There is a theorem by A.A. Markov that tells us that the decision problem
of whether or not a pair of 4-manifolds are smoothly diffeomorphic is
NP-Complete. How close does GR get to non-computable, given this?
On Thu, Jan 16, 2014 at 3:11 AM, Stathis Papaioannou <stath...@gmail.com>wrote:
> On 16 January 2014 16:26, Jason Resch <jasonre...@gmail.com> wrote:
> > The computational metaphor in the sense of the brain works like the Intel
> > CPU inside the box on your desk is clearly misleading, but the sense
> that a
> > computer can in theory do everything your brain can do is almost
> > correct. It is not that the brain is like a computer, but rather, that a
> > computer can be like almost anything, including your brain or body, or
> > entire planet and all the people on it.
> > Jason
> I think neuroscientists have, over decades, used the computational
> metaphor in too literal a way. It is obviously not true that the brain
> is a digital computer, just as it is not true that the weather is a
> digital computer. But a digital computer can simulate the behaviour of
> any physical process in the universe (if physics is computable),
> including the behaviour of weather or the human brain. That means
> that, at least, it would be possible to make a philosophical zombie
> using a computer. The only way to avoid this conclusion would be if
> physics, and specifically the physics in the brain, is not computable.
> Pointing out where the non-computable physics is in the brain rarely
> figures on the agenda of the anti-computationalists. And even if there
> is non-computational physics in the brain, that invalidates
> computationalism, but not its superset, functionalism.
> Stathis Papaioannou
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Stephen Paul King
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