Four-Dimensional Vistas

by Claude Fayette Bragdon

II THE DIMENSIONAL LADDER

LEARNING TO THINK IN TERMS OF SPACES

The Reader who is willing to consider the Higher Space Hypothesis seriously, who would discover, by its aid, new and profound truths closely related to life and conduct, should first of all endeavor to arouse in himself a new power of perception. This he will best accomplish by learning to discern dimensional sequences, not alone in geometry, but in the cosmos and in the natural world. By so doing he may erect for himself a veritable Jacob's ladder,

"Pitched between Heaven and Charing Cross."

He should accustom himself to ascend it, step by step, dimension by dimension. Then he will learn to trust Emerson's dictum, "Nature geometrizes," even in regions where the senses fail him, and the mind alone leads on. Much profitable amusement is to be gained by such exercises as follow. They are in the nature of a running up and down the scales in order to give strength and flexibility to a new set of mental fingers. Learning to think in terms of spaces contributes to our emancipation from the tyranny of space.

FROM THE COSMOS TO THE CORPUSCLE

By way of a beginning, proceed, by successive stages, from the contemplation of the greatest thing conceivable to the contemplation of the most minute, and note the space sequences revealed by this shifting of the point of view.

The greatest thing we can form any conception of is the starry firmament made familiar to the mind through the study of astronomy. No limit to this vastitude has ever been assigned. Since the beginning of recorded time, the earth, together with the other planets and the sun, has been speeding through interstellar space at the rate of 300,000,000 miles a year, without meeting or passing a single star. A ray of light, travelling with a velocity so great as to be scarcely measurable within the diameter of the earth's orbit, takes years to reach even the nearest star, centuries to reach those more distant. Viewed in relation to this universe of suns, our particular sun and all its satellites—of which the earth is one—shrinks to a point (a physical point, so to speak—not geometrical one).

The mind recoils from these immensities: let us forsake them, then, for more familiar spaces, and consider the earth in its relation to the sun. Our planet appears as a moving point, tracing out a line—a one-space—its path around the sun. Now let us remove ourselves in imagination only far enough from the earth for human beings thereon to appear as minute moving things, in the semblance, let us say, of insects infesting an apple. It is clear that from this point of view these beings have a freedom of movement in their "space" (the surface of the earth), of which the larger unit is not possessed; for while the earth itself can follow only a line, its inhabitants are free to move in the two dimensions of the surface of the earth.

Abandoning our last coign of vantage, let us descend in imagination and mingle familiarly among men. We now perceive that these creatures which from a distance appeared as though flat upon the earth's surface, are in reality erect at right angles to its plane, and that they are endowed with the power to move their members in three dimensions. Indeed, man's ability to traverse the surface of the earth is wholly dependent upon his power of three-dimensional movement. Observe that with each transfer of our attention from greater units to smaller, we appear to be dealing with a power of movement in an additional dimension.

Looking now in thought not at the body of man, but within it, we apprehend an ordered universe immensely vast in proportion to that physical ultimate we name the electron, as is the firmament immensely vast in proportion to a single star. It has been suggested that in the infinitely minute of organic bodies there is a power of movement in a fourth dimension. If so, such four-dimensional movement may be the proximate cause of the phenomenon of growth—of those chemical changes and renewals whereby an organism is enabled to expand in three-dimensional space, just as by a three-dimensional power of movement (the act of walking) man is able to traverse his two-dimensional space—the surface of the earth.

—AND BEYOND

Proceed still further. Behind such organic change—assumed to be four-dimensional—there is the determination of some will-to-live, which manifests itself to consciousness as thought and as desire. Into these the idea of space does not enter: we think of them as in time. But if there are developments of other dimensions of space, thought and emotion may themselves be discovered to have space relations; that is, they may find expression in the forms of higher spaces. Thus is opened up one of those rich vistas in which the subject of the fourth dimension abounds, but into which we can only glance in passing. If there are such higher-dimensional thought-forms, our normal consciousness, limited to a world of three dimensions, can apprehend 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 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.