From: erwin@trwacs.fp.trw.com (Harry Erwin)
Newsgroups: comp.ai.philosophy
Subject: Rosen's New Book
Date: 10 Apr 92 12:10:24 GMT
Organization: TRW Systems Division, Fairfax VA



tomh.bbs@cybernet.cse.fau.edu writes:

>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.

Rosen is correct in this claim. The effectively calculable models are
countable, and the physically realizable processes are uncountable. I saw
him present this argument at the Cambridge modelling conference in 1990,
and I questioned this point, because he didn't restrict himself to
effectively calculable models then. His claim that life and probably
'intelligence' are not effectively calculable processes is reasonable in
my view.

> 
>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.

Also correct. However Grebogi and Yorke have pointed out that a computer
representation _will_ track one trajectory of the aperiodic process for
extremely long times.
> 
>Issues this raises are:
>1) Is a physical turbulent flow really aperiodic?  If not then brains
>   are computers and we can all go home.

It is conjectured that physical turbulence is chaotic and aperiodic. The
data seem to have a continuous fourier spectrum, which implies
aperiodicity.

>2) Is a turbulent flow an effective form of computation?  That is,
>   does a turbulent flow comprise an algorithm for computing something?

Phase-locking from a chaotic process is an efficient way to implement
pattern-recognition. I can discuss other chaotic processes that provide
effective computation (if only as a model of a non-linear process...).

>3) What happens if we use an analog computer instead of a digital one?
>   The analog computer still has the 'initial condition' problem.
>
I'm not sure what problem you're aluding to here. Do you mean the problem
of calibration?
 
>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.

I'm currently writing a paper where I address this issue. I'll send you a
copy when it's done.

>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

Cheers,


























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-- 
Harry Erwin
Internet: erwin@trwacs.fp.trw.com

Newsgroups: comp.ai.philosophy