Re: Does provability matter?

From: Wei Dai <weidai.domain.name.hidden>
Date: Thu, 15 Nov 2001 08:15:37 -0800

On Thu, Nov 15, 2001 at 10:35:58AM +0100, Juergen Schmidhuber wrote:
> > Why do you prefer the Speed Prior? Under the Speed Prior, oracle universes
> > are not just very unlikely, they have probability 0, right? Suppose one
> > day we actually find an oracle for the halting problem, or even just find
> > out that there is more computing power in our universe than is needed to
> > explain our intelligence. Would you then (1) give up the Speed Prior and
> > adopt a more dominant prior, or (2) would you say that you've encountered
> > an extremely unlikely event (i.e. more likely you're hallucinating)?
> >
> > If you answer (1) then why not adopt the more dominant prior now?
>
> Why not adopt a more dominant prior now? I just go for the simplest
> explanation consistent with available data, where my simplicity measure
> reflects what computer scientists find simple: things that are easy
> to compute.

You didn't explicitly answer my question about what you would do if you
saw something that is very unlikely under the Speed Prior but likely under
more dominant priors, but it seems that your implicit answer is (1). In
that case you must have some kind of prior (in the Baysian sense) for the
Speed Prior vs. more dominant priors. So where does that prior come from?

Or let me put it this way. What do you think is the probability that the
Great Programmer has no computational resource constraints? If you don't
say the probability is zero, then what you should adopt is a weighted
average of the Speed Prior and a more dominant prior, but that average
itself is a more dominant prior. Do you agree?
Received on Thu Nov 15 2001 - 08:17:01 PST