The fourth dimension

188 VHE FOURTH DIMENSION

whatever cubic view we take of them we can say exactly what sides of the tesseracts we are handling, and how they touch each other.*

Thus, for instance, if we have the sixteen tesseracts shown below, we can ask how does null touch blue.

In the arrangement given in fig. 111 we have the axes white, red, yellow, in space, blue running in the fourth dimension. Hence we have the ochre cubes as bases. Imagine now the tesseractic group to pass transverse to our space—we ‘have first of all null ochre cube, white

direction

Light yellow hidden Light green

A, ° f Fig. 111.

ochre cube, ete.; these instantly vanish, and we get the section shown in the middle cube in fig. 103, and finally, just when the tesseract block has moved one inch transverse to our space, we have null ochre cube, and then immediately afterwards the ochre cube of blue comes in. Hence the tesseract null touches the tesseract blue by its ochre cube, which is in contact, each and every point of it, with the ochre cube of blue.

How does null touch white, we may ask? Looking at the beginning A, fig. 111, where we have the ochre

* At this point the reader will find it advantageous, if he has the models, to go through the manipulations described in the appendix.