The fourth dimension

APPENDIX II 261

1. Eatension. Call the large squares in fig. 2 by the name written in them. It is evident that each can be divided as shown in fig. 1. Then the small square marked 1 will be “en” in “En,” or “ Enen.” The square marked 2 will be “et” in “En” or “ Enet,” while the square marked 4 will be “en” in “Et” or “Eten.” Thus the square Fig. 2. 5 will be called “ Tlil.” This principle of extension can be applied in any number of dimensions.

2. Application to Three-Dimensional Space. To name a three-dimensional collocation of cubes take _ the upward direction first, secondly the [ten | te} | direction towards the observer, thirdly the ; direction to his right hand. These form a word in which the first fin | ww] a letter gives the place of the cube upwards, the second letter its place towards the observer, the third letter its place to the

feo] |e] ight.

jean | aa | at We have thus the following seheme, which represents the set of cubes of

vin | oe | ot | column 1, fig. 101, page 165.

We begin with the remote lowest cube at the left hand, where the asterisk is placed (this proves to be by far the most convenient origin to take for the normal system).

Thus “nen” is a “null” cube, “ten” a red cube on it, and “len” a “null” cube above “ten.”