Gödel, Turing and Cantor: The Math
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Gödel, Turing and Cantor: The Math
1–10 of 27 posts
Re: Gödel, Turing and Cantor: The Math
#2Oh wow! This is a great write up on Godel's work. Anybody who even vaguely cares about fundamentals of computer science should definitely give it a read, and if possible a thorough read.
Slightly related: Although a more technical/deeper discussion, but the book "Godel's Proof"[1] by Nagel and Newman is a very approachable text in this domain, and explains many aspects of the incompleteness theorems.
[1] http://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814...
Re: Gödel, Turing and Cantor: The Math
#3Oh wow! This is a great write up on Godel's work. Anybody who even vaguely cares about fundamentals of computer science should definitely give it a read, and if possible a thorough read. Slightly related: Although a more technical/deeper discussion, but the book "Godel's Proof"[1] by Nagel and Newman is a very approachable text in this domain, and explains many aspects of the incompleteness theorems. [1] http://www.a…
Honorable mention for http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach which has been mentioned many times on HN. Has many different ways of explaining Godel's genius. Though to be fair you could just read this article and be good.
Re: Gödel, Turing and Cantor: The Math
#4Oh wow! This is a great write up on Godel's work. Anybody who even vaguely cares about fundamentals of computer science should definitely give it a read, and if possible a thorough read. Slightly related: Although a more technical/deeper discussion, but the book "Godel's Proof"[1] by Nagel and Newman is a very approachable text in this domain, and explains many aspects of the incompleteness theorems. [1] http://www.a…
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Re: Gödel, Turing and Cantor: The Math
#5Oh wow! This is a great write up on Godel's work. Anybody who even vaguely cares about fundamentals of computer science should definitely give it a read, and if possible a thorough read. Slightly related: Although a more technical/deeper discussion, but the book "Godel's Proof"[1] by Nagel and Newman is a very approachable text in this domain, and explains many aspects of the incompleteness theorems. [1] http://www.a…
Honorable mention for http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach which has been mentioned many times on HN. Has many different ways of explaining Godel's genius. Though to be fair you could just read this article and be good.
+1 for GEB. I have been reading it on and off for about 2 years. It's a fun book, but every time I finish a reading session, I am exhausted. I am about 25% through.
Re: Gödel, Turing and Cantor: The Math
#6Chaitin is cool, too.
Re: Gödel, Turing and Cantor: The Math
#7Does this mean that the antivirus industry is nothing but a scam?
Re: Gödel, Turing and Cantor: The Math
#8Does this mean that the antivirus industry is nothing but a scam?
it means antivirus industry will never be "complete"
Re: Gödel, Turing and Cantor: The Math
#9Chaitin is cool, too.
Chaitin's work is genius, but one thing bugs me: he uses a Cantor space in exchange for Gödel's countable numbering. I haven't found any commentary on that, but I find it suspicious.
The problem with Cantor space is you simply can't even begin to approximate Chaitin's constant, but it seems like you could by using a countable numbering (all else being equal.) Of course that would blow everything up, so the takeaway is there is something very important which I'm not convinced we've learned yet.
Re: Gödel, Turing and Cantor: The Math
#10Earlier quoted context omitted.
Honorable mention for http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach which has been mentioned many times on HN. Has many different ways of explaining Godel's genius. Though to be fair you could just read this article and be good.
+1 for GEB. I have been reading it on and off for about 2 years. It's a fun book, but every time I finish a reading session, I am exhausted. I am about 25% through.
Yeah it took me about 7 months to finish it, and you are right, every time I just felt beat and my mind was racing, what a great book.