Earlier quoted context omitted.
> A ball dropped near the earth's surface will always fall towards the centre of the earth How exactly does this address "whether it was recently thrown upward or dropped from above"? A ball in a given location will do something unpredictable if you have no information about its past. Is that hysteresis?
You don’t need information about its past. Everything you need to know to predict its future state is contained in its current position and velocity at the moment you measure it.
I'd be surprised if that were the case: seems like it'd violate some sort of "locality", where the future should depend entirely on the present state.
Is it just that there's unidentified present state that's perhaps more easily characterized by knowing the history? Or is it somehow unidentifiable in principle?