Let's define free will as the ability for a human being to make a choice that does not completely depend on the history of the universe. The universe may be assumed to be indeterministic. Any simple choice will do: am I going to order a Coke or a Sprite?  Has anyone described what the universe must be like in order for this kind of free will to be able to exist? A universe where an agent making the choice exerts causal influence on the universe? In what kind of universe would this be possible, while not running afoul of dualism?   [1]
Why is free will a widely discussed, established concept? Does this concept emerge from religious / spiritual doctrine? Why is there so much interest in this topic?  If a neural-network based AI machine with a certain high degree of complexity scores a perfect 100 every run in a turing test, have we not already refuted the idea of free will? In fact, let me extend this reasoning, if ANY machine scores a single point in a turing test (and not 100), have we not already disproved (or alternatively put in great doubt the existence of) free will? If we already created a machine that can master a certain degree of human interaction, have we not then demonstrated that human interaction is programmable? (given enough time for the creation of a complex or more appropriately elaborative neural system).   From the perspective of an external observer, such a machine would be qualitatively human although intrinsically quantitative behind a stream of 1's and 0's. It would exhibit a type of decision making indistinguishable from that of a human. Does this not reduce the type of decision making we understand to be "free will" to something quantitative, deterministic, materialist?
How to get back Windows 10 [UEFI] after Legacy installation of Fedora 24? JSON URL from StackExchange API returning jibberish? Excel automatic hyperlinks Irrationality proofs not by contradiction Per now, I have basically come upon proofs of the irrationality of $\sqrt{2}$ (and so on) and the proof of the irrationality of $e$. However, both proofs were by contradiction.  When thinking about it, it seems like the definition of irrationality itself demands proofs by contradiction. An irrational number is a number that is not a rational number. It seems then that if we were to find direct irrationality proofs, this would rely on some equivalent definition of irrational numbers, not involving rational numbers themselves.   Are there any irrationality proofs not using contradiction? Game State 'Stack'? I was thinking about how to implement game states into my game. The main things I want for it are:   Semi-transparent top states-being able to see through a pause menu to the game behind Something OO-I find this easier to use and understand the theory behind, as well as keeping orgranised and adding more to.    I was planning on using a linked list, and treat it as a stack. This means I could access the state below for the semi-transparency.  Plan: Have the state stack be a linked list of pointers to IGameStates. The top state handles its own update and input commands, and then has a member isTransparent to decide whether the state underneath should be drawn.  Then I could do:  states.push_back(new MainMenuState()); states.push_back(new OptionsMenuState()); states.pop_front();   To represent the player loading, then going to options, and then main menu.  Is this a good idea, or...? Should I look at something else?   Thanks. No more than 10,000 results are visible in search If you make a search for something that returns more than 10,000 items in result. For example, search for  return 161,338 results on MSE. But if you select a page where 10,000+ result should be shown:        In the edge case  shows zero results:        But this is actual for any page where per_page * page_number is more than 10,000.  Though this does not happen for Stack Overflow in English. It looks like all other sites are affected.  Related bug report on ruSO.meta: Someone from Mars is called a Martian. Someone from America is called an American. Someone from Europe is a European. Someone from Hyrule is a Hyrulean.  We are not far from colonizing other planets, let alone Earth's only moon. Obviously you wouldn't call someone from the moon a lunatic right? What if you are on Mars? What would I call a foreigner from Earth? Earthean doesn't sound right. I have a HP 14-AN001NA laptop. It came with Windows 10 installed on which the Wi-Fi worked fine anywhere in the house.   However I removed Windows 10 and installed Ubuntu 16.04 instead and since I have had terrible Wi-Fi anywhere aside from about three foot away from the router. I don't know if it's relevant but my Wi-Fi is not called wlan0 but wlo1 for some reason (I didn't change it).  When running lspci -knn | grep Net -A3     I get the following output:  05:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter [10ec:b723] DeviceName:   Subsystem: Hewlett-Packard Company RTL8723BE PCIe Wireless Network Adapter [103c:81c1] Kernel driver in use: rtl8723be Kernel modules: wl, rtl8723be If I take the $k \in \mathbb{N}$ power of 10 and mod it by a large prime, I notice that the remainders repeat at some point.  For instance $10^k mod~7$ seems to repeat every $8$th value of $k$.  Given $k$ (the power of ten), and a large prime number $p$, how can I compute the size of the cycle?  I tried writing a python script that computes the first instance of a repeat. However, I don't know if this works since a single instance of a repeat may not necessarily mean a full cycle. Drawing/Sketching Tool for elaborating questions More often than not I need to elaborate my question put up on Stack Overflow with a custom sketch, UML class diagram, flow chart.    It is in these times I have to open up a custom paint software, factor out some diagrams, export it as an image, attach it to Stack Overflow. I wouldn't know how complicated it is to invest in having such a sketching or drawing tool integrated, It could even be a basic pen stripped off all the advanced features leaving it a bare minimum.  Such a tool if incorporated into the Stack Overflow "ask question" UI would be certainly helpful.  As of Today this Question has been visited around 170 times and 7 answers, This was meant to be the voice of Stack Overflow users. Would you need a Drawing Tool for you on the Stack Overflow site, would it help you to express you questions and answers better? Sadly, only 2, or 3 answers are in the context of the question. The bounty was meant to be a bait and even that ends tomorrow. Hope you'll get the will and the zest to comment on this question today and in the future . How can I get grub2 to boot a different option only on the next boot? Can we say that $\frac{0}{0}$ is every number? Alice has a secp256k1 key pair that she used some time ago when she communicated with Bob. Bob can no longer user secp256k1 but he only uses ed25519 instead.  Is there a secure algorithm that Bob can use to derive an ed25519 pubkey from original Alice's secp256k1 pub key and also Alice can derive the matching ed25519 private key from her original secp256k1 private key such that they can communicate securely via ed25519 encrypted messages?  Thanks! Show that any prime ideal from such a ring is maximal. Let R be a commutative ring with an identity such that for all $r\in$ R, there exists some $n&gt;1$ such that $r^n = r$. Show that any prime ideal is  maximal. (Atiyah and MacDonald, Introduction to Commutative Algebra, Chapter 1, Exercise 7.)    Any hints? All html canvas shapes are given the color of the last object added I have a project where I have a few layers (State of Texas, cities, roads, etc.). They are all resaved and projected to NAD83 / UTM zone 14N EPSG: 26914. The project CRS is also NAD83 / UTM zone 14N EPSG: 26914 and on the fly projection is enabled. I added a text delimited file and cannot get them to line up. I checked the attribute table of the delimited file and the coordinates are correct. I cross-checked this with a point close to where a few of the points from the delimited file are and they are very close so in theory they should be lining up. I tried to save the delimited file and save it with the same projection and add the shp file back in and that did not work. Anyone have any ideas? I can't think of anything else to try. How to reduce title bar height? Easiest way to solve $y''+y=\frac{1}{\cos x}$ Say I have a module $M$ over a ring $R$ that is   $1.$ finitely-generated, i.e. $\exists$ finite $X \subset M$ such that $M = \sum_{i=1}^{n} Rx_{i}, x_{i}\in X$ (but $X$ is not necessarily free)  $2.$ free, i.e. $\exists$ a basis $Y \subset M$ a.k.a. $Y$ is free and generates M, (but $Y$ is not necessarily finite).  Now I want to show, that there exists a finite basis for $M$. For vector spaces, this would obviously be trivial, but for some  $R$-Modul, I'm not sure how to proceed.   Furthermore, is every minimal generating subset of $M$ a basis? Is it generally true that if $|P(A)|=|P(B)|$ then $|A|=|B|$?  Why? Thanks.