I had trouble getting this posted, so I am resending this. Fred Chen wrote:

> Juergen Schmidhuber wrote: > > >Continuations corresponding to longer algorithms also get computed, of > >course. But they are less probable indeed. According to the universal > >prior the probability of an algorithm is the probability of successively > >guessing each of its bits. The longer the algorithm, the smaller its > >probability. > > This insight adds some more naturalness. Maybe with a universal prior, we can get > by with the original uniform bitstring distribution (f=constant k, i.e., each > bitstring gets represented k times) used by Dr. Standish in his Occam's Razor > paper and all the participants in the white rabbit discussion. There would then > be no need for an unnatural non-uniform distribution which would have served the > same purpose as a universal prior. I would still ask, out of curiosity, what is > k? > > > >So what about the continuations corresponding to the longer algorithms? > > >Those worlds still exist, don't they? If so, then for every shorter > > >algorithm, there are continuations of longer algorithms, which were > > >identical up to that point, but which now represent worlds which don't > > >follow the laws of QM, but in which people neverthless still live in. You > > >can say that the universal prior determines that I will probably follow a > > >short algorithm, but what can you possibly say about all those people in all > > >those worlds who didn't follow the shortest algorithm? Unless there are > > >less worlds like theirs than like ours, I just can't see how you can dismiss > > >their worlds as less probable. > > I suppose as long as we exist, it doesn't matter how probable we are, but it is > interesting to speculate on how probable we are. With the self-sampling > assumption (from the Occam's Razor paper), we assume we are pretty probable. > > Fred