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Now check this: physical world has its own "computational complexity class", i.e. the "strongest" machine that can be built according to laws of physics. My thesis:

**the world is exactly Turing complete**. Fact 1: it's

*at least*Turing complete, because we can build physical Turing machine (the computer). Fact 2: it's

*no more*than Turing complete, because the fundamental laws of physics are merely some differential equations not capable of embedding any Turing undecidable problems.

World, however,

*could*be over-Turing complete. The problem of checking, if two five-dimensional manifolds are homeomorphic, is undecidable. Maybe we could prepare such two manifolds and let physics do the work. The manifolds would deform into some canonical lowest-energy form and prove their homeomorphism. But I doubt it really would be possible.

Another way to bring higher complexity classes to the physical world is to claim existence of time loops. A computation could loop literally

*forever*and compute anything that requires infinite number of steps.

On the other hand,

**conciousness can solve Turing undecidable problems**. That is, we are not Turing machines, but something more. Have you ever solved some diophantine equations? It's an undecidable problem, so it would be hard for a Turing machine.

However, we still

*could*be just Turing complete. Some "simple" solutions of diophantine equations could be just written into us, and we are not

*solving*them, but simply look up in some database. This would mean that some day we will "hang up" on some equation instance.

And what are your opinions? I can see 3 possibilities:

1. We are not over-Turing and our ability to solve undecidable problems is just a trick.

2. The physical world is over-Turing.

3. We are over-Turing, world is not.

I'm for the third option.