This just escapes being the kind of proof demanded by science. If
the independence of all the possible distances between the atoms of
a molecule is absolutely required by theoretical chemical research,
then science is really compelled, in dealing with molecules of more
than four atoms, to make use of the idea of a space of more than
three dimensions.


THE ORBITAL MOTION OF SPHERES: CELL SUB-DIVISION

There is in nature another representation of hyper-dimensionality
which, though difficult to demonstrate, is too interesting and
significant to be omitted here.

Imagine a helix, intersected, in its vertical dimension, by a moving
plane. If necessary to assist the mind, suspend a spiral spring
above a pail of water, then raise the pail until the coils, one
after another, become immersed. The spring would represent the helix,
and the surface of the water the moving plane. Concentrating
attention upon this surface, you would see a point--the elliptical
cross-section of the wire where it intersected the plane--moving
round and round in a circle. Next conceive of the wire itself as a
lesser helix of many convolutions, and repeat the experiment. The
point of intersection would then continually return upon its own
track in a series of minute loops forming those lesser loops, which,
moving circle-wise, registered the involvement of the helix in the
plane.

It is easy to go on imagining complicated structures of the nature