Conciousness and Turing undecidability

  • Thread starter haael
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Hello, guys. I'm a dualist - that is, I believe that conciousness, thoughts and intelligence are not driven by material particles and laws of physics as we currently know. I also believe in God, for that matter.

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.
 

Answers and Replies

  • #2
baywax
Gold Member
1,940
1
Hello, guys. I'm a dualist - that is, I believe that conciousness, thoughts and intelligence are not driven by material particles and laws of physics as we currently know. I also believe in God, for that matter.

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.
I really don't think allegory and metaphor are a good way to explore a phenomenon of nature such as conscious/awareness. Using the word machine to describe nature is a de-evolutionary trait where the accomplishments of humans become the benchmark to which all else is compared. This is the sort of practice that can lead to mad cow disease... as in feeding cows to cows.
 

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