Four-Dimensional Vistas | Page 8

because, on the Higher Space
Hypothesis, each space is the container of all phenomena of its own
order, the futility, for practical purposes, of going outside is at once
apparent. The highly intelligent threadworm neither knows nor cares
that the point of intersection of two lines in his diagram represents a
point in a space to which he is a stranger. The point is there, on his
page: it is what he calls a fact. "Why raise" (he says) "these puzzling
and merely academic questions? Why attempt to turn the universe
completely upside down?"
But though no proofs of hyper-dimensionality have been found in
nature, there are equally no contradictions of it, and by using a method
not inductive, but deductive, the Higher Space Hypothesis is plausibly
confirmed. Nature affords a sufficient number of representations of
four-dimensional forms and movements to justify their consideration.
SYMMETRY
Let us first flash the light of our hypothesis upon an all but universal
characteristic of living forms, yet one of the most
inexplicable--symmetry.
Animal life exhibits the phenomenon of the right-and left-handed
symmetry of solids. This is exemplified in the human body, wherein

the parts are symmetrical with relation to the axial plane. Another more
elementary type of symmetry is characteristic of the vegetable kingdom.
A leaf in its general contour is symmetrical: here the symmetry is about
a _line_--the midrib. This type of symmetry is readily comprehensible,
for it involves simply a revolution through 180 degrees. Write a word
on a piece of paper and quickly fold it along the line of writing so that
the wet ink repeats the pattern, and you have achieved the kind of
symmetry represented in a leaf.
With the symmetry of solids, or symmetry with relation to an axial
plane, no such simple movement as the foregoing suffices to produce
or explain it, because symmetry about a plane implies
_four-dimensional_ movement. It is easy to see why this must be so. In
order to achieve symmetry in any space--that is, in any given number of
dimensions--there must be revolution in the next higher space: one
more dimension is necessary. To make the (two-dimensional) ink
figure symmetrical, it had to be folded over in the third dimension. The
revolution took place about the figure's line of symmetry, and in a
higher dimension. In _three_-dimensional symmetry (the symmetry of
solids) revolution must occur about the figure's plane of symmetry, and
in a higher--i.e., the fourth dimension. Such a movement we can reason
about with mathematical definiteness: we see the result in the right- and
left-handed symmetry of solids, but we cannot picture the movement
ourselves because it involves a space of which our senses fail to give
any account.
Now could it be shown that the two-dimensional symmetry observed in
nature is the result of a three-dimensional movement, the right-and
left-handed symmetry of solids would by analogy be the result of a
_four_-dimensional movement. Such revolution (about a plane) would
be easily achieved, natural and characteristic, in four space, just as the
analogous movement (about a line) is easy, natural, and characteristic,
in our space of three dimensions.
OTHER ALLIED PHENOMENA
In the mirror image of a solid we have a representation of what would
result from a four-dimensional revolution, the surface of the mirror
being the plane about which the movement takes place. If such a
change of position were effected in the constituent parts of a body as a
mirror image of it represents, the body would have undergone a

revolution in the fourth dimension. Now two varieties of tartaric acid
crystallize in forms bearing the relation to one another of object to
mirror image. It would seem more reasonable to explain the existence
of these two identical, but reversed, varieties of crystal, by assuming
the revolution of a single variety in the fourth dimension, than by any
other method.
There are two forms of sugar found in honey, dextrose and levulose.
They are similar in chemical constitution, but the one is the reverse of
the other when examined by polarized light--that is, they rotate the
plane of polarization of a ray of light in opposite ways. If their atoms
are conceived to have the power of motion in the fourth dimension, it
would be easy to understand why they differ. Certain snails present the
same characteristics as these two forms of sugar. Some are coiled to the
right and others to the left; and it is remarkable that, like dextrose and
levulose, their juices are optically the reverse of each other when
studied by polarized light.
Revolution in the fourth dimension would also explain the change in a
body from producing a right-handed, to producing a left-handed,
polarization of light.
ISOMERISM
In chemistry the molecules of a compound are assumed to consist of
the atoms of the elements