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.
On Wed, Jan 23, 2008 at 01:31:40PM -0800, Rosy At Random wrote:
> 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.
> On Nov 27 2007, 1:54 am, Gene Ledbetter <[EMAIL PROTECTED]>
> > 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)
UNSW SYDNEY 2052 [EMAIL PROTECTED]
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