To Galileo and Newton, on the other hand, the time which it took a body to pass from one point of its path to another was of paramount importance. The motion itself was the object of their study, and they recognized the part played by velocity. But Galileo and Newton were still sufficiently under the influence of Euclid to fit the observed phenomena of motion, so far as they could, upon Euclid's static world of points. This they effected by falling in with the age-old procedure of regarding time and space as something entirely disassociated and distinct. The motion of an object--in theory, of a point--was to be recorded by observing its successive positions. With each of these positions a time was to be associated, marking the instant at which the point attained that position. But in the face of this association, space and time were to be maintained as entirely separate entities. THE FOUR-DIMENSIONAL WORLD OF EVENTS This severe separation of time and space Minkowski has now questioned, with the statement that the elements of which the external world is composed, and which we observe, are not points at all, but are events. This calls for a revision of our whole habit of thought. It means that the perceptual world is four-dimensioned, not three-dimensioned as we have always supposed; and it means, at the very least, that the distinction between time and space is not so fundamental as we had supposed. [This should not impress us as strange or incomprehensible. What do we mean when we say that a plane is two-dimensional? Simply that two coordinates, two numbers, must be given to specify the position of any point of the plane. Similarly for a point in the space of our accustomed concepts we must give three numbers to fix the position--as by giving the latitude and longitude of a point on the earth and its height above sea-level. So we say this space is three-dimensional. But a material body is not merely somewhere; it is somewhere now,]182 or was somewhere yesterday, or will be somewhere tomorrow. The statement of position for a material object is meaningless unless we at the same time specify the time at which it held that position. [If I am considering the life-history of an object on a moving train, I must give three space-coordinates and one time-coordinate to fix each of its positions.]182 And each of its positions, with the time pertaining to that position, constitutes an event. The dynamic, ever-changing world about us, that shows the same aspect at no two different moments, is a world of events; and since four measures or coordinates are required to fix an event, we say this world of events is four-dimensional. If we wish to test out the soundness of this viewpoint, we may well do so by asking whether the naming of values for the four coordinates fixes the event uniquely, as the naming of three under the old system fixes the point uniquely.