OK, at last some time to sit down and reply properly. I want to come back on this point about measuring proportions of an infinite set - the measure theory you speak of. Now it seems clear enough that to measure such proportions (say, the proportion of even numbers in the set of natural numbers) one needs to iterate through that set in a specific order. If one uses the counting algorithm n=n+1 iteratively, then the result will be 50%, but if you use some other algorithm such as the alternative one I provided, you get a completely different result.
You agree with this? Now this is an issue for UDA (it seems), because in order to calculate the proportion of calculations in the infinite set in which I become a giraffe, then we must iterate through those calculations in a specific order. Otherwise, by arranging things the right way, I can get *any result I want*. I demonstrated this in my post by showing how there are more natural numbers divisible by a million than by 2. Again, agreed? OK, so I assume the order of calculations used to determine the measure on the set must be the order they run in the UD. But my point is that this order is *arbitrary*. This is because wherever the UD uses a natural number n in its calculation, I can imagine some other UD that uses someFunction(n) instead, where someFunction() transforms n in such a way that all natural numbers are generated, but in a different sequence. There are infinite such alternative UDs. So why should your UD algorithm be the 'real' one, simply because it uses the limiting case where someFunction(n) is the identity function (return n)? It seems fatal to me - unless some other less arbitrary means of counting the algorithms is (implicitly) employed. I say implicitly since what I have read of the UDA from you seems to pass over this critical question in silence. I'd also like to put another question which relates to arithmetical realism. Mechanism seems to be able to escape the UDA by denying arithmetical realism in the first place - a doctrine which seems to me to be far from self-evident, and certainly anathema to many physicists. On this matter I could cite Deutsch's claim that computability is a function of the laws of physics, and that different laws would permit different proofs and calculations, so to place the computable functions prior to the physical world the way you have is to put the cart before the horse. We see a computable universe because the laws of physics determines our brains as well as the structure of the universe. This to me has a certain force to it, though no doubt you will beg to differ. BTW I disagree that I fail to understand the relation of 1-p and 3-p in your proof. I am not making the same argument as before about the infinite static field, and I do appreciate that our states are represented in infinite calculations in the UD trace and that these calculations are very deep, necessarily. I also see how from your reasoning, we would see an Everett-like uncertainty in our future states. I don't see that you have pointed out any particular misunderstanding on my part, though I am open to you explaining exactly where in my reasoning this failure is. Thanks for your explanation of my great-grandfather's work. I'm afraid my physics is that of the very well read layperson, so I've never really appreciated the ins and outs of what his contribution was - other than "the statistical interpretation of quantum physics". I read the Einstein-Born letters too, many years ago, and enjoyed what I understood! On Nov 19, 8:49 pm, Bruno Marchal <marc...@ulb.ac.be> wrote: > 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 UDA > shows that it is a problem we met when we assume that the brain (or > generalized 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 by step: > it is a proof (in the theory "mechanism"), so to refute UDA you have > to say where it goes wrong. I insist: UDA is a problem, not a > solution. Indeed it is a subproblem of the mind-body problem in the > 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 everything at > once, so mechanism seems to be disproved by UDA. The point will be > that such a quick disprove does not work, and when we do the math we > see mechanism is not yet disproved, but that it predicts or explain > 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 pov > distinction in the reasoning. UDA shows that physics is determined by > a relative measure on computations. If this leads to predict that > electron weight one ton then mechanism is disproved. UDA shows that > physics is entirely reduce to computer science/number theory in a very > specific and unique way (modulo a variation on the arithmetical > definition 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 the > UDA is like asking for the use of the theorem saying that no numbers n > and m are such that (n/m)^2 = 2. > UDA shows a fact to be true and that we have to live with it. UDA > shows 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 computer > science can show it false, and so refute mechanism. But the math shows > that such a refutation, if it exists, is not trivial at all, and the > logic of self-reference shows that we are led to absurdities, not > contradiction (yet), and the absurdities are quite similar to the > quantum weirdness that we can "observe" (non locality, indeterminacy, > many worlds/dreams/states, symmetry at the bottom, 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 been > invented 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_measure > > Think about the repeated self-duplication. It shows that self- > duplication is a Bernouilli experience, so that in the limit (which > define the uncertainty domain for the first person experience), we can > use the usual normal distribution based on e^(- x^2) with the > normalisation 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 non trivial > 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 yet > been completely proved) then the UDA conclusion is that the Everett > simultion in the UD wins the "measure battle", and we HAVE to justify > this from computer science alone. > > It would mean that the quantum computation are statistically more > frequent 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 mechanism already > 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 an easy > task, but again, you have to take into account the non triviality of > the 1 and 3 pov relation, and of computer science and mathematical > self-reference (G, G*, S4Grz, etc.) Then the shadows of why quanta and > qualia already appear. > > Recently Eric Vandenbush (a guy who solved the first open problem in > my thesis) has found an explanation why the UD leads necessarily to > complex numbers for the measure problem (that's new! but I have yet to > be entirely convinced). > > Pierz, I insist that the UD is not proposed as a solution, but as a > problem for DM. It is shown to be an unavoidable problem we have to > solve if we keep digital mechanism in cognitive science. I am open > that it will lead to a refutation of mechanism, but the contraidiction > has not yet appear, and on the contrary, what we get is a similar > "many-world" problem that the physicists encounter too. This confirms > Digital Mechanism (DM) instead of refuting it. ... > > read more » -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.