Space As A Thought-category
( Originally Published 1916 )
" AND I KNOW NOT IF, SAVE IN THIS, SUCH GIFT BE ALLOWED TO MAN, THAT OUT OF THREE SOUNDS HE FRAME, NOT A FOURTH SOUND, BUT A STAR."
The human mind has so long followed its early cow-paths through the wilderness of sense that great hardihood is required even to suggest that there may be other and better ways of traversing the empirical common. It is in full consciousness of the danger of jungles that I proceed.
Three dimensions do not suffice to set forth the ways of our joy in the sense world about us. What of this perceptual residue? Obviously to give it ex-tension we shall have to ascribe to reality other dimensions than those of our present space-realm. Some disciple of Bergson interrupts : " Ah, this whereof you speak is a spiritual thing and as such is given by the intuition. Why, then, do you seek to spatialise it? " And the layman out of his mental repugnance to things mathematical echoes,
" Why? " I would answer that the process of creative involution makes imperative the transfixion by the intellect of these so-called spiritual perceptions. Although the intuition transcends the intelligence in its grasp of beauty and truth, we may attain to the higher insight it has to offer only if the things of the spirit become known to the intellect — a point in Bergson's philosophy which the majority of his readers overlook. " We have," he says, " to engender the categories of our thought; it is not enough that we determine what these are." Bergson is pre-eminently the prophet of the higher-space concept. We had done better to hold to Kant, for now we are not only confronted with the fourth dimension as a thought-form, but with the duty as well of furthering its creation. And in that light we have to regard what of worth and meaning our spiritual perceptions have for us.
The space wherein we live and move and have our being, ostensibly, is just so much of reality as our thought is able to compass. In fine, it is our thought which sets boundaries and marks out the ways by which we come and go. What wonder then that we regard space as a projection of the thinking principle ! And so it is — this finite space to which we ascribe length, breadth, and thickness, and think we have said it all; but quite otherwise that eternal realm which we occupy in common with beings higher than ourselves.
That the majority of persons are still feeling their way over the surface of things is attested by the general mental ineptitude for the study of solid geometry. Depth and height play little part in our physical perception. For nearly all of us the third dimension is practically unknown beyond the reach of a few feet. The aviator soaring aloft—why all the bravado of curve and loop? Sooner or later he will fall to his death. Ay, verily! but his is a joyous martyrdom making for the evolution of consciousness. Not always shall we crawl like flies the surface of our globe !
Although the scientist has found it useful on occasion to postulate the fourth dimension, he has not thought it necessary as yet to put it in the category of reality; much less has the layman. Consequently the mathematician holds the sole title to its knowledge unless we recognise the claims of the medium to a fourth-dimensional insight. There is much to-day, however, which points to our coming to such perception as. the natural result of our evolution and quite apart from geometrical abstractions or occultism. It is as though some great tidal wave had swept over space and we have, unbeknown to ourselves, been lifted by it to new heights. And when we have once obtained our spiritual balance we shall doubtless find that our space-world has taken to itself another direction, inconceivable as that now seems.
Space is more than room wherein to move about ; it is, first of all, the room in which we think, and upon the way we do so depends the number of its dimensions. If the attention has become " riveted to the object of its practical interest " to the extent that this is the only good the creature knows, then is its thought-form one-dimensional even though its bodily movements are three-spaced. The great Peacock Moth wings a sure course mate-ward to the mystification of the scientist ; the dog finds the direct way home — his master cannot tell how ; Rockefeller knows his goal and attains it, regardless of other moral worths. For these the way is certain. They can suffer no deflection since there are no relative values, no possible choices. Their purpose makes the road one-dimensional.
While a man's space-world is limited by his thought, it is, on the other hand, as boundless as his thought. That the world evolves with our consciousness, is at once the philosophy of " Creative Evolution " and of the higher-space theory, which is Creative Involution. Our present spatial milieu has settled down to a seemingly three-dimensional finality because our thought-form has become so habitual as to give rise to certain geometric axioms. All we need in order to come to a fourth-dimensional consciousness, said Henri Poincaré, " the greatest of moderns," is a new table of distribution : that is, a breaking up of old associations of ideas and the forming of new relations — a simple matter were it not for our mental inertia. Lester Ward speculates that life remained aquatic for the vast periods that paleontology would indicate : Cambrian, Silurian, Devonian, Carboniferous — a duration greater than all subsequent time — for the reason that the creature had not sufficiently progressed to move otherwise than in a straight line when actuated by the desire for food or mate. Life was not able to maintain it-self on land until it had overcome this one-dimensional limitation. A venturesome Pterodactyl was he who first essayed to make his way among the many obstructions to be found ashore! By what intuition was he impelled?
The significance of the much fumbling and groping of earth's creatures is the desire for a larger out-look. Man has to feel his way out of a three-fold world even as the worm out of his hole. That we are hearing much of the principle of relativity is perhaps the best indication we have that the collective human consciousness is about to enter a higher dimension. So long as man knew only an absolute good was his world a definitely determined world. Now that the question of relative values obtrudes itself on every side, the range of consciousness promises to be infinite.
" EARTH HERE, REBUKED BY OLYMPUS THERE."
All knowledge is a matter of proper placing — the relating of things one to another. The trained thinker, said Kant, is one in whom the space-sense is well developed. We have come to our present concept of space through long learning of the laws wherewith our sensations follow one another. None of these alone could have brought us to a three-way extension of matter ; for example, a purely visual space is four-dimensional. Nor is the external world the unmodified resultant of our bodily movements, for a strictly motor space would have as many directions as we have muscles.
Are we to regard geometry, then, as an experimental science? "Nature geometrises," but so did the gods before it — hence no earthborn thing this, the purest of all pastimes ! The experiment in the case concerns not what is the truth ; rather how to choose from all possible truths that one which best fits our human needs. What particular geometry we are destined to have is a question only of our understanding. As to its truth — as well ask if the metric system is true.
Of the infinite number of causes which give richness and depth to human experience, the intellect is able to grasp only a small part. Some of these we denominate love, justice, colour, distance. But whether the occurrence be due to change of state or of position, we perceive it as a transformation within an aggregate of sense impressions. In order, then, to reduce the realm of consciousness to unity, each cause must work uniformly with the others : that is, be expressible in terms of the others. And since what lawdom the mind has thus far achieved is based on spatial relations, the hyper-space theory offers the quickest method to the systematisation of experience.
The scientist is finding that, as he studies matter more closely, he has need of other dimensions than the conventional three. While the larger movements of the physical realm are still duly categorised on the hypothesis of a three-dimensional space, there are other movements within the minute structure of organisms which require a finer net for their snaring. But given the proper leeway, a molecular force takes on the aspect of a motor force and is quickly classified.
Psychic phenomena are fast yielding to measurement, as the psychological laboratories of our universities attest. That things transcendental will give up their mystery with a larger spatial outlook is highly probable in view of the analogy obtaining between spiritual laws and fourth-dimensional proper-ties. Mr. Hinton found, for instance, that the first requisite to higher space perception was the doing away with self-elements (right and left; up and down) ; he had, as he phrases it, to acquire an altruistic knowledge 3 of a block of cubes. And in order to take the view of a higher being, in general one has to live openly,— to understand one's fellows as they are in their true selves, and not in their outward forms. Indeed, it may well be that those who feel within them the immanence of a higher life are best fitted to visualise for us the fourth-dimensional reaches that lie all about our mundaneness.
How is it that four-dimensional processes and motions can be limited to the three-dimensional representations that we observe? In other words, what is the reality of which the present sense experience is but the shadow? 4 These are the questions we have to ask ourselves, and to solve if we would attain to the fourth dimension of being,— for greatly do we delude ourselves if we think it is to come " out of the blue." To illustrate the sort of one-to-one correspondence that may be set up between the new world and this, our old: a fourth-dimensional movement may be, as Mr. Bragdon suggests, the proximate cause of the phenomenon of growth. Likewise the density of a body, according to Dr. Blake, may be taken as our perception of its thickness in hyper-space. In fine, to acquire the sense of another direction, we have to regard this all-too-solid world as merely the kinematographic representation of realities beyond our physical ken.