On Tue, Nov 25, 2008 at 04:58:41PM -0500, Abram Demski wrote: > > Russel, > > Can you point me to any references? I am curious to hear why the > universality goes away, and what "crucially depends" means, et cetera. > > -Abram Demski >

This is sort of discussed in my book "Theory of Nothing", but not in technical detail. Excuse the LaTeX notation below. Basically any mapping O(x) from the set of infinite binary strings {0,1}\infty (equivalently the set of reals [0,1) ) to the integers induces a probability distribution relative to the uniform measure dx over {0,1}\infty P(x) = \int_{y\in O^{-1}(x)} dx In the case where O(x) is a universal prefix machine, P(x) is just the usual Solomonoff-Levin universal prior, as discussed in chapter 3 of Li and Vitanyi. In the case where O(x) is not universal, or perhaps even not a machine at all, the important Coding theorem (Thm 4.3.3 in Li and Vitanyi) no longer holds, so the distribution is no longer universal, however it is still a probability distribution (provided O(x) is defined for all x in {0,1}\infty) that depends on the choice of observer map O(x). Hope this is clear. -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---