Page:Eddington A. Space Time and Gravitation. 1920.djvu/73

III] and time. Just in that process of relation to an individual, the order falls apart into the distinct manifestations of space and time. An individual is a four-dimensional object of greatly elongated form; in ordinary language we say that he has considerable extension in time and insignificant extension in space. Practically he is represented by a line—his track through the world. When the world is related to such an individual, his own asymmetry is introduced into the relation; and that order of events which is parallel with his track, that is to say with himself, appears in his experience to be differentiated from all other orders of events.

Probably the best known exposition of the fourth dimension is that given in E. Abbott's popular book Flatland. It may be of interest to see how far the four-dimensional world of space-time conforms with his anticipations. He lays stress on three points.

(1) As a four-dimensional body moves, its section by the three-dimensional world may vary; thus a rigid body can alter size and shape.

(2) It should be possible for a body to enter a completely closed room, by travelling into it in the direction of the fourth dimension, just as we can bring our pencil down on to any point within a square without crossing its sides.

(3) It should be possible to see the inside of a solid, just as we can see the inside of a square by viewing it from a point outside its plane.

The first phenomenon is manifested by the FitzGerald contraction.

If quantity of matter is to be identified with its mass, the second phenomenon does not happen. It could easily be conceived of as happening, but it is provided against by a special law of nature—the conservation of mass. It could happen, but it does not happen.

The third phenomenon does not happen for two reasons. A natural body extends in time as well as in space, and is therefore four-dimensional; but for the analogy to hold, the object must have one dimension less than the world, like the square seen from the third dimension. If the solid suddenly went out of existence so as to present a plane section towards time, we should still fail to see the interior of it; because light-tracks in four-dimensions are restricted to certain lines like