It was Minkowski who first formulated all this in a form susceptible of use in connection with the theory of relativity. His starting point lies in the distinction between the point and the event. Mr. Francis has brought this out rather well in his essay, being the only competitor to present the Euclidean geometry as a real predecessor of Newtonian science, rather than as a mere part of the Newtonian system. I think his point here is very well taken. As he says, Euclid looked into the world about him and saw it composed of points. Ignoring all dynamic considerations, he built up in his mind a static world of points, and constructed his geometry as a scientific machine for dealing with this world in which motion played no part. It could to be sure be introduced by the observer for his own purposes, but when so introduced it was specifically postulated to be a matter of no moment at all to the points or lines or figures that were moved. It was purely an observational device, intended for the observer's convenience, and in the bargain a mental device, calling for no physical action and the play of no force. So far as Euclid in his daily life was obliged to take cognizance of the fact that in the world of work-a-day realities motion existed, he must, as a true Greek, have looked upon this as a most unfortunate deviation of the reality from his beautiful world of intellectual abstraction, and as something to be deplored and ignored. Even in their statuary the Greeks clung to this idea. A group of marvelous action, like the Laocoon, they held to be distinctly a second rate production, a prostitution of the noble art; their ideal was a figure like the majestic Zeus--not necessarily a mere bust, be it understood, but always a figure in repose without action. Their statuary stood for things, not for action, just as their geometry stood for points, not for events. Galileo and Newton took a different viewpoint. They were interested in the world as it is, not as it ought to be; and if motion appears to be a fundamental part of that world, they were bound to include it in their scheme. This made it necessary for them to pay much more attention to the concept of time and its place in the world than did the Greeks. In the superposition process, and even when he allowed a curve to be generated by a moving point, the sole interest which Euclid had in the motion was the effect which was to be observed upon his static figures after its completion. In this effect the rate of the motion did not enter. So all questions of velocity and time are completely ignored, and we have in fact the curious spectacle of motion without time.