If we want a theory explaining how people play billiards, we do not want a theory of perfect billiard balls; we want a theory of what heuristics a human billiard player uses in order to plan and make a (often not quite accurate) shot. These heuristics and actions do not involve solving the differential equations of the billiard board; they involve rules of thumb and it is these practice guides to action we are trying to discover in order to explain the behavior.