Azad has this description of imaginary numbers that really tickled me: “numbers can rotate”.
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.
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.