Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
sense of that axis which goes out of the plane into the
unknown dimension.
It is obvious that the unknown direction, the direction
in which the white lines runs at first, is quite distinct from
any direction which the plane creature knows. The white
line may come in towards him, or running down. If he
is looking at a square, which is the face of a cube
(looking at it by a line), then any one of the bounding lines
remaining unmoved, another face of the cube may come
in, any one of the faces, namely, which have the white line
in them. And the white line comes sometimes in one of
the space directions he knows, sometimes in another.
Now this turning which leaves a line unchanged is
something quite unlike any turning he knows in the
plane. In the plane a figure turns round a point. The
square can turn round the null point in his plane, and
the red and yellow lines change places, only of course, as
with every rotation of lines at right angles, if red goes
where yellow went, yellow comes in negative of red’s old
direction.
This turning, as the plane creature conceives it, we
should call turning about an axis perpendicular to the
plane. What he calls turning about the null point we
call turning about the white line as it stands out from
his plane. There is no such thing as turning about a
point, there is always an axis, and really much more turns
than the plane being is aware of.
Taking now a different point of view, let us suppose the
cubes to be presented to the plane being by being passed
transverse to his plane. Let us suppose the sheet of
matter over which the plane being and all objects in his
world slide, to be of such a nature that objects can pass
through it without breaking it. Let us suppose it to be
of the same nature as the film of a soap bubble, so that
it closes around objects pushed through it, and, however