Four-Dimensional Vistas | Page 6

only their
three-dimensional aspects, and these not simultaneously, but
successively--that is, in time. According to this view, any unified series
of _actions_--for example, the life of an individual, or of a
group--would represent the straining, so to speak, of a thought-form
through our time, as the bodies subject to these actions would represent
its straining through our space.
EVOLUTION AS SPACE-CONQUEST
Evolution is a struggle for, and a conquest of, space; for evolution, as
the word implies, is a drawing out of what is inherent from latency into
objective reality, or in other words into spatial--and
temporal--extension.
This struggle for space, by means of which the birth and growth of
organisms is achieved, is the very texture of life, the plot of every
drama. Cells subdivide; micro-organisms war on one another; plants
contend for soil, light, moisture; flowers cunningly suborn the bee to
bring about their nuptials; animals wage deadly warfare in their rivalry
to bring more hungry animals into a space-hungry world. Man is not
exempt from this law of the jungle. Nations intrigue and fight for
land--of which wealth is only the symbol--and a nation's puissance is
measured by its power to push forward into the territory of its neighbor.
The self-same impulse drives the individual. One measure of the
difference between men in the matter of efficiency is the amount of
space each can command: one has a house and grounds in some locality
where every square inch has an appreciable value; another some

fractional part of a lodging house in the slums. When this bloodless, but
none the less deadly, contest for space becomes acute, as in the
congested quarters of great cities, man's ingenuity is taxed to devise
effective ways of augmenting his _space-potency_, and he expands in a
vertical direction. This third-dimensional extension, typified in the
tunnel and in the skyscraper, is but the latest phase of a conquest of
space which began with the line of the pioneer's trail through an
untracked wilderness.
DIMENSIONAL SEQUENCES
Not only does nature everywhere geometrize, but she does so in a
particular way, in which we discover dimensional sequences. Consider
the transformation of solid, liquid, gas, from one to another, under the
influence of heat. A solid, set in free motion, can follow only a
_line_--as is the case of a thrown ball. A liquid has the added power of
lateral extension. Its tendency, when intercepted, is to spread out in the
two dimensions of a _plane_--as in the case of a griddle cake; while a
gas expands universally in all directions, as shown by a soap-bubble. It
is a reasonable inference that the fourth state of matter, the corpuscular,
is affiliated to some four-dimensional manner of extension, and that
there may be states beyond this, involving even higher development of
space.
Next glance at the vegetable kingdom. The seed, a point, generates a
line system, in stem, branches, twigs, from which depend planes in the
form of leaves and flowers, and from these come fruit, solids.
"The point, the line, the surface and the sphere, In seed, stem, leaf and
fruit appear."
A similar sequence may be noted within the body: the _line_-network
of the nerves conveys the message of sensation from the surface of the
body to some center in the solid, of the brain--and thence to the Silent
Thinker, "he who is without and within," or in terms of our hypothesis,
"he who dwells in higher space."
MAN THE GEOMETER
When man essays the rôle of creator he cannot do otherwise than
follow similar sequences: it is easy to discern dimensional progression
in the products of man's ingenuity and skill. Consider, for example, the
evolution of a building from its inception to its completion. It exists
first of all in the mind of the architect, and there it is indubitably

higher-spatial, for he can interpenetrate and examine every part, and he
can consider it all at once, viewing it simultaneously from without and
from within, just as one would be able to do in a space of four
dimensions. He begins to give his idea physical embodiment by making
with a pencil-_point, lines_ on a plane (a piece of paper), the third
dimension being represented by means of the other two. Next (if he is
careful and wise) he makes a three-dimensional model. From the
architect's drawings the engineer establishes his points, lays out his
angles, and runs his lines upon the site itself. The mason follows, and
with his footing courses makes ponderable and permanent the lines of
the engineer. These lines become in due course walls--vertical planes.
Floors and roofs--horizontal planes--follow, until some portion of
three-dimensional space has been enclosed.
Substantially the same sequence holds, whatever the kind of building or
the character of the construction--whether a steel-framed skyscraper or
a wooden shanty. A