Re: Bruno's UDA argument

From: Bruno Marchal <>
Date: Tue, 23 Jul 2002 16:28:31 +0200

At 10:25 -0700 22/07/2002, Hal Finney wrote:

> [snip]

>To sum up, I agree with Bruno (I think) on the following points:
> - Functional substitution is adequate to maintain consciousness

OK. (We suppose the functional substitution is done at *some* right level)

> - Mental states must be (in some sense) shared across all equivalent
> functional implementations

OK. (Accepting being still a bit fuzzy on the "equivalence relation" and
     on what is an implementations).

> - The UDA program produces multiple functional equivalents of all possible
> observers

OK. And what is nice is that once we agree on the existence of a
    level of substitution, we know the UD will produce those multiple functional
    equivalents of our mental states. That is: we don't need to know the level
    of substitution (or to agree on such or such level), nor do we need to know
    the equivalence relation. This is capital because there are evidence we
    cannot know those things for sure.

> - If we accept a certain view of Platonic reality of mathematics, then the
> UDA exists even if it is not implemented in our reality

OK. (I guess you mean the UD, the "A" being for Argument). Note only the UD
exists, but UD*, the infinite trace of the UD exists also.[ For Tim I would
say that UD and UD* make sense in any topoi having a natural number object].

> - In that case our current mental states can be viewed as being created
> by a UDA or some similar program

OK. (not taking the word "created" in a too literal dynamical sense)

>I may disagree on some points:
> - Not all functional substitutions have equal measure

No. Er... I mean I still agree on this point :)

> - Universes are well defined: each universe is the output of one of the
> programs which are simulated in "dovetailed" fashion by the UDA

In a very general sense of the word universe this could make sense. But
I think it would be preferable to keep the word "universe" for our "apparent
cosmic physical universe". For this one the UD-Argument shows that it is
a sort of average of the "universe in your sense" going through our states.
Note that quantum mechanics (without collapse, a la Everett) force the
averaging on universes. The precise way for making this averaging is hard
to find. That's the motivation for translating the whole UD-argument in the
language of universal sound machines, and interviewing such machines.

> - Each observer-moment spans a specific set of universes - that is, those
> specific programs which functionally implement it

I still agree. It is even *because* an observer-moment spans a specific set
of universes, that the measure on my most probable computational continuation
must take into account that whole span, and that is why the "Universe" I will
observe results from some averaging on all the continuations of each
observer moment in that span. This is why comp force us to predict that
if we look at the details of our Universe, we will discover a vast set of many
similar universes. That why the "many-world" is a natural consequence of
believing we are (digital) machines. This does not explain why some universes
interfere destructively. Let us remember that we still need to explain that.
For sake of future reference let us call that the "x -> e^ix mystery"
Perhaps you can guess why (cf also my CC&Q paper). It is linked to the fact
that we must deduce the quantum from the 1-comp-indeterminacy (with the

>And my very tentative theory for measure, which was first proposed by
>Wei Dai:
> - The measure of an observer-moment is proportional to the fraction of
> programs that implement it, and proportional to the fraction of each
> programs' trace that it occupies. That is, observer moments have
> higher measure if they are implemented by more programs, and also if
> they use up more of the "resources" of the universe created by each
> of these programs.

Very nice. Does Wei Dai still agree with this? (because Wei Dai changes
its mind once: cf the RSSA versus ASSA debate).
I say this because the "proportion of each trace it occupies" defines the
relative proportion (relative to the 1-observer-moment) I was defending in
the Relative-SSA.
Of course such definition of measure is to fuzzy to be computable.
There are a lot of problems: for example for each program the Dovetailer
dovetails on the execution of that program + dummy dovetailing on the reals,
or random oracle, augmenting the "resources" in arbitrary ways. So relevant
generators of histories must be able to use that randomness in the limit.
Li & Vitany books (Wei Dai suggested a long time ago) is still very
important in that setting. Bennett's depth, I think, should be very useful,
too. (And I would bet the "x -> e^ix" also, but we should not use it in an ad
hoc way, this would undermine the enterprise).
These moves are just orthogonal to the AUDA, which role is to give "at once"
the abstract skeleton of the logical relation between physical
propositions (as I said also more than one time). The AUDA is useful also
for distinguishing, by the G/G* distinction, the physical laws (communicable
physical proposition) and the physical *sensation* (uncommunicable...).
But your "very tentative theory for measure" is quite similar to what
I expect. AUDA could help to make clearer the role of the 1-3 distinction
relatively to "the fraction of each programs' trace that it occupies".

Received on Tue Jul 23 2002 - 07:34:05 PDT

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