Have a look at Tegmark's 'does the universe inf fact contain almost no
information' and Juergen Schmidhuber's paper, which is along similar lines.

> -----Original Message-----
> From: Christopher Maloney [SMTP:[EMAIL PROTECTED]]
> Sent: Monday, June 07, 1999 11:05 AM
> To:   everything-list
> Subject:      Re: Why physical laws
> Alastair Malcolm wrote:
> > 
> >     Christopher,
> > 
> > I have found your recent posts to everything-list very interesting, and
> the
> > ideas presented overlap to a degree with my own, but there is one
> question
> > that I have, if I may, which I mention below.
> > 
> > From: Christopher Maloney <[EMAIL PROTECTED]>
> > >In Tegmark's paper,
> > >in section 2G, he makes a crucial point that the fewer axioms
> > >you use to define your mathematical structure, the larger is
> > >the ensemble.  This provides a concrete justification for the
> > >principle of Occam's Razor.  Similarly to the argument given
> > >above, we would expect to find ourselves in worlds with fairly
> > >few laws of physics, since those admit the most SAS's.  You
> > >can always add any bizarre behavior to the structure by adding
> > >ad hoc axioms, but worlds in which that is the case
> > >have a smaller measure than those that do not.
> > 
> > Could you please explain how Tegmark justifies that fewer axioms give
> rise
> > to larger ensembles? I have read his article and can't see how he has
> > convincingly made a case for this. Naively one might think that there
> are
> > more complex mathematical structures than simple ones, so that we ought
> to
> > be in a more complex universe than we are (hence by a kind of reductio
> ad
> > absurdem, Tegmark's scheme could not hold up).
> I've reread section two of his paper, and noticed what you are talking
> about -- he never does support that claim.  In fact, in section 2-G, he
> twice refers us to earlier in the paper, but as I said, I've just reread
> it, and can't find anything that's refered to.  It almost seems as if
> section 2-G were originally in some other part of the paper, and he
> moved it to its current spot as a last-minute edit.  Evidence for that 
> is that he refers to "ensembles" before ever having defined what he 
> means by that term.
> When you say "there are more complex mathematical structures than simple
> ones", that is not the same as talking about the ensemble of structures 
> that hold a given SAS, and I think that's what Tegmark was refering to.
> -- 
> Chris Maloney
> http://www.chrismaloney.com
> "Knowledge is good"
> -- Emil Faber

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