Suppose we expand the algebraic number system as it is composed now by making a slight change to the rules of exponentiation?
What would that create?
It would open a new way to perform mathematical operations and fundamentally change the structure of algebra in general. Below is the article in which I propose to introduce addition as an exponential operation. Something I don’t think has ever been explored.
This is short musical piece I wrote and put on my Youtube site to express the idea of additive exponentiation musically. Have a listen it's very, very brief
The Additive Exponentiation Melody