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 <ledbetterg....domain.name.hidden>
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
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Received on Wed Jan 23 2008 - 18:43:04 PST