Re: Does provability matter?

From: Juergen Schmidhuber <>
Date: Wed, 28 Nov 2001 17:27:43 +0100

Wei Dai wrote:
> 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?

If someone can use large scale quantum computing to solve a problem
solution requires much more computation time than necessary to compute
the history of our own particular universe, then one could take this
as evidence against the Speed Prior. You are right: to quantify this
evidence in a Bayesian framework we need a prior on priors.

Which one? Hm. Let me extend your question and ask: what's the
that the Great Programmer is more than a mere programmer in the sense
that he is not bound by the limits of computability? For instance,
if someone were able to show that our universe somehow makes use of an
entire continuum of real numbers we'd be forced to accept some even more
dominant prior that is not even computable in the limit. We could not
even formally specify it.

So what's my prior on all priors? Since the attempt to answer such a
question might lead outside what's formally describable, I'll remain
silent for now.

Juergen Schmidhuber
Received on Wed Nov 28 2001 - 08:29:06 PST

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