Huh? I'm having a little bit of difficulty following you.

The triangle just captures that there are three quantities involved (with any two determining the third). I don't know what you mean with references to bifurcations and binary trees and so on.

If the mention of different domains is about the fact that you can't divide by zero, sure; in the same way, we find problems taking the logarithm of zero, or raising zero to negative powers, with uniquely pinning down roots of negative numbers, etc. For now, I am glossing over these things; let us suppose, for example, that in the ternary relation a * b = c, I intend all quantities to be drawn from some multiplicative group (thus, nonzero, and thus, with any two determining the third).

I didn't watch the video for several reasons, so if I was off, I'm sorry. From the comments I couldn't deduce what's actually wrong with the notation, or which notation for that matter. Yes, bad HN ettiquette is to respond anyway.

> If the mention of different domains is about the fact that you can't divide by zero

> I intend all quantities to be drawn from some multiplicative group

That's it. Still, I was trying to draw some hierarchical network, where log and root are both inverses of exp.

In the same way, multiplication is a special case of addition. Although It might not have to be, if it's just my preference to look at it that way. It reminds me of the diamond dependency problem (https://en.wikipedia.org/wiki/Diamond_problem#The_diamond_pr...).

Multiplicative groups to me look like a special case, too. The arrow diagrams look like category theory. I on the other hand just talk from intuition and my experience with the elementary functions, the order I learned in school.

EDIT: Subtraction and division as well aren't associative, so do they really form a subgroup? Another problem besides needlessly complicated notation is ambiguous notation. Wikipedia lists two alternatives for multiplicative groups. One is a special case of a ring which does have a null element. Now, in c/b=a, c can be the null element, but then a would be too, so c/a=b is still undefined. I'd guess that holds for the non-commutative version as well.