Hinton - The Fourth Dimension.pdf

THE HIGHER WORLD 73
revolution, there would be in reality one line which
remained unaltered, that is the line which stretches away
in the fourth dimension, following the axis of the axle. The
four-dimensional wheel can rotate in any number of planes,
but all these planes are such that there is a line at right
angles to them all unaffected by rotation in them.
An objection is sometimes experienced as to this mode
of reasoning from a plane world to a higher dimensionality.
How artificial, it is argued, this conception of a plane
world is. If any real existence confined to a superficies
could be shown to exist, there would be an argument for
one relative to which our three-dimensional existence is
superficial. But, both on the one side and the other of
the space we are familiar with, spaces either with less
or more than three dimensions are merely arbitrary
conceptions.
In reply to this I would remark that a plane being
having one less dimension than our three would have onethird
of our possibilities of motion, which we have only
one-fourth less than those of the higher space. It may
very well be that there may be a certain amount of
freedom of motion which is demanded as a condition of an
organised existence, and that no material existence is
possible with a more limited dimensionality than ours.
This is well seen if we try to construct the mechanics of a
two-dimensional world. No tube could exist, for unless
joined together completely at one end two parallel lines
would be completely separate. The possibility of an
organic structure, subject to conditions such as this, is
highly problematical; yet, possibly in the convolutions
of the brain there may be a mode of existence to be
described as two-dimensional.
We have but to suppose the increase in surface and
the diminution in mass carried on to a certain extent
to find a region which, though without mobility of the