Re: (OT) Re: Object identity


Dmitry A. Kazakov wrote:
On 29 Jun 2006 06:05:52 -0700, David Barrett-Lennard wrote:

I'm quite interested in the idea that Quantum Mechanics (with all its
weirdness) can come out of number theory. If physicists develop a self
consistent, computable TOE that passes experimental testing then a
mathematician will say : There exists turing machine T st T is
isomorphic to our universe.

Hmm, why are you so sure that it would be computable?

I'm not sure of that at all. No one knows.

For what we know now,
it is quite probable that it could stay incomputable. So far, TOE includes
randomness, which is incomputable, and has an uncountable number of states
[as long as no observer forces it to a definite state.]

The randomness is not at odds with computability. According to the
Many Worlds Interpretation of QM the universe continually splits into
slightly different versions of itself. This has led to the term
multiverse instead of a universe. From a third person perspective it
is quite deterministic because all possible paths are taken. However
from a first person perspective we are tricked into thinking that the
universe is random.

I find it interesting that pure mathematics may predict that QM
uncertainty is inevitable. That makes modern physics a lot easier to
stomach.


Much more exciting were to get grip on some hardware capable to solve
problems beyond Turing completeness. Maybe we could, maybe not.

That is rather startling for philosophy,
because the mathematician will say that T exists independently of a
postulate of physical reality.

So? It wouldn't make any difference.

By Occam's razor the need to postulate physical reality should be
dropped. Rather than argue over whether mathematical entities exist,
the argument is now over whether there is anything but mathematical
entities.

Of course that's philosophy, not science. I only have a passing
interest in philosophy.


Real difference would be a mathematical reality shaping the physical one.
Summa Technologiae [the fundamental philosophic work on this issue]
considers such scenario as a high-end product of technological progress.


BTW the 'everything' group discusses this sort of stuff, if you are
interested. I once subscribed to this group for a short while, but
didn't find it particularly productive.


Cheers,
David Barrett-Lennard

.

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