Uncertainty

The concept of velocity has been around for so long that it is easy to forget that originally it wasn't independent from that of location. You can still see this (one-sided) dependence in a 3rd grade science class: $$\text{velocity }= \text{ distance }/ \text{ time },$$ with the distance being equal to the change of location. In calculus (and physics), the formula "disappears" after the limit is taken: $$\text{average velocity }= \text{ change of location }/ \text{ change of time}=\Delta y /\Delta x,$$ becomes $$\text{velocity }=y'= \lim_{\Delta x\to 0}\frac{ \Delta y }{ \Delta x}.$$ Without limits to worry about, however, the original formula continues to rule in discrete calculus (and discrete physics). So, to know the velocity you need to know the change of location and to know that you need to know two (consecutive) locations! Hence, uncertainty. Furthermore, the acceleration needs three points to be known and so on.