outlook of relativity, and the reader may feel some doubt as to whether the strange phenomena of contraction and time-retardation, that were described in the last chapter, are to be taken seriously, or are part of a reductio ad absurdum argument. The answer is that we believe that the phenomena do occur as described; only the description (like that of all observed phenomena) concerns the relations of the external world to some observer, and not the external world itself. The startling character of the phenomena arises from the natural but fallacious inference that they involve intrinsic changes in the objects themselves.
We have been considering chiefly the observer's end of the observation; we must now turn to the other end—the thing observed. Although length and duration have no exact counterparts in the external world, it is clear that there is a certain ordering of things and events outside us which we must now find more appropriate terms to describe. The order of events is a four-fold order; we can arrange them as right-and-left, backwards-and-forwards, up-and-down, sooner-and-later. An individual may at first consider these as four independent orders, but he will soon attempt to combine some of them. It is recognised at once that there is no essential distinction between right-and-left and backwards-and-forwards. The observer has merely to turn through a right angle and the two are interchanged. If he turns through a smaller angle, he has first to combine them, and then to redivide them in a different way. Clearly it would be a nuisance to continually combine and redivide; so we get accustomed to the thought of leaving them combined in a two-fold or two-dimensional order. The amalgamation of up-and-down is less simple. There are obvious reasons for considering this dimension of the world as fundamentally distinct from the other two. Yet it would have been a great stumbling-block to science if the mind had refused to combine space into a three-dimensional whole. The combination has not concealed the real distinction of horizontal and vertical, but has enabled us to understand more clearly its nature—for what phenomena it is relevant, and for what irrelevant. We can understand how an observer in another country redivides the combination into a different vertical and horizontal. We must
