On 06 Jan 2010, at 01:21, Nick Prince wrote:
Hi Brent Perhaps Bruno could give some clarification here. Just prior to his conclusion on the sane paper I quoted from was this: "So if we keep comp at this stage, we are forced to relate the inner experience only to the type of computation involved. The reason is that only those types are univocally related to all their possible counterfactuals. This entails that, from a first person point of view, not only the physical cannot be distinguished from the virtual, but the virtual can no more be distinguished from the arithmetical. Now DU is emulated platonistically by the verifiable propositions of arithmetic. They are equivalent to sentences of the form ‘‘it exists n such that P(n)’’ with P(n) decidable. Their truth entails their provability, and they are known under the name of Sigma1 sentence. If comp is correct, the appearance of physics must be recovered from some point of views emerging from those propositions. Indeed, taking into account the seven steps once more, we arrive at the conclusion that the physical atomic (in the Boolean logician sense) invariant proposition must be given by a probability measure on those propositions. A physical certainty must be true in all maximal extensions, true in at least one maximal extension (we will see later why the second condition does not follow from the first) and accessible by the UD, that is arithmetically verifiable. Figure 8 illustrates our main conclusion, where the number 1 is put for the so called Sigma1 sentences of arithmetic." It sounds as if Bruno thinks that the computations of the UD invoke our inner experiences and also our understanding of physics. Both come from arithmetical platonicism ( because thats what the UD is all about). So the pictures in the "film" are stiched together by the arithmetical (computation necessity) rather than the laws of of physics... Hmm not what I thought and said earlier!! So according to Bruno the laws of physics come from something intrinsic in the computation? Not quite sure how. I just can't figure out any more at the moment and hope Bruno will give me a hint here.
But the quote you give is the conclusion of step 7 and 8. Except that I use a bit the vocabulary which will help to understand the "interview" of the Löbian machine.
Normally at step seven you understand that COMP + concrete UD => "I am already in UD*" and the physical laws have to result from a sum on my first person (hopefully plural) indeterminacy in UD*. (step 1 ->6 + 7)
Then step 8, MGA, shows (is supposed to show) that COMP makes any concrete running of the UD irrelevant. (but the MGA thread in this list is better, I may send a new version of MGA). MGA = Movie Graph Argument.
This is not *just* because UD* is represented, remarkably enough, in the elementary consequences of addition and multiplication, but mainly because, by MGA, comp together with the physical supervenience thesis makes it necessary to confuse a computation and a description of a computation. The computation has to consist in the logical relations, not in this or that implementation, (which, btw, can only be a reduction to a particular universal machine).
Do you see that COMP + concrete UD leads to an Everett-DeWitt shock? We am multiplied by 10^100+ at each instant. COMP leads, naively, to Aleph_zero + multiplication, or even 2^aleph_zero (in a sense)?
Then MGA is the next and last difficulty. (before the machine interview, if interested).
Bruno http://iridia.ulb.ac.be/~marchal/
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