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?

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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/