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Article 5025 of comp.ai.philosophy:
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>From: tomh.bbs@cybernet.cse.fau.edu
Newsgroups: comp.ai.philosophy
Subject: Robert Rosen & Physical form of Church's Thesis
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Date: 9 Apr 92 21:39:40 GMT
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Robert Rosen has a new book out, called "Life Itself" which
addresses many of the issues that have been discussed here.
It is similar in spirit to Penrose's book, but Rosen argues
the points much more effectively, I think.  I heartily
recommend it to anyone who reads this group.

Rosen claims that the physical form of Church's Thesis is false.
This means there are physically realizable processes that are
not effectively calculable.  He also claims that life and probably
'intelligence' are such processes.
 
One candidate is a turbulent flow, which (mathematically) is
aperiodic.  Clearly, any simulation on a digital computer is
going to be periodic, by the finiteness of the number of states
of the computer.  Therefore a digital computer cannot simulate an
aperiodic process perfectly.
 
Issues this raises are:
1) Is a physical turbulent flow really aperiodic?  If not then brains
   are computers and we can all go home.
2) Is a turbulent flow an effective form of computation?  That is,
   does a turbulent flow comprise an algorithm for computing something?
3) What happens if we use an analog computer instead of a digital one?
   The analog computer still has the 'initial condition' problem.
 
Perhaps the most important issue:
 
If I write a computer program that simulates the Lorenz system, or any
turbulent (chaotic) system, then that program will NOT perfectly
track the flow in an analog implementation (or indeed, in some other
digital implementation).  The question is: does this matter?  The two
are qualitatively the same - both produce trajectories lying on the
Lorenz attractor (or arbitrarily close to it).
 
Another way to say this is that two simulations of a brain (with even the
tiniest difference in input) will diverge from each other, as well as
the brain they simulate (no matter what).  But the trajectories will
all be on the "attractor of the brain," if that in fact exists.  I
suspect it does, but this remains an open issue as well.
 
Note that "being on the attractor of the brain" means that the behavior
of the systems are qualitatively, functionally, the same.  So would
the simulation be intelligent?        I think so.

Here's the reference:

Life Itself
Robert Rosen
Columbia University Press, NY, 1992
Complexity in Ecological Systems Series

The book covers a lot of ground, syntax/semantics, Goedel, etc.
He uses Category theory to formalize it all.  I may post a
summary later, but I wanted to get these questions posted first.

Tom Holroyd
Center for Complex Systems and Brain Sciences
Florida Atlantic University, Boca Raton, FL
tomh@bambi.ccs.fau.edu


