Nice, indeed at the deeper level it's that if you want to make time shifts equivalent to rotation, you need to move in a circular fashion. Minor point: to me d

Nice, indeed at the deeper level it's that if you want to make time shifts equivalent to rotation, you need to move in a circular fashion. Minor point: to me derivatives are just one specific linear time invariant operator, a kind of convolution (with a generalized function) so I think LTI is the thing we really care about.