Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
you first saw. This finished up the cube—it is the further
face in the unknown dimension.
The white line, which extends in length just like the
red or the yellow, you do not see as extensive; you apprehend
it simply as an enduring white point. The null
point, under the condition of movement of the cube,
vanishes in a moment, the lasting white point is really
your apprehension of a white line, running in the unknown
dimension. In the same way the red line of the face by
which the cube is first in contact with the plane lasts only
a moment, it is succeeded by the pink line, and this pink
line lasts for the inside of a minute. This lasting pink
line is your apprehension of a surface, which extends in
two dimensions just like the orange surface extends, as you
know it, when the cube is at rest.
But the plane creature might answer, “This orange
object is substance, solid substance, bounded completely
and on every side.”
Here, of course, the difficulty comes in. His solid is our
surface—his notion of a solid is our notion of an abstract
surface with no thickness at all.
We should have to explain to him that, from every point
of what he called a solid, a new dimension runs away.
From every point a line can be drawn in a direction
unknown to him, and there is a solidity of a kind greater
than that which he knows. This solidity can only be
realised by him by his supposing an unknown direction,
by motion in which what he conceives to be solid matter
instantly disappears. The higher solid, however, which
extends in this dimension as well as in those which he
knows, lasts when a motion of that kind takes place,
different sections of it come consecutively in the plane of
his apprehension, and take the place of the solid which he
at first sign conceives to be all. Thus, the higher solid—our
solid in contradistinction to his area solid, his two-