE}}
| location_signed = Geneva, Switzerland
| date_sealed | date_effective 1 July 1975
| condition_effective = 10 ratifications
| date_expiration | signatories
| parties = 185
| depositor = Government of the Swiss Confederation
| language = * English
* French
* Spanish
| wikisource = Convention on International Trade in Endangered Species of Wild Fauna and Flora
}}
CITES (shorter name for the Convention on International Trade in Endangered Species of Wild Fauna and Flora, also known as the Washington Convention) is a multilateral treaty to protect endangered plants and animals from the threats of international trade. It was drafted as a result of a resolution adopted in 1963 at a meeting of members of the International Union for Conservation of Nature (IUCN). The convention was opened for signature in 1973 and CITES entered into force on 1 July 1975.
Its aim is to ensure that international trade (import/export) in specimens of animals and plants included under CITES does not threaten the survival of the species in the wild. This is achieved via a system of permits and certificates. CITES affords varying degrees of protection to more than 40,900 species.
, the Secretary-General of CITES is Ivonne Higuero.
Background
CITES is one of the largest and oldest conservation and sustainable use agreements in existence. There are three working languages of the Convention (English, French and Spanish) in which all documents are made available. Participation is voluntary and countries that have agreed to be bound by the convention are known as Parties. Although CITES is legally binding on the Parties, it does not take the place of national laws. Rather it provides a framework respected by each Party, which must adopt their own domestic legislation to implement CITES at the national level.
Originally, CITES addressed depletion resulting from demand for luxury goods such as furs in Western countries, but with the rising wealth of Asia, particularly in China, the focus changed to products demanded there, particularly those used for luxury goods such as elephant ivory or rhinoceros horn. As of 2022, CITES has expanded to include thousands of species previously considered unremarkable and in no danger of extinction such as manta rays or pangolins.
Ratifications
is covered by CITES regulations through Denmark.
The CITES Convention includes provisions and rules for trade with non-Parties. All member states of the United Nations are party to the treaty, with the exception of North Korea, Federated States of Micronesia, Haiti, Kiribati, Marshall Islands, Nauru, South Sudan, East Timor, Turkmenistan, and Tuvalu. UN observer the Holy See is also not a member. The Faroe Islands, an autonomous region in the Kingdom of Denmark, is also treated as a non-Party to CITES (both the Danish mainland and Greenland are part of CITES).
An amendment to the text of the convention, known as the Gaborone Amendment allows regional economic integration organizations (REIO), such as the European Union, to have the status of a member state and to be a Party to the convention. The REIO can vote at CITES meetings with the number of votes representing the number of members in the REIO, but it does not have an additional vote.
In accordance with Article XVII, paragraph 3, of the CITES Convention, the Gaborone Amendment entered into force on 29 November 2013, 60 days after 54 (two-thirds) of the 80 States that were party to CITES on 30 April 1983 deposited their instrument of acceptance of the amendment. At that time it entered into force only for those States that had accepted the amendment. The amended text of the convention will apply automatically to any State that becomes a Party after 29 November 2013. For States that became party to the convention before that date and have not accepted the amendment, it will enter into force 60 days after they accept it. The secretariat position has been held by a variety of people from different nations. Timeline of CITES Secretary-General Offices 1978-1981: Peter H. Sand
He was born in Bavaria, Germany and was educated in international law in Germany, France and Canada. He became a professor and an author, focusing on environmental law, holding other positions such as the Director-General of the IUCN and legal advisor for environmental affairs to the World Bank.
1982-1990: Eugene Lapointe
1991 - 1998: Izgrev Topkov
1999 - 2010: Willem Wijnstekers
2018- Current: Ivonne Higuero CITES specimens can include a wide range of items including the whole animal/plant (whether alive or dead), or a product that contains a part or derivative of the listed taxa such as cosmetics or traditional medicines.
Four types of trade are recognized by CITES - import, export, re-export (export of any specimen that has previously been imported) and introduction from the sea (transportation into a state of specimens of any species which were taken in the marine environment not under the jurisdiction of any state). The CITES definition of "trade" does not require a financial transaction to be occurring. All trade in specimens of species covered by CITES must be authorized through a system of permits and certificates prior to the trade taking place. CITES permits and certificates are issued by one or more Management Authorities in charge of administering the CITES system in each country. Management Authorities are advised by one or more Scientific Authorities on the effects of trade of the specimen on the status of CITES-listed species. CITES permits and certificates must be presented to relevant border authorities in each country in order to authorize the trade.
Each party must enact their own domestic legislation to bring the provisions of CITES into effect in their territories. Parties may choose to take stricter domestic measures than CITES provides (for example by requiring permits/certificates in cases where they would not normally be needed or by prohibiting trade in some specimens).
in the United Kingdom]]
Appendices
Over 40,900 species, subspecies and populations are protected under CITES. Each protected taxa or population is included in one of three lists called Appendices. The Appendix that lists a taxon or population reflects the level of the threat posed by international trade and the CITES controls that apply.
Taxa may be split-listed meaning that some populations of a species are on one Appendix, while some are on another. The African bush elephant (Loxodonta africana) is currently split-listed, with all populations except those of Botswana, Namibia, South Africa and Zimbabwe listed in Appendix I. Those of Botswana, Namibia, South Africa and Zimbabwe are listed in Appendix II. There are also species that have only some populations listed in an Appendix. One example is the pronghorn (Antilocapra americana), a ruminant native to North America. Its Mexican population is listed in Appendix I, but its U.S. and Canadian populations are not listed (though certain U.S. populations in Arizona are nonetheless protected under other domestic legislation, in this case the Endangered Species Act).
Taxa are proposed for inclusion, amendment or deletion in Appendices I and II at meetings of the Conference of the Parties (CoP), which are held approximately once every three years. Amendments to listing in Appendix III may be made unilaterally by individual parties.
Appendix I
Appendix I taxa are those that are threatened with extinction and to which the highest level of CITES protection is afforded. Commercial trade in wild-sourced specimens of these taxa is not permitted and non-commercial trade is strictly controlled by requiring an import permit and export permit to be granted by the relevant Management Authorities in each country before the trade occurs.
Notable taxa listed in Appendix I include the red panda (Ailurus fulgens), western gorilla (Gorilla gorilla), the chimpanzee species (Pan spp.), tigers (Panthera tigris sp.), Asian elephant (Elephas maximus), snow leopard (Panthera uncia), red-shanked douc (Pygathrix nemaeus), some populations of African bush elephant (Loxodonta africana), and the monkey puzzle tree (Araucaria araucana).
Appendix II
Appendix II taxa are those that are not necessarily threatened with extinction, but trade must be controlled in order to avoid utilization incompatible with their survival. Appendix II taxa may also include species similar in appearance to species already listed in the Appendices. The vast majority of taxa listed under CITES are listed in Appendix II. Any trade in Appendix II taxa standardly requires a CITES export permit or re-export certificate to be granted by the Management Authority of the exporting country before the trade occurs.
Examples of taxa listed on Appendix II are the great white shark (Carcharodon carcharias), the American black bear (Ursus americanus), Hartmann's mountain zebra (Equus zebra hartmannae), green iguana (Iguana iguana), queen conch (Strombus gigas), emperor scorpion (Pandinus imperator), Mertens' water monitor (Varanus mertensi), bigleaf mahogany (Swietenia macrophylla), lignum vitae (Guaiacum officinale), the chambered nautilus (Nautilus pompilius), all stony corals (Scleractinia spp.), Jungle cat (Felis chaus) and American ginseng (Panax quinquefolius).
Appendix III
Appendix III species are those that are protected in at least one country, and that country has asked other CITES Parties for assistance in controlling the trade.
Any trade in Appendix III species standardly requires a CITES export permit (if sourced from the country that listed the species) or a certificate of origin (from any other country) to be granted before the trade occurs.
Examples of species listed on Appendix III and the countries that listed them are the Hoffmann's two-toed sloth (Choloepus hoffmanni) by Costa Rica, sitatunga (Tragelaphus spekii) by Ghana and African civet (Civettictis civetta) by Botswana.
Exemptions and special procedures
Under Article VII, the Convention allows for certain exceptions to the general trade requirements described above.
Pre-Convention specimens
CITES provides for a special process for specimens that were acquired before the provisions of the Convention applied to that specimen. These are known as "pre-Convention" specimens and must be granted a CITES pre-Convention certificate before the trade occurs. Only specimens legally acquired before the date on which the species concerned was first included in the Appendices qualify for this exemption.Personal and household effectsCITES provides that the standard permit/certificate requirements for trade in CITES specimens do not generally apply if a specimen is a personal or household effect. However there are a number of situations where permits/certificates for personal or household effects are required and some countries choose to take stricter domestic measures by requiring permits/certificates for some or all personal or household effects.
In the case of commercial trade of Appendix I taxa, captive bred or artificially propagated specimens may be traded as if they were Appendix II. This reduces the permit requirements from two permits (import/export) to one (export only).
In the case of non-commercial trade, specimens may be traded with a certificate of captive breeding/artificial propagation issued by the Management Authority of the state of export in lieu of standard permits.
Scientific exchange
Standard CITES permit and certificates are not required for the non-commercial loan, donation or exchange between scientific or forensic institutions that have been registered by a Management Authority of their State. Consignments containing the specimens must carry a label issued or approved by that Management Authority (in some cases Customs Declaration labels may be used). Specimens that may be included under this provision include museum, herbarium, diagnostic and forensic research specimens. Registered institutions are listed on the CITES website.Amendments and reservations
Amendments to the Convention must be supported by a two-thirds majority who are "present and voting" and can be made during an extraordinary meeting of the COP if one-third of the Parties are interested in such a meeting. The Gaborone Amendment (1983) allows regional economic blocs to accede to the treaty. Trade with non-Party states is allowed, although permits and certificates are recommended to be issued by exporters and sought by importers.
Species in the Appendices may be proposed for addition, change of Appendix, or de-listing (i.e., deletion) by any Party, whether or not it is a range State and changes may be made despite objections by range States if there is sufficient (2/3 majority) support for the listing. Species listings are made at the Conference of Parties.
Upon acceding to the Convention or within 90 days of a species listing being amended, Parties may make reservations. In these cases, the party is treated as being a state that is not a Party to CITES with respect to trade in the species concerned. Notable reservations include those by Iceland, Japan, and Norway on various baleen whale species and those on Falconiformes by Saudi Arabia.
Shortcomings and concerns
Implementation
As of 2002, 50% of Parties lacked one or more of the four major CITES requirements - designation of Management and Scientific Authorities; laws prohibiting the trade in violation of CITES; penalties for such trade and laws providing for the confiscation of specimens.
Although the Convention itself does not provide for arbitration or dispute in the case of noncompliance, 36 years of CITES in practice has resulted in several strategies to deal with infractions by Parties. The Secretariat, when informed of an infraction by a Party, will notify all other parties. The Secretariat will give the Party time to respond to the allegations and may provide technical assistance to prevent further infractions. Other actions the Convention itself does not provide for but that derive from subsequent COP resolutions may be taken against the offending Party. These include:
*Mandatory confirmation of all permits by the Secretariat
*Suspension of cooperation from the Secretariat
*A formal warning
*A visit by the Secretariat to verify capacity
*Recommendations to all Parties to suspend CITES related trade with the offending party
*Dictation of corrective measures to be taken by the offending Party before the Secretariat will resume cooperation or recommend resumption of trade
Bilateral sanctions have been imposed on the basis of national legislation (e.g. the USA used certification under the Pelly Amendment to get Japan to revoke its reservation to hawksbill turtle products in 1991, thus reducing the volume of its exports).
Infractions may include negligence with respect to permit issuing, excessive trade, lax enforcement, and failing to produce annual reports (the most common).
Approach to biodiversity conservation
General limitations about the structure and philosophy of CITES include: by design and intent it focuses on trade at the species level and does not address habitat loss, ecosystem approaches to conservation, or poverty; it seeks to prevent unsustainable use rather than promote sustainable use (which generally conflicts with the Convention on Biological Diversity), although this has been changing (see Nile crocodile, African elephant, South African white rhino case studies in Hutton and Dickinson 2000). It does not explicitly address market demand. In fact, CITES listings have been demonstrated to increase financial speculation in certain markets for high value species. Funding does not provide for increased on-the-ground enforcement (it must apply for bilateral aid for most projects of this nature).
There has been increasing willingness within the Parties to allow for trade in products from well-managed populations. For instance, sales of the South African white rhino have generated revenues that helped pay for protection. Listing the species on Appendix I increased the price of rhino horn (which fueled more poaching), but the species survived wherever there was adequate on-the-ground protection. Thus field protection may be the primary mechanism that saved the population, but it is likely that field protection would not have been increased without CITES protection. In another instance, the United States initially stopped exports of bobcat and lynx hides in 1977 when it first implemented CITES for lack of data to support no detriment findings.[https://commons.wikimedia.org/wiki/File:ESSA_30_Aug_1977.pdf] However, in this Federal Register notice, issued by William Yancey Brown, the U.S. Endangered Species Scientific Authority (ESSA) established a framework of no detriment findings for each state and the Navajo nation and indicated that approval would be forthcoming if the states and Navajo nation provided evidence that their furbearer management programs assured the species would be conserved. Management programs for these species expanded rapidly, including tagging for export,[https://www.fishwildlife.org/afwa-inspires/furbearer-management] and are currently recognized in program approvals under regulations of the U.S. Fish and Wildlife Service.[https://www.ecfr.gov/current/title-50/chapter-I/subchapter-B/part-23/subpart-E/section-23.69]Drafting
By design, CITES regulates and monitors trade in the manner of a "negative list" such that trade in all species is permitted and unregulated unless the species in question appears on the Appendices or looks very much like one of those taxa. Then and only then, trade is regulated or constrained. Because the remit of the Convention covers millions of species of plants and animals, and tens of thousands of these taxa are potentially of economic value, in practice this negative list approach effectively forces CITES signatories to expend limited resources on just a select few, leaving many species to be traded with neither constraint nor review. For example, recently several bird classified as threatened with extinction appeared in the legal wild bird trade because the CITES process never considered their status. If a "positive list" approach were taken, only species evaluated and approved for the positive list would be permitted in trade, thus lightening the review burden for member states and the Secretariat, and also preventing inadvertent legal trade threats to poorly known species.
Specific weaknesses in the text include: it does not stipulate guidelines for the 'non-detriment' finding required of national Scientific Authorities; non-detriment findings require copious amounts of information; the 'household effects' clause is often not rigid enough/specific enough to prevent CITES violations by means of this Article (VII); non-reporting from Parties means Secretariat monitoring is incomplete; and it has no capacity to address domestic trade in listed species.
In order to ensure that the General Agreement on Tariffs and Trade (GATT) was not violated, the Secretariat of GATT was consulted during the drafting process.
Animal sourced pathogens
During the coronavirus pandemic in 2020 CEO Ivonne Higuero noted that illegal wildlife trade not only helps to destroy habitats, but these habitats create a safety barrier for humans that can prevent pathogens from animals passing themselves on to people.
Reform suggestions
Suggestions for improvement in the operation of CITES include: more regular missions by the Secretariat (not reserved just for high-profile species); improvement of national legislation and enforcement; better reporting by Parties (and the consolidation of information from all sources-NGOs, TRAFFIC, the wildlife trade monitoring network and Parties); more emphasis on enforcement-including a technical committee enforcement officer; the development of CITES Action Plans (akin to Biodiversity Action Plans related to the Convention on Biological Diversity) including: designation of Scientific/Management Authorities and national enforcement strategies; incentives for reporting and timelines for both Action Plans and reporting. CITES would benefit from access to Global Environment Facility (GEF), funds-although this is difficult given the GEFs more ecosystem approach-or other more regular funds. Development of a future mechanism similar to that of the Montreal Protocol (developed nations contribute to a fund for developing nations) could allow more funds for non-Secretariat activities.
Traffic released a report in December, 2024 outlining illegal trade in animal products occurring in Vietnam:
Additional information about the documented trade can be extracted through queries on the [https://trade.cites.org/ CITES website].
Meetings
The Conference of the Parties (CoP) is held once every three years. The location of the next CoP is chosen at the close of each CoP by a secret ballot vote.
The CITES Committees (Animals Committee, Plants Committee and Standing Committee) hold meetings during each year that does not have a CoP, while the Standing committee meets also in years with a CoP. The Committee meetings take place in Geneva, Switzerland (where the Secretariat of the CITES Convention is located), unless another country offers to host the meeting. The Secretariat is administered by UNEP. The Animals and Plants Committees have sometimes held joint meetings. The previous joint meeting was held in March 2012 in Dublin, Ireland, and the latest one was held in Veracruz, Mexico, in May 2014.
{| class="wikitable sortable plainrowheaders"
|-
!scope"col" rowspan1 width=90|Meeting
!scope"col" colspan1 width=110|City
!scope"col" rowspan1 width=120|Country
!scope"col" rowspan1 width=200|Duration
|-
!scope="row"|CoP 1
|Bern
|
| 2–6 November 1976
|-
!scope="row"|CoP 2
|San José
|
| 19–30 March 1979
|-
!scope="row"|CoP 3
|New Delhi
|
| 25 February – 8 March 1981
|-
!scope="row"|CoP 4
|Gaborone
|
| 19 – 30 April 1983
|-
!scope="row"|CoP 5
|Buenos Aires
|
| 22 April – 3 May 1985
|-
!scope="row"|CoP 6
|Ottawa
|
| 12–24 July 1987
|-
!scope="row"|CoP 7
|Lausanne
|
| 9–20 October 1989
|-
!scope="row"|CoP 8
|Kyoto
|
| 2–13 March 1992
|-
!scope="row"|CoP 9
|Fort Lauderdale
|
| 7–18 November 1994
|-
!scope="row"|CoP 10
|Harare
|
| 9–20 June 1997
|-
!scope="row"|CoP 11
|Nairobi
|
| 10–20 April 2000
|-
!scope="row"|CoP 12
|Santiago de Chile
|
| 3–15 November 2002
|-
!scope="row"|CoP 13
|Bangkok
|
| 2–14 October 2004
|-
!scope="row"|CoP 14
|The Hague
|
| 3–15 June 2007
|-
!scope="row"|CoP 15
|Doha
|
| 13–25 March 2010
|-
!scope="row"|CoP 16
|Bangkok
|
| 3–14 March 2013
|-
!scope="row"|CoP 17
|Johannesburg
|
| 24 September – 5 October 2016
|-
!scope="row"|CoP 18
|Geneva
|
| 17–28 August 2019
|-
!scope="row"|CoP 19
|Panama City
|
| 14–25 November 2022
|-
!scope="row"|CoP 20
|Samarkand
|
|25 November - 06 December 2025
|}
A current list of upcoming meetings appears on the CITES calendar.
At the seventeenth Conference of the Parties (CoP 17), Namibia and Zimbabwe introduced proposals to amend their listing of elephant populations in Appendix II. Instead, they wished to establish controlled trade in all elephant specimens, including ivory. They argue that revenue from regulated trade could be used for elephant conservation and rural communities' development. However, both proposals were opposed by the US and other countries.
See also
<!-- New links in alphabetical order please -->
*Environmental agreements
*Illegal logging
*IUCN Red List
*Ivory trade
*Lacey Act
*List of species protected by CITES Appendix I
*List of species protected by CITES Appendix II
*List of species protected by CITES Appendix III
*Shark finning
*Wildlife conservation
*Wildlife Enforcement Monitoring System
*Wildlife management
*Wildlife smuggling
*World Wildlife Day
Footnotes
References
Further reading
*Oldfield, S. and McGough, N. (Comp.) 2007. A CITES manual for botanic gardens [http://www.bgci.org/files/Worldwide/Publications/PDFs/cites.pdf English version], [http://www.bgci.org/files/Worldwide/Publications/PDFs/citesspanish.pdf Spanish version], [http://www.bgci.org/files/Worldwide/Publications/PDFs/citesitalian.pdf Italian version] Botanic Gardens Conservation International (BGCI)
External links
*
* [https://web.archive.org/web/20160313225840/http://shapingsustainablemarkets.iied.org/cites CITES Profile on database of market governance mechanisms] (archived 13 March 2016)
;Member countries (Parties)
* [http://www.cites.org/eng/disc/parties/chronolo.php Chronological list of Parties]
* Alphabetical list of Parties [https://web.archive.org/web/20120125111255/http://www.cites.org/eng/disc/parties/alphabet.php at CITES] and at the [https://web.archive.org/web/20141015184257/https://www.eda.admin.ch/etc/medialib/downloads/edazen/topics/intla/intrea/depch/intcom.Par.0001.File.tmp/mt_130227_cites73part_f.pdf depositary] (PDF)
* [https://web.archive.org/web/20110120150226/http://www.cites.org/cms/index.php/lang-en/component/ncd/ National contacts] (archived 20 January 2011)
;Lists of species included in Appendices I, II and III (i.e. species protected by CITES)
* [http://www.cites.org/eng/app/index.php Explanation of the Appendices]
* [http://www.cites.org/eng/disc/species.php Number of species on the Appendices]
* [http://www.cites.org/eng/app/appendices.php Species lists (Appendices I, II and III)]
Category:Environmental treaties
Category:Endangered species
Category:Treaties concluded in 1973
Category:Treaties entered into force in 1975
Category:Wildlife smuggling
Category:1975 in the environment
Category:Treaties of the Democratic Republic of Afghanistan
Category:Treaties of Albania
Category:Treaties of Algeria
Category:Treaties of Angola
Category:Treaties of Antigua and Barbuda
Category:Treaties of Argentina
Category:Treaties of Armenia
Category:Treaties of Australia
Category:Treaties of Austria
Category:Treaties of Azerbaijan
Category:Treaties of the Bahamas
Category:Treaties of Bahrain
Category:Treaties of Bangladesh
Category:Treaties of Barbados
Category:Treaties of Belarus
Category:Treaties of Belgium
Category:Treaties of Belize
Category:Treaties of the People's Republic of Benin
Category:Treaties of Bhutan
Category:Treaties of Bolivia
Category:Treaties of Bosnia and Herzegovina
Category:Treaties of Botswana
Category:Treaties of the military dictatorship in Brazil
Category:Treaties of Brunei
Category:Treaties of Bulgaria
Category:Treaties of Burkina Faso
Category:Treaties of Burundi
Category:Treaties of Cambodia
Category:Treaties of Cameroon
Category:Treaties of Canada
Category:Treaties of Cape Verde
Category:Treaties of the Central African Republic
Category:Treaties of Chad
Category:Treaties of Chile
Category:Treaties of the People's Republic of China
Category:Treaties of Colombia
Category:Treaties of the Comoros
Category:Treaties of the Republic of the Congo
Category:Treaties of Costa Rica
Category:Treaties of Ivory Coast
Category:Treaties of Croatia
Category:Treaties of Cuba
Category:Treaties of Cyprus
Category:Treaties of Czechoslovakia
Category:Treaties of the Czech Republic
Category:Treaties of Zaire
Category:Treaties of Denmark
Category:Treaties of Djibouti
Category:Treaties of Dominica
Category:Treaties of the Dominican Republic
Category:Treaties of Ecuador
Category:Treaties of Egypt
Category:Treaties of El Salvador
Category:Treaties of Equatorial Guinea
Category:Treaties of Eritrea
Category:Treaties of Estonia
Category:Treaties of the People's Democratic Republic of Ethiopia
Category:Treaties of Fiji
Category:Treaties of Finland
Category:Treaties of France
Category:Treaties of Gabon
Category:Treaties of the Gambia
Category:Treaties of Georgia (country)
Category:Treaties of West Germany
Category:Treaties of East Germany
Category:Treaties of Ghana
Category:Treaties of Greece
Category:Treaties of Grenada
Category:Treaties of Guatemala
Category:Treaties of Guinea
Category:Treaties of Guinea-Bissau
Category:Treaties of Guyana
Category:Treaties of Honduras
Category:Treaties of the Hungarian People's Republic
Category:Treaties of Iceland
Category:Treaties of India
Category:Treaties of Indonesia
Category:Treaties of Pahlavi Iran
Category:Treaties of Iraq
Category:Treaties of Ireland
Category:Treaties of Israel
Category:Treaties of Italy
Category:Treaties of Jamaica
Category:Treaties of Japan
Category:Treaties of Jordan
Category:Treaties of Kazakhstan
Category:Treaties of Kenya
Category:Treaties of Kuwait
Category:Treaties of Kyrgyzstan
Category:Treaties of Laos
Category:Treaties of Latvia
Category:Treaties of Lebanon
Category:Treaties of Lesotho
Category:Treaties of Liberia
Category:Treaties of the Libyan Arab Jamahiriya
Category:Treaties of Liechtenstein
Category:Treaties of Lithuania
Category:Treaties of Luxembourg
Category:Treaties of Madagascar
Category:Treaties of Malawi
Category:Treaties of Malaysia
Category:Treaties of the Maldives
Category:Treaties of Mali
Category:Treaties of Malta
Category:Treaties of Mauritania
Category:Treaties of Mauritius
Category:Treaties of Mexico
Category:Treaties of Monaco
Category:Treaties of Mongolia
Category:Treaties of Montenegro
Category:Treaties of Morocco
Category:Treaties of the People's Republic of Mozambique
Category:Treaties of Myanmar
Category:Treaties of Namibia
Category:Treaties of Nepal
Category:Treaties of the Netherlands
Category:Treaties of New Zealand
Category:Treaties of Nicaragua
Category:Treaties of Niger
Category:Treaties of Nigeria
Category:Treaties of Norway
Category:Treaties of Oman
Category:Treaties of Pakistan
Category:Treaties of Palau
Category:Treaties of Panama
Category:Treaties of Papua New Guinea
Category:Treaties of Paraguay
Category:Treaties of Peru
Category:Treaties of the Philippines
Category:Treaties of Poland
Category:Treaties of Portugal
Category:Treaties of Qatar
Category:Treaties of South Korea
Category:Treaties of Moldova
Category:Treaties of Romania
Category:Treaties of Russia
Category:Treaties of Rwanda
Category:Treaties of Samoa
Category:Treaties of San Marino
Category:Treaties of São Tomé and Príncipe
Category:Treaties of Saudi Arabia
Category:Treaties of Senegal
Category:Treaties of Serbia and Montenegro
Category:Treaties of Seychelles
Category:Treaties of Sierra Leone
Category:Treaties of Singapore
Category:Treaties of Slovakia
Category:Treaties of Slovenia
Category:Treaties of the Solomon Islands
Category:Treaties of the Somali Democratic Republic
Category:Treaties of South Africa
Category:Treaties of Spain
Category:Treaties of Sri Lanka
Category:Treaties of Saint Kitts and Nevis
Category:Treaties of Saint Lucia
Category:Treaties of Saint Vincent and the Grenadines
Category:Treaties of the Democratic Republic of the Sudan
Category:Treaties of Suriname
Category:Treaties of Eswatini
Category:Treaties of Sweden
Category:Treaties of Switzerland
Category:Treaties of Syria
Category:Treaties of Tajikistan
Category:Treaties of Thailand
Category:Treaties of North Macedonia
Category:Treaties of Togo
Category:Treaties of Tonga
Category:Treaties of Trinidad and Tobago
Category:Treaties of Tunisia
Category:Treaties of Turkey
Category:Treaties of Uganda
Category:Treaties of Ukraine
Category:Treaties of the United Arab Emirates
Category:Treaties of the United Kingdom
Category:Treaties of Tanzania
Category:Treaties of the United States
Category:Treaties of Uruguay
Category:Treaties of Uzbekistan
Category:Treaties of Vanuatu
Category:Treaties of Venezuela
Category:Treaties of Vietnam
Category:Treaties of Yemen
Category:Treaties of Yugoslavia
Category:Treaties of Zambia
Category:Treaties of Zimbabwe
Category:Animal treaties
Category:Treaties extended to Aruba
Category:Treaties extended to the Netherlands Antilles
Category:Treaties extended to Greenland
Category:Treaties extended to Portuguese Macau
Category:Treaties extended to British Honduras
Category:Treaties extended to Bermuda
Category:Treaties extended to the British Indian Ocean Territory
Category:Treaties extended to the British Virgin Islands
Category:Treaties extended to the Cayman Islands
Category:Treaties extended to the Falkland Islands
Category:Treaties extended to Gibraltar
Category:Treaties extended to Guernsey
Category:Treaties extended to British Hong Kong
Category:Treaties extended to Jersey
Category:Treaties extended to the Gilbert and Ellice Islands
Category:Treaties extended to the Isle of Man
Category:Treaties extended to Montserrat
Category:Treaties extended to the Pitcairn Islands
Category:Treaties extended to Saint Helena, Ascension and Tristan da Cunha
Category:Treaties entered into by the European Union
|
https://en.wikipedia.org/wiki/CITES
|
2025-04-05T18:27:44.463284
|
6203
|
Environmental Modification Convention
|
| type | date_drafted10 December 1976
| date_signed = 18 May 1977
| location_signed = Geneva, Switzerland
| date_sealed | date_effective 5 October 1978
| condition_effective = Ratification by 20 states
| date_expiration | signatories 48
| parties 78 (complete list)
| depositor = Secretary-General of the United Nations
| language | languagesEnglish, Arabic, Chinese, French, Russian, and Spanish
| website | wikisource Environmental Modification Convention
}}
The Environmental Modification Convention (ENMOD), formally the Convention on the Prohibition of Military or Any Other Hostile Use of Environmental Modification Techniques, is an international treaty prohibiting the military or other hostile use of environmental modification techniques having widespread, long-lasting or severe effects. It opened for signature on 18 May 1977 in Geneva and entered into force on 5 October 1978.
The Convention bans weather warfare, which is the use of weather modification techniques for the purposes of inducing damage or destruction. The Convention on Biological Diversity of 2010 would also ban some forms of weather modification or geoengineering.
Many states do not regard this as a complete ban on the use of herbicides in warfare, such as Agent Orange, but it does require case-by-case consideration.Parties
The convention was signed by 48 states; 16 of the signatories have not ratified. As of 2022 the convention has 78 state parties.
Anthropogenic climate change
ENMOD treaty members are responsible for 83% of carbon dioxide emissions since the treaty entered into force in 1978. The ENMOD treaty could potentially be used by ENMOD member states seeking climate-change loss and damage compensation from other ENMOD member states at the International Court of Justice. With the knowledge that carbon dioxide emissions can enhance extreme weather events, the continued unmitigated greenhouse gas emissions from some ENMOD member states could be viewed as ‘reckless’ in the context of deliberately declining emissions from other ENMOD member states. It is unclear whether the International Court of Justice will consider the ENMOD treaty when it issues a legal opinion on international climate change obligations requested by the United Nations General Assembly on 29 March 2023.See also
* Arms control agreements
* Environmental agreements
* Climate engineering
* Operation Popeye
* United Nations General Assembly Resolution 31/72
References
*[http://www.unog.ch Welcome! | UN GENEVA]
External links
* [https://treaties.un.org/doc/Treaties/1978/10/19781005%2000-39%20AM/Ch_XXVI_01p.pdf The text of the agreement] compiled by the NGO Committee on Education
* [https://treaties.un.org/Pages/ViewDetails.aspx?srcIND&mtdsg_noXXVI-1&chapter26&clang_en Ratifications]
* [https://web.archive.org/web/20080411175143/http://www.sunshine-project.org/enmod/ A Political Primer on the ENMOD Convention] from the Sunshine Project.
Category:Weather modification
Category:Cold War treaties
Category:International humanitarian law treaties
Category:Environmental treaties
Category:Treaties concluded in 1977
Category:Treaties entered into force in 1978
Category:1978 in the environment
Category:Treaties of the Democratic Republic of Afghanistan
Category:Treaties of Algeria
Category:Treaties of Antigua and Barbuda
Category:Treaties of Argentina
Category:Treaties of Armenia
Category:Treaties of Australia
Category:Treaties of Austria
Category:Treaties of Bangladesh
Category:Treaties of the Byelorussian Soviet Socialist Republic
Category:Treaties of Belgium
Category:Treaties of the People's Republic of Benin
Category:Treaties of the military dictatorship in Brazil
Category:Treaties of Brunei
Category:Treaties of Cameroon
Category:Treaties of Canada
Category:Treaties of Cape Verde
Category:Treaties of Chile
Category:Treaties of the People's Republic of China
Category:Treaties of Costa Rica
Category:Treaties of Cuba
Category:Treaties of Cyprus
Category:Treaties of the Czech Republic
Category:Treaties of Denmark
Category:Treaties of Dominica
Category:Treaties of Egypt
Category:Treaties of Estonia
Category:Treaties of Finland
Category:Treaties of West Germany
Category:Treaties of East Germany
Category:Treaties of Ghana
Category:Treaties of Greece
Category:Treaties of Guatemala
Category:Treaties of Honduras
Category:Treaties of the Hungarian People's Republic
Category:Treaties of India
Category:Treaties of Ireland
Category:Treaties of Japan
Category:Treaties of Kazakhstan
Category:Treaties of Kuwait
Category:Treaties of Kyrgyzstan
Category:Treaties of Laos
Category:Treaties of Lithuania
Category:Treaties of Malawi
Category:Treaties of Mauritius
Category:Treaties of the Mongolian People's Republic
Category:Treaties of the Netherlands
Category:Treaties of New Zealand
Category:Treaties of Nicaragua
Category:Treaties of Niger
Category:Treaties of North Korea
Category:Treaties of Norway
Category:Treaties of Pakistan
Category:Treaties of Panama
Category:Treaties of Papua New Guinea
Category:Treaties of the Polish People's Republic
Category:Treaties of the Socialist Republic of Romania
Category:Treaties of Saint Kitts and Nevis
Category:Treaties of the Soviet Union
Category:Treaties of Saint Lucia
Category:Treaties of Saint Vincent and the Grenadines
Category:Treaties of São Tomé and Príncipe
Category:Treaties of Slovakia
Category:Treaties of Slovenia
Category:Treaties of the Solomon Islands
Category:Treaties of South Korea
Category:Treaties of Spain
Category:Treaties of Sri Lanka
Category:Treaties of Sweden
Category:Treaties of Switzerland
Category:Treaties of Tajikistan
Category:Treaties of Tunisia
Category:Treaties of the Ukrainian Soviet Socialist Republic
Category:Treaties of the United Kingdom
Category:Treaties of the United States
Category:Treaties of Uruguay
Category:Treaties of Uzbekistan
Category:Treaties of Vietnam
Category:Treaties of the Yemen Arab Republic
Category:Treaties of South Yemen
Category:Treaties extended to Akrotiri and Dhekelia
Category:Treaties extended to the Netherlands Antilles
Category:Treaties extended to the Cook Islands
Category:Treaties extended to Niue
Category:Treaties extended to Greenland
Category:Treaties extended to the Faroe Islands
Category:United Nations treaties
Category:Treaties extended to Anguilla
Category:Treaties extended to Bermuda
Category:Treaties extended to the British Virgin Islands
Category:Treaties extended to the Cayman Islands
Category:Treaties extended to the Falkland Islands
Category:Treaties extended to Gibraltar
Category:Treaties extended to Montserrat
Category:Treaties extended to the Pitcairn Islands
Category:Treaties extended to Saint Helena, Ascension and Tristan da Cunha
Category:Treaties extended to South Georgia and the South Sandwich Islands
Category:Treaties extended to the Turks and Caicos Islands
Category:Treaties extended to Brunei (protectorate)
Category:Treaties extended to British Antigua and Barbuda
Category:Treaties extended to Saint Christopher-Nevis-Anguilla
Category:Treaties extended to British Saint Vincent and the Grenadines
Category:Treaties extended to British Saint Lucia
Category:Treaties extended to the British Solomon Islands
Category:Treaties extended to British Hong Kong
Category:Treaties extended to Macau
Category:Treaties extended to British Dominica
|
https://en.wikipedia.org/wiki/Environmental_Modification_Convention
|
2025-04-05T18:27:44.468307
|
6205
|
Chaitin's constant
|
In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt. These numbers are formed from a construction due to Gregory Chaitin.
Although there are infinitely many halting probabilities, one for each (universal, see below) method of encoding programs, it is common to use the letter to refer to them as if there were only one. Because depends on the program encoding used, it is sometimes called '''Chaitin's construction' when not referring to any specific encoding.
Each halting probability is a normal and transcendental real number that is not computable, which means that there is no algorithm to compute its digits. Each halting probability is Martin-Löf random, meaning there is not even any algorithm which can reliably guess its digits.
Background
The definition of a halting probability relies on the existence of a prefix-free universal computable function. Such a function, intuitively, represents a program in a programming language with the property that no valid program can be obtained as a proper extension of another valid program.
Suppose that is a partial function that takes one argument, a finite binary string, and possibly returns a single binary string as output. The function is called computable if there is a Turing machine that computes it, in the sense that for any finite binary strings and , if and only if the Turing machine halts with on its tape when given the input .
The function is called universal if for every computable function of a single variable there is a string such that for all , ; here represents the concatenation of the two strings and . This means that can be used to simulate any computable function of one variable. Informally, represents a "script" for the computable function , and represents an "interpreter" that parses the script as a prefix of its input and then executes it on the remainder of input.
The domain of is the set of all inputs on which it is defined. For that are universal, such a can generally be seen both as the concatenation of a program part and a data part, and as a single program for the function .
The function is called prefix-free if there are no two elements , in its domain such that is a proper extension of . This can be rephrased as: the domain of is a prefix-free code (instantaneous code) on the set of finite binary strings. A simple way to enforce prefix-free-ness is to use machines whose means of input is a binary stream from which bits can be read one at a time. There is no end-of-stream marker; the end of input is determined by when the universal machine decides to stop reading more bits, and the remaining bits are not considered part of the accepted string. Here, the difference between the two notions of program mentioned in the last paragraph becomes clear; one is easily recognized by some grammar, while the other requires arbitrary computation to recognize.
The domain of any universal computable function is a computably enumerable set but never a computable set. The domain is always Turing equivalent to the halting problem.
Definition
Let }} be the domain of a prefix-free universal computable function . The constant }} is then defined as
<math display"block">\Omega_F \sum_{p \in P_F} 2^{-|p|},</math>
where }} denotes the length of a string . This is an infinite sum which has one summand for every in the domain of . The requirement that the domain be prefix-free, together with Kraft's inequality, ensures that this sum converges to a real number between 0 and 1. If is clear from context then }} may be denoted simply , although different prefix-free universal computable functions lead to different values of .
Relationship to the halting problem
Knowing the first bits of , one could calculate the halting problem for all programs of a size up to . Let the program for which the halting problem is to be solved be bits long. In dovetailing fashion, all programs of all lengths are run, until enough have halted to jointly contribute enough probability to match these first bits. If the program has not halted yet, then it never will, since its contribution to the halting probability would affect the first bits. Thus, the halting problem would be solved for .
Because many outstanding problems in number theory, such as Goldbach's conjecture, are equivalent to solving the halting problem for special programs (which would basically search for counter-examples and halt if one is found), knowing enough bits of Chaitin's constant would also imply knowing the answer to these problems. But as the halting problem is not generally solvable, and therefore calculating any but the first few bits of Chaitin's constant is not possible for a universal language. This reduces hard problems to impossible ones, much like trying to build an oracle machine for the halting problem would be.
Interpretation as a probability
The Cantor space is the collection of all infinite sequences of 0s and 1s. A halting probability can be interpreted as the measure of a certain subset of Cantor space under the usual probability measure on Cantor space. It is from this interpretation that halting probabilities take their name.
The probability measure on Cantor space, sometimes called the fair-coin measure, is defined so that for any binary string the set of sequences that begin with has measure }}}}. This implies that for each natural number , the set of sequences in Cantor space such that 1 has measure , and the set of sequences whose th element is 0 also has measure .
Let be a prefix-free universal computable function. The domain of consists of an infinite set of binary strings
<math display"block">P \{p_1,p_2,\ldots\}.</math>
Each of these strings }} determines a subset }} of Cantor space; the set }} contains all sequences in cantor space that begin with }}. These sets are disjoint because is a prefix-free set. The sum
<math display="block">\sum_{p \in P} 2^{-|p|}</math>
represents the measure of the set
<math display="block">\bigcup_{i \in \mathbb{N}} S_i.</math>
In this way, }} represents the probability that a randomly selected infinite sequence of 0s and 1s begins with a bit string (of some finite length) that is in the domain of . It is for this reason that }} is called a halting probability.
Properties
Each Chaitin constant has the following properties:
* It is algorithmically random (also known as Martin-Löf random or 1-random). This means that the shortest program to output the first bits of must be of size at least . This is because, as in the Goldbach example, those bits enable us to find out exactly which programs halt among all those of length at most .
* As a consequence, it is a normal number, which means that its digits are equidistributed as if they were generated by tossing a fair coin.
* It is not a computable number; there is no computable function that enumerates its binary expansion, as discussed below.
* The set of rational numbers such that is computably enumerable; a real number with such a property is called a left-c.e. real number in recursion theory.
* The set of rational numbers such that is not computably enumerable. (Reason: every left-c.e. real with this property is computable, which is not.)
* It is an arithmetical number.
* It is Turing equivalent to the halting problem and thus at level |2|0}}}} of the arithmetical hierarchy.
Not every set that is Turing equivalent to the halting problem is a halting probability. A finer equivalence relation, Solovay equivalence, can be used to characterize the halting probabilities among the left-c.e. reals. One can show that a real number in is a Chaitin constant (i.e. the halting probability of some prefix-free universal computable function) if and only if it is left-c.e. and algorithmically random. is among the few definable algorithmically random numbers and is the best-known algorithmically random number, but it is not at all typical of all algorithmically random numbers. Uncomputability
A real number is called computable if there is an algorithm which, given , returns the first digits of the number. This is equivalent to the existence of a program that enumerates the digits of the real number.
No halting probability is computable. The proof of this fact relies on an algorithm which, given the first digits of , solves Turing's halting problem for programs of length up to . Since the halting problem is undecidable, cannot be computed.
The algorithm proceeds as follows. Given the first digits of and a , the algorithm enumerates the domain of until enough elements of the domain have been found so that the probability they represent is within }} of . After this point, no additional program of length can be in the domain, because each of these would add }} to the measure, which is impossible. Thus the set of strings of length in the domain is exactly the set of such strings already enumerated.
Algorithmic randomness
A real number is random if the binary sequence representing the real number is an algorithmically random sequence. Calude, Hertling, Khoussainov, and Wang showed that a recursively enumerable real number is an algorithmically random sequence if and only if it is a Chaitin's number.
Incompleteness theorem for halting probabilities
For each specific consistent effectively represented axiomatic system for the natural numbers, such as Peano arithmetic, there exists a constant such that no bit of after the th can be proven to be 1 or 0 within that system. The constant depends on how the formal system is effectively represented, and thus does not directly reflect the complexity of the axiomatic system. This incompleteness result is similar to Gödel's incompleteness theorem in that it shows that no consistent formal theory for arithmetic can be complete.
Super Omega
The first bits of Gregory Chaitin's constant are random or incompressible in the sense that they cannot be computed by a halting algorithm with fewer than bits. However, consider the short but never halting algorithm which systematically lists and runs all possible programs; whenever one of them halts its probability gets added to the output (initialized by zero). After finite time the first bits of the output will never change any more (it does not matter that this time itself is not computable by a halting program). So there is a short non-halting algorithm whose output converges (after finite time) onto the first bits of . In other words, the enumerable first bits of are highly compressible in the sense that they are limit-computable by a very short algorithm; they are not random with respect to the set of enumerating algorithms. Jürgen Schmidhuber constructed a limit-computable "Super " which in a sense is much more random than the original limit-computable , as one cannot significantly compress the Super by any enumerating non-halting algorithm.
For an alternative "Super ", the universality probability of a prefix-free universal Turing machine (UTM) namely, the probability that it remains universal even when every input of it (as a binary string) is prefixed by a random binary string can be seen as the non-halting probability of a machine with oracle the third iteration of the halting problem (i.e., }} using Turing jump notation).
See also
* Gödel's incompleteness theorems
* Kolmogorov complexity
References
<references />
Works cited
*
*
*
External links
* [https://arxiv.org/abs/1707.08109 Aspects of Chaitin's Omega] Survey article discussing recent advances in the study of Chaitin's .
* [http://www.plus.maths.org.uk/issue37/features/omega/index.html Omega and why maths has no TOEs] article based on one written by Gregory Chaitin which appeared in the August 2004 edition of Mathematics Today, on the occasion of the 50th anniversary of Alan Turing's death.
* [https://web.archive.org/web/20160211170316/https://www.cs.auckland.ac.nz/~chaitin/sciamer3.html The Limits of Reason], Gregory Chaitin, originally appeared in Scientific American, March 2006.
* [http://www.idsia.ch/~juergen/kolmogorov.html Limit-computable Super Omega more random than Omega] and generalizations of algorithmic information, by Jürgen Schmidhuber
Category:Algorithmic information theory
Category:Theory of computation
Category:Real transcendental numbers
|
https://en.wikipedia.org/wiki/Chaitin's_constant
|
2025-04-05T18:27:44.479904
|
6206
|
Computable number
|
thumb|π can be computed to arbitrary precision, while almost every real number is not computable.
In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. They are also known as the recursive numbers, effective numbers, computable reals, or recursive reals. The concept of a computable real number was introduced by Émile Borel in 1912, using the intuitive notion of computability available at the time.
Equivalent definitions can be given using μ-recursive functions, Turing machines, or λ-calculus as the formal representation of algorithms. The computable numbers form a real closed field and can be used in the place of real numbers for many, but not all, mathematical purposes.
Informal definition
In the following, Marvin Minsky defines the numbers to be computed in a manner similar to those defined by Alan Turing in 1936; i.e., as "sequences of digits interpreted as decimal fractions" between 0 and 1:
The key notions in the definition are (1) that some n is specified at the start, (2) for any n the computation only takes a finite number of steps, after which the machine produces the desired output and terminates.
An alternate form of (2) – the machine successively prints all n of the digits on its tape, halting after printing the nth – emphasizes Minsky's observation: (3) That by use of a Turing machine, a finite definition – in the form of the machine's state table – is being used to define what is a potentially infinite string of decimal digits.
This is however not the modern definition which only requires the result be accurate to within any given accuracy. The informal definition above is subject to a rounding problem called the table-maker's dilemma whereas the modern definition is not.
Formal definition
A real number a is computable if it can be approximated by some computable function f:\mathbb{N}\to\mathbb{Z} in the following manner: given any positive integer n, the function produces an integer f(n) such that:
{f(n)-1\over n} \leq a \leq {f(n)+1\over n}.
A complex number is called computable if its real and imaginary parts are computable.
Equivalent definitions
There are two similar definitions that are equivalent:
There exists a computable function which, given any positive rational error bound \varepsilon, produces a rational number r such that |r - a| \leq \varepsilon.
There is a computable sequence of rational numbers q_i converging to a such that |q_i - q_{i+1}| for each i.
There is another equivalent definition of computable numbers via computable Dedekind cuts. A computable Dedekind cut is a computable function D\; which when provided with a rational number r as input returns D(r)\mathrm{true}\; or D(r)\mathrm{false}\;, satisfying the following conditions:
\exists r D(r)=\mathrm{true}\;
\exists r D(r)=\mathrm{false}\;
(D(r)\mathrm{true}) \wedge (D(s)\mathrm{false}) \Rightarrow r
D(r)\mathrm{true} \Rightarrow \exist s>r, D(s)\mathrm{true}.\;
An example is given by a program D that defines the cube root of 3. Assuming q>0\; this is defined by:
p^3
p^3>3 q^3 \Rightarrow D(p/q)=\mathrm{false}.\;
A real number is computable if and only if there is a computable Dedekind cut D corresponding to it. The function D is unique for each computable number (although of course two different programs may provide the same function).
Properties
Not computably enumerable
Assigning a Gödel number to each Turing machine definition produces a subset S of the natural numbers corresponding to the computable numbers and identifies a surjection from S to the computable numbers. There are only countably many Turing machines, showing that the computable numbers are subcountable. The set S of these Gödel numbers, however, is not computably enumerable (and consequently, neither are subsets of S that are defined in terms of it). This is because there is no algorithm to determine which Gödel numbers correspond to Turing machines that produce computable reals. In order to produce a computable real, a Turing machine must compute a total function, but the corresponding decision problem is in Turing degree 0′′. Consequently, there is no surjective computable function from the natural numbers to the set S of machines representing computable reals, and Cantor's diagonal argument cannot be used constructively to demonstrate uncountably many of them.
While the set of real numbers is uncountable, the set of computable numbers is classically countable and thus almost all real numbers are not computable. Here, for any given computable number x, the well ordering principle provides that there is a minimal element in S which corresponds to x, and therefore there exists a subset consisting of the minimal elements, on which the map is a bijection. The inverse of this bijection is an injection into the natural numbers of the computable numbers, proving that they are countable. But, again, this subset is not computable, even though the computable reals are themselves ordered.
Properties as a field
The arithmetical operations on computable numbers are themselves computable in the sense that whenever real numbers a and b are computable then the following real numbers are also computable: a + b, a - b, ab, and a/b if b is nonzero.
These operations are actually uniformly computable; for example, there is a Turing machine which on input (A,B,\epsilon) produces output r, where A is the description of a Turing machine approximating a, B is the description of a Turing machine approximating b, and r is an \epsilon approximation of a + b.
The fact that computable real numbers form a field was first proved by Henry Gordon Rice in 1954.
Computable reals however do not form a computable field, because the definition of a computable field requires effective equality.
Non-computability of the ordering
The order relation on the computable numbers is not computable. Let A be the description of a Turing machine approximating the number a. Then there is no Turing machine which on input A outputs "YES" if a > 0 and "NO" if a \le 0. To see why, suppose the machine described by A keeps outputting 0 as \epsilon approximations. It is not clear how long to wait before deciding that the machine will never output an approximation which forces a to be positive. Thus the machine will eventually have to guess that the number will equal 0, in order to produce an output; the sequence may later become different from 0. This idea can be used to show that the machine is incorrect on some sequences if it computes a total function. A similar problem occurs when the computable reals are represented as Dedekind cuts. The same holds for the equality relation: the equality test is not computable.
While the full order relation is not computable, the restriction of it to pairs of unequal numbers is computable. That is, there is a program that takes as input two Turing machines A and B approximating numbers a and b, where a \ne b, and outputs whether a or a > b. It is sufficient to use \epsilon-approximations where \epsilon so by taking increasingly small \epsilon (approaching 0), one eventually can decide whether a or a > b.
Other properties
The computable real numbers do not share all the properties of the real numbers used in analysis. For example, the least upper bound of a bounded increasing computable sequence of computable real numbers need not be a computable real number. A sequence with this property is known as a Specker sequence, as the first construction is due to Ernst Specker in 1949. Despite the existence of counterexamples such as these, parts of calculus and real analysis can be developed in the field of computable numbers, leading to the study of computable analysis.
Every computable number is arithmetically definable, but not vice versa. There are many arithmetically definable, noncomputable real numbers, including:
any number that encodes the solution of the halting problem (or any other undecidable problem) according to a chosen encoding scheme.
Chaitin's constant, \Omega, which is a type of real number that is Turing equivalent to the halting problem.
Both of these examples in fact define an infinite set of definable, uncomputable numbers, one for each universal Turing machine.
A real number is computable if and only if the set of natural numbers it represents (when written in binary and viewed as a characteristic function) is computable.
The set of computable real numbers (as well as every countable, densely ordered subset of computable reals without ends) is order-isomorphic to the set of rational numbers.
Digit strings and the Cantor and Baire spaces
Turing's original paper defined computable numbers as follows:
(The decimal expansion of a only refers to the digits following the decimal point.)
Turing was aware that this definition is equivalent to the \epsilon-approximation definition given above. The argument proceeds as follows: if a number is computable in the Turing sense, then it is also computable in the \epsilon sense: if n > \log_{10} (1/\epsilon), then the first n digits of the decimal expansion for a provide an \epsilon approximation of a. For the converse, we pick an \epsilon computable real number a and generate increasingly precise approximations until the nth digit after the decimal point is certain. This always generates a decimal expansion equal to a but it may improperly end in an infinite sequence of 9's in which case it must have a finite (and thus computable) proper decimal expansion.
Unless certain topological properties of the real numbers are relevant, it is often more convenient to deal with elements of 2^{\omega} (total 0,1 valued functions) instead of reals numbers in [0,1]. The members of 2^{\omega} can be identified with binary decimal expansions, but since the decimal expansions .d_1d_2\ldots d_n0111\ldots and .d_1d_2\ldots d_n10 denote the same real number, the interval [0,1] can only be bijectively (and homeomorphically under the subset topology) identified with the subset of 2^{\omega} not ending in all 1's.
Note that this property of decimal expansions means that it is impossible to effectively identify the computable real numbers defined in terms of a decimal expansion and those defined in the \epsilon approximation sense. Hirst has shown that there is no algorithm which takes as input the description of a Turing machine which produces \epsilon approximations for the computable number a, and produces as output a Turing machine which enumerates the digits of a in the sense of Turing's definition. Similarly, it means that the arithmetic operations on the computable reals are not effective on their decimal representations as when adding decimal numbers. In order to produce one digit, it may be necessary to look arbitrarily far to the right to determine if there is a carry to the current location. This lack of uniformity is one reason why the contemporary definition of computable numbers uses \epsilon approximations rather than decimal expansions.
However, from a computability theoretic or measure theoretic perspective, the two structures 2^{\omega} and [0,1] are essentially identical. Thus, computability theorists often refer to members of 2^{\omega} as reals. While 2^{\omega} is totally disconnected, for questions about \Pi^0_1 classes or randomness it is easier to work in 2^{\omega}.
Elements of \omega^{\omega} are sometimes called reals as well and though containing a homeomorphic image of \mathbb{R}, \omega^{\omega} isn't even locally compact (in addition to being totally disconnected). This leads to genuine differences in the computational properties. For instance the x \in \mathbb{R} satisfying \forall(n \in \omega)\phi(x,n), with \phi(x,n) quantifier free, must be computable while the unique x \in \omega^{\omega} satisfying a universal formula may have an arbitrarily high position in the hyperarithmetic hierarchy.
Use in place of the reals
The computable numbers include the specific real numbers which appear in practice, including all real algebraic numbers, as well as e, π, and many other transcendental numbers. Though the computable reals exhaust those reals we can calculate or approximate, the assumption that all reals are computable leads to substantially different conclusions about the real numbers. The question naturally arises of whether it is possible to dispose of the full set of reals and use computable numbers for all of mathematics. This idea is appealing from a constructivist point of view, and has been pursued by the Russian school of constructive mathematics.
To actually develop analysis over computable numbers, some care must be taken. For example, if one uses the classical definition of a sequence, the set of computable numbers is not closed under the basic operation of taking the supremum of a bounded sequence (for example, consider a Specker sequence, see the section above). This difficulty is addressed by considering only sequences which have a computable modulus of convergence. The resulting mathematical theory is called computable analysis.
Implementations of exact arithmetic
Computer packages representing real numbers as programs computing approximations have been proposed as early as 1985, under the name "exact arithmetic". Modern examples include the CoRN library (Coq), and the RealLib package (C++). A related line of work is based on taking a real RAM program and running it with rational or floating-point numbers of sufficient precision, such as the package.
See also
Constructible number
Definable number
Semicomputable function
Transcomputational problem
Notes
References
Computable numbers (and Turing's a-machines) were introduced in this paper; the definition of computable numbers uses infinite decimal sequences.
Further reading
This paper describes the development of the calculus over the computable number field.
§1.3.2 introduces the definition by nested sequences of intervals converging to the singleton real. Other representations are discussed in §4.1.
Category:Computability theory
Category:Theory of computation
|
https://en.wikipedia.org/wiki/Computable_number
|
2025-04-05T18:27:44.879242
|
6207
|
Electric current
|
An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor. In electric circuits the charge carriers are often electrons moving through a wire. In semiconductors they can be electrons or holes. In an electrolyte the charge carriers are ions, while in plasma, an ionized gas, they are ions and electrons.
In the International System of Units (SI), electric current is expressed in units of ampere (sometimes called an "amp", symbol A), which is equivalent to one coulomb per second. The ampere is an SI base unit and electric current is a base quantity in the International System of Quantities (ISQ). Electric current is also known as amperage and is measured using a device called an ammeter. Current intensity is often referred to simply as current. The symbol was used by André-Marie Ampère, after whom the unit of electric current is named, in formulating Ampère's force law (1820). The notation travelled from France to Great Britain, where it became standard, although at least one journal did not change from using to until 1896.
Conventions
thumb|left|230px|The electrons, the charge carriers in an electrical circuit, flow in the direction opposite that of the conventional electric current.
thumb|right|100px|The symbol for a battery in a circuit diagram
The conventional direction of current, also known as conventional current, is arbitrarily defined as the direction in which charges flow. In a conductive material, the moving charged particles that constitute the electric current are called charge carriers. In metals, which make up the wires and other conductors in most electrical circuits, the positively charged atomic nuclei of the atoms are held in a fixed position, and the negatively charged electrons are the charge carriers, free to move about in the metal. In other materials, notably the semiconductors, the charge carriers can be positive or negative, depending on the dopant used. Positive and negative charge carriers may even be present at the same time, as happens in an electrolyte in an electrochemical cell.
A flow of positive charges gives the same electric current, and has the same effect in a circuit, as an equal flow of negative charges in the opposite direction. Since current can be the flow of either positive or negative charges, or both, a convention is needed for the direction of current that is independent of the type of charge carriers. Negatively charged carriers, such as the electrons (the charge carriers in metal wires and many other electronic circuit components), therefore flow in the opposite direction of conventional current flow in an electrical circuit. This is called the reference direction of the current I. When analyzing electrical circuits, the actual direction of current through a specific circuit element is usually unknown until the analysis is completed. Consequently, the reference directions of currents are often assigned arbitrarily. When the circuit is solved, a negative value for the current implies the actual direction of current through that circuit element is opposite that of the chosen reference direction.
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:
I = \frac{V}{R},
where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.
Alternating and direct current
In alternating current (AC) systems, the movement of electric charge periodically reverses direction. AC is the form of electric power most commonly delivered to businesses and residences. The usual waveform of an AC power circuit is a sine wave, though certain applications use alternative waveforms, such as triangular or square waves. Audio and radio signals carried on electrical wires are also examples of alternating current. An important goal in these applications is recovery of information encoded (or modulated) onto the AC signal.
In contrast, direct current (DC) refers to a system in which the movement of electric charge in only one direction (sometimes called unidirectional flow). Direct current is produced by sources such as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Alternating current can also be converted to direct current through use of a rectifier. Direct current may flow in a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams. An old name for direct current was galvanic current.
Occurrences
Natural observable examples of electric current include lightning, static electric discharge, and the solar wind, the source of the polar auroras.
Man-made occurrences of electric current include the flow of conduction electrons in metal wires such as the overhead power lines that deliver electrical energy across long distances and the smaller wires within electrical and electronic equipment. Eddy currents are electric currents that occur in conductors exposed to changing magnetic fields. Similarly, electric currents occur, particularly in the surface, of conductors exposed to electromagnetic waves. When oscillating electric currents flow at the correct voltages within radio antennas, radio waves are generated.
In electronics, other forms of electric current include the flow of electrons through resistors or through the vacuum in a vacuum tube, the flow of ions inside a battery, and the flow of holes within metals and semiconductors.
A biological example of current is the flow of ions in neurons and nerves, responsible for both thought and sensory perception.
Measurement
Current can be measured using an ammeter.
Electric current can be directly measured with a galvanometer, but this method involves breaking the electrical circuit, which is sometimes inconvenient.
Current can also be measured without breaking the circuit by detecting the magnetic field associated with the current.
Devices, at the circuit level, use various techniques to measure current:
Shunt resistors
Hall effect current sensor transducers
Transformers (however DC cannot be measured)
Magnetoresistive field sensors
Rogowski coils
Current clamps
Resistive heating
Joule heating, also known as ohmic heating and resistive heating, is the process of power dissipation by which the passage of an electric current through a conductor increases the internal energy of the conductor, converting thermodynamic work into heat. Given a surface through which a metal wire passes, electrons move in both directions across the surface at an equal rate. As George Gamow wrote in his popular science book, One, Two, Three...Infinity (1947), "The metallic substances differ from all other materials by the fact that the outer shells of their atoms are bound rather loosely, and often let one of their electrons go free. Thus the interior of a metal is filled up with a large number of unattached electrons that travel aimlessly around like a crowd of displaced persons. When a metal wire is subjected to electric force applied on its opposite ends, these free electrons rush in the direction of the force, thus forming what we call an electric current."
When a metal wire is connected across the two terminals of a DC voltage source such as a battery, the source places an electric field across the conductor. The moment contact is made, the free electrons of the conductor are forced to drift toward the positive terminal under the influence of this field. The free electrons are therefore the charge carrier in a typical solid conductor.
For a steady flow of charge through a surface, the current I (in amperes) can be calculated with the following equation:
I = {Q \over t} \, ,
where Q is the electric charge transferred through the surface over a time t. If Q and t are measured in coulombs and seconds respectively, I is in amperes.
More generally, electric current can be represented as the rate at which charge flows through a given surface as:
I = \frac{\mathrm{d}Q}{\mathrm{d}t} \, .
Electrolytes
thumb|A proton conductor in a static electric field
Electric currents in electrolytes are flows of electrically charged particles (ions). For example, if an electric field is placed across a solution of Na+ and Cl− (and conditions are right) the sodium ions move towards the negative electrode (cathode), while the chloride ions move towards the positive electrode (anode). Reactions take place at both electrode surfaces, neutralizing each ion.
Water-ice and certain solid electrolytes called proton conductors contain positive hydrogen ions ("protons") that are mobile. In these materials, electric currents are composed of moving protons, as opposed to the moving electrons in metals.
In certain electrolyte mixtures, brightly coloured ions are the moving electric charges. The slow progress of the colour makes the current visible.
Gases and plasmas
In air and other ordinary gases below the breakdown field, the dominant source of electrical conduction is via relatively few mobile ions produced by radioactive gases, ultraviolet light, or cosmic rays. Since the electrical conductivity is low, gases are dielectrics or insulators. However, once the applied electric field approaches the breakdown value, free electrons become sufficiently accelerated by the electric field to create additional free electrons by colliding, and ionizing, neutral gas atoms or molecules in a process called avalanche breakdown. The breakdown process forms a plasma that contains enough mobile electrons and positive ions to make it an electrical conductor. In the process, it forms a light emitting conductive path, such as a spark, arc or lightning.
Plasma is the state of matter where some of the electrons in a gas are stripped or "ionized" from their molecules or atoms. A plasma can be formed by high temperature, or by application of a high electric or alternating magnetic field as noted above. Due to their lower mass, the electrons in a plasma accelerate more quickly in response to an electric field than the heavier positive ions, and hence carry the bulk of the current. The free ions recombine to create new chemical compounds (for example, breaking atmospheric oxygen into single oxygen [O2 → 2O], which then recombine creating ozone [O3]).
Vacuum
Since a "perfect vacuum" contains no charged particles, it normally behaves as a perfect insulator. However, metal electrode surfaces can cause a region of the vacuum to become conductive by injecting free electrons or ions through either field electron emission or thermionic emission. Thermionic emission occurs when the thermal energy exceeds the metal's work function, while field electron emission occurs when the electric field at the surface of the metal is high enough to cause tunneling, which results in the ejection of free electrons from the metal into the vacuum. Externally heated electrodes are often used to generate an electron cloud as in the filament or indirectly heated cathode of vacuum tubes. Cold electrodes can also spontaneously produce electron clouds via thermionic emission when small incandescent regions (called cathode spots or anode spots) are formed. These are incandescent regions of the electrode surface that are created by a localized high current. These regions may be initiated by field electron emission, but are then sustained by localized thermionic emission once a vacuum arc forms. These small electron-emitting regions can form quite rapidly, even explosively, on a metal surface subjected to a high electrical field. Vacuum tubes and sprytrons are some of the electronic switching and amplifying devices based on vacuum conductivity.
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic fields occurring in certain materials when cooled below a characteristic critical temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor as it transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics.
Semiconductor
In a semiconductor it is sometimes useful to think of the current as due to the flow of positive "holes" (the mobile positive charge carriers that are places where the semiconductor crystal is missing a valence electron). This is the case in a p-type semiconductor. A semiconductor has electrical conductivity intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 10−2 to 104 siemens per centimeter (S⋅cm−1).
In the classic crystalline semiconductors, electrons can have energies only within certain bands (i.e. ranges of levels of energy). Energetically, these bands are located between the energy of the ground state, the state in which electrons are tightly bound to the atomic nuclei of the material, and the free electron energy, the latter describing the energy required for an electron to escape entirely from the material. The energy bands each correspond to many discrete quantum states of the electrons, and most of the states with low energy (closer to the nucleus) are occupied, up to a particular band called the valence band. Semiconductors and insulators are distinguished from metals because the valence band in any given metal is nearly filled with electrons under usual operating conditions, while very few (semiconductor) or virtually none (insulator) of them are available in the conduction band, the band immediately above the valence band.
The ease of exciting electrons in the semiconductor from the valence band to the conduction band depends on the band gap between the bands. The size of this energy band gap serves as an arbitrary dividing line (roughly 4 eV) between semiconductors and insulators.
With covalent bonds, an electron moves by hopping to a neighboring bond. The Pauli exclusion principle requires that the electron be lifted into the higher anti-bonding state of that bond. For delocalized states, for example in one dimensionthat is in a nanowire, for every energy there is a state with electrons flowing in one direction and another state with the electrons flowing in the other. For a net current to flow, more states for one direction than for the other direction must be occupied. For this to occur, energy is required, as in the semiconductor the next higher states lie above the band gap. Often this is stated as: full bands do not contribute to the electrical conductivity. However, as a semiconductor's temperature rises above absolute zero, there is more energy in the semiconductor to spend on lattice vibration and on exciting electrons into the conduction band. The current-carrying electrons in the conduction band are known as free electrons, though they are often simply called electrons if that is clear in context.
Current density and Ohm's law
Current density is the rate at which charge passes through a chosen unit area. It is defined as a vector whose magnitude is the current per unit cross-sectional area. As discussed in Reference direction, the direction is arbitrary. Conventionally, if the moving charges are positive, then the current density has the same sign as the velocity of the charges. For negative charges, the sign of the current density is opposite to the velocity of the charges. In SI units, current density (symbol: j) is expressed in the SI base units of amperes per square metre.
In linear materials such as metals, and under low frequencies, the current density across the conductor surface is uniform. In such conditions, Ohm's law states that the current is directly proportional to the potential difference between two ends (across) of that metal (ideal) resistor (or other ohmic device):
I = {V \over R} \, ,
where I is the current, measured in amperes; V is the potential difference, measured in volts; and R is the resistance, measured in ohms. For alternating currents, especially at higher frequencies, skin effect causes the current to spread unevenly across the conductor cross-section, with higher density near the surface, thus increasing the apparent resistance.
Drift speed
The mobile charged particles within a conductor move constantly in random directions, like the particles of a gas. (More accurately, a Fermi gas.) To create a net flow of charge, the particles must also move together with an average drift rate. Electrons are the charge carriers in most metals and they follow an erratic path, bouncing from atom to atom, but generally drifting in the opposite direction of the electric field. The speed they drift at can be calculated from the equation:
I=nAvQ \, ,
where
I is the electric current
n is number of charged particles per unit volume (or charge carrier density)
A is the cross-sectional area of the conductor
v is the drift velocity, and
Q is the charge on each particle.
Typically, electric charges in solids flow slowly. For example, in a copper wire of cross-section 0.5 mm2, carrying a current of 5 A, the drift velocity of the electrons is on the order of a millimetre per second. To take a different example, in the near-vacuum inside a cathode-ray tube, the electrons travel in near-straight lines at about a tenth of the speed of light.
Any accelerating electric charge, and therefore any changing electric current, gives rise to an electromagnetic wave that propagates at very high speed outside the surface of the conductor. This speed is usually a significant fraction of the speed of light, as can be deduced from Maxwell's equations, and is therefore many times faster than the drift velocity of the electrons. For example, in AC power lines, the waves of electromagnetic energy propagate through the space between the wires, moving from a source to a distant load, even though the electrons in the wires only move back and forth over a tiny distance.
The ratio of the speed of the electromagnetic wave to the speed of light in free space is called the velocity factor, and depends on the electromagnetic properties of the conductor and the insulating materials surrounding it, and on their shape and size.
The magnitudes (not the natures) of these three velocities can be illustrated by an analogy with the three similar velocities associated with gases. (See also hydraulic analogy.)
The low drift velocity of charge carriers is analogous to air motion; in other words, winds.
The high speed of electromagnetic waves is roughly analogous to the speed of sound in a gas (sound waves move through air much faster than large-scale motions such as convection)
The random motion of charges is analogous to heatthe thermal velocity of randomly vibrating gas particles.
See also
Current density
Displacement current (electric) and
Electric shock
Electrical measurements
History of electrical engineering
Polarity symbols
International System of Quantities
SI electromagnetism units
Single-phase electric power
Static electricity
Three-phase electric power
Two-phase electric power
Notes
References
Category:SI base quantities
Category:Electromagnetic quantities
|
https://en.wikipedia.org/wiki/Electric_current
|
2025-04-05T18:27:44.940602
|
6208
|
Charles Ancillon
|
| death_place = Berlin, Germany
| othername | occupation Diplomat<br>Jurist<br>Educator
| years_active | spouse
| signature =
}}
Charles Ancillon (28 July 16595 July 1715) was a French jurist and diplomat.LifeAncillon was born in Metz into a distinguished family of Huguenots. His father, David Ancillon (1617–1692), was obliged to leave France on the revocation of the Edict of Nantes, and became pastor of the French Protestant community in Berlin.
Ancillon studied law at Marburg, Geneva and Paris, where he was called to the bar. At the request of the Huguenots at Metz, he pleaded its cause at the court of King Louis XIV, urging that it should be excepted in the revocation of the Edict of Nantes, but his efforts were unsuccessful, and he joined his father in Berlin. He was at once appointed by Elector Frederick III "juge et directeur de colonie de Berlin." He also became the first headmaster of Französisches Gymnasium Berlin. Before this, he had published several works on the revocation of the Edict of Nantes and its consequences, but his literary capacity was mediocre, his style stiff and cold, and it was his personal character rather than his reputation as a writer that earned him the confidence of the elector.<ref name="EB1911"/>
In 1687 Ancillon was appointed head of the so-called Academie des nobles, the principal educational establishment of the state; later on, as councillor of embassy, he took part in the negotiations which led to the assumption of the title of "King in Prussia" by the elector. In 1699 he succeeded Samuel Pufendorf as historiographer to the elector, and the same year replaced his uncle Joseph Ancillon as judge of all the French refugees in the Margraviate of Brandenburg.<ref name="EB1911"/>
Ancillon is mainly remembered for what he did for education in Brandenburg-Prussia, and the share he took, in co-operation with Gottfried Leibniz, in founding the Academy of Berlin. Of his fairly numerous works the most valued is the "''Histoire de l'etablissement des Francais refugies dans les etats de Brandebourg''" published in Berlin in 1690.<ref name"EB1911"/>Family* Friedrich Ancillon, his grandson, a Prussian historian and statesmanReferencesExternal links*
*
Category:1659 births
Category:1715 deaths
Category:Lawyers from Metz
Category:18th-century French historians
Category:Diplomats for the Kingdom of Prussia
Category:17th-century French lawyers
Category:Members of the Prussian Academy of Sciences
Category:Huguenots
|
https://en.wikipedia.org/wiki/Charles_Ancillon
|
2025-04-05T18:27:44.948136
|
6210
|
Clark Ashton Smith
|
Clark Ashton Smith (January 13, 1893 – August 14, 1961) was an influential American writer of fantasy, horror, and science fiction stories and poetry, and an artist. He achieved early recognition in California (largely through the enthusiasm of George Sterling) for traditional verse in the vein of Swinburne. As a poet, Smith is grouped with the West Coast Romantics alongside Joaquin Miller, Sterling, and Nora May French and remembered as "The Last of the Great Romantics" and "The Bard of Auburn". Smith's work was praised by his contemporaries. H. P. Lovecraft stated that "in sheer daemonic strangeness and fertility of conception, Clark Ashton Smith is perhaps unexcelled", and Ray Bradbury said that Smith "filled my mind with incredible worlds, impossibly beautiful cities, and still more fantastic creatures". Additional writers influenced by Smith include Leigh Brackett, Harlan Ellison, Stephen King, Fritz Lieber, George R. R. Martin, and Donald Sidney-Fryer.
Smith was one of "the big three of Weird Tales, with Robert E. Howard and H. P. Lovecraft", though some readers objected to his morbidness and violation of pulp traditions. The fantasy writer and critic L. Sprague de Camp said of him that "nobody since Poe has so loved a well-rotted corpse". Smith was a member of the Lovecraft circle, and his literary friendship with Lovecraft lasted from 1922 until Lovecraft's death in 1937. His work is marked by an extraordinarily rich and ornate vocabulary, a cosmic perspective and a vein of sardonic and sometimes ribald humor.
Of his writing style, Smith stated: "My own conscious ideal has been to delude the reader into accepting an impossibility, or series of impossibilities, by means of a sort of verbal black magic, in the achievement of which I make use of prose-rhythm, metaphor, simile, tone-color, counter-point, and other stylistic resources, like a sort of incantation."
Biography
Early life and education
Smith was born January 13, 1893, in Long Valley, Placer County, California, into a family of English and New England heritage. He spent most of his life in the small town of Auburn, California, living in a cabin built by his parents, Fanny and Timeus Smith. Smith professed to hate the town's provincialism but rarely left it until he married late in life.
His formal education was limited: he suffered from psychological disorders including intense agoraphobia, and although he was accepted to high school after attending eight years of grammar school, his parents decided it was better for him to be taught at home. An insatiable reader with an extraordinary eidetic memory, Smith appeared to retain most or all of whatever he read. After leaving formal education, he embarked upon a self-directed course of literature, including Robinson Crusoe, Gulliver's Travels, the fairy tales of Hans Christian Andersen and Madame d'Aulnoy, the Arabian Nights and the poems of Edgar Allan Poe. He read an unabridged dictionary word for word, studying not only the definitions of the words but also their etymology.
The other main course in Smith's self-education was to read the complete 11th edition of the Encyclopædia Britannica at least twice. Smith later taught himself French and Spanish to translate verse out of those languages, including works by Gérard de Nerval, Paul Verlaine, Amado Nervo, Gustavo Adolfo Bécquer and all but 6 of Charles Baudelaire's 157 poems in The Flowers of Evil.
Early writing
thumb|right|Smith as depicted in Wonder Stories in 1930
His first literary efforts, at the age of 11, took the form of fairy tales and imitations of the Arabian Nights. Later, he wrote long adventure novels dealing with Oriental life. By 14 he had already written a short adventure novel called The Black Diamonds which was lost for years until published in 2002. Another juvenile novel was written in his teenaged years: The Sword of Zagan (unpublished until 2004). Like The Black Diamonds, it uses a medieval, Arabian Nights-like setting, and the Arabian Nights, like the fairy tales of the Brothers Grimm and the works of Edgar Allan Poe, are known to have strongly influenced Smith's early writing, as did William Beckford's Vathek.
When he was 15, Smith read George Sterling's fantasy-horror poem "A Wine of Wizardry" in a national magazine (which he later described as "In the ruck of magazine verse it was like finding a fire-opal of the Titans in a potato bin") and decided he wanted to become a poet. At age 17, he sold several tales to The Black Cat, a magazine which specialized in unusual tales. He also published some tales in the Overland Monthly in this brief foray into fiction which preceded his poetic career.
However, it was primarily poetry that motivated the young Smith and he confined his efforts to poetry for more than a decade. In his later youth, Smith met Sterling through a member of the local Auburn Monday Night Club, where Smith read several of his poems with considerable success. On a month-long visit to Sterling in Carmel, California, Smith was introduced by Sterling to the poetry of Charles Baudelaire.
He became Sterling's protégé and Sterling helped him to publish his first volume of poems, The Star-Treader and Other Poems, at the age of 19. Smith received international acclaim for the collection. The Star-Treader was received very favorably by American critics, one of whom named Smith "the Keats of the Pacific". Smith briefly moved among the circle that included Ambrose Bierce and Jack London, but his early fame soon faded away.
Health breakdown period
A little later, Smith's health broke down and for eight years his literary production was intermittent, though he produced his best poetry during this period. A small volume, Odes and Sonnets, was brought out in 1918. Smith came into contact with literary figures who would later form part of H.P. Lovecraft's circle of correspondents; Smith knew them far earlier than Lovecraft. These figures include poet Samuel Loveman and bookman George Kirk. It was Smith who in fact later introduced Donald Wandrei to Lovecraft. For this reason, it has been suggested that Lovecraft might as well be referred to as a member of a "Smith" circle as Smith was a member of a Lovecraft one.
In 1920 Smith composed a celebrated long poem in blank verse, The Hashish Eater, or The Apocalypse of Evil, published in Ebony and Crystal (1922). This was followed by a fan letter from H. P. Lovecraft, which was the beginning of 15 years of friendship and correspondence. With studied playfulness, Smith and Lovecraft borrowed each other's coinages of place names and the names of strange gods for their stories, though so different is Smith's treatment of the Lovecraft theme that it has been dubbed the "Clark Ashton Smythos."
In 1925 Smith published Sandalwood, which was partly funded by a gift of $50 from Donald Wandrei. He wrote little fiction in this period with the exception of some imaginative vignettes or prose poems. Smith was poor for most of his life and often did hard manual jobs such as fruit picking and woodcutting to support himself and his parents. He was an able cook and made many kinds of wine. He also did well digging, typing and journalism, as well as contributing a column to The Auburn Journal and sometimes worked as its night editor.
One of Smith's artistic patrons and frequent correspondents was San Francisco businessman Albert Bender.
Prolific fiction-writing period
At the beginning of the Depression in 1929, with his aged parents' health weakening, Smith resumed fiction writing and turned out more than a hundred short stories between 1929 and 1934, nearly all of which can be classed as weird horror or science fiction. Like Lovecraft, he drew upon the nightmares that had plagued him during youthful spells of sickness. Brian Stableford has written that the stories written during this brief phase of hectic productivity "constitute one of the most remarkable oeuvres in imaginative literature".
He published at his own expense a volume containing six of his best stories, The Double Shadow and Other Fantasies, in an edition of 1000 copies printed by the Auburn Journal. The theme of much of his work is egotism and its supernatural punishment; his weird fiction is generally macabre in subject matter, gloatingly preoccupied with images of death, decay and abnormality.
Most of Smith's weird fiction falls into four series set variously in Hyperborea, Poseidonis, Averoigne and Zothique. Hyperborea, which is a lost continent of the Miocene period, and Poseidonis, which is a remnant of Atlantis, are much the same, with a magical culture characterized by bizarreness, cruelty, death and postmortem horrors. Averoigne is Smith's version of pre-modern France, comparable to James Branch Cabell's Poictesme. Zothique exists millions of years in the future. It is "the last continent of earth, when the sun is dim and tarnished". These tales have been compared to the Dying Earth sequence of Jack Vance.
In 1933 Smith began corresponding with Robert E. Howard, the Texan creator of Conan the Barbarian. From 1933 to 1936, Smith, Howard and Lovecraft were the leaders of the Weird Tales school of fiction and corresponded frequently, although they never met. The writer of oriental fantasies E. Hoffmann Price is the only man known to have met all three in the flesh.
Critic Steve Behrends has suggested that the frequent theme of 'loss' in Smith's fiction (many of his characters attempt to recapture a long-vanished youth, early love, or picturesque past) may reflect Smith's own feeling that his career had suffered a "fall from grace":
Mid-late career: return to poetry and sculpture
In September 1935, Smith's mother Fanny died. Smith spent the next two years nursing his father through his last illness. Timeus died in December 1937. Aged 44, Smith now virtually ceased writing fiction. He had been severely affected by several tragedies occurring in a short period of time: Robert E. Howard's death by suicide (1936), Lovecraft's death from cancer (1937) and the deaths of his parents, which left him exhausted. As a result, he withdrew from the scene, marking the end of Weird Taless Golden Age. He began sculpting and resumed the writing of poetry. However, Smith was visited by many writers at his cabin, including Fritz Leiber, Rah Hoffman, Francis T. Laney and others.
In 1942, three years after August Derleth founded Arkham House for the purpose of preserving the work of H.P. Lovecraft, Derleth published the first of several major collections of Smith's fiction, Out of Space and Time (1942). This was followed by Lost Worlds (1944). The books sold slowly, went out of print and became costly rarities. Derleth published five more volumes of Smith's prose and two of his verse, and at his death in 1971 had a large volume of Smith's poems in press.
Later life, marriage and death
In 1953, Smith suffered a coronary attack. Aged 61, he married Carol(yn) Jones Dorman on November 10, 1954. Dorman had much experience in Hollywood and radio public relations. After honeymooning at the Smith cabin, they moved to Pacific Grove, California, where he set up a household including her three children from a previous marriage. For several years he alternated between the house on Indian Ridge and their house in Pacific Grove. Smith having sold most of his father's tract, in 1957 the old house burned – the Smiths believed by arson, others said by accident.
Smith now reluctantly did gardening for other residents at Pacific Grove, and grew a goatee. He spent much time shopping and walking near the seafront but despite Derleth's badgering, resisted the writing of more fiction. In 1961 he suffered a series of strokes and in August 1961 he quietly died in his sleep, aged 68. After Smith's death, Carol remarried (becoming Carolyn Wakefield) and subsequently died of cancer.
The poet's ashes were buried beside, or beneath, a boulder to the immediate west of where his childhood home (destroyed by fire in 1957) stood; some were also scattered in a stand of blue oaks near the boulder. There was no marker. Plaques recognizing Smith have been erected at the Auburn Placer County Library in 1985 and in Bicentennial Park in Auburn in 2003.
Bookseller Roy A. Squires was appointed Smith's "west coast executor", with Jack L. Chalker as his "east coast executor". Squires published many letterpress editions of individual Smith poems.
Smith's literary estate is represented by his stepson, Prof William Dorman, director of CASiana Literary Enterprises. Arkham House owns the copyright to many Smith stories, though some are now in the public domain.
For 'posthumous collaborations' of Smith (stories completed by Lin Carter), see the entry on Lin Carter.
Artistic periods
While Smith was always an artist who worked in several very different media, it is possible to identify three distinct periods in which one form of art had precedence over the others.
Poetry: until 1925
Smith published most of his volumes of poetry in this period, including the aforementioned The Star-Treader and Other Poems, as well as Odes and Sonnets (1918), Ebony and Crystal (1922) and Sandalwood (1925). His long poem The Hashish-Eater; Or, the Apocalypse of Evil was written in 1920.
Weird fiction: 1926–1935
thumb|"The Hunters from Beyond", one of Clark Ashton Smith's best-known stories, was first published in the October 1932 issue of Strange Tales.
Smith wrote most of his weird fiction and Cthulhu Mythos stories, inspired by H. P. Lovecraft. Creatures of his invention include Aforgomon, Rlim-Shaikorth, Mordiggian, Tsathoggua, the wizard Eibon, and various others. In an homage to his friend, Lovecraft referred in "The Whisperer in Darkness" and "The Battle That Ended the Century" (written in collaboration with R. H. Barlow) to an Atlantean high-priest, "Klarkash-Ton".
Smith's weird stories form several cycles, called after the lands in which they are set: Averoigne, Hyperborea, Mars, Poseidonis, Zothique. To some extent Smith was influenced in his vision of such lost worlds by the teachings of Theosophy and the writings of Helena Blavatsky. Stories set in Zothique belong to the Dying Earth subgenre. Amongst Smith's science fiction tales are stories set on Mars and the invented planet of Xiccarph.
His short stories originally appeared in the magazines Weird Tales, Strange Tales, Astounding Stories, Stirring Science Stories and Wonder Stories.
Clark Ashton Smith was the third member of the great triumvirate of Weird Tales, with Lovecraft and Robert E. Howard.
Many of Smith's stories were published in six hardcover volumes by August Derleth under his Arkham House imprint. For a full bibliography to 1978, see Sidney-Fryer, Emperor of Dreams (cited below). S. T. Joshi is working with other scholars to produce an updated bibliography of Smith's work.
A selection of Smith's best-known tales includes:
"The Last Incantation" — Weird Tales, June 1930 LW2
"A Voyage to Sfanomoe" — Weird Tales, August 1931 LW2
"The Tale of Satampra Zeiros" — Weird Tales November 1931 LW2
"The Door to Saturn" — Strange Tales, January 1932 LW2
"The Planet of the Dead" — Weird Tales, March 1932 LW2
"The Gorgon" — Weird Tales, April 1932 LW2
"The Letter from Mohaun Los" (under the title of "Flight into Super-Time") — Wonder Stories, August 1932 LW1
"The Empire of the Necromancers" — Weird Tales, September 1932 LW1
"The Hunters from Beyond" — Strange Tales, October 1932 LW1
"The Isle of the Torturers" — Weird Tales, March 1933 LW1
"The Light from Beyond" — Wonder Stories, April 1933 LW1
"The Beast of Averoigne" — Weird Tales, May 1933 LW1
"The Holiness of Azedarac" — Weird Tales, November 1933 LW1
"The Demon of the Flower" — Astounding Stories, December 1933 LW2
"The Death of Malygris" — Weird Tales, April 1934 LW2
"The Plutonium Drug" — Amazing Stories, September 1934 LW2
"The Seven Geases" — Weird Tales, October 1934 LW2
"Xeethra" — Weird Tales, December 1934 LW1
"The Flower-Women" — Weird Tales, May 1935 LW2
"The Treader of the Dust" — Weird Tales, August 1935 LW1
"Necromancy in Naat" — Weird Tales, July 1936 LW1
"The Maze of Maal Dweb" — Weird Tales, October 1938 LW2
"The Coming of the White Worm" — Stirring Science Stories, April 1941 LW2
Visual art: 1935–1961
By this time his interest in writing fiction began to lessen and he turned to creating sculptures from soft rock such as soapstone. Smith also made hundreds of fantastic paintings and drawings.
Bibliography
The authoritative bibliography on Smith's work is S. T. Joshi, David E. Schultz, and Scott Conners' Clark Ashton Smith: A Comprehensive Bibliography. NY: Hippocampus Press, 2020. The first Smith bibliography, which focused on his short fiction, was The Tales Of Clark Ashton Smith, published by Thomas G L Cockcroft in New Zealand in 1951.
Books published in Smith's lifetime
thumb|First edition
thumb|First edition
1912: The Star-Treader and Other Poems. San Francisco: A.M. Robertson, Nov 1912. 100 pages. 2000 copies. Some copies have a frontispiece photo by Bianca Conti; others lack it.
1918: Odes and Sonnets. San Francisco: The Book Club of California, June 1918. 28 pages. 300 copies.
1922: Ebony and Crystal: Poems in Verse and Prose. Auburn CA: The Auburn Journal Press, Oct 1925. 43 pages. Limited to 500 copies signed by Smith. Some copies are found with corrections in Smith's hand to typos in the text.
1925: Sandalwood. Auburn CA: The Auburn Journal Press, Oct 1925. Verse. 43 pages. Limited to 250 (i.e. 225) numbered copies signed by Smith. Some copies are found with corrections in Smith's hand to typos in the text.
1933: The Double Shadow and Other Fantasies. Auburn, CA: The Auburn Journal Press, 1933. Short stories. Limited to 1000 copies in grey paper wrappers.
1937: Nero and Other Poems. Lakeport CA: The Futile Press, May 1937. 24 pages. c.250 copies. The poems herein were revised by Smith from their first appearances in The Star-Treader and Other Poems. Some copies have laid in the three page essay "The Price of Poetry", on Smith's verse, by David Warren Ryder, which was printed to accompany the book. According to the official Smith bibliography, the volume was also issued with a broadside, "Outlanders" - a 1934 sonnet which made its first appearance in print here. Roy A. Squires purchased spare sheets of the volume from Groo Beck of Futile Press, sufficient to produce a 'second state' of 13 copies, which was specially bound by Kristina Etchison and published by bookdealer Terence McVicker. (This 2nd state not noted in the official bibliography.)
1951: The Dark Chateau and Other Poems. Sauk City, WI: Arkham House, Dec 1951. 63 pages. 563 copies.
1958: Spells and Philtres. Sauk City: Arkham House, March 1958. Verse. 54 pages. 519 copies.
Books published posthumously
1962: The Hill of Dionysus – A Selection. Pacific Grove, CA: Roy A. Squires and Clyde Beck. Verse. This volume was prepared while Smith was still living but he died before it could see print. It was published 'In memoriam'.
1971: Selected Poems. Sauk City, WI: Arkham House, Nov 1971. This volume was delivered by the author to Arkham House in December 1949 but remained unpublished until 1971.
Night Shade Books
The Collected Fantasies of Clark Ashton Smith 5-volume work
Miscellaneous Writings. Originally announced as Tales of India and Irony (a collection of non-fantasy/science fiction/horror tales, planned to be available only to subscribers of above collection). Now commercially available.
Red World of Polaris (complete tales of Captain Volmar)
Hippocampus Press
The Complete Poetry and Translations of Clark Ashton Smith (3 vols)
The Black Diamonds. A juvenile Oriental fantasy.
The Last Oblivion: Best Fantastic Poems of Clark Ashton Smith
The Sword of Zagan and Other Writings. Juvenile Oriental fantasy.
The Shadow of the Unattained: Letters of George Sterling and Clark Ashton Smith
The Freedom of Fantastic Things: Selected Criticism on Clark Ashton Smith
The Hashish-Eater. (2008). Edited with notes etc. by Donald Sidney-Fryer. Introduction by Ron Hilger. Includes a CD audio recording of Sidney-Fryer reading "The Hashish-Eater" and (on a hidden track) a selection of other poems by Smith.
The Averoigne Chronicles: The Complete Averoigne Stories of Clark Ashton Smith
Zothique: The Final Cycle by Clark Ashton Smith
Arkham House
Out of Space and Time
Lost Worlds
Genius Loci and Other Tales
The Dark Chateau
Spells and Philtres
The Abominations of Yondo
Tales of Science and Sorcery
Poems in Prose
Other Dimensions (o.o.p.)
Selected Poems
The Black Book of Clark Ashton Smith
A Rendezvous in Averoigne
Selected Letters of Clark Ashton Smith
Spearman (reprinted from Arkham House)
Lost Worlds hardcover 1971
Out of Space and Time 1971
Genius Loci and Other Tales hardcover 1972
The Abominations of Yondo 1972
Panther (reprinted from Arkham House)
Lost Worlds (published in 2 volumes, , )
Genius Loci
The Abominations of Yondo
Other Dimensions (published in 2 volumes, , )
Out of Space and Time (published in 2 volumes, , )
Tales of Science and Sorcery
Ballantine Adult Fantasy series
Zothique 1970
Hyperborea 1971
Xiccarph 1972
Poseidonis 1973
Averoigne (reportedly compiled by series editor Lin Carter, but never released)
Roy A. Squires
Roy A. Squires, California-based bookman and letterpress printer, issued many limited edition pamphlets consisting of individual Smith poems and prose poems during the 1970s.
Wildside Press
The Double Shadow
The Maker of Gargoyles and Other Stories
The White Sybil and Other Stories
Timescape Books
The City of the Singing Flame 1981
The Last Incantation 1982
The Monster of the Prophecy 1983
Gollancz
The Emperor of Dreams. Ed, Stephen Jones. 2002. An omnibus edition in paperback of Smith's best tales.
Bancroft Library
In the Line of the Grotesque and Monstrous. Introduction by D.S. Black. Berkeley: The Bancroft Library, 2004. Prints the text of three letters by Smith to Samuel Loveman. 50 copies only printed, in burnt orange wrappers. Printed on the Bancroft library's 1856 Albion handpress.
The RAS Press
The Black Abbot of Puthuum. Glendale, CA: The RAS Press, Oct 2007. Limited to 250 numbered copies.(This press was founded by Roy. A. Squires and is currently run by bookseller Terence McVicker).
HIH Art Studios
Shadows Seen and Unseen: Poetry from the Shadows. Edited by Raymond L.F. Johnson and Ardath W. Winterowd and signed by both editors. San Jose, CA: HIH Art Studios, 2007.
Penguin Books
The Dark Eidolon and Other Fantasies. Ed, S. T. Joshi. 2014.
Other (essays, letters, etc)
Smith, Clark Ashton. Planets and Dimensions: Collected Essays. Edited by Charles K. Wolfe. Baltimore MD: Mirage Press, 1973.
David E. Schultz and S. T. Joshi (eds). The Shadow of the Unattained: The Letters of George Sterling and Clark Ashton Smith NY: Hippocampus Press, 2005.
David E. Schultz and S. T. Joshi (eds). Dawnward Spire, Lonely Hill: The Letters of H. P. Lovecraft and Clark Ashton Smith. NY: Hippocampus Press, 2017.
David E. Schultz and S.T. Joshi (eds). Eccentric, Impractical Devils: The Letters of August Derleth and Clark Ashton Smith. NY: Hippocampus Press, 2020.
S.T. Joshi and David E. Schultz (eds). Born Under Saturn: The Letters of Samuel Loveman and Clark Ashton Smith NY: Hippocampus Press, 2021.
David E. Schultz and S. T. Joshi (eds). "To Worlds Unknown: The Letters of Clark Ashton Smith, Donald Wandrei, Howard Wandrei, and R. H. Barlow. NY: Hippocampus Press, 2023.
Schultz and Joshi are preparing a volume of Smith's letters to miscellaneous correspondents.
Media adaptations
Visual
"The Double Shadow" was filmed by Azathoth Productions, Newcastle, Australia, on Super 8 film in 1975, with a script by Leigh Blackmore.
"The Return of the Sorcerer" was adapted for an episode of the television series Night Gallery, starring Vincent Price and Bill Bixby.
"The Seed from the Sepulcher", "The Vaults of Yoh Vombis" and "The Return of the Sorcerer" were adapted as ten-page comics by Richard Corben, published in DenSaga 1, 2 and 3 respectively (Fantagor Press 1992–1993).
"Mother of Toads" was adapted as segment one of the six-segment horror anthology film The Theatre Bizarre (2011).
Audio
Clark Ashton Smith: Live from Auburn: The Elder Tapes. In the late 1950s Smith recorded a number of his poems on the tape-recorder of his friend Robert B. Elder. Elder chose the 11 poems at random from Smith's books The Dark Chateau and "Spells and Philtres". (Elder had first met Smith when reporting on his 1954 wedding to the former Carol Dorman for The Auburn Courier and they became friends when Smith praised Elder's novel Whom the Gods Destroy.) In 1995 Necronomicon Press released the audiocassette Clark Ashton Smith: Live from Auburn: The Elder Tapes, which includes an introduction by Elder and then Smith reading his poems. The recording was produced by Wayne Haigh. The cassette was accompanied by a booklet featuring a c.1960 photo of Smith and reprints all 11 poems. Gahan Wilson provided the cover art for the cassette and booklet. The recording has not been released on CD.
The Hashish-Eater and Other Poems. Nampa, Idaho: Fedogan and Bremer, 2018. Running time 68 mins. Includes Donald Sidney-Fryer's readings of "The Hashish-Eater" and a selection of other Smith poems, identical to the selection on the CD which accompanied the 2008 Hippocampus Press volume "The Hashish-Eater"; here, however, an orchestral soundtrack by Graham Plowman has been added. Booklet notes by Ron Hilger.
See also
Cordwainer Smith Rediscovery Award
"A Wine of Wizardry"
References
Citations
General and cited sources
Herron, Don (October 2000). "Collecting Clark Ashton Smith". Firsts.
Joshi, S. T. (2008). "Clark Ashton Smith: Beauty Is for the Few," chapter 2 in Emperors of Dreams: Some Notes on Weird Poetry. Sydney: P'rea Press. (pbk) and (hbk).
Murray, Will. "The Clark Ashton Smythos" in Price, Robert M. (ed.). The Horror of It All: Encrusted Gems from the Crypt of Cthulhu. Mercer Island WA: Starmont House, 1990. .
Further reading
Bibliographies
Cockcroft, Thomas G. L. The Tales of Clark Ashton Smith: A Bibliography. Lower Hutt, New Zealand: Cockcroft, Nov 1961 (500 copies). The first published bibliography on Smith; superseded by Donald Sidney-Fryer's Emperor of Dreams (1978) – see below.
Joshi, S. T., David E. Schultz and Scott Connors. Clark Ashton Smith: A Comprehensive Bibliography. NY: NY: Hippocampus Press, 2020.
Sidney-Fryer, Donald. Emperor of Dreams: A Clark Ashton Smith Bibliography. West Kingston, RI: Donald M. Grant Publishers, 1978. A substantial work of scholarship which remains valuable for its critical appreciations but is now over thirty years out of date. A quantity of more recent bibliographical information can be found at the Bibliography section of the Eldritch Dark site online (see External Links). Both are completely superseded bibliographically by the Joshi, Schultz and Connors bibliography of 2020.
Journals devoted to Smith's life and work
Behrends, Steve. Klarkash-Ton: The Journal of Smith Studies No 1 (June 1988), Cryptic Publications. This journal was retitled by the new publisher as from Issue 2, thus the first issue of The Dark Eidolon: The Journal of Smith Studies, (Necronomicon Press) is numbered "2" (it appeared June 1989). There were only 3 issues in total. No 3 appeared in Dec 2002.
Connors, Scott and Ronald S. Hilger (eds). Lost Worlds: The Journal of Clark Ashton Smith Studies, Seele Brennt Publications. Issued annually, five numbers (2003–2008).
Morris, Harry O. (ed). Nyctalops magazine. Special Clark Ashton Smith issue, 96 pp. (1973)
Essays and standalone critical works
Behrends, Steve. Clark Ashton Smith. Starmont Reader's Guide 49. Mercer Island, WA: Starmont House, 1990.
Behrends, Steve. "The Song of the Necromancer: 'Loss' in Clark Ashton Smith's Fiction." Studies in Weird Fiction, 1, No 1 (Summer 1986): 3–12.
Connors, Scott. The Freedom of Fantastic Things: Selected Criticism on Clark Ashton Smith. NY: Hippocampus Press, 2006.
de Camp, L. Sprague. "Sierra Shaman: Clark Ashton Smith," in Literary Swordsmen and Sorcerers: The Makers of Heroic Fantasy. Sauk City,. WI: Arkham House, 1976, 211–12.
Fait, Eleanor. "Auburn Artist-Poet Utilizes Native Rock in Sculptures.". Sacramento Union (Dec 21, 1941), 4C.
Haefele, John D. "Far from Time: Clark Ashton Smith, August Derleth, and Arkham House." Weird Fiction Review No 1 (Fall 2010), 154–189.
Hilger, Ronald. One Hundred Years of Klarkash-Ton. Averon Press, 1996.
Schultz, David E. and Scott Connors (ed). Selected Letters of Clark Ashton Smith. Sauk City, WI: Arkham House, 2003.
Schultz, David E and S.T. Joshi. The Shadow of the Unattained: The Letters of George Sterling and Clark Ashton Smith. NY: Hippocampus Press, 2005.
Sidney-Fryer, Donald. The Last of the Great Romantic Poets. Albuquerque NM: Silver Scarab Press, 1973.
Sidney-Fryer, Donald. Clark Ashton Smith: The Sorcerer Departs. West Hills, CA: Tsathoggua Press, Jan 1997. Dole: Silver Key Press, 2007. An updated/revised version of Sidney-Fryer's essay in the Special CAS Issue of Nyctalops (see above under Morris). An uncredited extract from this work, as "A Biography of Clark Ashton Smith," may be found online at
External links
The Eldritch Dark – This website contains almost all of Clark Ashton Smith's written work, as well as a comprehensive selection of his art, biographies, a bibliography, a discussion board, readings, fiction tributes and more.
Eldonejo 'Mistera Sturno' – A growing collection of authorized translations into Esperanto for free distribution as ebooks.
Smith's poem "A Chant to Sirius" read by Leigh Blackmore
Clark Ashton Smith: Poems – A collection of Clark Ashton Smith's early poetry.
Clark Ashton Smith at the Encyclopedia of Science Fiction
Clark Ashton Smith at the Encyclopedia of Fantasy
Category:1893 births
Category:1961 deaths
Category:20th-century American male writers
Category:20th-century American novelists
Category:American fantasy writers
Category:American horror writers
Category:American male novelists
Category:American male poets
Category:American male short story writers
Category:American people of English descent
Category:American science fiction writers
Category:20th-century American short story writers
Category:Cthulhu Mythos writers
Category:People from Auburn, California
Category:People from Mono County, California
Category:People from Pacific Grove, California
Category:Pulp fiction writers
Category:American weird fiction writers
Category:Writers from California
Category:Translators of Charles Baudelaire
Category:Translators of Gérard de Nerval
|
https://en.wikipedia.org/wiki/Clark_Ashton_Smith
|
2025-04-05T18:27:45.017593
|
6211
|
Context-sensitive grammar
|
A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that there are languages that can be described by a CSG but not by a context-free grammar. Context-sensitive grammars are less general (in the same sense) than unrestricted grammars. Thus, CSGs are positioned between context-free and unrestricted grammars in the Chomsky hierarchy.
A formal language that can be described by a context-sensitive grammar, or, equivalently, by a noncontracting grammar or a linear bounded automaton, is called a context-sensitive language. Some textbooks actually define CSGs as non-contracting, although this is not how Noam Chomsky defined them in 1959. This choice of definition makes no difference in terms of the languages generated (i.e. the two definitions are weakly equivalent), but it does make a difference in terms of what grammars are structurally considered context-sensitive; the latter issue was analyzed by Chomsky in 1963.
Chomsky introduced context-sensitive grammars as a way to describe the syntax of natural language where it is often the case that a word may or may not be appropriate in a certain place depending on the context. Walter Savitch has criticized the terminology "context-sensitive" as misleading and proposed "non-erasing" as better explaining the distinction between a CSG and an unrestricted grammar.
Although it is well known that certain features of languages (e.g. cross-serial dependency) are not context-free, it is an open question how much of CSGs' expressive power is needed to capture the context sensitivity found in natural languages. Subsequent research in this area has focused on the more computationally tractable mildly context-sensitive languages. The syntaxes of some visual programming languages can be described by context-sensitive graph grammars.
Formal definition
Formal grammar
Let us notate a formal grammar as G = (N, \Sigma, P, S), with N a set of nonterminal symbols, \Sigma a set of terminal symbols, P a set of production rules, and S \in N the start symbol.
A string u \in (N \cup \Sigma)^* directly yields, or directly derives to, a string v \in (N \cup \Sigma)^*, denoted as u \Rightarrow v, if v can be obtained from u by an application of some production rule in P, that is, if u \gamma L \delta and v \gamma R \delta, where (L \to R) \in P is a production rule, and \gamma, \delta \in (N \cup \Sigma)^* is the unaffected left and right part of the string, respectively.
More generally, u is said to yield, or derive to, v, denoted as u \Rightarrow^* v, if v can be obtained from u by repeated application of production rules, that is, if u u_0 \Rightarrow ... \Rightarrow u_n v for some n ≥ 0 and some strings u_1, ..., u_{n-1} \in (N \cup \Sigma)^*. In other words, the relation \Rightarrow^* is the reflexive transitive closure of the relation \Rightarrow.
The language of the grammar G is the set of all terminal-symbol strings derivable from its start symbol, formally: L(G) = \{ w \in \Sigma^* \mid S \Rightarrow^* w \}.
Derivations that do not end in a string composed of terminal symbols only are possible, but do not contribute to L(G).
Context-sensitive grammar
A formal grammar is context-sensitive if each rule in P is either of the form S \to \varepsilon where \varepsilon is the empty string, or of the form
αAβ → αγβ
with A ∈ N, \alpha, \beta\in (N \cup \Sigma \setminus\{S\})^*, and \gamma\in (N \cup \Sigma \setminus\{S\})^+.
The name context-sensitive is explained by the α and β that form the context of A and determine whether A can be replaced with γ or not.
By contrast, in a context-free grammar, no context is present: the left hand side of every production rule is just a nonterminal.
The string γ is not allowed to be empty. Without this restriction, the resulting grammars become equal in power to unrestricted grammars.
Some authors use the term context-sensitive grammar to refer to noncontracting grammars in general.
The left-context- and right-context-sensitive grammars are defined by restricting the rules to just the form αA → αγ and to just Aβ → γβ, respectively. The languages generated by these grammars are also the full class of context-sensitive languages. The equivalence was established by Penttonen normal form.
Examples
anbncn
The following context-sensitive grammar, with start symbol S, generates the canonical non-context-free language { anbncn | n ≥ 1 } :
1. S → a B C 2. S → a S B C 3. C B → C Z 4. C Z → W Z 5. W Z → W C 6. W C → B C 7. a B → a b 8. b B → b b 9. b C → b c10. c C → c c
Rules 1 and 2 allow for blowing-up S to anBC(BC)n−1; rules 3 to 6 allow for successively exchanging each CB to BC (four rules are needed for that since a rule CB → BC wouldn't fit into the scheme αAβ → αγβ); rules 7–10 allow replacing a non-terminal B or C with its corresponding terminal b or c, respectively, provided it is in the right place.
A generation chain for is:
S
→2
→2
→1
→3
→4
→5
→6
→3
→4
→5
→6
→3
→4
→5
→6
→7
→8
→8
→9
→10
→10
anbncndn, etc.
More complicated grammars can be used to parse { anbncndn | n ≥ 1 }, and other languages with even more letters. Here we show a simpler approach using non-contracting grammars:
Start with a kernel of regular productions generating the sentential forms
(ABCD)^{n}abcd and then include the non contracting productions
p_{Da} : Da\rightarrow aD,
p_{Db} : Db\rightarrow bD,
p_{Dc} : Dc\rightarrow cD,
p_{Dd} : Dd\rightarrow dd,
p_{Ca} : Ca\rightarrow aC,
p_{Cb} : Cb\rightarrow bC,
p_{Cc} : Cc\rightarrow cc,
p_{Ba} : Ba\rightarrow aB,
p_{Bb} : Bb\rightarrow bb,
p_{Aa} : Aa\rightarrow aa.
ambncmdn
A non contracting grammar (for which there is an equivalent CSG) for the language L_{Cross} = \{ a^mb^nc^{m}d^{n} \mid m \ge 1, n \ge 1 \} is defined by
p_0 : S \rightarrow RT,
p_1 : R\rightarrow aRC | aC,
p_3 : T\rightarrow BTd | Bd,
p_5 : CB\rightarrow BC,
p_6 : aB\rightarrow ab,
p_7 : bB\rightarrow bb,
p_8 : Cd\rightarrow cd, and
p_9 : Cc\rightarrow cc.
With these definitions, a derivation for a^3b^2c^3d^2 is:
S
\Rightarrow_{p_0} RT
\Rightarrow_{p^{2}_{1}p_{2}} a^3C^3T
\Rightarrow_{p_{3}p_{4} } a^3C^3B^2d^2
\Rightarrow_{p^{6}_{5} } a^3B^2C^3d^2
\Rightarrow_{p_{6}p_{7} } a^3b^2C^3d^2
\Rightarrow_{p_{8}p^{2}_{9}} a^3b^2c^3d^2
.
a2i
A noncontracting grammar for the language { a2i | i ≥ 1 } is constructed in Example 9.5 (p. 224) of (Hopcroft, Ullman, 1979):
S\rightarrow [ACaB]
\begin{cases}
\ [Ca]a\rightarrow aa[Ca] \\
\ [Ca][aB]\rightarrow aa[CaB] \\
\ [ACa]a\rightarrow [Aa]a[Ca] \\
\ [ACa][aB]\rightarrow [Aa]a[CaB] \\
\ [ACaB]\rightarrow [Aa][aCB] \\
\ [CaB]\rightarrow a[aCB]
\end{cases}
[aCB]\rightarrow [aDB]
[aCB]\rightarrow [aE]
\begin{cases}
\ a[Da]\rightarrow [Da]a \\
\ [aDB]\rightarrow [DaB] \\
\ [Aa][Da]\rightarrow [ADa]a \\
\ a[DaB]\rightarrow [Da][aB] \\
\ [Aa][DaB]\rightarrow [ADa][aB]
\end{cases}
[ADa]\rightarrow [ACa]
\begin{cases}
\ a[Ea]\rightarrow [Ea]a \\
\ [aE]\rightarrow [Ea] \\
\ [Aa][Ea]\rightarrow [AEa]a
\end{cases}
[AEa]\rightarrow a
Kuroda normal form
Every context-sensitive grammar which does not generate the empty string can be transformed into a weakly equivalent one in Kuroda normal form. "Weakly equivalent" here means that the two grammars generate the same language. The normal form will not in general be context-sensitive, but will be a noncontracting grammar.
The Kuroda normal form is an actual normal form for non-contracting grammars.
Properties and uses
Equivalence to linear bounded automaton
A formal language can be described by a context-sensitive grammar if and only if it is accepted by some linear bounded automaton (LBA). In some textbooks this result is attributed solely to Landweber and Kuroda. (Myhill introduced the concept of deterministic LBA in 1960. Peter S. Landweber published in 1963 that the language accepted by a deterministic LBA is context sensitive. Kuroda introduced the notion of non-deterministic LBA and the equivalence between LBA and CSGs in 1964.)
it is still an open question whether every context-sensitive language can be accepted by a deterministic LBA.
Closure properties
Context-sensitive languages are closed under complement. This 1988 result is known as the Immerman–Szelepcsényi theorem. inverse homomorphism, and Kleene plus.
Every recursively enumerable language L can be written as h(L) for some context-sensitive language L and some string homomorphism h.
Computational problems
The decision problem that asks whether a certain string s belongs to the language of a given context-sensitive grammar G, is PSPACE-complete. Moreover, there are context-sensitive grammars whose languages are PSPACE-complete. In other words, there is a context-sensitive grammar G such that deciding whether a certain string s belongs to the language of G is PSPACE-complete (so G is fixed and only s is part of the input of the problem).
The emptiness problem for context-sensitive grammars (given a context-sensitive grammar G, is L(G)=∅ ?) is undecidable.
As model of natural languages
Savitch has proven the following theoretical result, on which he bases his criticism of CSGs as basis for natural language: for any recursively enumerable set R, there exists a context-sensitive language/grammar G which can be used as a sort of proxy to test membership in R in the following way: given a string s, s is in R if and only if there exists a positive integer n for which scn is in G, where c is an arbitrary symbol not part of R.
Ongoing research on computational linguistics has focused on formulating other classes of languages that are "mildly context-sensitive" whose decision problems are feasible, such as tree-adjoining grammars, combinatory categorial grammars, coupled context-free languages, and linear context-free rewriting systems. The languages generated by these formalisms properly lie between the context-free and context-sensitive languages.
More recently, the class PTIME has been identified with range concatenation grammars, which are now considered to be the most expressive of the mild-context sensitive language classes.
See also
Chomsky hierarchy
Growing context-sensitive grammar
Definite clause grammar#Non-context-free grammars
List of parser generators for context-sensitive grammars
Notes
References
Further reading
External links
Earley Parsing for Context-Sensitive Grammars
Category:Formal languages
Category:Grammar frameworks
|
https://en.wikipedia.org/wiki/Context-sensitive_grammar
|
2025-04-05T18:27:45.081455
|
6212
|
Context-sensitive language
|
In formal language theory, a context-sensitive language is a language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar). Context-sensitive is known as type-1 in the Chomsky hierarchy of formal languages.
Computational properties
Computationally, a context-sensitive language is equivalent to a linear bounded nondeterministic Turing machine, also called a linear bounded automaton. That is a non-deterministic Turing machine with a tape of only kn cells, where n is the size of the input and k is a constant associated with the machine. This means that every formal language that can be decided by such a machine is a context-sensitive language, and every context-sensitive language can be decided by such a machine.
This set of languages is also known as NLINSPACE or NSPACE(O(n)), because they can be accepted using linear space on a non-deterministic Turing machine. The class LINSPACE (or DSPACE(O(n))) is defined the same, except using a deterministic Turing machine. Clearly LINSPACE is a subset of NLINSPACE, but it is not known whether LINSPACE = NLINSPACE.
Examples
One of the simplest context-sensitive but not context-free languages is L = \{ a^nb^nc^n : n \ge 1 \}: the language of all strings consisting of occurrences of the symbol "a", then "b"s, then "c"s (abc, , , etc.). A superset of this language, called the Bach language, is defined as the set of all strings where "a", "b" and "c" (or any other set of three symbols) occurs equally often (, , etc.) and is also context-sensitive.
can be shown to be a context-sensitive language by constructing a linear bounded automaton which accepts . The language can easily be shown to be neither regular nor context-free by applying the respective pumping lemmas for each of the language classes to .
Similarly:
L_\textit{Cross} = \{ a^mb^nc^{m}d^{n} : m \ge 1, n \ge 1 \} is another context-sensitive language; the corresponding context-sensitive grammar can be easily projected starting with two context-free grammars generating sentential forms in the formats
a^mC^m
and
B^nd^n
and then supplementing them with a permutation production like
CB\rightarrow BC, a new starting symbol and standard syntactic sugar.
L_{MUL3} \{ a^mb^nc^{mn} : m \ge 1, n \ge 1 \} is another context-sensitive language (the "3" in the name of this language is intended to mean a ternary alphabet); that is, the "product" operation defines a context-sensitive language (but the "sum" defines only a context-free language as the grammar S\rightarrow aSc|R and R\rightarrow bRc|bc shows). Because of the commutative property of the product, the most intuitive grammar for L_\textit{MUL3} is ambiguous. This problem can be avoided considering a somehow more restrictive definition of the language, e.g. L_\textit{ORDMUL3} \{ a^mb^nc^{mn} : 1 . This can be specialized to
L_\textit{MUL1} \{ a^{mn} : m > 1, n > 1 \} and, from this, to L_{m^2} \{ a^{m^2} : m > 1 \}, L_{m^3} = \{ a^{m^3} : m > 1 \}, etc.
L_{REP} \{ w^{|w|} : w \in \Sigma^* \} is a context-sensitive language. The corresponding context-sensitive grammar can be obtained as a generalization of the context-sensitive grammars for L_\textit{Square} \{ w^2 : w \in \Sigma^* \}, L_\textit{Cube} = \{ w^3 : w \in \Sigma^* \}, etc.
L_\textit{EXP} = \{ a^{2^n} : n \ge 1 \} is a context-sensitive language.
L_\textit{PRIMES2} = \{ w : |w| \mbox { is prime } \} is a context-sensitive language (the "2" in the name of this language is intended to mean a binary alphabet). This was proved by Hartmanis using pumping lemmas for regular and context-free languages over a binary alphabet and, after that, sketching a linear bounded multitape automaton accepting L_{PRIMES2}.
L_\textit{PRIMES1} = \{ a^p : p \mbox { is prime } \} is a context-sensitive language (the "1" in the name of this language is intended to mean a unary alphabet). This was credited by A. Salomaa to Matti Soittola by means of a linear bounded automaton over a unary alphabet (pages 213-214, exercise 6.8) and also to Marti Penttonen by means of a context-sensitive grammar also over a unary alphabet (See: Formal Languages by A. Salomaa, page 14, Example 2.5).
An example of recursive language that is not context-sensitive is any recursive language whose decision is an EXPSPACE-hard problem, say, the set of pairs of equivalent regular expressions with exponentiation.
Properties of context-sensitive languages
The union, intersection, concatenation of two context-sensitive languages is context-sensitive, also the Kleene plus of a context-sensitive language is context-sensitive.
The complement of a context-sensitive language is itself context-sensitive a result known as the Immerman–Szelepcsényi theorem.
Membership of a string in a language defined by an arbitrary context-sensitive grammar, or by an arbitrary deterministic context-sensitive grammar, is a PSPACE-complete problem.
See also
Linear bounded automaton
List of parser generators for context-sensitive languages
Chomsky hierarchy
Indexed languages – a strict subset of the context-sensitive languages
Weir hierarchy
References
Sipser, M. (1996), Introduction to the Theory of Computation, PWS Publishing Co.
Category:Formal languages
|
https://en.wikipedia.org/wiki/Context-sensitive_language
|
2025-04-05T18:27:45.107568
|
6216
|
Chinese room
|
The Chinese room argument holds that a computer executing a program cannot have a mind, understanding, or consciousness, regardless of how intelligently or human-like the program may make the computer behave. The argument was presented in a 1980 paper by the philosopher John Searle entitled "Minds, Brains, and Programs" and published in the journal Behavioral and Brain Sciences. Before Searle, similar arguments had been presented by figures including Gottfried Wilhelm Leibniz (1714), Anatoly Dneprov (1961), Lawrence Davis (1974) and Ned Block (1978). Searle's version has been widely discussed in the years since. The centerpiece of Searle's argument is a thought experiment known as the Chinese room.
In the thought experiment, Searle imagines a person who does not understand Chinese isolated in a room with a book containing detailed instructions for manipulating Chinese symbols. When Chinese text is passed into the room, the person follows the book's instructions to produce Chinese symbols that, to fluent Chinese speakers outside the room, appear to be appropriate responses. According to Searle, the person is just following syntactic rules without semantic comprehension, and neither the human nor the room as a whole understands Chinese. He contends that when computers execute programs, they are similarly just applying syntactic rules without any real understanding or thinking.
The argument is directed against the philosophical positions of functionalism and computationalism, which hold that the mind may be viewed as an information-processing system operating on formal symbols, and that simulation of a given mental state is sufficient for its presence. Specifically, the argument is intended to refute a position Searle calls the strong AI hypothesis:.}} "The appropriately programmed computer with the right inputs and outputs would thereby have a mind in exactly the same sense human beings have minds."
Although its proponents originally presented the argument in reaction to statements of artificial intelligence (AI) researchers, it is not an argument against the goals of mainstream AI research because it does not show a limit in the amount of intelligent behavior a machine can display. The argument applies only to digital computers running programs and does not apply to machines in general. While widely discussed, the argument has been subject to significant criticism and remains controversial among philosophers of mind and AI researchers.Searle's thought experimentSuppose that artificial intelligence research has succeeded in programming a computer to behave as if it understands Chinese. The machine accepts Chinese characters as input, carries out each instruction of the program step by step, and then produces Chinese characters as output. The machine does this so perfectly that no one can tell that they are communicating with a machine and not a hidden Chinese speaker.
The questions at issue are these: does the machine actually <em>understand</em> the conversation, or is it just <em>simulating</em> the ability to understand the conversation? Does the machine have a mind in exactly the same sense that people do, or is it just acting <em>as if</em> it has a mind?
Now suppose that Searle is in a room with an English version of the program, along with sufficient pencils, paper, erasers and filing cabinets. Chinese characters are slipped in under the door, he follows the program step-by-step, which eventually instructs him to slide other Chinese characters back out under the door. If the computer had passed the Turing test this way, it follows that Searle would do so as well, simply by running the program by hand.
Searle asserts that there is no essential difference between the roles of the computer and himself in the experiment. Each simply follows a program, step-by-step, producing behavior that makes them appear to understand. However, Searle would not be able to understand the conversation. Therefore, he argues, it follows that the computer would not be able to understand the conversation either.
Searle argues that, without "understanding" (or "intentionality"), we cannot describe what the machine is doing as "thinking" and, since it does not think, it does not have a "mind" in the normal sense of the word. Therefore, he concludes that the strong AI hypothesis is false: a computer running a program that simulates a mind would not have a mind in the same sense that human beings have a mind.HistoryGottfried Leibniz made a similar argument in 1714 against mechanism (the idea that everything that makes up a human being could, in principle, be explained in mechanical terms. In other words, that a person, including their mind, is merely a very complex machine). Leibniz used the thought experiment of expanding the brain until it was the size of a mill. Leibniz found it difficult to imagine that a "mind" capable of "perception" could be constructed using only mechanical processes.
Peter Winch made the same point in his book The Idea of a Social Science and its Relation to Philosophy (1958), where he provides an argument to show that "a man who understands Chinese is not a man who has a firm grasp of the statistical probabilities for the occurrence of the various words in the Chinese language" (p. 108).
Soviet cyberneticist Anatoly Dneprov made an essentially identical argument in 1961, in the form of the short story "The Game". In it, a stadium of people act as switches and memory cells implementing a program to translate a sentence of Portuguese, a language that none of them know. The game was organized by a "Professor Zarubin" to answer the question "Can mathematical machines think?" Speaking through Zarubin, Dneprov writes "the only way to prove that machines can think is to turn yourself into a machine and examine your thinking process" and he concludes, as Searle does, "We've proven that even the most perfect simulation of machine thinking is not the thinking process itself."
In 1974, Lawrence H. Davis imagined duplicating the brain using telephone lines and offices staffed by people, and in 1978 Ned Block envisioned the entire population of China involved in such a brain simulation. This thought experiment is called the China brain, also the "Chinese Nation" or the "Chinese Gym".
Searle's version appeared in his 1980 paper "Minds, Brains, and Programs", published in Behavioral and Brain Sciences. It eventually became the journal's "most influential target article", generating an enormous number of commentaries and responses in the ensuing decades, and Searle has continued to defend and refine the argument in many papers, popular articles and books. David Cole writes that "the Chinese Room argument has probably been the most widely discussed philosophical argument in cognitive science to appear in the past 25 years".
Most of the discussion consists of attempts to refute it. "The overwhelming majority", notes Behavioral and Brain Sciences editor Stevan Harnad, "still think that the Chinese Room Argument is dead wrong". The sheer volume of the literature that has grown up around it inspired Pat Hayes to comment that the field of cognitive science ought to be redefined as "the ongoing research program of showing Searle's Chinese Room Argument to be false".
Searle's argument has become "something of a classic in cognitive science", according to Harnad. Varol Akman agrees, and has described the original paper as "an exemplar of philosophical clarity and purity". Philosophy Although the Chinese Room argument was originally presented in reaction to the statements of artificial intelligence researchers, philosophers have come to consider it as an important part of the philosophy of mind. It is a challenge to functionalism and the computational theory of mind, David Cole agrees that "the argument also has broad implications for functionalist and computational theories of meaning and of mind".}} and is related to such questions as the mind–body problem, the problem of other minds, the symbol grounding problem, and the hard problem of consciousness. Strong AI <!--This section title is linked to from several places -->
Searle identified a philosophical position he calls "strong AI":
}} and is also quoted in Daniel Dennett's Consciousness Explained. Searle's original formulation was "The appropriately programmed computer really is a mind, in the sense that computers given the right programs can be literally said to understand and have other cognitive states." Strong AI is defined similarly by Stuart J. Russell and Peter Norvig: "weak AI—the idea machines could act a <em>as if</em> they were intelligent—and strong AI—the assertions that do so are <em>actually</em> consciously thinking (not just <em>simulating</em> thinking)."}}
}}
The definition depends on the distinction between simulating a mind and actually having one. Searle writes that "according to Strong AI, the correct simulation really is a mind. According to Weak AI, the correct simulation is a model of the mind."
The claim is implicit in some of the statements of early AI researchers and analysts. For example, in 1955, AI founder Herbert A. Simon declared that "there are now in the world machines that think, that learn and create". Simon, together with Allen Newell and Cliff Shaw, after having completed the first program that could do formal reasoning (the Logic Theorist), claimed that they had "solved the venerable mind–body problem, explaining how a system composed of matter can have the properties of mind." John Haugeland wrote that "AI wants only the genuine article: <em>machines with minds</em>, in the full and literal sense. This is not science fiction, but real science, based on a theoretical conception as deep as it is daring: namely, we are, at root, <em>computers ourselves</em>."
Searle also ascribes the following claims to advocates of strong AI:
* AI systems can be used to explain the mind;
* The study of the brain is irrelevant to the study of the mind; He writes elsewhere, "I thought the whole idea of strong AI was that we don't need to know how the brain works to know how the mind works." This position owes its phrasing to Stevan Harnad.}} and
* The Turing test is adequate for establishing the existence of mental states.}} Strong AI as computationalism or functionalism In more recent presentations of the Chinese room argument, Searle has identified "strong AI" as "computer functionalism" (a term he attributes to Daniel Dennett). Functionalism is a position in modern philosophy of mind that holds that we can define mental phenomena (such as beliefs, desires, and perceptions) by describing their functions in relation to each other and to the outside world. Because a computer program can accurately represent functional relationships as relationships between symbols, a computer can have mental phenomena if it runs the right program, according to functionalism.
Stevan Harnad argues that Searle's depictions of strong AI can be reformulated as "recognizable tenets of <em>computationalism</em>, a position (unlike "strong AI") that is actually held by many thinkers, and hence one worth refuting." Computationalism and is held by Allen Newell, Zenon Pylyshyn and Steven Pinker, among others.}} is the position in the philosophy of mind which argues that the mind can be accurately described as an information-processing system.
Each of the following, according to Harnad, is a "tenet" of computationalism:
* Mental states are computational states (which is why computers can have mental states and help to explain the mind);
* Computational states are implementation-independent—in other words, it is the software that determines the computational state, not the hardware (which is why the brain, being hardware, is irrelevant); and that
* Since implementation is unimportant, the only empirical data that matters is how the system functions; hence the Turing test is definitive.
Recent philosophical discussions have revisited the implications of computationalism for artificial intelligence. Goldstein and Levinstein explore whether large language models (LLMs) like ChatGPT can possess minds, focusing on their ability to exhibit folk psychology, including beliefs, desires, and intentions. The authors argue that LLMs satisfy several philosophical theories of mental representation, such as informational, causal, and structural theories, by demonstrating robust internal representations of the world. However, they highlight that the evidence for LLMs having action dispositions necessary for belief-desire psychology remains inconclusive. Additionally, they refute common skeptical challenges, such as the "stochastic parrots" argument and concerns over memorization, asserting that LLMs exhibit structured internal representations that align with these philosophical criteria.
David Chalmers suggests that while current LLMs lack features like recurrent processing and unified agency, advancements in AI could address these limitations within the next decade, potentially enabling systems to achieve consciousness. This perspective challenges Searle's original claim that purely "syntactic" processing cannot yield understanding or consciousness, arguing instead that such systems could have authentic mental states.
Strong AI vs. biological naturalism
Searle holds a philosophical position he calls "biological naturalism": that consciousness and understanding require specific biological machinery that are found in brains. He writes "brains cause minds" and that "actual human mental phenomena [are] dependent on actual physical–chemical properties of actual human brains". Searle argues that this machinery (known in neuroscience as the "neural correlates of consciousness") must have some causal powers that permit the human experience of consciousness. Searle's belief in the existence of these powers has been criticized.
Searle does not disagree with the notion that machines can have consciousness and understanding, because, as he writes, "we are precisely such machines". Searle holds that the brain is, in fact, a machine, but that the brain gives rise to consciousness and understanding using specific machinery. If neuroscience is able to isolate the mechanical process that gives rise to consciousness, then Searle grants that it may be possible to create machines that have consciousness and understanding. However, without the specific machinery required, Searle does not believe that consciousness can occur.
Biological naturalism implies that one cannot determine if the experience of consciousness is occurring merely by examining how a system functions, because the specific machinery of the brain is essential. Thus, biological naturalism is directly opposed to both behaviorism and functionalism (including "computer functionalism" or "strong AI"). Biological naturalism is similar to identity theory (the position that mental states are "identical to" or "composed of" neurological events); however, Searle has specific technical objections to identity theory.}} Searle's biological naturalism and strong AI are both opposed to Cartesian dualism, the classical idea that the brain and mind are made of different "substances". Indeed, Searle accuses strong AI of dualism, writing that "strong AI only makes sense given the dualistic assumption that, where the mind is concerned, the brain doesn't matter". Consciousness Searle's original presentation emphasized understanding—that is, mental states with intentionality—and did not directly address other closely related ideas such as "consciousness". However, in more recent presentations, Searle has included consciousness as the real target of the argument.
|John R. Searle| Consciousness and Language, p. 16}}
David Chalmers writes, "it is fairly clear that consciousness is at the root of the matter" of the Chinese room.
Colin McGinn argues that the Chinese room provides strong evidence that the hard problem of consciousness is fundamentally insoluble. The argument, to be clear, is not about whether a machine can be conscious, but about whether it (or anything else for that matter) can be shown to be conscious. It is plain that any other method of probing the occupant of a Chinese room has the same difficulties in principle as exchanging questions and answers in Chinese. It is simply not possible to divine whether a conscious agency or some clever simulation inhabits the room.
Searle argues that this is only true for an observer outside of the room. The whole point of the thought experiment is to put someone inside the room, where they can directly observe the operations of consciousness. Searle claims that from his vantage point within the room there is nothing he can see that could imaginably give rise to consciousness, other than himself, and clearly he does not have a mind that can speak Chinese. In Searle's words, "the computer has nothing more than I have in the case where I understand nothing".Applied ethics
—proposed as a real-life analog to the Chinese room]]
Patrick Hew used the Chinese Room argument to deduce requirements from military command and control systems if they are to preserve a commander's moral agency. He drew an analogy between a commander in their command center and the person in the Chinese Room, and analyzed it under a reading of Aristotle's notions of "compulsory" and "ignorance". Information could be "down converted" from meaning to symbols, and manipulated symbolically, but moral agency could be undermined if there was inadequate 'up conversion' into meaning. Hew cited examples from the USS Vincennes incident.
Computer science
The Chinese room argument is primarily an argument in the philosophy of mind, and both major computer scientists and artificial intelligence researchers consider it irrelevant to their fields. However, several concepts developed by computer scientists are essential to understanding the argument, including symbol processing, Turing machines, Turing completeness, and the Turing test. Strong AI vs. AI research Searle's arguments are not usually considered an issue for AI research. The primary mission of artificial intelligence research is only to create useful systems that act intelligently and it does not matter if the intelligence is "merely" a simulation. AI researchers Stuart J. Russell and Peter Norvig wrote in 2021: "We are interested in programs that behave intelligently. Individual aspects of consciousness—awareness, self-awareness, attention—can be programmed and can be part of an intelligent machine. The additional project making a machine conscious in exactly the way humans are is not one that we are equipped to take on."
Searle does not disagree that AI research can create machines that are capable of highly intelligent behavior. The Chinese room argument leaves open the possibility that a digital machine could be built that acts more intelligently than a person, but does not have a mind or intentionality in the same way that brains do.
Searle's "strong AI hypothesis" should not be confused with "strong AI" as defined by Ray Kurzweil and other futurists, who use the term to describe machine intelligence that rivals or exceeds human intelligence—that is, artificial general intelligence, human level AI or superintelligence. Kurzweil is referring primarily to the <em>amount</em> of intelligence displayed by the machine, whereas Searle's argument sets no limit on this. Searle argues that a superintelligent machine would not necessarily have a mind and consciousness.
Turing test
The Chinese room implements a version of the Turing test. Alan Turing introduced the test in 1950 to help answer the question "can machines think?" In the standard version, a human judge engages in a natural language conversation with a human and a machine designed to generate performance indistinguishable from that of a human being. All participants are separated from one another. If the judge cannot reliably tell the machine from the human, the machine is said to have passed the test.
Turing then considered each possible objection to the proposal "machines can think", and found that there are simple, obvious answers if the question is de-mystified in this way. He did not, however, intend for the test to measure for the presence of "consciousness" or "understanding". He did not believe this was relevant to the issues that he was addressing. He wrote:
}}
To Searle, as a philosopher investigating in the nature of mind and consciousness, these are the relevant mysteries. The Chinese room is designed to show that the Turing test is insufficient to detect the presence of consciousness, even if the room can behave or function as a conscious mind would.
Symbol processing
Computers manipulate physical objects in order to carry out calculations and do simulations. AI researchers Allen Newell and Herbert A. Simon called this kind of machine a physical symbol system. It is also equivalent to the formal systems used in the field of mathematical logic.
Searle emphasizes the fact that this kind of symbol manipulation is syntactic (borrowing a term from the study of grammar). The computer manipulates the symbols using a form of syntax, without any knowledge of the symbol's semantics (that is, their meaning).
Newell and Simon had conjectured that a physical symbol system (such as a digital computer) had all the necessary machinery for "general intelligent action", or, as it is known today, artificial general intelligence. They framed this as a philosophical position, the physical symbol system hypothesis: "A physical symbol system has the necessary and sufficient means for general intelligent action." The Chinese room argument does not refute this, because it is framed in terms of "intelligent action", i.e. the external behavior of the machine, rather than the presence or absence of understanding, consciousness and mind.
Twenty-first century AI programs (such as "deep learning") do mathematical operations on huge matrixes of unidentified numbers and bear little resemblance to the symbolic processing used by AI programs at the time Searle wrote his critique in 1980. Nils Nilsson describes systems like these as "dynamic" rather than "symbolic". Nilsson notes that these are essentially digitized representations of dynamic systems—the individual numbers do not have a specific semantics, but are instead samples or data points from a dynamic signal, and it is the signal being approximated which would have semantics. Nilsson argues it is not reasonable to consider these signals as "symbol processing" in the same sense as the physical symbol systems hypothesis.
Chinese room and Turing completeness
The Chinese room has a design analogous to that of a modern computer. It has a Von Neumann architecture, which consists of a program (the book of instructions), some memory (the papers and file cabinets), a machine that follows the instructions (the man), and a means to write symbols in memory (the pencil and eraser). A machine with this design is known in theoretical computer science as "Turing complete", because it has the necessary machinery to carry out any computation that a Turing machine can do, and therefore it is capable of doing a step-by-step simulation of any other digital machine, given enough memory and time. Turing writes, "all digital computers are in a sense equivalent." The widely accepted Church–Turing thesis holds that any function computable by an effective procedure is computable by a Turing machine.
The Turing completeness of the Chinese room implies that it can do whatever any other digital computer can do (albeit much, much more slowly). Thus, if the Chinese room does not or can not contain a Chinese-speaking mind, then no other digital computer can contain a mind. Some replies to Searle begin by arguing that the room, as described, cannot have a Chinese-speaking mind. Arguments of this form, according to Stevan Harnad, are "no refutation (but rather an affirmation)" of the Chinese room argument, because these arguments actually imply that no digital computers can have a mind.
There are some critics, such as Hanoch Ben-Yami, who argue that the Chinese room cannot simulate all the abilities of a digital computer, such as being able to determine the current time.
Complete argument
Searle has produced a more formal version of the argument of which the Chinese Room forms a part. He presented the first version in 1984. The version given below is from 1990. (A1-3) and (C1) are described as 1,2,3 and 4 in David Cole.}} The Chinese room thought experiment is intended to prove point A3. }}
He begins with three axioms:<!--these should maybe be a description list but gotta put it together as one or else it defeats the entire purpose!-->
:(A1) "Programs are formal (syntactic)."
::A program uses syntax to manipulate symbols and pays no attention to the semantics of the symbols. It knows where to put the symbols and how to move them around, but it does not know what they stand for or what they mean. For the program, the symbols are just physical objects like any others.
:(A2) "Minds have mental contents (semantics)."
::Unlike the symbols used by a program, our thoughts have meaning: they represent things and we know what it is they represent.
:(A3) "Syntax by itself is neither constitutive of nor sufficient for semantics."
::This is what the Chinese room thought experiment is intended to prove: the Chinese room has syntax (because there is a man in there moving symbols around). The Chinese room has no semantics (because, according to Searle, there is no one or nothing in the room that understands what the symbols mean). Therefore, having syntax is not enough to generate semantics.
Searle posits that these lead directly to this conclusion:
:(C1) Programs are neither constitutive of nor sufficient for minds.
::This should follow without controversy from the first three: Programs don't have semantics. Programs have only syntax, and syntax is insufficient for semantics. Every mind has semantics. Therefore no programs are minds.
This much of the argument is intended to show that artificial intelligence can never produce a machine with a mind by writing programs that manipulate symbols. The remainder of the argument addresses a different issue. Is the human brain running a program? In other words, is the computational theory of mind correct? He begins with an axiom that is intended to express the basic modern scientific consensus about brains and minds:
:(A4) Brains cause minds.
Searle claims that we can derive "immediately" and "trivially" that:
:(C2) Any other system capable of causing minds would have to have causal powers (at least) equivalent to those of brains.
::Brains must have something that causes a mind to exist. Science has yet to determine exactly what it is, but it must exist, because minds exist. Searle calls it "causal powers". "Causal powers" is whatever the brain uses to create a mind. If anything else can cause a mind to exist, it must have "equivalent causal powers". "Equivalent causal powers" is whatever <em>else</em> that could be used to make a mind.
And from this he derives the further conclusions:
:(C3) Any artifact that produced mental phenomena, any artificial brain, would have to be able to duplicate the specific causal powers of brains, and it could not do that just by running a formal program.
::This follows from C1 and C2: Since no program can produce a mind, and "equivalent causal powers" produce minds, it follows that programs do not have "equivalent causal powers."
:(C4) The way that human brains actually produce mental phenomena cannot be solely by virtue of running a computer program.
::Since programs do not have "equivalent causal powers", "equivalent causal powers" produce minds, and brains produce minds, it follows that brains do not use programs to produce minds.
Refutations of Searle's argument take many different forms (see below). Computationalists and functionalists reject A3, arguing that "syntax" (as Searle describes it) <em>can</em> have "semantics" if the syntax has the right functional structure. Eliminative materialists reject A2, arguing that minds don't actually have "semantics"—that thoughts and other mental phenomena are inherently meaningless but nevertheless function as if they had meaning.
Replies
Replies to Searle's argument may be classified according to what they claim to show:}}
* Those which identify who speaks Chinese
* Those which demonstrate how meaningless symbols can become meaningful
* Those which suggest that the Chinese room should be redesigned in some way
* Those which contend that Searle's argument is misleading
* Those which argue that the argument makes false assumptions about subjective conscious experience and therefore proves nothing
Some of the arguments (robot and brain simulation, for example) fall into multiple categories.
Systems and virtual mind replies: finding the mind
These replies attempt to answer the question: since the man in the room does not speak Chinese, where is the mind that does? These replies address the key ontological issues of mind versus body and simulation vs. reality. All of the replies that identify the mind in the room are versions of "the system reply".
System reply
The basic version of the system reply argues that it is the "whole system" that understands Chinese.}} While the man understands only English, when he is combined with the program, scratch paper, pencils and file cabinets, they form a system that can understand Chinese. "Here, understanding is not being ascribed to the mere individual; rather it is being ascribed to this whole system of which he is a part" Searle explains.
Searle notes that (in this simple version of the reply) the "system" is nothing more than a collection of ordinary physical objects; it grants the power of understanding and consciousness to "the conjunction of that person and bits of paper" without making any effort to explain how this pile of objects has become a conscious, thinking being. Searle argues that no reasonable person should be satisfied with the reply, unless they are "under the grip of an ideology;" In order for this reply to be remotely plausible, one must take it for granted that consciousness can be the product of an information processing "system", and does not require anything resembling the actual biology of the brain.
Searle then responds by simplifying this list of physical objects: he asks what happens if the man memorizes the rules and keeps track of everything in his head? Then the whole system consists of just one object: the man himself. Searle argues that if the man does not understand Chinese then the system does not understand Chinese either because now "the system" and "the man" both describe exactly the same object.
Critics of Searle's response argue that the program has allowed the man to have two minds in one head. If we assume a "mind" is a form of information processing, then the theory of computation can account for two computations occurring at once, namely (1) the computation for universal programmability (which is the function instantiated by the person and note-taking materials independently from any particular program contents) and (2) the computation of the Turing machine that is described by the program (which is instantiated by everything including the specific program). The theory of computation thus formally explains the open possibility that the second computation in the Chinese Room could entail a human-equivalent semantic understanding of the Chinese inputs. The focus belongs on the program's Turing machine rather than on the person's. However, from Searle's perspective, this argument is circular. The question at issue is whether consciousness is a form of information processing, and this reply requires that we make that assumption.
More sophisticated versions of the systems reply try to identify more precisely what "the system" is and they differ in exactly how they describe it. According to these replies, the "mind that speaks Chinese" could be such things as: the "software", a "program", a "running program", a simulation of the "neural correlates of consciousness", the "functional system", a "simulated mind", an "emergent property", or "a virtual mind". Virtual mind reply Marvin Minsky suggested a version of the system reply known as the "virtual mind reply". Tim Maudlin, David Chalmers and David Cole.}} The term "virtual" is used in computer science to describe an object that appears to exist "in" a computer (or computer network) only because software makes it appear to exist. The objects "inside" computers (including files, folders, and so on) are all "virtual", except for the computer's electronic components. Similarly, Minsky that a computer may contain a "mind" that is virtual in the same sense as virtual machines, virtual communities and virtual reality.
To clarify the distinction between the simple systems reply given above and virtual mind reply, David Cole notes that two simulations could be running on one system at the same time: one speaking Chinese and one speaking Korean. While there is only one system, there can be multiple "virtual minds," thus the "system" cannot be the "mind".
Searle responds that such a mind is at best a simulation, and writes: "No one supposes that computer simulations of a five-alarm fire will burn the neighborhood down or that a computer simulation of a rainstorm will leave us all drenched." Nicholas Fearn responds that, for some things, simulation is as good as the real thing. "When we call up the pocket calculator function on a desktop computer, the image of a pocket calculator appears on the screen. We don't complain that it isn't really a calculator, because the physical attributes of the device do not matter." The question is, is the human mind like the pocket calculator, essentially composed of information, where a perfect simulation of the thing just <em>is</em> the thing? Or is the mind like the rainstorm, a thing in the world that is more than just its simulation, and not realizable in full by a computer simulation? For decades, this question of simulation has led AI researchers and philosophers to consider whether the term "synthetic intelligence" is more appropriate than the common description of such intelligences as "artificial."
These replies provide an explanation of exactly who it is that understands Chinese. If there is something besides the man in the room that can understand Chinese, Searle cannot argue that (1) the man does not understand Chinese, therefore (2) nothing in the room understands Chinese. This, according to those who make this reply, shows that Searle's argument fails to prove that "strong AI" is false.}}
These replies, by themselves, do not provide any evidence that strong AI is true, however. They do not show that the system (or the virtual mind) understands Chinese, other than the hypothetical premise that it passes the Turing test. Searle argues that, if we are to consider Strong AI remotely plausible, the Chinese Room is an example that requires explanation, and it is difficult or impossible to explain how consciousness might "emerge" from the room or how the system would have consciousness. As Searle writes "the systems reply simply begs the question by insisting that the system must understand Chinese" and thus is dodging the question or hopelessly circular.Robot and semantics replies: finding the meaningAs far as the person in the room is concerned, the symbols are just meaningless "squiggles." But if the Chinese room really "understands" what it is saying, then the symbols must get their meaning from somewhere. These arguments attempt to connect the symbols to the things they symbolize. These replies address Searle's concerns about intentionality, symbol grounding and syntax vs. semantics. Robot reply Suppose that instead of a room, the program was placed into a robot that could wander around and interact with its environment. This would allow a "causal connection" between the symbols and things they represent.}} Hans Moravec comments: "If we could graft a robot to a reasoning program, we wouldn't need a person to provide the meaning anymore: it would come from the physical world."}}
Searle's reply is to suppose that, unbeknownst to the individual in the Chinese room, some of the inputs came directly from a camera mounted on a robot, and some of the outputs were used to manipulate the arms and legs of the robot. Nevertheless, the person in the room is still just following the rules, and does not know what the symbols mean. Searle writes "he doesn't <em>see</em> what comes into the robot's eyes." Derived meaning Some respond that the room, as Searle describes it, is connected to the world: through the Chinese speakers that it is "talking" to and through the programmers who designed the knowledge base in his file cabinet. The symbols Searle manipulates are already meaningful, they are just not meaningful to him.
Searle says that the symbols only have a "derived" meaning, like the meaning of words in books. The meaning of the symbols depends on the conscious understanding of the Chinese speakers and the programmers outside the room. The room, like a book, has no understanding of its own.}}Contextualist replySome have argued that the meanings of the symbols would come from a vast "background" of commonsense knowledge encoded in the program and the filing cabinets. This would provide a "context" that would give the symbols their meaning. Proponents of this position include Roger Schank, Doug Lenat, Marvin Minsky and (with reservations) Daniel Dennett, who writes "The fact is that any program [that passed a Turing test] would have to be an extraordinarily supple, sophisticated, and multilayered system, brimming with 'world knowledge' and meta-knowledge and meta-meta-knowledge." }}
Searle agrees that this background exists, but he does not agree that it can be built into programs. Hubert Dreyfus has also criticized the idea that the "background" can be represented symbolically.
To each of these suggestions, Searle's response is the same: no matter how much knowledge is written into the program and no matter how the program is connected to the world, he is still in the room manipulating symbols according to rules. His actions are syntactic and this can never explain to him what the symbols stand for. Searle writes "syntax is insufficient for semantics."}}
However, for those who accept that Searle's actions simulate a mind, separate from his own, the important question is not what the symbols mean to Searle, what is important is what they mean to the virtual mind. While Searle is trapped in the room, the virtual mind is not: it is connected to the outside world through the Chinese speakers it speaks to, through the programmers who gave it world knowledge, and through the cameras and other sensors that roboticists can supply.
Brain simulation and connectionist replies: redesigning the room
These arguments are all versions of the systems reply that identify a particular kind of system as being important; they identify some special technology that would create conscious understanding in a machine. (The "robot" and "commonsense knowledge" replies above also specify a certain kind of system as being important.)
Brain simulator reply
Suppose that the program simulated in fine detail the action of every neuron in the brain of a Chinese speaker.}} This strengthens the intuition that there would be no significant difference between the operation of the program and the operation of a live human brain.
Searle replies that such a simulation does not reproduce the important features of the brain—its causal and intentional states. He is adamant that "human mental phenomena [are] dependent on actual physical–chemical properties of actual human brains." Moreover, he argues:
}}}}
China brain
What if we ask each citizen of China to simulate one neuron, using the telephone system to simulate the connections between axons and dendrites? In this version, it seems obvious that no individual would have any understanding of what the brain might be saying.}} It is also obvious that this system would be functionally equivalent to a brain, so if consciousness is a function, this system would be conscious.
Brain replacement scenario
In this, we are asked to imagine that engineers have invented a tiny computer that simulates the action of an individual neuron. What would happen if we replaced one neuron at a time? Replacing one would clearly do nothing to change conscious awareness. Replacing all of them would create a digital computer that simulates a brain. If Searle is right, then conscious awareness must disappear during the procedure (either gradually or all at once). Searle's critics argue that there would be no point during the procedure when he can claim that conscious awareness ends and mindless simulation begins. and it is now associated with Ray Kurzweil's version of transhumanism.}}}} (See Ship of Theseus for a similar thought experiment.)Connectionist replies:Closely related to the brain simulator reply, this claims that a massively parallel connectionist architecture would be capable of understanding. as well as Paul and Patricia Churchland.}} Modern deep learning is massively parallel and has successfully displayed intelligent behavior in many domains. Nils Nilsson argues that modern AI is using digitized "dynamic signals" rather than symbols of the kind used by AI in 1980. Here it is the sampled signal which would have the semantics, not the individual numbers manipulated by the program. This is a different kind of machine than the one that Searle visualized.Combination reply:This response combines the robot reply with the brain simulation reply, arguing that a brain simulation connected to the world through a robot body could have a mind.Many mansions / wait till next year reply:Better technology in the future will allow computers to understand. uses the name "Wait 'Til Next Year Reply".}} Searle agrees that this is possible, but considers this point irrelevant. Searle agrees that there may be other hardware besides brains that have conscious understanding.
These arguments (and the robot or common-sense knowledge replies) identify some special technology that would help create conscious understanding in a machine. They may be interpreted in two ways: either they claim (1) this technology is required for consciousness, the Chinese room does not or cannot implement this technology, and therefore the Chinese room cannot pass the Turing test or (even if it did) it would not have conscious understanding. Or they may be claiming that (2) it is easier to see that the Chinese room has a mind if we visualize this technology as being used to create it.
In the first case, where features like a robot body or a connectionist architecture are required, Searle claims that strong AI (as he understands it) has been abandoned. Stevan Harnad makes the same point, writing: "Now just as it is no refutation (but rather an affirmation) of the CRA to deny that [the Turing test] is a strong enough test, or to deny that a computer could ever pass it, it is merely special pleading to try to save computationalism by stipulating ad hoc (in the face of the CRA) that implementational details do matter after all, and that the computer's is the 'right' kind of implementation, whereas Searle's is the 'wrong' kind."}} The Chinese room has all the elements of a Turing complete machine, and thus is capable of simulating any digital computation whatsoever. If Searle's room cannot pass the Turing test then there is no other digital technology that could pass the Turing test. If Searle's room could pass the Turing test, but still does not have a mind, then the Turing test is not sufficient to determine if the room has a "mind". Either way, it denies one or the other of the positions Searle thinks of as "strong AI", proving his argument.
The brain arguments in particular deny strong AI if they assume that there is no simpler way to describe the mind than to create a program that is just as mysterious as the brain was. He writes "I thought the whole idea of strong AI was that we don't need to know how the brain works to know how the mind works." If computation does not provide an explanation of the human mind, then strong AI has failed, according to Searle.
Other critics hold that the room as Searle described it does, in fact, have a mind, however they argue that it is difficult to see—Searle's description is correct, but misleading. By redesigning the room more realistically they hope to make this more obvious. In this case, these arguments are being used as appeals to intuition (see next section).
In fact, the room can just as easily be redesigned to weaken our intuitions. Ned Block's Blockhead argument suggests that the program could, in theory, be rewritten into a simple lookup table of rules of the form "if the user writes S, reply with P and goto X". At least in principle, any program can be rewritten (or "refactored") into this form, even a brain simulation. In the blockhead scenario, the entire mental state is hidden in the letter X, which represents a memory address—a number associated with the next rule. It is hard to visualize that an instant of one's conscious experience can be captured in a single large number, yet this is exactly what "strong AI" claims. On the other hand, such a lookup table would be ridiculously large (to the point of being physically impossible), and the states could therefore be overly specific.
Searle argues that however the program is written or however the machine is connected to the world, the mind is being simulated by a simple step-by-step digital machine (or machines). These machines are always just like the man in the room: they understand nothing and do not speak Chinese. They are merely manipulating symbols without knowing what they mean. Searle writes: "I can have any formal program you like, but I still understand nothing." Speed and complexity: appeals to intuition
The following arguments (and the intuitive interpretations of the arguments above) do not directly explain how a Chinese speaking mind could exist in Searle's room, or how the symbols he manipulates could become meaningful. However, by raising doubts about Searle's intuitions they support other positions, such as the system and robot replies. These arguments, if accepted, prevent Searle from claiming that his conclusion is obvious by undermining the intuitions that his certainty requires.
Several critics believe that Searle's argument relies entirely on intuitions. Block writes "Searle's argument depends for its force on intuitions that certain entities do not think." Daniel Dennett describes the Chinese room argument as a misleading "intuition pump" and writes "Searle's thought experiment depends, illicitly, on your imagining too simple a case, an irrelevant case, and drawing the obvious conclusion from it."
Some of the arguments above also function as appeals to intuition, especially those that are intended to make it seem more plausible that the Chinese room contains a mind, which can include the robot, commonsense knowledge, brain simulation and connectionist replies. Several of the replies above also address the specific issue of complexity. The connectionist reply emphasizes that a working artificial intelligence system would have to be as complex and as interconnected as the human brain. The commonsense knowledge reply emphasizes that any program that passed a Turing test would have to be "an extraordinarily supple, sophisticated, and multilayered system, brimming with 'world knowledge' and meta-knowledge and meta-meta-knowledge", as Daniel Dennett explains. Speed and complexity replies Many of these critiques emphasize speed and complexity of the human brain, Daniel Dennett points out the complexity of world knowledge.}} which processes information at 100 billion operations per second (by some estimates). Several critics point out that the man in the room would probably take millions of years to respond to a simple question, and would require "filing cabinets" of astronomical proportions. This brings the clarity of Searle's intuition into doubt.
An especially vivid version of the speed and complexity reply is from Paul and Patricia Churchland. They propose this analogous thought experiment: "Consider a dark room containing a man holding a bar magnet or charged object. If the man pumps the magnet up and down, then, according to Maxwell's theory of artificial luminance (AL), it will initiate a spreading circle of electromagnetic waves and will thus be luminous. But as all of us who have toyed with magnets or charged balls well know, their forces (or any other forces for that matter), even when set in motion produce no luminance at all. It is inconceivable that you might constitute real luminance just by moving forces around!" Churchland's point is that the problem is that he would have to wave the magnet up and down something like 450 trillion times per second in order to see anything.
Stevan Harnad is critical of speed and complexity replies when they stray beyond addressing our intuitions. He writes "Some have made a cult of speed and timing, holding that, when accelerated to the right speed, the computational may make a phase transition into the mental. It should be clear that is not a counterargument but merely an ad hoc speculation (as is the view that it is all just a matter of ratcheting up to the right degree of 'complexity.')" This "phase transition" idea is a version of strong emergentism (what Dennett derides as "Woo woo West Coast emergence"). Harnad accuses Churchland and Patricia Churchland of espousing strong emergentism. Ray Kurzweil also holds a form of strong emergentism.}}
Searle argues that his critics are also relying on intuitions, however his opponents' intuitions have no empirical basis. He writes that, in order to consider the "system reply" as remotely plausible, a person must be "under the grip of an ideology". The system reply only makes sense (to Searle) if one assumes that any "system" can have consciousness, just by virtue of being a system with the right behavior and functional parts. This assumption, he argues, is not tenable given our experience of consciousness. Other minds and zombies: meaninglessness <!-- Linked to in a footnote above -->
Several replies argue that Searle's argument is irrelevant because his assumptions about the mind and consciousness are faulty. Searle believes that human beings directly experience their consciousness, intentionality and the nature of the mind every day, and that this experience of consciousness is not open to question. He writes that we must "presuppose the reality and knowability of the mental." The replies below question whether Searle is justified in using his own experience of consciousness to determine that it is more than mechanical symbol processing. In particular, the other minds reply argues that we cannot use our experience of consciousness to answer questions about other minds (even the mind of a computer), the epiphenoma replies question whether we can make any argument at all about something like consciousness which can not, by definition, be detected by any experiment, and the eliminative materialist reply argues that Searle's own personal consciousness does not "exist" in the sense that Searle thinks it does. Other minds reply The "Other Minds Reply" points out that Searle's argument is a version of the problem of other minds, applied to machines. There is no way we can determine if other people's subjective experience is the same as our own. We can only study their behavior (i.e., by giving them our own Turing test). Critics of Searle argue that he is holding the Chinese room to a higher standard than we would hold an ordinary person.}}
Nils Nilsson writes "If a program behaves <em>as if</em> it were multiplying, most of us would say that it is, in fact, multiplying. For all I know, Searle may only be behaving <em>as if</em> he were thinking deeply about these matters. But, even though I disagree with him, his simulation is pretty good, so I'm willing to credit him with real thought."
Turing anticipated Searle's line of argument (which he called "The Argument from Consciousness") in 1950 and makes the other minds reply. He noted that people never consider the problem of other minds when dealing with each other. He writes that "instead of arguing continually over this point it is usual to have the polite convention that everyone thinks." The Turing test simply extends this "polite convention" to machines. He does not intend to solve the problem of other minds (for machines or people) and he does not think we need to.}} Replies considering that Searle's "consciousness" is undetectable
If we accept Searle's description of intentionality, consciousness, and the mind, we are forced to accept that consciousness is epiphenomenal: that it "casts no shadow" i.e. is undetectable in the outside world. Searle's "causal properties" cannot be detected by anyone outside the mind, otherwise the Chinese Room could not pass the Turing test—the people outside would be able to tell there was not a Chinese speaker in the room by detecting their causal properties. Since they cannot detect causal properties, they cannot detect the existence of the mental. Thus, Searle's "causal properties" and consciousness itself is undetectable, and anything that cannot be detected either does not exist or does not matter.
Mike Alder calls this the "Newton's Flaming Laser Sword Reply". He argues that the entire argument is frivolous, because it is non-verificationist: not only is the distinction between <em>simulating</em> a mind and <em>having</em> a mind ill-defined, but it is also irrelevant because no experiments were, or even can be, proposed to distinguish between the two.
Daniel Dennett provides this illustration: suppose that, by some mutation, a human being is born that does not have Searle's "causal properties" but nevertheless acts exactly like a human being. This is a philosophical zombie, as formulated in the philosophy of mind. This new animal would reproduce just as any other human and eventually there would be more of these zombies. Natural selection would favor the zombies, since their design is (we could suppose) a bit simpler. Eventually the humans would die out. So therefore, if Searle is right, it is most likely that human beings (as we see them today) are actually "zombies", who nevertheless insist they are conscious. It is impossible to know whether we are all zombies or not. Even if we are all zombies, we would still believe that we are not. Eliminative materialist reply Several philosophers argue that consciousness, as Searle describes it, does not exist. Daniel Dennett describes consciousness as a "user illusion".}}
This position is sometimes referred to as eliminative materialism: the view that consciousness is not a concept that can "enjoy reduction" to a strictly mechanical description, but rather is a concept that will be simply eliminated once the way the material brain works is fully understood, in just the same way as the concept of a demon has already been eliminated from science rather than enjoying reduction to a strictly mechanical description. Other mental properties, such as original intentionality (also called “meaning”, “content”, and “semantic character”), are also commonly regarded as special properties related to beliefs and other propositional attitudes. Eliminative materialism maintains that propositional attitudes such as beliefs and desires, among other intentional mental states that have content, do not exist. If eliminative materialism is the correct scientific account of human cognition then the assumption of the Chinese room argument that "minds have mental contents (semantics)" must be rejected.
Searle disagrees with this analysis and argues that "the study of the mind starts with such facts as that humans have beliefs, while thermostats, telephones, and adding machines don't ... what we wanted to know is what distinguishes the mind from thermostats and livers." He takes it as obvious that we can detect the presence of consciousness and dismisses these replies as being off the point. Other replies Margaret Boden argued in her paper "Escaping from the Chinese Room" that even if the person in the room does not understand the Chinese, it does not mean there is no understanding in the room. The person in the room at least understands the rule book used to provide output responses.
Carbon chauvinism
Searle conclusion that "human mental phenomena [are] dependent on actual physical–chemical properties of actual human brains" have been sometimes described as a form of "Carbon chauvinism". Steven Pinker suggested that a response to that conclusion would be to make a counter thought experiment to the Chinese Room, where the incredulity goes the other way. He brings as an example the short story ''They're Made Out of Meat'' which depicts an alien race composed of some electronic beings who upon finding Earth express disbelief that the meat brain of humans can experience consciousness and thought.
However, Searle himself denied being "Carbon chauvinist". He said "I have not tried to show that only biological based systems like our brains can think. [...] I regard this issue as up for grabs". He said that even silicon machines could theoretically have human-like consciousness and thought, if the actual physical–chemical properties of silicon could be used in a way that can produce consciousness and thought, but "until we know how the brain does it we are not in a position to try to do it artificially". See also
* Computational models of language acquisition
* Emergence
* I Am a Strange Loop
* Synthetic intelligence
* Leibniz's gap
Notes
, which discusses the relationship between the Chinese room argument and consciousness.}}
}}
Citations
References
*
* Also available at
*
*
* |publisherOxford University Press |isbn978-0-19-983935-3 |author-linkDavid Chalmers }}
*
*
* Page numbers refer to the PDF of the article.
*
*
*
*
*
*
* Page numbers refer to the PDF of the article.
* Page numbers refer to the PDF of the article.
*
*
* Page numbers refer to the PDF of the article.
*
*
*
*
* |publisherHarvard University Press |author-link=Hans Moravec }}
*
*
* |publisherBasic |isbn=978-0786725168 }}
*
*
*
*
*
*
*
* |publisherOxford University Press |isbn=978-0-19-825057-9 }}
*
*
*
* . Reprinted in .
* Page numbers refer to the PDF of the article. See also Searle's [https://web.archive.org/web/20010221025515/http://www.bbsonline.org/Preprints/OldArchive/bbs.searle2.html original draft].''
*
*
* }}
* }}
* |placeCambridge, MA |publisherMIT Press |isbn978-0-262-26113-5 }}
*
* |publisherOxford University Press |isbn=978-0-19-515733-8 }}
* |publisherCambridge University Press |isbn=978-0-521-59744-9 }}
*
*
* Page numbers refer to the PDF of the article.
*
*
* Page numbers refer to the PDF of the article.
*
Further reading
*
* Works involving Searle *
*
** Reviews and
* [http://globetrotter.berkeley.edu/people/Searle/searle-con4.html The Chinese Room Argument], part 4 of the September 2, 1999 interview with Searle [http://globetrotter.berkeley.edu/people/Searle/searle-con0.html Philosophy and the Habits of Critical Thinking] in the Conversations With History series
Category:Philosophical arguments
Category:Philosophy of artificial intelligence
Category:Qualia
Category:Thought experiments in philosophy of mind
|
https://en.wikipedia.org/wiki/Chinese_room
|
2025-04-05T18:27:45.155012
|
6217
|
Charon (disambiguation)
|
Charon, in Greek mythology, is the ferryman who carried the souls of the dead to the underworld.
Charon may also refer to:
Arts, entertainment, and media
Caronte (album) (Charon), a 1971 album by Italian band The Trip
Charon (band), a Finnish gothic metal band
Charon (CrossGen), a comic book character from CrossGen Entertainment's Sigilverse
Charon (Dungeons & Dragons), a lord of the Yugoloths whose primary function is to provide passage across the River Styx for a steep price
Charon (Marvel Comics), a villainous wizard
Charon (The Three Worlds), a fictional human species from Ian Irvine's arc of novels, The Three Worlds Cycle
Charon, an Eve Online freighter
Charon, a summon from a password-enhanced Golden Sun: The Lost Age and Golden Sun: Dark Dawn
Charon V, a fictional submarine in Michael Crichton's novel Sphere
Commander Charon, one of the Galactic Commanders from Pokémon Platinum
People with the name
Charon, a Theban military commander (fl. mid-4th century BC); see Androcydes
Charon of Naucratis, a historian
Charon of Carthage, a historian
Charon of Lampsacus, a historian
Alexios Charon, early 11th-century Byzantine official
Charon Asetoyer (born 1951), Comanche activist and women's health advocate
Carl Charon (born 1940), former American football player
Jacques Charon (1920–1975), French actor and film director
Jean-Émile Charon (1920–1998), French nuclear physicist, philosopher and writer.
Joel M. Charon (1939–2018), professor emeritus of sociology at Minnesota State University at Moorhead
Rita Charon (born 1949), physician and literary scholar
Viala Charon (1794–1880), French soldier, Governor General of Algeria, Senator of France
Places
Charon (moon), a moon of the dwarf planet Pluto
Charon, Louisiana, United States, an unincorporated community in Vermilion Parish
Science and technology
Charon (gun), an open source 3D-printable gun
Charon (arachnid), a genus of whipspider
Charon (software), a legacy hardware emulator for VAX, Alpha, HP 3000, PDP-11, and SPARC systems
Blue Origin Charon, the first flight test vehicle of Blue Origin
Other uses
Charon (horse), a racehorse
HMS Charon, several ships of the British Royal Navy
See also
Caron (disambiguation)
Eugenie Margeurite Honoree Charen (1786–1855), French painter
Mona Charen (born 1957), American columnist, political analyst and writer
Charron (disambiguation)
Charun (disambiguation)
Chaeron (disambiguation)
|
https://en.wikipedia.org/wiki/Charon_(disambiguation)
|
2025-04-05T18:27:45.209605
|
6220
|
Circle
|
|symmetry =
|area =
|perimeter
|type = Conic section
}}
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the<!-- This article is written using British English – see WP:ENGVAR, Wikipedia articles should remain with the original variant 'center' is the American English spelling --> centre.<!--see comment before about 'center'--> The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc.
The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus.
<!--To avoid layout breaking when TOC is hidden-->
Terminology
* Annulus: a ring-shaped object, the region bounded by two concentric circles.
* Arc: any connected part of a circle. Specifying two end points of an arc and a centre allows for two arcs that together make up a full circle.
* Centre: the point equidistant from all points on the circle.
* Chord: a line segment whose endpoints lie on the circle, thus dividing a circle into two segments.
* Circumference: the length of one circuit along the circle, or the distance around the circle.
* Diameter: a line segment whose endpoints lie on the circle and that passes through the centre; or the length of such a line segment. This is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord for a given circle, and its length is twice the length of a radius.
* Disc: the region of the plane bounded by a circle. In strict mathematical usage, a circle is only the boundary of the disc (or disk), while in everyday use the term "circle" may also refer to a disc.
* Lens: the region common to (the intersection of) two overlapping discs.
* Radius: a line segment joining the centre of a circle with any single point on the circle itself; or the length of such a segment, which is half (the length of) a diameter. Usually, the radius is denoted <math>r</math> and required to be a positive number. A circle with <math>r=0</math> is a degenerate case consisting of a single point.
* Sector: a region bounded by two radii of equal length with a common centre and either of the two possible arcs, determined by this centre and the endpoints of the radii.
* Segment: a region bounded by a chord and one of the arcs connecting the chord's endpoints. The length of the chord imposes a lower boundary on the diameter of possible arcs. Sometimes the term segment is used only for regions not containing the centre of the circle to which their arc belongs.
* Secant: an extended chord, a coplanar straight line, intersecting a circle in two points.
* Semicircle: one of the two possible arcs determined by the endpoints of a diameter, taking its midpoint as centre. In non-technical common usage it may mean the interior of the two-dimensional region bounded by a diameter and one of its arcs, that is technically called a half-disc. A half-disc is a special case of a segment, namely the largest one.
* Tangent: a coplanar straight line that has one single point in common with a circle ("touches the circle at this point").
All of the specified regions may be considered as open, that is, not containing their boundaries, or as closed, including their respective boundaries.
{| class"skin-invert-image" style"float:left;" cellspacing"0" cellpadding"0"
|-
|
|
|}
Etymology
The word circle derives from the Greek κίρκος/κύκλος (kirkos/kuklos), itself a metathesis of the Homeric Greek κρίκος (krikos), meaning "hoop" or "ring". The origins of the words circus and circuit are closely related.
History
]]
astronomical drawing.]]
Prehistoric people made stone circles and timber circles, and circular elements are common in petroglyphs and cave paintings. Disc-shaped prehistoric artifacts include the Nebra sky disc and jade discs called Bi.
The Egyptian Rhind papyrus, dated to 1700 BCE, gives a method to find the area of a circle. The result corresponds to (3.16049...) as an approximate value of .
Book 3 of Euclid's Elements deals with the properties of circles. Euclid's definition of a circle is:
}}
In Plato's Seventh Letter there is a detailed definition and explanation of the circle. Plato explains the perfect circle, and how it is different from any drawing, words, definition or explanation. Early science, particularly geometry and astrology and astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles.
In 1880 CE, Ferdinand von Lindemann proved that is transcendental, proving that the millennia-old problem of squaring the circle cannot be performed with straightedge and compass.
With the advent of abstract art in the early 20th century, geometric objects became an artistic subject in their own right. Wassily Kandinsky in particular often used circles as an element of his compositions.Symbolism and religious use
thumb|right|200px|
The compass (drafting)|compass in this 13th-century manuscript is a symbol of God's act of Creation. Notice also the circular shape of the halo.
From the time of the earliest known civilisations – such as the Assyrians and ancient Egyptians, those in the Indus Valley and along the Yellow River in China, and the Western civilisations of ancient Greece and Rome during classical Antiquity – the circle has been used directly or indirectly in visual art to convey the artist's message and to express certain ideas.
However, differences in worldview (beliefs and culture) had a great impact on artists' perceptions. While some emphasised the circle's perimeter to demonstrate their democratic manifestation, others focused on its centre to symbolise the concept of cosmic unity. In mystical doctrines, the circle mainly symbolises the infinite and cyclical nature of existence, but in religious traditions it represents heavenly bodies and divine spirits.
The circle signifies many sacred and spiritual concepts, including unity, infinity, wholeness, the universe, divinity, balance, stability and perfection, among others. Such concepts have been conveyed in cultures worldwide through the use of symbols, for example, a compass, a halo, the vesica piscis and its derivatives (fish, eye, aureole, mandorla, etc.), the ouroboros, the Dharma wheel, a rainbow, mandalas, rose windows and so forth. Magic circles are part of some traditions of Western esotericism.Analytic resultsCircumference
The ratio of a circle's circumference to its diameter is (pi), an irrational constant approximately equal to 3.141592654. The ratio of a circle's circumference to its radius is }}. (tau).}} Thus the circumference C is related to the radius r and diameter d by:
<math display"block">C 2\pi r \pi d.</math>Area enclosed
As proved by Archimedes, in his Measurement of a Circle, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, which comes to multiplied by the radius squared:
<math display"block">\mathrm{Area} \pi r^2.</math>
Equivalently, denoting diameter by d,
<math display"block">\mathrm{Area} \frac{\pi d^2}{4} \approx 0.7854 d^2,</math>
that is, approximately 79% of the circumscribing square (whose side is of length d).
The circle is the plane curve enclosing the maximum area for a given arc length. This relates the circle to a problem in the calculus of variations, namely the isoperimetric inequality.
Radian
If a circle of radius is centred at the vertex of an angle, and that angle intercepts an arc of the circle with an arc length of , then the radian measure of the angle is the ratio of the arc length to the radius:
<math display"block">\theta \frac{s}{r}.</math>
The circular arc is said to subtend the angle, known as the central angle, at the centre of the circle. One radian is the measure of the central angle subtended by a circular arc whose length is equal to its radius. The angle subtended by a complete circle at its centre is a complete angle, which measures }} radians, 360 degrees, or one turn.
Using radians, the formula for the arc length of a circular arc of radius and subtending a central angle of measure is
<math display"block">s \theta r,</math>
and the formula for the area of a circular sector of radius and with central angle of measure is
<math display"block">A \frac{1}{2} \theta r^2.</math>
In the special case 2}}, these formulae yield the circumference of a complete circle and area of a complete disc, respectively.
Equations
Cartesian coordinates
Equation of a circle
In an x–y Cartesian coordinate system, the circle with centre coordinates (a, b) and radius r is the set of all points (x, y) such that
<math display"block">(x - a)^2 + (y - b)^2 r^2.</math>
This equation, known as the equation of the circle, follows from the Pythagorean theorem applied to any point on the circle: as shown in the adjacent diagram, the radius is the hypotenuse of a right-angled triangle whose other sides are of length |x − a| and |y − b|. If the circle is centred at the origin (0, 0), then the equation simplifies to
<math display"block">x^2 + y^2 r^2.</math>
One coordinate as a function of the other
The circle of radius with center at in the – plane can be broken into two semicircles each of which is the graph of a function, and , respectively:
<math display=block>\begin{align}
y_+(x) = y_0 + \sqrt{ r^2 - (x - x_0)^2}, \\[5mu]
y_-(x) = y_0 - \sqrt{ r^2 - (x - x_0)^2},
\end{align}</math>
for values of ranging from to .
Parametric form
The equation can be written in parametric form using the trigonometric functions sine and cosine as
<math display="block">\begin{align}
x &= a + r\,\cos t, \\
y &= b + r\,\sin t,
\end{align}</math>
where t is a parametric variable in the range 0 to 2, interpreted geometrically as the angle that the ray from (a, b) to (x, y) makes with the positive x axis.
An alternative parametrisation of the circle is
<math display="block">\begin{align}
x &= a + r \frac{1 - t^2}{1 + t^2}, \\
y &= b + r \frac{2t}{1 + t^2}.
\end{align}</math>
In this parameterisation, the ratio of t to r can be interpreted geometrically as the stereographic projection of the line passing through the centre parallel to the x axis (see Tangent half-angle substitution). However, this parameterisation works only if t is made to range not only through all reals but also to a point at infinity; otherwise, the leftmost point of the circle would be omitted.
3-point form
The equation of the circle determined by three points <math>(x_1, y_1), (x_2, y_2), (x_3, y_3)</math> not on a line is obtained by a conversion of the 3-point form of a circle equation:
<math display="block">
\frac{({\color{green}x} - x_1)({\color{green}x} - x_2) + ({\color{red}y} - y_1)({\color{red}y} - y_2)}
{({\color{red}y} - y_1)({\color{green}x} - x_2) - ({\color{red}y} - y_2)({\color{green}x} - x_1)} =
\frac{(x_3 - x_1)(x_3 - x_2) + (y_3 - y_1)(y_3 - y_2)}
{(y_3 - y_1)(x_3 - x_2) - (y_3 - y_2)(x_3 - x_1)}.</math>
Homogeneous form
In homogeneous coordinates, each conic section with the equation of a circle has the form
<math display"block">x^2 + y^2 - 2axz - 2byz + cz^2 0.</math>
It can be proven that a conic section is a circle exactly when it contains (when extended to the complex projective plane) the points I(1: i: 0) and J(1: −i: 0). These points are called the circular points at infinity.
Polar coordinates
In polar coordinates, the equation of a circle is
<math display"block">r^2 - 2 r r_0 \cos(\theta - \phi) + r_0^2 a^2,</math>
where a is the radius of the circle, <math>(r, \theta)</math> are the polar coordinates of a generic point on the circle, and <math>(r_0, \phi)</math> are the polar coordinates of the centre of the circle (i.e., r<sub>0</sub> is the distance from the origin to the centre of the circle, and φ is the anticlockwise angle from the positive x axis to the line connecting the origin to the centre of the circle). For a circle centred on the origin, i.e. 0}}, this reduces to a}}. When a}}, or when the origin lies on the circle, the equation becomes
<math display"block">r 2 a\cos(\theta - \phi).</math>
In the general case, the equation can be solved for r, giving
<math display"block">r r_0 \cos(\theta - \phi) \pm \sqrt{a^2 - r_0^2 \sin^2(\theta - \phi)}.</math>
Without the ± sign, the equation would in some cases describe only half a circle.
Complex plane
In the complex plane, a circle with a centre at c and radius r has the equation
<math display"block">|z - c| r.</math>
In parametric form, this can be written as
<math display"block">z re^{it} + c.</math>
The slightly generalised equation
<math display"block">pz\overline{z} + gz + \overline{gz} q</math>
for real p, q and complex g is sometimes called a generalised circle. This becomes the above equation for a circle with <math>p 1,\ g -\overline{c},\ q r^2 - |c|^2</math>, since <math>|z - c|^2 z\overline{z} - \overline{c}z - c\overline{z} + c\overline{c}</math>. Not all generalised circles are actually circles: a generalised circle is either a (true) circle or a line.
Tangent lines
The tangent line through a point P on the circle is perpendicular to the diameter passing through P. If (x<sub>1</sub>, y<sub>1</sub>)}} and the circle has centre (a, b) and radius r, then the tangent line is perpendicular to the line from (a, b) to (x<sub>1</sub>, y<sub>1</sub>), so it has the form c}}. Evaluating at (x<sub>1</sub>, y<sub>1</sub>) determines the value of c, and the result is that the equation of the tangent is
<math display"block">(x_1 - a)x + (y_1 - b)y (x_1 - a)x_1 + (y_1 - b)y_1,</math>
or
<math display"block">(x_1 - a)(x - a) + (y_1 - b)(y - b) r^2.</math>
If , then the slope of this line is
<math display"block">\frac{dy}{dx} -\frac{x_1 - a}{y_1 - b}.</math>
This can also be found using implicit differentiation.
When the centre of the circle is at the origin, then the equation of the tangent line becomes
<math display"block">x_1 x + y_1 y r^2,</math>
and its slope is
<math display"block">\frac{dy}{dx} -\frac{x_1}{y_1}.</math>
Properties
* The circle is the shape with the largest area for a given length of perimeter (see Isoperimetric inequality).
* The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry, and it has rotational symmetry around the centre for every angle. Its symmetry group is the orthogonal group O(2,R). The group of rotations alone is the circle group T.
* All circles are similar.
** A circle circumference and radius are proportional.
** The area enclosed and the square of its radius are proportional.
** The constants of proportionality are 2 and respectively.
* The circle that is centred at the origin with radius 1 is called the unit circle.
** Thought of as a great circle of the unit sphere, it becomes the Riemannian circle.
* Through any three points, not all on the same line, there lies a unique circle. In Cartesian coordinates, it is possible to give explicit formulae for the coordinates of the centre of the circle and the radius in terms of the coordinates of the three given points. See circumcircle.
Chord
* Chords are equidistant from the centre of a circle if and only if they are equal in length.
* The perpendicular bisector of a chord passes through the centre of a circle; equivalent statements stemming from the uniqueness of the perpendicular bisector are:
** A perpendicular line from the centre of a circle bisects the chord.
** The line segment through the centre bisecting a chord is perpendicular to the chord.
* If a central angle and an inscribed angle of a circle are subtended by the same chord and on the same side of the chord, then the central angle is twice the inscribed angle.
* If two angles are inscribed on the same chord and on the same side of the chord, then they are equal.
* If two angles are inscribed on the same chord and on opposite sides of the chord, then they are supplementary.
** For a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.
* An inscribed angle subtended by a diameter is a right angle (see Thales' theorem).
* The diameter is the longest chord of the circle.
** Among all the circles with a chord AB in common, the circle with minimal radius is the one with diameter AB.
* If the intersection of any two chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then cd}}.
* If the intersection of any two perpendicular chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then equals the square of the diameter.
* The sum of the squared lengths of any two chords intersecting at right angles at a given point is the same as that of any other two perpendicular chords intersecting at the same point and is given by 8r<sup>2</sup> − 4p<sup>2</sup>, where r is the circle radius, and p is the distance from the centre point to the point of intersection.
* The distance from a point on the circle to a given chord times the diameter of the circle equals the product of the distances from the point to the ends of the chord.
Tangent
* A line drawn perpendicular to a radius through the end point of the radius lying on the circle is a tangent to the circle.
* A line drawn perpendicular to a tangent through the point of contact with a circle passes through the centre of the circle.
* Two tangents can always be drawn to a circle from any point outside the circle, and these tangents are equal in length.
* If a tangent at A and a tangent at B intersect at the exterior point P, then denoting the centre as O, the angles ∠BOA and ∠BPA are supplementary.
* If AD is tangent to the circle at A and if AQ is a chord of the circle, then arc(AQ)}}.Theorems
* The chord theorem states that if two chords, CD and EB, intersect at A, then AB × AE}}.
* If two secants, AE and AD, also cut the circle at B and C respectively, then AB × AE}} (corollary of the chord theorem).
* A tangent can be considered a limiting case of a secant whose ends are coincident. If a tangent from an external point A meets the circle at F and a secant from the external point A meets the circle at C and D respectively, then AC × AD}} (tangent–secant theorem).
* The angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (tangent chord angle).
* If the angle subtended by the chord at the centre is 90°, then r √2}}, where ℓ is the length of the chord, and r is the radius of the circle.
* If two secants are inscribed in the circle as shown at right, then the measurement of angle A is equal to one half the difference of the measurements of the enclosed arcs (<math>\overset{\frown}{DE}</math> and <math>\overset{\frown}{BC}</math>). That is, <math>2\angle{CAB} \angle{DOE} - \angle{BOC}</math>, where O is the centre of the circle (secant–secant theorem).Inscribed angles
An inscribed angle (examples are the blue and green angles in the figure) is exactly half the corresponding central angle (red). Hence, all inscribed angles that subtend the same arc (pink) are equal. Angles inscribed on the arc (brown) are supplementary. In particular, every inscribed angle that subtends a diameter is a right angle (since the central angle is 180°).
Sagitta
The sagitta (also known as the versine) is a line segment drawn perpendicular to a chord, between the midpoint of that chord and the arc of the circle.
Given the length y of a chord and the length x of the sagitta, the Pythagorean theorem can be used to calculate the radius of the unique circle that will fit around the two lines:
<math display"block">r \frac{y^2}{8x} + \frac{x}{2}.</math>
Another proof of this result, which relies only on two chord properties given above, is as follows. Given a chord of length y and with sagitta of length x, since the sagitta intersects the midpoint of the chord, we know that it is a part of a diameter of the circle. Since the diameter is twice the radius, the "missing" part of the diameter is () in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that ( (y / 2)<sup>2</sup>}}. Solving for r, we find the required result.Compass and straightedge constructions
There are many compass-and-straightedge constructions resulting in circles.
The simplest and most basic is the construction given the centre of the circle and a point on the circle. Place the fixed leg of the compass on the centre point, the movable leg on the point on the circle and rotate the compass.
Construction with given diameter
* Construct the midpoint of the diameter.
* Construct the circle with centre passing through one of the endpoints of the diameter (it will also pass through the other endpoint).
Construction through three noncollinear points
* Name the points , and ,
* Construct the perpendicular bisector of the segment }}.
* Construct the perpendicular bisector of the segment }}.
* Label the point of intersection of these two perpendicular bisectors . (They meet because the points are not collinear).
* Construct the circle with centre passing through one of the points , or (it will also pass through the other two points).
Circle of Apollonius
<!--This section is linked from Sphere among others-->
Apollonius of Perga showed that a circle may also be defined as the set of points in a plane having a constant ratio (other than 1) of distances to two fixed foci, A and B. (The set of points where the distances are equal is the perpendicular bisector of segment AB, a line.) That circle is sometimes said to be drawn about two points.
The proof is in two parts. First, one must prove that, given two foci A and B and a ratio of distances, any point P satisfying the ratio of distances must fall on a particular circle. Let C be another point, also satisfying the ratio and lying on segment AB. By the angle bisector theorem the line segment PC will bisect the interior angle APB, since the segments are similar:
<math display"block">\frac{AP}{BP} \frac{AC}{BC}.</math>
Analogously, a line segment PD through some point D on AB extended bisects the corresponding exterior angle BPQ where Q is on AP extended. Since the interior and exterior angles sum to 180 degrees, the angle CPD is exactly 90 degrees; that is, a right angle. The set of points P such that angle CPD is a right angle forms a circle, of which CD is a diameter.
Second, see for a proof that every point on the indicated circle satisfies the given ratio.Cross-ratios
A closely related property of circles involves the geometry of the cross-ratio of points in the complex plane. If A, B, and C are as above, then the circle of Apollonius for these three points is the collection of points P for which the absolute value of the cross-ratio is equal to one:
<math display"block">\bigl|[A, B; C, P]\bigr| 1.</math>
Stated another way, P is a point on the circle of Apollonius if and only if the cross-ratio is on the unit circle in the complex plane.
Generalised circles
If C is the midpoint of the segment AB, then the collection of points P satisfying the Apollonius condition
<math display"block">\frac{|AP|}{|BP|} \frac{|AC|}{|BC|}</math>
is not a circle, but rather a line.
Thus, if A, B, and C are given distinct points in the plane, then the locus of points P satisfying the above equation is called a "generalised circle." It may either be a true circle or a line. In this sense a line is a generalised circle of infinite radius.
Inscription in or circumscription about other figures
In every triangle a unique circle, called the incircle, can be inscribed such that it is tangent to each of the three sides of the triangle.
About every triangle a unique circle, called the circumcircle, can be circumscribed such that it goes through each of the triangle's three vertices.
A tangential polygon, such as a tangential quadrilateral, is any convex polygon within which a circle can be inscribed that is tangent to each side of the polygon. Every regular polygon and every triangle is a tangential polygon.
A cyclic polygon is any convex polygon about which a circle can be circumscribed, passing through each vertex. A well-studied example is the cyclic quadrilateral. Every regular polygon and every triangle is a cyclic polygon. A polygon that is both cyclic and tangential is called a bicentric polygon.
A hypocycloid is a curve that is inscribed in a given circle by tracing a fixed point on a smaller circle that rolls within and tangent to the given circle.
Limiting case of other figures
The circle can be viewed as a limiting case of various other figures:
* The series of regular polygons with n sides has the circle as its limit as n approaches infinity. This fact was applied by Archimedes to approximate π.
* A Cartesian oval is a set of points such that a weighted sum of the distances from any of its points to two fixed points (foci) is a constant. An ellipse is the case in which the weights are equal. A circle is an ellipse with an eccentricity of zero, meaning that the two foci coincide with each other as the centre of the circle. A circle is also a different special case of a Cartesian oval in which one of the weights is zero.
* A superellipse has an equation of the form <math>\left|\frac{x}{a}\right|^n\! + \left|\frac{y}{b}\right|^n\! 1</math> for positive a, b, and n. A supercircle has . A circle is the special case of a supercircle in which 2}}.
* A Cassini oval is a set of points such that the product of the distances from any of its points to two fixed points is a constant. When the two fixed points coincide, a circle results.
* A curve of constant width is a figure whose width, defined as the perpendicular distance between two distinct parallel lines each intersecting its boundary in a single point, is the same regardless of the direction of those two parallel lines. The circle is the simplest example of this type of figure.
Locus of constant sum
Consider a finite set of <math>n</math> points in the plane. The locus of points such that the sum of the squares of the distances to the given points is constant is a circle, whose centre is at the centroid of the given points.
A generalisation for higher powers of distances is obtained if, instead of <math>n</math> points, the vertices of the regular polygon <math>P_n</math> are taken. The locus of points such that the sum of the <math>2m</math>-th power of distances <math>d_i</math> to the vertices of a given regular polygon with circumradius <math>R</math> is constant is a circle, if
<math display"block">\sum_{i1}^n d_i^{2m} > nR^{2m} , \quad \text{ where } ~ m = 1, 2, \dots, n-1;</math>
whose centre is the centroid of the <math>P_n</math>.
In the case of the equilateral triangle, the loci of the constant sums of the second and fourth powers are circles, whereas for the square, the loci are circles for the constant sums of the second, fourth, and sixth powers. For the regular pentagon the constant sum of the eighth powers of the distances will be added and so forth.
Squaring the circle
Squaring the circle is the problem, proposed by ancient geometers, of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge.
In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi () is a transcendental number, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. Despite the impossibility, this topic continues to be of interest for pseudomath enthusiasts.
Generalisations
In other p-norms
) in different -norms (every vector from the origin to the unit circle has a length of one, the length being calculated with length-formula of the corresponding ).]]
Defining a circle as the set of points with a fixed distance from a point, different shapes can be considered circles under different definitions of distance. In p-norm, distance is determined by
<math display"block"> \left\| x \right\| _p \left( \left|x_1\right|^p + \left|x_2\right|^p + \dotsb + \left|x_n\right|^p \right) ^{1/p} .</math>
In Euclidean geometry, p = 2, giving the familiar
<math display"block"> \left\| x \right\| _2 \sqrt{ \left|x_1\right|^2 + \left|x_2\right|^2 + \dotsb + \left|x_n\right|^2 } .</math>
In taxicab geometry, p 1. Taxicab circles are squares with sides oriented at a 45° angle to the coordinate axes. While each side would have length <math>\sqrt{2} r</math> using a Euclidean metric, where r is the circle's radius, its length in taxicab geometry is 2r. Thus, a circle's circumference is 8r. Thus, the value of a geometric analog to <math>\pi </math> is 4 in this geometry. The formula for the unit circle in taxicab geometry is <math>|x| + |y| 1</math> in Cartesian coordinates and
<math display"block">r \frac{1}{\left| \sin \theta\right| + \left|\cos\theta\right|}</math>
in polar coordinates.
A circle of radius 1 (using this distance) is the von Neumann neighborhood of its centre.
A circle of radius r for the Chebyshev distance (L<sub>∞</sub> metric) on a plane is also a square with side length 2r parallel to the coordinate axes, so planar Chebyshev distance can be viewed as equivalent by rotation and scaling to planar taxicab distance. However, this equivalence between L<sub>1</sub> and L<sub>∞</sub> metrics does not generalise to higher dimensions.
Topological definition
The circle is the one-dimensional hypersphere (the 1-sphere).
In topology, a circle is not limited to the geometric concept, but to all of its homeomorphisms. Two topological circles are equivalent if one can be transformed into the other via a deformation of R<sup>3</sup> upon itself (known as an ambient isotopy).
Specially named circles
* Apollonian circles
* Archimedean circle
* Archimedes' twin circles
* Bankoff circle
* Carlyle circle
* Chromatic circle
* Circle of antisimilitude
* Ford circle
* Geodesic circle
* Johnson circles
* Schoch circles
* Woo circles
Of a triangle
* Apollonius circle of the excircles
* Brocard circle
* Excircle
* Incircle
* Lemoine circle
* Lester circle
* Malfatti circles
* Mandart circle
* Nine-point circle
* Orthocentroidal circle
* Parry circle
* Polar circle (geometry)
* Spieker circle
* Van Lamoen circle
Of certain quadrilaterals
* Eight-point circle of an orthodiagonal quadrilateral
Of a conic section
* Director circle
* Directrix circle
Of a torus
* Villarceau circles
See also
*
*
*
*
*
*
*
*
*
*
*
Notes
References
Further reading
* External links
*
*
*
*
*
*
Category:Elementary shapes
Category:Conic sections
Category:Pi
|
https://en.wikipedia.org/wiki/Circle
|
2025-04-05T18:27:45.267812
|
6221
|
Cardinal (Catholic Church)
|
(wide-brimmed hat) with 15 tassels on each side (the motto and escutcheon are proper to the individual cardinal).]]
A cardinal () is a senior member of the clergy of the Catholic Church. As titular members of the clergy of the Diocese of Rome, they serve as advisors to the pope, who is the bishop of Rome. Cardinals are chosen and formally created by the pope, and typically hold the title for life. Collectively, they constitute the College of Cardinals. The most solemn responsibility of the cardinals is to elect a new pope in a conclave, almost always from among themselves (with a few historical exceptions), when the Holy See is vacant. During the period between a pope's death or resignation and the election of his successor, the day-to-day governance of the Holy See is in the hands of the College of Cardinals. The right to participate in a conclave is limited to cardinals who have not reached the age of 80 years by the day the vacancy occurs. In addition, cardinals collectively participate in papal consistories, in which matters of importance to the Church are considered and new cardinals may be created. Cardinals of working age are also appointed to roles overseeing dicasteries of the Roman Curia, the central administration of the Catholic Church.
Cardinals are drawn from a variety of backgrounds, being appointed as cardinals in addition to their existing roles within the Church. Most cardinals are bishops and archbishops leading dioceses and archdioceses around the world – often the most prominent diocese or archdiocese in their country. Others are titular bishops who are current or former officials within the Roman Curia (generally the heads of dicasteries and other bodies linked to the Curia). A very small number are priests recognised by the pope for their service to the Church; canon law requires them to be generally consecrated as bishops before they are made cardinals, but some are granted a papal dispensation.) is Raniero Cantalamessa.}} There are no strict criteria for elevation to the College of Cardinals. Since 1917, a potential cardinal must already be at least a priest, but laymen have been cardinals in the past. The selection is entirely up to the pope, and tradition is his only guide.
there are serving cardinals, of whom are eligible to vote in a conclave to elect a new pope.
History
, chief minister of France]]
There is general disagreement about the origin of the term, but a chief consensus is that the Latin comes from the term (meaning 'pivot' or 'hinge'), and was first used in late antiquity to designate a bishop or priest who was incorporated into a church for which he had not originally been ordained. In Rome the first persons to be called cardinals were the deacons of the seven regions of the city at the beginning of the 6th century, when the word began to mean 'principal', 'eminent', or 'superior'. The name was also given to the senior priest in each of the "title" churches (the parish churches) of Rome and to the bishops of the seven sees surrounding the city. By the 8th century the Roman cardinals constituted a privileged class among the Roman clergy. They took part in the administration of the Church of Rome and in the papal liturgy. By decree of a synod of 769, only a cardinal was eligible to become Bishop of Rome. Cardinals were granted the privilege of wearing the red hat by Pope Innocent IV in 1244.
In cities other than Rome, the name cardinal began to be applied to certain churchmen as a mark of honour. The earliest example of this occurs in a letter sent by Pope Zacharias in 747 to Pippin the Younger, ruler of the Franks, in which Zacharias applied the title to the priests of Paris to distinguish them from country clergy. This meaning of the word spread rapidly, and from the 9th century various episcopal cities had a special class among the clergy known as cardinals. The use of the title was reserved for the cardinals of Rome in 1567 by Pius V.
In 1059 (five years after the East-West Schism), the right of electing the pope was reserved to the principal clergy of Rome and the bishops of the seven suburbicarian sees. In the 12th century the practice of appointing ecclesiastics from outside Rome as cardinals began, with each of them assigned a church in Rome as his titular church or linked with one of the suburbicarian dioceses, while still being incardinated in a diocese other than that of Rome.
The term cardinal at one time applied to any priest permanently assigned or incardinated to a church, or specifically to the senior priest of an important church, based on the Latin ('hinge'), meaning 'pivotal' as in "principal" or "chief". The term was applied in this sense as early as the 9th century to the priests of the (parishes) of the diocese of Rome.
The earlier influence of temporal rulers, notably the kings of France, reasserted itself through the influence of cardinals of certain nationalities or politically significant movements. Traditions even developed entitling certain monarchs, including those of Austria, Spain, and France, to nominate one of their trusted clerical subjects to be created cardinal, a so-called "crown-cardinal".
In early modern times, cardinals often had important roles in secular affairs. In some cases, they took on powerful positions in government. In Henry VIII's England, his chief minister was for some time Cardinal Wolsey. Cardinal Richelieu's power was so great that he was for many years effectively the ruler of France. Richelieu's successor was also a cardinal, Jules Mazarin. Guillaume Dubois and André-Hercule de Fleury complete the list of the four great cardinals to have ruled France.
While the incumbents of some sees are regularly made cardinals, and some countries are entitled to at least one cardinal by concordat (usually earning either its primate or the metropolitan of the capital city the cardinal's hat), almost no see carries an actual right to the cardinalate, not even if its bishop is a patriarch: the notable exception is the Patriarch of Lisbon who, by Pope Clement XII's 1737 bull , is accorded the right to be elevated to the rank of cardinal in the consistory following his appointment.
Papal elections
In 1059, Pope Nicholas II gave cardinals the right to elect the Bishop of Rome in the papal bull . For a time this power was assigned exclusively to the cardinal bishops, but in 1179 the Third Lateran Council restored the right to the whole body of cardinals.NumbersIn 1586, Pope Sixtus V limited the number of cardinals to 70: six cardinal bishops, 50 cardinal priests, and 14 cardinal deacons. Pope John XXIII exceeded that limit citing the need to staff church offices. In November 1970, in , Pope Paul VI established that electors would be under the age of 80 years. When it took effect on 1 January 1971, it deprived 25 cardinals of the right to participate in a conclave. In October 1975 in , he set the maximum number of electors at 120, while establishing no limit on the overall size of the college.
Popes can set aside church laws and they have regularly brought the number of cardinals under the age of 80 to more than 120, twice reaching as high as 135 with Pope John Paul II's consistories of February 2001 and October 2003. No more than 120 electors have ever participated in a conclave, but most canon lawyers believe that if their number exceeded 120 they would all participate. is that "No Cardinal elector can be excluded from active or passive voice in the election of the Supreme Pontiff, for any reason or pretext."}}
Pope Paul VI also increased the number of cardinal bishops by assigning that rank, in 1965, to patriarchs of the Eastern Catholic Churches when named cardinals. In 2018, Pope Francis expanded the cardinal bishops of Roman title, because this had not been done despite recent decades' expansion in the two lower orders of cardinals, besides having all six such cardinals being over the age limit for a conclave.Titular churches
, Archbishop of Vienna and Cardinal-Priest of San Crisogono, pictured in the early 1930s]]
Each cardinal is assigned a titular church upon his creation, which is always a church in the city of Rome. Through the process of opting (), a cardinal can rise through the ranks from cardinal deacon to priest, and from cardinal priest to that of cardinal bishop – in which case he obtains one of the suburbicarian sees located around the city of Rome. The only exception is for patriarchs of the Eastern Catholic Churches. Nevertheless, cardinals possess no power of governance nor are they to intervene in any way in matters which pertain to the administration of goods, discipline, or the service of their titular churches. They are allowed to celebrate Mass and hear confessions and lead visits and pilgrimages to their titular churches, in coordination with the staff of the church. They often support their churches monetarily, and many cardinals do keep in contact with the pastoral staffs of their titular churches.
The Dean of the College of Cardinals in addition to such a titular church also receives the titular bishopric of Ostia, the primary suburbicarian see. Cardinals governing a particular church retain that church.
Title and reference style
In 1630, Pope Urban VIII decreed their title to be Eminence (previously, it had been and ) and ; but Pope Urban VIII (of the Barberini family), in 1630, established the above as their title of honour." Edward Wigglesworth, Thomas Gamaliel Bradford: Encyclopædia Americana: a popular dictionary of arts, sciences. Volume 4, page 493.}} and decreed that their secular rank would equate to prince, making them second only to the pope and crowned monarchs.[...] A decree of 10 June 1630, by Urban VII bestowed the title "His Eminence", historically reserved for high nobility, upon the cardinals, thus elevating them above 'His Excellency', then being used to refer to Italian princes." Guruge, Anura. The Next Pope. Alton, New Hampshire. 2010. p. 81.}}
In accordance with tradition, they sign by placing the title "Cardinal" (abbreviated Card.) after their personal name and before their surname as, for instance, "John Card(inal) Doe" or, in Latin, "Ioannes Card(inalis) Doe". Some writers, such as James-Charles Noonan, hold that, in the case of cardinals, the form used for signatures should be used also when referring to them in English. However, official sources, such as the Catholic News Service, say that the correct form for referring to a cardinal in English is normally as "Cardinal [First name] [Surname]". This is the rule given also in stylebooks not associated with the church. This style is also generally followed on the websites of the Holy See and episcopal conferences. Oriental patriarchs who are created cardinals customarily use as their full title, probably because they do not belong to the Roman clergy. (Meaning: "I announce to you a great joy; we have a Pope: The Most Eminent and Most Reverend Lord, Lord [first name] Cardinal of the Holy Roman Church [last name], ...")}} if the new pope is a cardinal, as has been the case since 1389.
The title Prince of the Church has historically been applied to cardinals of the Catholic Church, and sometimes more broadly to senior members of the church hierarchy. It has been rejected by Pope Francis, who stated to a group of newly created cardinals "He (Jesus) does not call you to become 'princes' of the Church, to 'sit on his right or on his left.' He calls you to serve like Him and with Him." The title is still applied contemporarily, both officially and other times in criticism of the perceived attitudes of some cardinals.
Orders and their chief offices
of a cardinal]]
Cardinal bishops
was Dean of the College of Cardinals from 2005 to 2019.]]
Cardinal bishops (cardinals of the episcopal order; ) are the senior order of cardinals. Though in modern times the vast majority of cardinals are also bishops or archbishops, few are "cardinal bishops". For most of the second millennium there were six cardinal bishops, each presiding over one of the seven suburbicarian sees around Rome: Ostia, Albano, Porto and Santa Rufina, Palestrina, Sabina and Mentana, Frascati, and Velletri. Velletri was united with Ostia from 1150 until 1914, when Pope Pius X separated them again, but decreed that whichever cardinal bishop became Dean of the College of Cardinals would keep the suburbicarian see he already held, adding to it that of Ostia, with the result that there continued to be only six cardinal bishops. Since 1962, the cardinal bishops have only a titular relationship with the suburbicarian sees, each of which is governed by a separate ordinary.
Until 1961, membership in the order of cardinal bishops was achieved through precedence in the College of Cardinals. When a suburbicarian see fell vacant, the most senior cardinal by precedence could exercise his option to claim the see and be promoted to the order of cardinal bishops. Pope John XXIII abolished that privilege on 10 March 1961 and made the right to promote someone to the order of cardinal bishops the sole prerogative of the pope.
In 1965, Pope Paul VI decreed in his that patriarchs of the Eastern Catholic Churches who were named cardinals (i.e. "cardinal patriarchs") would also be cardinal bishops, ranking after the six Latin Church cardinal bishops of the suburbicarian sees. (Latin Church patriarchs who become cardinals are cardinal priests, not cardinal bishops: for example Angelo Scola was made Patriarch of Venice in 2002 and cardinal priest of Santi XII Apostoli in 2003.) Those of cardinal patriarch rank continue to hold their patriarchal see and are not assigned any Roman title (suburbicarian see or title or deaconry).
At the June 2018 consistory, Pope Francis increased the number of Latin Church cardinal bishops to match the expansion in cardinal priests and cardinal deacons in recent decades. He elevated four cardinals to this rank granting their titular churches and deaconries suburbicarian rank (temporarily) and making them equivalent to suburbicarian see titles. At the time of the announcement, all six cardinal bishops of suburbicarian see titles, as well as two of the three cardinal patriarchs, were non-electors as they had reached the age of 80. Pope Francis created another cardinal bishop in the same way on 1 May 2020, bringing the number of Latin Church cardinal bishops to 11.
The Dean of the College of Cardinals, the highest ranking cardinal, was formerly the longest serving cardinal bishop, but since 1965 is elected by the Latin Church cardinal bishops from among their number, subject to papal approval. Likewise the Vice-Dean, formerly the second longest serving, is also elected. Seniority of the remaining Latin Church cardinal bishops is still by date of appointment to the rank. The current Dean is Giovanni Battista Re and the Vice-Dean is Leonardo Sandri.
Cardinal priests
Cardinal priests () are the most numerous of the three orders of cardinals in the Catholic Church, ranking above the cardinal deacons and below the cardinal bishops. Those who are named cardinal priests today are generally also bishops of important dioceses throughout the world, though some hold Curial positions.
In modern times, the term cardinal priest is interpreted as meaning a cardinal who is of the order of priests. Originally, however, this referred to certain key priests of important churches of the Diocese of Rome, who were recognized as the priests – the important priests chosen by the pope to advise him in his duties as Bishop of Rome. Certain clerics in many dioceses at the time, not just that of Rome, were said to be the key personnel—the term gradually became exclusive to Rome to indicate those entrusted with electing the Bishop of Rome, the pope.
]]
While the cardinalate has long been expanded beyond the Roman pastoral clergy and Roman Curia, every cardinal priest has a titular church in Rome, though they may be bishops or archbishops elsewhere, just as cardinal bishops were given one of the suburbicarian dioceses around Rome. Pope Paul VI abolished all administrative rights cardinals had with regard to their titular churches, though the cardinal's name and coat of arms are still posted in the church, and they are expected to celebrate Mass and preach there if convenient when they are in Rome.
While the number of cardinals was small from the times of the Roman Empire to the Renaissance, and frequently smaller than the number of recognized churches entitled to a cardinal priest, in the 16th century the college expanded markedly. In 1587, Pope Sixtus V sought to arrest this growth by fixing the maximum size of the college at 70, including 50 cardinal priests, about twice the historical number. This limit was respected until 1958, and the list of titular churches modified only on rare occasions, generally when a building fell into disrepair. When Pope John XXIII abolished the limit, he began to add new churches to the list, which Popes Paul VI and John Paul II continued to do. Today there are close to 150 titular churches, out of over 300 churches in Rome.
The cardinal who is the longest-serving member of the order of cardinal priests is titled cardinal protopriest. He had certain ceremonial duties in the conclave that have effectively ceased because he would generally have already reached age 80, at which cardinals are barred from the conclave. The current cardinal protopriest is Michael Michai Kitbunchu of Thailand.
Cardinal deacons
The cardinal deacons () are the lowest-ranking cardinals. Cardinals elevated to the diaconal order are either officials of the Roman Curia or priests elevated after their 80th birthday, chosen mainly for the honor of it (since those over 80 are not able to vote in a conclave). While bishops with diocesan responsibilities are created cardinal priests, it is generally not so for cardinal deacons.
Cardinal deacons derive originally from the seven deacons in the Papal Household who supervised the church's works in the 14 districts of Rome during the early Middle Ages, when church administration was effectively the government of Rome and provided all social services. They came to be called "cardinal deacons" by the late eighth century, and they were granted active rights in papal elections and made eligible for the election as pope by the decree of 769.
Cardinals elevated to the diaconal order are mainly officials of the Roman Curia holding various posts in the church administration. Their number and influence has varied through the years. While historically predominantly Italian, the group has become much more internationally diverse in later years. While in 1939 about half were Italian, by 1994 the number was reduced to one third. Their influence in the election of the pope has been considered important. They are better informed and connected than the dislocated cardinals but their level of unity has been varied. Under the 1587 decree of Pope Sixtus V, which fixed the maximum size of the College of Cardinals, there were 14 cardinal deacons. Later the number increased. As late as 1939 almost half of the cardinals were members of the Curia. Pius XII reduced this percentage to 24 percent. John XXIII brought it back up to 37 percent but Paul VI brought it down to 27 percent. John Paul II maintained this ratio.}} from the central balcony of St. Peter's Basilica in Vatican City. The protodeacon also bestows the pallium on the new pope and crowns him with the papal tiara, although the crowning has not been celebrated since Pope John Paul I opted for a simpler papal inauguration ceremony in 1978. The current cardinal protodeacon is Dominique Mamberti.
Cardinal protodeacons since 1887
, current Cardinal Protodeacon]]
* Giuseppe Pecci, S.J. (20 December 1887 – 8 February 1890)
* John Henry Newman, C.O. (8 February 1890 – 11 August 1890)
* Joseph Hergenröther (11 August 1890 – 3 October 1890)
* Tommaso Maria Zigliara, O.P. (3 October 1890 – 1 June 1891)
* Isidoro Verga (1 June 1891 – 22 June 1896)
* Luigi Macchi (22 June 1896 – 29 March 1907); announced election of Pope Pius X (1903)
* Andreas Steinhuber, S.J. (29 March 1907 – 15 October 1907)
* Francesco Segna (15 October 1907 – 4 January 1911)
* Francesco Salesio Della Volpe (4 January 1911 – 5 November 1916 (his death)); announced election of Pope Benedict XV (1914)
* Gaetano Bisleti (5 November 1916 – 17 December 1928); announced election of Pope Pius XI (1922)
* Camillo Laurenti (17 December 1928 – 16 December 1935)
* Camillo Caccia-Dominioni (16 December 1935 – 12 November 1946 (his death)); announced election of Pope Pius XII (1939)
* Nicola Canali (12 November 1946 – 3 August 1961 (his death)); announced election of Pope John XXIII (1958)
* Alfredo Ottaviani (3 August 1961 – 26 June 1967); announced election of Pope Paul VI (1963)
* Arcadio Larraona Saralegui, CMF (26 June 1967 – 28 April 1969)
* William Theodore Heard (28 April 1969 – 18 May 1970)
* Antonio Bacci (18 May 1970 – 20 January 1971 (his death))
* Michael Browne, OP (20 January 1971 – 31 March 1971 (his death))
* Federico Callori di Vignale (31 March 1971 – 8 August 1971†)
* Charles Journet (8 August 1971 – 5 March 1973)
* Pericle Felici (5 March 1973 – 30 June 1979); announced elections of Pope John Paul I (1978) and Pope John Paul II (1978)
* Sergio Pignedoli (30 June 1979 – 15 June 1980 (his death))
* Umberto Mozzoni (15 June 1980 – 2 February 1983)
* Opilio Rossi (2 February 1983 – 22 June 1987)
* Giuseppe Caprio (22 June 1987 – 26 November 1990)
* Aurelio Sabattani (26 November 1990 – 5 April 1993)
* Duraisamy Simon Lourdusamy (5 April 1993 – 29 January 1996)
* Eduardo Martínez Somalo (29 January 1996 – 9 January 1999)
* Pio Laghi (9 January 1999 – 26 February 2002)
* Luigi Poggi (26 February 2002 – 24 February 2005)
* Jorge Medina (24 February 2005 – 23 February 2007); announced election of Pope Benedict XVI (2005)
* Darío Castrillón Hoyos (23 February 2007 – 1 March 2008)
* Agostino Cacciavillan (1 March 2008 – 21 February 2011)
* Jean-Louis Tauran (21 February 2011 – 12 June 2014); announced election of Pope Francis (2013)
* Renato Raffaele Martino (12 June 2014 – 28 October 2024 (his death))
* Dominique Mamberti (28 October 2024 – present)
Special types of cardinals
Camerlengo
The Cardinal Camerlengo of the Holy Roman Church, assisted by the Vice-Camerlengo and the other prelates of the office known as the Apostolic Camera, has functions that in essence are limited to a period of of the papacy. He is to collate information about the financial situation of all administrations dependent on the Holy See and present the results to the College of Cardinals, as they gather for the papal conclave.Cardinals who are not bishops
was a cardinal for 18 years before he was ordained a priest.]]
Until 1918, any cleric, even one only in minor orders, could be created a cardinal (see "lay cardinals", below), but enrolled only in the order of cardinal deacons. For example, in the 16th century, Reginald Pole was a cardinal for 18 years before he was ordained a priest. The 1917 Code of Canon Law mandated that all cardinals, even cardinal deacons, had to be priests, and, in 1962, Pope John XXIII set the norm that all cardinals be consecrated as bishops, even if they are only priests at the time of appointment. As a consequence of these two changes, canon 351 of the 1983 Code of Canon Law requires that a cardinal be at least in the order of priesthood at his appointment, and that those who are not already bishops must receive episcopal consecration. Several cardinals near to or over the age of 80 when appointed have obtained dispensation from the rule of having to be a bishop. These were all appointed cardinal-deacons, but Roberto Tucci and Albert Vanhoye lived long enough to exercise the right of option and be promoted to the rank of cardinal-priest. No cardinal who was not a bishop has participated in a papal conclave since the 1962 rule change.
A cardinal who is not a bishop is entitled to wear and use the episcopal vestments and other pontificalia (episcopal regalia: mitre, crozier, zucchetto, pectoral cross, and ring). He has both actual and honorary precedence over archbishops, and bishops who are not cardinals. However, he cannot perform the sacrament of ordination or other rites reserved solely to bishops.
"Lay cardinals"
At various times, there have been cardinals who had only received first tonsure and minor orders but not yet been ordained as deacons or priests. Though clerics, they were inaccurately called "lay cardinals". Teodolfo Mertel was among the last of the lay cardinals. When he died in 1899 he was the last surviving cardinal who was not at least ordained a priest. With the revision of the Code of Canon Law promulgated in 1917 by Pope Benedict XV, only those who are already priests or bishops may be appointed cardinals. Since the time of Pope John XXIII a priest who is appointed a cardinal must be consecrated a bishop, unless he obtains a dispensation.
Cardinals or secret cardinals
In addition to the named cardinals, the pope may name secret cardinals or cardinals (Latin for 'in the breast'). During the Western Schism, many cardinals were created by the contending popes. Beginning with the reign of Pope Martin V, A cardinal named is known only to the pope. In the modern era, popes have named cardinals to protect them or their congregations from political reprisals. If conditions change, the pope makes the appointment public. The cardinal in question then ranks in precedence with those made cardinals at the time of his appointment. If a pope dies before revealing the identity of an cardinal, the person's status as cardinal expires. The last pope known to have named a cardinal is Pope John Paul II, who named four, including one whose identity was never revealed.
Vesture and privileges
<gallery heights"220" widths"165" style"font-size:95%; line-height:130%;" class"center" caption="Pontifical vestments">
File:Cardinal Théodore Adrien Sarr 2.JPG|alt=A Black man wearing a red cassock and cap with his hands raised.|Cardinal Sarr with a ferraiolo and wearing a red cassock, but not the rest of the choir dress.
File:Kardinaal III Danneels en Kasper.JPG|alt=Two older white men wearing choir dress.|Cardinals Walter Kasper (left) and Godfried Danneels (right) wearing their choir dress: scarlet (red) cassock, white rochet trimmed with lace, scarlet mozetta, scarlet biretta (over the usual scarlet zucchetto), and pectoral cross on a cord (or, in Danneels' case, wrongly on a chain).
File:Missione del Guaricano-cardinale Tarcisio Bertone.jpg|alt=A white man wearing a white cassock and a red cap.|Cardinal Bertone in dress for hot tropical countries (white cassock with scarlet piping and buttons).
</gallery>
When in choir dress, a Latin Church cardinal wears scarlet garments—the blood-like red symbolizes a cardinal's willingness to die for his faith. Excluding the rochet—which is always white—the scarlet garments include the cassock, mozzetta, and biretta (over the usual scarlet zucchetto). The biretta of a cardinal is distinctive not merely for its scarlet color, but also for the fact that it does not have a pompom or tassel on the top as do the birettas of other prelates. Until the 1460s, it was customary for cardinals to wear a violet or blue cape unless granted the privilege of wearing red when acting on papal business. His normal-wear cassock is black but has scarlet piping and a scarlet fascia (sash). Occasionally, a cardinal wears a scarlet which is a cape worn over the shoulders, tied at the neck in a bow by narrow strips of cloth in the front, without any 'trim' or piping on it. It is because of the scarlet color of cardinals' vesture that the bird of the same name has become known as such.
(Morgan Library and Museum, New York City)]]
Eastern Catholic cardinals continue to wear the normal dress appropriate to their liturgical tradition, though some may line their cassocks with scarlet and wear scarlet fascias, or in some cases, wear Eastern-style cassocks entirely of scarlet.
In previous times, at the consistory at which the pope named a new cardinal, he would bestow upon him a distinctive wide-brimmed hat called a galero. This custom was discontinued in 1969
To symbolize their bond with the papacy, the pope gives each newly appointed cardinal a gold ring, which is traditionally kissed by Catholics when greeting a cardinal (as with a bishop's episcopal ring). Before the new uniformity imposed by John Paul II, each cardinal was given a ring, the central piece of which was a gem, usually a sapphire, with the pope's stemma engraved on the inside. There is now no gemstone, and the pope chooses the image on the outside: under Pope Benedict XVI it was a modern depiction of the crucifixion of Jesus, with Mary and John to each side. The ring includes the pope's coat of arms on the inside.
Cardinals have in canon law a "privilege of forum" (i.e., exemption from being judged by ecclesiastical tribunals of ordinary rank): only the pope is competent to judge them in matters subject to ecclesiastical jurisdiction (cases that refer to matters that are spiritual or linked with the spiritual, or with regard to infringement of ecclesiastical laws and whatever contains an element of sin, where culpability must be determined and the appropriate
ecclesiastical penalty imposed). The pope either decides the case himself or delegates the decision to a tribunal, usually one of the tribunals or congregations of the Roman Curia. Without such delegation, no ecclesiastical court, even the Roman Rota, is competent to judge a canon law case against a cardinal.
Additionally, canon law gives cardinals the faculty of hearing confessions validly and licitly everywhere, whereas other priests and bishops must be granted this faculty and might be restricted in its use by the local bishop.
Candidates for Sainthood
A handful of cardinals were raised to the altars on account of their holiness.
Saints
* Bernardo degli Uberti, O.S.B.Vall. (c. 1060 – 4 December 1133), Bishop of Parma, canonized on 3 December 1139.
* Guarino Foscari da Palestrina, C.R.S.A. (c. 1080 - 6 February 1158), Cardinal-Bishop of Palestrina, canonized in 1159
* Bonaventura da Bagnoregio, O.F.M. (c. 1221 – 15 July 1274), scholar, Cardinal Bishop of Albano, and Doctor of the Church (Seraphic Doctor), canonized on 14 April 1482.
* John Fisher (c. 19 October 1469 – 22 June 1535), Bishop of Rochester executed by order of Henry VIII during the English Reformation for refusing to accept him as the supreme head of the Church of England, canonized on 19 May 1935.
* Carlo Borromeo (2 October 1538 – 3 November 1584), Archbishop of Milan, founder of the Confraternity of Christian Doctrine, and a leading figure of the Counter-Reformation, canonized on 1 November 1610.
* Roberto Bellarmino, S.J. (4 October 1542 – 17 September 1621), a leading figure of the Counter-Reformation, and Doctor of the Church, canonized on 29 June 1930.
* Gregorio Barbarigo (16 September 1625 – 18 June 1697), Bishop of Padua who distinguished himself for his diplomatic and scholastic service, canonized on 26 May 1960.
* Giuseppe Maria Tomasi, C.R. (12 September 1649 – 1 January 1713), Cardinal-Priest of Santi Silvestro e Martino ai Monti, whose scholarship was a significant source of the reforms in the liturgy of the Catholic Church during the 20th century, canonized on 12 October 1986.
* John Henry Newman, C.O. (21 February 1801 – 11 August 1890), convert from Anglicanism and appointed Cardinal-Deacon of San Giorgio in Velabro, canonized on 13 October 2019.
Blesseds
* Pietro "Igneo" Aldobrandini, O.S.B.Vall. (died 11 November 1089), Cardinal-Bishop of Albano, beatified on 4 March 1673.
* Pierre de Luxembourg, O.Cart. (19 July 1369 – 2 July 1387), Bishop of Metz, beatified on 9 April 1527.
* Bonaventura Badoer da Peraga, O.S.A. (22 June 1332 - 10 June 1389), Prior General of the Order of Saint Augustine, beatified in 1440.
* Giovanni Dominici, O.P. (c. 1355 – 10 June 1419), Apostolic Administrator of Bova, beatified on 9 April 1832.
* Niccolò Albergati, O.Cart. (c. 1373 – 9 May 1443), Bishop of Bologna and papal diplomat to France and England, beatified on 25 September 1744.
* Louis Aleman, C.R.S.J. (<abbr>c.</abbr> February 1390 – 16 September 1450), Archbishop of Arles, beatified on 9 April 1527.
* Alessandro Oliva da Sassoferato, O.S.A. (c. 1407 - 20 August 1463), Cardinal-Priest of Santa Susanna, declared Blessed by popular acclaim, especially the Order of Saint Augustine.
* Paolo Burali d'Arezzo, C.R. (c. 1511 – 17 June 1578), Archbishop of Naples, beatified on 18 June 1772.
* Giuseppe Benedetto Dusmet, O.S.B. (15 August 1818 – 4 April 1894), Archbishop of Catania, beatified on 25 September 1988.
* Marcelo Spínola y Maestre (14 January 1835 - 19 January 1906), Archbishop of Seville and founder of the Handmaids of the Divine Heart, beatified on 29 March 1987.
* Ciriaco María Sancha y Hervás (17 June 1833 – 25 February 1909), Archbishop of Toledo, Primate of Spain and the Patriarch of the West Indies, and founder of the Sisters of Charity of Cardinal Sancha, beatified on 18 October 2009.
* Andrea Carlo Ferrari (13 August 1850 – 2 February 1921), Archbishop of Milan, beatified on 10 May 1987.
* Clemens August Graf von Galen (16 March 1878 – 22 March 1946), former count and Bishop of Münster, who denounced Gestapo lawlessness and the persecution of the Church in Nazi Germany, beatified on 9 October 2005.
* Alfredo Ildefonso Schuster, O.S.B. (8 January 1880 – 30 August 1954), Archbishop of Milan, beatified on 12 May 1996.
* Alojzije Stepinać (8 May 1898 – 10 February 1960), Archbishop of Zagreb martyred by communist forces, beatified on 3 October 1998.
* Stefan Wyszyński (3 August 1901 – 28 May 1981), Archbishop of Warsaw and Archbishop of Gniezno, well known for his stands against both Nazism and Communism, beatified on 12 September 2021.
* Eduardo Francisco Pironio (3 December 1920 – 5 February 1998), Argentinian Cardinal-Bishop of Sabina-Porto Mirteto, beatified on 16 December 2023.
Venerables
* Marcantonio Barbarigo (6 March 1640 – 26 May 1706), relative of Gregorio Barbarigo, Archbishop of Montefiascone e Corneto, founder of the Pontifical Institute of the Religious Teachers Filippini, Religious Teachers Filippini of Montefiascone and the Augustinian Sisters of Divine Love, declared Venerable on 6 July 2007.
* Pietro Marcellino Corradini (2 June 1658 - 8 February 1743), Cardinal-Bishop of Frascati, founder of the Congregation of the Collegine Sisters of the Holy Family, declared Venerable on 24 April 2021.
* Sisto Riario Sforza (5 December 1810 – 29 September 1877), Archbishop of Naples who aided victims of two cholera epidemics and the 1861 eruption of Mount Vesuvius, declared Venerable on 28 June 2012.
* Guglielmo da Piova (Lorenzo Antonio Massaja), O.F.M. Cap. (9 June 1809 - 6 August 1889), Cardinal-Priest of Ss. Vitale, Gervasio e Protasio missionary, declared Venerable on 1 December 2016.
* August Jozef Hlond, S.D.B. (5 July 1881 – 22 October 1948), Archbishop of Poznań and Gniezno and as Primate of Poland, declared Venerable on 19 May 2018.
* Elia Dalla Costa (14 May 1872 – 22 December 1961), Archbishop of Florence, declared Venerable on 4 May 2017.
* Phanxicô Xaviê Nguyễn Văn Thuận (17 April 1928 – 16 September 2002), Vietnamese cardinal and President of the Pontifical Council for Justice and Peace, declared Venerable on 4 May 2017.
Servants of God
* Hélie de Bourdeilles, O.F.M. (c. 1423 – 5 July 1484), Archbishop of Tours, declared as a Servant of God on 26 February 1913.
* Francisco Jiménez de Cisneros, O.F.M. (c. 1436 – 8 November 1517), inquisitor, Archbishop of Toledo, and Primate of Spain, declared as a Servant of God on 15 October 1669.
* Stanisław Hozjusz (5 May 1504 – 5 August 1579), Prince-Bishop of Warmia
* Cesare Baronio, C.R. (30 October 1538 - 10 June 1607), Cardinal Priest of Santi Nereo ed Achilleo
* Marcello d'Aste (21 July 1657 – 11 June 1709), Cardinal-Priest of Santi Silvestro e Martino ai Monti
* Giovanni Antonio Guadagni, OCD (14 September 1674 – 15 January 1759), Vicar General of Rome
* Carlo Odescalchi, S.J. (5 March 1785 – 17 August 1841), Archbishop of Ferrara and Cardinal-Bishop of Sabina
* Lodovico Altieri (17 July 1805 – 11 August 1867), Bishop of Albano and Camerlengo of the Holy Roman Church, declared as a Servant of God on 14 March 2009.
* Giuseppe Guarino (6 March 1827 – 21 September 1897), Archbishop of Messina and founder of the Apostles of the Holy Family, declared as a Servant of God on 20 January 1986.
* François-Marie-Benjamin Richard de la Vergne (1 March 1819 – 27 January 1908), Archbishop of Paris
* Émile Biayenda (c. 1927 – 23 March 1977), Congolese Archbishop of Brazzaville whose cause of murder is still undetermined, declared as a Servant of God on 20 March 1995.
* Peter Porekuu Dery (10 May 1918 – 6 March 2008), Ghanian Cardinal-Deacon of Sant'Elena fuori Porta Prenestina and Archbishop of Tamale, declared as a Servant of God in mid-2013.
See also
* Cardinal-Infante (disambiguation)
* Cardinal-nephew
* Cardinal protector
* Hierarchy of the Catholic Church
* List of current cardinals
* List of the creations of the cardinals
Notes
References
Bibliography
*
*
<!-- *Mirriam-Webster (1997 HTML edition). [https://www.cs.harvard.edu/oldwikis/data/mW/Mwed00000140.html Handbook of Style] — Clerical and Religious forms of address. Accessdate=2006-09-22. -->
*
*
*
* Hollingswirth, Mary, Miles Pattenden and Arnold Witte, eds (2020), [https://brill.com/view/title/32766 A Companion to the Early Modern Cardinal]. Leiden/Boston: Brill. ISBN 978-90-04-41544-7
External links
* Salvador Miranda. [http://cardinals.fiu.edu The Cardinals of the Holy Roman Church]. A digital resource consisting of the biographical entries of the cardinals from 494 to 2014 and of the events and documents concerning the origin of the Roman cardinalate and its historical evolution
* (including statistical data and links). Popes and the Papacy website (Anura Guruge). Retrieved 2010-09-08.
* [http://www.gcatholic.org/hierarchy/cardinals.htm GCatholic on all Cardinals]
** [http://www.gcatholic.org/hierarchy/cardinals-alive-precedence.htm List of All Cardinals By Precedence] by GCatholic
** [http://www.gcatholic.org/hierarchy/cardinals-title-c2.htm List of all Cardinal Titular Churches] by GCatholic
** [http://www.gcatholic.org/hierarchy/cardinals-title-c3.htm List of all Cardinal Deaconries] by GCatholic
* [https://web.archive.org/web/20060829055027/http://www.catholic-pages.com/hierarchy/cardinals_list.asp Catholic-pages List of Cardinals]
* Thomas J. Reese, Inside the Vatican: The Politics and Organization of the Catholic Church, Harvard University Press, 1996 [https://books.google.com/books?idFYMKOgA5lSAC&dqhow+many+curial+cardinals&pg=PA92]
*[https://web.archive.org/web/20160708031251/http://www.cardinalrating.com/ Cardinal Rating] a website listing the day to day statements printed in the news by current cardinals
Category:Bishops by type
Category:Catholic ecclesiastical titles
Category:Religious leadership roles
Category:Princes of the Holy See
|
https://en.wikipedia.org/wiki/Cardinal_(Catholic_Church)
|
2025-04-05T18:27:45.309150
|
6225
|
Cantigas de Santa Maria
|
thumb|Illumination with buisine players from the E Codex (Bl-2, fol. 286R)
The Cantigas de Santa Maria (, ; "Canticles of Holy Mary") are 420 poems with musical notation, written in the medieval Galician-Portuguese language during the reign of Alfonso X of Castile El Sabio (1221–1284). Traditionally, they are all attributed to Alfonso, though scholars have since established that the musicians and poets of his court were responsible for most of them, with Alfonso being credited with a few as well.
It is one of the largest collections of monophonic (solo) songs from the Middle Ages and is characterized by the mention of the Virgin Mary in every song, while every tenth song is a hymn.
The Cantigas have survived in four manuscript codices: two at El Escorial, one at Madrid's National Library, and one in Florence, Italy. The E codex from El Escorial is illuminated with colored miniatures showing pairs of musicians playing a wide variety of instruments. The Códice Rico (T) from El Escorial and the one in the Biblioteca Nazionale Centrale of Florence (F) are richly illuminated with narrative vignettes.
Description
thumb|200px|left|An illustration from the E Codex, Codex of the musicians, Cantigas de Santa Maria.
The Cantigas are written in the early Medieval Galician variety of Galician-Portuguese, using Galician spelling; this was because of Galician-Portuguese being fashionable as a lyrical language in Castile at the time, as well as Alfonso X having passed part of his early years in Galicia and so probably being a fluent speaker since his childhood.
The Cantigas are a collection of 420 poems, 356 of which are in a narrative format relating to Marian miracles; the rest of them, except an introduction and two prologues, are of songs of praise or involve Marian festivities. The Cantigas depict the Virgin Mary in a very humanized way, often having her play a role in earthly episodes.
The authors are unknown, although several studies have suggested that Galician poet Airas Nunes might have been the author of a large number of the Cantiga poems. King Alfonso X — named as Affonso in the Cantigas — is also believed to be an author of some of them as he refers himself in first person. Support for this theory can be found in the prologue of the Cantigas. Also, many sources credit Alfonso owing to his influence on other works within the poetic tradition, including his introduction on religious song. Although King Alfonso X's authorship is debatable, his influence is not. While the other major works that came out of Alfonso's workshops, including histories and other prose texts, were in Castilian, the Cantigas are in Galician-Portuguese, and reflect the popularity in the Castilian court of other poetic corpuses such as the cantigas d'amigo and cantigas d'amor.
The metrics are extraordinarily diverse: 280 different formats for the 420 Cantigas. The most common are the virelai and the rondeau. The length of the lines varies between two and 24 syllables. The narrative voice in many of the songs describes an erotic relationship, in the troubadour fashion, with the Divine.
The music is written in notation which is similar to that used for chant, but also contains some information about the length of the notes. Several transcriptions exist. The Cantigas are frequently recorded and performed by early music groups, and quite a few CDs featuring music from the Cantigas are available.
Codices
thumb|left|Miniatures, Codex Rico, Cantiga #35
The Cantigas are preserved in four manuscripts:
To (códice de Toledo, Biblioteca Nacional de España, MS 10069, link to manuscript)
T (códice rico, Biblioteca de El Escorial, MS T.I.1, link to manuscript)
F (códice de Florencia, Florence, Biblioteca Nazionale, MS b.r. 20, link to manuscript)
E (códice de los músicos, Biblioteca de El Escorial MS B.I.2, link to manuscript)
E contains the largest number of songs (406 Cantigas, plus the Introduction and the Prologue); it contains 41 carefully detailed miniatures and many illuminated letters. To is the earliest collection and contains 129 songs. Although not illustrated, it is richly decorated with pen flourished initials, and great care has been taken over its construction. The T and F manuscripts are sister volumes. T contains 195 surviving cantigas (8 are missing due to loss of folios) which roughly correspond in order to the first two hundred in E, each song being illustrated with either 6 or 12 miniatures that depict scenes from the cantiga. F follows the same format but has only 111 cantigas, of which 7 have no text, only miniatures. These are basically a subset of those found in the second half of E, but are presented here in a radically different order. F was never finished, and so no music was ever added. Only the empty staves display the intention to add musical notation to the codex at a later date. It is generally thought that the codices were constructed during Alfonso's lifetime, To perhaps in the 1270s, and T/F and E in the early 1280s up until the time of his death in 1284.
The music
The musical forms within the Cantigas, and there are many, are still being studied. There have been many false leads, and there is little beyond pitch value that is very reliable. Mensuration is a particular problem in the Cantigas, and most attempts at determining meaningful rhythmic schemes have tended, with some exceptions, to be unsatisfactory. This remains a lively topic of debate and study. Progress, while on-going, has nevertheless been significant over the course of the last 20 years.
See also
right|thumb|200px|A lute player.
Literature of Alfonso X
Cantiga de amigo
Llibre Vermell de Montserrat
Pergaminho Sharrer
Martin Codax
The Legend of Ero of Armenteira
References
Bibliography
Drummond, Henry T., The Cantigas de Santa Maria: Power and Persuasion at the Alfonsine Court, New Cultural History of Music. Oxford University Press, New York, 2024.
Katz, Israel J. and John E. Keller, Studies on the "Cantigas de Santa Maria": Art, Music, and Poetry: Proceedings of the International Symposium on the "Cantigas de Santa Maria" of Alfonso X, el Sabio (1221–1284) in Commemoration of Its 700th Anniversary Year–1981. Associate Editors Samuel G. Armistead & Joseph T. Snow. Hispanic Seminary of Medieval Studies, Madison, 1987.
Kulp-Hill, Kathleen, ed., The Songs of Holy Mary by Alfonso X, the Wise: A Translation of the Cantigas de Santa Maria. Arizona Center for Medieval and Renaissance Studies, Tempe 2000.
Parkinson, Stephen, ed., Cobras e Son: Papers on the Text Music and Manuscripts of the "Cantigas de Santa Maria". European Humanities Research Centre, University of Oxford, Modern Humanities Research Association, 2000.
Pena, Xosé Ramón, "Historia da litratura medieval galego-portuguesa", Santiago de Compostela, 2002, 199–210.
External links
Cantigas de Santa María, Códice rico, Real Biblioteca del Monasterio de San Lorenzo de El Escorial, Ms. T-I-1, link to manuscript
http://www.pbm.com/~lindahl/cantigas/ (facsimiles, illuminations, links to transcriptions)
Cantigas de Santa Maria for Singers (full text with syllable marks, pronunciation guide and concordance)
Cantigas de Santa Maria (Texto crítico completo) (full text, ed. José-Martinho Montero Santalha)
http://www.medieval.org/emfaq/composers/cantigas.html (a comprehensive database of the released Cantigas recordings)
http://csm.mml.ox.ac.uk/ (the Centre for the Study of the Cantigas de Santa Maria of Oxford University)
https://web.archive.org/web/20041013090228/http://perso.club-internet.fr/brassy/PartMed/Cantigas/CSMIDI.html (French site: MIDI files based on Anglés transcriptions; also texts but with many OCR errors and thousands of missing letters.)
Portuguese wikisource (the same inaccurate texts as the French site above).
Category:13th-century books
Category:13th-century illuminated manuscripts
Category:Music illuminated manuscripts
Category:Music of Spain
Category:Galician language
Category:Galician-Portuguese
Category:Chansonniers (books)
Category:Marian devotions
Category:Alfonso X of Castile
|
https://en.wikipedia.org/wiki/Cantigas_de_Santa_Maria
|
2025-04-05T18:27:45.341397
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.