Hinton - The Fourth Dimension.pdf

144
THE FOURTH DIMENSION
line leaves the plane—goes absolutely out of the range
of the plane being’s apprehension. But when the yellow
line points straight out from the plane then the pink
face comes into contact with it. Thus the same red line
remaining as he saw it at first, now towards him comes
a face surrounded by white and red lines.
If we call the direction to the right the unknown
direction, then the line he saw before, the yellow line,
goes out into this unknown direction, and the line which
before went into the unknown direction, comes in. It
comes in in the opposite direction to that in which the
yellow line ran before; the interior of the face now
A
O B O A
Fig. 88.
B
against the plane is pink. It is a
property of two lines at right
angles that, if one turns out of a
given direction and stands at
right angles to it, then the other
of the two lines comes in, but
runs the opposite way in that
given direction, as in fig. 88.
Now these two presentations of the cube would seem
to the plane creature like perfectly different material
bodies, with only that line in common in which they
both meet.
Again our cube can be turned about the yellow line.
In this case the yellow square would disappear as before,
but a new square would come into the plane after the
cube had rotated by an angle of 90° about this line.
The bottom square of the cube would come in thus
in figure 89. The cube supposed in contact with the
plane is rotated about the lower yellow line and then
the bottom face is in contact with the plane.
Here, as before, the red line going out into the unknown
dimension, the white line white before ran in the
unknown dimension would come in downwards in the