Four-Dimensional Vistas | Page 9

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 we mingle our own, since ours will have for its dwelling, instead of the sublime and open world, the narrow prison of the breast_!"

That the soul--the so-called subliminal self--draws from a broader, deeper experience than the purely rational consciousness is a commonplace of modern psychology. Hinton conceives of the soul as _higher-dimensional_ with relation to the body, but so concerned with the management and direction of its lower-dimensional vehicle as to have lost, for the time being, its orientation, thinking and moving only in those ways of which the body is capable. The analogy he uses, of a ship and its captain, is so happy, and the whole passage has so direct a bearing upon the Hermetic fragment quoted, that