Wei Dai writes: > When I learn a new way to thinking I tend to forget how to think the old > way. I just typed into Mathematica "N[Pi]" and it displayed to me > "3.14159". So I think that gives me reason to believe the first 6 digits > in the decimal expansion of Pi is 3.14159 because if it wasn't the case > my current experience would be very atypical. More formally, the > probability that I am reading "N[Pi] = 3.14159" given that the first 6 > digits of Pi is not 3.14159 is very small compared to the probability that > I am reading "N[Pi] = 3.14159" given that the first 6 digits of Pi IS > 3.14159.
> This and similar kinds of reasoning depend on the Strong SSA (as defined > by Hal and Nick). I don't follow where the dependence on SSSA comes from. This is the assumption that each observer-moment should be considered as a random selection from all observer-moments in the universe (broadly defined). Your example would seem to be classical Bayesian reasoning. A priori you don't know whether the sixth digit of pi is a 9, so you give that 1/10 probability. After seeing Mathematica's output, you estimate the probability that it would say it is a 9 when the actual digit is not a 9 (i.e. make a mistake), which is very small. You feed that into the Bayes formula and end up with a strong probability that the sixth digit is 9. Are you saying that Bayesian analysis depends on the Strong SSA? Could you elaborate on this? Hal
