Many on this list have discussed the anthropic principle. It essentially says that the conditional probability of finding yourself in a universe compatible with your existence equals 1.
But unfortunately the anthropic principle does not have any predictive power. It does NOT predict there won't be any flying rabbits tomorrow. Clearly we need more than the anthropic principle to explain the predictability of our universe. In particular, we need an optimal way of predicting the future, given past observations. And there is one! Normally we do not know the true conditional probability distribution p(next event | past). But assume we do know that p is in some set P of distributions. Choose a fixed weight w_q for each q in P such that the w_q add up to 1 (for simplicity, let P be countable). Then construct the Bayesmix M(x) = Sum_q w_q q(x), and predict using M instead of the optimal but unknown p. How wrong is it to do that? The recent exciting work of my postdoc Marcus Hutter (IDSIA) provides general and sharp (!) loss bounds: Let LM(n) and Lp(n) be the total expected losses of the M-predictor and the p-predictor, respectively, for the first n events. Then LM(n)-Lp(n) is at most of the order of sqrt[Lp(n)]. That is, M is not much worse than p. And in general, no other predictor can do better than that! In particular, if p is deterministic, then the M-predictor soon won't make any errors any more. If P contains ALL recursively computable distributions, then M becomes the celebrated enumerable universal prior. That is, after decades of somewhat stagnating research we now have sharp loss bounds for Solomonoff's universal (but incomputable) induction scheme. And if we also include the distributions computable in the limit, we get sharp loss bounds for the even more general priors introduced in "Algorithmic Theories of Everything": http://www.idsia.ch/~juergen/toesv2/ Similarly, if we replace M by the Speed Prior S - where S(x) is small if x is hard to compute by any method - we obtain appropriate loss bounds for computable S-based induction: http://www.idsia.ch/~juergen/toesv2/node32.html Alternatively, reduce M to what you get if you just add up weighted estimated future finance data probabilities generated by 1000 commercial stock-market prediction software packages. If only one of them happens to work fine (but you do not know which) you still should get rich. To learn more, please read Optimality of Universal Bayesian Sequence Prediction for General Loss and Alphabet: ftp://ftp.idsia.ch/pub/techrep/IDSIA-02-02.ps.gz and also check out Hutter's other recent papers at ICML, ECML, NIPS, Int. J. of Foundations of CS: www.idsia.ch/~marcus Juergen Schmidhuber http://www.idsia.ch/~juergen/
