4 ms·

While a notation for this case makes for an interesting discussion (which the post is), the "blast radius" of this situation is so small that (to me) it wouldn'

by sriku 6y ago

While a notation for this case makes for an interesting discussion (which the post is), the "blast radius" of this situation is so small that (to me) it wouldn't be worth adopting any of the proposals (not saying anyone there pushed them). For a notation to be worth adoption,its impact must be far reaching. The "graphical linear algebra" makes a good case with a larger blast radius, for example. However even that has nowhere near the impact of, say, Feynman diagrams. The x^y notation is repurposed elsewhere - ex: power set of a set S is written 2^S .. with no implication that the "logarithm" of the power set to the base 2 is S. Same for matrices raised to a power, where matrices are usually not thought of as a base for doing logarithms. Same for operators in calculus (ex: laplacian .. now that would be confusing to club with a triangle!)

alanbernstein 6y ago
I'm not sure what you mean by blast radius, but if you were to think about the amount of people learning these concepts - as explained in the SE post here - the order would obviously be the reverse of what you suggest (exponents most important).
- sriku 6y ago
  By "blast radius" I meant the impact of the notation beyond the originating case into other areas. I wasn't referring to the number of people it would impact. The notation in the OP doesn't play well with "nearby" areas like powerset and matrices .. which are well served by the conventional exponentiation notation.
umvi 6y ago
Speaking of Feynman, I remember when he was in high school he invented his own notation[0] for sin/cos/tan to use little angular lines, but then the issue he ran into was that nobody could decipher his math notation and he had trouble helping others learn, so he conformed to the sin/cos/tan notation. [0] https://tex.stackexchange.com/questions/274463/feynman-trig-notation-creating-custom-characters https://tex.stackexchange.com/questions/274463/feynman-trig-...
OscarCunningham 6y ago
> The "graphical linear algebra" makes a good case with a larger blast radius, for example. However even that has nowhere near the impact of, say, Feynman diagrams. These are sort of the same example! They're both string diagrams (https://en.wikipedia.org/wiki/String_diagram https://en.wikipedia.org/wiki/String_diagram), just in different monoidal categories.

by sriku 6y ago

alanbernstein 6y ago

I'm not sure what you mean by blast radius, but if you were to think about the amount of people learning these concepts - as explained in the SE post here - the order would obviously be the reverse of what you suggest (exponents most important).

sriku 6y ago
By "blast radius" I meant the impact of the notation beyond the originating case into other areas. I wasn't referring to the number of people it would impact. The notation in the OP doesn't play well with "nearby" areas like powerset and matrices .. which are well served by the conventional exponentiation notation.

umvi 6y ago

Speaking of Feynman, I remember when he was in high school he invented his own notation[0] for sin/cos/tan to use little angular lines, but then the issue he ran into was that nobody could decipher his math notation and he had trouble helping others learn, so he conformed to the sin/cos/tan notation. [0] https://tex.stackexchange.com/questions/274463/feynman-trig-notation-creating-custom-characters https://tex.stackexchange.com/questions/274463/feynman-trig-...

OscarCunningham 6y ago

> The "graphical linear algebra" makes a good case with a larger blast radius, for example. However even that has nowhere near the impact of, say, Feynman diagrams. These are sort of the same example! They're both string diagrams (https://en.wikipedia.org/wiki/String_diagram https://en.wikipedia.org/wiki/String_diagram), just in different monoidal categories.