CHAPTER IV
In what direction may the fourth dimension lie? What is motion? Two kinds of motion—motion in space and motion in time—which are contained in every movement. What is time? Two ideas contained in the conception of time. The new dimension of space, and motion upon that dimension. Time as the fourth dimension of space. Impossibility of understanding the fourth dimension without the idea of motion. The idea of motion and the "time-sense." The time-sense as a limit (surface) of the "space-sense." Hinton on the law of surfaces. The "ether" as a surface. Riemann's idea concerning the translation of time into space in the fourth dimension. Present, past, and future. Why we do not see the past and the future. Life as a feeling of one's way. Wundt on the subject of our sensuous knowledge.
WE have established by a comparison of the relation of lower dimensional figures to higher dimensional ones that it is possible to regard a four-dimensional body as the tracing of the motion of a three-dimensional body upon the dimension not contained in it; i.e., that the direction of the motion upon the fourth dimension lies outside of all the directions which are possible in three-dimensional space.
But in what direction is it?
In order to answer this question it will be necessary to discover whether we do not know some motion not confined in three-dimensional space.
We know that every motion in space is accompanied by that which we call motion in time. Moreover, we know that everything existing, even if not moving in space, moves eternally in time.
And equally in all cases, whether speaking of motion or absence of motion, we have in mind an idea of what was before, what now becomes, and what will follow after. In other words, we have in mind the idea of time. The idea of motion of any kind, also the idea of absence of motion, is indissolubly bound up with the idea of time. Any motion or absence of motion proceeds in time and cannot proceed out of time. Consequently, before speaking of what motion is, we must answer the question, what is time?
Time is the most formidable and difficult problem which confronts humanity.
Kant regards time as he does space: as a subjective form of our receptivity; i.e., he says that we create time ourselves, as a function of our receptive apparatus, for convenience in perceiving the outside world. Reality is continuous and constant, but in order to make possible the perception of it, we must dissever it into separate moments; imagine it as an infinite series of separate moments out of which there exists for us only one. In other words, we perceive reality as if through a narrow slit, and what we are seeing through this slit we call the present; what we did see and now do not see—the past; and what we do not quite see but are expecting—the future.
Regarding each phenomenon as an effect of another, or others, and this in its turn as a cause of a third; that is, regarding all phenomena in functional interdependence one upon another, by this very act we are contemplating them in time, because we picture to ourselves quite clearly and precisely first a cause, then an effect; first an action, then its function; and cannot contemplate them otherwise. Thus we may say that the idea of time is bound up with the idea of causation and functional interdependence. Without time, causation cannot exist, just as without time, motion or the absence of motion cannot exist.
But our perception concerning our "being in time" is entangled and misty up to improbability.
First of all let us analyze our relation toward the past, present and future. Usually we think that the past already does not exist. It has passed, disappeared, altered, transformed itself into something else. The future also does not exist—it does not exist as yet. It has not arrived, has not formed. By the present we mean the moment of transition of the future into the past, i.e., the moment of transition of a phenomenon from one non-existence into another non-existence. For that moment only does the phenomenon exist for us in reality; before, it existed in potentiality, afterward it will exist in remembrance. But this short moment is after all only a fiction: it has no measurement. We have a full right to say that the present does not exist. We can never catch it. That which we did catch is always the past!
If we are to stop at that we must admit that the world does not exist, or exists only in some phantasmagoria of illusions, flashing and disappearing.
Usually we take no account of this, and do not reflect that our customary view of time leads to utter absurdity.
Let us imagine a stupid traveller going from one city to another and half way between these two cities. A stupid traveller thinks that the city from which he has departed last week does not exist now: only the memory of it is left; the walls are ruined, the towers fallen, the inhabitants have either died or gone away. Also, that city at which he is destined to arrive in several days does not exist now either, but is being hurriedly built for his arrival, and on the day of that arrival will be ready, populated, and set in order, and on the day after his departure will be destroyed just as was the first one.
We are thinking of things in time exactly in this way—everything passes away, nothing returns! The spring has passed, it does not exist still. The autumn has not come, it does not exist as yet.
But what does exist?
The present.
But the present is not a seizable moment, it is continuously transitory into the past.
So, strictly speaking, neither the past, nor the present, nor the future exists for us. Nothing exists! And yet we are living, feeling, thinking—and something surrounds us. Consequently, in our usual attitude toward time there exists some mistake. This error we shall endeavor to detect.
We accepted at the very beginning that something exists. We called that something the world. How then can the world exist if it is not existing in the past, in the present and in the future?
That conception of the world which we deduced from our usual view of time makes the world appear like a continuously gushing out igneous fountain of fireworks, each spark of which flashes for a moment and disappears, never to appear any more. Flashes are going on continuously, following one after another, there are an infinite number of sparks, and everything together produces the impression of a flame, though it does not exist in reality.
The autumn has not yet come. It will be, but it does not exist now. And we give no thought to how that can appear which is not.
We are moving upon a plane, and recognize as really existing only the small circle lighted by our consciousness. Everything out of this circle, which we do not see, we negate; we do not like to admit that it exists. We are moving upon the plane in one direction. This direction we consider as eternal and infinite. But the direction at right angles to it, those lines which we are intersecting, we do not like to recognize as eternal and infinite. We imagine them as going into non-existence at once, as soon as we, have passed them, and that the lines before us have not as yet risen out of non-existence. If, presupposing that we are moving upon a sphere, upon its equator or one of its parallels, then it will appear that we recognize as really existing only one meridian: those which are behind us have disappeared and those ahead of us have not appeared as yet. .
We are going forward like a blind man, who feels paving stones and lanterns and walls of houses with his stick and believes in the real existence of only that which he touches now, which he feels now. That which has passed has disappeared and will never return! That which has not as yet been does not exist. The blind man remembers the route which he has traversed; he expects that ahead the way will continue, but he sees neither forward nor backward because he does not see anything; because his instrument of knowledge—the stick—has a definite, and not very great length, and beyond the reach of his stick non-existence begins.
Wundt, in one of his books, called attention to the fact that our vaunted five organs of sense are in reality just feelers by which we feel the world around us. We live groping about. We never see anything. We are always just feeling everything. With the help of the microscope and the telescope, the telegraph and the telephone, we are extending our feelers a little, so to speak, but we are not beginning to see. To say that we are seeing would be possible only in case we could know the past and the future. But we do not see, and because of this we can never assure ourselves of that which we cannot feel.
This is the reason why we count as really existing only that circle which our feelers grasp at a given moment. Beyond that—darkness and non-existence.
But have we any right to think in this way?
Let us imagine a consciousness that is not bound by the conditions of sensuous receptivity. Such a consciousness can rise above the plane upon which we are moving; it can see far beyond the limits of the circle enlightened by our usual consciousness; it can see that not only does the line upon which we are moving exist, but also all lines perpendicular to it which we are intersecting, which we have ever intersected, and which we shall intersect. After rising above the plane this consciousness can see the plane, can convince itself that it is really a plane, and not a single line. Then it can see the past and the future, lying together and existing simultaneously.
That consciousness which is not bound by the conditions of sensuous receptivity can outrun the stupid traveller, ascend the mountain to see in the distance the town to which he is going, and be convinced that this town is not being built anew for his arrival, but exists quite independently of the stupid traveller. And that consciousness can look off and see on the horizon the towers of that city where that traveller had been, and be convinced that those towers have not fallen, that the city continues to stay and live just as it stayed and lived before the traveller's advent.
It can rise above the plane of time and see the spring behind and the autumn ahead, see simultaneously the budding flowers and ripening fruits. It can make the blind man recover his sight and see the road along which he passed and that which still lies before him.
The past and the future cannot not exist, because if they do not exist then neither does the present exist. Unquestionably they exist somewhere together, but we do not see them.
The present, compared with the past and the future, is the most unreal of all unrealities.
We are forced to admit that the past, the present and the future do not differ in anything, one from another; there exists just one present—the Eternal Now of Hindu philosophy. But we do not perceive this, because in every given moment we experience just a little bit of that present, and this alone we count as existent, denying a real existence to everything else.
If we admit this, then our view of everything with which we are surrounded will change very considerably.
Usually we regard time as an abstraction, made by us during the observation of really existing motion. That is, we think that observing motion, or changes of relations between things and comparing the relations which existed before, which exist now, and which may exist in the future, that we are deducing the idea of time. We shall see later on how far this view is correct.
Thus the idea of time is composed of the conception of the past, of the present, and of the future.
Our conceptions of the past and present, though not very clear, are yet very much alike. As to the future there exists a great variety of views.
It is necessary for us to analyze the theories of the future as they exist in the mind of contemporary man.
There are in existence two theories—that of the foreordained future, and that of the free future.
Foreordination is established in this way: we say that every future event is the result of those which happened before, and is created such as it will be and not otherwise as a consequence of a definite direction of forces which are contained in preceding events. This means, in other words, that future events are 'wholly contained in preceding ones, and if we could know the force and direction of all events which have happened up to the present moment, i.e., if we knew all the past, by this we could know all the future. And sometimes, knowing the present moment thoroughly, in all its details, we may really foretell the future. If the prophecy is not fulfilled, we say that we did not know all that had been, and we discover in the past some cause which had escaped our observation.
The idea of the free future is founded upon the possibility of voluntary action and accidental new combinations of causes. The future is regarded as quite indefinite, or defined only in part, because in every given moment new forces, new events and new phenomena are born which lie in a potential state, not causeless, but so incommensurable with causes—as the firing of a city from one spark—that it is impossible to detect or measure them.
This theory affirms that one and the same action can have different results; one and the same cause, different effects; and it introduces the hypothesis of quite arbitrary volitional actions on the part of a man, bringing about profound changes in the subsequent events of his own life and the lives of others.
Supporters of the foreordination theory contend on the contrary that volitional, involuntary actions depend also upon causes, making them necessary and unavoidable at a given moment; that there is nothing accidental, and that there cannot be; that we call accidental only those things the causes of which we do not see by reason of our limitations; and that different effects of causes seemingly the same occur because the causes are different in reality and only seem similar for the reason that we do not understand them well enough nor see them sufficiently clearly.
The dispute between the theory of the foreordained future and that of the free future is an infinite dispute. Neither of these theories can say anything decisive. This is so because both theories are too literal, too inflexible, too material, and one repudiates the other: both say, "either this or the other." In the one case there results a complete cold predestination: that which will be, will be, nothing can be changed—that which will befall tomorrow was predestined tens of thousands of years ago. There results in the other case a life upon some sort of needle-point called the present, which is surrounded on all sides by an abyss of non-existence, a journey in a country which does not as yet exist, a life in a world which is born and dies every moment, in which nothing ever returns. And both these opposite views are equally untrue, because the truth, in the given case, as in so many others, is contained in a union of two opposite understandings in one.
In every given moment all the future of the world is predestined and is existing, but is predestined conditionally, i.e., it will be such or another future according to the direction of events at a given moment, unless there enters a new fact, and a new fact can enter only from the side of consciousness and the will resulting from it. It is necessary to understand this, and to master it.
Besides this we are hindered from a right conception of the relation of the present toward the future by our misunderstanding of the relation of the present to the past. The difference of opinion exists only concerning the future; concerning the past all agree that it has passed, that it does not exist now!—and that it was such as it has been. In this last lies the key to the understanding of the incorrectness of our views of the future. As a matter of fact, in reality our relation both to the past and to the future is far more complicated than it seems to us. In the past, behind us, lies not only that which really happened, but that which could have been. In the same way, in the future lies not only that which will be, but everything that may be.
The past and the future are equally undetermined, equally exist in all their possibilities, and equally exist simultaneously with the present.
By time we mean the distance separating events in the order of their succession and binding them in different wholes. This distance lies in a direction not contained in three-dimensional space, therefore it will be the new dimension of space.
This new dimension satisfies all possible requirements of the fourth dimension on the ground of the preceding reasoning.
It is incommensurable with the dimensions of three-dimensional space, as a year is incommensurable with St. Petersburg. It is perpendicular to all directions of three-dimensional space and is not parallel to any of them.
As a deduction from all the preceding we may say that time (as it is usually understood) includes in itself two ideas: that of a certain to us unknown space (the fourth dimension), and that of a motion upon this space. Our constant mistake consists in the fact that in time we never see two ideas, but see always only one. Usually we see in time the idea of motion, but cannot say from whence, where, whither, nor upon what space. Attempts have been made heretofore to unite the idea of the fourth dimension with the idea of time. But in those theories which have attempted to combine the idea of time with the idea of the fourth dimension appeared always the idea of some spatial element as existing in time, and along with it was admitted motion upon that space. Those who were constructing these theories evidently did not understand that leaving out the possibility of motion they were advancing the demand for a new time, because motion cannot proceed out of time. And as a result time goes ahead of us, like our shadow, receding according as we approach it. All our perceptions of motion have become confused. If we imagine the new dimension of space and the possibility of motion upon this new dimension, time will still elude us, and declare that it is unexplained, exactly as it was unexplained before.
It is necessary to admit that by one term, time, we designate really two ideas—"a certain space" and "motion upon that space." This motion does not exist in reality, and it seems to us as existing only because we do not see the spatiality of time. That is, the sensation of motion in time (and motion out of time does not exist) arises in us because we are looking at the world as if through a narrow slit, and are seeing the lines of intersection of the time-plane with our three-dimensional space only.
Therefore it is necessary to declare how profoundly incorrect is our usual theory that the idea of time is deduced by us from the observation of motion, and is really nothing more than the idea of that succession which is observed by us in motion.
It is necessary to recognize quite the reverse: that the idea of motion is deduced by us out of an incomplete sensation of time, or of the time-sense, i.e., out of a sense or sensation of the fourth dimension, but out of an incomplete sensation. This incomplete sensation of time (of the fourth dimension)—the sensation through the slit—gives us the sensation of motion, that is, creates an illusion of motion which does not exist in reality, but instead of which there exists in reality only the extension upon a direction inconceivable to us.
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One other aspect of the question has very great significance. The fourth dimension is bound up with the ideas of "time" and "motion." But up to this point we shall not be able to understand the fourth dimension unless we shall understand the fifth dimension.
Attempting to look at time as at an object, Kant says that it has one dimension: i.e., he imagines time as a line extending from the infinite future into the infinite past. Of one point of this line we are conscious—always only one point. And this point has no dimension because that which in the usual sense we call the present, is the recent past, and sometimes also the near future.
This would be true in relation to our illusory perception of time. But in reality eternity is not the infinite dimension of time, but the one perpendicular to time; because, if eternity exists, then every moment is eternal. The line of time extends in that order of succession of phenomena which are in causal interdependence—first the cause, then the effect: before, now, after. The line of eternity extends perpendicularly to that line.
It is impossible to understand the idea of time without conceiving in imagination the idea of eternity; it is likewise impossible to understand space if we have no idea of time.
From the standpoint of eternity, time does not differ in anything from the other lines and dimensions of space—length, breadth, and height. This means that just as in space exist the things that we do not see, or speaking differently, not alone that which we see, so in time "events" exist before our consciousness has touched them, and they still exist after our consciousness has left them behind.
Consequently, extension in time is extension into unknown space, and therefore time is the fourth dimension of space.
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It is necessary that we should regard time as a spatial conception considered with relation to our two data—the world and consciousness (psychic life).
The idea of time arises through the knowledge of the world by means of sensuous receptivity. It has been previously explained that because of the properties of our sensuous receptivity we see the world as through a narrow slit.
Out of this the following questions arise:
1. What accounts for the existence in the world of illusionary motion? That is, why do we not see, through this slit, the same thing? Why, behind the slit, do changes proceed creating the illusion of motion: that is, how and in what manner does the focus of our receptivity run over the world of phenomena? In addition to all this it is necessary to remember that through the same slit through which we see the world we observe ourselves and see in ourselves changes similar to the changes in the rest of things.
2. Why can we not extend that slit?
It is necessary to answer these questions.
First of all it is important to note that within the limits of our usual observation our receptivity is always conditioned in the same way and cannot escape these conditions. In other words, it is chained, as it were, to some plane above which it cannot rise. These conditions, or that plane we call, in the inner world, consciousness or level of consciousness; in the outer world we call them matter or the density of matter. (The word density is used in this connection not in the sense of a solid, liquid or gaseous state, but in the sense of the physical, the astral and the mental plane—accepting temporarily the terminology employed in contemporary theosophical literature.) Our usual psychic life proceeds upon some definite plane (of consciousness or matter) and never rises above it. If our receptivity could rise above this plane it would undoubtedly perceive simultaneously, below itself, a far greater number of events than it usually sees while on a plane. Just as a man, ascending a mountain, or going up in a balloon, begins to see simultaneously and at once many things which it is impossible to see simultaneously and at once from below—the movement of two trains toward one another between which a collision will occur; the approach of an enemy detachment to a sleeping camp; two cities divided by a ridge, etc.—so consciousness rising above the plane in which it usually functions, must see simultaneously the events divided for ordinary consciousness by periods of time. These will be the events which ordinary consciousness never sees together, as: cause and effect; the work and the payment; the crime and the punishment; the movement of trains toward one another and their collision; the approach of the enemy and the battle; the sunrise and the sunset; the morning and the evening; the day and the night; spring, autumn, summer and winter; the birth and the death of a man.
The angle of vision will enlarge during such an ascent, the moment will expand.
If we imagine a receptivity which is on a level higher than our consciousness, possessing a broader angle of view, then this receptivity will be able to grasp, as something simultaneous, i.e., as a moment, all that is happening for us during a certain length of time—minutes, hours, a day, a month. Within the limits of its moment such a receptivity will not be in a position to discriminate between before, now, after; all this will be for it now. Now will expand.
But in order for this to happen it would be necessary for us to liberate ourselves from matter, because matter is nothing more than the conditions of space and time in which we dwell. Thence arises the question: can consciousness leave the conditions of a given material existence without itself undergoing fundamental changes, or without disappearing altogether, as men of positivistic views would affirm?
This is a debatable question, and later I shall give examples and proofs, speaking on behalf of the idea that our consciousness can leave the conditions of a given materiality. For the present I wish to establish what must proceed during this leaving.
There would ensue the expansion of the moment, i.e., all that we are apprehending in time would become something like a single moment, in which the past, the present, and the future would be seen at once. This shows the relativity of motion, as depending for us upon the limitation of the moment, which includes only a very small part of the moments of life perceived by us.
We have a perfect right to say, not that "time" is deduced from "motion," but that motion is sensed because of the time-sense. We have that sense, therefore we sense motion. The time-sense is the sensation of changing moments. If we did not have this time-sense we could not feel motion. The "time-sense" is itself, in substance, the limit or the surface of our "space-sense." Where the "space-sense" ends, there the "time-sense" begins. It has been made clear that "time" is identical in its properties with "space," i.e., it has all the signs of space extension. However, we do not feel it as spatial extension, but we feel it as time, that is, as something specific, inexpressible—in other words, uninterruptedly bound up with "motion." This inability to sense time spatially has its origin in the fact that the time-sense is a misty space-sense; by means of our time-sense we feel obscurely the new characteristics of space, which extend out from the sphere of three dimensions.
But what is the time-sense and why does there arise the illusion of motion?
To answer this question at all satisfactorily is possible only by studying the forms and levels of psychic life.
"I" is a complicated quantity, and within it goes on a continuous motion. About the nature of this motion we shall speak later, but this very motion inside of us creates the illusion of motion around us, motion in the material world.
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The noted mathematician Riemann understood that when higher dimensions of space are in question, time, by some means, translates itself into space, and he regarded the MATERIAL ATOM as the entrance of the fourth dimension into three-dimensional space.
In one of his books Hinton writes very interestingly about "surface tensions."
The relationship of a surface to a solid or of a solid to a higher solid is one which we often find in nature.
A surface is nothing more nor less than the relation between two things. Two bodies touch each other. The surface is the relationship of one to the other.
If our space is in the same co-relation with higher space as is the surface to our space, then it may be that our space is really the surface, that is, the place of contact, of two higher-dimensional spaces.
It is a fact worthy of notice that in the surface of a fluid different laws obtain from those which hold throughout the mass. There is a whole series of facts which are grouped together under the name of surface tensions, which are of great importance in physics, and by which the behavior of the surfaces of liquids is governed.
And it may well be that the laws of our universe are the surface tensions of a higher universe.
If the surface be regarded as a medium lying between bodies, then indeed it will have no weight, but be a powerful means of transmitting vibrations. Moreover, it would be unlike any other substance, and it would be impossible to get rid of it. However perfect a vacuum be made, there would be in this vacuum just as much of this unknown medium (i.e., of that surface) as there was before.
Matter would pass freely through this medium . . . vibrations of this medium would tear asunder portions of matter. And involuntarily the conclusion would be drawn that this medium was unlike any ordinary matter. . . . These would be very different properties to reconcile in one and the same substance.
Now is there anything in our experience which corresponds to this medium? . . .
Do we suppose the existence of any medium through which matter freely moves, which yet by its vibrations destroys the combinations of matter—some medium which is present in every vacuum however perfect, which penetrates all bodies, is weightless, and yet can never be laid hold of.
The "substance" which possesses all these qualities is called the "ether."
The properties of the ether are a perpetual object of investigation in science. . . . But taking into consideration the ideas expressed before it would be interesting to look at the world supposing that we are not in it but on the ether; where the "ether" is the surface of contact of two bodies of higher dimensions. 1
Hinton here expresses an unusually interesting thought, and brings the idea of the "ether" nearer to the idea of time. The materialistic, or even the energetic understanding of contemporary physics of the ether is perfectly fruitless—a dead-end siding. For Hinton the ether is not a substance but only a "surface," the "boundary" of something. But of what? Again not that of a substance, but the boundary, the surface, the limit of one form of receptivity and the beginning of another. . . .
In one sentence the walls and fences of the materialistic dead-end siding are broken down and before our thought open wide horizons of regions unexplored.
