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.