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From: josh@topaz.ARPA (J Storrs Hall)
Newsgroups: net.physics
Subject: Re: Non-linear systems.
Message-ID: <214@topaz.ARPA>
Date: Thu, 10-Jan-85 14:47:07 EST
Article-I.D.: topaz.214
Posted: Thu Jan 10 14:47:07 1985
Date-Received: Mon, 14-Jan-85 00:38:05 EST
References: <209@talcott.UUCP>, <328@rlgvax.UUCP> <384@hou2g.UUCP> <273@harvard.ARPA>
Organization: Rutgers Univ., New Brunswick, N.J.
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> > The concept of "predicable, in principle" is usefull if and only if 
> > it has some connection with reality.  If 10^70 Cray's calculating for
> > 10^10 years cannot predict next year's weather then next year's weather
> > is unpredictable.
...
> Sorry, you're wrong. The technical term for "predictable in principle"
> is computable. This is a sensible notion of great interest and
> significance in modern information science.  What you're aiming at is
> the notion of "computational complexity".

Let's try to keep something straight here:  there are lots of things
that a mathemetician assumes trivially, like adding two real numbers,
that are not computable--they're infinitely long, remember?
So something that's computable in principle to a mathemetician or
a very theoretical physicist has little to do with what we can actually
compute.  Predicting the motion of a perfectly deterministic Newtonian
system is impossible *because you can't "know" the initial conditions:
they entail an infinite number of bits*.

One way to look at QM uncertainty is to say that it, or something like
it, is necessary merely to avoid having to say that each particle in
the universe represents an infinite amount of information.

--JoSH