Finding pi and G in Mathland
This post is a Cunningham's law draft, c. 75% finished. Consider a) waiting until this notice has disappeared to read a more coherent post, or b) criticizing it with a focus on what would be right, not just what is wrong.Science explains physical phenomena through mathematical theories. If an explanation is true,[1] the physical phenomena form a model[2] of the mathematical theory. Because mathematicians explore theories independently of their connection to our universe, it creates the false impression that the only direction relevant for science (and thus for the real world) goes from physical phenomena to theories: one finds the mathematical theories that describe our universe by abstracting from physical phenomena. Mathematicians might occasionally find theories that are relevant for not yet discovered / understood physical phenomena, but the relevant link (according to this wrong view) goes from those physical phenomena (once understood) to the mathematical theory.However, not all mathematical theories are equal. In "Mathland", each of them sits next to (usually infinitely many) other similar but (potentially infinitesimally) different theories. A question that can be asked is: inside Mathland, how visible is a theory?Let's start with a simpler case: how visible is pi? That depends on where in Mathland we are. If we are in the regions with all the possibles series of the form mjx-container[jax="CHTML"] { line-height: 0; } mjx-container [space="1"] { margin-left: .111em; } mjx-container [space="2"] { margin-left: .167em; } mjx-container [space="3"] { margin-left: .222em; } mjx-container [space="4"] { margin-left: .278em; } mjx-container [space="5"] { margin-left: .333em; } mjx-container [rspace="1"] { margin-right: .111em; } mjx-container [rspace="2"] { margin-right: .167em; } mjx-container [rspace="3"] { margin-right: .222em; } mjx-container [rspace="4"] { margin-right: .278em; } mjx-container [rspace="5"] { margin-right: .333em; } mjx-container [size="s"] { fon