"This is the corrected version of the one I put out a month or so ago, in which my animation for all the inverse operations was incorrect": https://www.youtube.com/watch?v=sULa9Lc4pck.

This really hammers home the advantage of this notation. It leads naturally to the question, "What is the operation when we leave the bottom right constant?" which Grant calls "O-plus" (tex call it \oplus), which is in fact related to the harmonic mean (which is n times the o-plus of the terms). I don't know if there's a better term for "o-plus" other than "reciprocal sum of reciprocals". Maybe "optical sum" which kind of makes o-plus make even more sense?

https://en.wikipedia.org/wiki/Optic_equation

https://en.wikipedia.org/wiki/List_of_sums_of_reciprocals

> which is in fact related to the harmonic mean (which is n times the o-plus of the terms). I don't know if there's a better term for "o-plus" other than "reciprocal sum of reciprocals"

I would call it the "harmonic norm", which is consistent with is being the "norm version" of the harmonic mean. It might also be called the "(p=-1) norm" since it would be a p-norm with p=-1. Also "L-1 norm" to put it in the "L norm" family.

https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm