LOOKING FOR THE GREATER IN THE LESS

After the assured way in which the author has conducted the reader repeatedly up and down the dimensional ladder, it may be a surprise to learn that physical phenomena offer no irrefragable evidences of hyper-dimensionality.  We could not think in higher space if consciousness were limited to three dimensions.  The mathematical reality of higher space is never in question:  the higher dimensions are as valid as the lower, but the hyper-dimensionality of matter is still unproven.  Man’s ant-like efforts to establish this as a truth have thus far been vain.

Lest this statement discourage the reader at the very outset, he should understand the reason for such failure.  We are embedded in our own space, and if that space be embedded in higher space, how are we going to discover it?  If space is curved, how are we going to measure its curvature?  Our efforts to do so may be compared to measuring the distance between the tips of a bent bow by measuring along the bow instead of along the string.

Imagine a scientifically-minded threadworm to inhabit a page of Euclid’s solid geometry:  the evidences of three-dimensionality are there, in the very diagrams underneath his eyes; but you could not show him a solid—­the flat page could not contain it, any more than our space can contain a form of four dimensions.  You could only say to him, “These lines represent a solid.”  He would have to depend on his faith for belief and not on that “knowledge gained by exact observation and correct thinking” in which alone the scientist finds a sure ground for understanding.

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.