On 01 Oct 2011, at 22:23, meekerdb wrote:
On 10/1/2011 8:15 AM, Bruno Marchal wrote:
On 01 Oct 2011, at 09:31, Russell Standish wrote:
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, ...
Wouldn't that require that all the infinite UD calculations be
completed before all the "you" could be indentified?
The infinite UD calculations are just number relations, which are out
of space and time.
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.
But aside from the quantum level, doesn't the measure problem have
the same drawback and Boltzman's brains. Shouldn't I find myself in
a world where everyone is Brent Meeker?
Well, if you prove this, then you refute comp (and most of its "super-
Turing" weakenings).
The big difference between Boltzman brains and UD*, is that the first
are not well defined and depends on physical assumption, the second is
well defined and depends only of the addition and multiplication laws
of non negative integers.
Bruno
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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Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics hpco...@hpcoders.com.au
University of New South Wales http://www.hpcoders.com.au
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http://iridia.ulb.ac.be/~marchal/
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