Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
Under this supposition, the whole cube moving in the
unknown dimension, traces out something new—a new
kind of volume, a higher volume. This higher volume
is a four-dimensional volume, and we designate it in colour
by adding blue to the colour of that which by moving
generates it.
It is generated by the motion of the ochre solid, and
hence it is of the colour we call light brown (white, yellow,
red, blue, mixed together). It is represented by a number
of sections like 2 in fig. 103.
Now this light brown higher solid has for boundaries:
first. the ochre cube in its initial position, second, the
same cube in its final position, 1 and 3, fig. 103. Each
of the squares which bound the cube, moreover, by movement
in this new direction traces out a cube, so we have
from the front pink faces of the cube, third, a pink blue or
light purple cube, shown as a light purple face on cube 2
in fig. 103, this face standing for any number of intermediate
sections; fourth, a similar cube from the opposite
pink face; fifth, a cube traced out by the orange face—
this is coloured brown and is represented by the brown
face of the section cube in fig. 103; sixth, a corresponding
brown cube on the right hand; seventh, a cube
starting from the light yellow square below; the unknown
dimension is at right angles to this also. This cube is
coloured light yellow and blue or light green; and
finally, eighth, a corresponding cube from the upper
light yellow face, shown as the light green square at the
top of the section cube.
The tesseract has thus eight cubic boundaries. These
completely enclose it, so that it would be invisible to a
four-dimensional being. Now, as to the other boundaries,
just as the cube has squares, lines, points, as boundaries,
so the tesseract has cubes, squares, lines, points, as
boundaries.