I submit this link to Shmidhuber's second paper, which discusses various
probability distributions on the set of computable Universes.
Sorry if this has been already covered. I'm not a mathematician, and I'm
entirely "into" hardcore computer science.
This other site contains the links to Shmidhuber's other works.
----- 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