The fourth dimension

THE HIGHER WORLD 65

If now he turns the square about the point a in the plane of ay, each parallel section turns with the square he moves. In each of the sections there is a point at rest, that vertically over 4. Hence he would conclude that in the turning of a three-dimensional body there is one line which is at rest. That is a three-dimensional turning in a turning about a line.

In a similar way let us regard ourselves as limited to a three-dimensional world by a physical condition. Let us imagine that there is a direction at right angles to every direction in which we can move, and that we are prevented from passing in this direction by a vast solid, that against which in every movement we make we slip as the plane being slips against his plane sheet.

We can then consider a four-dimensional body as consisting of a series of sections, each parallel to our space, and each a little farther off than the preceding on the unknown dimension.

Take the simplest four-dimensional body—one which begins as a cube, fig. 36, in our space, and consists of sections, each a cube like fig. 36, lying away from our space. If we turn the cube which is its base in our space about a line, if, eg., in fig. 36 we turn the cube about the line as, not only it but each of the parallel

Fig. 36. cubes moves about a line. The cube we see moves about the line as, the cube beyond it about a line parallel to aB and soon. Hence the whole four-dimensional body moves about a plane, for the assemblage of these lines is our way of thinking about the plane which, starting from the line aB in our space, runs off in the unknown direction.

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