On Sat, Feb 8, 2020 at 5:23 AM Bruno Marchal <[email protected]> wrote:
> On 7 Feb 2020, at 05:59, Bruce Kellett <[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. 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. > > 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. Since no meaningful concept of probability applies when all outcome are guaranteed to happen, 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. 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