> 
> Russell Standish wrote:
> 
> >I really am trying to understand your argument. I know I'm from a
> >different conceptual background, but somewhere either you or I have an
> >incorrect concept. I can't accept a statement that A is equivalent to
> >B obviously, when to my understanding A and B are such different things.
> 
> I agree. We must work until we understand the roots of our
> misunderstanding.
> 
> >i) COMP means that I can survive the replacement of my brain by some
> >Turing emulation.
> 
> 
> Not really. Look at the UDA. COMP is 3 things:
> 
> 1) = what you are saying (survive a substitution done at 
> the right digital level, which is supposed to exist)
> 
> 2) Church thesis (I realise Schmidhuber does not cite it
> explicitely!, but the use of the compiler theorem and the use of
> his "great programmer" would not work without it).
> 
> 3) Arithmetical Realism (here is Schmidhuber plenitude!!!).
> Arithmetical Realism makes all steps of the UD work (Great Programmer's
> work) existing independantly of me.
> 

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 could well imagine conscious entities diagonalising the
> >UD* output to generate an experience which is not an explicit
> >computation.
> 
> Well. This is false, and even importantly false. You point
> here on my deeper motivation for Church thesis: the set of all
> computable functions, and the set of all computations, i.e. UD*
> is closed for diagonalisation.
> This is exactly why Godel, who takes time to accept Church thesis,
> called that thesis really a miracle.

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.

> 
> >Of course you can can compute the ensemble (UD*) - this follows from
> >Schmidhuber's Plenitude. Also (in a sense) you can compute the
> >wavefunction in Multiverse, which in turn defines a probability
> >distribution. What you can't compute (or so it seems to me) is the
> >outcome of a projection (1st postulate of consciousness). It is this
> >projection that introduces randomness, or indeterminism into the 1st
> >person view of the world.
> 
> This is another point where we disagree. And the disagreement is 
> deep (but that is what makes our conversation genuine, isn'it?).
> I say that the disagreement is deep because it is independant of
> comp: it bears even on Everett's MWI.
> In fact it seems to me that with your notion of "projection" you
> are introducing a sort of collapse in comp!
> But it is really computationnalism (in a weak sense) which has
> helped Everett to prove QM does not need any collapses.
> In comp, it is the same. The indeterminism is the consequence of
> the way machines describe the statistics of their self-localisations
> and other self-measures after the natural self-multiplication
> and self-delocalisation forced by the UD.
> If I duplicate you, nobody, including GOD or any quasi omniscient
> being can predict what you will *feel* (1-person concept) precisely.
> Like Everett, comp can predict that you will not feel the split.
> 
> Bruno
> 

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, 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.

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. 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.

                                                Cheers


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Dr. Russell Standish                    Director
High Performance Computing Support Unit,
University of NSW                       Phone 9385 6967
Sydney 2052                             Fax   9385 6965
Australia                               [EMAIL PROTECTED]
Room 2075, Red Centre                   http://parallel.hpc.unsw.edu.au/rks
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