On Sat, Feb 15, 2020 at 3:17 PM 'Brent Meeker' via Everything List < [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. When the button is pushed, two new worlds are created, one with a 0 written on its tape and the other with a 1. 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. 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. 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. > 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? 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