The ’s are no longer constants, as when we had and , with all other ’s vanishing; they now have variable values from place to place, and as for , , , these no longer necessarily represent space and time differences; they are mere mathematical Gaussian number differences. In spite of all this, the numerical value of , the square of the interval, remains the same regardless of the mesh-system selected. Psychological duration, or aging, can also be represented in space-time. By psychological duration we mean the flow of time which the observer experiences; or, more precisely still, the duration that would be marked out by a clock held in his hand. Psychological duration is measured by the length of the space-time world-line followed by the observer. When we keep this point in mind the paradox of the travelling twin to be discussed in a later chapter loses much of its paradoxical appearance. [Pg 200] We can also understand how it comes that the discovery of space-time permits us to account for the duality in the nature of motion, relative when translationary and uniform, absolute when accelerated or rotationary. As long as we were endeavouring to account for this duality by attributing an appropriate structure to three-dimensional space, we were met by a peculiar difficulty: If we assumed space to have a flat structure, that is, one of planes and straight lines, it would be possible to understand why a free body, when set in motion with any definite velocity, should be guided along one of these straight lines or grooves in space. It would be following its natural course and there would be complete symmetry all around it; everything would run smoothly and no forces would arise. Then, if we attempted to tear the body away from its straight course, compelling it to follow a curve, we should be forcing it to violate the laws of the space-structure, tearing it away from the space-groove which it would normally follow. It was not impossible to assume that the groove would react and that antagonistic forces would arise. Thus the fact that curved or rotationary motion was accompanied by forces of inertia, hence manifested itself as absolute, did not constitute a difficulty of an insuperable order. But a real difficulty arose when we considered the other species of accelerated motion, i.e., variable motion along a straight line. In this case, the paths of the bodies being straight (hence in harmony with the flat structure of space), no violation of the laws of this spatial structure was evidenced. And yet forces of inertia were again present. It was difficult to interpret their appearance in terms of the space-structure.