Geometry, Time and the Law of Continuity
Velimir Abramovic
"The law of continuity ... consists of ... that each quantity, in experiencing a transition from one magnitude into another, must pass through all the intermediary quantities of the same sort. This is usually expressed by stating that the transition occurs through intermediate stages. Maupertuis considered these stages to be a number of minute additions occurring in a moment of time. He thought that the law must be violated at the same time for it is violated equally by the smallest leap or the greatest leap, since the concepts of small and great are quite relative. He was right if the term 'stage' denotes an instantaneous increment in any quantity. Really, it should be so conceived that particular states correspond to particular instants, whereas increases or decreases correspond exclusively to very small continuous intervals of time".
