Hinton - The Fourth Dimension.pdf

64
THE FOURTH DIMENSION
To see the whole he must relinquish part of that which
he has, and take the whole portion by portion.
Consider now a plane being in front of a square, fig. 34.
y
The square can turn about any point
in the plane—say the point A. But it
C D cannot turn about a line, as AB. For,
in order to turn about the line AB,
A’ B’ the square must leave the plane and
move in the third dimension. This
A B x motion is out of his range of observa-
Fig. 34. tion, and is therefore, except for a
process of reasoning, inconceivable to him.
Rotation will therefore be to him rotation about a point.
Rotation about a line will be inconceivable to him.
The result of rotation about a line he can apprehend.
He can see the first and last positions occupied in a half
revolution about the line AC. The result of such a half revolution
is to place the square ABCD on the left hand instead
of on the right hand of the line AC. It would correspond
to a pulling of the whole bode ABCD through the line AC,
or to the production of a solid body which was the exact
reflection of it in the line AC. It would be as if the square
ABCD turned into its image, the line acting as a mirror.
Such a reversal of the positions of the parts of the square
would be impossible in his space. The occurrence of it
would be a proof of the existence of a higher dimensionality.
Let him now, adopting the conception of a three-
z
dimensional body as a series of
sections lying, each removed a
little farther than the preceding
B1
one, in direction at right angles to
his plane, regard a cube, fig. 36, as
a series of sections, each like the
A B
x square which forms its base, all
Fig. 35.
rigidly connected together.