On 14 Aug 2012, at 06:33, Jason Resch wrote:

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On Mon, Aug 13, 2012 at 10:53 AM, Bruno Marchal <marc...@ulb.ac.be>wrote:The choice of the initial universal system does not matter. Ofcourse it does matter epistemologically. If you choose a quantumcomputing system as initial system, the derivation of the physicallaws will be confusing, and you will have an hard time to convincepeople that you have derived the quantum from comp, as you will haveseemed to introduce it at the start. So it is better to start withthe less "looking physical" initial system, and it is preferable tostart from one very well know, like number + addition andmultiplication.So, let us take it to fix the thing. The theory of everything isthen given by the minimal number of axioms we need to recover Turinguniversality.Amazingly enough the two following axioms are already enough, wherethe variable are quantified universally. I assume also some equalityrules, but not logic!x + 0 = x x + s(y) = s(x + y) x * 0 = 0 x*s(y) = (x *y) + xThis define already a realm in which all universal number exists,and all their behavior is accessible from that simple theory: it issigma_1 complete, that is the arithmetical version of Turing-complete. Note that such a theory is very weak, it has no negation,and cannot prove that 0 ≠ 1, for example. Of course, it isconsistent and can't prove that 0 = 1 either. yet it emulates a UDthrough the fact that all the numbers representing proofs can beproved to exist in that theory.Now, in that realm, due to the first person indeterminacy, you aremultiplied into infinity. More precisely, your actual relativecomputational state appears to be proved to exist relatively tobasically all universal numbers (and some non universal numberstoo), and this infinitely often.So when you decide to do an experience of physics, dropping anapple, for example, the first person indeterminacy dictates thatwhat you will feel to be experienced is given by a statistic on allcomputations (provably existing in the theory above) defined withrespect to all universal numbers.Is every program given equal weight in this theory, or mightprograms that run more efficiently, longer, or appear morefrequently (as embedded sub-programs) have greater weight in settingthe probability of future first person extensions?

`Only "appear more frequently in the UD*" can play a role, by the`

`invariance of the probabilities for the first person indeterminacies.`

Does the universal system have any bearing on the above? Forexample, intuitively it seems to me that when considering twouniversal systems, say Java, and FORTRAN, that due to syntacticaldifferences, different programs might appear more or less often oreasily.

`The UD in Java, and the UD in FORTRAN will generates all possible UDs.`

`If one particular one win the measure game, one (or many) special`

`universal systems will play bigger role than other, but that has to be`

`proved starting from any initial UD. So your question depends on the`

`points of view taken. Ontologically, the answer is no.`

`Epistemologically, the answer is yes, but that has to be deduced from`

`the ontology (and the definition of person, belief, knowledge,`

`observation, etc.). The theoretical result is that quantum universal`

`system wins (as proved by the fact that arithmetical observation leads`

`to an arithmetical quantization), and this is confirmed,`

`retrospectively, by the existence of the quantum features in Nature.`

Perhaps all universal systems compete amongst each other, based notonly on the frequency of their programs, but how easily thatuniversal system is realized in some meta-system.

`Only if that easiness entails a bigger measure. Then yes, and that is`

`even quite plausible, if not empirically obvious for the high physical`

`reality levels.`

`Keep in mind that if you are duplicated in virtual dreams in W and M,`

`and that in W you are executed with a quantum efficient computer, and`

`in M you are executed by monks playing inefficiently (but correctly)`

`with pebbles, comp entails that *you* will not feel any difference, as`

`you cannot be directly aware of the universal level which execute you`

`at (or below) your substitution level.`

Bruno

So if comp is correct, and if some physical law is correct (like'dropped apples fall'), it can only mean that the vast majority ofcomputation going in your actual comp state compute a state ofaffair where you see the apple falling. If you want, the reason whyapple fall is that it happens in the majority of your computationalextensions, and this has to be verified in the space of allcomputations. Everett confirms this very weird self-multiplication(weird with respect to the idea that we are unique and are living ina unique reality). This translated the problem of "why physicallaws" into a problem of statistics in computer science, or in numbertheory.Now, instead of using the four axioms above, I could have startedwith the combinators, and use the two combinator axioms:((K x) y) = x (((S x) y) z) = ((x z) (y z))This define exactly the same set of "all computations", and the samestatistical measure problem, and that is what I mean by saying thatthe initial axioms choice is indifferent as long as you start fromsomething which define a UD, or all computations (that is: is Turingor sigma_1 complete).Now, clearly, from the first person points of view, it does looklike many universal system get relatively more important role. Somecan be geographical, like the local chemical situation on earth (avery special universal system), or your parents, but the point isthat their stability must be justified by the "winning universalsystem" emerging from the competition of all universal numbers goingthrough your actual state. The apparent winner seems to be thequantum one, and it has already the shape of a universal systemwhich manage to eliminate abnormal computations by a process ofdestructive interferences. But to solve the mind body problem wehave to justify this destructive interference processes through thesolution of the arithmetical or combinatorial measure problem.Bruno

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