I trust Solomonoff induction as being pretty theoretically sound. The typical number takes around log(n)+log(log(n)) bits to express, as you have to say how many bits you are using to express the number. Some numbers, like Graham’s number can be expressed with far fewer bits. I think that theories are a useful conceptual tool for bundling hypothesis about series of observations, and that T1 and T2 are equally likely.
I trust Solomonoff induction as being pretty theoretically sound. The typical number takes around log(n)+log(log(n)) bits to express, as you have to say how many bits you are using to express the number. Some numbers, like Graham’s number can be expressed with far fewer bits. I think that theories are a useful conceptual tool for bundling hypothesis about series of observations, and that T1 and T2 are equally likely.
Good catch—I’m missing some extra factors of 2 (on average).
And gosh, I expected more people defending the anthropics side of the dilemma here.