Wei Dai wrote:

> > But in fact, the only thing that privileges the set of all
> > computational operations that we see in nature, is that they are instantiated by
> > the laws of physics.
>
> I would dispute this. The set of computable operations may also be
> privileged in that only a universe with laws of physics that instantiate
> all of these operations and none others can evolve intellegence (or
> alternatively these universes have the greatest chance of evolving
> intelligence).
>
> > It is only through our knowledge of the physical world
> > that we know of the di.erence between computable and not computable. So
> > it's only through our laws of physics that the nature of computation can be
> > understood. It can never be vice versa."
>
> So Deutsch is basically saying that we should not rule out the possibility
> that we may discover a new law of physics that will allow us to solve the
> halting problem, for example. I agree with this, given that we don't
> know that what I wrote above is actually true (instead of just a
> possibility).

Deutsch has mantained consistently that the Church-Turing Hypothesis
(essentially Computable = Turing Computable) is undercut by the Bennett-
-Church-Turing Hypothesis (essentially that Physically Computable >=
Turing Computable). Bennett bever agreed to this but that may be
beside the point, these days. A few people have been involved in
what is called "SuperTuring computing" spiked by the whole
Quantum Computing revolution but not limited to it...

The following paper deals with these issues specifically with some of
what Jesse Mazer brought up in this discussion:

http://arXiv.org/abs/math.GM/0305055
or
http://alixcomsi.com/The_formal_roots_of_Platonism.htm

Check it out...

-Joao Leao



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Joao Pedro Leao  :::  [EMAIL PROTECTED]
Harvard-Smithsonian Center for Astrophysics
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