I have been interested in Category Theory for over a year now, but only recently have I started to see some direct bridges into other areas I’m interested in.
Starting with Joel Chan’s
Discourse Graph concept in Roam, I began down the rabbit hole of thinking about ontologies and grammars and how to structure notes and writing such that it can be queryable, parseable, and ideally, transferable.
A spaced repetition card requires the content to be
atomic (restricted to one core idea), and whatever knowledge could be broken down into atomic units could also be “remembered forever” through spaced repetition.
This is certainly an oversimplification, but the questions about spaced repetition aside, in principle it was interesting to know whether knowledge was decomposable like this.
If Category Theory can represent many different types of mathematics, it seems likely that it will be able to represent knowledge, or at least a significant subset of the type of knowledge I want to store in a note-taking system.
I believe it matters to make one’s personal knowledge future proof and transferable. It also makes ones notes fully queryable (due to the nature of all relationships being functional), I think. But there may be other benefits I haven’t digested yet.
Probably. Currently I’m thinking of this as a possible expanded version of a discourse graph that can possibly apply to more than academic-style research.
I hope to put together the resources I’ve found most useful for learning Category Theory on my own at some point. Please reach out if you would find that useful!