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– The word 'teenager' wasn't really needed – there were adolescents (aged around 12-15) and there were young adults.
– In the past, many people below the age of 19 were already working, in apprenticeships, or even married with children of their own. This declined after the 1800s in the UK and USA as young people were required to stay in school longer and longer.
– By the 1900s, the quality of life was increasing. With more technology around the house, there was more leisure time and young people had more opportunities to do typical 'teenager things' like socialising, listening to music, going to the beach or for a barbecue.
– The wars of the 20th century disrupted family life. In 1914-1918 many young boys in Europe were sent off from home to fight, so they were forced to grow up quickly. In 1939 – 1944 there were attacks directly on London and other British cities, and many children were directly involved, looking after younger brothers or sisters when their parents died, or working in industry (for older teenage boys) or on farms (for girls). They couldn't go back to being children once the war ended! The Vietnam War in the 1960s changed things forever for American kids – boys could be sent off to die once they got older, girlfriends could lose their boyfriends forever, so young people wanted to enjoy as much freedom as possible in their teenage years.
Here are some links, for further reading:


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Categories: Arduino, by Schiavone Sandro Cattaneo. Date: July 02nd 2018.


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Online Giving Announcement
Free Online Giving for PCA Churches
We recognize many congregations will likely see reduced attendance or defer gathering for worship due to advice from national and local health officials, and may experience delayed or even ultimately reduced giving as a result. To help mitigate this problem and serve both churches and members, the PCA Foundation will facilitate and accept online gifts for the benefit of each church that would like to participate. The Foundation will bear the costs of this online cash giving without charge through the end of May.
The PCA Foundation is committed to helping churches facilitate generosity. We will set up online giving for your church FREE OF CHARGE. The process is simple:
1. Complete the online form below requesting online giving capabilities for your church.
2. The Foundation will respond within the next business day with a link to a webpage customized for your church. You can post this link on your website and distribute it to members with a message encouraging online gifts. Members can click the link to give using their bank account or credit cards (in the latter case subject to a fee charged by the card merchant).
3. The PCA Foundation will process all gifts through the end of May and distribute the funds to your church once per week. It will distribute the funds via electronic funds transfer, which is faster and more secure than distribution by check, if the church chooses.
Here are three other things to keep in mind as you consider this offer:
1. The Foundation will provide each giver the required gift receipt, relieving the church of the burden of record-keeping and receipting.
2. It will provide to the church along with each distribution a listing of givers and gifts (excluding those givers who choose anonymity).
3. The Foundation can also facilitate and accept gifts of marketable stock and other securities for the church's benefit (requesting a small contribution depending on the size of the gift).


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in reply to Re: Net::FTP put failing silently? (problem src)
in thread Net::FTP put failing silently?
Yes, indeed. Any clue what could be involved? I have a transfer via Net::FTP that doesn't work while one over simple commandline ftp does work. This is to an NT FTP service. It would violate my expectation if security software were treating one FTP client differently, and I have tried passive on and off.
In Section Seekers of Perl Wisdom


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An Adventurer's Playground
Explore Water Adventures
Snorkeling & Scuba
Come face to face with tropical fish, spotted eagle rays and green sea turtles on an underwater adventure in Hawaii's 1,200 miles of coral reef.More
Mountain Tubing
Strap on a headlamp and hop into a tube to explore inland canals, tunnels and flumes on this only-in-Kauai adventure.More
Lift off on a parasailing adventure and get a bird's eye view of Hawaii's breathtaking coastline from up to 1,200 feet in the air.More
Deep Sea Fishing
Hawaii is home to some of the biggest marlin in the world as well as one of the oldest billfish tournaments, plus scores of other game fish – from wahoo to mahimahi to giant trevally.More
Whale Watching
Each winter, Hawaii is the stage for some of the best whale watching on the planet, when thousands of kohola (humpback whales) migrate to our warm waters to breed and nurse their young. Tours from just about every island can bring you thrillingly close to these magnificent creatures.More
Adventures on Land
Soar through Hawaii's lush canopies on some of the longest ziplines in the U.S. – and some of the most scenic in the world.More
Whether you want to descend jungle cliffs or cascading waterfalls, Hawaii's knowledgeable guides will show you the ropes.More
Browse Hawaii Adventures
Valley Isle Excursions takes you on one of the most breathtaking drives on earth down the road to Hana Maui. Spectacular cliffs, bamboo jungles, hawaiian waterfalls, tropical scenery and colorful fragrant flowers are part of our "Heavenly Hana" tour.
Experience the thrill of ziplining on either of our 2 beautiful and unique Maui locations! Enjoy breathtaking views and thrilling zipline adventure in the rugged valleys above Ka'anapali or on the green slopes of Haleakala.
As America's original and most award-winning zipline company, Skyline Hawaii has hosted thousands of eye-opening and memory-making eco-adventures from thrilling zipline tours over 250-foot waterfalls, to sunrises near Haleakalā's peak to the illuminating Road to Hana tour.
Haleakala Bike Company Inc now does business as Bike Maui, Cruiser Phil Volcano Riders, and Haleakala Ecotours. We offer seven different tours for biking down the volcano. Bike Maui offers the "Self-Guided" tours and Cruiser Phil's offers the "Guided" tours.
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Owns & manages Maui's acclaimed Wailea Golf & Tennis Clubs, including operations and property leasing.
Sunshine Helicopters offers helicopter tours of Maui, Molokai, Big Island Hawaii and Kauai. With over 90% of the State of Hawaii accessible only by air, enjoy a helicopter ride and soar with us in the blue skies above the Hawaiian Islands aboard our state-of-the-art helicopters.


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LITTLE ROCK, Ark. (AP) – An Arkansas panel set a cutoff date for farmers to spray an herbicide next year but abandoned two proposals that critics said would be too expensive.
The Arkansas State Plant Board voted in a public hearing Wednesday that farmers have until May 25 to spray dicamba. The board also allowed the use of dicamba through May 25 this year, the Arkansas Democrat-Gazette reported.
Opponents argued for an April 15 cutoff date to protect other crops and native vegetation.
Terry Fuller, a board member who represents the Arkansas Seed Growers Association, voted against the proposed regulation. He said it doesn't reflect public sentiment for an earlier cutoff date, increasing the likelihood of dicamba damaging nearby crops that arent dicamba tolerant.
But some farmers said they wanted a longer period to spray, at least deeper until June, when pigweed, now resistant to other herbicides, is threatening crop fields.
Danny Townsend, a landscaper, said if he caused plant damage by using discamba, the board would shut him down. "I'd be out of business," he said, adding that Bayer and other dicamba manufacturers have a responsibility to put out a less volatile product than what have on the market now.
The board also dropped two proposals. One would have required farmers to equip their spray rigs with a GPS device to map the coordinates of any field where dicamba was applied and have the information readily available for Department of Agriculture inspectors. Another rule required farmers to register their dicamba applications online with the agriculture department within 10 days after spraying.
Andrew Grobmyer, of the Arkansas Agriculture Council, said those proposals were too expensive and would duplicate other record-keeping requirements of both the Plant Board and the federal Environmental Protection Agency.
In 2018, Arkansas lawmakers approved banning dicamba. But the Arkansas Supreme Court dismissed the state's appeal of a judges decision to block the enforcement of the ban earlier this year.
The regulations will now to the governor and lawmakers for review.
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FAYETTEVILLE, N.C. (WNCN) — There will be lane closures this week near Fort Bragg.
The North Carolina Department of Transportation said it needs to perform mandatory bridge inspections along the new section of Interstate 295 between the All American Freeway and Cliffdale Road. The work is required within 90 days of opening to traffic.
At least one lane in both directions will close this week from 9 a.m. to 4 p.m.
Traffic impact is expected to be medium. Weather could delay work.
More headlines from CBS17.com:
- Trump considering quarantine for NY, NJ and Connecticut
- NC State Highway Patrol community mourns death of trooper in Wayne County crash
- NC jobless claims hit 26k in a day after averaging 25k a week during Great Recession
- NC-based Krispy Kreme is giving out a free dozen doughnuts to healthcare workers
- Infant among 13 new COVID-19 deaths in Illinois; Nearly 3,500 cases reported
For more stories like this that matter to you, click here to download the CBS 17 News app for free.
Watch live newscasts, get breaking news and sign up for push alerts – download now


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For those of you whose cats enjoyed the Rad Cat brand of raw cat food, there's a new brand on the market that is very similar. It's called Lotus. Single protein with appropriate organs, calcium source is eggshell. The grind is very very fine, so the texture is more like canned food than other brands. Same style packaging, three tub sizes. We've tried lamb, turkey, and chicken - all with great success! Clean plates are the best recommendation I can think of.


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A WAR hero has been told he will be kicked out of the country unless he stumps up £1300 to get his visa renewed.
Former Royal Scots private Fereti 'Freddie' Bureqele, 28, will have to find the cash if he wants to stay in Scotland with his wife Nicola, 30, and children Ryan, nine, Junior, four, and Oni, three.
Freddie served with distinction in Bosnia and Iraq during six years in the Army and is now with the Territorials.
He is due to leave for a tour of duty in Afghanistan in October, where he will be based for five months.
But he has been told he will have to fork out cash to the UK Border Agency for an Indefinite Leave to Remain (ILR) visa on his passport - or be deported back to Fiji.
He is being forced to pay £1000 to fly to the South Pacific island to get a new passport, as his current document is running out, then pay another £300 to get a new UK Border Agency stamp.
Gutted Freddie already paid £750 to get the stamp when he left the Army in 2008.
Under strict immigration laws, Freddie must always have an up-to-date passport or he will be booted out of the UK.
If he wants British citizenship, he will have to pay another £800 and sit the Life In The UK test - a Government exam immigrants must pass before being granted a UK passport.
Freddie, of West Linton in the Borders, said: "It's as if the Government don't want me to remain in the United Kingdom despite my years of service.
"When I tell people about my situation, they think I must be joking.
"It's a real worry for me and my family but we have to find the money somehow or I'll be deported back to Fiji.
"I was proud to serve this country with the Royal Scots and I'm still proud to do my bit with the Territorial Army.
"But the whole problem with my visa has left a bitter taste in my mouth.
"If I don't get it resolved by October, I'll be sent back to Fiji and I can forget about staying here and going to serve in Afghanistan.
"I'm allowed to apply for UK citizenship now but I must have a valid Fijian passport first.
"Then I'll have to sit a 'right to stay in the UK 'exam - which feels l ike another slap in the face consider ing my service in the military."
His wife Nicola said: "The way my husband is being treated is an absolute disgrace.
"The Government were happy for him to join the Army and send him to Iraq to fight, yet they make it so difficult for him to stay in Scotland.
"Unless we can find the cash to fly Freddie to Fiji and pay to have the visa renewed, the future is very uncertain.
"Men like Freddie have put their lives on the line for this country and this is how they are repaid for their service."
Freddie's former sergeant major in the Royal Scots, George Gaff, said: "Freddie was a brilliant soldier and I'm furious that the Government are treating him like this.
"It makes me so angry that a fine man like Freddie who served this country proudly is now facing a fight to remain in the UK with his family."
Freddie joined the Army in 2002 and served in Basra during the Iraq conflict.
Figures released four years ago revealed that Fiji was the top Commonwealth country for new recruits.
More than 2000 Fijians serve in the British forces.
Freddie knew tragic Fijian rifleman Aminiasi 'Togey' Toge, from the 2nd Battalion The Rifles, who was killed in an explosion while on foot patrol in Helmand Province in Afghanistan in July last year.
Freddie was also friends with Fijian fusilier Petero 'Pat' Suesue, of the 2nd Battalion The Royal Regiment of Fusiliers, who was killed in Afghanistan last May.
He said: "Fiji is a small island and when a Fijian soldier is killed the loss is felt by everyone.
"Pat and I joined the Army around the same time and I was so sad when he was killed. I'm proud to have known him and Togey."
The UK Border Agency said: "The cost to apply for settlement within the UK and from abroad is the same for everyone, including soldiers and individuals.
"The requirement to pay the fee is set out in law and we have no provisions to waive it."


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Date: 1 Oct 1906, Person ID: 163, Location ID: 172
114 N Main St, Los Angeles which is a restaurant named "Skaric Bros".
Source: 1906 International Directory of Los Angeles. Slavonian. p1094
Notes for this connection:
Notes for the address: 1909 Grand Pacific Restaurant
Updated 02 Dec 2019, 20:20 PST


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Marle is a female name.
Marle is a short form of Maria Madgalena.
Marle means "sea of bitterness", "rebelliousness" and "wished for child" or "beloved" (from Maria) and "of Magdala" and "sublime" (from Magdalena).
No need to look further, then. Find a beautiful first name for your baby with our free Baby Names App. Just try it now!


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Location, location, location! Highly sought after, Bridgewater condo in the Mill District. Building amenities include fitness center, community room overlooking downtown Minneapolis and rooftop pool and patio. Located across from Gold Medal Park and only steps away from the farmers market, Trader Joe's, restaurants, new Vikings stadium, running and biking paths and the Guthrie.
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The data relating to real estate for sale on this site comes in part from the Broker Reciprocity program of the Regional Multiple Listing Service of Minnesota, Inc. Real Estate listings held by brokerage firms other than Lakes | Sotheby's International Realty are marked with the Broker Reciprocity logo or the Broker Reciprocity house icon and detailed information about them includes the names of the listing brokers. Lakes | Sotheby's International Realty is not a Multiple Listing Service MLS, nor does it offer MLS access. This website is a service of Lakes | Sotheby's International Realty, a broker Participant of the Regional Multiple Listing Service of Minnesota, Inc.
Information deemed reliable but not guaranteed.
Copyright 2020 Regional Multiple Listing Service of Minnesota, Inc. All rights reserved.
By searching, you agree to the EULA Terms Agreement.
Listing information last updated on March 28th, 2020 at 6:21am CDT.


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Microsoft announced the latest edition of Microsoft Office Communications Server 2007, Microsoft's platform for streamlining presence awareness, instant messaging, web conferencing, and Voice over IP. The most recent edition of Microsoft Communications Server 2007 features enhancements that give IT organizations additional flexibility for supporting their communications infrastructure effectively while representing an extensible platform for collaborative work activity.
To lower expenses, increase efficiency, and promote collaboration, the new version of Microsoft Office Communications Server 2007 allows dial-in audioconferencing to replace expensive outside services with an on-premises audioconferencing bridge that is administered as part of a company's overall communications environment. Microsoft Office Communications Server also now features desktop sharing, which allows users to share their PC transparently and initiate audio communications and collaborate with others external to the organization on Windows PC, Macintosh, or Linux-powered computers via a web connection. The new version of Office Communications Server also allows geographically scattered teams to collaborate by taking part in topic-based discussions that persist indefinitely. This application provides users with an index of all available discussion rooms and topics, periodically archives discussions in an XML file format that meets compliance requirements, provides tools to search the entire record of chat on a given theme, and provides triggers and alarms to notify someone of new posts.
The new version of Microsoft Communications Server also incorporates improved support for voice communications and mobile workers. The innovative attendant window allows support personnel or team administrators to manage calls and conferences on behalf of associates, set up workflows to route phone calls, and handle higher volumes of incoming calls via an intuitive software console. A new SIP trunking feature enables businesses to cut expenses by establishing up a direct Voice over IP connection between an Internet phone service supplier and Microsoft Office Communications Server 2007 without needing on-premises gateways. In addition, Office Communicator Mobile functionality has been extended to more device platforms such as the Motorola RAZR, RIM Blackberry, and Windows Mobile.
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A Standard Edition Microsoft Office Communications Server 2007 manages all required services on a single Front End Server. The small expense in computer hardware and simplicity of administration make this configuration is ideal for small and medium-sized businesses and for remote offices. Office Communications Server is powered by Microsoft Windows Server and takes advantage of core Windows technologies like as Active Directory, Microsoft SQL Server, Microsoft System Center Operations Manager, and Exchange Server. With Microsoft Office Communications Server 2007, you can add instant teamwork features and presence awareness to popular Microsoft Office programs such as Microsoft Office Outlook, Excel, and Microsoft Word. Presence information from your server can also be integrated into productivity applications. Microsoft Communications Server 2007 also acts as the presence engine for collaborative web sites and web portals, delivering presence awareness and IM access from within Windows SharePoint Services sites.
Progent's Microsoft-Gold certified professionals can provide professional consulting support for all these areas and can assist your company in planning and executing a rollout of Microsoft Office Communications Server 2007 in order to maximize the business impact of this communications platform. Progent can in addition assist you to migrate from Microsoft Live Communications Server 2005 to the latest version of Office Communications Server.
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If there ever was a time to ominously say the words, "They walk among us", it's now. There's your regular, everyday people like you and me, and then there's people who have somehow managed to go above and beyond the limitations of a human body and mind with startling results. Sometimes it's genetic, and sometimes it's through a process of intense and mysterious training. Either way, there are some people in the world who almost prove that superhuman powers can be real.
Check them out!
1. Liew Thow Lin
Malaysian 'Magnet Man' Liew Thow Lin has the unique ability to stick metal objects in his body. I'm not just talking about the solitary spoon on the nose either, Liew can straight up stick objects weighing up to 36 Kg on his body. Scientists have found that he's not actually magnetic, however, his skin just exhibits very high levels of friction leading to a 'suction effect'.
2. Veronica Seider
Veronica has eyesight 20 times better than the average human.
In 1972, it was reported that a girl named Veronica Seider from the University of Stuttgart had visual abilities 20 times better than an average person. This meant she could literally identify a face 1.6 Km away. The regular eye can barely see details like that from 20 feet away!
3. Kevin Richardson
Kevin can tame almost any animal in the world including lions and hyenas.
This South African animal behaviorist is a
bonafide animal whisperer. Using almost nothing more than his gut instinct and a seriously good understanding of animals, Kevin has been accepted into numerous prides of lions as well as clans of hyenas.
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4. Liam Hoekstra
Liam could pick up, two 20kg dumbbells by the age of 3 and will always have a high muscle definition regardless of what he eats
He could do an iron cross when he was just 5 months old, and at the age of 3, Liam had 40% body muscle and minimal amounts of fat. Due to a rare condition called Muscle hypertrophy, Liam's body builds muscle fast while inhibiting body fat, and amazingly, he faces no side effects from the condition. He could effortlessly pick up, two 20 kilo dumbbells at the age of four!
5. Dean Karnazes
Dean can run marathons for days on end with no need for sleep.
In 2005, Dean ran 560 km in 80 hours and 44 minutes without any sleep. He once also ran a marathon a day for 50 consecutive days. He is able to do this due to his superior muscles that don't tire in the same manner that normal human muscles do.
6. Isao Machii
7. Wim Hof
Wim can turn up his body heat to withstand freezing temperatures.
You might remember seeing this guy in an episode of Ripley's Believe It or Not. Wim Hof, nicknamed 'The Iceman' (not to be confused with the hitman), can control his autonomous nervous system to withstand extreme cold. He's climbed Mt. Kilimanjaro
wearing only shorts, completed a marathon in -20 degrees and even stayed immersed in ice for 1 hour and 13 minutes.
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8. Daniel Tammet
Daniel has a highly advanced memory and can actually see and feel
Daniel Tammet's powers of memory are so advanced, he can recite the value of pi to over 22,000 digits and can learn a language in less than a week. Daniel is an autistic savant, which means a person with a mental disability who also has prodigious mental talents. He has explained that he can memorize so much thanks to a form of synesthesia where he can feel and see the numbers up to 10,000.
9. Natasha Demkina
Natasha can see inside a person's body for a few seconds and give them medical advice.
Since the age of ten, Natasha has been able to use a form of x-ray vision with her eyes where she can tell what's inside a person's body. A Discovery Channel documentary even showed Demkina successfully identifying all the fractures and metal pins in a woman who had recently been a victim of a car crash.
Velu Rathakrishnan
In 2003, Velu Rathakrishnan used his teeth to pull two KTM commuter trains, with a total weight of 260.8 tonnes, a distance of 13 ft 9 in along rails at Kuala Lumpur Railway Station. Apparently, he got the power to do this from an Indian guru, who taught him to channel all his power to a single part of his body.
11. Zhao Rui
Zhao can hold a running electric drill to his head and can bend metal bars with his throat.
24-year-old Shaolin monk is a bit of a celebrity in his home town thanks to the incredible feats he performs. His martial arts training has allowed him to hold a running electric drill to his head without leaving anything other than a red mark. He can also bend steel rods using just his throat. These monks are at a whole different level!
scoopwhoop | 2
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Britain has accused the EU of being in disarray in its approach to the post-Brexit trade talks, stepping up a war of words between the two sides.
A week before the first round of formal talks in Brussels, a source close to the negotiations claimed that EU countries appeared "divided" and were "distracted" by issues such as securing the return of the Elgin Marbles to Greece, rather than focusing on the "important decisions".
The claim escalates a propaganda war between Downing Street and Brussels, which saw the two sides engage in a public row last week over the type of trade deal that the UK could strike with the EU.
This week, senior ministers will sign off on the UK's list of demands for the negotiations in a meeting of the Cabinet's "exit strategy", or XS, committee on Tuesday, with the paper due to be published online on Thursday. During the following week, the Government will publish its negotiating mandate for a free trade agreement with the US, in a move that will put further pressure on EU negotiators.
The mandate for the EU talks is likely to spark fresh rows with Brussels. Last week David Frost, Boris Johnson's chief negotiator, issued a public rebuke over the EU's own draft list of demands, which insists that a trade deal must include onerous "level playing field" requirements to prevent the UK from becoming an ultra-competitive competitive "low tax, low regulation" economy on its doorstep.
Mr Frost now leads a 40-strong unit, called Taskforce Europe, which is dedicated to the talks.
The first round of negotiations is due to take place in Brussels during the week beginning March 2.
A source close to the negotiations said: "On the UK side, progress has been remarkably smooth, with a clear decision-making framework in place and a sense of unity amongst ministers.
"By contrast, the EU seem divided, distracted by other issues like marbles, instead of the important decisions on what our trading relationship will actually look like. The new plan is for them to approve their mandate on February 25 but it's anyone's guess whether they will."
Last week it emerged that the EU had added an "Elgin Marbles clause" to its demands for a post-Brexit trade deal with Britain, raising fears that the move would bolster Greek calls for their repatriation to Athens.
The demand was revealed as Michel Barnier, the EU's chief negotiator, rejected demands by Mr Frost for a Canada-style trade agreement.
EU governments have been revising the bloc's mandate for the negotiations but the process has been subject to delays.
A copy of a draft obtained by The Telegraph last week stated: "The Parties should, consistently with Union rules, address issues relating to the return or restitution of unlawfully removed cultural objects to their countries of origin."
One official said the clause – demanded by Greece, Cyprus, Spain and Italy – was understood to refer to the Marbles, a collection of sculptures, inscriptions and architectural features which originally formed part of the Parthenon temple and other structures on the Acropolis in Athens. They were acquired by Lord Elgin between 1801 and 1805.
But Greek authorities denied reports that their return was a condition of the trade deal and claimed the clause did not refer to them. A diplomatic source said it did not specifically concern the Marbles, but covered all antiquities.
A Downing Street source said: "We left the EU on January 31 in line with the referendum result. We regain full independence for the people of the UK at the end of this year: the negotiation is about defining the terms on which we do that."


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"Leadership Practices Inventory LPI" (2004, October 19) Retrieved March 30, 2020, from https://www.paperdue.com/essay/leadership-practices-inventory-lpi-176821
"Leadership Practices Inventory LPI" 19 October 2004. Web.30 March. 2020. <https://www.paperdue.com/essay/leadership-practices-inventory-lpi-176821>
"Leadership Practices Inventory LPI", 19 October 2004, Accessed.30 March. 2020, https://www.paperdue.com/essay/leadership-practices-inventory-lpi-176821
Leadership, according to La Monica (1938), is when a person has authority that is recognized by others, and the person has followers/subordinates under them, who believe that the person will assist them in attaining certain goals (carrying out specific objectives for the followers). Furthermore, anyone that is willing to assist and help others could be referred to as a leader (p.8)
Leaders see what others do not Most leaders have
Evidence-Based Practice & Transformational Leadership
Change Model
Transformational leadership may be defined as an innovation as it is not in wide or general practice across the medical and healthcare fields. An innovation must, by definition be characterized by benefits that are accrued only through adoption of the innovation into practice or general use. Transformational leadership has been shown to have benefits for patients and patient care, as well as for those practice
Evidence-Based Practice Section G: Evaluation
Section G -- Evaluation
Methodology and data collection rationale. The role of leadership styles and training in nursing situations has been described in the literature and there is a substantive body of work suggesting that leadership can significantly affect the praxis of nurses and the outcomes of patients (Looke, 2001). Training that occurs over time is believed to enhance adoption of desirable behaviors in the workplace environment,
Leadership philosophy denotes the values, beliefs, and principles that define or influence how a leader leads their followers. There are many different leadership philosophies, but one philosophy that particularly resonates with the author's leadership philosophy is servant leadership. Servant leadership is about serving others and prioritising the needs of others. As demonstrated in this paper, servant leadership is a leadership philosophy that is applicable at the workplace as well as
Al-Sawai, A. (2013). Leadership of Healthcare Professionals: Where Do We Stand?.
Oman Medical Journal, 28(4), 285-287 3p. doi:10. 5001/omj.2013.79
This study defines leadership as behavior that drives a group towards an identified goal, and it describes a variety of leadership theories (such as transformational leadership, collaborative leadership, conflict management and shared leadership), beginning with the "early Great Man theory" (the idea that some people have the quality of leadership and some do


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Relay for Life of Evansville 2018
Sat., Jun 9, 4:00pm
Bethel UCC, 3029 N. Green River Road
The American Cancer Society Relay for Life is the world's largest and most impactful fundraising event to end cancer.
For more info:812-475-9486 or http://www.cancer.org
Want to Submit an Event? Contact us!
Upcoming Events in the Tri-State:
- Eli Young Band
Fri., Apr 10
- Autism Evansville Walk and 5K
Sat., Apr 11, 9:00am
- Harmonie State Park Easter Egg Hunt
Sat., Apr 11, 10:00am
- West Side Nut Club Easter Egg Hunt
Sat., Apr 11, 1:00pm


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About Masahiro Sakurai
Masahiro Sakurai (桜井 政博, Sakurai Masahiro) (born August 3, 1970) is a Japanese video game designer of the Kirby and the Super Smash Bros. series on Nintendo platforms, currently Director of Software Development for his companies Sora Ltd. and Project Sora. He is also the author of a weekly column for Famitsu magazine and has developed a cult following for his streamlined, yet deep gameplay. One of Sakurai's earliest experiences in the video game industry began when he worked for HAL Laboratory, where he created the character Kirby at age 19 and directed his first title, Kirby's Dream Land. Sakurai left HAL on August 5, 2003, ending his work on the Kirby series. Reasons for his departure are said to be because he was seeking more freedom and was disappointed there, but most of all Sakurai grew tired of the sequelization from HAL. On September 30, 2005, Sakurai announced that he had formed his own company, Sora. Two titles have been announced to be in development but any information on the titles (other than that they are in development) has not yet been divulged. As for the future of the Super Smash Bros. series, Nintendo and HAL Laboratory's President Satoru Iwata, during the


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Halsey has become one of the biggest names in pop music with hits such as 'Without Me' and 'Nightmare'. She made her Summertime Ball debut in 2019!
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KITTERY, Maine — Winds whipping and harbor waves raging did not slow the USS Hyman G. Rickover submarine from arriving at the Portsmouth Naval Shipyard Friday morning.
The submarine is scheduled to be deactivated at the shipyard, following more than 20 years of service, a process that involves defueling and safe deactivation of the ship and its systems. A formal deactivation ceremony was held in December in Norfolk, Va.
The vessel will then be towed to Puget Sound Naval Shipyard and Intermediate Maintenance Facility for ship recycling.
On Friday, the submarine entered the harbor without fanfare, escorted by a Portsmouth tug and one of the shipyard's own. Members of its crew could be spotted atop the conning tower and the hull.
The submarine is the only one named after the "Father of the Nuclear Navy," according to Public Affairs officer Danna Eddy. Rickover lead the effort to develop the world's first nuclear submarine, the USS Nautilus in the mid-1950s.
The Nautilus technology, combined with the teardrop design of the hull introduced by the USS Albacore, has influenced the design of every submarine built in the world.
The Rickover spent its last six months in the North Atlantic, making port visits in Haakonsvern, Norway; Faslane, Scotland; and Rota, Spain.
The submarine carries a crew of 12 officers and 115 enlisted men.
The vessel is the Navy's 22nd Los Angeles class fast-attack submarine and the only one not to be named after a United States city.
The Rickover received two Navy Unit Commendation awards, three Meritorious Unit Commendation awards; numerous Navy Expeditionary medals; and the Armed Forces Expeditionary Medal.
Cmdr. Robert E. Cosgriff, the Rickover's commanding officer, has also been commended for his service.
He has received the Meritorious Service Medal, the Navy Commendation Medal with four Gold Stars and the Navy Achievement Medal with a Gold Star.
The Rickover joins three other submarines at the shipyard — the USS Hartford, the USS Santa Fe and the former Salt Lake City.
Exeter is the host community for the submarine.


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Tinseled trees and snowy landscapes are not the only signs of the upcoming holiday season. Red kettles, staffed by men and women in street clothes, Santa suits and Salvation Army uniforms also telegraph Christmastime. Read more.
Rev. Joseph Lowery, a co-founder of the Southern Christian Leadership Conference and a social justice icon often hailed as the "dean" of the American civil rights movement, died on Friday night. He was 98 years old. Read more.


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This blog post is about two pieces of writing released in the last week, and how having a tiny bit of knowledge can be very dangerous.
The story starts with an open letter written to the UK Government signed by 200+ scientists, condemning the government's response to the Coronavirus epidemic, that the response was not forceful enough, and that the government was risking lives by their current course of action. The letter was widely reported and even made it to the BBC frontpage, pretty compelling stuff.
The issue is that as soon as you start scratching beneath the surface, all is not quite what it seems. Of the 200+ scientists, about 1/3 are PhD students, not an issue in and of itself, but picking out some of the subjects we've got:
And so on, just eyeballing the list I'd hazard a guess that a vast majority of the PhD student signatories are non-specialists in this field. Even among the lecturers we've got the following specialisms:
Just because they are not specialists what's the problem? Shouldn't they be allowed to have an opinion?
I've got two responses to this, the first is not a criticism of the signatories – it's with how this message was relayed in the media. Simply stating that 200+ scientists have written an open letter condemning the Government response is misleading if no information is included as to the relative expertise of the scientists. To call a lecturer in Employment Law a scientists is stretching the definition of scientist beyond any reasonable bounds! The BBC article gave no such indication that the letter had been signed by such a range of individuals.
The second issue is with the references provided within the letter to back up the points being made – these sources contain some pretty glaring errors! I'll explain below what these errors are. I think we can and should hold the scientists accountable for not properly scrutinising their sources, to my mind this is exactly the issue with highly educated people with a non-relevant specialisms commenting on an unfamiliar area.
So what is my the issue with their sources?
Tomas Pueyo's Medium article
The open letter referenced the following Medium .com article written by Tomas Pueyo which appears (ironically?) to have gone viral:
Once again, this is an article written by a non-specialist, and is more evidence of how a small amount of knowledge can be a very dangerous thing! I feel like there's a theme here. Before we start digging into the article too much, what is this guy's background?
Well for one thing he has written a book on Star Wars "The Star Wars Rings: The Hidden Structure Behind the Star Wars Story - Tomas Pueyo Brochard", not a great start. He's worked at a number of tech start ups, and writes online quite a lot, his Medium articles are predominantly about public speaking, building viral apps, and effective writing. Going viral appears to be something he is very good at, so I'd be inclined to listen to his advice on this subject, the analysis of infectious diseases not so much!
The first thing that struck me as strange when reading his article was the following section (pasted below) which gives statistics on the proportion of cases requiring hospitalisation. Note the numbers are worryingly big!
Something felt off about this, then I realised - the numbers don't actually add up to 100%, hmm, that's a bit strange…. what happens when we start to scratch under the surface?
Tomas states that 5% of cases require ICU admission and 2.5% require very intensive treatment i.e. mechanical ventilation or similar. I followed the link that Tomas quoted, and firstly the actual value is 2.3% in the study, not sure why he has rounded up here to 2.5%, that's quite minor though. The more serious issue is that the study was an analysis of the outcomes of approx. 1,000 patients who were admitted to hospital. The study itself appears to be rigorous, and is presented in a clear manner; the issue is purely in how the figures have been quoted by Tomas. Link to article:
In his Medium article Tomas states that 2.5% of all cases require mechanical ventilation or some other form of intensive treatment, and that 5% of all cases require ICU admission. Based on the data he has presented, this should actually be scaled by the % of cases requiring hospitalisation (given by Tomas at 20%) – i.e. 0.5% of all cases not 2.5% of all cases for the intensive intervention, and 1% of all cases which require ICU admission not 5%. So Tomas is out by a factor of 5, just by correcting using his own estimates of the hospitalisation rate. Here is the relevant table from the study:
Okay, so that first sentence has two mistakes already, what about that graphic which didn't add up to 100%?
I went on the following journey to try to find the original study the data is taken from:
Medium article -> Information is Beautiful (another website) which produced the infographic -> A Google Spreadsheet provided by Information is Beautiful which contains 3 links. The links were the following:
1) A Guardian article which is seemingly unrelated to this specific point?!
2) A Statista article which repeats the same values:
3) An article published by the Chinese Centre for Disease Control (CCDC):
Ah ha, this article actually contains the research being quoted! It appears to be carried out by respectable scientists on real clinical data, okay, now we are getting somewhere.
The article is an analysis of the characteristics of approx. 44k confirmed cases, and among other things, breaks out the percentage of these confirmed cases which required hospitalisation. We find out in this paper what happened to the missing 0.6% – in the original paper, these cases were marked up as 'missing', i.e. not reported. A fairly innocuous explanation, but one I would have preferred that to have been noted in the Medium graphic in some way – have an asterix and explain at the bottom, or allocate proportionate across the other categories, but do something about it!
This is where I am going to strongly disagree with Tomas's analysis. Hospitalisation numbers are very unlikely to be underreported – the CCDC article explains that all hospitals were required by law to report any cases to the CCDC. The possibility of over-reporting was handled through the inclusion of citizen's national identity numbers in the data gathered to prevent double counting. In other words, the absolute number of hospitalisations and deaths quoted in the study are probably pretty accurate, the number of confirmed cases are also probably pretty accurate.
We have to be careful though when applying this denominator to the population as a whole, using the number of confirmed cases as a proxy for the actual number of cases is very prone to underreporting, I would consider this value (approx. 20% requiring hospitalisation) as simply an upper bound on the percentage of infections which require hospitalisation. The Medium article however is not careful about this, and references the CCDC study as if it is an estimate of what percentage of the total population would require hospitalisation if infected by the virus – very different things! Without answering the question of what ratio of confirmed cases to actual infections we are dealing with in the underlying Chinese data, we are not making a valid inference about how these stats will apply to the total population.
Note that the word 'case' in the way used by Tomas might actually be valid, here is the CDC definition:
CASE. In epidemiology, a countable instance in the population or study group of a particular disease, health disorder, or condition under investigation. Sometimes, an individual with the particular disease.
So in terms of the study, the hospitalisation rate to Cases (where Case has a capital C) could correctly be said to be 20%. I suspect that Tomas has not understood this subtlety, and if he has then he has presented the data in a very misleading way. Moreover when talking about the % of future cases that will lead to hospitalisation, this would require adjustment. This subtlety is never explained.
The UK Government has stated they believe the proportion of actual infections to reported cases may be out by a factor 5-10. If we use the value of 5 to be on the more conservative side of their range, then we need to scale down all of Tomas's numbers as follows:
Note that the ICU and ventilation numbers are now lower than the estimated fatality rate from Coronavirus! The UK Government has stated that their estimate is approximately 1%. So even though we've now made these numbers internally consistent, they are now too low to be believable.... Why is this?
The first study which Tomas linked to (the table I've pasted above) is actually very immature, of the 1,099 patients in the study, 94% were still in the hospital at the end of the study! i.e. could very easily get much worse, therefore the 2.5% and 5% are actually underestimated! Once again we've scratched under the surface and found another glaring error. Nowhere in his study did Tomas mention that the 2.5% requiring ventilation and the 5% requiring ICU admission were based on just 25 and 50 people respectively and that he had not adjusted for the bias from right censoring (a study ends before a final value is known):
So what's my point?
As numerically literate people who are non-experts in infectious disease and epidemiology (and I consider myself in this category by the way, I am very ignorant of almost all epidemiology) we have to be soooo careful when producing analysis on Coronavirus which is getting disseminated to the wider public. It's more important than ever to properly scrutinise sources, to stop and think if the person you are listening to truly knows what they are doing, and has taken the time to be careful in their analysis.
I feel like there was a breakdown in reporting at multiple stages here. Tomas misinterpreted various otherwise well written and rigorous studies, the 200+ 'scientists' then appear to have swallowed this uncritically and referenced it as evidence which was cited to the UK Government, and the BBC has then quoted these scientists sending up their warning cry without really scrutinising the expertise of the scientists or the sources referenced by the scientists.
So I finally finished Thomas Piketty's book - Capital in the 21st Century. I thought I'd write up an interesting result that Piketty mentions, but does not elaborate on. given the book is already about 700 pages, he did have to draw the line somewhere!
The result is specifically, that under basic models of the evolution over time of wealth distribution in a society, it can be shown that when growth is equal to $g$, and return on capital is $r$, then wealth has a Pareto distribution with parameter $r-g$. That sounds quite interesting right?
My notes below are largely based on following paper by Charles I. Jones of Standford Business School addressing the same question, my addition is to derive the assumption of an exponential distribution of income from more basic assumptions about labour and capital income. Link to Jones's paper:
Pareto inequality of Income
The simplest version of the problem is to investigate the inequality of income rather than capital, this way we leave aside issues of inheritance, inter-generational effects, shocks to capital, etc.
In this case, the model as described in the link above from Jones only requires two assumptions:
Where $\delta$ is the death rate.
This is my kind of model! I'm pretty sure we derived this distribution in one of the actuarial exams (CT4 or CT5?), and this distribution can be derived just from the assumption of a constant death rate. It's not without limitations (death rates have a mini-increase in adolescent for example), but the overall shape of the curve is pretty close to the empirical distribution.
What's our other assumption?
2. Income $y$, increases exponentially with age $x$:
$$y = e^{\mu x}$$
I was happy following the paper until this point, is this a reasonable assumption? Empirically income does not tend to increase exponentially right? Salaries tends to increase up until middle age, but then peak around age 50-55. Before falling off slightly. After more consideration, I realised I was considering the wrong type of income, the important distinction is we are talking about total income here, not just income from labour. We know that:
$$ \text{Income(x)} = \text{Labour income(x)} + \text{Capital income(x)}$$
Below I give a demonstration of why we might be more willing to assume total income increases exponentially with age.
Exponential distribution of Income
Assume we have a constant savings rate $s$, capital earns interest at rate $r$, and let $C_x$ denote capital at time $x$, and $L_x$ denote labour income at time $x$.
Then we can easily link capital at time $x$ to capital at time $x+1$ using the following:
$$ C_x = C_{x-1}(1+r)+ s*L_x$$
And this formula can then be used to examine individual's capital over time:
$$ C_1 = 0 + s * L_0 $$
$$ C_2 = C_1 (1+r) + s * L_1 = (s*L_0)(1+r) +s L_1 $$
$$ C_3 = C_2 (1+r) + s * L_2 = (s*L_0)(1+r)^2 +s L_1(1+r)+s*L_2 $$
And generalising (which we can prove by induction, but I'm just going to take as given here):
$$C_n = s(L_0 *(1+r)^{n-1} + L_1*(1+r)^{n-2} + … + L_{n-1})$$
Or in short hand:
$$C_n = s \sum_{i=0}^{n-1} L_{-i}* (1+r)^{n-1-i} $$
We now need to commit to a particular form for $L_n$ to progress any further. It turns out even with a linearly increasing function of $L$, we still end up with an exponential aggregate income over time. Using a linear function for $L_n$ is weaker than using an exponential function (as we would just be begging the question if we already assumed $L_n$ increased exponentially.)
Using $L_n = \alpha n$, gives us:
$$C_n = s \sum_{i=0}^{n-1} \alpha n * (1+r)^{n-1-i} $$
Taking $\alpha$, and a $(1+r)$ outside gives the following:
$$C_n = \frac{\alpha s}{1+r} \sum_{i=0}^{n-1} n * (1+r)^{n-i} $$
The trick now is to think of this sum, which I'll refer to as $S$ (i.e. ignoring the factors outside the sum), as the following:
(1+r) & + & (1+r) & + & ... &...& ... & ...& +& (1+r)\\
(1+r)^2 & + & (1+r)^2 & + &...& ... & ... & + & (1+r)^2&\\
(1+r)^3 & + & (1+r)^3 & + &...& + &(1+r)^3 &\\
... & & & & & & & &\\
(1+r)^{n-1} & & & & & & & &
We now rewrite this as a series of sums of columns as follows:
$$S = \sum_{i=1}^{1} (1+r)^i + \sum_{i=1}^{2} (1+r)^i + … + \sum_{i=1}^{n-1} (1+r)^i$$
But each of these is now just a geometric series, that is to say our sum is equal to:
$$S = \frac{(1+r)^2-1}{r} + \frac{(1+r)^3-1}{r} + … +\frac{(1+r)^n-1}{r} – (n-1)$$
And writing this with summation notation:
$$S = \frac{\sum_{i=2}^{n} (1+r)^i – (n-1)}{r} – (n-1) $$
The trick now is to once again apply the formula for a geometric sum giving:
$$S = \frac{ (1+r)^{n+1} – 1 -2r – r^2}{r^2} - \frac{n-1}{r} - \frac{r (n-1)}{r}$$
Which we can simply slightly:
$$S = \frac{ (1+r)^{n+1} – (1+r)^2}{r^2} - \frac{(n-1)(1+r)}{r}$$
And then plugging this into the formula for $C_n$:
$$C_n = \frac { s \alpha }{1+r} \left( \frac{ (1+r)^{n+1} – (1+r)^2}{r^2} - \frac{(n-1)(1+r)}{r} \right)$$
And this is the result we require. We can see that capital, and hence income increases exponentially with age (though we are subtracting a term which increases linearly with age to slow it down).
Pareto distribution
Now that we've motivated the two assumptions, all that remains is to combine them, and show that we end up with a Pareto distribution.
Inverting the assumption about income gives the age at which an individual earns a given level of income:
$$y = e^{\mu x}$$
$$x(y) = \frac{1}{\mu} \text(log) y $$
And then, using this to evaluate the probability of income being greater than y:
$$P(\text{Income} > y) = P(\text{Age} > x(y)) = e^{-\delta x(y)} = y^{-\frac{\delta}{\mu}}$$
As required.
Stirling's Approximation
I'm reading 'Information Theory, inference and learning algorithms' by David MacKay at the moment and I'm really enjoying it so far. One cool trick that he introduces early in the book is a method of deriving Stirling's approximation through the use of the Gaussian approximation to the Poisson Distribution.
Suppose we have a Poisson Distribution with parameter $\lambda$, by definition:
$$P(X=k)=e^{- \lambda} \frac{\lambda^k}{k!}$$
If we replace $\lambda$ with $r$, and consider the probability that $X=r$, we get:
$$P(X=r)=e^{- r} \frac{r^r }{r!}$$
Now suppose we are restricting ourselves to large value of $r$, in which case, a Poisson distribution is well approximated by a Gaussian distribution with mean and variance both equal to $r$.
Setting up this approximation.
$$e^{- r} \frac{r^r }{r!} \approx \frac{1}{\sqrt{2 \pi r}} e^{- \frac{(r-r)^2}{2}}$$
From which the right hand side simplifies further to give:
$$ e^{- r} \frac{r^r }{r!} \approx \frac{1}{\sqrt{2 \pi r}} e^{0}$$
$$ e^{- r} \frac{r^r }{r!} \approx \frac{1}{\sqrt{2 \pi r}}$$
Which when we rearrange to obtain Stirling's approximation:
$$r! \approx e^{-r} r^r \sqrt{2 \pi r}$$
We probably shouldn't be surprised that we've found a link between $e^r$ and $\pi$. The fact that the two are linked can be easily drawn out using Euler's formula:
And examining the value $\pi$:
$$e^{i\pi }+1=0$$
So there is a clearly a link between $e^x$, and $\pi$, but its not obvious we can draw in the factorial as well.
Above we teased out a link between all of the following: $n!$, $n^n$, $e^r$, and $\pi$, which is interesting for its own sake, but moreover provides intuition as to why the Gaussian approximation to the Poisson distribution works.
It should probably be noted that we've implicitly invoked the Central Limit Theorem to establish the approximation, and the CTL is some pretty heavy machinery! The proof from first principles of the CTL is much more involved that the proof of Stirling's approximation, so the derivation above should be thought of as strictly a process of drawing out interesting parallels, rather than a path for proving the result from first principles.
Use in Actuarial Modelling
I tend to use the Gaussian approximation quite a lot at work – any time I'm modelling a claim count frequency in a Spreadsheet and I've got a reasonable number of annual claims, I'm a proponent of just using a discretised Gaussian, with a min applied at 0, and with a variance and mean set as required.
This has a couple of advantages to using either a Poisson or Negative Binomial:
Coming up with interesting problems
David Mackay seemed to have an eye for interesting problems – reading up on Wikipedia about him he competed in a Maths Olympiad while a student. I do wonder if there is a correlation between well-written, entertaining textbooks, and authors who have a background in competitive maths problems. The link between Stirling's approximation, Gaussian, and Poisson is just the sort of thing that could make an interesting problem in a competitive maths competition.
I also realised after writoing this post that I'd already written about something pretty similar before, where we can use Stirling's approximation to easily estimate the probability that a Poisson value is equal to it's mean. Here's the link:
Piketty also adds colour by tying his observations to the literature written at the time (Austen, Dumas, Balzac), and how the assumptions made by the authors around how money, income and capital work are also reflected in the economic data that Piketty obtained.
Hopefully I've convinced you Piketty's programme is a worthwhile one, but that still leaves the fundamental question - is his analysis correct? That's a much harder question to answer, and to be honest I really don't feel qualified to pass judgement on the entirety of the book, other than to say it strikes me as pretty convincing from the limited amount of time I've spent on it.
In an attempt to contribute in some small way to the larger conversation around Piketty's work, I thought I'd write about one specific argument that Piketty makes that I found less convincing than other parts of the book. Around 120 pages in, Piketty introduces what he calls the 'Second Fundamental Law of Capitalism', and this is where I started having difficulties in following his argument.
The Second Fundamental Law of Capitalism
The rule is defined as follows:
$$ B = \frac{s} { g} $$
Where $B$ , as in Piketty's first fundamental rule, is defined as the ratio of Capital (the total stock of public and private wealth in the economy) to Income (NNP):
$$B = \frac{ \text{Capital}}{\text{Income}}$$
And where $g$ is the growth rate, and $s$ is the saving rate.
Unlike the first rule which is an accounting identity, and therefore true by definition, the second rule is only true 'in the long run'. It is an equilibrium that the market will move to over time, and the following argument is given by Piketty:
"The argument is elementary. Let me illustrate it with an example. In concrete terms: if a country is saving 12 percent of its income every year, and if its initial capital stock is equal to six years of income, then the capital stock will grow at 2 percent a year, thus at exactly the same rate as national income, so that the capital/income ratio will remain stable.
By contrast, if the capital stock is less than six years of income, then a savings rate of 12 percent will cause the capital stock to grow at a rate greater than 2 percent a year and therefore faster than income, so that the capital/income ratio will increase until it attains its equilibrium level.
Conversely, if the capital stock is greater than six years of annual income, then a savings rate of 12 percent implies that capital is growing at less than 2 percent a year, so that the capital/income ratio cannot be maintained at that level and will therefore decrease until it reaches equilibrium."
I've got to admit that this was the first part in the book where I really struggled to follow Piketty's reasoning – possibly this was obvious to other people, but it wasn't to me!
Analysis – what does he mean?
Before we get any further, let's unpick exactly what Piketty means by all the terms in his formulation of the law:
Income = Net national product = Gross Net product *0.9
(where the factor of 0.9 is to account for depreciation of Capital)
$g$ = growth rate, but growth of what? Here it is specifically growth in income, so while this is not exactly the same as GDP growth it's pretty close. If we assume net exports do not change, and the depreciation factor (0.9) is fixed, then the two will be equal.
$s$ = saving rate – by definition this is the ratio of additional capital divided by income. Since income here is net of depreciation, we are already subtracting capital depreciation from income and not including this in our saving rate.
Let's play around with a few values, splitting growth $g$, into per capita growth and demographic growth we get the following. Note that Total growth is simply the sum of demographic and per capita growth, and Beta is calculated from the other values using the law.
So why does Piketty introduce this law?
The argument that Piketty is intending to tease out from this equality is the following:
In fact using $g=1.5 \%$ as a long term average, we can expect Beta to crystallise around a Beta of $8$! Much higher than it has been for the past 100 years.
Analysis - convergence
As Piketty is quick to point out, this is a long run equilibrium towards which an economy will move. Moreover, it should be noted that the convergence of this process is incredibly slow.
Here is a graph plotting the evolution of Beta, from a starting point of 5, under the assumption of $g=1.5 \%$, $s = 12 \%$:
So we see that after 30 years ( i.e. approx. one generation), Beta has only increased from its starting point of $5$ to around $6$, it then takes another generation and a half to get to $7$, which is still short of its long run equilibrium of $8$.
Analysis - Is this rule true?
Piketty is of course going to want to use his formula to say interesting things about the historic evolution of the Capital/Income ratio, and also use it to help predict future movements in Beta. I think this is where we start to push the boundaries of what we can easily reason, without first slowing down and methodically examining our implicit assumptions.
For example – is a fixed saving rate (independent of changes in both Beta, and Growth) reasonable? Remember that the saving rate here is a saving rate on net income. So that as Beta increases, we are already having to put more money into upkeep of our current level of capital, so that a fixed net saving rate is actually consistent with an increasing gross saving rate, not a fixed gross saving rate. An increasing gross saving rate might be a reasonable assumption or it might not – this then becomes an empirical question rather than something we can reason about a priori.
Another question is how the law performs for very low rates of $g$, which is in fact how Piketty is intending to use the equation. By inspection, we can see that:
As $g \rightarrow 0$, $B \rightarrow \infty $.
What is the mechanism by which this occurs in practice? It's simply that if GDP does not grow from one year to the next, but the net saving rate is still positive, then the stock of capital will still increase, however income has not increased. This does however mean that an ever increasing share of the economy is going towards paying for capital depreciation.
Piketty's law is still useful, and I do find it convincing to a first order of approximation. But I do think this section of the book could have benefited from more time spent highlighting some of the distortions potentially caused by using net income as our primary measure of income. There are multiple theoretical models used in macroeconomics, and it would have been useful for Piketty to help frame his law within the established paradigm.
The Rule of 72
I'm always begrudgingly impressed by brokers and underwriters who can do most of their job without resorting to computers or a calculator. If you give them a gross premium for a layer, they can reel off gross and net rates on line, the implied loss cost, and give you an estimate of the price for a higher layer using an ILF in their head. When I'm working, so much actuarial modelling requires a computer (sampling from probability distributions, Monte Carlo methods, etc.) that just to give any answer at all I need to fire up Excel and make a Spreadsheet. So anytime there's a chance to do some shortcuts I'm always all for it!
One mental calculation trick which is quite useful when working with compound interest is called the Rule of 72. It states that for interest rate $i$, under growth from annual compound interest, it takes approximately $\frac{72}{i} $ years for a given value to double in size.
Why does it work?
Here is a quick derivation showing why this works, all we need is to manipulate the exact solution with logarithms and then play around with the Taylor expansion.
We are interested in the following identity, which gives the exact value of $n$ for which an investment doubles under compound interest:
$$ \left( 1 + \frac{i}{100} \right)^n = 2$$
Taking logs of both sides gives the following:
$$ ln \left( 1 + \frac{i}{100} \right)^n = ln(2)$$
And then bringing down the $n$:
$$n* ln \left( 1 + \frac{i}{100} \right) = ln(2)$$
And finally solving for $n$:
$$n = \frac {ln(2)} { ln \left( 1 + \frac{i}{100} \right) }$$
So the above gives us a formula for $n$, the number of years. We now need to come up with a simple approximation to this function, and we do so by examining the Taylor expansion denominator of the right have side:
We can compute the value of $ln(2)$:
$$ln(2) \approx 69.3 \%$$
The Taylor expansion of the denominator is:
$$ln \left( 1 + \frac{i}{100} \right) = \frac{r}{100} – \frac{r^2}{20000} + … $$
In our case, it is more convenient to write this as:
$$ln \left( 1 + \frac{i}{100} \right) = \frac{1}{100} \left( r – \frac{r^2}{200} + … \right) $$
For $r<10$, the second term is less than $\frac{100}{200} = 0.5$. Given the first term is of the order $10$, this means we are only throwing out an adjustment of less than $5 \%$ to our final answer.
Taking just the first term of the Taylor expansion, we end up with:
$$n \approx \frac{69.3 \%}{\frac{1}{100} * \frac{1}{r}}$$
And rearranging gives:
$$n \approx \frac{69.3}{r}$$
So we see, we are pretty close to $ n \approx \frac{72}{r}$.
Why 72?
We saw above that using just the first term of the Taylor Expansion suggests we should be using the 'rule of 69.3%' instead. Why then is this the rule of 72?
There are two main reasons, the first is that for most of the interest rates we are interested in, the Rule of 72 actually gives a better approximation to the exact solution, the following table compares the exact solution, the approximation given by the 'Rule of 69', and the approximation given by the Rule of 72:
The reason for this is that for interest rates in the 4%-10% range, the second term of the Taylor expansion is not completely negligible, and act to make the denominator slightly smaller and hence the fraction slightly bigger. It turns out 72 is quite a good fudge factor to account for this.
Another reason for using 72 over other close numbers is that 72 has a lot of divisors, in particular out of all the integers within 10 of 72, 72 has the most divisors. The following table displays the divisors function d(n), for values of n between 60 and 80. 72 clearly stands out as a good candidate.
The rule of 72 in Actuarial Modelling
The main use I find for this trick is in mentally adjusting historic claims for claims inflation. I know that if I put in 6% claims inflation, my trended losses will double in size from their original level approximately every 12 years. Other uses include when analysing investment returns, thinking about the effects of monetary inflation, or it can even be useful when thinking about the effects of discounting.
Can we apply the Rule of 72 anywhere else?
As an aside, we should be careful when attempting to apply the rule of 72 over too long a time period. Say we are watching a movie set in 1940, can we use the Rule of 72 to estimate what values in the movie are equivalent to now? Let's set up an example and see why it doesn't really work in practice. Let's suppose an item in our movie costs 10 dollars. First we need to pick an average inflation rate for the intervening period (something in the range of 3-4% is probably reasonable). We can then reason as follows; 1940 was 80 years ago, at 4% inflation, $\frac{72}{4} = 18$, and we've had approx. 4 lots of 18 years in that time. Therefore the price would have doubled 4 times, or will now be a factor of 16. Suggesting that 10 dollars in 1940 is now worth around 160 dollars in today's terms.
It turns out that this doesn't really work though, let's check it against another calculation. The average price of a new car in 1940 was around 800 dollars and the average price now is around 35k, which is a factor of 43.75, quite a bit higher than 16. The issue with using inflation figures like these over very long time periods, is for a given year the difference in the underlying goods is fairly small, therefore a simple percentage change in price is an appropriate measure. When we chain together a large number of annual changes, after a certain number of years, the underlying goods have almost completely changed from the first year to the last. For this reason, simply multiplying an inflation rate across decades completely ignores both improvements in the quality of goods over time, and changes in standards of living, so doesn't really convey the information that we are actually interested in.
Photo by David Preston
What is a floating deductible?
Excess of Loss contacts for Aviation books, specifically those covering airline risks (planes with more than 50 seats) often use a special type of deductible, called a floating deductible. Instead of applying a fixed amount to the loss in order to calculate recoveries, the deductible varies based on the size of the market loss and the line written by the insurer. These types of deductibles are reasonably common, I'd estimate something like 25% of airline accounts I've seen have had one.
As an aside, these policy features are almost always referred to as deductibles, but technically are not actually deductibles from a legal perspective, they should probably be referred to as floating attachment instead. The definition of a deductible requires that it be deducted from the policy limit rather than specifying the point above which the policy limit sits. That's a discussion for another day though!
The idea is that the floating deductible should be lower for an airline on which an insurer takes a smaller line, and should be higher for an airline for which the insurer takes a bigger line. In this sense they operate somewhat like a surplus lines contract in property reinsurance.
Before I get into my issues with them, let's quickly review how they work in the first place.
An example
When binding an Excess of Loss contract with a floating deductible, we need to specify the following values upfront:
And we need to know the following additional information about a given loss in order to calculate recoveries from said loss:
A standard XoL recovery calculation with the fixed attachment given above, would first calculate the UNL (200m*0.75%=1.5m), and then deduct the fixed attachment from this (1.5m-1.5m=0). Meaning in this case, for this loss and this line size, nothing would be recovered from the XoL.
To calculate the recovery from XoL with a floating deductible, we would once again calculate the insured's UNL 1.5m. However we now need to calculate the applicable deductible, this will be the lesser of 1.5m (the fixed attachment), and the insurer's effective line (defined as their UNL divided by the market loss = 1.5m/200m) multiplied by the Original Market Loss as defined in the contract. In this case, the effective line would be 0.75%, and the Original Market Loss would be 150m, hence; 0.75%*150m = 1.125m. Since this is less than the 1.5m fixed attachment, the attachment we should use is 1.125m our limit is always just 18.5m, and doesn't change if the attachment drops down. We would therefore calculate recoveries to this contract, for this loss size and risk, as if the layer was a 18.5m xs 1.125. Meaning the ceded loss would be 0.375m, and the net position would be 1.125m.
Here's the same calculation in an easier to follow format:
So…. what's the issue?
This may seem quite sensible so far, however the issue is with the wording. The following is an example of a fairly standard London Market wording, taken from an anonymised slip which I came across a few years ago.
Priority: USD 10,000,000 each and every loss or an amount equal to the "Reinsured's Portion' of the total Original Insured Loss sustained by the original insured(s) of USD 200,000,000 each and every loss, whichever the lesser.
Reinsuring Clause
Reinsurers shall only be liable if and when the ultimate net loss paid by the Reinsured in respect of the interest as defined herein exceeds USD 10,000,000 each and every loss or an amount equal to the Reinsured's Proportion of the total Original Insured Loss sustained by the original insured(s) of USD 200,000,000 or currency equivalent, each and every loss, whichever the lesser (herein referred to as the "Priority")
For the purpose herein, the Reinsured's Proportion shall be deemed to be a percentage calculated as follows, irrespective of the attachment dates of the policies giving rise to the Reinsured's ultimate net loss and the Original Insured Loss:
Reinsured Ultimate Net Loss
Original Insured Loss
The Original Insured Loss shall be defined as the total amount incurred by the insurance industry including any proportional co-insurance and or self-insurance of the original insured(s), net of any recovery from any other source
What's going on here is that we've defined the effective line to be the Reinsured's unl divided by the 100% market loss.
First problem
From a legal perspective, how would an insurer (or reinsurer for that matter), prove what the 100% insured market loss is? The insurer obviously knows their share of the loss, however what if this is a split placement with 70% placed in London on the same slip, 15% placed in a local market (let's say Indonesia?), and a shortfall cover (15%) placed in Bermuda. Due to the different jurisdictions, let's say the Bermudian cover has a number of exclusions and subjectivities, and the Indonesian cover operates under the Indonesian legal system which does not publically disclose private contract details.
Even if the insurer is able to find out through a friendly broker what the other markets are paying, and therefore have a good sense of what the 100% market loss is, they may not have a legal right to this information. The airline does have a legal right to the information, however the reinsurance contract is a contract between the insured and reinsured, the airline is not a party to the reinsurance contract. The point is whether the insurer and reinsured have the legal right to the information.
The above issues may sound quite theoretical, and in practice there are normally no issues with collecting on these types of contracts. But to my mind, legal language should bear up to scrutiny even when stretched – that's precisely when you are going to rely on it. My contention is that as a general rule, it is a bad idea to rely on information in a contract which you do not have an automatic legal right to obtain.
The second problem
The intention with this wording, and with contracts of this form is that the effective line should basically be the same as the insured's signed line. Assuming everything is straightforward, if the insurer takes a x% line with a limit of Y bn. If the loss is anything less than Y bn, then the insured's effective line will simply be x%*Size of Loss / Size of loss. i.e. x%.
My guess as to why it is worded this way rather than just taking the actual signed line is that we don't want to open ourselves to a issues around what exactly we mean by 'the signed line' – what if the insured has exposure through two contracts both of which have different signed lines, what if there is an inuring Risk Excess which effectively nets down the gross signed line – should we then use the gross or net line? By couching the contract in terms of UNLs and Market losses we attempt to avoid these ambiguities
Let me give you a scenario though where this wording does fall down:
Scenario 1 – clash loss
Let's suppose there is a mid-air collision between two planes. Each results in an insured market loss of USD 1bn, then the Original Insured Loss is USD 2bn. If our insurer takes a 10% line on the first airline, but does not write the second airline, then their effective line is 10% * 1bn / 2bn = 5%... hmmm this is definitely equal to their signed line of 10%.
You may think this is a pretty remote possibility, after all in the history of modern commercial aviation such an event has not occurred. What about the following scenario which does occur fairly regularly?
Scenario 2 – airline/manufacturer split liability
Suppose now there is a loss involving a single plane, and the size of the loss is once again USD 1bn, and that our insurer once again has a 10% line. In this case though, what if the manufacturer is found 50% responsible? Now the insurer only has a UNL of USD 500m, and yet once again, in the calculation of their floating deductible, we do the following: 10% * 500m/1bn = 5%.
Hmmm, once again our effective line is below our signed line, and the floating deductible will drop down even further than intended.
Suggested alternative wording
My suggested wording, and I'm not a lawyer so this is categorically not legal advice, is to retain the basic definition of effective line - as UNL divided by some version of the 100% market loss - by doing so we still neatly sidestep the issues mentioned above around gross vs net lines, or exposure from multiple slips, but instead to replace the definition of Original Insured Loss with some variation of the following 'the proportion of the Original Insured Loss, for which the insured derives a UNL through their involvement in some contract of insurance, or otherwise'.
Basically the intention is to restrict the market loss, only to those contracts through which the insurer has an involvement. This deals with both issues – the insurer would not be able to net down their line further through references to insured losses which are nothing to do with them, as in the case of scenario 1 and 2 above, and secondly it restrict the information requirements to contracts which the insurer has an automatic legal right to have knowledge of since by definition they will be a party to the contract.
I did run this idea past a few reinsurance brokers a couple of years ago, and they thought it made sense. The only downside from their perspective is that it makes the client's reinsurance slightly less responsive i.e. they knew about the strange quirk whereby the floating deductible dropped in the event of a manufacturer involvement, and saw it as a bonus for their client, which was often not fully priced in by the reinsurer. They therefore had little incentive to attempt to drive through such a change. The only people who would have an incentive to push through this change would be the larger reinsurers, though I suspect they will not do so until they've already been burnt and attempted to rely on the wording in a court case and, at which point they may find it does not quite operate in the way they intended.
I work as a pricing actuary at a reinsurer in London.
March 2020


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