I submit this link to Shmidhuber's second paper, which discusses various probability distributions on the set of computable Universes. ftp://ftp.idsia.ch/pub/juergen/toesv2.pdf
Sorry if this has been already covered. I'm not a mathematician, and I'm not entirely "into" hardcore computer science. This other site contains the links to Shmidhuber's other works. http://www.idsia.ch/~juergen/computeruniverse.html Peace ----- Original Message ----- > From: "David Barrett-Lennard" <[EMAIL PROTECTED]> > To: "'Hal Finney'" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> > Sent: Monday, November 03, 2003 11:52 PM > Subject: RE: Is the universe computable? > > > > An interesting idea. > > > > Where can I read a more comprehensive justification of this > > distribution? > > > > If a number of programs are isomorphic the inhabitants naturally won't > > know the difference. As to whether we call this one program or lots of > > programs seems to be a question of taste and IMO shows that "probability > > calculations" are only relative to how one wants to define equivalence > > classes of programs. > > > > I would expect that the probability distribution will depend on the way > > in which we choose to express, and enumerate our programs. Eg with one > > instruction set, infinite loops or early exits may occur often - so that > > there is a tendency for simplistic programs. On the other hand, an > > alternative instruction set and enumeration strategy may lead to a > > distribution favoring much longer and more complex programs. Perhaps it > > tends to complicate programs with long sequences of conditional > > assignment instructions to manipulate the program state, without risking > > early exit. Importantly such "tampering" doesn't yield a program that is > > isomorphic to a simple one. We seem to have a vast number of > > complicated programs that aren't reducible to simpler versions. This > > seems to be at odds with the premise (of bits that are never executed) > > behind the Universal Distribution. > > > > - David > >