The fourth dimension

APPENDIX I 239

can be used instead of the models. It has three axes, red, white, yellow, in our space. Hence the cube determined by these axes is the face of the tesseract which we now have before us. It is the ochre face. It is enough, however, simply to say null f, red f. for the cubes which we use.

To impress this in your mind, imagine that tesseracts do actually run from each cube. Then, when you move the cubes about, you move the tesseracts about with them. You move the face but the tesseract follows with it, as the cube follows when its face is shifted in a plane.

The cube null in the normal position is the cube which has in it the red, yellow, white axes. It is the face having these, but wanting the blue. In this way you can define which face it is you are handling. I will write an “f” after the name of each tesseract just as the plane being might call each of his slabs null slab, yellow slab, ete., to denote that they were representations.

We have then in the first block of twenty-seven cubes, the following—null f, red f., null f., going up; white f., null f., lying to the right, and so on. Starting from the null point and travelling up one inch we are in the null region, the same for the away and the right-hand directions. And if we were to travel in the fourth dimension for an inch we should still be in a null region, The tesseract stretches equally all four ways. Hence the appearance we have in this first block would do equally well if the tesseract block were to move across our space for a certain distance. For anything less than an inch of their transverse motion we should still haye the same appearance. You must notice, however, that we should not have null face after the motion had begun.

When the tesseract, null for instance, had moved ever so little we should not have a face of null but a section of null in our space. Hence, when we think of the motion