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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Thu, 06 Nov 2003 18:42:58 +0100

At 16:54 05/11/03 -0500, Jesse Mazer wrote:

*>Hal Finney wrote:
*

*>
*

*>>
*

*>>One correction, in the descriptions below I should have said multiverse
*

*>>for all of them instead of universe. The distinction between the SSA
*

*>>and the SSSA is not multiverse vs universe, it is observers vs observer-
*

*>>moments. I'll send out an updated copy when I get some more links and/or
*

*>>corrections and new definitions.
*

*>>
*

*>>Hal
*

*>>
*

*>> > SSA - The Self-Sampling Assumption, which says that you should consider
*

*>> > yourself as a randomly sampled observer from among all observers in the
*

*>> > multiverse.
*

*>> >
*

*>> > SSSA - The Strong Self-Sampling Assumption, which says that you should
*

*>> > consider this particular observer-moment you are experiencing as being
*

*>> > randomly sampled from among all observer-moments in the universe.
*

*>> >
*

*>> > ASSA - The Absolute Self-Sampling Assumption, which says that you should
*

*>> > consider your next observer-moment to be randomly sampled from among all
*

*>> > observer-moments in the universe.
*

*>> >
*

*>> > RSSA - The Relative Self-Sampling Assumption, which says that you should
*

*>> > consider your next observer-moment to be randomly sampled from among all
*

*>> > observer-moments which come immediately after your current observer-moment
*

*>> > and belong to the same observer.
*

*>
*

*>In your definition of the ASSA, why do you define it in terms of your next
*

*>observer moment? Wouldn't it be possible to have a version of the SSA
*

*>where you consider your *current* observer moment to be randomly sampled
*

*>from the set of all observer-moments, but you use something like the RSSA
*

*>to guess what your next observer moment is likely to be like?
*

*>
*

*>Also, what about a weighted version of the ASSA? I believe other animals
*

*>are conscious and thus would qualify as observers/observer-moments, which
*

*>would suggest I am extraordinarily lucky to find myself as an
*

*>observer-moment of what seems like the most intelligent species on the
*

*>planet...but could there be an element of the anthropic principle here?
*

*>Perhaps some kind of theory of consciousness would assign something like a
*

*>"mental complexity" to different observer-moments, and the self-sampling
*

*>assumption could be biased in favor of more complex minds.
*

*>
*

*>Likewise, one might use a graded version of the RSSA to deal with "degrees
*

*>of similarity", instead of having it be a simple either-or whether a
*

*>future observer-moment "belongs to the same observer" or not as you
*

*>suggest in your definition. There could be some small probability that my
*

*>next observer-moment will be of a completely different person, but in most
*

*>cases it would be more likely that my next observer-moment would be
*

*>basically similar to my current one. But one might also have to take into
*

*>account the absolute measure on all-observer moments that I suggest above,
*

*>so that if there is a very low absolute probability of a brain that can
*

*>suggest a future observer-moment which is very similar to my current one
*

*>(because, say, I am standing at ground zero of a nuclear explosion) then
*

*>the relative probability of my next observer-moment being completely
*

*>different would be higher. Again, one would need something like a theory
*

*>of consciousness to quantify stuff like "degrees of similarity" and the
*

*>details of how the tradeoff between relative probability and absolute
*

*>probability would work.
*

In my opinion, and if I understand Jesse Mazer

properly, he is right. Now, with the comp. hyp. you have

(obviously) constraints coming from computer science

(itself related to number theory including universal one

not depending of any particular implementation).

A theory of consciousness which suits well both the

traditional thought experiment (self-duplicability) and

self-referential discourse can be extracted from what

a machine can, in general, correctly bet

on its possible consistent computational extensions.

That moves corresponds to comp-immortality,

we just don't take into account the cul-de-sac worlds, (which

corresponds to the world with no more accessible worlds

in the Kripke semantics of the logic of self-reference).

It is the move going from the logic of machine-provability

to the logic of machine "provability & consistency",

or the move from []p to a *new* box defined by []p&-[]-p.

From this (when p is restricted on the DU accessible proposition),

(the $\Sigma_1 proposition for the logicians), you get A quantum

logic, from which you get, I think, the similarity relations

you are searching. (This because from the yes/no quantum

logic you can derive an angle of PI/2 radians, and from that angle

you can derive all the angles, well if THAT quantum logic behaves

sufficiently well, and that's not yet clear at this point.

Of course at this point things are rather technical.

Just to make a link with what Hal Finney said, I have provide

indeed an argument showing that if we (I) are machine then

physics comes from computer science, but I have also provide

the more technically involved arithmetical translation of that

argument in the language of a "mean" self-referentially consistent

universal Turing machine (from which I extract that special

"quantum logic"). We can also drop "Turing" by the use of Church

Thesis (CT).

Hope that helps (to talk like Matt).

Bruno

PS A collegue of mine *did* find an error in my thesis where I say that

the more natural first candidate (the move from []p to []p & p ) for

the modelisation of the first person.

collapse into elementary logic when p is restricted to the \Sigma_1

sentences. I indeed forget that this last moves forces a weakening

of the substitution rule. This makes the S4Grz1 logic also a non trivial

candidate for the quantum logic, and, because this one is a Brouwerian

solipsistic logic, it is still open if physics could rely on a solipsistic

psychology. which I hope not!

I realise also we should perhaps need an acronym for the

first person/third person distinction (which corresponds to the subjective/

objective distinction in Everett papers, and which is akin to the

Tegmark frog/bird (though vague) distinction, and which is absent in

Schmidhuber approach. I propose "the F/T distinction". Read more

in the beginning of the UDA.

Received on Thu Nov 06 2003 - 12:39:33 PST

Date: Thu, 06 Nov 2003 18:42:58 +0100

At 16:54 05/11/03 -0500, Jesse Mazer wrote:

In my opinion, and if I understand Jesse Mazer

properly, he is right. Now, with the comp. hyp. you have

(obviously) constraints coming from computer science

(itself related to number theory including universal one

not depending of any particular implementation).

A theory of consciousness which suits well both the

traditional thought experiment (self-duplicability) and

self-referential discourse can be extracted from what

a machine can, in general, correctly bet

on its possible consistent computational extensions.

That moves corresponds to comp-immortality,

we just don't take into account the cul-de-sac worlds, (which

corresponds to the world with no more accessible worlds

in the Kripke semantics of the logic of self-reference).

It is the move going from the logic of machine-provability

to the logic of machine "provability & consistency",

or the move from []p to a *new* box defined by []p&-[]-p.

From this (when p is restricted on the DU accessible proposition),

(the $\Sigma_1 proposition for the logicians), you get A quantum

logic, from which you get, I think, the similarity relations

you are searching. (This because from the yes/no quantum

logic you can derive an angle of PI/2 radians, and from that angle

you can derive all the angles, well if THAT quantum logic behaves

sufficiently well, and that's not yet clear at this point.

Of course at this point things are rather technical.

Just to make a link with what Hal Finney said, I have provide

indeed an argument showing that if we (I) are machine then

physics comes from computer science, but I have also provide

the more technically involved arithmetical translation of that

argument in the language of a "mean" self-referentially consistent

universal Turing machine (from which I extract that special

"quantum logic"). We can also drop "Turing" by the use of Church

Thesis (CT).

Hope that helps (to talk like Matt).

Bruno

PS A collegue of mine *did* find an error in my thesis where I say that

the more natural first candidate (the move from []p to []p & p ) for

the modelisation of the first person.

collapse into elementary logic when p is restricted to the \Sigma_1

sentences. I indeed forget that this last moves forces a weakening

of the substitution rule. This makes the S4Grz1 logic also a non trivial

candidate for the quantum logic, and, because this one is a Brouwerian

solipsistic logic, it is still open if physics could rely on a solipsistic

psychology. which I hope not!

I realise also we should perhaps need an acronym for the

first person/third person distinction (which corresponds to the subjective/

objective distinction in Everett papers, and which is akin to the

Tegmark frog/bird (though vague) distinction, and which is absent in

Schmidhuber approach. I propose "the F/T distinction". Read more

in the beginning of the UDA.

Received on Thu Nov 06 2003 - 12:39:33 PST

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