From: utzoo!decvax!harpo!esquire!cmcl2!philabs!sdcsvax!davidson
Newsgroups: net.misc
Title: Re: Can determinism be proven?
Article-I.D.: sdcsvax.2296
Posted: Mon Aug 23 05:48:00 1982
Received: Thu Aug 26 01:47:26 1982
References: ihuxv.213

Interestingly, it does not necessarily involve an infinite regress to
have part of a system completely model the whole system.  It does, however,
require that the system be describable with less information than it
contains (and there are other requirements too).  An analogous situation
is with the common programming exercise of writing a program which prints
itself out.  Indeed, a deterministic universe with simple physical laws
and a simple initial state is easily modelled completely from within.  A
non-deterministic universe, on the other hand, can not be completely modeled
at all.

This brings up one of my favorite speculations about the universe:  assuming
that the universe is finite in extent, or taking a finite subset of it, does
the universe or that subset contain a finite or an infinite amount of
information?  That is, could one completely specify an instantaneous time
slice with a finite amount of information?  The answer to this question
depends, I think, on whether space, as well as everything else, is quantized.