Discovering the Categorical Knowledge Graph

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Discovering the Categorical Knowledge Graph

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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.

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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.

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From another side, I dove back in to thinking about Category Theory.

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Knowledge as a graph

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Spaced repetition was the first reason I began to wonder how much of knowledge could be represented as atomic units with connections.

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Connections could also be considered atomic units of their own.

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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.

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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.

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My intuition to favor reducibility leads me to think that this sort of structure would be an accurate representation of knowledge.

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Category Theory

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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.

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The idea that propositional logic could be represented as a category is what opened my mind to the power of what categories might be able to do.

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Categorical Knowledge Graph

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So, this is what I’m thinking about right now. I’ll write more about it as a I progress further along.

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Some questions that I’m pursuing:

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Why does making my notes structured like a category matter?

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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.

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What is the way to unlock some of the benefits of this and minimize the note writing effort?

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This seems to be useful for large enterprise databases, is it overkill for an individual’s personal data and knowledge?

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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.

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Side note

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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!

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