without, during any of the motion, any change having occurred in
the positions of the parts of the body.

It is very curious that, in these transcendental speculations, the
most rigorous mathematical methods correspond to the most
mystical ideas of the Swedenborgian and other forms of religion.
Right around us, but in a direction which we cannot conceive any
more than the inhabitants of "flat-land" can conceive up and down,
there may exist not merely another universe, but any number of
universes. All that physical science can say against the
supposition is that, even if a fourth dimension exists, there is
some law of all the matter with which we are acquainted which
prevents any of it from entering that dimension, so that, in our
natural condition, it must forever remain unknown to us.

Another possibility in space of four dimensions would be that of
turning a hollow sphere, an india-rubber ball, for example, inside
out by simple bending without tearing it. To show the motion in
our space to which this is analogous, let us take a thin, round
sheet of india-rubber, and cut out all the central part, leaving
only a narrow ring round the border. Suppose the outer edge of
this ring fastened down on a table, while we take hold of the
inner edge and stretch it upward and outward over the outer edge
until we flatten the whole ring on the table, upside down, with
the inner edge now the outer one. This motion would be as
inconceivable in "flat-land" as turning the ball inside out is to
us.