On 10/25/2011 4:40 PM, Russell Standish wrote:

On Mon, Oct 24, 2011 at 04:08:38PM +0200, Bruno Marchal wrote:On 23 Oct 2011, at 04:41, Russell Standish wrote: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.The 3-OM. But the first person indeterminacy depends on all the (infinite) computations going through all possible intermediary 3-OMs states.So does the OM I'm referring to. Does that still make is a 3 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.I have explained this to Stephen a long time ago, when explaining why the work of Pratt, although very interesting fails to address the comp mind body problem. Basically Pratt's duality is recover by the "duality" between Bp (G) and Bp& Dt (Z1*) or Bp& Dt& p (X1*). You might serach what I said by looking at Pratt in the archive, with some luck.This is above my level of understanding at present. Hopefully, there will be some quiet time soon to study this, as it sounds interesting!

Hi Russell and Bruno,,

`I recommend that you read Steve Vickers' "Topology Via Logic"`

`first. Pratt's ideas are a bit more abstract.`

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,How? UD* structure relies on computer science, and give a non random countable sets, or strings. The set of binary strings is the set of reals, and it appears in UD*, but only from a first person views, with the real playing the role of oracles.Exactly!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?What do you mean by the reference machine? What is an observer? How would S-L distribution be applied to the first person expectancy?The S-L distribution relies upon a universal machine for its definition, called the reference machine. Observer is exactly what you and I mean by it. The person with subjective experience, attaching meaning to experiential data. The observer map o is a map from data to meaning, the former being strings of some alphabet (eg binary), the latter being a countable set - can be modelled by the whole numbers N. The S-L distribution arises naturally if you ask the question: "What is the probability of a given meaning being attached to the data by an observer if the data strings were distributed uniformly" I think it probably still arises if the data strings were distributed in other ways a priori - eg being the output of a universal machine acting as an oracle, for instance. But I haven't sat down to work out what the limits are to this. Presumably some priori distributions will affect the final result.

`Why does the distribution have to exist a priori? What if it`

`obtains from interactions of many machines? Looking at just one UTM wil`

`never show this.`

This would seem to be applying S-L theory to the first person description.How will you avoid huge programs accessing your current states. It might work if we were able to justify why little programs multiply much more observer's state than huge programs, but I doubt S-L could explain this. Any idea?You don't avoid huge programs accessing your current states. They are exponentially suppressed, AFAIC see.But isn't first person view of the UD given by a slice of UD*?UD* is a countable structure, but the math of the first person involves a continuum, so I doubt it can be a slice of UD*.Then we are completely lost by terminology. I thought the UD* was the trace of the dovetailer, as seen from inside the dovetailer.This makes the measure problem very difficult, and that is why I tackle it by the self-reference modal logic, which gives the complete math of the propositional logic of observation (together with belief, knowledge, feelings, etc.). If such logics behaves well, as they should if comp is true, the whole physics can be extracted with a complete bypassing of the measure problem.That still seems a big "if". I appreciate that some of these modal logics give something like the quantum logics of von Neumann, but which ones correspond to our world? Neither the Theatetus knowledge definition, nor the match with our world is so startlingly obvious as to say "This must be it!". Also the lack of Kripke frames in X and Z bothers me a bit with this approach.In a sense the comp-physics is the solution of the measure problem, in that approach. We have already that the bottom of the physical reality behaves symmetrically and linearly. It harder to derive the Hamiltonian reality, and may be here could the S-L provides some help (but this would make the Hamiltonians more geographical than physical).Most of the Hamiltonian structure comes from considerations of symmetry (see Vic Stengar's book Comprehensible Cosmos). But why this symmetry, and not that is harder to answer. (A bit like why this modal logic, not that :) If all symmetries applied to observed reality, it would be too simple.

`I suspect that the logic is forced to be bivalent by the mutual`

`non-contradiction of interactions over many machines. Like a language's`

`words are forced by the habituation of the speakers.`

The other reason to use the self-reference logics is that it distinguish automatically the quanta (sharable, communicable at least in a first person plural way) from the qualia (not sharable, purely individual), all this by the Gödel-Löb-Solovay proof/truth splitting of the modal logics.Yes - that is interesting, but is true of any modal logic (apart from S4Grz, it would appear).

`But how do you obtain the mutual orthogonality of observables on a`

`quantum logic? We must address the relationship between orthocomplete`

`lattices and Boolean algebras at some point!`

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