Hinton - The Fourth Dimension.pdf

REMARKS ON THE FIGURES 179
ochre cube, and the last bounding cube, the other ochre
cube. Practically three intermediate sectional cubes will
be found sufficient for most purposes. We will take then
a series of five figures—two terminal cubes and three
intermediate sections—and show how the different regions
appear in space when we take each set of three out
of the four axes of the tesseract as lying in our space.
In fig. 107 initial letters are used for the colours.
A reference to fig. 103 will show the complete nomenclature,
which is merely indicated here.
b0 b1 b2 b3 b4
x
interior
Ochre
interior
L. Brown
interior
L. Brown
Fig. 107.
interior
L. Brown
interior
Ochre
In this figure the tesseract is shown in fig stages
distant from our face: first, zero; second 1⁄4 in.; third,
1⁄2 in.; fourth, 3⁄4 in.; fifth, 1 in.; which are called 0, b b1,
b2, b3, b4, because they are sections taken at distances
0, 1, 2, 3, 4 quarter inches along the blue line. All the
regions can be named from the first cube, the b0 cube,
as before, simply by remembering that transference along
the b axis gives the addition of blue to the colour of
the region in the ochre, the b0 cube. In the final cube
b4, the colouring of the original b0 cube is repeated.
Thus the red line moved along the blue axis gives a red
and blue or purple square. This purple square appears
as the three purple lines in the sections b1, b2, b3, taken
at 1⁄4, 1⁄2, 3⁄4 of an inch in the fourth dimension. If the
tesseract moves transverse to our space we have them in
this particular region, first of all a red line which lasts
for a moment, secondly a purple line which takes its