The fourth dimension

4 THE FOURTH DIMENSION

another begins is a point, and the straight line itself can be generated by the motion of the point.

One portion of a plane is bounded from another by a straight line, and the plane itself can be generated by the straight line moving in a direction not contained in itself.

Again, two portions of solid space are limited with regard to each other by a plane; and the plane, moving in a direction not contained in itself, can generate solid _ Space.

Thus, going on, we may say that space is that which limits two portions of higher space from each other, and that our space will generate the higher space by moving | in a direction not contained in itself.

Another indication of the nature of four-dimensional space can be gained by considering the problem of the arrangement of objects.

If I have a number of swords of varying degrees of brightness, I can represent them in respect of this quality by points arranged along a straight line.

If I place a sword at 4, fig. 1, and regard it as having

a certain brightness, then the other swords

A__8 can be arranged in a series along the

Fig. 1. line, as at 4, B, ©, etc., according to their degrees of brightness.

If now I take account of another quality, say length, they can be arranged ina plane. Starting from A, 8, c, I GB can find points to represent different

D € degrees of length along such lines as

AF, BD, CE, drawn from a and B and ©.

A__i8 © Points on these lines represent different

Rig. 2. degrees of length with the same degree of

brightness. Thus the whole plane is occupied by points

representing all conceivable varieties of brightness and length.