On 2/21/2020 2:41 AM, Bruce Kellett wrote:
On Fri, Feb 21, 2020 at 9:30 PM Bruno Marchal <[email protected] <mailto:[email protected]>> wrote:On 21 Feb 2020, at 04:40, Bruce Kellett <[email protected] <mailto:[email protected]>> wrote:From: *Brent Meeker* <[email protected] <mailto:[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.
In the limit N->oo almost all worlds will observe results arbitrarily close to the expected value. So why isn't that enough for statistical inference? One path thru the binomial branches of the MW is just like one sequence of bernoulli trials in a single world in terms of its statistics? Or are you considering cases where p>0.5, so that simple one branch per result doesn't work?
Brent -- 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/adf1bf17-e696-31f1-6069-6a112210ae88%40verizon.net.
