The fourth dimension

APPENDIX I 263

the number of squares in it can be enlarged and the whole kept the same size.

Compare fig. 79, p. 138, for instance, or the bottom layer of fig. 84.

Now use an initial “s” to denote the result of carrying this process on to a great extent, and we obtain the limit names, that is the point, line, area names for a square. “Sat” is the whole interior. The corners are “ sen,”

“sel,” “sin,” “sil,” while the lines sen___set sel are “san,” “sal,” “set,” “sit.”

I find that by the use of the initial “s” these names come to be practically entirely disconnected with the systematic names for the square

snl 21 from which they are derived. They

are easy to learn, and when learned can be used readily with the axes running in any direction,

To derive the limit names for a four-dimensional rectangular figure, like the tesseract, is a simple extension of this process. These point, line, etc., names include those which apply to a cube, as will be evident on inspection of the first cube of the diagrams which follow.

All that is necessary is to place an “ s” before each of the names given for a tesseract block. We then obtain apellatives which, like the colour names on page 174, fig. 103, apply to all the points, lines, faces, solids, and to