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.

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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