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From: stekas@hou2g.UUCP (J.STEKAS)
Newsgroups: net.physics
Subject: Re: Re: Non-linear systems.
Message-ID: <386@hou2g.UUCP>
Date: Fri, 11-Jan-85 10:08:29 EST
Article-I.D.: hou2g.386
Posted: Fri Jan 11 10:08:29 1985
Date-Received: Sat, 12-Jan-85 05:47:02 EST
References: <209@talcott.UUCP>, <328@rlgvax.UUCP> <384@hou2g.UUCP>, <1027@sunybcs.UUCP>
Organization: AT&T Bell Labs, Holmdel NJ
Lines: 15

Randomness and predictability are two different things.  Randomness
is sufficient for unpredictability but not the only source.

In linear types of systems, like Newtonian orbital mechanics,
one can easily show that intitial states which are infinitesimally
different at t=0 will be infinitesimally different at t=T.  For
many non-linear systems, infinitesimally different states at t=0 can
be arbitrarily "far apart" at t=T.   When such things occur it becomes
impossible, even in principle, for a computer to predict the future
because one does not even know the precision to which the calculation
must be carried.  One cannot guarentee that the truncation error on even
a 10^10 bit computer would not introduce unacceptable error.

						Jim
						ihnp4!hou2g!stekas