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
