Page:Eddington A. Space Time and Gravitation. 1920.djvu/202

186 and do not, form any idea of the meaning of each individual symbol; it is only certain elaborate combinations of them that we recognise.

Thus, although the elementary concepts of the theory are of undefined nature, at some later stage we must link the derivative concepts to the familiar objects of experience.

We shall now collect the results arrived at in the previous chapters by successive steps, and set the theory out in more logical order. The extension in Chapter will not be considered here, partly because it would increase the difficulty of grasping the main ideas, partly because it is less certainly established.

In the relativity theory of nature the most elementary concept is the point-event. In ordinary language a point-event is an instant of time at a point of space; but this is only one aspect of the point-event, and it must not be taken as a definition. Time and space—the familiar terms—are derived concepts to be introduced much later in our theory. The first simple concepts are necessarily undefinable, and their nature is beyond human understanding. The aggregate of all the point-events is called the world. It is postulated that the world is four-dimensional, which means that a particular point-event has to be specified by the values of four variables or coordinates, though there is entire freedom as to the way in which these four identifying numbers are to be assigned.

The meaning of the statement that the world is four-dimensional is not so clear as it appears at first. An aggregate of a large number of things has in itself no particular number of dimensions. Consider, for example, the words on this page. To a casual glance they form a two-dimensional distribution; but they were written in the hope that the reader would regard them as a one-dimensional distribution. In order to define the number of dimensions we have to postulate some ordering relation; and the result depends entirely on what this ordering relation is—whether the words are ordered according to sense or to position on the page. Thus the statement that the world is four-dimensional contains an implicit reference to some ordering relation. This relation appears to be the interval, though I am not sure whether that alone suffices without some relation corresponding to proximity. It must be remembered that if the