Hinton - The Fourth Dimension.pdf

192
THE FOURTH DIMENSION
From this section a cube goes off in the fourth dimension,
which is formed by moving each point of the section
in the blue direction.
4
44
Light green
L. yellow
L. pur.
Pink
4
x
41
Null White
Light blue White
Fig. 115. Fig. 116.
Drawing this cube we have fig. 116.
Now this cube occurs as a series of sections in our
original representation of the tesseract. Taking four steps
as before this cube appears as the sections drawn in b0, b1,
b2, b3, b4, fig. 117, and if the line 4 is subjected to a
movement equal in the blue and yellow directions, it will
occupy the positions designated by 4, 41, 42, 43, 44.
4
41
42
b0 b1 b2 b3 b4
Fig. 117.
Hence, reasoning in a similar manner about every line,
it is evident that, moved equally in the blue and yellow
directions, the pink plane will trace out a space which is
shown by the series of section planes represented in the
diagram.
Thus the space traced out by the pink face, if it is
moved equally in the yellow and blue directions, is represented
by the set of planes delineated in Fig. 118, pink
43
43
42
44