Three Dollar Quill

Okay, yesterday in the summary, I promised to motivate my efforts to represent algebraic structures in OCaml. The motivation is a little abstract, but I'm going to try anyway.

One common aspect of mathematics is to build complex concepts on top of simpler ones. In some cases, it's essentially possible to swap out the specific "simpler concept" for a different one with similar properties. To get even more hand-wavy, there is a type of algebraic structure called a "field", which is basically "something that you can do high-school algebra to", and "being able to do high-school algebra to something" is a prerequisite for being able to do college-level algebra to it.

In other words, if you have a bunch of fields, and a bunch of things that do something to fields, you can snap them together arbitrarily like legos with no physical form. Basically, I want to really grasp stuff like geometric algebra, and, um, things that Norman Wildberger thinks would be easier to teach than current curricula, and also have the tools to pose questions like "what's the weirdest thing I can come up with that's still technically a 'triangle'?"

I'll see when I'm up for actually working on this; I was kind of tired and out of it today, so maybe tomorrow, maybe later. For now...

Good night.