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.


>ii) Schmidhuber means that all computations exist. (via UD*)

That is equivalent to the arithmetical realism. (AR)
To be sure AR seems to say that a little more than "all the
computations exists", and so, at this stage comp looks like
lying in between Tegmark and Schmidhuber. But ... see below.

>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.
This is a wonderfull feature of the set of computable functions 
because it gives us the FIRST mathematical (and until today the only)
mathematical structure which does not lead us to paradoxes when it
is conceived as a Totality, or an Everything Ontology.
That is why in some sense Schmidhuber plenitude, or my UD*, are
vastly more bigger than a priori Tegmark-like form of Platonisme.
Of course there is a price, which is the non recursive axiomatisation
of the set of all truth. But by Godel this is true even for
elementary arithmetical truth (which indeed is somewhat equivalent to
UD* although I should add some nuance here).

Actually, we don't need more than arithmetical plenitude: if
we are machine, we cannot prove that there is more than machines.
>From the Chaitin version of Godel's theorem (also found by Post in 
the twinties!) a machine cannot prove that something more complex than
itself is not a machine. In my annexe on Church thesis in my thesis, I
explain that point and I explicitely show that Church thesis makes a
case for the rehabilitation of the old Pythagorism. 

So remember: UD* is closed for diagonalisation. You cannot diagonalised
again UD*. Any diagonalisation on UD* create something which exists in 
UD*. It is important: without that closure I would just be mad thinking
the physical as a subspecies of the informatical.

>By me - I assume you mean COMP. Lets talk about Tegmark, and yes I
>believe Tegmark is referring to formal axiomatic systems (he seems to
>go on about them in his paper). I can see clearly that Tegmark \subset
>Schmidhuber, however it is less clear that the reverse relationship
>holds. If the reverse relationship did hold, then it would make little
>difference, apart from the White Rabbit problem vanishing.

I'm not sure I understand. (I propose we go back to tegmark later).
At this stage it is out of our basic misunderstanding, I guess.

>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




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