Jerry Clark wrote: > > > > > Let R be the ratio of blue to green SAS's, R = b/g. I want to compute > > the probability distribution as a function of R on the domain [0,1]: > > > > I'm assuming you mean 'R = b/(b+g)'...

Right. Thanks! > > > > P(R) P(1 blue | R) > > P(R | 1 blue) = ---------------------- > > P(1 blue) > > > > Now, P(R) is the prior, and I said above that the assumption is that > > this is constant over [0,1], and P(1 blue) = 50%, so P(R)/P(1 blue) is > > a constant, and is just a normalizing factor. > > > > Clearly, P(1 blue | R) = R. Therefore, with the normalizing condition > > that the integral of P from 0 to 1 = 1, we get > > > > P(R | 1 blue) = 2R > > > > Which has an expection value for R of 2/3. That is, given a sample of > > one blue SAS, and the prior mentioned above, I would compute that the > > probablity of any SAS being blue is 2/3. > > > > > > > > > > > > > So if the set of life-SAS's is not isomorphic to the set of (3+1 > > > > dim. pseudo-Riemannian manifold quantum field)-SAS's, then we'd > > > > have no a priori reason to assume that the measures of these sets > > > > are the same. If the measures are different, then one is larger > > > > than the other. My money will be on our set having the larger > > > > measure. If the measures > > > > are transfinite but of different orders, then I conclude that the > > > > probability of finding oneself to be a life-SAS is zero. > > > > I stand by this. Note that I explicitly give a new prior: *if* the > > measures of each set are of different orders of transfinite numbers. > > Using blue and green again, that would mean that either R=0 or R=1. > > > > We still have the ratio of prior probabilities, P(R)/P(1 blue), is a > > constant. But now P(1 blue|R=0) = 0, and P(1 blue|R=1) = 1. The > > normalization integral becomes a sum, and we get, simply, > > > > P(R=0 | 1 blue) = 0 > > P(R=1 | 1 blue) = 1 > > > > Which is pretty easy to interpret. > > Jerry -- Chris Maloney http://www.chrismaloney.com "Donuts are so sweet and tasty." -- Homer Simpson