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?
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/
