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From: Fred Chen <flipsu5.domain.name.hidden>

Date: Tue, 23 Nov 1999 08:05:54 -0800

I had trouble getting this posted, so I am resending this.

Fred Chen wrote:

*> Juergen Schmidhuber wrote:
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*>
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*> >Continuations corresponding to longer algorithms also get computed, of
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*> >course. But they are less probable indeed. According to the universal
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*> >prior the probability of an algorithm is the probability of successively
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*> >guessing each of its bits. The longer the algorithm, the smaller its
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*> >probability.
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*>
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*> This insight adds some more naturalness. Maybe with a universal prior, we can get
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*> by with the original uniform bitstring distribution (f=constant k, i.e., each
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*> bitstring gets represented k times) used by Dr. Standish in his Occam's Razor
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*> paper and all the participants in the white rabbit discussion. There would then
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*> be no need for an unnatural non-uniform distribution which would have served the
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*> same purpose as a universal prior. I would still ask, out of curiosity, what is
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*> k?
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*>
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*> > >So what about the continuations corresponding to the longer algorithms?
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*> > >Those worlds still exist, don't they? If so, then for every shorter
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*> > >algorithm, there are continuations of longer algorithms, which were
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*> > >identical up to that point, but which now represent worlds which don't
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*> > >follow the laws of QM, but in which people neverthless still live in. You
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*> > >can say that the universal prior determines that I will probably follow a
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*> > >short algorithm, but what can you possibly say about all those people in all
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*> > >those worlds who didn't follow the shortest algorithm? Unless there are
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*> > >less worlds like theirs than like ours, I just can't see how you can dismiss
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*> > >their worlds as less probable.
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*>
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*> I suppose as long as we exist, it doesn't matter how probable we are, but it is
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*> interesting to speculate on how probable we are. With the self-sampling
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*> assumption (from the Occam's Razor paper), we assume we are pretty probable.
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*>
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*> Fred
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Received on Tue Nov 23 1999 - 08:18:13 PST

Date: Tue, 23 Nov 1999 08:05:54 -0800

I had trouble getting this posted, so I am resending this.

Fred Chen wrote:

Received on Tue Nov 23 1999 - 08:18:13 PST

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