Hinton - The Fourth Dimension.pdf

THE HIGHER WORLD 71
turn these rods in our space about the lines A and B, as
the upper end of one, F, is going down, the lower end of
the other, C, will be coming up. They will meet and
conflict. But it is quite possible for these two rods
each of them to turn about the two lines without altering
their relative distances.
To see this suppose the y axis to go, and let the w axis
take its place. We shall see the lines A and B no longer,
for they run in the y direction from the points G and H.
Fig. 43 is a picture of the two rods seen in the space
z
D
C
w
Fig. 43.
F
G H
E
x
of xzw. If they rotate in the
direction shown by the arrows—
in the z to w direction—they
move parallel to one another,
keeping their relative distances.
Each will rotate about its own
line, but their rotation will not
be inconsistent with their forming
part of a rigid body.
Now we have but to suppose
a central plane with rods crossing
it at every point, like CD and EF cross the plane of xy,
to have an image of a mass of matter extending equal
distances on each side of a diametral plane. As two of
these rods can rotate round, so can all, and the whole
mass of matter can rotate round its diametral plane.
This rotation round a plane corresponds, in four
dimensions, to the rotation round an axis in three
dimensions. Rotation of a body round a plane is the
analogue of rotation of a rod round an axis.
In a plane we have rotation round a point, in threespace
rotation round an axis line, in four-space rotation
round an axis plane.
The four-dimensional being’s shaft by which he transmits
power is a disk rotating round its central plane—