On Jun 13, 9:25 am, Russell Standish <[EMAIL PROTECTED]> wrote: > I'm not sure his application of Bayes is correct. Given the facts of > his hypothetical scenario, and writing e=10^{-4050} > > p(1|A) = e > p(2|A) = 1-e > p(1|B) = 1-e > p(2|B) = e > > This is my translation of: > > "Now suppose that (somehow) we're able to extract the following (somewhat > fanciful) predictions: theory A implies that in the entire history of > the universe, there will be 10^50 observers* of class 1 and 10^5000 observers > of class 2, while theory B implies that in the entire history of >the universe, there will be 10^5000 observers of class 1 and 10^50 observers >of class 2."

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Hi Russell The p(2|A) you give above is the probability for selecting one observer at random from the totality of all observers throughout the history of the universe, and finding that he/she/it belongs to class 2 (given theory A). But no such selection process has taken place. Given that humans are class 2 observers, all we have is the fact H: H := "The number of class 2 observers in the history of the universe is at least of the order 10^10." (We could argue that this ought to be somewhat higher than 10^10, depending on how we classify our ancestors, but the point is that any reasonable number we pick will be less than 10^50. And of course this whole scenario is just a toy model for the sake of having a concrete example to discuss.) We then have: P(H|A) = P(H|B) = 1 P(A) = P(B) = 1/2 P(H) = P(A) P(H|A) + P(B) P(H|B) = 1 P(A|H) = P(H|A) P(A) / P(H) = 1/2 P(B|H) = P(H|B) P(B) / P(H) = 1/2 In other words, the data we have, expressed in the observation H, does nothing to discriminate between theory A and theory B, and leaves the initial prior probabilities unchanged. We, in the here and now, have no access to any process that randomly samples the set of all observers in the history of the universe. Of course it's possible to construct various sums over the set of *all* observers and seek to maximise some kind of global average, and to ask questions such as "What strategy, if adopted uniformly by every single observer in the history of the universe, would maximise the expectation value for the number of observers in the history of the universe who correctly guessed whether A or B was the true description of the universe." But whether or not there are any plausible scenarios in which maximising that number could be a desirable goal ... the fact remains that if we're discussing the *information* available to *us* -- the human population of Earth at the present moment -- we do not have access to the probabilities p(1|A), p(2|A), p(1|B), p(2|B) that you describe. The context in which I was discussing this at the N-Category Café is the claim by some cosmologists that we ought to favour A-type cosmological theories in which class 2 observers like us, with a clear Darwinian history, will not be outnumbered (over the whole history of the universe) by class 1 observers (Boltzmann brains). My contention is that we have no empirical data at the present time that tells us anything at all about the relative frequencies (over the whole history of the universe) of class 1 and class 2 observers, and that our own existence should not be mistaken for the outcome of a random sampling of that whole-of-spacetime population. These issues are discussed in more detail in: "Are We Typical?" by James Hartle and Mark Srednicki, http://arxiv.org/abs/0704.2630 --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---