Four-Dimensional Vistas | Page 9

contained in the compound. These atoms are
supposed to be at certain distances from one another. It sometimes
happens that two compound substances differ in their chemical or
physical properties, or both, even though they have like chemical
elements in the same proportion. This phenomenon is called isomerism,
and the generally accepted explanation is that the atoms in isomeric
molecules are differently arranged, or grouped, in space. It is difficult
to imagine how atoms, alike in number, nature, and relative proportion,
can be so grouped as somehow to produce compounds with different
properties, particularly as in three-dimensional space four is the
greatest number of points whose mutual distances, six in number, are
all independent of each other. In four-dimensional space, however, the
ten equal distances between any two of five points are geometrically
independent, thus greatly augmenting the number and variety of
possible arrangements of atoms.
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 of the
spiral, and to suppose also that these structures are distinguishable from
each other at every section. If we think of the intersection of these with
the rising surface, as the atoms, or physical units, of a plane universe,
we shall have a world of apparent motion, with bodies moving
harmoniously amongst one another, each a cross-section of some part
of an unchanging and unmoving three-dimensional entity.
Now augment the whole by an additional dimension--raise everything
one space. The helix of many helices would become four-dimensional,
and superficial space would change to solid space: each tiny circle of
intersection would become a sphere of the same diameter, describing,
instead of loops, helices. Here we would be among familiar forms,
describing familiar motions: the forms, for example, of the earth and
the moon and of their motion about the sun; of the atom, as we imagine
it, the molecule and the cell. For is not the sphere, or ovoid, the unit
form of nature; and is not the spiral vortex its characteristic motion,

from that of the nebula in the sky to the electron in the atom? Thus, on
the hypothesis that our space is traversing four-dimensional space, and
that the forms of our space are cross-sections of four-dimensional
forms, the unity and harmony of nature would be accounted for in a
remarkably simple manner.
The above exercise of the imagination is a good preparation for the
next demand upon it. Conceive a dichotomous tree--one that always
divides into two branches--to pass through a plane. We should have, as
a plane section, a circle of changing size, which would elongate and
divide into two circles, each of which would do the same. This reminds
us of the segmentation of cell life observed under the microscope, as
though a four-dimensional figure were registering its passage through
our space.
THE ELECTRIC CURRENT
Hinton conceived of an electric current as a four-dimensional vortex.
He declared that on the Higher Space Hypothesis the revolution of the
ether would yield the phenomenon of the electric current. The re
more may our eyes distinguish the souls divine! Hardly through these
watery spheres shall we perceive, with sighs, our ancestral heaven: at
intervals even we shall cease altogether to behold it. By this disastrous
sentence direct vision is denied to us; we can see only by the aid of the
outer light; these are but windows that we possess--not eyes. Nor will
our pain be less when we hear in the fraternal breathing of the winds
with which no longer can