Hinton - The Fourth Dimension.pdf

170
THE FOURTH DIMENSION
as drawn by a plane being, are not the cubes themselves,
but represent the faces or the sections of a cube. Thus
in the plane being’s diagram a cube of twenty-seven cubes
“null” represents a cube, but is really, in the normal
position, the orange square of a null cube, and may be
called null, orange square.
A plane being would save himself confusion if he named
his representative squares, not by using the names of the
cubes simply, but by adding to the names of the cubes a
word to show what part of a cube his representative square
was.
Thus a cube null standing against his plane touches it
by null orange face, passing through his plane it has in
the plane a square as trace, which is null white section, if
we use the phrase white section to mean a section drawn
perpendicular to the white line. In the same way the
cubes which we take as representative of the tesseract are
not the tesseract itself, but definite faces or sections of it.
In the preceding figures we should say then, not null, but
“null tesseract ochre cube,” because the cube we actually
have is the one determined by the three axes, white, red,
yellow.
There is another way in which we can regard the colour
nomenclature of the boundaries of a tesseract.
Consider a null point to move tracing out a white line
one inch in length, and terminating in a null point,
see fig. 103 or in the coloured plate.
Then consider this white line with its terminal points
itself to move in a second dimension, each of the points
traces out a line, the line itself traces out an area, and
give two lines as well, its initial and final position.
Thus, if we call “a region” any element of the figure,
such as a point, or a line, etc., every “region” in moving
traces out a new kind of region, “a higher region,” and
give two regions of its own kind, an initial and a final