Modern "Set Theory" - is it a religious belief system? by Dr. N. Wildberger
Some of us who study the Bucky stuff are likewise attracted to the mathematical research of Dr. N. Wildberger.
Why? Because he is:
(A) not afraid to talk about Foundations and
(B) questions the ones a lot of us grew up with in the 1900s.
At one point he says explicitly that his questioning of the dogma that Set Theory somehow provides logical underpinnings, is deliberately designed to bring mathematics more into alignment with computer science, wherein the Set is one data structure among many.
Furthermore, computer science is resolutely discrete and content with Finitude, at least in some circles. Dr. Wildberger is, philosophically speaking, a Finitist.
What I anticipate is the unwillingness of mathematics faculties to take on Learning to Code at the high school level is going to result in a corresponding loss of influence when it comes to preaching, I mean teaching, about mathematical foundations.
Are we so sure we need "infinity" as a central concept then?
Years ago, the National Council of Teachers of Mathematics (NCTM) changed its logo from something promising, an octet truss looking thing, to an infinity symbol. This could be interpreted as a symbol of self defeat, as we leave Cantor dust in the dust, so to speak.
What's missing in our selection of a coordinate system is a sense of its frequency, scale, degree of resolution. The assumption is that any grid is immediately resting upon some continuum, that stable reality that makes "solids" solid.
Even if we don't find much justification for such a reality in physics, many still believe we're able to access this continuum through some third eye (the "mind's eye"), and therefore the continuum remains an object of mathematical study. I'm not saying it shouldn't be, only that said eye might be critical (in the sense of skeptical).
