I remember my high school teacher teaching imaginary numbers in the trig class, and one of the other kids asked what they could be used for. This was an honors class and the kid skipped a math grade. Our math teacher couldn’t talk about it off the bat, and unconvincingly told us about applications in electrical and electronic engineering. We still went through it, but none of use knew why any of it was relevant.
I think if he had said “numbers can rotate”, maybe some of us (maybe not me!) might have been intrigued by the idea. It would have been a way to describe how EM rotate.
My own personal motivation for pursuing CT has to do with working with paradigms, and how are they related, and how they are not. Categories and morphisms seem to talk about the kind of things we can talk about with paradigms, yet much more precisely.
Complex numbers: the number line is just a metaphor. What would happen if you make it 2D? Oh you can solve negative roots. Whenever a number needs to spin or have a negative root, it’s a useful tool. Numbers are tools. Cool, that’s “real” enough for me.
I know I will never ever use it. Or at least, not in my current state of how I live my life. I liked learning it, there’s something to be said for what is beyond your horizon. But I do think just like complex numbers, category theory needs a motivation that is compelling. In retrospect, learning complex numbers is most likely not useful for me.
Oh wait a second, complex numbers helped me to understand trig. I never understood it in high school but 3B1B made it intuitive with complex numbers
Nevermind, I’ll just let this all stand here. It’s fun to be open and convinced by myself to the other side while writing my comment :’)
I’m sure if I would have learned category theory, I would have written a similar comment as I think there are a lot of parallels there.