Math is not physics. I'm not sure what math is. I kind of like Gisin's support of intuitive math. I agree that the next billion digits of pi mean nothing real, also that there should be some constructivist dimension to the infinities in math (e.g. renormalization).

11y

Oh, and statistics is not math, it's physics. You can test the results of
statistics against the real world, but math is merely consistent.

We are free to think we are free. Freedom is the opiate of the optimists, so be sour and you will be free of freedom.

Regarding digits of pi, N. Gisin promotes the constructivist idea that certain mathematical expressions mean nothing in that they do not relate to anything real. One cannot make a scientific hypothesis involving them. The hundred-billionth twenty digit sequence of pi is smaller than the Plank length.

22y

There's still a well-defined answer to the question of what the digits mean, and
indeed of what they mean as digits of pi; e.g., the hundred-billionth digit of
pi is what you get by carrying out a pi-computing algorithm and looking at the
hundred-billionth digit of its output. Anyway, no one is memorizing that many
digits of pi.
[EDITED to add:] On the other hand, people certainly memorize enough digits of
pi that, e.g., an error in the last digit they memorize would make a
sub-Planck-length difference to the length of a (euclidean-planar) circle whose
diameter is that of the observable universe. (Size of observable universe is
tens of billions of light-years; a year is 3x10^7 seconds so that's say 10^18
light-seconds; light travels at 3x10^8 m/s so that's < 10^27m; I forget just how
short the Planck length is but I'm pretty sure it's > 10^-50m; so 80 digits
should be enough, and even I have memorized that many digits of pi (and
forgotten many of them again).

Try books by Gerd Gigerenzer (search on Amazon). I particularly like his Empire of Chance, about different schools of probability analysis. Bounded Rationality is pretty good, too. The difference between Gigerenzer's and Tversky's attitudes is not particularly impressive (they apparently hate each other, even though one is dead). One is decision making when in a hurry (Gigerenzer) and the other is decision-making with insufficient data (Tversky) (or maybe it's the other way around, tedious stuff). Discussions of biases is fascinating by both authors.

12y

Thanks

Oh, and statistics is not math, it's physics. You can test the results of statistics against the real world, but math is merely consistent.