This use of dimensionality is unfamiliar to me. When I hear "a bunch of discrete points" to me that says most likely 2 or 3 dimensions - if we're talking about cloth, probably 2 unless the cloth is really thick. But they refer to that as 0-dimensional. I'm guessing the dimensions here are referring to the... coordinate space you would use to address locations within it? And when it's just a bunch of discrete points there's no real coordinate space, not until you connect them with some sort of volume or space?
And here I thought you might start talking about locales.
[Lol this is truly scary I was just browsing that barycentric page yesterday (a day of otherwise not much webby) for my other stuff, thinking about what a Laplacian e.g. in Barycentric coords would look like]
Update: a quick gogling returns this short writeup
What is there to say about locales? (I don't understand them well enough — I don't know their geometric use at all!)
If you're interested in the boundary between abstract simplices and topological (or even geometric) ones, I ran across someone's (UK CS person?) slides a few years back on redoing Elements from an algebraic POV and would be happy to try to dig it back up.
The imbecile habitually flouts Wittgenstein's dictum "wovon..."? If you do it vibing health.. I'm guessing that I shant be triggered :) I'll remember to look up slides of Tanya's brother later today for hints.
The other slides, they'll defo be helpful!
The other thing I'm reading today is, btw, Kolmogorov-Fomine, page 337 (Mir-Ellipses,1994) Not implying there's anything, just curious if it might be helpful to expose my attention sometimes for the collaborative fuzzing..
> Thm 9.32.4) If f is of bounded variation on [a, b], then f can be represented as the difference between two nondecreasing functions on [a, b].
reminds me of double-entry accounting.
(or of using xor to get non-monotonic functions out of ratchets — although to have a useful notion of xor one must first have a useful notion of [in]equality)
