Vinaire's Blog

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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Reference: Tertium Organum

NOTE: Text in color contains my comments.

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Chapter 2: Existence

A new view of the Kantian problem. The Ideas of Hinton. The “space sense” and its evolution. A system for the development of a sense of the fourth dimension by exercises with colored cubes. The geometrical conception of space. Three perpendiculars—why three? Can everything existing be measured by three perpendiculars? Facts physical and metaphysical. The indices of existence. Reality of ideas. Insufficient evidence of the existence of matter and motion. Matter and motion are only logical concepts, like “good” and “evil.”

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As already stated, Kant propounded the problem, but gave no solution of it, nor did he point the way to a solution. And not one of the known commentators, interpreters, followers or adversaries of Kant has found a solution, nor the way to it.

Kant put forth the question, “How are synthetic a priori judgments possible?” His solution was the enumeration of sensibility and categories (see Kant’s Subjective Framework). These categories may be referred to as postulates that give meaning to sensations.

I find the first flashes of a right understanding of the Kantian problem, and the first suggestions in regard to a possible way toward its solution in the writings of C. H. Hinton, author of the books, “A New Era of Thought” and “The Fourth Dimension.” 

These books contain interesting synopses of many things previously written about problems of higher dimensions, together with ideas of the author’s own which have a bearing upon the subject under discussion here.

Hinton notes that in commenting upon Kantian ideas, only their negative side is usually insisted upon, namely, the fact that we can cognize things in a sensuous way, in terms of space and time only, is regarded as an obstacle, hindering us from seeing what things in themselves really are, preventing the possibility of cognizing them as they are, imposing upon them that which is not inherent in them, shutting them off from us.

Kant proposed things-in-themselves to be the causes of sensations which are then perceived in terms of space and time. This is thought of as space and time hindering us from seeing what things-in-themselves really are.

But [says Hinton] if we take Kant’s statement simply as it is—not seeing in the spatial conception a hindrance to right receptivity—that we apprehend things by means of space—then it is equally allowable to consider our space sense not as a negative condition, hindering our perception of the world, but as a positive means by which the mind grasps its experiences, i.e., by which we cognize the world.

There is, in so many books in which the subject is treated, a certain air of despondency—as if this space apprehension were a kind of veil which shut us off from nature. But there is no need to adopt this feeling. The first postulate of this book is a full recognition of the fact that it is by means of space that we apprehend what is. 

Space is the instrument of the mind.

Very often a statement which seems to be very deep and abstruse and hard to grasp, is simply the form into which deep thinkers have thrown a very simple and practical observation. And for the present let us look on Kant’s great doctrine of space from a practical point of view, and it comes to this—it is important to develop the space sense, for it is the means by which we think about real things. 

Now according to Kant [Hinton goes on to say] the space sense, or the intuition of space, is the most fundamental power of the mind. But I do not find anywhere a systematic and thorough-going education of the space sense. It is left to be organized by accident. Yet the special development of the space sense makes us acquainted with a whole series of new conceptions.

Fichte, Schelling, Hegel, have developed certain tendencies and have written remarkable books, but the true successors of Kant are Gauss and Lobachevsky. 

For if our intuition of space is the means whereby we apprehend, then it follows that there may be different kinds of intuitions of space. Who can tell what the absolute space intuition is? This intuition of space must be colored, so to speak, by the conditions (of psychical activity) of the being which uses it. 

By a remarkable analysis the great geometers above mentioned have shown that space is not limited as ordinary experience would seem to inform us, but that we are quite capable of conceiving different kinds space. [A New Era of Thought]

The sensations are caused by things-in-themselves. The space sense recognizes the dimensions of sensations. We may say that as these dimensions are assimilated (made continuous, consistent and harmonious) the perception gets closer to approximating the things-in-themselves.

Hinton invented a complicated system for the education and development of the space sense by means of exercises with groups of cubes of different colors. The books above mentioned are devoted to the exposition of this system. In my opinion Hinton’s exercises are interesting from a theoretical standpoint, but they are practically valuable only for such as have the same turn of mind as Hinton’s own. 

Exercises of the mind according to his system must first of all lead to the development of the ability to imagine objects, not as the eye sees them, i.e., in perspective, but as they are geometrically—to learn to imagine the cube, for example, simultaneously from all sides. Moreover, such a development of the imagination as overcomes the illusions of perspective results in the expansion of the limits of consciousness, thus creating new conceptions and augmenting the faculty for perceiving analogies.

Any exercise should help assimilate the dimensions that are applied to sensations. The dimensions may derive initially from the categories of Kant.

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Kant established the fact that the development of knowledge under the existing conditions of receptivity will not bring us any closer to things in themselves. But Hinton asserts that it is possible, if desired, to change the very conditions of receptivity, and thus to approach the true substance of things. 

Our space as we ordinarily think of it is conceived as limited—not in extent, but in a certain way which can only be realized when we think of our ways of measuring space objects. It is found that there are only three independent directions in which a body can be measured—it must have height, length and breadth, but it has no more than these dimensions, if any other measurement be taken in it, this new measurement will be found to be compounded of the old measurements. 

It is impossible to find a point in the body which could not be arrived at by traveling in combinations of the three directions already taken. 

But why should space be limited to three independent directions? 

Currently, the three dimensions of space are derived from the consideration of three-dimensional matter. Is matter the only substance underlying objects?

Geometers have found that there is no reason why bodies which we can measure should be thus limited. As a matter of fact all the bodies which we can measure are thus limited. So we come to this conclusion, that the space which we use for conceiving ordinary objects in the world is limited to three dimensions. But it might be possible for there to be beings living in a world such that they would conceive a space of four dimensions.

The three dimensions referenced by geometers apply only to space filled by solid matter. The “empty space” is not really empty because it is filled with invisible radiation. Radiation being different from matter will supply additional dimensions to space.

It is possible to say a great deal about space of higher dimensions than our own, and to work out analytically many problems which suggest themselves. But can we conceive four-dimensional space in the same way in which we can conceive our own space? Can we think of a body in four dimensions as a unit having properties in the same way as we think of a body having a definite shape in the space with which we are familiar? 

Since space derives its dimensions from the substance that fills it, we may refer to this property as substantiality of space. We may then examine this substantiality for higher dimensions.

There is really no more difficulty in conceiving four-dimensional shapes, when we go about it in the right way, than in conceiving the idea of solid shapes, nor is there any mystery at all about it. 

When the faculty to apprehend in four dimensions is acquired—or rather when it is brought into consciousness, for it exists in everyone in imperfect form—a new horizon opens. The mind acquires a development of power, and in this use of ampler space as a mode of thought, a path is opened by using that very truth which, when first stated by Kant, seemed to close the mind within such fast limits. Our perception is subject to the condition of being in space. But space is not limited as we at first think.

Substance is anytihng substantial enough to be sensed. This means that substance is anything that has inertia and momentum. According to this definition, not only matter and radiation, but thought also is a substance. Space filled with thought can have infinity of dimensions. This definition of substance, and the resulting substantiality of space opens the mind to new horizons.

The next step after having formed this power of conception in ampler space, is to investigate nature and see what phenomena are to be explained by four-dimensional relations. 

The thought of past ages has used the conception of a three-dimensional space, and by that means has classified many phenomena and has obtained rules for dealing with matters of great practical utility. The path which opens immediately before us in the future is that of applying the conception of four-dimensional space to the phenomena of nature, and of investigating what can be found out by this new means of apprehension…

The dimensions beyond the three dimensions that we are familiar with, need not be of the same nature as “direction.” For example, the consistency (a degree of density, firmness, viscosity, etc.) of the substantiality of space is a good example of the fourth dimension.

For development of knowledge it is necessary to separate the self elements, i.e., the personal element which we put in everything cognized by us from that which is cognized, in order that our attention may not be distracted (upon ourselves) from the properties which we, in substance, perceive. 

Only by getting rid of the self elements in our receptivity do we put ourselves in a position in which we can propound sensible questions. Only by getting rid of the notion of a circular motion of the sun around the earth (i.e., around us—self-element) do we prepare our way to study the sun as it really is. 

But the worst about a self element is that its presence is never dreamed of till it is got rid of. 

In order to understand what the self element in our receptivity means, imagine ourselves to be translated suddenly to another part of the universe, and to find there intelligent beings and to hold conversation with them. If we told them that we came from this world, and were to describe the sun to them, saying that it was a bright, hot body which moved around us, they would reply: “You have told us something about the sun, but you have also told us something about yourselves.” 

Therefore, desiring to tell something about the sun, we shall first of all get rid of the self element which is introduced into our knowledge of the sun by the movement of the earth, upon which we are, round it…

One of our serious pieces of work will be to get rid of the self elements in the knowledge of the arrangement of objects. 

We identify ourselves with the “inner” consciousness, and look at the world of objects to be “external” to us. Here we are assigning the self element to consciousness. Consciousness can be considered as formed by the substance of thought, which can be sensed. Thus, we can get rid of the self-element from consciousness.

The relations of our universe or our space with regard to the wider universe of four-dimensional space are altogether undetermined. The real relationship will require a great deal of study to apprehend, and when apprehended will seem as natural to us as the position of the earth among the other planets seems to us now. 

The best approach to get rid of the self element is to consider consciousness also to be part of the universe; where the substance of the universe consists of matter, radiation and thought. We then consider this universe with uniform awareness. In other words, we consider this universe to be continuous, consistent and harmonious throughout.

I would divide studies of arrangement into two classes: those which create the faculty of arrangement, and those which use it and exercise it. Mathematics exercises it, but I do not think it creates it; and unfortunately, in mathematics as it is now often taught, the pupil is launched into a vast system of symbols: the whole use and meaning of symbols, (namely, as means to acquire a clear grasp of facts) is lost to him…

Of the possible units which will serve for the study of arrangement, I take the cube; and I have found that whenever I took any other unit I got wrong, puzzled, and lost my way. With the cube one does not get along very fast, but everything is perfectly obvious and simple, and builds up into a whole of which every part is evident… 

Our work then will be this: a study, by means of cubes, of the facts of arrangement; and the process of learning will be an active one of actually putting up the cubes. Thus we will bring our minds into contact with nature. [A New Era of Thought]

Mathematics can postulate infinite dimensions of “space” that are independent of each other; but, in reality, all such dimensions would be aspects of consciousness made of thought. In practical terms, all dimensions may be attributed to the universe. They would have to be assimilated for the universe to be perceived more accurately.

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I shall return again to Hinton’s books several times, but meanwhile it is necessary to establish our relation to the ideas which Kant’s problem touches. 

What is space? 

Taken as object, that is, perceived by our consciousness, space is for us the form of the universe or the form of the matter in the universe. 

We first need to understand SPACE. Space consists of the dimensions of the substance of the universe.

Space possesses an infinite extension in all directions. But it can be measured in only three directions independent of one another; in length, breadth, and height; these directions we call the dimensions of space, and we say that our space has three dimensions: it is three-dimensional. 

By independent direction we mean in this case a line at right angles to another line. 

Our geometry, (or the science of measurement of the earth, or matter in space) knows only three such lines, which are mutually at right angles to one another and not parallel among themselves. 

Should we mean by independent direction the line which is not at right angles, i.e., which does not form with the others an angle of 90 degrees, but an angle, say, of 30 degrees, then we would have the number of dimensions not three, but nine. 

It is seen from this that the three-dimensionality of our space is simply a geometrical condition, and depends upon the fact that we are using right angles as a unit of measurement. 

But at the same time, in our space and our universe we know only three perpendiculars, i.e., only three independent right angles. 

But why three only, and not ten or fifteen? 

This we do not know.

And here is another very significant fact: either because of some mysterious property of the universe, or because of some mental limitation, we cannot even imagine to ourselves more than three independent directions. 

But we speak of the universe as infinite, and because the first condition of infinity is infinity in all directions and in all possible relations, so we must presuppose in space an infinite number of dimensions: that is, we must presuppose an infinite number of lines perpendicular and not parallel to each other: and yet out of these lines we know, for some reason, only three. 

It is usually in some such guise that the question of higher dimensionality appears to normal human consciousness. 

Since we cannot construct more than three mutually independent perpendiculars, and if the three-dimensionality of our space is conditional upon this, we are forced to admit the indubitable fact of the limitedness of our space in relation to geometrical possibilities: though of course if the properties of space are created by some limitation of consciousness, then the limitedness lies in ourselves. 

No matter what this limitedness depends on, it is a fact that it exists. 

A given point can be the vertex of only eight independent tetrahedrons. Through a given point it is possible to draw only three perpendicular and not parallel straight lines. 

Upon this as a basis, we define the dimensionality of space by the number of lines it is possible to draw in it which are mutually at right angles one with another. 

The line upon which there cannot be a perpendicular, that is, another line, constitutes linear, or one-dimensional space. 

Upon the surface two perpendiculars are possible. This is superficial, or two-dimensional space. 

In “space” three perpendiculars are possible. This is solid, or three-dimensional space. 

The idea of the fourth dimension arose from the assumption that in addition to the three dimensions known to our geometry there exists still a fourth, for some reason unknown and inaccessible to us, i.e., that in addition to the three known to us, a mysterious fourth perpendicular is possible. 

This assumption is practically founded on the consideration that there are things and phenomena in the world undoubtedly really existing, but quite incommensurable in terms of length, breadth and thickness, and lying as it were outside of three-dimensional space.

The three dimensions of space are derived from the idea of inflexible solid matter. Mental limitation lies in considering matter to be the only substance of the universe. In reality, substance is anything with inertia and momentum that is substantial enough to be sensed. The substance of the universe actually consists of matter, radiation and thought, that provides more than three dimensions.

Lines and their perpendicularity are mathematical representations of dimensions. Line means that the measurement of substance can be plotted on a continuous scale. Perpendicularity points to the uniqueness of that measurement of substance. Points, lines, angles, surfaces and volumes are mathematical representations of the various aspects or views of substance. Mental limitation lies in considering such mathematical representation to be the literal reality. Distance in a direction is a dimension; but the substantiality of substance is a dimension too. In this universe the substantiality of substance varies in a continuous manner from matter to radiation to thought.

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By really existing we understand that which produces definite action, which possesses certain functions, which appears to be the cause of something else. 

That which does not exist cannot produce any action, has no function, cannot be a cause. 

But there are different modes of existence. There is physical existence, recognized by certain sorts of actions and functions, and there is metaphysical existence, recognized by its actions and its functions. 

Mental limitation lies also in how we understand EXISTENCE. Only that exists which can be sensed physically or mentally. That which cannot be sensed does not exist. The basis of existence is substance. Physical existence can be sensed as matter and radiation. Metaphysical existence can be sensed as thought.

A house exists, and the idea of good and evil exists. But they do not exist in like manner. One and the same method of proof of existence does not suffice for the proof of the existence of a house and for the proof of the existence of an idea. A house is a physical fact, an idea is a metaphysical fact. Physical and metaphysical facts exist, but they exist differently. 

In order to prove the idea of a division into good and evil, i.e., a metaphysical fact, I have only to prove its possibility. This is already sufficiently established. But if I should prove that a house, i.e., a physical fact, may exist, it does not at all mean that it exists really. If I prove that a man may own the house it is no proof that he owns it. 

The existence does not require proof beyond the fact that it can be sensed physically or mentally. The correctness of the reality of that existence is a different matter.

Our relation to an idea and to a house are quite different. It is possible by a certain effort to destroy a house—to burn, to wreck it. The house will cease to exist. But suppose you attempt to destroy, by an effort, an idea. The more you try to contest, argue, refute, ridicule, the more the idea is likely to spread, grow, strengthen. And contrarywise, silence, oblivion, non-action, “nonresistance” will exterminate, or in any case will weaken the idea. Silence, oblivion, will not wreck a house, will not hurt a stone. It is clear that the existence of a house and that of an idea are quite different existences. 

Of such different existences we know very many. A book exists, and also the contents of a book. Notes exist, and so does the music that the notes combine to make. A coin exists, and so does the purchasing value of a coin. A word exists, and the energy which it contains.

We discern on the one hand, a whole series of physical facts, and on the other hand, a series of metaphysical facts. 

As facts of the first kind exist, so also do facts of the second kind exist, but differently. 

From the usual positivist point of view it will seem naive in the highest degree to speak of the purchasing value of a coin separately from the coin: of the energy of a word separately from the word: of the contents of a book separately from the book, and so on. We all know that these are only “what people say,” that in reality purchasing value, energy of a word, and contents of a book do not exist, that by these conceptions we only denote a series of phenomena in some way linked with coin, word, book, but in substance quite separate from them. 

The physical and metaphysical existences may be sensed differently, but these different existences are integrated together in the reality we perceive.

But is it so? 

We decided to accept nothing as given, consequently we shall not negate anything as given. 

We see in things, in addition to what is external, something internal. We know that this internal element in things constitutes a continuous part of things, usually their principal substance. And quite naturally we ask ourselves, where is this internal element, and what does it represent in and by itself. We see that it is not embraced within our space. We begin to conceive of the idea of a “higher space” possessing more dimensions than ours. Our space then appears to be somehow a part of higher space, i.e., we begin to believe that we know, feel, and measure only part of space, that part which is measurable in terms of length, width and height.

The division of dimensions into external and internal is arbitrary. All dimensions are part of space. The substantiality of existence may be considered the “fourth dimension” of space.

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As was said before, we usually regard space as a form of the universe, or as a form of the matter of the universe. To make this clear it is possible to say that a “cube” is the form of the matter in a cube; a “sphere” is the form of the matter in a sphere; “space”—an infinite sphere—is the form of the entire matter of the universe. 

H. P. Blavatsky, in “The Secret Doctrine” has this to say about space: 

The superficial absurdity of assuming that Space itself is measurable in any direction is of little consequence. The familiar phrase (the fourth dimension of space) can only be an abbreviation of the fuller form—the “Fourth dimension of Matter in Space” … The progress of evolution may be destined to introduce us to new characteristics of matter…”

The new characteristic of matter is expanding the understanding of the substance of the universe to include radiation and thought in addition to matter.

But the formula defining “space” as “the form of matter in the universe” suffers from this deficiency, that there is introduced in it the concept of “matter,” i.e., the unknown. 

I have already spoken of that “dead end siding,” x = y, y = x, to which all attempts at the physical definition of matter inevitably lead. 

Psychological definitions lead to the same thing. 

In a well known book, “The Physiology of the Soul,” A. I. Gerzen says:

We call matter everything which directly or indirectly offers resistance to motion, directly or indirectly produced by us, manifesting a remarkable analogy with our passive states. 

And we call force (motion) that which directly or indirectly communicates movement to us or to other bodies, thus manifesting the greatest similitude to our active states.

Consequently, “matter” and “motion” are something like projections of our passive and active states. It is clear that it is possible to define the passive state only in terms of the active, and the active in terms of the passive—again two unknowns, defining one another. 

Substance is sensed because it resists motion. This property is called inertia. Both motion and inertia are simply the characteristics of all substance (matter, radiation and thought) that complement each other.

E. Douglas Fawcett, in an article entitled “Idealism and the Problem of Nature” in “The Quest” (April, 1910), discusses matter from this point of view.

Matter (like force) does not give us any trouble. We know all about it, for the very good reason that we invented it. By “matter” we think of sensuous objects. It is mental change of concrete, but too complicated facts, which are difficult to deal with. 

Strictly speaking, matter exists only as a concept. Truth to tell, the character of matter, even when treated only as a conception, is so unobvious that the majority of persons are unable to tell us exactly what they mean by it.

An important fact is here brought to light: matter and force are just logical concepts, i.e., only words accepted for the designation of a lengthy series of complicated facts. It is difficult for us, educated almost exclusively along physical lines, to understand this clearly, but in substance it may be stated as follows: Who has seen matter and force, and when? We see things, see phenomena. Matter, independently of the substance from which a given thing is made, or of which it consists, we have never seen and never will see; but the given substance is not quite matter, this is wood, or iron or stone. Similarly, we shall never see force separately from motion. What does this mean? It means that “matter” and “force” are just such abstract conceptions, as “value” or “labor,” as “the purchasing value of a coin” or the “contents” of a book; it means that matter is “such stuff as dreams are made of.” And because we can never touch this “stuff” and can see it only in dreams, so we can never touch physical matter, nor see, nor hear, nor photograph it, separately from the object. We cognize things and phenomena which are bad or good, but we never cognize “matter” and “force” separately from things and phenomena. 

Matter is as much an abstract conception as are truth, good and evil.

It is as impossible to put matter or any part of matter into a chemical retort or crucible as it is impossible to sell “Egyptian darkness” in vials. However as it is said that “Egyptian darkness” is sold as a black powder in Athos, therefore perhaps even matter, somewhere, by some one, has been seen.

When we talk about logical concepts and abstraction, we are talking about thought; and thought is a substance because it can be sensed. Thought is sensed mentally. Mind is also a sense organ. This fact should not be ignored. As thought gets increasingly condensed we get radiation and matter; which are sensed physically through physical sense organs.

In order to discuss questions of this order a certain preparation is necessary, or a high degree of intuition; but unfortunately it is customary to consider fundamental questions of cosmogony very lightly. 

A man easily admits his incompetency in music, dancing, or higher mathematics, but he always maintains the privilege of having an opinion and being a judge of questions relating to “first principles.”

It is difficult to discuss with such men. 

For how will you answer a man who looks at you in perplexity, knocks on the table with his finger and says, “This is matter. I know it; feel! How can it be an abstract conception?” To answer this is as difficult as to answer the man who says: “I see that the sun rises and sets!”

When the man says, “I know it; feel!” he is simply saying that it is substantial and he senses it. This is the definition of substance. So, it is substance to him. How he interprets that substance is another matter.

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Returning to the consideration of space, we shall under no circumstances introduce unknown quantities in the definition of it. We shall define it only in terms of those two data which we decided to accept at the very beginning. 

The world and consciousness are the facts which we decided to recognize as existing.

By the world we mean the combination of unknown causes of our sensations. 

By the material world we mean the combination of unknown causes of a definite series of sensations, those of sight, hearing, touch, smell, taste, sensations of weight, and so on. 

Space is either a property of the world or a property of our knowledge of the world. 

Three-dimensional space is either a property of the material world or a property of our receptivity of the material world. 

Our inquiry is confined to the problem : how shall we approach the study of space?

Existence depends on sensations. Sensations are caused by “unknown causes”, but we are able to perceive these causes, as sensations get assimilated. The better is the assimilation, the clearer is the perception of the unknown cause.

The world is objective, but consciousness is considered to be subjective. This subjectivity is there because we identify self with consciousness. The inclusion of this self element generates a limitation. We can get rid of this limitation by recognizing that consciousness is made up of thought, and thought is also a substance.

Thus, consciousness can be seen as part of the objective world that is sensed as matter, radiation and thought. It is only upon the assimilation of these sensations that we start to perceive those “unknown causes” more clearly.

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