5 ms·

I mean the notion of compactness is inspired pretty clearly from the continuum. I also have a degree in pure math and disagree strongly with your characterizati

by smus 5y ago

I mean the notion of compactness is inspired pretty clearly from the continuum. I also have a degree in pure math and disagree strongly with your characterization of topology, which is literally defined up to homeomorphism which is itself defined by it's continuity. Arguably the whole point of topology is characterized by that which is preserved by continuous deformation, which clearly is inspired by more continuous math. I think you are using incredibly strong language and in a misguided way.

__MatrixMan__ 5y ago
Yeah, I think you're right. There's something about real analysis that makes me uncomfortable. I've been struggling for years to put my finger on it. Whatever it is, topology doesn't have it. I had mistakenly decided that it was an overappreciation of continuity, but I think it must be something else.
- smus 5y ago
  Maybe it's the differential structure itself? Or an (over?)emphasis on the study of functions from space to space instead of the study of the space itself? Or the specificity of calculus (the study of one specific space) instead of the generality of topology (thinking about a lot of spaces and comparing them to each other)
  - __MatrixMan__ 5y ago
    Hmm, I'll have to ponder those. Specificity seems closest. Whatever it is, it's not a rational critique. Despite the discomfort, I'm also fascinated by it because one should not have an emotional response to specific types of math, but I very much do. Something about the homework in Real Analysis left me feeling angry. Not because it was difficult or presented poorly, but because it was somehow... untrustworthy? As if my betters had decided which ideas were the good ones and the only thing left for me to do was optimize along the one dimension that they had assigned me. I realize that this is nonsense, but I can't seem to shake it.
    - smus 5y ago
      I think it's totally good and human to have preferences for one sort of math over another :)

by smus 5y ago

__MatrixMan__ 5y ago

Yeah, I think you're right. There's something about real analysis that makes me uncomfortable. I've been struggling for years to put my finger on it. Whatever it is, topology doesn't have it. I had mistakenly decided that it was an overappreciation of continuity, but I think it must be something else.

smus 5y ago
Maybe it's the differential structure itself? Or an (over?)emphasis on the study of functions from space to space instead of the study of the space itself? Or the specificity of calculus (the study of one specific space) instead of the generality of topology (thinking about a lot of spaces and comparing them to each other)
- __MatrixMan__ 5y ago
  Hmm, I'll have to ponder those. Specificity seems closest. Whatever it is, it's not a rational critique. Despite the discomfort, I'm also fascinated by it because one should not have an emotional response to specific types of math, but I very much do. Something about the homework in Real Analysis left me feeling angry. Not because it was difficult or presented poorly, but because it was somehow... untrustworthy? As if my betters had decided which ideas were the good ones and the only thing left for me to do was optimize along the one dimension that they had assigned me. I realize that this is nonsense, but I can't seem to shake it.
  - smus 5y ago
    I think it's totally good and human to have preferences for one sort of math over another :)