Hinton - The Fourth Dimension.pdf

APPENDIX I: THE MODELS 233
in an opposite sense to that in which the line ran which
has just left the plane. If the cube does not break
through the plane this is always the rule.
Again turn the cube back to the normal position with
red running up, white to the right, and yellow away, and
try another turning.
You can keep the yellow line fixed, and turn the cube
about it. In this case, the red line going out to the
right, the white line will come in pointing downwards.
You will be obliged to elevate the cube form the table
in order to carry out this turning. It is always necessary
when a vertical axis goes out of a space to imagine a
movable support which will allow the line which ran out
before to come in below.
Having looked at the three ways of turning the cube
so as to present different faces to the plane, examine what
would be the appearance if a square hole were cut in the
piece of cardboard, and the cube were to pass through it.
A hole can be actually cut, and it will be seen that in the
normal position, with red axis running up, yellow away,
and white to the right, the square first perceived by the
plane being—the one contained by red and yellow lines—
would be replaced by another square of which the line
towards you is pink—the section line of the pink face.
The line above is light yellow, below is light yellow and
on the opposite side away from you is pink.
In the same way the cube can be pushed through a
square opening in the plane from any of the positions
which you have already turned it into. In each case
the plane being will perceive a different set of contour
lines.
Having observed these facts about the catalogue cube,
turn now to the first block of twenty-seven cubes.
You notice that the colour scheme on the catalogue cube
and that of this set of blocks is the same.