Page:Eddington A. Space Time and Gravitation. 1920.djvu/208

192 scarcely be said to be less adapted to the purposes of thought than one made, say, out of tiny billiard balls! But I think we may even go a little beyond this negative justification. The primary interval relation is of an undefined nature, and the $$g$$'s contain this undefinable element. The expression $$G_{\mu\nu}$$ is therefore of defined form, but of undefined content. By its form alone it is fitted to account for all the physical properties of matter; and physical investigation can never penetrate beneath the form. The matter of the brain in its physical aspects is merely the form; but the reality of the brain includes the content. We cannot expect the form to explain the activities of the content, any more than we can expect the number 4 to explain the activities of the Big Four at Versailles.

Some of these views of matter were anticipated with marvellous foresight by W. K. Clifford forty years ago. Whilst other English physicists were distracted by vortex-atoms and other will-o'-the-wisps, Clifford was convinced that matter and the motion of matter were aspects of space-curvature and nothing more. And he was no less convinced that these geometrical notions were only partial aspects of the relations of what he calls "elements of feeling."—"The reality corresponding to our perception of the motion of matter is an element of the complex thing we call feeling. What we might perceive as a plexus of nerve-disturbances is really in itself a feeling; and the succession of feelings which constitutes a man's consciousness is the reality which produces in our minds the perception of the motions of his brain. These elements of feeling have relations of nextness or contiguity in space, which are exemplified by the sight-perceptions of contiguous points; and relations of succession in time which are exemplified by all perceptions. Out of these two relations the future theorist has to build up the world as best he may. Two things may perhaps help him. There are many lines of mathematical thought which indicate that distance or quantity may come to be expressed in terms of position in the wide sense of the analysis situs. And the theory of space-curvature hints at a possibility of describing matter and motion in terms of extension only." (Fortnightly Review, 1875.)

The equation $$G_{\mu\nu} = K_{\mu\nu}$$ is a kind of dictionary explaining what the different components of world-curvature mean in