> 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.


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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