But, Turing wrote exactly the opposite in his article: “A number which is a description number of a *circle-free machine* will be called a satisfactory number”.

A circular machine being a machine that gets stuck or loops forever without printing symbols of interest (aka “figures” in Turing’s article).

]]>https://archive.bridgesmathart.org/2010/bridges2010-111.pdf

Gerdes has other relevant papers.

]]>[1] https://github.com/sanketsudake/spm

[2] https://github.com/sanketsudake/spm/blob/fb6d62674831acb2ddac4c5dddce24b2d2c89caa/src/detectball.cpp#L179

The late Edward Nelson has a number of papers discussing potential and actual infinity on his personal page https://web.math.princeton.edu/~nelson/papers.html

One could look at https://web.math.princeton.edu/~nelson/papers/warn.pdf

]]>There’s a reference to the formula here: https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

It converges quite slowly, but it does indeed converge to π.

]]>It starts with 4 – 4/3. I think you’re reading the subtractions as multiplications?

]]>