4 ms·

Absolutely agreed—it's a little funny to see dismissals of the article (which, as I mentioned elsewhere in the thread is actually quite good), even though, as a

Absolutely agreed—it's a little funny to see dismissals of the article (which, as I mentioned elsewhere in the thread is actually quite good), even though, as a mathematician [0] we use these analogies (and sometimes really the whole idea) all the time. To add to your list (for less number-theory specific topics): - Lyapunov functions? Energy in physics (just a mathematical surrogate) - Exponential families? Canonical ensemble in physics - Convex duality? Lagrange duality in classical mechanics and the list continues. ----- [0] And, admittedly, a member of a physics lab, even though I don't really do any physics.

danharaj 6y ago
Yea! And here's a metaphor to... baking!! The moment this metaphor clicked for me reading a musty textbook with yellowing pages was delightful, I can go back to that moment just by thinking about it. https://en.wikipedia.org/wiki/Milnor%E2%80%93Thurston_kneading_theory https://en.wikipedia.org/wiki/Milnor%E2%80%93Thurston_kneadi...
- LolWolf 6y ago
  I love it! I had heard of some of these results in relation to Persi Diaconis's work (e.g., [0]). I'm curious, what is the textbook? Would love to take a quick glance at it at least! :) EDIT: I also really like the fact that even the original paper mentioned in the quanta article references other (quite pictorially fun) things, such as the aptly named Hedgehog spaces [1] (see Theorem 3, for example). Perhaps it's violating the prime directive to be mentioning this, but it's a little bit of a shame to see what I think is a good article so quickly dismissed by what is essentially just bikeshedding (that isn't even justified!). ---- [0] https://link.springer.com/article/10.1007/s10955-011-0284-x https://link.springer.com/article/10.1007/s10955-011-0284-x [1] https://en.wikipedia.org/wiki/Hedgehog_space https://en.wikipedia.org/wiki/Hedgehog_space
  - danharaj 6y ago
    Thought about it, and it was definitely the original paper in some journal volume. I remember the pictures, and the ones I drew myself :) Found it here: http://www-personal.umich.edu/~kochsc/MilnorThurston.pdf http://www-personal.umich.edu/~kochsc/MilnorThurston.pdf
    - LolWolf 6y ago
      Awesome, thank you!
      - danharaj 6y ago
        the paper by Persi Diaconis you linked to was so fun that I want to learn about markov chain mixing now.
        LolWolf 6y ago
        Oh it’s an absolutely lovely overview. Honestly I would highly recommend most stuff from Diaconis, he’s got a fantastic expository style (and all of his papers are quite readable!)

danharaj 6y ago

Yea! And here's a metaphor to... baking!! The moment this metaphor clicked for me reading a musty textbook with yellowing pages was delightful, I can go back to that moment just by thinking about it. https://en.wikipedia.org/wiki/Milnor%E2%80%93Thurston_kneading_theory https://en.wikipedia.org/wiki/Milnor%E2%80%93Thurston_kneadi...

LolWolf 6y ago
I love it! I had heard of some of these results in relation to Persi Diaconis's work (e.g., [0]). I'm curious, what is the textbook? Would love to take a quick glance at it at least! :) EDIT: I also really like the fact that even the original paper mentioned in the quanta article references other (quite pictorially fun) things, such as the aptly named Hedgehog spaces [1] (see Theorem 3, for example). Perhaps it's violating the prime directive to be mentioning this, but it's a little bit of a shame to see what I think is a good article so quickly dismissed by what is essentially just bikeshedding (that isn't even justified!). ---- [0] https://link.springer.com/article/10.1007/s10955-011-0284-x https://link.springer.com/article/10.1007/s10955-011-0284-x [1] https://en.wikipedia.org/wiki/Hedgehog_space https://en.wikipedia.org/wiki/Hedgehog_space
- danharaj 6y ago
  Thought about it, and it was definitely the original paper in some journal volume. I remember the pictures, and the ones I drew myself :) Found it here: http://www-personal.umich.edu/~kochsc/MilnorThurston.pdf http://www-personal.umich.edu/~kochsc/MilnorThurston.pdf
  - LolWolf 6y ago
    Awesome, thank you!
    - danharaj 6y ago
      the paper by Persi Diaconis you linked to was so fun that I want to learn about markov chain mixing now.
      - LolWolf 6y ago
        Oh it’s an absolutely lovely overview. Honestly I would highly recommend most stuff from Diaconis, he’s got a fantastic expository style (and all of his papers are quite readable!)