The type of measuring instruments is thus exactly the same as in classical science; and all that relativity tells us is that if our classical measurements had been pursued with greater precision, we should have realised long ago that the classical anticipations were belied by experiment. There is no use in pursuing the study of the theory any farther unless we succeed in understanding its physical significance. So far as the mathematician is concerned, with the Lorentz-Einstein transformations issuing as they do from ultra-precise experiment, their mathematical consequences must be deemed to correspond to the workings of the real world; and these consequences indicate clearly that length, duration and simultaneity must be relatives in a real physical sense. However, in view of the importance of the new ideas, we may consider the problem in an indirect way and thereby throw additional light on the concrete significance of these transformations. Accordingly we shall have to discuss what the physicist means by an “event.” An event is exemplified by a something happening in a certain region of space at a certain moment of time. It matters not what actually happens. It may be a thought flashing through our minds, a bird bursting into song, or two billiard balls colliding; what is essential is a specification of position in space and in time. [Pg 164] When we try to think of an event, we are compelled to credit it with more or less extension in space, and more or less duration in time. But in all problems where accuracy of localisation is demanded, we must conceive of an event as ideally restricted to an instantaneous point in space; or, if we prefer, to a mathematical point in space at a mathematical instant in time. We then get what has been called by Minkowski a Point-Event. This procedure of restricting events ideally is of course purely a mathematical abstraction and is in every way similar to the procedure followed by the geometrician when he speaks of points without dimensions, lines without width, or surfaces without thickness. Even in ordinary life we are obliged to follow this same method of restricting dimensions ideally, in order to render a precise localisation possible. For instance, when we say we are so many miles from New York our assertion is extremely vague. What part of New York are we referring to? Even when we specify a definite building in the city, it could always be asked: “What part of the building?” We see, then, that to obtain any degree of precision we must select a definite point, and our statement that we are fifty miles from New York is equivalent to regarding New York as reduced to a point. Of course we know full well that a city is not reduced to a point; but arguments of this sort are irrelevant to the problem of localisation with which we are faced.