> On 16 Feb 2020, at 08:10, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 2/15/2020 10:03 PM, Bruce Kellett wrote: >> On Sat, Feb 15, 2020 at 3:17 PM 'Brent Meeker' via Everything List >> <[email protected] <mailto:[email protected]>> >> wrote: >> On 2/14/2020 2:17 PM, Bruce Kellett wrote: >>> I attach an extract from Kent's paper. Take up your argument with him if >>> you think he has got the statistics wrong. >> >> I don't find it very convincing >> >> Whether you are convinced or not does not really affect the logic of Kent's >> argument. I think, as I have thought for some time, that your intuitions are >> too conditioned by the probabilities of coin tosses in a single world. You >> slip single word intuitions into your criticisms of the many-worlds picture. >> >> He asserts “After N trials, the multiverse contains 2 N branches, >> corresponding to all 2 N possible binary string >> outcomes." which is not true if pushing the red button produces 0 or 1 with >> some fixed probability p0 (which isn't made clear). >> >> It is true, whatever the probability associated with pushing the red button. >> And, in the case I consider, there simply is no matter-of-fact about such >> probabilities. > > I took, " Suppose too that the inhabitants believe (correctly) that this is a > series of independent identical experiments," to mean there there is some > unknown, but fixed probability of writing a 0 or 1. Otherwise I don't know > what "independent identical" means? Those are commonly statistical terms. > >> When the button is pushed, two new worlds are created, one with a 0 written >> on its tape and the other with a 1. > > Which implies that number of 0's and 1's will be equal, though not along a > give tape. > >> The button is pushed afresh in each of the created worlds, so in each world, >> two new worlds are created. This give 2^N branches or worlds for N trials. >> And these worlds will contain tapes, one in each world, on which is written >> the binary string corresponding to the history of results for that world. So >> there are 2^N different binary strings; that exhausts the space of possible >> binary strings of length N. Unless you get hold of this fact, the rest >> probably will not make sense. >> >> Translate the red button into a Stern-Gerlach magnet measuring the x-spin of >> an ensemble of particles all prepared in a z-spin up eigenstate. If we >> record x-spin up as 0, and x-spin down as 1, we get exactly the same set of >> 2^N binary sequences after N trials, all sequences different, as we got from >> pushing the red button. The crunch comes when we rotate the S-G magnet by 10 >> degrees and repeat. We still get all possible 2^N binary strings -- the same >> set of strings as we found before, because this set of exhausts the space of >> N binary strings. If If you are still not convinced, rotate your S-G magnet >> by a further 20 degrees and repeat the N trials. Do you get any new binary >> strings? Of course not, the space of possible strings has already been >> exhausted. >> >> The message is clear, the data that any observer in any world can get is >> independent of the coefficients in the original expansion of the prepared >> state in an appropriate basis. The Born rule can have no relevance in >> many-worlds -- whether Everettian or not. >> >> >> There is nothing which guarantees that all sequences will occur in any >> finite sample. >> >> Think again, all 2^N sequences will occur in any set of N trials. > > OK, each time the button is pushed and two new worlds created, which are > identical in their records up to the current writing and in one world 0 is > added to the tape and in the other 1 is added to the tape. I understand that > is not consistent with observation. And that there is no mechanism described > in Everett's evolution to deviate from this. That's why I said that in order > to get the Born rule there must be many-worlds before the experiment which > are then divided, possibly unevenly, to produce the Born rule. > >> >> But I suppose we can pass over this noting that for large enough N it is >> highly probable, though not certain. >> >> He's right that the citizens of different branches of the multiverse will >> infer different values of p from their experiments. But isn't it also true >> that most of them will infer a value close to the true value. >> >> Close to the true value? Have you not grasped the point that in the red >> button case, there is no "true value". And whatever the coefficients in the >> original state, the majority of binary strings will have close to equal >> number of 0s and 1s -- that is just a fact about the binomial expansion. It >> says nothing about the "true value", because no such true value may exist. > > That's just metaphysical angst. 1/2 is as "true" a value as science can ever > infer. That's why I find these two paragraphs misleading: > > “Let’s consider further the perspective of inhabitants on a branch with > pN zero outcomes and > (1 − p)N one outcomes. They do not have the delusion that all observed > strings have the same > relative frequency as theirs: they understand that, given the hypothesis that > they live in a multiverse, > every binary string, and hence every relative frequency, will have been > observed by someone. So how > do they conclude that the theory that the weights are (p,1 − p) has > nonetheless been confirmed?. > Because they have concluded that the weights measure the importance of the > branches for theory > confimation. Since they believe they have learned that the weights are > (p,1−p), they conclude that a > branch with r zeros and (N −r) ones has importance p r (1−p) N−r . Summing > over all branches with > pN zeros and (1 − p)N ones, or very close to those frequencies, thus gives a > set of total importance > very close to 1; the remaining branches have total importance very close to > zero. So, on the set > of branches that dominate the importance measure, the theory that the weights > are (very close to) > (p,1 − p) is indeed correct. All is well! By definition, the important > branches are the ones that > matter for theory confimation. The theory is inded confirmed! > “The problem, of course, is that this reasoning applies equally well for > all the inhabitants, whatever > relative frequency p they see on their branch. All of them conclude that > their relative frequencies > represent (to very good approximation) the branching weights. All of them > conclude that their own > branches, together with those with identical or similar relative frequencies, > are the important ones > for theory confirmation. All of them thus happily conclude that their > theories have been confirmed. > And, recall, all of them are wrong: there are actually no branching weights.” > > The "all of them" who conclude a branch weighting very different from 0.5 > will be a vanishingly small fraction. The whole argument is "There will > necessarily be outliers and they can't tell they are outliers. Therefore > science is impossible because we can never be certain we are not misled into > seeing patterns were none exist." > >> And the fact that 50/50 seems to be obtained on the majority of branches is >> true, even if the true probabilities are 0.99 and 0.01. > > But you postulated that every time a 0 is printed on a tape, a 1 is printed > of the other world's tape. So every tape will be a branching graph with 0 > and 1 at each branch point. Almost all paths thru this tree will have > approximately equal numbers of 0s and 1s per the binomial theorem. Each path > corresponds to an experimenter. So almost all experimenters will estimate > P(0)=P(1)=0.5 or nearly so. > >> >> >> And the larger is N, the greater the percentage of branches within a small >> interval around the true value. Are there some branches in which the >> citizen infer values very different from the true value p0? Sure. But in a >> single world where N experiments have been performed to use in estimating p, >> there is a probability that some value far from p0 will be observed. >> >> >> This is where you fall back on your single-world intuitions about >> probability. You have to get away from this, those intuitions fail in the >> many-worlds case. >> >> This is untrue: "In the many-worlds case, recall, all observers are aware >> that other observers with other data must exist, but each is led to >> construct a spurious measure of importance that favours their own >> observations against the others" If they have any understanding of >> statistics they will infer that it is highly probable that most other >> universes obtained a value close to theirs. >> >> >> That is rather like Bruno's "frequency operator". Sure, they infer that it >> is highly probable that most other universes obtained a value close to >> theirs -- that is another simple property of the binomial expansion. But >> everyone infers this -- even those with widely disparate observed relative >> frequencies. They can't all be right, so the inference along these lines >> that any individual makes is clearly wrong. >> >> Of course some of them will be wrong about that...some of them will be >> outliers. >> >> How do they know that they are outliers? Or how can you even define an >> "outlier" when there is no underlying probability -- as in Bruno's WM >> duplication scenario. >> >> >> So Kent's argument is really that in a universe with randomness we can never >> be sure we're not an outlier. But as Ring Lardner would say, "But that's >> the way to bet." >> >> You are basing probabilities on a one-world model again. You can't really >> mean that everyone in the two-outcome case should bet 50/50, regardless of >> the data? > > No. I'm arguing they should bet p/(1-p) for whatever p they observe. It's > inductive inference. > > Note that this exact same argument could be made in which there is a "true > value" p=0.5. Would you then conclude that it is impossible to > experimentally infer p=0.5? > > That is not to say I don't agree with the point that for MWI to work the > value of p must depend on the prepared system; which brings me back to the > idea there must be many (infinitely many) branches or weights which just get > divided proportionately at measurement. It must be MW+Born.
I am rather OK with this. I would have said MW + Gleason, but that is a detail. I think Bruce has a problem with the self-duplication already (independently of QM). I will try to answer his posts on this. Bruno > > Brent > >> >> Bruce >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] >> <mailto:[email protected]>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/CAFxXSLS2nP%3DO%3Dr0VT1n3N%3DUpPjEMyQ7rwHUo3ibZdVwkmUjUyA%40mail.gmail.com >> >> <https://groups.google.com/d/msgid/everything-list/CAFxXSLS2nP%3DO%3Dr0VT1n3N%3DUpPjEMyQ7rwHUo3ibZdVwkmUjUyA%40mail.gmail.com?utm_medium=email&utm_source=footer>. > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/8633a1ea-8c53-e465-3927-d12fe484ee27%40verizon.net > > <https://groups.google.com/d/msgid/everything-list/8633a1ea-8c53-e465-3927-d12fe484ee27%40verizon.net?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/22DA68C5-4E02-4AA1-8BEA-5080587B6E12%40ulb.ac.be.
