On Tue, Jul 09, 2002 at 05:51:22PM +0200, Bruno Marchal wrote:
> Have you understand what I call the invariance lemma? (The fact that
> if I am multiplied into 1000 copies in a whole space-time decor, real,
> virtual or arithmetical) the measure of comp indeterminacy depends
> only on "1000").

I'm not sure I do understand it. Do you think the "measure of comp 
indeterminacy" is relevant in decision theory? Before you answer that 
question, please read the book _Foundations of Causal Decision Theory_ 
that I recommended earlier so you can understand what it is that I'm 
asking. If the answer is yes, then please explain how it can be used in 
decision theory. If the answer is no, then I believe the "lemma" is 
meaningless.

> Perhaps the trouble is that you are not really aware of the mind-body
> problem?

I'm aware of *a* mind-body problem. I'm not sure if it's the same one you 
have in mind. The one I have in mind is this: how do I derive a 
probability distribution for the (absolute) SSA from a third-person 
description of the multiverse?

> I don't yet understand how Schmidhuber attach the mind to its computa-
> tional history.

I don't either, but I don't think he's claiming to have solved it.

> This is where the list splits in two. Those aware of a measure problem
> and the other ... It is linked to our all debate between RSSA and ASSA
> (Relative Self-Sampling Assumption/Absolute SSA).

I guess we're going in circles a little bit, except I now have a better
understanding of how decision theory would work given the absolute SSA. (I
still have to write down my thoughts on this matter.) But I still do not
see how it could work with the RSSA.

> Because we want to understand the nature of reality and where does it comes
> from. 

I think we can do that without first-person indeterminancy.

> Consciousness is part of the data we must explain, 

That's still a hard problem (i.e. we have no theory of consciousness) but 
I don't see how first-person indeterminancy helps.

> physicals laws also. 

I think that's fairly easy, at least conceptually. It's "just" a matter of 
showing that almost all observer-moments are experiencing or 
remembering lawful phenomena. Again, I think that can be done without 
first-person indeterminancy.

> With comp the laws emerge from the relation between numbers, but as
> seen from inside, so that I don't see how to avoid the modal distinctions in
> a search toward a toe. I think you fail to appreciate the "proof" character
> of the uda.

What axioms are you assuming for the proof?

> I'm not sure you are not a sound machine especially when proving
> things on numbers. In the worst case take my "restriction" as a
> simplifying assumption. But I don't think there is any restriction here.
> The amazing fact is that the sound machine has (through the Z logics) an
> amazingly large non-monotonical layer. Remember that "inconsistency" has
> been shown consistent in Peano Arithmetic, ZF theory, etc. Sound machines,
> sound at the basic level I interrogate them, can be consistently very unsound
> once entangled to deep computational histories. I am taking the full nuance
> given by the second incompleteness theorem into account here.

Unfortunately I don't understand much of what you say in this paragraph, 
especially these two sentences:

> Remember that "inconsistency" has   
> been shown consistent in Peano Arithmetic, ZF theory, etc. Sound machines,
> sound at the basic level I interrogate them, can be consistently very unsound
> once entangled to deep computational histories.

The first sentence obviously refers to some result from metamathematics, 
but you have to remember that I'm still learning about it and be more 
explicit (at least use a standard name to refer to the result so I can 
look it up). I have no idea what the second sentence means.

> You would be really unsound, through my basic use of the term, only if you
> were able to give a finite proof of a false proposition, not just pretend
> you could find it.

Of course I can give a finite proof of a false proposition. I just have to
use an unsound logic to do the proof. If you restrict us to using sound
logics, then nobody can give a finite proof of a false proposition, so if
that's your definition of sound machine, I'm not sure what the point of
qualifying "machine" with "sound" is.

> Because with comp the relation between our first person inspired decisions
> and third person (or first person plural) realities remains to be explained.
> The comp indeterminacy, by the invariance lemma, pertains on the whole
> of UD* (the computationalist form of everything).
> Of course you can forget comp, postulate a reality (defined by what you
> see and expect to see) and take your decisions. But we are looking for
> a toe, not a recipe for life. You don't need quantum gravity for everyday
> decision do you? But you can imagine quantum gravity being related to the
> search of a TOE, ok? Well, what I try to say is that if you take seriously
> the hypothesis that our private experience are invariant for functional
> substitution at some level, then the utimate explanation of quantum gravity
> is accessible by UTMS pure introspection, and that the toe is a mixture
> of machine's machine psychology (G), and machine psychology (G*).
> The advantage of my way is that it gives an explanation for the origin
> of physical laws and at the same time of physical sensations. It has no direct
> use in decision theory, except perhaps by predicting new phenomena, perhaps
> exploitable, like any new theory.
> No doubt I make simplifications here and there, but what remains is
> very complex and unknown. I would be glad if someone find a flaw or some
> implicit hypothesis I use unconsciously ...

I would be happy to try to find some flaw or implicit hypothesis in your 
argument, but I'm still waiting for the English paper you've promised us. 
:( Until then I'm just trying to understand your explicit assumptions and 
conclusions.

BTW, quantum gravity will be useful in everyday decisions when we have the 
necessary technology to make use of it (for example to construct 
microscopic black holes for catalytic matter to energy conversion).

> About Schmidhuber's toe, perhaps you could try to explain me how you keep
> being in the same computation in front of the invariance lemma, knowing
> that all computations exist.

I don't have to explain how I "keep being in the same computation" because
I don't know or claim that. I'm not sure that's even a meaningful
sentence. All I do claim is that for any given computation, if I am in
that computation, I care about the future version of me in that
computation, and I can causally affect its future (and only its future).
In other words, the causal influence of my actions stay in the same
computation.

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