Vinaire's Blog

Reference: Tertium Organum

NOTE: Text in color contains my comments.

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Chapter 5: Change

Four-dimensional space. “Temporal body”—Linga Sharira. The form of a human body from birth to death. Incommensurability of three-dimensional and four-dimensional bodies. Newton’s fluents. The unreality of constant quantities in our world. The right and the left hands in three-dimensional and in four-dimensional space. Difference between three-dimensional and four-dimensional space. Not two different spaces but different methods of receptivity of one and the same world.

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Four-dimensional space, if we try to imagine it to ourselves, will be the infinite repetition of our space, of our infinite three-dimensional sphere, as a line is the infinite repetition of a point. 

If no changes are made then that infinite repetition shall appear simply as that 3D form enduring forever.

Many things that have been said before will become much clearer to us when we dwell on the fact that the fourth dimension must be sought for in time. 

The fourth-dimension shall be the endurance of a form. But, when that form changes then the endurance of one form ends and the endurance of the next form start. And so it continues.

It will become clear what is meant by the fact that it is possible to regard a four-dimensional body as the tracing of the movement in space of a three-dimensional body in a direction not confined within that space. Now the direction not confined in three-dimensional space in which any three-dimensional body moves—this is the direction of time. Any three-dimensional body, existing, is at the same time moving in time and leaves as a tracing of its movement the temporal, or four-dimensional body. We never see nor feel this body, because of the limitations of our receptive apparatus, but we see the section of it only, which section we call the three-dimensional body. Therefore we are in error in thinking that the three-dimensional body is in itself something real. It is the projection of the four-dimensional body—its picture—the image of it on our plane. 

The four-dimensional body is the infinite number of three-dimensional ones. That is, the four-dimensional body is the infinite number of moments of existence of the three-dimensional one—its states and positions. The three-dimensional body which we see appears as a single figure—one of a series of pictures on a cinematographic film as it were. 

We see the 3D body enduring. If make a movie of it then that movie recording shall constitute a 4D body. Each frame of that recording shall contain a snapshot of the existence of the 3D body. It will represent a section of the 4D body.

Four-dimensional space—time—is really the distance between forms, states, and positions, of one and the same body (and different bodies, i.e., those seeming different to us). It separates those states, forms, and positions each from the other, and it binds them also into some to us incomprehensible whole. This incomprehensible whole can be formed in time out of one physical body—and out of different bodies.

The faster is the change in form, the shorter is the duration of each individual form.

It is easier for us to imagine the temporal whole as related to one physical body. 

If we consider the physical body of a man, we will find in it besides its “matter” something, it is true, changing, but undoubtedly one and the same from birth until death. 

This something is the Linga-Sharira of Hindu philosophy, i.e., the form on which our physical body is moulded. (H. P. Blavatsky “The Secret Doctrine.”) Eastern philosophy regards the physical body as something impermanent, which is in a condition of perpetual interchange with its surroundings. The particles come and go. After one second the body is already not absolutely the same as it was one second before. To-day it is in a considerable degree not that which it was yesterday. After seven years it is a quite different body. But despite all this, something always persists from birth to death, changing its aspect a little, but remaining the same. This is the Linga-Sharira. 

The Linga Sharira may be translated as the Genetic Entity.

The Linga-Sharira is the form, the image, it changes, but remains the same. That image of a man which we are able to represent to ourselves is not the Linga-Sharira. But if we try to represent to ourselves mentally the image of a man from birth to death, with all the particularities and traits of childhood, manhood and senility, as though extended in time, then it will be the Linga-Sharira. 

If a form changes, it means that, that particular form is changing. It is not being constant. But something else may remain relatively constant.

Form pertains to all things. We say that everything consists of matter and form. Under the category of “matter,” as already stated, the cause of a lengthy series of mixed sensations is predicated, but matter without form is not comprehensible to us; we cannot even think of matter without form. But we can think and imagine form without matter. 

There is no form without substance. But there can be forms without matter whose substance is radiation or thought. Radiation and thought are categories of substance beside matter.

The thing, i.e., the union of form and matter, is never constant; it always changes in the course of time. This idea afforded Newton the possibility of building his theory of fluents and fluxions.

Newton came to the conclusion that constant quantities do not exist in Nature. Variables do exist flowing, fluents only. The velocities with which different fluents change were called by Newton fluxions. 

From the standpoint of this theory all things known to us— men, plants, animals, planets—are fluents, and they differ by the magnitude of their fluxions. But the thing, changing continuously in time, sometimes very much, and quickly, as in the case of a living body for example, still remains one and the same. The body of a man in youth, the body of a man in senility—these are one and the same, though we know that in the old body there is not one atom left that was in the young one. The matter changes, but something remains one under all changes, this something is the Linga-Sharira. Newton’s theory is valid for the three-dimensional world existing in time. In this world there is nothing constant. All is variable because every consecutive moment the thing is already not that which it was before. We never see the Linga-Sharira, we see always its parts, and they appear to us variable. But if we observe more attentively we shall see that it is an illusion. Things of three dimensions are unreal and variable. They cannot be real because they do not exist in reality, just as the imaginary sections of a solid do not exist. Four-dimensional bodies alone are real. 

The form made of substance. The shape of the form may change. The consistency of substance may also change. But the concept “form made of substance” continues as a constant. This constant may be viewed as a “thought object.” This is linga-sharira.

In one of the lectures contained in the book, “A Pluralistic Universe,” Prof. James calls attention to Prof. Bergson’s remark that science studies always the t of the universe only, i.e., not the universe in its entirety, but the moment, the “temporal section” of the universe. 

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The properties of four-dimensional space will become clearer to us if we compare in detail three-dimensional space with the surface, and discover the difference existing between them. 

Hinton, in his book, “A New Era of Thought,” examines these differences very attentively. He represents to himself, on a plane, two equal rectangular triangles, cut out of paper, the right angles of which are placed in opposite directions. These triangles will be equal, but for some reason quite different. The right angle of one is directed to the right, that of the other to the left. If anyone wants to make them quite similar, it is possible to do so only with the help of three-dimensional space. That is, it is necessary to take one triangle, turn it over, and put it back on the plane. Then they will be two equal, and exactly similar triangles. But in order to effect this, it was necessary to take one triangle from the plane into three-dimensional space, and turn it over in that space. If the triangle is left on the plane, then it will never be possible to make it identical with the other, keeping the same relation of angles of the one to those of the other. If the triangle is merely rotated in the plane this similarity will never be established. In our world there are figures quite analogous to these two triangles.

We know certain shapes which are equal the one to the other, which are exactly similar, and yet which we cannot make fit into the same portion of space, either practically or by imagination. 

If we look at our two hands we see this clearly, though the two hands represent a complex case of a symmetrical similarity. Now there is one way in which the right hand and the left hand may practically be brought into likeness. If we take the right hand glove and the left hand glove, they will not fit any more than the right hand will coincide with the left hand; but if we turn one glove inside out, then it will fit. Now suppose the same thing done with the solid hand as is done with the glove when it is turned inside out, we must suppose it, so to speak, pulled through itself. . . If such an operation were possible, the right hand would be turned into an exact model of the left hand.

But such an operation would be possible in the higher dimensional space only, just as the overturning of the triangle is possible only in a space relatively higher than the plane. Even granting the existence of four-dimensional space it is possible that the turning of the hand inside out and the pulling of it through itself is a practical impossibility on account of causes independent of geometrical conditions. But this does not diminish its value as an example. Things like the turning of the hand inside out are possible theoretically in four-dimensional space because in this space different, and even distant points of our space and time touch, or have the possibility of contact. All points of a sheet of paper lying on a table are separated one from another, but by taking the sheet from the table it is possible to fold it in such a way as to bring together any given points. If on one corner is written St. Petersburg, and on another Madras, nothing prevents the putting together of these corners. And if on the third corner is written the year 1812, and on the fourth 1912, these corners can touch each other too. If on one corner the year is written in red ink, and the ink has not yet dried, then the figures may imprint themselves on the other corner. And if afterwards the sheet is straightened out and laid on the table, it will be perfectly incomprehensible, to a man who has not followed the operation, how the figure from one corner could transfer itself to another corner. For such a man the possibility of the contact of remote points of the sheet will be incomprehensible, and it will remain incomprehensible so long as he thinks of the sheet in two-dimensional space only. The moment he imagines the sheet in three-dimensional space this possibility will become real and obvious to him.

In considering the relation of the fourth dimension to the three known to us, we must conclude that our geometry is obviously insufficient for the investigation of higher space. 

As before stated, a four-dimensional body is as incommensurable with a three-dimensional one as a year is incommensurable with St. Petersburg. 

It is quite clear why this is so. The four-dimensional body consists of an infinitely great number of three-dimensional ones; accordingly, there cannot be a common measure for them. The three-dimensional body, in comparison with the four-dimensional one is equivalent to the point in comparison with the line. 

And just as the point is incommensurable with the line, so is the line incommensurable with the surface; as the surface is incommensurable with the solid body, so is the three-dimensional body incommensurable with the four-dimensional one. 

It is clear also why the geometry of three dimensions is insufficient for the definition of the position of the region of the fourth dimension in relation to three-dimensional space. 

Just as in the geometry of one dimension, that is, upon the line, it is impossible to define the position of the surface, the side of which constitutes the given line; just as in the geometry of two dimensions, i.e., upon the surface, it is impossible to define the position of the solid, the side of which constitutes the given surface, so in the geometry of three dimensions, in three-dimensional space, it is impossible to define a four-dimensional space. Briefly speaking, as planimetry is insufficient for the investigation of the problems of stereometry, so is stereometry insufficient for four-dimensional space.

As a conclusion from all of the above we may repeat that every point of our space is the section of a line in higher space, or as B. Riemann expressed it: the material atom is the entrance of the fourth dimension into three-dimensional space.

All we can say is that the 3D object of one moment is continuous with the 3D object of the next moment. In other words, the 4D object is continuous in the fourth-dimension.

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For a nearer approach to the problem of higher dimensions and of higher space it is necessary first of all to understand the constitution and properties of the higher dimensional region in comparison with the region of three dimensions. Then only will appear the possibility of a more exact investigation of this region, and a classification of the laws governing it. 

What is it that it is necessary to understand? 

It seems to me that first of all it is necessary to understand that we are considering not two regions spatially different, and not two regions of which one (again spatially, “geometrically”) constitutes a part of the other, but two methods of receptivity of one and the same unique world of a space which is unique.

Furthermore it is necessary to understand that all objects known to us exist not only in those categories in which they are perceived by us, but in an infinite number of others in which we do not and cannot sense them. And we must learn first to think things in other categories, and then so far as we are able, to imagine them therein. Only after doing this can we possibly develop the faculty to apprehend them in higher space—and to sense “higher” space itself. 

Or perhaps the first necessity is the direct perception of everything in the outside world which does not fit into the frame of three dimensions, which exists independently of the categories of time and space—everything that for this reason we are accustomed to consider as non-existent. If variability is an indication of the three-dimensional world, then let us search for the constant and thereby approach to an understanding of the four-dimensional world. 

We have become accustomed to count as really existing only that which is measurable in terms of length, breadth and height, but as has been shown it is necessary to expand the limits of the really existing. Mensurability is too rough an indication of existence, because mensurability itself is too conditioned a conception. We may say that for any approach to the exact investigation of the higher dimensional region the certainty obtained by the immediate sensation is probably indispensable, that much that is immeasurable exists just as really as, and even more really than, much that is measurable.

The object is continuous in dimensions one, two, three and four. We can predict that the object will be continuous in higher dimensions. A dimension applies to an aspect of the object.

The fifth dimension can apply to the consistency (a degree of density, firmness, viscosity, etc.) of the substance. In an atom, there are shells in the nucleus, which then interface with the shells in the electronic region. This atom exists in an environment of a spectrum of radiation. We can say that the substance is continuous from the “solid mass” of the nucleus to the “liquid mass” of the electronic region to the “gaseous mass” of the radiation environment.

All properties of an object, such as color, may be assigned their own dimensions. The object shall be continuous in the dimension of each of these properties.

We may conclude that any change in the object will always be continuous.

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Reference: Tertium Organum

NOTE: Text in color contains my comments.

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Chapter 4: Time

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.

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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. 

Physical motion is viewed as movement from one point fixed in space to another point fixed in space. But this requires space to be viewed like an “inflexible solid.” The three dimensions in space then represent three inflexible scales that measure distances in three directions perpendicular to each other. The motion in this case is the change in measurement along a certain scale. The point on the scale representing a certain measurement does not itself shift.

But in what direction is it? 

Adding a new direction means the integration of a new property into the object, which then requires a new scale of measurement.

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. 

There is no fourth physical direction perpendicular to these three directions. But we observe that this inflexible space is enduring from one moment to the next from past through present to future. Mathematically, this is a direction; but it is mental rather than physical.

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. 

We must remember that motion, as defined here, is the change in the measure of some property along an inflexible scale. Complications arise when the scale itself becomes flexible as in the theory of relativity.

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. 

Time as a dimension simply adds the property to an object of endurance. The object then continues to be.

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 though 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. 

Space and time are basic dimensions that we use to make sense out of a constant and continuous reality. The moments in time are continuous, just like the locations in space. The spread of our awareness determines how much reality we perceive in terms of time and space.

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. 

Each moment in time is continuous with the moment just before it. This produces a connected sequence. This may be looked upon as functional interdependence. This may also be looked upon as forms of cause and effect.

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 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 one. Only for that short moment does the phenomenon exist for us in reality; before, it existed in potentiality, afterward it will exist in remembrance. But this short moment is in substance 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 usual 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 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 in the very beginning that something exists. We called that something the world. How then can the world exist it it is not existing in the past, in the present, 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 come yet. 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 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 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 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 famous 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? 

The assumption here is that the assimilated sensations have no valid existence. Therefore, it focuses on immediate sensual receptivity and disregards sensation assimilated in the forms of perceptions, memories, experiences and knowledge.

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 traveler, 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 traveler. And that consciousness can look off and see on the horizon the towers of that city where that traveler 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 traveler’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.

Our awareness is not limited to a narrow slit of sensuous receptivity. The awareness includes the past in the form of sensations assimilated as perceptions, memory, experience and knowledge. The awareness includes the future in the form of real time projections from assimilated sensations. This awareness is there all the time.

Thus the idea of time is composed of the conception of the past, of that of the present, and of that 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 preordained future, and that of the free future. 

Preordination 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, and 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 preordination 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 clear.

The dispute between the theory of the preordained 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 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. 

The future is a prediction based on past and present knowledge that takes into account the laws of nature. The better is the assimilation of this knowledge the more accurate is the prediction of future. But, still, there is always the factor of Unknowable and the predictions of future are never totally certain.

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. 

There are laws of nature, so there is predestination. But there is also evolution, so there are new factors coming in.

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.

The is always the possibility of some sensations, especially traumatic sensations, not getting assimilated in real time. The unassimilated sensations sink into subconscious and out of awareness. There they wait to get assimilated. Any lack of assimilation thus distorts our view of past, present and future. Thus, we may perceive both past and future with uncertainty.

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. 

Time is the distance separating events, just like space is the distance separating objects. Time is possible because objects are enduring. This endurance of an object is understood as the dimension of Time, just like the extents of an object are understood as the dimensions of Space. If we define Space solely in terms of dimensions, then Time provides the fourth dimension to “space.”

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 designated, properly, 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 though 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.

As explained at the start of this chapter, motion is the change in the measurement of distance along a certain inflexible scale/direction. As this change becomes faster, so does the “motion in that direction.” The same applies to the dimension of time, which also has its own inflexible scale. As the changes in the measurement of time become faster so does the “motion in the direction of time.” It is like speeding up a movie. Here we are assuming total assimilation of sensations; followed by commensurate awareness of past, present and future.

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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. 

The dimension of time is, therefore, the dimension of endurance of the object. Motion appears due to change in that dimensional value.

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. 

It is not true that we are conscious of only one point on the time line. Assimilation of sensations into knowledge gives us awareness of past, present and possible 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. We can discover in time two dimensions. The second dimension of time, i.e., eternity, will be the fifth dimension of space. The line of the first dimension 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 the second dimension of time—the line of eternity—extends perpendicularly to that line. 

It is impossible to understand the idea of time without conceiving to ourselves the idea of eternity; it is likewise impossible to understand space if we have no idea of eternity. 

Eternity would mean that an object is enduring without change. There is no succession of change in that object while it is enduring through the changes other objects are going through. No change means no motion because motion means succession of change in distance.

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. 

But as has been shown already, time is not a simple, but a complex conception. And we shall have this in view—it consists of a conception of unknown space, vanishing in the past and future, and of illusory motion upon this space.

Eternity refers to the dimension of Time, the same way that distance refers to the dimension of Space. It is incorrect to say that eternity is the fifth dimension. It is a concept related to the fourth dimension.

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It is necessary for us to regard time as a spatial conception considered with relation to our two data—the universe and consciousness. 

The idea of time appears when consciousness comes in contact with the world through sensuous receptivity. It has been already shown that because of the properties of sensuous receptivity, consciousness sees the world as through a narrow slit. 

The idea of time is no different than the ides of space. Both of these ideas appear when consciousness arises through sensuous receptivity. The idea of seeing the world through a narrow slit is erroneous because consciousness includes assimilated sensations of past, present and future.

Out of this the following questions arise: 

1. Why does there exist in the world illusionary motion? That is, why does not consciousness see through this slit the same thing at all times? Why, behind the slit, do changes proceed creating the illusion of motion, i.e., in what manner, and how does the focus of our consciousness run over the world of phenomena? In addition to all this it is necessary to remember that through the very same slit through which it sees the world, consciousness observes itself as part of the world, and sees in itself changes similar to the changes in the rest of things. 
2. Why cannot consciousness extend that slit? 

We shall endeavor to answer these questions. 

These questions are better posed as: (1) Why are we fixated on immediate sensation and do not consider the total awareness of past, present and future? (2) Why aren’t we addressing subconsciousness?

First of all we shall remark that within the limits of our usual observation consciousness is always in the same conditions and cannot escape these conditions. In other words, it is as it were chained to some plane above which it cannot rise. These conditions or that plane we call MATTER. Our consciousness lives, so to speak, upon the very plane, and never rises above it. If consciousness could rise above this plane, so undoubtedly it would see underneath itself simultaneously, 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.

It is incorrect to think that our consciousness cannot rise above the plane of MATTER. It can certainly rise when we realize that that the substance of the universe includes radiation and thought in addition to matter. The space filled only with radiation allows for a flexible scale. The space filled only with thought allows for additional metaphysical dimensions.

The angle of vision will enlarge during such an ascent, the moment will expand. 

If we imagine a consciousness higher than our consciousness, possessing a broader angle of view, then this consciousness 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 consciousness 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 material existence without itself undergoing fundamental changes or without disappearing altogether, as men of positivistic views would affirm. 

Space and time account for the dimensions of substance. Currently, we limit substance to inflexible matter. We just need to expand the sense of substance to include radiation and thought.

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 materiality. For the present I wish to establish purely theoretically 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. 

Currently, we limit consciousness to sensuous receptivity only. We need to expand the sense of consciousness to include memory, experience and knowledge. We should also work on assimilating sensations stored in the subconscious.

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. ., 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 emerge from the sphere of three dimensions. 

Motion is not correctly described above. Motion is successive change of values on a dimensional scale whether it is changing distance from some fixed point, or if it is changing form from eternity. NOTE: Eternity is endurance of a form without change.

But what is the time-sense and why does there arise the illusion of motion? 

Time-sense is simply the sense of endurance; while, space-sense is the sense of extent. We confuse it with “change.” The truth is that time (duration) can change, just like space (extent) can change. Change is a concept more basic than either space or time, just like the concept of substance.

To answer this question at all satisfactorily is possible only by studying our consciousness, our I. 

“I” is a complicated quantity, and within itself goes on a continuous motion. About the nature of this motion we shall speak later, but this very motion inside of our I creates the illusion of motion around us, motion in the material world.

The premise of “I” stated above is problematic. The whole function of “I” is to spot and resolve anomalies that violate continuity, consistency and harmony of observations.

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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. 

This claim is apparently not true.

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 are 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.

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 deadend siding are broken down and before our thought open wide horizons of regions unexplored.

What is being considered “ether” here, could very well be “thought,” which is a valid substance.

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