This has been discussed on the list before. See my book Theory of Nothing, in particular page 88. Its available as a free download if you haven't bought a copy.

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Cheers On Wed, Jan 23, 2008 at 01:31:40PM -0800, Rosy At Random wrote: > > Hi, > > I'm just mulling this over in my head, but what effect do you guys > think a many worlds context would have on the Doomsday argument? There > seems to be an implicit assumption that we're _either_ in a universe > where the human race has a long future, _or_ we're not. The missing > possibility there, of course, being _and_. Here, we can't really just > compare balls from two urns, but from all possible urns in all > possible futures, no matter how many experiments we run. And quantum > immortality would seem to imply that we would find it very difficult > to make measurements that place us in imminent and unavoidable danger. > > Unfortunately, I'm not thinking straight enough right now to properly > consider it. > > Michael > > > > On Nov 27 2007, 1:54 am, Gene Ledbetter <[EMAIL PROTECTED]> > wrote: > > In his article, "Investigations into the Doomsday Argument", Nick > > Bostrom introduces the Doomsday Argument with the following example: > > > > << Imagine that two big urns are put in front of you, and you know > > that one of them contains ten balls and the other a million, but you > > are ignorant as to which is which. You know the balls in each urn are > > numbered 1, 2, 3, 4 ... etc. Now you take a ball at random from the > > left urn, and it is number 7. Clearly, this is a strong indication > > that that urn contains only ten balls. If originally the odds were > > fifty-fifty, a swift application of Bayes' theorem gives you the > > posterior probability that the left urn is the one with only ten > > balls. (Pposterior (L=10) = 0.999990). >> > > > > The Use of Unnumbered Balls > > > > Let us first consider the case where the balls are not numbered. We > > remove a ball from the left urn, and we wonder whether it came from > > the urn containing ten balls or from the urn containing one million > > balls. > > > > The ball was chosen at random from one of the two urns. Therefore, > > there is a 50% probability that it came from either urn. It is > > important to realize that this probability is based on the number of > > urns, not the number of balls in each urn, which could be any number > > greater than zero. > > > > There is nothing here to suggest a statistical limitation on the > > maximum size of a group of balls. > > > > The Use of Numbered Balls > > > > Since the statistical limitation proposed by the Doomsday Argument is > > not apparent with unnumbered balls, it may be a consequence of > > numbering the balls. > > > > The balls in the ten-ball urn have been numbered according to the > > series of integers used to count ten objects (1, 2, 3, 4, 5, 6, 7, 8, > > 9, 10). The fact that each of these integers has been written on one > > of the balls suggests that the balls have been counted in the order > > indicated by the numbers. But if the balls had been counted in any of > > numerous other different orders, the sum would have always been the > > same, so the actual order used is of no significance. > > > > Furthermore, if the physical distribution of the balls in the urn had > > been arranged according to the series of integers written on the > > balls, their distribution would not be at all random. If we imagine a > > column of balls in each urn, ranging from 1 to 10 and from 1 to > > 1,000,000, the first ball selected at random from the two urns would > > be numbered either 10 or 1,000,000. But we know from the statement of > > Bostrom's example that the balls are arranged at random within the > > urns. > > > > Naming the Balls Uniquely > > > > If the order in which the balls were counted is not significant, and > > the balls have not been arranged physically in the order in which they > > were counted, the numbers on the balls could still be used to identify > > each ball uniquely, i.e., to give each ball a unique name. This idea > > is supported by the fact that Bostrom wonders whether the ball 7 > > selected at random is the ball 7 from one urn or the other. > > > > Because of the naming scheme used in the example, we could be certain > > that any ball with a number greater than 10 came from the million-ball > > urn. But the naming scheme has the flaw that it provides ambiguous > > names for balls 1 through 10, which are found in both urns. It is, I > > believe, this ambiguity in the naming of the balls that produces the > > statistical result mentioned by Bostrom. The very same effect could be > > produced by filling both urns with unnumbered white balls, except for > > a single unnumbered blue ball in each urn. The two blue balls would > > produce the same statistical effect as the two ball 7's. > > > > If all of the balls had been numbered unambiguously from 1 through > > 1,000,010, the statistical effect produced by Bostrom's ambiguous ball > > 7 would vanish. > > > > Gene Ledbetter > > -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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