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Waiting for Gödel
- kazinator 10y agoLikely allusion to: https://en.wikipedia.org/wiki/Waiting_for_Godot https://en.wikipedia.org/wiki/Waiting_for_Godot
- auggierose 10y agoReally?
- insulanian 10y agoWhy not?
- auggierose 10y agoJust tried to joke :)
- mirimir 10y agoPoe's Law ;)
- grimoald 10y agoIt's only easy to see if you think 'ö' is pronounced like 'o'.
- mathgenius 10y agoSo great to see an article about Godel incompleteness in the new yorker. I think in general Godel incompleteness and Turing incompleteness should get more press. Chaitin has written some good books about this, but there needs to be more. There are these fundamental limits to knowledge and this is an important fact that people should know about. > “There is more to truth than can be caught by proof.” That's a nice way of putting it.
- curiousgal 10y agoI can sadly see that quote taken out of context to justify the paranormal or other crap.
- greyman 10y agoWhy such an usage is "out of context"? [Not saying it isn't, but I'd like to see some proof. :-)]
- juk3 10y agoYup. These articles much more than their focus on Godel and his fan club would do us all a favor to focus on - How do people day to day deal with ambiguity, where the truth is uncertain or unknowable? The default action always is - they choose the truth they want to be true. And this has long term consequences. They should develop self awareness that it is a chosen truth and feel a sense of responsibility for its consequences. The example I given students when I teach where things worked out well, is Thomas Jefferson's - "We hold these truths to be self-evident, that all men are created equal". We still know 240 years later there is nothing self-evident or truthful about equality. We don't know if it will ever be. Jefferson knew that. Yet he made a choice about what he wanted the truth to be. We face similar choices everyday in life. Choose well.
- deleted 10y ago[deleted]
- dllthomas 10y agoICYMI: http://www.lel.ed.ac.uk/~gpullum/loopsnoop.html http://www.lel.ed.ac.uk/~gpullum/loopsnoop.html
- sandebert 10y agoI can recommend reading Logicomix, a graphic novel about Bertrand Russell and his work in mathematics. There are lots of other people making appearances, for instance Gödel who makes quite the splash (as one can imagine). I read it a couple of weeks ago and thoroughly enjoyed it. https://www.logicomix.com/ https://en.wikipedia.org/wiki/Logicomix
- NotUsingLinux 10y agoThanks for sharing! This looks awesome!
- acqq 10y agoWorth considering (especially since the preview button on the main site doesn't work, gives "the content is restricted"): https://www.amazon.com/review/R3FH3WXNKEOZR9/ref=cm_cr_dp_title?ie=UTF8&ASIN=1596914521&channel=detail-glance&nodeID=283155&store=books https://www.amazon.com/review/R3FH3WXNKEOZR9/ref=cm_cr_dp_ti...
- wingcommander 10y agoIf you want a more in-dept popular science treatment I would recommend Gödel's Proof. Logicomix has quite a bit of slightly annoying digressions. https://www.goodreads.com/book/show/695429.G_del_s_Proof https://www.goodreads.com/book/show/695429.G_del_s_Proof
- moehm 10y agoOh, yes, absolutely recommended!
- curiousgal 10y agoWhat a fun read! Probably worth mentioning that Russell's opposition to recursion which lead to him formulating "his" paradox offered type theory as a solution. Type theory also has quite the impact on computer science.
- chriswarbo 10y agoI think a more precise wording than "recursive" would be objecting to impredicative definitions; those which quantify over (something containing or pertaining to) themselves. For example, it's fine to define an arithmetic function recursively; it's not so fine to define a set based on whether it contains itself.
- kriro 10y ago"""Gödel’s masterpiece was his incompleteness theorem, which ranks in scientific folklore with Einstein’s relativity and Heisenberg’s uncertainty.""" nitmode: theorems (there's two). It's mentioned later in the article but a little odd that they don't just add the s and be done with it. Great article though. Sidenote: I always thought a tragedy about Cantor would be fun to write.
- Grue3 10y agoThere's also Godel's completeness theorem for first order logic. Much easier to prove, and also extremely important.
- Intermernet 10y ago>I asked my classmates whether they had heard of the sci-fi writer Rudy Rucker’s book Rudy Rucker was/is also one of the most prominent cellular automata researchers of recent history. I can highly recommend "Cellab" [1], which I first encountered as CA Lab. You may need to install a virtual machine to get it running properly [2]. [1]: http://www.rudyrucker.com/oldhomepage/cellab.htm http://www.rudyrucker.com/oldhomepage/cellab.htm [2]: [In the spring of 2010, the Cellab software became semi-obsolete---in that it won't run under Windows 7. The "good" news is that Windows 7 can in fact run a virtual machine in Windows XP mode, if you download and install some free Microsoft virtual XP software. I tried this just now, and it works pretty well. You get a little window or a full screen which is an XP desktop. And CELLAB runs fine in the XP window—to make it easy to find your files, you drag the CELLAB folder from your normal C: drive (if that’s where it lives) onto the desktop of the XP Virtual machine window.]
- ericssmith 10y agoAlthough it's nice to see Gödel show up in the popular press, I didn't get what the point of this was. His Incompleteness paper is not that impenetrable. Sometimes it does pay to at least look at primary sources in addition to listening to others' efforts to summarize or dissect. I don't think the author of this article made much of an effort to understand what or who she was writing about. Sad, really, given Gödel's importance in understanding the beginnings of a science of computation (easily one of the most significant achievements in human history), where there is already too much myth-making and mischaracterizations.
- bgilroy26 10y agoThank you for your Godel notes below! I'm going to check out the links. I have the Brooklyn Institute for Social Research in my Facebook feed and they're mentioned in the article. I think the point of the article is to mark the work the teacher of the Godel class at the Institute did to digest the material for the students of his/her class. The preliminary milestone of digestion of a subject for teaching is a syllabus, also mentioned in the article.
- brahadeesh 10y ago"His Incompleteness paper is not that impenetrable." May I ask what do you mean by that?
- ericssmith 10y agoSure. The original 1931 paper is 20-something pages long: http://www.w-k-essler.de/pdfs/goedel.pdf http://www.w-k-essler.de/pdfs/goedel.pdf Here's an English translation (with a lengthy introduction) http://jacqkrol.x10.mx/assets/articles/godel-1931.pdf http://jacqkrol.x10.mx/assets/articles/godel-1931.pdf Even without trying to follow the proof proper, the sub-sections of the second part are interesting on their own, particularly Gödel numbering and primitive recursive functions. Here is another translation that covers just this part: http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf http://www.research.ibm.com/people/h/hirzel/papers/canon00-g... It's true that if you know nothing about formal logic, history of metamathematics, and decidability, then it's going to be particularly hard going, but there are a lot of accessible resources for each of those topics and the paper is well structured (meaning you can concentrate on the pieces). The encoding that Gödel used for formulas should be fascinating for anyone familiar with Turing work on decidability as well as how computers work generally. Primitive recursive functions don't handle computation generally, but seem to be a first step in understanding what it means. Anyone familiar with Alonzo Church, lambda calculus, functional programming, McCarthy's first paper on Lisp would probably be interested in this bit. Of course, Gödel's result on formal systems shattered the idea of an axiomatic basis for mathematics, but I personally think its greater long-term impact is helping to usher in computation. It's worth recognizing both.