[tel]

I think there's an odd sense where people think derivatives arise from "change in things" instead of being principal. It's sensible from our personal mindset to believe this but there's no reason a priori.

So that's kind of the question: can things like derivatives be the structure of space time or must they be arising from some underlying thing? Since the underlying thug involves some arbitrary, unobservable choice... it's a bit challenging.

[rrmm]

I've run across stuff in mathematical contexts where they'll throw in a derivative (or other operator) just to get the expression in the form they want.

It struck me as a bit odd, because hey, where's the change happening? But ultimately it was just a convenience, and maybe it had some underlying meaning in the original context, and maybe it didn't.

[tel]

But then sometimes it might be the case that the truly persistent thing is the derivative and the algebra forced your hand for good reason!