On Thu, Jun 12, 2008 at 11:43:26PM +0200, Günther Greindl wrote: > > Hi all, > > someone on another list alerted me to this post, there is a very > interesting discussion going on on that blog related to Observer Moments: > > http://golem.ph.utexas.edu/category/2008/06/urban_myths_in_contemporary_co.html > > Greg Egan has posted too; and has some very interesting things to say. > Specifically, he says the right things why DA fails:

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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\u2019re able to extract the following (somewhat fanciful) predictions: theory A implies that in the entire history of the universe, there will be 1050 observers* of class 1 and 105000 observers of class 2, while theory B implies that in the entire history of the universe, there will be 105000 observers of class 1 and 1050 observers of class 2." Now we further suppose there is no reason to prefer theory A over B, ie p(A)=p(B). Then we need to compute the likelihood of theory A given the fact that we're an observer of class 2, ie: p(A|2) = p(A & 2) / p(2) = p(2|A) p(A) / p(2) ... (1) and p(B|2) = p(B & 2) / p(2) = p(2|B) p(B) / p(2) ... (2) dividing (1) by (2) gives p(A|2) / p(B|2) = p(2|A) / p(2|B) = (1-e) / e = 10^{4050} ie Bayes' theorem most definitely implies theory A is overwhelmingly supported. Have I missed something, or is Greg Egan wrong? In a later posting, he gives absurd example of some extremely improbably theory A, and applying the above reasoning. Yet the above reasoning assumes p(A)=p(B), which is not the case in his absurd example. It may be relevant to the BB argument though. If theory A was "we are a statistical fluctuation (ie Boltzmann brains)", and theory B was "evolved by Darwinian evolution", then p(A) << p(B). One cannot comment on whether one should prefer A or B, since the numerical values are just pulled out of a hat in any case. -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---