In the preceding chapter, when we were considering a discrete space-time, we defined a time-like interval as the number of intervening points on the longest causal route connecting the two given points. The natural way to generalize this so as to become applicable to a continuous space-time would be to regard the number of points as the measure of geodesic distance; this would enable us to say that the geodesic distance traversed by a unit of matter measures the amount of causal action which it has undergone. If we further assume that, in comparing different units of matter, we must multiply by the mass to obtain a measure of the amount of causal action, then the amount in a finite motion is the integral of . But this is the amount of "action" in the technical sense.[71] It seems therefore—though this is only a tentative suggestion—that we can regard a time-like separation as the measure of the maximum amount of causal action on the various causal routes which lead from one point to another. It is to be observed that, since points are classes of events, motion from one point to another consists in the cessation of certain events and the coming into existence of others; every such change is causal when it happens along the route of a piece of matter, since the unity of a piece of matter at different times is defined by means of the concept of a causal route. There is, therefore, so far as I can see, no fundamental objection to regarding time-like separations as measuring amounts of intervening causal action, and small time-like intervals as limits of separations. Space-like intervals, as we have seen, are derivative from time-like intervals; hence they, also, depend upon amount of causal action. Passing now to the hypothesis of a discrete space-time, in which each point consists of a finite number of events, we find that a similar analysis to the above is still possible, and is in fact considerably easier than when we assume continuity.[Pg 380] In a discrete space-time, if and are two points containing events which belong to the biography of one material unit, the number of points on the route of this unit between and is always finite. If several geodesic routes lead from to , there will be a maximum to the number of points on such routes; this maximum will be the measure of the interval between and , which will therefore always be an integer. A longer route means a greater number of intermediate events, and therefore a greater amount of causal action. Thus again the interval measures the greatest amount of causal action on any causal route from to . And causal routes consist of a succession of rhythms or steady events separated by transactions.