Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!apple!agate!shelby!unix!hplabs!hp-sdd!ucsdhub!sdcsvax!beowulf!demers
From: demers@beowulf.ucsd.edu (David E Demers)
Newsgroups: comp.ai
Subject: Re: free will
Message-ID: <6774@sdcsvax.UCSD.Edu>
Date: 6 Jul 89 20:51:04 GMT
References: <317@ucl-cs.UUCP>
Sender: nobody@sdcsvax.UCSD.Edu
Reply-To: demers@beowulf.UCSD.EDU (David E Demers)
Organization: EE/CS Dept. U.C. San Diego
Lines: 43

In article <317@ucl-cs.UUCP> Gordon@ucl-cs.UUCP writes:
>> From: Michael Ellis <ellis@chips2.sri.com>
[... Ergo, QM+CT *together* demonstrate that sufficiently
					     ^^^^^^^^^^^^
>> complex systems are genuinely unpredictable on both micro- and macro-
   ^^^^^^^
>> scopic levels. QED.
>
Gordon says:
>Chaos does not depend on "complexity". The logistic map,
>      
>            x -> x*x + c 
>
>is only chaotic above c ~= 3.7

I believe Gordon "misspoke".  The logistic map is x -> c * x * (1 - x),
and is, as he said chaotic for c slightly less than 4.

The map x -> x*x + c is interesting since for c > 1/4 there are no
attractors, while c < 1/4 has two fixed points; the rightmost being
a repellor and the leftmost generally an attractor.  Well, maybe that's
not interesting after all, but it IS a pretty simple example of 
bifurcation behavior in a map.

But on to what chaos tells us.  Chaos "theory" shows that very
simple (completely deterministic!) systems with only a few 
degrees of freedom can exhibit
complex behavior that is unpredictable in the long run and which
passes many statistical tests of randomness.  These systems
exhibit powerful sensitivity to their initial conditions.  The
argument which was made, I think, is that quantum mechanics
indicates that there is some level below which we CANNOT have
certainty, thus it is not possible to measure any chaotic system 
accurately enough in order to predict the future state of the
system beyond some limiting period of time.  All predictions
will be in error, with the amount of error growing exponentially
until all significant bits are garbage...

This is getting far away from AI... is it reasonable to take the
position that there may or may not be free will, and thus act as
if one HAS free will just in case? :-) 
 
Dave