On Sun, Mar 08, 2020 at 06:50:52PM +1100, Bruce Kellett wrote: > On Sun, Mar 8, 2020 at 5:32 PM Russell Standish <[email protected]> wrote: > > On Fri, Mar 06, 2020 at 10:44:37AM +1100, Bruce Kellett wrote: > > > That is, in fact, false. It does not generate the same strings as > flipping a > > coin in single world. Sure, each of the strings in Everett could have > been > > obtained from coin flips -- but then the probability of a sequence of > 10,000 > > heads is very low, whereas in many-worlds you are guaranteed that one > observer > > will obtain this sequence. There is a profound difference between the > two > > cases. > > You have made this statement multiple times, and it appears to be at > the heart of our disagreement. I don't see what the profound > difference is. > > If I select a subset from the set of all strings of length N, for example > all strings with exactly N/3 1s, then I get a quite specific value for the > proportion of the whole that match it: > > / N \ > | | 2^{-N} = p. > \N/3/ > > Now this number p will also equal the probability of seeing exactly > N/3 coins land head up when N coins are tossed. > > What is the profound difference? > > > > Take a more extreme case. The probability of getting 1000 heads on 1000 coin > tosses is 1/2^1000. > If you measure the spin components of an ensemble of identical spin-half > particles, there will certainly be one observer who sees 1000 spin-up results. > That is the difference -- the difference between probability of 1/2^1000 and a > probability of one. > > In fact in a recent podcast by Sean Carroll (that has been discussed on the > list previously), he makes the statement that this rare event (with > probability > p = 1/2^1000) certainly occurs. In other words, he is claiming that the > probability is both 1/2^1000 and one. That this is a flat contradiction > appears > to escape him. The difference in probabilities between coin tosses and > Everettian measurements couldn't be more stark.
That is because you're talking about different things. The rare event that 1 in 2^1000 observers see certainly occurs. In this case certainty does not refer to probability 1, as no probabilities are applicable in that 3p picture. Probabilities in the MWI sense refers to what an observer will see next, it is a 1p concept. And that 1p context, I do not see any difference in how probabilities are interpreted, nor in their numerical values. Perhaps Caroll is being sloppy. If so, I would think that could be forgiven. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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/20200308084635.GD2903%40zen.
