Hinton - The Fourth Dimension.pdf

REMARKS ON THE FIGURES 199
Hence when this cube had passed half-way through he
would have—instead of the orange line with null points,
which he had at first—an ochre line of half its length,
with pink and light yellow points. Thus, as the cube
passed slowly through his plane, he would have a succession
of lines gradually diminishing in length and
forming an equilateral triangle. The whole interior would
be ochre, the line from which it started would be orange.
The succession of points at the ends of the succeeding
lines would form pink and light yellow lines and the
final point would be null. Thus looking at the successive
lines in the section plane as it and the cube passed across
his plane he would determine the figure cut out bit
by bit.
Coming now to the section of the tesseract, let us
imagine that the tesseract and its cutting space pass
slowly across our space; we can examine portions of it,
and their relation to portions of the cutting space. Take
the section space which passes through the four points,
null r., wh., y., b.; we can see in the ochre cube (fig. 119)
the plane belonging to this section space, which passes
through the three extremities of the red, white, yellow
axes.
Now let the tesseract pass half way through out space.
Instead of our original axes we have parallels to them,
purple, pink and green, each of the same length as the
first axes, for the section of the tesseract is of exactly
the same shape as its ochre cube.
But the sectional space seen at this stage of the transference
would not cut the section of the tesseract in a
plane disposed as at first.
To see where the sectional space would cut these
parallels to the original axes let the tesseract swing so
that, the orange face remaining stationary, the blue line
comes in to the left.