Re: practical reasoning and strong SSA

From: <hal.domain.name.hidden>
Date: Tue, 1 Jun 1999 20:59:47 -0700

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
Received on Tue Jun 01 1999 - 20:59:48 PDT