We shall say, then, that all causal relations consist of a series of rhythms or steady events separated by "transactions." If such a series connects a rhythm or steady event with a rhythm or steady event , we shall say that is a "causal ancestor" of , and is a "causal descendant" of . We may assume that, in such a case, the number of transactions between and is always finite, since one supposes that the time between two transactions cannot fall below a certain minimum, or at any rate that the number of causally connected transactions in a finite time is never infinite. Perhaps we may assume that a rhythm must last long enough to achieve an amount of action ; perhaps, even, we could construct a discrete theory of time from which[Pg 369] this result would follow. All this, however, is very speculative. Now let us consider the stock case of a light-signal sent from to , and reflected back from to . Only two transactions are involved, namely the emission and reflection of the light; perhaps we ought to add the final transaction, namely the re-absorption of the light by . In any case, there need be only two steady events, one in the outward beam and one in the returning beam. But the interval between the departure and return of the light may have any magnitude. This is all the more curious, as the interval between the departure of the light from and its arrival at is zero, and so is the interval between its departure from and its return to . This suggests that too much effort has been made to regard interval as analogous to distance in conventional geometry and time in conventional kinematics. Suppose we say that, if an event is a causal ancestor of an event , we take all the possible causal routes from to , and choose that which contains the greatest number of events: then the "interval" from to is defined as the number of events in this longest route. It is obvious that, if a measurable time elapses between the departure of the light from and its return to , there must have been a variety of events at meanwhile. When I say "at" , I have a meaning to be considered shortly; but for the moment it is enough to say that this meaning includes causal inheritance. Thus we have a meaning for the view that the interval at is quite long, and also for the view that the interval between the departure of the light from and its arrival at is zero. This latter statement means that it is the very same event that starts from and arrives at , and moreover that there is no longer causal route connecting the two transactions of starting from and arriving at . This event which starts from and arrives at I call a "luminous event." [Pg 370]