Russell Standish wrote:

>Aha - this is the source of one of our misunderstandings. You actually
>say this on page 1 of your thesis - I had just forgotten. As you say,
>Schmidhuber's Plenitude is really the conjunction of assumptions 2&3,
>so you explicitly assume Schmidhuber Plenitude in the first place.

I'm glad you realise that!

> ...
>Fair enough - this was only a shot in the dark anyway. I was trying to
>relate my intuitive understanding of conscious projection to some
>formal mathematical process - diagonalisation is not the way to go.

OK. Note that I *do* think diagonalisation has something to do with
(high form of) self-consciousness. Mainly for "jumping out of oneself".
A similar idea has been proposed by Hofstadter in his GEB book.
In computer science self-reference is handled by a sort of double
diagonalisation. The basic idea is simple: let D be a self-applier
operator, i.e. D(X) gives X(X) (D is really a duplicator in fact). 
D captures the first diagonalisation. Then apply D to itself (second
diagonalisation) and you get the self-replicator: D(D) gives D(D).

>It is a "sort" of collapse, however I would argue that this "collapse"
>is inherent in Everett's MWI anyway. However, before people go
>charging at the red flag I'm waving, ...

...provocating red flag indeed!

>I should point the very big
>difference between this and the Copenhagen wavefunction collapse. With
>Copenhagen, the wavefunction collapse is physical, i.e. to use your
>excellent terminology - is a 3-phenomenon. In my case, the projection,
>is merely the act of an observer resolving a measurement. It is a pure
>1-phenomenon - a different observer will see a different projection
>(although clearly in their shared histories these observation need to
>be consistent). The picture as I see it is identical to the diagram
>you have on page 83 of your thesis.

Exactly.

>Now you seem to be saying that this projection is computable - ie
>Turing machines embedded within the ensemble are able to have first
>person experiences like this. 

The fact is that if I survive teleportation through comp, I will
survive duplication and I will not been able to predict with certainty
the result, as I measure it myself, of the self-duplication.
But the mystery of ``reawakening" is no greater in the duplication
than in the simple teleportation case.

>This is the part I'm having trouble
>with. I seen some attempts to formulate Quantum measurement theory in
>terms of induced correlations between the environment and the observer
>(or measurement device) - eg Zurek's attempts in the late '80s, but
>none that I've been particularly satisfied with.

That's OK and I think Zurek contribution is important and could help
us to bridge the gap between 3-experiment and 1-experience. But
I don't think it is need for the projection case of self-duplication.
It will be useful in any case (including simple teleportation, or even
the experiment "do nothing, stay conscious").

                                   ***

Now I answer a question you made about the UDA.
It is related to the search of "effective probability" (Mallah's
term); the definition of observer moments, etc. (actually: the current
thread "Renormalisation").

>> BM: Exercice: why should we search a measure on the computational
>> continuations and not just the computational states? Hint: with
>> just the computational states only, COMP predicts white noise for
>> all experiences. (ok Chris ?). With the continuations, a priori 
>> we must just hunt away the 'white rabbit' continuations. 
>> You can also show that Schmidhuber's 'universal prior' solution 
>>  works only in the case the level of substitution
>> is so low that my generalised brain is the entire multiverse.
>> 
>
>RS: Again, I do not know what you mean by this last comment.

Damned! Professional duties call for. I'l go back to this
'exercice' ASAP. 

Bruno

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