It is the same for time. An event lasts, it manifests duration; but in order to obtain precision we must conceive of it as ideally restricted. We thus obtain an instantaneous event occurring at a definite point of our space. We may say, then, that a billiard ball, subsisting motionless at a point of the space of our frame, constitutes a continuous succession of point-events all located at the same point of our space (where the point-event itself would be represented by the instantaneous existence of the ball considered as reduced in size to a spatial point). Likewise, a billiard ball moving through the space of our frame would be represented by a succession of points in space at a succession of instants in time; hence by a chain of point-events. It is not absolutely necessary to conceive of an event as something objective, actually occurring or existing. We may conceive of events and point-events as empty. Thus, a point of our space a million miles away in a definite direction at six o’clock constitutes a point-event. In the same way it is not absolutely necessary to designate a point on our sheet of paper by a pencil mark; for we can define its position by numbers. In physics, however, we are more generally interested in discussing events that are observable; so although in theory a point-event is merely the localisation of an abstract entity at a point of space at an instant of time, in practice the majority of events to which we shall refer will serve to localise observable existents. For similar reasons we usually tint the colourless liquid in the thermometer so as to render it observable; though by so doing, nothing is changed, of course, in the reading of the instrument. [Pg 165]