Re: Several Criticisms of the Doomsday Argument
Günther Greindl [EMAIL PROTECTED] wrote: 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. Agreed. Also consider another version: do not name the balls in the first urn 1 to 10, but with uniform random numbers of the interval [1,100]. Then, if you would draw the ball 517012 you would not know from which urn it was either. It is definitely a labeling artefact. Agreed. 8-) Gene Ledbetter - Get easy, one-click access to your favorites. Make Yahoo! your homepage. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Several Criticisms of the Doomsday Argument
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) = 0.90). 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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Why wasn't I born there instead of here?
In another thread Rolf mentioned a variant of the Doomsday Argument where the universe is infinite: ...This variant DA asks, if there's currently a Galactic Empire 1 Hubble Volumes away with an immensely large number of people, why wasn't I born there instead of here? The implication of the question seems to be that the questioner (Q) could have been born in either of the two populations at random, and, assuming the number of people in the Galactic Empire is sufficiently immense, the probability that he could have been born on Earth is close to nil. But Q could not have been born in either of the two populations; he could only have been born on Earth, and his failure to realize this suggests that he has ignored his own material and biological nature. Q is a material object and a living organism. He is composed of atoms from Earth's interior that could in no way be part of a remote Galactic Empire. Q's birth occurred because humans reproduce sexually, and his birth occurred on Earth because his parents lived on Earth. Q could not have been born in the Galactic Empire because he could not have been born anywhere but on Earth. If Q could only have been born on Earth, then the probability that he would have been born on Earth is 100%. The answer to Q's question, ...why wasn't I born there instead of here?, is that the probability of his having been born there is 0%. Gene Ledbetter - Get easy, one-click access to your favorites. Make Yahoo! your homepage. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Introduction
Hello, I came upon this group entirely by chance and concluded that I had somehow found evidence of Intelligent Life on the Internet. I had been doing an Internet search on memory in single-celled organisms, such as the amoeba. Amoebas seem to move purposefully, which would suggest that they have at least one rudimentary sensory organ and some kind of memory. My search was not fruitful, except that it found a 'hit' in one of the discussions in this group. Fortunately, I do not possess any specialized knowledge that you would not understand, so this introduction is really unnecessary. I am retired from a university laboratory and have done a little reading in logic after retirement. It is possible that I might contribute here occasionally when I notice some point that seems susceptible to simple logical analysis. Gene Ledbetter --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---