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 -----Original Message----- From: Hal Finney [mailto:[EMAIL PROTECTED] Sent: Tuesday, 4 November 2003 2:24 PM To: [EMAIL PROTECTED] Subject: RE: Is the universe computable? IMO the best idea we have discussed for why the universe is and remains lawful is that the set of descriptions (equivalently, programs) for the universes are governed by the Universal Distribution. This is the description where a string whose shortest description has length n bits is given measure 1 / 2^n. An heuristic argument for this distribution is that if programs are self delimiting, then there are 2^x more programs of length n+x than of length n, created by appending the 2^x x-bit strings to each n-bit program. Since the appended x bits are never executed, all 2^(n+x) of these programs are the same as the basic 2^n programs. A program which says "obey these simple laws" is shorter than a program which says "obey these simple laws for a zillion steps, then start obeying these other laws", or a program that says "obey these simple laws everywhere except where this incredibly complicated configuration occurs, and then do this complicated other thing." Hal Finney
