Ricardo, On 19 Nov 2011, at 16:33, R AM wrote:

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Has Eric Vandenbush written a paper about how complex numbers arederived from UDA?

`He has some health problem, and rarely finish papers. Sorry. I work`

`hard to encourage him to finish a paper on those complex numbers. I`

`will let you know if he succeeds in that task.`

Bruno

RicardoEl nov 19, 2011 9:49 a.m., "Bruno Marchal" <marc...@ulb.ac.be>escribió:On 19 Nov 2011, at 03:02, Pierz wrote: In a previous post I launched a kamizake assault on UDA which was justly cut to shreds on the basis of a number of misunderstandings on my part, perhaps most crucially my conflation of information and computation. I claimed that the UD cannot be distinguished from the set of all possible information states and therefore from an infinite field of static, within which all possible realities can be found, none of which, however, have the slightest coherence. I also mistakenly used the word 'random' to describe this bit field, which of course is wrong. I should instead have used the word 'incoherent'. Bruno and others quickly put me straight on these errors. I am still troubled however by the suspicion that UDA, by explaining 'everything' (except itself - there is always that lacuna in any explanatory framework) also explains nothing.The UD is not proposed as an explanation per se. On the contrary UDAshows that it is a problem we met when we assume that the brain (orgeneralized brain) is Turing emulable.Because the UD executes every computation, it cannot explain why certain computations (say Schroedinger's equation, or those of general relativity) are preferred within our presenting reality. That is basically my critics of Schmidhuber I have made on this list. I'm afraid that you miss the role of the first person indeterminacy.I will add explanation here asap. You have to follow UDA step bystep: it is a proof (in the theory "mechanism"), so to refute UDAyou have to say where it goes wrong. I insist: UDA is a problem, nota solution. Indeed it is a subproblem of the mind-body problem inthe mechanist theory.AUDA will be the solution, or the embryo of the solution. This very universality also insulates it against disproof, since although it allows everything we see, it is hard to conceive of something it would disallow.Not at all. A priori it predicts everything *at once*. That is the"white rabbit problem". We don't see white rabbits, or everythingat once, so mechanism seems to be disproved by UDA. The point willbe that such a quick disprove does not work, and when we do the mathwe see mechanism is not yet disproved, but that it predicts orexplain the quantum weirdness.David Deutsch's idea of a good explanation is one that closely matches the structure of the thing it describes, allowing for little variation. The vast variation in the possible worlds where UDA could be invoked makes it a bad explanation, in those terms.You have just not (yet) understood the role of the 1/3 person povdistinction in the reasoning. UDA shows that physics is determinedby a relative measure on computations. If this leads to predict thatelectron weight one ton then mechanism is disproved. UDA shows thatphysics is entirely reduce to computer science/number theory in avery specific and unique way (modulo a variation on the arithmeticaldefinition of knowledge).Of course the objection that nobody has yet found an application for UDA, a concrete example of its usefulness, is more of an objection to it as a scientific theory than a philosophical one.UDA is a proof. Unless wrong, it is done. Asking for the use of theUDA is like asking for the use of the theorem saying that no numbersn and m are such that (n/m)^2 = 2.UDA shows a fact to be true and that we have to live with it. UDAshows that mechanism and materialism are (epistemologically)incompatible.Still, I believe there is an argument against it at the philosophical level. The UDA invokes the notion of probability in relation to 1-p states on the basis of the "infinite union of all finite portions of the UD in which correct emulation occurs". Thus the indeterminacy of 1-p experience is a function of the distribution of states within the observer’s consistent histories. For instance, there’s a 20% chance of x happening, if it happens within 20% of my consistent histories. Please Bruno correct me if this is a misunderstanding. No, here I mainly agree with you. Now we know from QT there is a finite, if absurdly remote, probability of my turning into a giraffe in the next minute. So the UD, if not to contradict science as it stands, must allow this too. And indeed there is no reason for it not to, since there must be computational pathways that lead from human to giraffe - a sort of deep version of the morphing algorithms used in CGI - or a simple arbitrary transform. In fact there must be infinite such pathways leading to slight variations on the giraffe theme, as well as to all other animals, inanimate objects and so on - okay let’s leave out the inanimate objects since they possess no consciousness as far as we know, therefore no 1-p experience. Of course, these pathways are an extreme minority compared to the ones in which I retain my present form, behaving as we would expect on the basis of the past. "Of course"?No, what UDA shows is that it is not obvious, and that computerscience can show it false, and so refute mechanism. But the mathshows that such a refutation, if it exists, is not trivial at all,and the logic of self-reference shows that we are led toabsurdities, not contradiction (yet), and the absurdities are quitesimilar to the quantum weirdness that we can "observe" (nonlocality, indeterminacy, many worlds/dreams/states, symmetry at thebottom, etc.)But here’s where I see the problem. In a mathematical platonia we cannot make such a statement. The notion of probability within an infinite set is untenable.On the contrary. Probability calculus and measure theory have beeninvented to put measure on infinite spaces.It is analogous to expecting that a number selected at random from the set of natural numbers is more likely to be divisible by 2 than by, say, a million. This is only the case of the set is ordered to appear this way, eg 1,2,3,4... If we write the set thusly: 1, 1 million, 2 million, 3 million, 2, 4 million, 5 million, 6 million, 3, 7 million.... etc then our expectation breaks down. You can use the usual Lebesgue measure on the real. http://en.wikipedia.org/wiki/Lebesgue_measureThink about the repeated self-duplication. It shows that self-duplication is a Bernouilli experience, so that in the limit (whichdefine the uncertainty domain for the first person experience), wecan use the usual normal distribution based on e^(- x^2) with thenormalisation factor.So if there are infinite pathways where I turn into a giraffe, as there must be, there is no way for my 1-p experience to select probabilistically among these pathways. I can no longer say, if the set of calculation pathways is infinite, that giraffe transformation occurs in, say .000000001% of them, or 5%, or 99% of them.Yes, you can. The problem is that the UD does not just iterate self-multiplication (random noise), but it mixes it in a highly nontrivial way with infinitely many computations.This is not a problem for an Everett -type multiverse, in which the universes are bound together by consistent physical laws which allow one to speak of a proportion of universes in which event x occurs. However, in a mathematical platonia where all possible calculations occur, and nothing outside of them, there can be no such ordering principle.If the Everett idea works, and is the solution, (which has not yetbeen completely proved) then the UDA conclusion is that the Everettsimultion in the UD wins the "measure battle", and we HAVE tojustify this from computer science alone.It would mean that the quantum computation are statistically morefrequent than the non quantum computations. But this must be shown,or we miss the explanation of the origin of the physical laws,together with the distinction quanta/qualia that digital mechanismalready explained (by the Solovay split between truth and proof).I believe this same principle can be used to show that the calculations of the UD must be disorderly. Consider some calculation c which employs number n. In the UD there will also be a calculation which instead uses the number n+1, another which uses n+2 etc. There will also be calculations in which the ordering of the natural numbers is rearranged in arbitrary ways such as my example above. Instead of using simple n, the calculation will employ someFunction(n), where someFunction() transforms the number as per my example, i.e. (in pseudocode): if n modulo 4 = 0 return n else return (n-1) * 1,000,000 Thus the UD cannot rely even on the ordering of natural numbers to ‘prefer’ certain calculations, since the set of variants such as the above will be infinite, and overwhelm calculations involving simple n.This shows that the extraction of physics from numbers is not aneasy task, but again, you have to take into account the nontriviality of the 1 and 3 pov relation, and of computer science andmathematical self-reference (G, G*, S4Grz, etc.) Then the shadows ofwhy quanta and qualia already appear.Recently Eric Vandenbush (a guy who solved the first open problem inmy thesis) has found an explanation why the UD leads necessarily tocomplex numbers for the measure problem (that's new! but I have yetto be entirely convinced).Pierz, I insist that the UD is not proposed as a solution, but as aproblem for DM. It is shown to be an unavoidable problem we have tosolve if we keep digital mechanism in cognitive science. I am openthat it will lead to a refutation of mechanism, but thecontraidiction has not yet appear, and on the contrary, what we getis a similar "many-world" problem that the physicists encounter too.This confirms Digital Mechanism (DM) instead of refuting it. UDAjust transforms the mind body problem into a mathematical bodyappearances problem.BrunoPS have you see that edot has become enet? I will come back on theUDA there too! 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