But what's really amazing is that classical mechanics itself makes the assumption that infinite subdivision is possible, that's how it connects to calculus, yet we know this is not true, as you say. So the surprise is, we have a theory which requires an assumption that isn't true, yet the theory works anyway as long as you don't look too closely.

This is why I feel the profundity of Zeno's paradox with Achilles trying to catch a tortoise is not well appreciated. Many people dismiss it by saying "Zeno didn't understand that an infinite sum of smaller and smaller times can sum to a finite time". Maybe he didn't, I don't know, but the real point is-- we don't have physical access to that infinite sum of shorter and shorter times! Quantum mechanics would set in at some point if you actually tried to analyze Achilles catching the tortoise like that, and at some point the energy you'd need to see if that was "really happening" would fry both Achilles and the tortoise. So the infinite sum that calculus gives us is not "real", in the sense that it is not verifiable in detail with experiment, yet as an idealization of what is happening, it works great. In other words, classical mechanics is describable by mathematical idealizations that reality is not, yet its results describe the reality. I think Zeno's paradox is alive and well, and shows why our "laws" are not "what reality is actually doing", but are "mathematically elegant ways to organize our familiarities". Why this works is the deepest mystery of them all, one we are nowhere close to "unifying" with anything we observe. It's really the question, given that intelligence is the ability to unify familiarities, from whence comes intelligence?