Here's an entry for all the tech geeks out there

[draque]

This whole post is based on one hypothetical question. What would be the result of infinite processing power? Assume that you have a black box that has infinite memory and will calculate any value that can be computed within a finite period of time, then return it to you instantly

Comments

[_dw]

The concept of a computer with infinite processing power is ambiguous. Either it can be a computer that performs infinite steps in finite time, or it can be a computer that runs any finite program in constant time

[draque]

It specifies in the question that the computer is of the "finite program in constant time" type. A Turing oracle like the one you described would be able to return the last digit of pi (i.e. "reach infinity"). Given that is absurd, I think it's safe to assume that type is impossible to even discuss in a reasonable way.

Anyhow, in terms of hypercomputation, I'm familiar with the math and technicalities. The question here was mostly in terms of "what would you do with a magic toy like this? What would be the real world technological implications that you think might arise?

[_dw]

I think there's a distinction between an absurd question (find the last digit of pi) and one that has a consistent answer, but where finding that answer takes infinite time; probably because the last digit of pi is a contradiction (assume it's in position n. Then [use sine formula here] to show that position n+1 is nonzero, etc

[draque]

I suppose you're right in terms of the first issue, but I'm going to have to think about what would happen with a question requiring truly infinite processing time, but having a definitive answer (like the busy beaver problem or something like that). It might be that a system like I've described could return from any program, so long as it only had countably infinite steps, or it might be that it could return from any program so long as the number of steps to completion was finite. Either way, the Halting Problem would be solved

[_dw]

Either way, the Halting Problem would be solved.

And that means you can do brute-force theorem proving. Kinda. For instance, for Goldbach's conjecture, you could halt when you find a number that is not the sum of three primes. If it doesn't halt, then Goldbach's conjecture is true, although you don't have the mathematical proof for it.

Do you think that there would be a way to translate data into real world effect solely through data manipulation, though?There are two ways to do so. In the first, you simulate the entire universe. If you forget some exotic effect, the subuniverse won't have that effect. Even if you do, the universe will have some time lag because the computer isn't totally transparent (it needs cycles to simulate