X-Message-Number: 9322
From: Thomas Donaldson <>
Subject: Re: CryoNet #9284 - #9292
Date: Thu, 19 Mar 1998 22:44:29 -0800 (PST)

To Perry Metzgar, re #9284-9292:

You seem to find what I say amusing, but at the same time provide no actual
refutation. We all must get our laughs somehow, and I hardly resent your 
attitude, but perhaps you might wish to think over just how you really feel 
and think on the issues I raise.

Just like a true Turing machine, the Siegelmann device is an intellectual
construction only. Why is an infinite tape not laughable while use of 
infinite decimal numbers is?

As for chaos, as someone who has done lots of DEs both by computer and
in terms of theorems about their solutions, the issue of chaos for digital
computers arises precisely because digital computers do not admit infinite
decimal numbers. Naturally chaos takes a while to show itself --- our
calculations are approximately true for a while, but differ more and more
from reality as we continue them. A machine capable of true real number
calculation would obtain perfect accuracy for an indefinite time. 

And examining this, there is a suggestion that a GOOD NONdigital model (which
would have to be specially built) might do better calculations of the 
movements of bodies in our Solar System than a digital computer model. At
least one source of inaccuracy would not be present. However Poincare 
proved long ago that the equations for more than 2 bodies diverged, so that
even a very slight inaccuracy would ultimately fail to predict motions.

If these comments continue to amuse you, please be serious for a short
time and tell me why. To me it tells me much more about you than about
either computers or brains.

			Best and long long life,

				Thomas Donaldson

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