> On 7 Feb 2020, at 23:36, Bruce Kellett <[email protected]> wrote: > > On Sat, Feb 8, 2020 at 5:23 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > On 7 Feb 2020, at 05:59, Bruce Kellett <[email protected] > <mailto:[email protected]>> wrote: >> >> "After N trials, the multiverse contains 2^N branches, corresponding to all >> 2^N possible binary string outcomes. The inhabitants on a string with pN >> zero and (1 - p)N one outcomes will, with a degree of confidence that tends >> towards one as N gets large, tend to conclude that the weight 'p' is >> attached to zero outcome branches and weight (1 - p) is attached to one >> outcome branches. In other words, everyone, no matter what string they see, >> tends towards complete confidence in the belief that the relative >> frequencies they observe represent the weights. >> >> "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.” >> > I do not understand. If the multiverse is that sort of many classical world, > with the machine giving all outputs somewhere, the correct weighting will be > the one given by Pascal Binomial. That comes already with the fact that we > get all 2^N strings. I might have miss something. > > You certainly have. The argument that output strings that give results > inconsistent with your observations have vanishing measure overall -- an > argument based on the Pascal Binomial and the law of large numbers -- applies > equally to all observers, whatever output string they observe. So whatever > data you observe, you conclude that the theory that is consistent with that > data is confirmed by the data.
Only if confirmed by my peers. Take the iterated WM self-duplication, after 100 iterations, there is guy who will claim that his prediction is determined by the binary decimals of Pi, another that his prediction is “only W”, etc, but they have to convince their peers? In science, we cannot take any personal experience has confirming anything (except the quasi empty “theory" of self-consciousness). The vast majority of the resulting person will consider that they have no algorithm of prediction, as the majority of sequences will be incompressible, and so P = 1/2 will be used for the practical purpose. > Which is useless, because you reach that conclusion whatever data you > observe. The law of large numbers fails you when all possible outcomes are > observed by someone or the other. Yes, it fails me, but not the collectivity. > > > > Do you agree that in the iterated self- (WM)-duplication, the measure is just > the normal distribution? > > No. As I have said before, no meaningful concept of probability can be > applied in the WM-duplication case. But that is refuted by almost all first person (singular or plural) diaries. The same with a quantum lottery. Despite I am the big winner in some world, I remain a loser in most worlds, and that is what needed to be taken into account. Your probability one idea is refuted after one experience. A prediction is considered correct when all the participants agree. That happen with the predictionP( “W v M”) = 1 only, and is reftuetd by any prediction of the type “W”, or “M”, and of course still more in “W and M”, as this never occur (the letter W and M does not represent cities, but “first person experiences of self-localisation”). > Since no meaningful concept of probability applies when all outcome are > guaranteed to happen, All outcome are guaranteed to happen in the big 3p picture, but only one outcome happen in all first person experiences. Bruno > no probability measure can be assigned. > > >> This argument from Kent completely destroys Everett's attempt to derive the >> Born rule from his many-worlds approach to quantum mechanics. In fact, it >> totally undermines most attempts to derive the Born rule from any branching >> theory, and undermines attempts to justify ignoring branches on which the >> Born rule weights are disconfirmed. >> > They normally just get relatively rare. > > It is the attempted proof of this that breaks down when all outcomes are > guaranteed to occur. > >> 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', and this leads to an obvious absurdity. In the one-world case, >> observers treat what actually happened as important, and ignore what didn't >> happen: this doesn't lead to the same difficulty. >> > > With Mechanism (used in Darwin) I don’t see how we can evacuate that the > prediction are given by relative (even conditional) measure, on all > computations. > > This has nothing to do with mechanism: it is simple an observation about > Everettian quantum mechanics. If you want to talk about some other theory, > such as mechanism, we can do that. But I think mechanism fails at step 3 for > reasons similar to those that undermine Everett. > > 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/CAFxXSLT-MvW8DpXAS4i6WHRotdp2ZYzon2dDJrohGGDBJ3zdVA%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAFxXSLT-MvW8DpXAS4i6WHRotdp2ZYzon2dDJrohGGDBJ3zdVA%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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/7597FEF7-F84C-43F6-B2E5-C2C247147389%40ulb.ac.be.
