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
> 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?