That is almost the correct solution, Hal. If we ask what an observer
will make of a random description chosen at random, then you get
regular universes with probability exponentially related to the
inferred complexity. It is far clearer to see what happen when the
observer is a UTM, forcibly terminating programs after a
certain number of steps (representing the observer's resource bound)
(thus all descriptions are halting programs). Then one obtains a
Solomon-Levy distribution or universal prior. However, this argument
also works when the observer is not a UTM, but simply a classification
device of some kind.

The WAP has nothing to do with this issue, except inasmuch as
universes can only be observed through the eyes of some observer.

Again I reiterate that Juergen's resource-bounded "Great Programmer"
religion need be nothing but a reflection of our conscious selves stamped
upon our observations. 


> Juergen writes:
> > Some seem to think that the weak anthropic principle explains the
> > regularity. The argument goes like this: "Let there be a uniform measure
> > on all universe histories, represented as bitstrings.  Now take the tiny
> > subset of histories in which you appear.  Although the measure of this
> > subset is tiny, its conditional measure, given your very existence,
> > is not: According to the weak anthropic principle, the conditional
> > probability of finding yourself in a regular universe compatible with 
> > your existence equals 1."
> >
> > But it is essential to see that the weak anthropic principle does not
> > have any predictive power at all. It does not tell you anything about
> > the future.  It cannot explain away futures in which you still exist
> > but irregular things happen. Only a nonuniform prior can explain this.
> Isn't this fixed by saying that the uniform measure is not over all
> universe histories, as you have it above, but over all programs that
> generate universes?  Now we have the advantage that short programs
> generate more regular universes than long ones, and the WAP grows teeth.
> Hal Finney

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