Mathematicians who call themselves ultrafinitists think that extremely large numbers are holding back science, from logic to cosmology, and they have a radical plan to do something about it
Huge numbers are exceedingly common, but counting particles is the wrong way to find them. Combinatorics is where the real monster hunting lies. When you start calculating complex probabilities or numbers of possible arrangements of things, that’s where the squirrels boundary between “infinite” and “really, really, really finitely big” starts to blur.
I think looking to CompSci is the right move, but I still don’t see many folks discussing computational complexity as a real, mathematical limit. We often treat two equal statements as though theres an immediate, single-step, jump between them. But discovering the equality requires computation/calculation. Shannon shows that information and entropy are the same thing. Computation is the process by which information is created. Ultrafinitist need to show that there is a finite quantity of information, which I don’t think is true or possible.
Two things occurred to me reading this: