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!)
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).
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.
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.
> 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.
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!)