Non fungible numbers
Multiplication and addition that is no longer commutative
Imagine a world where added numbers are identical but not equivalent.
So 4 apples + 3 oranges = 4 apples then 3 oranges
This is identical to 7 but not equivalent.
I am thinking of potential use in government accounting and algebraic programming with numbers.
Rather than all taxes going into a single taxable account and then spread out to different funding initiatives, you track the income of each area and track the costs of each taxraising and each funding. So roads should be self funding.
When I have a configuration for a web server I want to add to it a particular behaviour and have it slot into the right place automatically. So the data structure is a polynomial and I add a polynomial confifuration that "fits" the shape of the polynomial that is already there.
Usually in Kubernetes configuration there is few places that can accept my configuration fragment. I should be capable of "adding" to a particular YAML key. There is only small subset where it is valid. The polynomials aren't compatible except for certain areas.