5 ms·

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

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?

082349872349872 2y ago
> the... coordinate space you would use to address locations within it yes! (if you like thinking along these lines, you may also be interested in exploring https://en.wikipedia.org/wiki/Barycentric_coordinate_system https://en.wikipedia.org/wiki/Barycentric_coordinate_system )
- gsf_emergency 2y ago
  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 https://www.math.auckland.ac.nz/deptdb/dept_reports/498.pdf https://www.math.auckland.ac.nz/deptdb/dept_reports/498.pdf
  - 082349872349872 2y ago
    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.
    - gsf_emergency 2y ago
      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..
      - 082349872349872 2y ago
        a finn, expressing "dafür muss man singen" (and channeling his inner Zhou?): https://www.youtube.com/watch?v=CGksgZKecKE https://www.youtube.com/watch?v=CGksgZKecKE
      - 082349872349872 2y ago
        > 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)

082349872349872 2y ago

> the... coordinate space you would use to address locations within it yes! (if you like thinking along these lines, you may also be interested in exploring https://en.wikipedia.org/wiki/Barycentric_coordinate_system https://en.wikipedia.org/wiki/Barycentric_coordinate_system )

gsf_emergency 2y ago
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 https://www.math.auckland.ac.nz/deptdb/dept_reports/498.pdf https://www.math.auckland.ac.nz/deptdb/dept_reports/498.pdf
- 082349872349872 2y ago
  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.
  - gsf_emergency 2y ago
    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..
    - 082349872349872 2y ago
      a finn, expressing "dafür muss man singen" (and channeling his inner Zhou?): https://www.youtube.com/watch?v=CGksgZKecKE https://www.youtube.com/watch?v=CGksgZKecKE
    - 082349872349872 2y ago
      > 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)