On 01 Oct 2011, at 09:31, Russell Standish wrote:

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On Thu, Sep 22, 2011 at 07:02:28PM +0200, Bruno Marchal wrote:OK. But note that in this case you are using the notion of 3-OM (or computational state), not Bostrom notion of 1-OM (or my notion of first person state). The 3-OM are countable, but the 1-OMs are not.Could you explain more why you think this? AFAICT, Bostrom makes no mention of the cardinality of his OMs.

`I don't think that Bostrom mentions the cardinality of his OMs,`

`indeed. I don't think that he clearly distinguish the 1-OMs and the 3-`

`OMs either. By "3-OM" I refer to the computational state per se, as`

`defined relatively to the UD deployment (UD*). Those are clearly`

`infinite and countable, even recursively countable.`

`The 1-OMs, for any person, are not recursively countable, indeed by an`

`application of a theorem of Rice, they are not even 3-recognizable. Or`

`more simply because you cannot know your substitution level. In front`

`of some portion of UD*, you cannot recognize your 1-OMs in general.`

`You cannot say "I am here, and there, etc." But they are (non`

`constructively) well defined. "God" can know that you are here, and`

`there, ... And the measure on the 1-OMs should be defined on those`

`unrecognizable 1-OMs.`

`Are the 1-OMs countable? In the quote above, I say that they are not`

`countable. What I meant by this is related to the measure problem,`

`which cannot be made on the states themselves, but, I think, on the`

`computational histories going through them, and, actually, on *all*`

`computational histories going through them. This includes the dummy`

`histories which duplicate you iteratively through some processes`

`similar to the infinite iteration of the WM self-duplication. Even if`

`you don't interact with the output (here: W or M) or the iteration,`

`such computations multiplies in the non-countable infinity. (I am`

`using implictly the fist person indeterminacy, of course). Those`

`computation will have the shape:`

you M you M you W you M You W You W You W You M ad infinitum

`This gives a white noise, which is not necessarily available to you,`

`but it still multiplies (in the most possible dumb way) your`

`computational histories. Such infinite computations, which are somehow`

`dovetailing on the reals (infinite sequence of W and M) have a higher`

`measure than any finite computations and so are good candidates for`

`the "winning" computations. Note that such an infinite background`

`noise, although not directly accessible through your 1-OMs, should be`

`experimentally detectable when you look at yourselves+neighborhood`

`below the substitution level, and indeed QM confirms this by the many`

`(up + down) superposition states of the particles states in the`

`(assumed to be infinite) multi-universes.`

`This might be also confirmed by some possible semantics for the logic`

`of the first person points of view (the quantified logic qS4Grz1, qX1*`

`have, I think, non countable important models).`

`3-OMs are relatively simple objects, but 1-OMs are more sophisticated,`

`and are defined together with the set of all computations going`

`through their correspondent states.`

`To be sure, I am not entirely persuaded that Bostrom's 1-OMs makes`

`sense with digital mechanism, and usually I prefer to use the label of`

`first person experiences/histories. With the rule Y = II, that is: a`

`bifurcation of a computations entails a doubling of the measure even`

`on its "past" (in the UD steps sense), this makes clear that we have a`

`continuum of infinite histories.`

`Again, this is made more complex when we take amnesia and fusion of`

`histories) into consideration.`

`I hope this helps a bit. In my opinion, only further progress on the`

`"hypostases" modal logics will make it possible to isolate a`

`reasonable definition of 1-OMs, which obviously is a quite intricate`

`notion.`

Bruno

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