The fourth dimension

THE HIGHER WORLD 69

simply the plane of zy and the square base of the cube ACEG, fig. 39, is all that could

" be seen of it. Let now the w axis y take the place of the z axis and E 6 we have, in fig. 39 again, a reprey sentation of the space of zyw, in A el Cc which all that exists of the cube is

ig. 39.

its square hase. Now, by a turning of x to w, this base can rotate around the line 4¥, it is shown on its way in fig. 40, and finally it will, after half a revolution, lie on the other side of the y axis. In a similar way we may rotate sections parallel to the base of the zw rotation, and each of them comes to run in the opposite direction from that which they oceupied at first. Thus een the cube comes from the position of fig. 36. to that of fig. 41. In this z to w turning, we see that it takes place by the rotations of sections parallel to the front face about lines parallel to AB, or else we may consider it as A x consisting of the rotation of Foy ‘position _ I" position sections parallel to the base Higneks about lines parallel to az. It is a rotation of the whole cube about the plane BEF. Two separate sections could not rotate about two separate lines in our space without conflicting, but their motion is consistent when we consider another dimension. Just, then, as a plane being can think of rotation about a line as a rotation about a number of points, these rotations not interfering as they would if they took place in his twodimensional space, so we can think of a rotation about a

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