I don't understand how you can believe that the probability of more
dominant priors is zero. That implies if I offered you a bet of $1
versus your entire net worth that large scale quantum computation will
in fact work, you'd take that bet. Would you really?

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On Tue, Dec 11, 2001 at 04:24:46PM +0100, Juergen Schmidhuber wrote:
> Wei Dai wrote:
> > 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?
>
> I have no idea. In fact, I guess it is impossible.
>
> > 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?
>
> In the Bayesian framework we derive consequences of assumptions
> represented as priors. The stronger the assumptions, the more specific
> the
> predictions. The Speed Prior assumption is stronger than the assumption
> of a formally describable prior. It is not redundant because it yields
> stronger
> predictions such as: The computer computing our universe won't compute
> much more of it; large scale quantum computation won't work; etc.
>
> In fact, I do believe the Speed Prior dominates the true prior from
> which our universe is sampled (which is all I need to make good
> computable predictions), and that the probability of even more
> dominant priors is zero indeed. But as a Bayesian I sometimes ignore
> my beliefs and also derive consequences of more dominant priors.
> I do find them quite interesting, and others who do not share my
> belief in the Speed Prior might do so too.
>
> Juergen Schmidhuber
>
> http://www.idsia.ch/~juergen/
> http://www.idsia.ch/~juergen/everything/html.html
> http://www.idsia.ch/~juergen/toesv2/