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From: gjk@talcott.UUCP (Greg Kuperberg)
Newsgroups: net.physics
Subject: Non-linear systems.
Message-ID: <209@talcott.UUCP>
Date: Fri, 4-Jan-85 23:34:45 EST
Article-I.D.: talcott.209
Posted: Fri Jan  4 23:34:45 1985
Date-Received: Mon, 7-Jan-85 03:14:14 EST
Distribution: net
Organization: Harvard
Lines: 45

There seems to be considerable skepticism about my proposition that a
non-linear system is a sufficient condition.  Well, here is a simple model
of a non-linear system in which there is exactly *zero* predictability.

In this "universe", time goes in discrete jumps, as in Conway's Game of
Life.  In fact, one could easily picture this universe as a cellular
automaton.  Anyway, the universe at any point in time consists of a
non-terminating sequence of 0's and 1's.  After each time unit, the sequence
has its first binary digit (bit, I guess) removed.  Thus, the whole
sequence shifts right by one.  The evolution of the universe would progress
like this:

Time 0:  1101110011...
Time 1:  1011100111...
Time 2:  0111001110...
Time 3:  1110011101...
Time 4:  1100111010...


And now, the twist.  The *observable* universe is only the first bit of the
sequence at each point in time.  So what is the state of the observable
universe as it progresses with time?  Simply any sequence of 0's and
1's.  Utterly unpredictable, even though the entire state of the universe
"existed" at the beginning of time!

Well, someone might object, "but it's only because of QM that we are
limited in our measurements, so we still need QM."  But I say that QM is
not our only limitation.  Even without QM, the thickness of the doping on
our silicon chips is limited to the size of the atom, the speed that the
signal in them propagates is limited to the speed of light, and the size of
our computers is limited to the size of the universe (and probably the size
of our galaxy).  These restrictions probably apply to *any* computing
device in our universe.  So, if we're lucky, we may get 10^200 megaflops
tops.  By the (exponentional) nature of non-linear systems, this would give
a predictive power of, say, 200 days of weather.  Less than one year of
weather predicted, even with a computer as big as the universe!
Furthermore, it would necessarily disrupt the weather patterns if we were
to take 10^200 data samples.  Thus, the exact weather for next year is
forever beyond our reach, without all those theories that the Nobel
Laureates have cooked up.
---
			Greg Kuperberg
		     harvard!talcott!gjk

"  " -Charlie Chaplin, for IBM