Part 3

Without going deep into the doctrine of the ideality--that is, the purely subjective reality--of space, it is easy to show that we have arrived at our conception of a space of three dimensions by an intellectual process. The sphere of the senses is two-dimensional: except for the slight aid afforded by binocular vision, sight gives us moving pictures on a plane, and touch contacts surfaces only. What circumstances, we may ask, have compelled our intellect to conceive of solid space? This question has been answered as follows:

"If a child contemplates his hand, he is conscious of its existence in a double manner--in the first place by its tangibility, the second by its image on the retina of his eye. By repeated groping about and touching, the child knows by experience that his hand retains the same form and extension through all the variations of distance and position under which it is observed, notwithstanding that the form and extension of the image on the retina constantly change with the different position and distance of his hand in respect to his eye. The problem is thus set to the child's understanding: how to reconcile to his comprehension the apparently contradictory facts of the invariableness of the object together with the variableness of its appearance. This is only possible within a space of three dimensions, in which, owing to perspective distortions and changes, these variations of projection can be reconciled with the constancy of the form of a body."

Thus we have come to the idea of a three-dimensional space in order to overcome the apparent contradictoriness of facts of sensible experience. Should we observe in three-dimensional space contradictory facts our reason would be forced to reconcile these contradictions, also, and if they could be reconciled by the idea of a four-dimensional space our reason would accept this idea without cavil. Furthermore, if from our childhood, phenomena had been of daily occurrence requiring a space of four or more dimensions for an explanation conformable to reason, we should feel ourselves native to a space of four or more dimensions.

Poincaré, the great French mathematician and physicist, arrived at these same conclusions by another route. By a process of mathematical reasoning of a sort too technical to be appropriately given here, he discovers an order in which our categories range themselves naturally, and which corresponds with the points of space; and that this order presents itself in the form of what he calls a "three circuit distribution board." "Thus the characteristic property of space," he says, "that of having three dimensions, is only a property of our distribution board, a property residing, so to speak, in human intelligence." He concludes that a different association of ideas would result in a different distribution board, and that might be sufficient to endow space with a fourth dimension. He concedes that there may be thinking beings, living in our world, whose distribution board has four dimensions, and who do consequently think in hyperspace.

THE NEED OF AN ENLARGED SPACE-CONCEPT

It is the contrariety in phenomena already referred to, that is forcing advanced minds to entertain the idea of higher space. Mathematical physicists have found that experimental contradictions disappear if, instead of referring phenomena to a set of three space axes and one time axis of reference, they be referred to a set of four interchangeable axes involving four homogeneous co-ordinates. In other words, time is made the fourth dimension. Psychic phenomena indicate that occasionally, in some individuals, the will is capable of producing physical movements for whose geometrico-mathematical definition a four-dimensional system of co-ordinates is necessary. This is only another step along the road which the human mind has always travelled: our conception of the cosmos grows more complete and more just at the same time that it recedes more and more beneath the surface of appearances.

Far from the Higher Space Hypothesis complicating thought, it simplifies by synthesis and co-ordination in a manner analogous to that by which plane geometry is simplified when solid geometry becomes a subject of study. By immersing the mind in the idea of many dimensions, we emancipate it from the idea of dimensionality. But the mind moves most readily, as has been said, in ordered sequence. Frankly submitting ourselves to this limitation, even while recognizing it as such, let us learn such lessons from it as we can, serving the illusions that master us until we have made them our slaves.

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."