I think this is underscoring my concern with this as a pedagogical thing. I have seen people try very hard to find analogs with basic algebra. And... by peopl

I think this is underscoring my concern with this as a pedagogical thing. I have seen people try very hard to find analogs with basic algebra. And... by people, I mainly mean younger me. Building algebras is, I think, still a very valuable thing if you can do it. Often times, though, the goal is not to fully mimic the basic algebra of grade school, but to map out what is doable with the abstractions that you have.