Four-Dimensional Vistas | Page 6

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 r?le 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 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