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.
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).
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.
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).