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Gödel, Turing and Cantor: The Math

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Re: Gödel, Turing and Cantor: The Math

#12
post #3

Earlier 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.

IMO just finish chapter 14 and you've basically finished the Godel portion of the book. The rest felt more like Hofstadter's random musings on AI, DNA and some other topics (some of which felt outdated). There's some crazy anecdotes of Ramanujin that I had never heard elsewhere though.

Re: Gödel, Turing and Cantor: The Math

#14
post #11

There'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.

Re: Gödel, Turing and Cantor: The Math

#17
post #8
post #7

Does this mean that the antivirus industry is nothing but a scam?

it means antivirus industry will never be "complete"

Indeed, many incompleteness results (the most famous being the Halting Problem) are known as "infinite employment theorems". For example, we can always make a compiler perform more optimisations as follows:

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

#18
post #11

There'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.

On the contrary.

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

#19

What 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...

I'm sceptical of Penrose's arguments. We don't see human brains as symbol-manipulating formal systems, but that doesn't mean that aren't (or, more correctly, that doesn't mean that there is no symbol-manipulating formal system which is isomorphic to a particular brain, or brains in general).

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

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