In Einstein’s theory, the rod is contracted, but we must add that this contraction holds only in the space of the frame with respect to which the rod is in motion. In the space of the frame accompanying the rod in its motion, no contraction would occur. We see, then, that as there exists no privileged space, only “my space,” “your space,” “his space,” there is no particular length to the rod, only a length “for me,” “for you” and “for him.” The contraction is thus embodied in a two-term relationship extending between the observer and the observed; it is a “relative.” But, once again, for a given observer it is as physically real as a chair or a table. Only when we consider the contraction from an impersonal standpoint, from that of space-time, without mentioning the conditions of observation, is the contraction not an illusion, but downright meaningless. It is, as we see, the concept of spatial magnitude, of primary qualities, which is at stake, in a form entirely different from anything science or philosophy had ever dreamed. Now although length, size and duration are relatives, the theory of relativity has discovered absolutes which transcend the observer, remaining the same for all. They are to be found in the absolute world of space-time; and it is this thought that Minkowski desired to convey when he said: “Henceforth space and time by themselves are mere shadows.” In the absence of some specified observer, space and time become indeterminate, and with them length and duration; that which endures and transcends the observer is a something in space-time, and this is neither a length nor a duration. Or, again, lengths and durations are the projections of something in absolute space-time on to the space and time directions of the observer. These latter are indeterminate (until the frame of the observer is specified), since no one space and no one time exists above all others. Space and time being indeterminate, the same will apply to those projections which we call length and duration. [Pg 221] Although we may be repeating ourselves unnecessarily, we cannot help but feel that the easiest way for the layman to grasp these difficult concepts will be to return to the well-known illustration of the relativity of a visual angle. When we perceive an object, say a telegraph pole, we see it under a certain angle, which we may call the visual angle. Is this visual angle real? Of course it is; we can measure it and define it physically as the angle subtended by two Euclidean straight lines extending between our eye and the two extremities of the pole. It is real but it expresses a relationship—a relationship between the positions of the observer and pole. It is certainly not inherent in the pole, since as the observer changes his position the visual angle changes in magnitude, though nothing happens to the pole in the meantime.