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From: guy@rlgvax.UUCP (Guy Harris)
Newsgroups: net.physics
Subject: Re: Re: why FTL is illegal (wrt: free will).
Message-ID: <327@rlgvax.UUCP>
Date: Sat, 5-Jan-85 22:48:50 EST
Article-I.D.: rlgvax.327
Posted: Sat Jan  5 22:48:50 1985
Date-Received: Tue, 8-Jan-85 03:06:09 EST
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> Sorting thru back net.physics articles, I encountered this item from 
> Guy Harris:
> 
> >If you assume ... and 3) enough computing ability to crank the model
> >forward from that initial state, you can predict all future states
> >of the universe.
> 
> That remaining item, number (3) seems to require closer scrutiny. Correct
> me if I'm mistaken, but I thought that even the simplest Newtonian models
> of the universe result in intrinsically INSOLUBLE differential equations
> (like the three-body problem). 

Note the magic word "computing ability".  The fact that there is no closed-form
solution to those differential equations is irrelevant.  A closed-form solution
is no better than numerical integration forward in time, assuming sufficient
computing ability (precision, in this case) that there are no numerical
problems in the integration; you can't compute the value of the closed-form
expression "sin(2*pi*t/T)" to arbitrary precision.  (Barring solutions which
don't have nice analytical properties, so that *no* precision is "good enough";
a step function could, in principle, cause problems, but are there any
real live step functions in nature?)

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