Four-Dimensional Vistas | Page 7

line system, represented by columns and girders in
the one case, and by studs and rafters in the other, becomes, by overlay
or interposition, a system of planes, so assembled and correlated as to
define a solid.
With nearly everything of man's creating--be it a bureau or a
battleship--the process is as above described. First, a pattern to scale;
next, an actual linear framework; then planes defining a solid. Consider
almost any of the industries practiced throughout the ages: they may be
conceived of thus in terms of dimensions; for example, those ancient
ones of weaving and basket making. Lines (threads in the one case,
rushes in the other) are wrought into planes to clothe a body or to
contain a burden. Or think, if you choose, of the modern industry of
book-making, wherein types are assembled, impressed upon sheets of
paper, and these bound into volumes-- _points, lines, planes, solids_.
The book in turn becomes the unit of another dimensional order, in the
library whose serried shelves form lines, which, combined into planes,
define the lateral limits of the room.
HIGHER--AND HIGHEST--SPACE
These are truisms. What have they to do, it may be asked, with the idea
of higher spaces? They have everything to do with it, for in achieving
the enclosure of any portion of solid space the limit of known
dimensions has been reached without having come to any end. More

dimensions--higher spaces--are required to account for higher things.
All of the products of man's ingenuity are inanimate except as he
himself animates them. They remain as they were made, machines, not
organisms. They have no inherent life of their own, no power of growth
and renewal. In this they differ from animate creation because the
highest achievement of the creative faculty in man in a mechanical way
lacks the life principle possessed by the plant. And as the most perfect
machine is inferior in this respect to the humblest flower that grows, so
is the highest product of the vegetable kingdom inferior to man himself,
the maker of the machine; for he can reflect upon his own and the
world's becoming, while the plant can only become.
What is the reason for these differences of power and function?
According to the Higher Space Hypothesis they are due to varying
potencies of movement in the secret causeways and corridors of space.
The higher functions of consciousness--volition, emotion,
intellection--may be in some way correlated with the higher powers of
numbers, and with the corresponding higher developments of space.
Thus would the difference between physics and metaphysics become a
difference of degree and not of kind. Evolution is to be conceived of as
a continuous pushing back of the boundary between representation and
reality, or as a conquest of space. We may conceive of space as of an
infinite number of dimensions, and of consciousness as a moving--or
rather as an expanding--point, embracing this infinity, involving worlds,
powers, knowledges, felicities, within itself in everlasting progression.

III PHYSICAL PHENOMENA
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