The fourth dimension

182 THE FOURTH DIMENSION

square in the transference along the blue axis by which this cube is generated from the orange face. This purple square made by the motion of the red line is the same purple face that we saw before as a series of lines in the sections 6,, 6., 63. Here, since both red and blue axes are in our space, we have no need of duration to represent the area they determine. In the motion of the tesseract across space this purple face would instantly disappear.

From the orange face, which is common to the initial cubes in fig. 107 and fig. 108, there goes in the blue direction a cube coloured brown. This brown cube is now all in our space, because each of its three axes run in space directions, up, away, to the left. It is the same brown cube which appeared as the successive faces on the sections 6,, b,, b;. Having all its three axes in our space, it is given in extension; no part of it needs to be represented as a succession. The tesseract is now in a new position with regard to our space, and when it moves across our space the brown cube instantly disappears.

In order to exhibit the other regions of the tesseract we must remember that now the white line runs in the unknown dimension. Where shall we put the sections at distances along the line? Any arbitrary position in our space will do: there is no way by which we can represent their real position.

However, as the brown cube comes off from the orange face to the left, let us put these successive sections to the left. We can call them why, wh,, whz, wh; wh, because they are sections along the white axis, which now runs in the unknown dimension.

Running from the purple square in the white direction we find the light purple cube. This is represented in the sections wh,, wh,, whs, wh, fig. 108. It is the same cube