Newsgroups: comp.theory.dynamic-sys
Path: utzoo!utgpu!cunews!rdb
From: rdb@scs.carleton.ca (Robert D. Black)
Subject: Re: Can Chaos Be Predictable?
Message-ID: <1991Jun21.190816.9136@cunews.carleton.ca>
Keywords: chaos, predictability
Sender: news@cunews.carleton.ca
Organization: School of Computer Science, Carleton University, Ottawa, Canada
References: <1991Jun20.194552.15875@cunews.carleton.ca> <1991Jun20.203628.14343@alchemy.chem.utoronto.ca> <1991Jun21.003436.28578@cunews.carleton.ca> <1991Jun21.064503.8325@netcom.COM>
Distribution: comp.theory.dynamic-sys
Date: Fri, 21 Jun 1991 19:08:16 GMT

In article <1991Jun21.064503.8325@netcom.COM> kmc@netcom.COM (Kevin McCarty) writes:
>
>...  Another way to look at it is that the absolute output error
>roughly *doubles* with each passing unit of time... 
>
Agreed.


>Compare this with your other example, f(x) = sqrt(x)...
>
Bad choice of example on my part.  I wasn't suggesting that sqrt has sensitivity 
to initial conditions.  I was suggesting that IF we knew the initial condition 
exactly, then the only source of error in the computation would come from calculating
the inverse cosine and the sine squared.  That alone would not contribute very
much error -- about as much error as any other common function like sqrt for example.


>... However, the promise of classical mechanics that motion is
>deterministic is an empty promise because it only works for
>exact initial values.  In practical problems using numerical
>computations, this is never the case.

True.  My confusion was on the theoretical side.  It was my impression that chaotic
systems did not admit closed form solutions and were necessarily unpredictable, even
in theory.  I guess not!  :-)


Robert Black

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Robert Black                               rdb@scs.carleton.ca
School of Computer Science
Carleton University, Ottawa, Canada