But there is no uniform prior over all programs!
Just like there is no uniform prior over the integers.
To see this, just try to write one down.
BTW, it's not Solomon-Levy but Solomonoff-Levin. And
it has nothing to do with resource bounds!
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
> From hal.domain.name.hidden Fri Oct 12 19:22:02 2001
>
> 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.
> From: Russell Standish <R.Standish.domain.name.hidden>
>
> 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.
Received on Mon Oct 15 2001 - 02:44:21 PDT