I was thinking how this relates to how a computer monitor, no matter how perfect and precise, can never show you a circle. It can only pretend. [this also allows programmers to use tricks that simplify the math]
Oo.. hm. wait… no even there there’s a width of the electron beam and the movement, while smooth-ish is still steps because – electrons. Then again, they’re as close as we’re gonna get I suppose.
Continuous functions “smear” over discreteness in realities. But since we don’t have precise measurements of all of the discrete parts — and because stuff is always moving (even the reference frames themselves) – we can usually get away with the statistical smears as ‘close enough’.
From a distance, stuff smears together. We’re all nearsighted in our brains. probably a good thing.