It seems like this post was appreciated mostly by those who already understand enough of abstract math to make sense of it, less so by the uninitiated. I’ve only ever had an intuitive understanding of CT, and my relevant math level is probably just around the first course in algebraic topology, which is still somewhat higher than the LW average, yet I still struggle to keep my interest reading through your post.
Ooh that’s a good comment you linked. You mention relating various applications of the poisson equation via natural transformation; could you unpack a bit what that would look like? One of the things I’ve had trouble with is how to represent the sorts of real-world abstractions I want to think about (e.g. poisson equation) in the language of category theory; it’s still unclear to me whether morphism relationships are enough to represent all the semantics. If you know how to do it with that example, it would be really helpful.
It seems like this post was appreciated mostly by those who already understand enough of abstract math to make sense of it, less so by the uninitiated. I’ve only ever had an intuitive understanding of CT, and my relevant math level is probably just around the first course in algebraic topology, which is still somewhat higher than the LW average, yet I still struggle to keep my interest reading through your post.
For comparison, I wrote a very informal comment on how embedded agent’s modeling abstraction levels can map into CT concepts. Which didn’t get much traction. But maybe starting with the examples already familiar and relevant to the audience could be something to try when introducing CT to the LW masses.
Ooh that’s a good comment you linked. You mention relating various applications of the poisson equation via natural transformation; could you unpack a bit what that would look like? One of the things I’ve had trouble with is how to represent the sorts of real-world abstractions I want to think about (e.g. poisson equation) in the language of category theory; it’s still unclear to me whether morphism relationships are enough to represent all the semantics. If you know how to do it with that example, it would be really helpful.
Trying to write it up better, we’ll see if this will work.