curious facts: he died of starvation; he was a theist http://en.wikipedia.org/wiki/Kurt_G%C3%B6del#Later_years_and...
Gödel, Turing and Cantor: The Math
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Re: Gödel, Turing and Cantor: The Math
#12Earlier 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.
Re: Gödel, Turing and Cantor: The Math
#13Chaitin is cool, too.
Re: Gödel, Turing and Cantor: The Math
#14There's a translation of Gödel's paper linked via his wikipedia entries https://docs.google.com/viewer?url=http://www.research.ibm.c... [google docs viewer] curious facts: he died of starvation; he was a theist http://en.wikipedia.org/wiki/Kurt_G%C3%B6del#Later_years_and...
Re: Gödel, Turing and Cantor: The Math
#15[1] https://en.wikipedia.org/wiki/Philosophy_of_artificial_intel...
Re: Gödel, Turing and Cantor: The Math
#16Chaitin is cool, too.
[1] https://www.amazon.co.uk/Meta-Maths-Gregory-J-Chaitin/dp/184... [2] http://arxiv.org/abs/math/0404335
Re: Gödel, Turing and Cantor: The Math
#17Does this mean that the antivirus industry is nothing but a scam?
it means antivirus industry will never be "complete"
1) Every diverging (non-terminating, non-co-terminating) program can be optimised to the following:
10 GOTO 10
2) The Halting Problem tells us that no compiler can spot every diverging program.
3) Hence there is room for more optimisation, by spotting more diverging programs.
4) Hence there is always more work to do for compiler developers.
Re: Gödel, Turing and Cantor: The Math
#18There's a translation of Gödel's paper linked via his wikipedia entries https://docs.google.com/viewer?url=http://www.research.ibm.c... [google docs viewer] curious facts: he died of starvation; he was a theist http://en.wikipedia.org/wiki/Kurt_G%C3%B6del#Later_years_and...
I found your semicolon quite confusing there - it seemed to suggest that there was some relationship between being a theist and dying of starvation.
I imagine 6ren went to extra lengths to use a semicolon instead of a simple comma, as semicolons are used to emphasize independent clauses.
Re: Gödel, Turing and Cantor: The Math
#19What I find interesting are the claims Penrose[1] and others make about human versus machine intelligence based on Godel's results. [1] https://en.wikipedia.org/wiki/Philosophy_of_artificial_intel...
Brains aren't implementing any known algorithm, but that doesn't mean they aren't implementing any unknown algorithm.
It brings to mind Minksky's advice to Sussman http://en.wikipedia.org/wiki/Hacker_koan#Uncarved_block