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