The spatial understanding of time. The angles and curves of the fourth dimension in our life. Does motion exist in the world or not? Mechanical motion and "life." Biological phenomena as the manifestation of motions going on in the higher dimension. Evolution of the space-sense. The growth of the space-sense and the diminution of the time-sense. The transformation of the time-sense into the space-sense. The difficulties of our language and of our concepts. The necessity for seeking a method of spatial expression for temporal concepts. Science in relation to the fourth dimension. The solid of four dimensions. The four-dimensional sphere.
NOW from the basis of those conclusions already made, let us seek to define how we may discover the real four-dimensional world obscured from us by the illusory three-dimensional world. "See" it we may by two methods: either by sensing it directly, by developing the "space-sense" and other higher faculties, which will be discussed later; or by understanding it mentally by a perception of its possible properties through the exercise of the reason.
By abstract reasoning, we have already come to the conclusion that the fourth dimension of space must lie in time, i.e., that time is the fourth dimension of space. We have already discovered psychological proofs of this thesis. Comparing the receptivity of the world by living beings of different grades of consciousness—snail, dog and man—we have seen how different for them are the properties of one and the same world; namely, those properties which are expressed for us in the concepts of time and space. We have seen that time and space are sensed by each in a different manner: that what for the lower being (the snail) is time, for the being standing one degree higher (the dog) becomes space, and that the time of this being becomes space to a being standing still higher—man.
This is a confirmation of the supposition previously expressed, that our idea of time is complex in its nature, and that in it are properly included two ideas—that of a certain space and that of motion upon this space. Or to put the matter more exactly, the contact with a certain space of which we are not clearly conscious calls forth in us the sensation of motion upon that space; and all this taken together, i.e., the unclear consciousness of a certain space and the sensation of motion upon that space, we call time.
This last confirms the conception that the idea of time has not arisen from the observation of motion existing in nature, but that the very sensation and idea of motion has arisen from a "time-sense" existing in ourselves, which is an imperfect sense of space: the fringe, or limit of our space-sense.
The snail feels the line as space, i.e., as something constant. It feels the rest of the world as time, i.e., as something eternally moving. The horse feels the plane as space. It feels the rest of the world as time.
We feel an infinite sphere as space; the rest of the world, that which was yesterday and that which will be tomorrow, we feel as time.
In other words, every being feels as space that which is grasped by his space-sense: the rest he refers to time; i.e., the imperfectly felt is referred to time. Or it is possible to formulate the matter thus: every being feels as space that which, by the aid of his space-sense he is able to represent to himself in form, outside of himself; and that which he is not able thus to represent he feels as time, i.e., eternally moving, impermanent, so unstable that it is impossible to imagine it in terms of form.
THE SENSE OF SPACE (SPACE-SENSE) IS THE POWER OF REPRESENTATION BY MEANS OF FORM.
The "infinite sphere" by which we represent the universe to ourselves is constantly and continuously changing: in every consecutive moment it is not that which it was before. A constant change of pictures, images, relations, is going on therein. It is for us as it were the screen of a cinematograph upon which the swiftly running images of pictures appear and disappear.
But where are the pictures themselves? Where is the light throwing the image upon the screen? Whence do the pictures come, and whither do they go?
If the "infinite sphere" is the screen of the cinematograph so our consciousness is the light, penetrating through our psyche: i.e., through the stores of our impressions (pictures) it (the light) throws upon the screen their images which we call life.
But where do the impressions come from to us?
From the same screen.
And herein dwells the most incomprehensible mystery of life as we see it. We are creating it and we are receiving everything from it.
Imagine a man sitting in the ordinary moving-picture theatre. Imagine that he knows nothing of the construction of the cinematograph, nothing of the existence of the lantern behind his back, nor of the small transparent picture on the moving film. Let us imagine that he wants to study the cinematograph, and begins to study that which proceeds on the screen, to make notes, to take pictures, to observe the order, to calculate, to construct hypotheses, and so forth.
At what will he arrive?
Evidently at nothing at all, unless he will turn his back to the screen, and will begin to study the cause of the appearance of the pictures upon the screen. The cause is confined in the lantern (i.e., in consciousness), and in the moving films of pictures (in the psyche). These it is necessary to study, desiring to understand the "cinematograph."
Positive philosophy studies only the screen and the pictures passing upon it. For this reason the eternal enigma remains for it: wherefrom are the pictures coming and where are they going, and why are they coming and going instead of remaining eternally the same?
But it is necessary to study the cinematograph beginning with the source of light, i.e., with consciousness, then to pass on to the pictures on the moving film, and only after that to study the projected image.
We have established that the animal (the horse, the cat, the dog) must perceive the immobile angles and curves of the third dimension as motion, i.e., as temporal phenomena.
The question arises: do not we perceive as motion, i.e., as temporal phenomena, the immobile angles and curves of the fourth dimension? We ordinarily say that our sensations are the moments of the apprehension of certain changes proceeding outside of us; such are sound, light, etc., all "vibrations of the ether." But what are these "changes?" Perhaps in reality there are no changes at all. Perhaps the immobile sides and angles of certain things which exist outside of us—of certain things which we know nothing about—only appear to us as motions, i.e., as changes.
It may be that our consciousness, not being able to embrace these things with the aid of the organs of sense, and to represent them to itself in their entirety, just as they are, and grasping only the separate moments of its contact with them, is constructing the illusion of motion, and conceives that something is moving outside of it (of consciousness), i.e., that the "things" are themselves moving.
If such is the case, then "motion" must be in reality something only "derived," arising in our intellect during its contact with things which it does not grasp in their totality. Let us imagine that we are approaching an unknown city, and that it is slowly "growing up" before us as we approach. It appears to us as if it is really growing up, i.e., as though it did not exist before. There disappeared the river, which was visible for so long a time; there appeared the bell-tower, which was invisible before.
Such, exactly, is our relation to time, which is a continual coming—arising, as it were, from nothing and going into naught.
Every thing lies for us in time, and only the section of the thing lies in space. Transferring our consciousness from the section of the thing to those parts of it which lie in time, we receive the illusion of motion on the part of the thing itself.
It is possible to formulate the matter thus: the sensation of motion is the consciousness of the transition from space to time, i.e., from a clear space-sense to one that is unclear. With this in mind it is not difficult to realize that we are receiving as sensations, and projecting into the outside world as phenomena, the immobile angles and curves of the fourth dimension.
On this account is it not necessary and possible to recognize that the world is immobile and constant, and that it seems to us to be moving and evolving simply because we are looking at it through the narrow slit of our sensuous receptivity?
We are returning again to the question: what is the world and what is consciousness? But now the question concerning the relation of our consciousness to the world is beginning to be formulated for us.
If the world is a Great Something, possessing the consciousness of itself, so we are rays of that consciousness which are conscious of themselves, but unconscious of the whole.
If there be no motion, if it be an illusion, then we must search further—whence could this illusion have arisen?
The phenomena of life—biological phenomena—much resemble the transition through our space of certain four-dimensional circles, the circles being extremely complicated, every one consisting of a great number of interlaced lines.
The life of a man or of any other living being suggests a complicated circle. It begins always at one point (birth) and ends always at one point (death). We have complete justification for supposing that it is one and the same point. The circles are large and small, but they begin and end similarly, and they end at the same point where they began, i.e., at the point of non-existence, from the physico-biological standpoint, or of some existence other than the psychological one.
What is the biological phenomenon, the phenomenon of life? Our science does not answer this question. This is the enigma. In the living organism, in the living cell, in the living protoplasm there is something indefinable, differentiating, living matter from dead matter. We recognize this something only by its functions. The chief of these functions is the power of self-reproduction—absent in the dead organism, the dead cell, dead matter.
The living organism multiplies infinitely, incorporating and assimilating dead matter into itself. This ability to reproduce itself and to absorb dead matters with its mechanical laws is the inexplicable function of "life," showing that life is not simply a complex of mechanical forces, as the positivist philosophy attempts to prove.
This thesis, that life is not a complex of mechanical forces, is corroborated also by the incommensurability of the phenomena of mechanical motion with the phenomena of life. Life phenomena cannot be expressed in terms of mechanical energy, calories of heat or units of horse power; nor can the phenomena of life be artificially created by the physico-chemical method.
If we shall regard every separate life as a circle of the fourth dimension, this will make clear to us why every circle is inevitably escaping from our space. This happens because the circle inevitably ends in the same point at which it began, and the "life" of the separate being, beginning with birth, must end in death, which is the return to the point of departure. But during its transit through our space, the circle puts forth from itself certain lines, which, uniting with others, yield new circles.
In reality of course all this proceeds quite otherwise: nothing is born and nothing dies; it only so represents itself to us, because we see but the sections of things. In reality, the circle of life is only the section of something, and that something undoubtedly exists before birth, i.e., before the appearance of the circle in our space, and continues to exist after death, i.e., after the disappearance of the circle from the field of our vision.
To our observation the phenomena of life are similar to the phenomena of motion as these appear to the two-dimensional being; and therefore it may be that this is "the motion in the fourth dimension."
We have seen that the two-dimensional being is bound to regard the properties of the three-dimensionality of solids as motions, and the real motions of solids, going on in the higher space as the phenomena of life.
In other words, that motion which remains a motion in the higher space appears to the lower being as a phenomenon of life, and that which disappears in the higher space, transforming itself into the property of an immobile solid, appears to the lower being as mechanical motion.
The phenomena of "life" and the phenomena of "motion" are just as incommensurable for us as are the two kinds of motion in its world for the two-dimensional being; one of these motions being real and the other illusory.
Hinton says of this incommensurability: "There is something in life not included in our conception of mechanical movement. Is this something a four-dimensional movement?
"If we look at it from the broadest point of view there is something striking in the fact that where life comes in there arises an entirely different set of phenomena from those of the inorganic world."
Upon this basis it is justifiable to assume that those phenomena which we call the phenomena of life are movements in higher space. Those phenomena which we call mechanical motion become in turn the phenomena of life in a space lower relatively to ours, and in one higher, simply the properties of immobile solids. This means that if we consider three kinds of existence—the two-dimensional, ours, and the higher dimensional—then it will appear that the "motion" which is observed by the two-dimensional being in two-dimensional space, is for us a property of immobile solids; "life" as it is apprehended in two-dimensional space, is "motion" as we observe it in our space. Moreover, motions in three-dimensional space, i.e., all our mechanical motions and the manifestations of physico-chemical forces—light, sound, heat, etc.,—are only our sensations of some to us incomprehensible properties of four-dimensional solids; and our "phenomena of life" are the motions of solids of higher space which appear to us as the birth, growth, and life of living beings. But if we presuppose a space not of four, but of five dimensions, then in it the "phenomena of life" would probably appear as the properties of immobile solids—genus, species, families, peoples, races, and so forth—and motions would seem, perhaps, only the phenomena of thought.
We know that the phenomena of motion or the manifestations of energy are involved with the expenditure of time, and we see how, with the gradual transcendence of the lower space by the higher, motion disappears, being converted into the properties of immobile solids; i.e., the expenditure of time disappears—and the necessity for time. To the two-dimensional being time is necessary for the understanding of the most simple phenomena—an angle, a hill, a ditch. For us time is not necessary for the understanding of such phenomena, but is necessary for the explanation of the phenomena of motion and physical phenomena. In a space still higher, our phenomena of motion and physical phenomena would probably be regarded independently of time, as properties of immobile solids; and biological phenomena— birth, growth, reproduction, death—would be regarded as phenomena of motion.
Thus we see how the idea of time recedes with the expansion of consciousness.
We see its complete conditionality.
We see that by time are designated the characteristics of a space relatively higher than a given space—i.e., the characteristics of the perceptions of a consciousness relatively higher than a given consciousness.
For the one-dimensional being all the indices of two-, three-, four-dimensional space and beyond, lie in time—all this is time. For the two-dimensional being time embraces within itself the indices of three-dimensional space, four-dimensional space, and all spaces beyond. For man, i.e., the three-dimensional being, time contains the indices of four-dimensional space and all spaces beyond.
Therefore, according to the degree of expansion and elevation of the consciousness and the forms of its receptivity the indices of space are augmented and the indices of time are diminished.
In other words, the growth of the space-sense is proceeding at the expense of the time-sense. Or one may say that the time-sense is an imperfect space-sense (i.e., an imperfect power of representation which, being perfected, translates itself into the space-sense, i.e., into the power of representation in forms.
If, taking as a foundation the principles elucidated here, we attempt to represent to ourselves the universe very abstractedly, it is clear that this will be quite other than the universe which we are accustomed to imagine to ourselves. Everything will exist in it always.
This will be the universe of the Eternal Now of Hindu philosophy—a universe in which will be neither before nor after, in which will be just one present, known or unknown.
Hinton feels that with the expansion of the space-sense our vision of the world will change completely, and he tells about this in his book, A New Era of Thought. (p. 66.)
The conception which we shall form of the universe will undoubtedly be as different from our present one, as the Copernican view differs from the more pleasant view of a wide, immovable earth beneath a vast vault. Indeed, any conception of our place in the universe will be more agreeable than the thought of being on a spinning ball, kicked into space without any means of communication with any other inhabitants of the universe.
But what does the world of many dimensions represent in itself—what are these solids of many dimensions the lines and boundaries of which we perceive as motion?
A great power of imagination is necessary to transcend the limits of our perceptions and to visualize mentally the world in other categories even for a moment.
Let us imagine some object, say a book, outside of time and space. What will this last mean? Were we to take the book out of time and space it would mean that all books which have existed, exist now, and will exist, exist together, i.e., occupy one and the same place and exist simultaneously, forming as it were one book which includes within itself the properties, characteristics and peculiarities of all books possible in the world. When we say simply, a book, we have in mind something possessing the common characteristic of all books—this is a concept. But that book about which we are talking now, possesses not only these common characteristics but the individual characteristics of all separate books.
Let us take other things—a table, a house, a tree, a man. Let us imagine them out of time and space. The mind will have to open its doors to objects each possessing such an enormous, such an infinite number of signs and characteristics that to comprehend them by means of the reason is absolutely impossible. And if one wants to comprehend them by his reason he will certainly be forced to dismember these objects somehow, to take them at first in some one sense, from one side, in one section of their being. What is "man" out of space and time? He is all humanity, man as the "species"—Homo Sapiens, but at the same time possessing the characteristics, peculiarities and individual ear-marks of all separate men. This is you, and I, and Julius Caesar and the conspirators who killed him, and the newsboy I pass every day—all kings, all slaves, all saints, all sinners—all taken together, fused into one indivisible being of a man, like a great living tree in which are bark, wood, and dry twigs; green leaves flowers and fruit. Is it possible to conceive of and understand such a being by our reason?
The idea of such a "great being" inspired the artist or artists who created the Sphinx.
But what is motion? Why do we feel it if it does not exist? About this last, Mabel Collins, a theosophical writer of the first period of modern theosophy, writes very beautifully in her poetical Story of the Year.
. . . The entire true meaning of the earthly life consists only in the mutual contact between personalities and in the efforts of growth. Those things which are called events and circumstances and which are regarded as the real contents of life—are in reality only the conditions which make these contacts and this growth possible.
In these words there sounds already quite a new understanding of the real. And truly the illusion of motion cannot arise out of nothing. When we are travelling by train, and the trees are running, overtaking one another, we know that this motion is an illusory one, that the trees are immobile, and that the illusion of their motion is created by our own.
As in these particular cases, so also in general as regards all motion in the material world, the foundation of which the "positivists" consider to be motion in the finest particles of matter, we, recognizing this motion as an illusory one, will ask: Is not an illusion of this motion created by some motion inside our consciousness?
So it will be.
And having established this, we shall endeavor to define what kind of motion is going on inside our consciousness, i.e., what is moving relatively to what?
H. P. Blavatsky, in her first book, Isis Unveiled, touched upon the same question concerning the relation of life to time and motion. She writes:
As our planet revolves every year around the sun and at the same time turns once in every twenty-four hours upon its own axis, thus traversing minor cycles within a larger one, so is the work of the smaller cyclic periods accomplished and recommenced.
The revolution of the physical world, according to the ancient doctrine, is attended by a like revolution in the world of intellect—the spiritual evolution of the world proceeding in cycles, like the physical one.
Thus we see in history a regular alternation of ebb and flow in the tide of human progress. The great kingdoms and empires of the world, after reaching the culmination of their greatness, descend again in accordance with the same law by which they ascended; till, having reached the lowest point, humanity reasserts itself and mounts up once more, the height of its attainment being, by this law of ascending progression by cycles, somewhat higher than the point from which it had before descended.
The division of the history of mankind into Golden, Silver, Copper and Iron Ages, is not a fiction. We see the same thing in the literature of peoples. An age of great inspiration and unconscious productiveness is invariably followed by an age of criticism and consciousness. The one affords material for the analyzing and critical intellect of the other.
Thus all those great characters who tower like giants in the history of mankind, like Buddha-Siddârtha, and Jesus, in the realm of spiritual, and Alexander the Macedonian and Napoleon the Great, in the realm of physical conquests, were but reflexed images of human types which had existed ten thousand years before, in the preceding decimillennium, reproduced by the mysterious powers controlling the destinies of our world. There is no prominent character in all the annals of sacred or profane history whose prototype we cannot find in the half-fictitious and half-real traditions of bygone religions and mythologies. As the star, glimmering at an immeasurable distance above our heads, in the boundless immensity of the sky, reflects itself in the smooth waters of a lake, so does the imagery of men of the antediluvian ages reflect itself in the periods we can embrace in an historical retrospect.
As above, so below. That which has been will return again. As in heaven, so on earth.
Anything that can be said about the understanding of temporal relations is inevitably extremely vague. This is because our language is absolutely inadequate to the spatial expression of temporal relations. We lack the necessary words for it, we have no verbal forms, strictly speaking, for the expression of these relations which are new to us, and some other quite new forms—not verbal—are indispensable. The language for the transmission of the new temporal relations must be a language without verbs. New parts of speech are necessary, an infinite number of new words. At present, in our human language we can speak about "time" by hints only. Its true essence is inexpressible for us.
We should never forget about this inexpressibility. This is the sign of the truth, the sign of reality. That which can be expressed, cannot be true.
All systems dealing with the relation of the human soul to time—all ideas of post-mortem existence, the theory of re-incarnation, that of the transmigration of souls, of karma—are symbols, trying to transmit relations which cannot be expressed directly because of the poverty and the weakness of our language. They should not be understood literally any more than it is possible to understand the symbols and allegories of art literally. It is necessary to search for their hidden meanings, that which cannot be expressed in words.
The literal understanding of these symbolical forms in certain lines of contemporary literature, and the union with them of ideas of "evolution" and "morals" taken in the most narrow, dualistic meaning, completely disfigures the inner content of these forms, and deprives them of their value and meaning.