On 25 Oct 2011, at 22:40, Russell Standish wrote:

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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") aresurelystill countable.This is not obvious for me. For any to computational states which are in a sequel when emulated by some universal UM,there areinfinitely many UMs, including one dovetailing on the reals,leadingto intermediate states. So I think that the "computational neighborhoods" are a priori uncoutable.Apriori, no. The UMs dovetailing on the reals will have onlyexecuteda finite number of steps, and read a finite number of bits for agivenOM. There are only a countable number of distinct UM states makingupthe 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.

But then why are you saying that they are countable?

Does that still make is a 3 OM?

Why would it?

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!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 preciselyzerofor the information content of this set.I do still think the universal dovetailer trace, UD*, isequivalent tothis 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 they are not the output of any computations? UD* has no random`

`part. The randomness is in the mind of the observers due to the first`

`person indterminacy, that is due to the invariance of the delay`

`introduced by the UD by its dovetailing.`

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 thecomputation of the first person indeterminacy, aka the derivationofphysics 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.

But that is not the observer.

Observer is exactly what you and I mean by it.

?

The person with subjective experience, attaching meaning to experiential data.

`In the comp case, this is given by Bp & p, that is the true-belief of`

`a machine, or by the personal diary (in UDA, it is enough).`

I have no idea what you mean by "meaning" in this context.

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.

I don't understand this.

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.

`An oracle cannot be an output of a machine. Oracle appears from inside`

`by the first person indeterminacy, but are never output of any`

`machine, nor even the UD (which has no output).`

But I haven't sat down to work out what the limits are to this. Presumably some priori distributions will affect the final result.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.

Exponentially suppressed? How and why?

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.

`The "seen-from-inside" are given by the points of view (either in the`

`diary of a teleporters guy taking his diary with him), or by the`

`variants of Gödel's Bp. UD* is the trace of the dovetailer. But not as`

`seen from inside.`

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".

`Not at all. The UDA shows that if comp is true, they have to behave`

`well. That is why comp has became refutable. If they don't behave well`

`we know that comp is false.`

I appreciate that some of these modal logics give something like the quantum logics of von Neumann,

`Not just some of those logics. Exactly the one which must give the`

`logic of the observable, by the UDA reasoning.`

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!".

`It follows entirely from the UDA. Physics have to appear either in`

`S4Grz1, Z1* or X1*. Where exactly will determine the role of Löbian`

`subjectivity in the emergence of the physical laws.`

Also the lack of Kripke frames in X and Z bothers me a bit with this approach.

`On the contrary. It fits well with the empiric data, and with UDA`

`which asks for topological neighborhoods for the first person points`

`of views. G* also lacks Kripke frames.`

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.

`The symmetry is already provided by the S4Grz1, Z1* or X1*, through`

`the "p -> BDp" formula, when "p" is sigma_1.`

(A bit like why this modal logic, not that :)

`They are just the arithmetical translations of the most standard`

`theory of knowledge we do have. And it works.`

If all symmetries applied to observed reality, it would be too simple.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).

`True for all hypostases, the intensional variants of self-reference,`

`that is the translation of belief, knowing, observing, feeling, in the`

`language of a Löbian machine (a universal machine clever enough to`

`know that she is a universal machine).`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.