The fourth dimension

100 THE FOURTH DIMENSION

premiss, mood £, the next to the mood 1, and the last to mood o,

The cube we see is as it were merely a tray against which the four-dimensional figure rests. Its section at any stage is a cube. But a transition in this direction being transverse to the whole of our space is represented by no space motion. We can exhibit successive stages of the result of transference of the cube in that direction, but cannot exhibit the product of a transference, however small, in that direction.

To return to the original method of representing our variables, consider fig. 56. These four cubes represent four sections of the figure derived from the first of them

Fig. 56.

by moving it in the fourth dimension. The first portion of the motion, which begins with 1, traces out a more than solid body, which is all in the first figure. The beginning of this body is shown in 1. The next portion of the motion traces out a more than solid body, all of which is in the second figure; the beginning of this body is shown in 2; 3 and 4 follow on in like manner. Here, then, in one four-dimensional figure we have all the combinations of the four variables, major premiss, minor premiss, figure, conclusion, represented, each variable going through its four varieties. The disconnected cubes drawn are our representation in space by means of disconnected sections of this higher body.