Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
of direction wanting in us, something which a being in
a four-dimensional world has, and which we have not. It
is a sense corresponding to a new space direction, a
direction which extends positively and negatively from
every point of our space, and which goes right away from
any space direction we know of. The perpendicular to a
plane is perpendicular, not only to two lines in it, but to
every line, and so we must conceive this fourth dimension
as running perpendicularly to each and every line we can
draw in our space.
And as the plane being had to suppose something
which prevented his moving off in the third, the
unknown dimension to him, so we have to suppose
something which prevents us moving off in the direction
unknown to us. This something, since we must be in
contact with it in every one of our movements, must not
be a plane surface, but a solid; it must be a solid, which
in every one of our movements we are against, not in. It
must be supposed as stretching out in every space dimension
that we know; but we are not in it, we are against it, we
are next to it, in the fourth dimension.
That is, as the plane being conceives himself as having
a very small thickness in the third dimension, of which
he is not aware in his new experience, so we must
suppose ourselves as having a very small thickness in
the fourth dimension, and, being thus four-dimensional
beings, to be prevented from realising that we are
such beings by a constraint which keeps us always in
contact with a vast solid sheet, which stretches on in
every direction. We are against that sheet, so that, if we
had the power of four-dimensional movement, we should
either go away from it or through it; all our space
movements as we know them being such that, performing
them, we keep in contact with this solid sheet.
Now consider the exposition a plane being would make