3 ms·

Nope, computation can never be the same as math, per Godel's incompleteness theorem. Which, perchance, is also a good illustration of the difference between pr

by yters 17y ago

Nope, computation can never be the same as math, per Godel's incompleteness theorem. Which, perchance, is also a good illustration of the difference between proof and merely cranking through a problem space.

iskander 17y ago
>Nope, computation can never be the same as math, per Godel's incompleteness theorem. lolwut? (first order logic w/ addition ain't math enough for you?)
roundsquare 17y ago
So, if you are going to refer to Godel's theorem, its best to explain your point. Godel's theorem is on of the most poorly understood popular ideas in mathematics and its easy to trip over (for you or the reader). I'm going to try to guess what you mean. You are trying to say that since a computer is essentially a formal system and humans are something more, we can't replace human mathematicians with computers to do the work because they won't be able to come up with new ideas outside a fixed problem space? In any event, I think you are misunderstanding @ihodes's question. The question is not "can we replace mathematicians with computers" but is more about the practice of mathematics. I.e., @ihodes is asking if the mental activity of experimenting and doing computations is conceptually similar to doing proofs.
Confusion 17y ago
As iskander put somewhat less eloquently: what you say does not make any sense. Godel's incompleteness theorem places a theoretical limit on the completeness of (non-trivial) formal mathematical systems. 'Computations' take place within such formal systems and are, by definition, math. Both are subject to the consequences of Godel's theorems and you can't distinguish between them based on those theorems.
- yters 17y ago
  Assuming math encompasses Godel's theorem, then computer science can only be a subset of math at best, since a computer can not prove Godel's theorem.

3 ms·

Nope, computation can never be the same as math, per Godel's incompleteness theorem. Which, perchance, is also a good illustration of the difference between pr

by yters 17y ago

iskander 17y ago
>Nope, computation can never be the same as math, per Godel's incompleteness theorem. lolwut? (first order logic w/ addition ain't math enough for you?)
roundsquare 17y ago
So, if you are going to refer to Godel's theorem, its best to explain your point. Godel's theorem is on of the most poorly understood popular ideas in mathematics and its easy to trip over (for you or the reader). I'm going to try to guess what you mean. You are trying to say that since a computer is essentially a formal system and humans are something more, we can't replace human mathematicians with computers to do the work because they won't be able to come up with new ideas outside a fixed problem space? In any event, I think you are misunderstanding @ihodes's question. The question is not "can we replace mathematicians with computers" but is more about the practice of mathematics. I.e., @ihodes is asking if the mental activity of experimenting and doing computations is conceptually similar to doing proofs.
Confusion 17y ago
As iskander put somewhat less eloquently: what you say does not make any sense. Godel's incompleteness theorem places a theoretical limit on the completeness of (non-trivial) formal mathematical systems. 'Computations' take place within such formal systems and are, by definition, math. Both are subject to the consequences of Godel's theorems and you can't distinguish between them based on those theorems.
- yters 17y ago
  Assuming math encompasses Godel's theorem, then computer science can only be a subset of math at best, since a computer can not prove Godel's theorem.