On Fri, Oct 21, 2011 at 02:14:48PM +0200, Bruno Marchal wrote: > > > >So the histories, we're agreed, are uncountable in number, but OMs > >(bundles of histories compatible with the "here and now") are surely > >still countable. > > This is not obvious for me. For any to computational states which > are in a sequel when emulated by some universal UM,there are > infinitely many UMs, including one dovetailing on the reals, leading > to intermediate states. So I think that the "computational > neighborhoods" are a priori uncoutable.
Apriori, no. The UMs dovetailing on the reals will have only executed a finite number of steps, and read a finite number of bits for a given OM. There are only a countable number of distinct UM states making up the OM. > That fits with the > topological semantics of the first person logics (S4Grz, S4Grz1, X, > X*, X1, X1*). But many math problems are unsolved there. > You will need to expand on this. I don't know what you mean. > > > > >If we take the no information ensemble, > > You might recall what you mean by this exactly. > It is the set of all infinite binary strings (isomorphic to [0,1) ). It is described in my book. Equation (2.1) of my book (which is a variant of Ray Solomonoff's "beautiful formula" http://world.std.com/~rjs/index.html) gives a value of precisely zero for the information content of this set. I do still think the universal dovetailer trace, UD*, is equivalent to this set, but part of this thread is to understand why you might think otherwise. > > > >and transform it by applying a > >universal turing machine and collect just the countable output string > >where the machine halts, then apply another observer function that > >also happens to be a UTM, the final result will still be a > >Solomonoff-Levin distribution over the OMs. > > This is a bit unclear to me. Solomonof-Levin distribution are very > nice, they are machine/theory independent, and that is quite in the > spirit of comp, but it seems to be usable only in ASSA type > approach. I do not exclude this can help for providing a role to > little program, but I don't see at all how it could help for the > computation of the first person indeterminacy, aka the derivation of > physics from computer science needed when we assume comp in > cognitive science. In the work using Solomonof-Levin, the mind-body > problem is still under the rug. They don't seem aware of the > first/third person description. > Not even if the reference machine is the observer erself? This would seem to be applying S-L theory to the first person description. I think I might be the only person to suggest doing this, though, which I first did in my "Why Occam's razor" paper. I'm not sure, because Marcus Hutter suggested something similar in a recent paper (quite independently of me, it appears). > > >This result follows from > >the compiler theorem - composition of a UTM with another one is still > >a UTM. > > > >So even if there is a rich structure to the OMs caused by them being > >generated in a UD, that structure will be lost in the process of > >observation. The net effect is that UD* is just as much a "veil" on > >the ultimate ontology as is the no information ensemble. > > UD*, or sigma_1 arithmetic, can be seen as an effective > (mechanically defined) definition of a zero information. It is the > everything for the computational approach, but it is tiny compared > to the first person view of it by internal observers accounted in > the limit by the UD. > But isn't first person view of the UD given by a slice of UD*? -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics [email protected] University of New South Wales 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.
