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From: guy@rlgvax.UUCP (Guy Harris)
Newsgroups: net.physics
Subject: Re: Non-linear systems.
Message-ID: <328@rlgvax.UUCP>
Date: Sat, 5-Jan-85 23:04:34 EST
Article-I.D.: rlgvax.328
Posted: Sat Jan  5 23:04:34 1985
Date-Received: Tue, 8-Jan-85 03:06:22 EST
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(Totally unpredictable universe proposed; you are given a hypothetical
infinite sequence of bits, and the state of the universe at time T (T an
integer, so that time goes in discrete jumps) is the value of the Tth
bit of the sequence.  This in response to the claim that the non-linearity
of a system can be a sufficient condition for unpredictability; this
system is described as "a simple model of a non-linear system" by the
original author.)

Objection, Your Honor; the defense's claim is irrelevant.  The system isn't
unpredictable because its equations of motion are non-linear; the system
is unpredictable because it *doesn't have* any equations of motion.  This
system is "non-linear" only in a trivial sense.

(Discussion of the restrictions of real live physical computing devices,
and of the fact that taking enough measurements to find the initial
state of a system will disrupt that state enough that perfect prediction
is in practice impossible).

Again, irrelevant.  We're not discussing whether enough Crays can be
constructed to produce real printouts and graphs predicting the future
state of the Universe.  We're discussing whether the future state of the
Universe is not predictable *in principle*.  If the model we construct
of the universe is based on the real numbers, the size of a silicon atom
doesn't even get a chance to enter into it, because the initial state
consists of C (where C is the cardinality of the continuum, a nice infinite
number) points, each one of which is specified with infinite precision
(and would require log2(C) bits to represent, which is still a nice infinite
number).  We all *K*N*O*W* that in practice the universe won't be perfectly
predictable.  Please don't waste our time informing us of the detailed
reasons why; I, for one, knew them before this discussion began and don't
really give a damn about hearing them again.

> Thus, the exact weather for next year is forever beyond our reach,
> without all those theories that the Nobel Laureates have cooked up.

Yes, we all know that; only an idiot would think otherwise (i.e., think that
you could compute the exact value of the temperature, to infinite precision,
at each one of the C locations on the earth).

	Guy Harris
	{seismo,ihnp4,allegra}!rlgvax!guy