It is an axiom of science never to look outside three-space horizons for an understanding of phenomena when these can logically be accounted for within those horizons. Now 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.