On Fri, Feb 21, 2020 at 9:30 PM Bruno Marchal <[email protected]> wrote:
> On 21 Feb 2020, at 04:40, Bruce Kellett <[email protected]> wrote: > > From: Brent Meeker <[email protected]> > > Of course that's true. But the more relevant value is the fraction of > sequences with the proportion of 1s within some narrow range of 0.5. For > large N, the distribution is Gaussian with std deviation ~sqrt(N) so almost > equal numbers of 1s and 0s do predominate. > > > I was aware of that, but they only dominate in a narrow range when p = > 0.5. My thinking was that since the confidence interval around the > estimated probability shrinks as 1/sqrt(N) for large N, outside a small > range of small deviations from equal numbers of zeros and ones, the > confidence interval on the probability estimates would no longer capture p > = 0.5. Also, looking at numbers of zeros within +- a small number of N/2 > would give results for the asymptotic proportion similar to those for N/2 > zeros. Since my calculation systematically ignores factors of the order of > one, I doubt that including such bit strings with close to equal numbers of > zeros and ones would make any significant difference to the conclusion that > such strings do not dominate in the limit. In other words, I think my > conclusion that the majority of the 2^N observers would not estimate > probabilities close to 0.5 is secure. (Ignoring factors of order one in the > calculation!) > > > But that argument would work for coin tossing too. That eliminate > basically all probabilistic inference, it seems to me. A dwarf and a giant > would not accept the Gaussian distribution of height. > You still don't get it, do you? The argument applies to all possible bit strings of length N. You do not get that from coin tosses in a single world. It is only when you claim that all possible results exist in separate branching worlds that the problem arises. So it is a problem for your WM-duplication, and for Everett. But not for single world theories. Statistical inference is perfectly intact as it is used in this world. 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQn1RdydCW73F6_P-je1DgeVG97TOydHRK5ttbCNkg63A%40mail.gmail.com.
