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Article 2446 of comp.ai.philosophy:
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>From: weemba@libra.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: comp.ai.philosophy
Subject: More replies to jbaez
Message-ID: <61194@netnews.upenn.edu>
Date: 30 Dec 91 19:58:33 GMT
References: <1991Dec28.194855.16543@galois.mit.edu>
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Reply-To: weemba@libra.wistar.upenn.edu (Matthew P Wiener)
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In-reply-to: jbaez@nevanlinna.mit.edu (John C. Baez)

In article <1991Dec28.194855.16543@galois.mit.edu>, jbaez@nevanlinna (John C. Baez) writes:
>Well, having a neuron whose functioning made essential use of infinitely
>many distinguishable states in order to repeatably compute unrecursive 
>functions goes against what we know about physics.  See for example my paper
>"Recursivity in Quantum Mechanics," Trans. A.M.S. 280, p. 339, or
>Pour-El and Richards' book on computability in physics.

These allusions to the literature evade the issue of mind itself.  The
brain is *not* a closed system, with some fixed set of interactions.
Your paper does not address such issues.  You claim that your methods
generalize, but how far?  If you throw in transport in/out and external
world recognition, I think your work stalls.  These considerations are
not academic about how the mind works: people do go nuts from too much
sensory deprivation.  Edelman, eg, took the outside world as the deciding
factor against the computability of his models.

Moreover, your mathematical evasion of Pour-El and Richard's theorem that
unbounded operators can transform recursive sequences into non-recursive
ones, by switching to the appropriate Sobolev spaces does not seem very
physically appealing.  A method which becomes computationally intractable
by arbitrarily small L^2 perturbations assumes a lot of lucky breaks from
Nature.  Good luck.

>If anyone believes that somehow quantum mechanics, or the fact that
>biological systems are continuous rather than discrete, gives the brain
>powers over and above that of a universal Turing machine with a random
>number generator oracle, then they have some explaining to do concerning
>HOW this is supposed to work.  

Here's some supposing for you.  What is our internal representation of
"self"?  It has a peculiarity compared to other such, in that it is not
transferable.  One way to achieve this directly is with a Wigner's friend
situation.  The internal wave function for "self" can be inspected by our
"Wigner's friend" of a mind, collapsing it, while to others this "self"
wave function is permanently uncollapsed.

Were such a representation present in our minds, it could not be properly
simulated with UTM+RNG.  Such a simulation would be at most conscious in
its own digital world, but not within the real world.
-- 
-Matthew P Wiener (weemba@libra.wistar.upenn.edu)


