Re: Does provability matter?

From: Wei Dai <weidai.domain.name.hidden>
Date: Thu, 29 Nov 2001 11:47:44 -0800

On Wed, Nov 28, 2001 at 05:27:43PM +0100, Juergen Schmidhuber wrote:
> Which one? Hm. Let me extend your question and ask: what's the
> probability
> 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.

I'm not sure I understand this. Can you give an example of how our
universe might make use of an entire continuum of real numbers? How might
someone show this if it were true?

> 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.

But if there is a formally describable prior that dominates the speed
prior, and you agree that the more dominant prior doesn't have a prior
probability of zero, then isn't the speed prior redundant? Wouldn't you
get equal posterior probabilities (up to a constant multiple) by
dropping the speed prior from your prior on priors, no matter what it
assigns to priors that are not formally describable?
Received on Thu Nov 29 2001 - 11:50:27 PST