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The Doomsday argument in a nutshell
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The Doomsday argument was conceived by the astrophysicist Brandon Carter some fifteen years ago, and it has since been developed in a Nature article by Richard Gott [1993], and in several papers by philosopher John Leslie and especially in his recent monograph The End of The World (Leslie [1996]). The core idea is this. 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). But now consider the case where instead of the urns you have two possible human races, and instead of balls you have individuals, ranked according to birth order. As a matter of fact, you happen to find that your rank is about sixty billion. Now, say Carter and Leslie, we should reason in the same way as we did with the urns. That you should have a rank of sixty billion or so is much more likely if only 100 billion persons will ever have lived than if there will be many trillion persons. Therefore, by Bayes' theorem, you should update your beliefs about mankind's prospects and realise that an impending doomsday is much more probable than you have hitherto thought.
Consider the objection: "But isn't the probability that I will have any given rank always lower the more persons there will have been? I must be unusual in some respects, and any particular rank number would be highly improbable; but surely that cannot be used as an argument to show that there are probably only a few persons?"
In order for a probability shift to occur, you have to conditionalise on evidence that is more probable on one hypothesis than on the other. When you consider your rank in the DA, the only fact about that number that is relevant is that it is lower than the total number of individuals that would have existed in either hypothesis, while for all you knew, it could have turned out to be a number higher than the total number of people that would have lived on one of the hypothesis, thereby refuting that hypothesis. It makes no difference whether you perform the calculation with a specific rank or an interval within which the true rank lies. The Bayesian calculation turns out the same posterior probability. The fact that you discover that you have this particular rank value gives you information only because you didn't know that you wouldn't discover a rank value that would have been incompatible with the hypothesis that there would have existed but few individuals. It is presupposed that you knew what rank values were compatible with which hypothesis. It is true that for any particular rank number, finding that you have that rank number is an improbable event, but a probability shift occurs not because of its improbability per se, but because of the difference between its conditional probabilities relative to either of the two hypotheses.
There are numerous objections such as this one, objections that can easily be seen to be mistaken. When people first encounter the Doomsday argument (hereafter the DA), what happens is that most of them think that it is obviously false. Then any sign of consensus disappears when it comes to explaining what is wrong with it. Each comes up with his own objection, these objections tend to be incompatible with each other, and typically they rest on simple misunderstandings. This paper will zoom in on those features of the DA that are genuinely problematic.
More:
www.anthropic-principle.com/prep....html
www.anthropic-principle.com/prep....html
The Doomsday argument was conceived by the astrophysicist Brandon Carter some fifteen years ago, and it has since been developed in a Nature article by Richard Gott [1993], and in several papers by philosopher John Leslie and especially in his recent monograph The End of The World (Leslie [1996]). The core idea is this. 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). But now consider the case where instead of the urns you have two possible human races, and instead of balls you have individuals, ranked according to birth order. As a matter of fact, you happen to find that your rank is about sixty billion. Now, say Carter and Leslie, we should reason in the same way as we did with the urns. That you should have a rank of sixty billion or so is much more likely if only 100 billion persons will ever have lived than if there will be many trillion persons. Therefore, by Bayes' theorem, you should update your beliefs about mankind's prospects and realise that an impending doomsday is much more probable than you have hitherto thought.
Consider the objection: "But isn't the probability that I will have any given rank always lower the more persons there will have been? I must be unusual in some respects, and any particular rank number would be highly improbable; but surely that cannot be used as an argument to show that there are probably only a few persons?"
In order for a probability shift to occur, you have to conditionalise on evidence that is more probable on one hypothesis than on the other. When you consider your rank in the DA, the only fact about that number that is relevant is that it is lower than the total number of individuals that would have existed in either hypothesis, while for all you knew, it could have turned out to be a number higher than the total number of people that would have lived on one of the hypothesis, thereby refuting that hypothesis. It makes no difference whether you perform the calculation with a specific rank or an interval within which the true rank lies. The Bayesian calculation turns out the same posterior probability. The fact that you discover that you have this particular rank value gives you information only because you didn't know that you wouldn't discover a rank value that would have been incompatible with the hypothesis that there would have existed but few individuals. It is presupposed that you knew what rank values were compatible with which hypothesis. It is true that for any particular rank number, finding that you have that rank number is an improbable event, but a probability shift occurs not because of its improbability per se, but because of the difference between its conditional probabilities relative to either of the two hypotheses.
There are numerous objections such as this one, objections that can easily be seen to be mistaken. When people first encounter the Doomsday argument (hereafter the DA), what happens is that most of them think that it is obviously false. Then any sign of consensus disappears when it comes to explaining what is wrong with it. Each comes up with his own objection, these objections tend to be incompatible with each other, and typically they rest on simple misunderstandings. This paper will zoom in on those features of the DA that are genuinely problematic.
More:
www.anthropic-principle.com/prep....html
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