Science and the problem of the fourth dimension. Paper read by Professor N. A. Oumoff at the Mendeleev Convention in 1911, The Characteristic Features and Problems of Contemporary Natural-scientific Thought'. New physics. Electromagnetic theory. Principles of relativity. The works of Einstein and Minkowsky. Simultaneous existence of the past and the future. The eternal Now. Van Manen's book on occult experiences. Diagram of a four-dimensional figure.

Speaking generally about the problems of time, space and higher dimensions, expounded in the preceding chapters, it is impossible to avoid dwelling once more on the attitude of science to those problems. To many people the attitude of 'exact knowledge' to those questions seems a riddle; and yet they are undoubtedly the most important of all the questions which at present engage the attention of human thought.
If it is important, then why does science not speak about it? And why, on the contrary, does science go on repeating opposite affirmations, pretending not to know, or not to notice, a whole series of theories and hypotheses which have been advanced?
Science should be the investigation of the unknown. Why then does it not strive to investigate this unknown which has been for so long brought to its notice and which very soon will even cease to be unknown?
To this one can only answer that, unfortunately, only a very small part of official academic science undertakes what it should, i.e. to investigate the new and the unknown. The greater part of it is merely instruction in what has long become commonplace for independent thought or, still worse, what has long become obsolete and discarded as useless.
Therefore, it is especially gratifying to note that, at times, even in science one may detect a tendency towards a quest for new horizons of thought; in other words, that academic routine and an obligatory reiteration of an endless number of commonplaces have not always and in all cases succeeded in killing love of knowledge and the capacity of independent thinking.
Although very timidly and tentatively, in some of its boldest representatives, SCIENCE, in the last decades has, after all, touched upon problems of higher dimensions, and in such cases arrived at results almost identical with those expounded in the preceding chapters.
In December 1911 the Second Mendeleev Convention was opened by a paper read by Professor N. A. Oumoff, devoted to problems of time and higher dimensions, under the title: The Characteristic Features and Problems of Contemporary Natural-scientific Thought'.
Professor N. A. Oumoff's paper, in spite of a certain incomplete-ness, is an event of great magnitude in the realm of science and will doubtless be, in time, recorded in the history of the development of exact knowledge as an unusually bold and outstanding attempt to proclaim, in the citadel of positivism which the Mendeleev Convention should have been, new ideas, which, in their essence, refute positivism in its entirety.
However, inertia and routine were bound to do their work. Professor N. A. Oumoff's paper was heard among a number of other papers, was duly published in the proceedings of the Convention and remained there, utterlyfailing to produce the effect of a bombshell which it should have done had the listeners been more able, and above all more willing, to appreciate its real meaning and significance.
Of course, the weakening of the significance of Professor Oumoff's paper was to a great extent due to certain reservations and limitations made byhimself, to the title of the paper, which failed to express its substance, and to its general tendency, striving to demonstrate that science is proceeding in a new direction, instead of stating the plain fact that the new direction goes against science.
Professor N. A. Oumoff died in 1916, and I have no desire to impose uponhim thoughts he did not share. I had a talk with him in January 1912 which showed me that he stood, as it were, midway between ideas of the fourth dimension very akin to those expounded by me in the first edition of Tertium Organum, and physical theories still recognizing motion as an independent fact. What I mean is that while he recognized time as the fourth dimension of space, Professor Oumoff did not regard motion as an illusion of our consciousness, but admitted the reality of motion in the world, as a fact independent of us and our mental make-up.
I point this out because, later, I shall quote extracts from Professor Oumoff's paper, choosing mainly those pans which contain ideas almost identical with the thoughts expressed by me in the preceding chapters.
I shall not deal with the greater part of the paper, depicting the evolution of modern physics from atom to electron, for this seems to me somewhat artificially joined to the ideas on which I would like to dwell, and has no inner connection with them.
From my point of view it is immaterial whether the atom or the electron is placed at the basis of matter. In my opinion, the basis of matter is illusion, or, in other words, the form of representation. And a consistent development of the ideas of higher space, which Professor Oumoff placed at the foundation of his paper, should, in my opinion, lead to the negation of motion, just as a consistent development of the ideas of mathematical physics led to the negation of matter, as a substance.
Having mentioned electrons, I should add that there is a means of reconciling the latest scientific ideas with the data of the psychological method; namely, by means of the very ancient systems of the Kabala, alchemy and others, which put at the foundation of the material world four principles or four elements, of which the first two, fire and water, correspond to the positive and negative electrons of modern physics.
But, for this electrons should be taken not simply as electromagnetic units, but as principles, i.e. as two opposing principles constituting the world.
Professor Oumoff's paper is interesting and noteworthy in that it already stands on the very threshold of metaphysics. Maybe the only thing that stands in his way is the lingering faith in the value of the positivist method, which in fact dies when the new watchwords of knowledge are proclaimed.

The introduction to our forthcoming work [says Professor N. A. Oumoff] should be, most properly, devoted to the experiences of scientific thought in its search for the image of the world. The urgent need of scientific work along these lines will be clear, if we turn to the precepts of our great pioneers of science. . . . These precepts represent the deep motives of an active service to natural science and to mankind. It is useful to express them in our times when thought is mainly directed towards questions of organization of life. . . . Let us remember the profession of faith of the natural scientist:
To affirm man's power over energy, time, space. . . . To know the architecture of the world and, in this knowledge, to find a basis for creative foresight. . . . This foresight inspires confidence that natural science will not fail to continue the great and responsible work of creating, in the midst of old nature, a new nature adapted to the increased requirements of mankind. New nature has become a vital necessity in individual and public activity. But its grandeur and its power seem to bring contentment to our thought.
The need for stability in daily life and the brevity of personal experience as compared with the evolution of the earth, lead men to faith, and create the mirage of the stability of the surrounding order of things not only in the present, but also in the future. The creators of natural science do not share this tranquil point of view, and to this circumstance natural science owes its constant development. I venture to lift this brilliant and familiar veil and to reveal the innermost recesses of scientific thought, poised on the dividing line between two conceptions of the world.
The steersman of science should be constantly vigilant, notwithstanding the prosperity of his voyage; stars should constantly shine above him, by which he plots his course in the ocean of the unknown.
At the present time, the constellations in the sky of our science have changed, and a new star has shone forth, having no equal in brilliance.
Persistent scientific investigation has expanded the volume of the knowable to dimensions which were inconceivable even a short while -twenty or fifteen years ago. Number still remains the legislator of nature, but, being capable of representation, it has eluded the conception of the world which considered it possible to represent the world by mechanical models.
The new that has been discovered provides a sufficient number of images for the construction of the world, but they destroy its old architecture, familiar to us, and can only be incorporated in a new order, the free lines of which extend far beyond the limits not only of the old external world, but also beyond the fundamental forms of our thinking.
I have to lead you to the summits from which open up perspectives which fundamentally re-form our idea of the world.
The ascent towards them, amid the ruins of classical physics, presents considerable difficulties, and I beg your indulgence in advance and shall endeavour to simplify and shorten our path, as far as it is possible.

Further, Professor Oumoff draws the picture of the evolution of form 'from atom to electron', from material and mechanical ideas of the universe to electro-magnetic ideas:
The axioms of mechanics are but fragments, and making use of them is equivalent to judging about the content of a whole chapter by means of a single sentence.

It is not surprising, therefore, that the attempt at a mechanical explanation of the
properties of electro-magnetic ether by means of axioms in which these properties
are either denied or are one-sidedly predetermined, proved a failure. . . .
The mechanical conception of the world proved one-sided. . . . The image of the world had no unity.
The electro-magnetic world could not remain as something alien, external, in relation to matter. The material conception of the world with its immutable foundations, had insufficient flexibility to allow fusion to take place with it and its principles. Only one way out remained-to sacrifice one of the worlds, either the material, mechanical world, or the electro-magnetic world. It was imperative to find sufficient basis for one decision or the other. This was not slow in presenting itself.
The subsequent development of physics is a process against matter, which ended in its rejection. But, side by side with this negative activity proceeded the creative work of reforming the electro-magnetic symbolism; it had to be capable of representing the properties of the material world, its atomic structure, momentum, radiation and absorption of energy, electromagnetic phenomena. . . .
On the horizon of scientific thought was rising the electronic theory of matter.
Through electrical units a connection was disclosed between matter and vacuum. . . . The idea of a special sub-stratum, filling the vacuum -ether - is superfluous. . . . Light and heat are born from the movements of electrons. They are the suns of the
microcosmos. . . . The universe consists of positive and negative units, bound together by electromagnetic fields.
Matter has disappeared; its variety is replaced by systems of electrical units, akin to one another and, in the place of the customary, material world, there takes shape before us the vastly different electro-magnetic world.
But even the recognition of the electro-magnetic world has not disposed of many insoluble problems and difficulties; the necessity of a unifying system was felt.
In our arduous ascent we have reached the point [says Professor Oumoff] where the road divides. One stretches out horizontally towards the plain which we have just depicted; the other leads towards the last summit, which is already visible and the ascent is not steep.
Let us examine the point we have reached. It is very dangerous; more than one theory has been wrecked on it. It is all the more dangerous because its subtlety is hidden by the mask of simplicity. Its foundations are the experimental attempts which gave a negative answer to the investigations of thorough and skilled observers.

Professor Oumoff points out the contradictions which resulted from some of the experiments. The need to explain these contradictions gave impetus to the finding of a unifying principle; this was the principle of relativity.
The deductions of Lorentz, made in 1909 and referring mainly to electro-optical phenomena, gave the impetus to the publication by Albert Einstein of a new principle, and to its remarkable generalization by the recently deceased Hermann Minkowsky.

We are approaching the summit of modern physics: it is occupied by the principle of relativity, the expression of which is so simple that its all-important significance is not immediately evident. It says; the laws of phenomena in a system of bodies, for an observer connected with it, appear to be the same whether the system is at rest or is moving uniformly and rectilinearly.
It follows hence that, by the aid of phenomena taking place in a system of bodies
with which he is connected, an observer is unable to discover whether this system
possesses a uniform progressive motion or not.
Thus, no phenomenon taking place on earth enables us to discern its progressive motion in space.
The principle of relativity includes in itself the observing intellect, which is a circumstance of the greatest importance. The intellect is connected with a complex physical instrument -the nervous system. Consequently, this principle gives indications concerning things which take place in moving bodies, not only in relation to physical and chemical phenomena, but also in relation to phenomena of life, and therefore also to the quest of man. It is remarkable as an example of a thesis based on strictly scientific experiment in the purely physical domain, which bridges the gulf between two worlds generally considered to be of different nature.
Professor Oumoff gives examples of explaining complex phenomena by means of the principle of relativity. And he further shows how the most enigmatic problems of life are explained from the point of view of electro-magnetic theories and the principle of relativity, and, finally, comes to what is especially interesting for us:
All spatial measurements involve time. We cannot define the geometrical form of a solid moving in relation to us; we always define its kinematic form. Therefore our spatial measurements actually take place not in a threedimensional manifold, i.e. one possesssing three dimensions of height, width and depth, such as this hall, but in a four-dimensional manifold. We can represent the first three dimensions by three tape measures upon which are marked feet, yards or other measures of length. We represent the fourth dimension by a cinematographic reel, on which each point corresponds to a new phase of the phenomena of the world. The distance between the points of this reel is measured by a clock which goes uniformly at any speed. One observer will measure the distance between two points by one year, another by a hundred years. The passage from one point on this reel to another corresponds to our conception of the flow of time. Therefore we shall call this fourth dimension - time. The cinematographic reel can replace the reel of any of the tape measures and vice versa. The mathematical genius Minkowsky, so prematurely deceased, has proved that all these four dimensions are equivalent. How to understand this? Those who came from Moscow to St Petersburg passed through Tver. They are no longer at that station, nevertheless it exists. In the same way, a moment which corresponded to some event, already past, as, for instance, to the birth of life on earth, has not disappeared but exists. It is not outlived by the universe, but only by the earth. The place of this event in a four-dimensional universe is defined by a certain point, and this point has existed, exists and will continue to exist. At present another wanderer is passing through it -through this station passed by the earth. Time does not flow, just as space does not flow. It is we that flow, wanderers in a four-dimensional universe. Time is as much a dimen-sion of space as height, width and length If we interchange them in the expression of some law of nature, we still arrive at this law
The new ideas are embodied by Minkowsky in an elegant mathematical theory, we shall not enter the majestic temple erected by his genius, a voice proclaims from there
'In the universe all is given for it there is no past or future, it is - the eternal present, it has no limits either in space or in time Changes take place in individualities and correspond to their displacements along the world ways in the four-dimensional, eternal and boundless manifold In the domain of philosophic thought these ideas should produce a greater revolution than the displacement of the earth from the centre of the universe by Copernicus'* From the tunes of Newton, natural science has never been faced with more brilliant perspectives Is not the power of natural science blazoned forth in the transition from the indisputable experimental fact -the impossibility of determining the absolute motion of the earth to problems of the mind! A contemporary philosopher exclaimed in confusion 'Beyond truth and falsehood!'
When the cult of a new god is born, his word is not always clearly understood; the true meaning becomes revealed in time I think that the same is true also as regards the principle of relativity.
The elimination of anthropomorphism from scientific ideas has rendered an enormous service to science.
The principle of relativity follows the same path, showing the dependence of our observations on the general conditions of phenomena.
The electro-magnetic theory of the world and the principle of relativity explain only those phenomena, the place of which is determined by the part of the universe occupied by matter; the remaining part, which appears to our senses as a vacuum, still remains outside science. But the shores of the material world are constantly bathed by the surf of energy coming from that agitated ocean which is empty for our senses but not for our reason.
Is not the dualism of matter and vacuum an anthropomorphism and, moreover, the last one in science? Let us put the fundamental question. What part of the universe is filled by matter? Let us surround our planetary system by a sphere, the radius of which is equal to half the distance between the sun and the nearest stars: the length of this radius is traversed by a ray of light in a year and a half Let us accept the volume of this sphere as the volume of our world. Now, starting from the sun, as the centre, let us trace another, a lesser, sphere, the radius of which is equal to the distance between our sun and the furthest planet. I presume that the matter of our world, concentrated in one place, will not take more than one tenth of the volume of the planetary sphere: I think that this figure is considerably exaggerated. Calculation of volumes will show that in our world the volume filled with matter relates to the volume of vacuum as one to a number represented by the figures 3 with 13 noughts. This relationship corresponds to the relationship of one second to a million years.
According to Lord Kelvin's calculation, the density of matter corresponding to such a relationship would be ten thousand million times less dense than water, i.e. it would be at the furthest limit of rarefaction.

* My italics - P D Ouspensky

Professor Oumoff gives an example of a number of spheres corresponding to the number of seconds in a million years. On one of these spheres (corresponding to the matter in the universe) is inscribed all we know, because all we do know refers to matter. And matter is only one sphere among millions and millions of 'spheres of vacuum':

The conclusion arrived at [he says] is this: Matter represents a highly improbable event in the universe.
This event came into being because improbability does not mean impossibility. But where and in what manner are realized more probable events? Is it in the domain of radiant energy?
The theory of probability embraces an immense part of the universe -the vacuum in the world of becoming. We know that radiant energy possesses gravitational mass. Among the varied phenomena in the world of intercrossing rays, do not their elements attracted to one another give birth to tiny particles, the accumulation of which constitutes our material world?
Could it be that vacuum is the laboratory of matter?
The material world is the limited horizon which opens up before a man who has come out into a field. For his senses life is teeming only within the limits of this horizon; outside it, for man's senses, is only vacuum.

I do not want to start a polemic against those thoughts in Professor Oumoff's paper with which I do not agree. Still, I shall point out and enumerate the questions which arise, in my opinion, from the incompatibility of some premises.
The antithesis between vacuum and the material world sounds almost naive after the just-quoted words of Minkowsky about the necessity for science to pass to the questions of the mind when dealing with purely physical problems. Further, I see no essential difference between the material or mechanical and the electromagnetic universe. All this is three-dimensional. In the electromagnetic universe there is, as yet, no proper transition to the fourth dimension. And Professor Oumoff makes only one unquestionable attempt to connect the electro-magnetic world with higher dimensions. He says:

The sheet of paper, covered with electro-magnetic symbols, which we have used as a cover for the vacuum, may be regarded as milliards of separate superimposed sheets each of which represents the field of one small electric quantity or charge.
This is all. The rest is, after all, as three-dimensional as the theory of atoms and ether. 'We are present at the funeral of old physics', says Professor Oumoff. And this is true. But old physics becomes lost and disappears not in electromagnetic theories, but in ideas of a new extension of space which, so far, we have called time and motion. The physics that is truly new will be the physics which does not contain motion, i.e. in which there is no dualism of rest and motion, and no dualism of matter and vacuum.
By taking the universe as thought and consciousness, we become completely free of the idea of vacuum. And this point of view explains the small probability of matter, to which Professor Oumoff has arrived. Matter, i.e. everything finite, is an illusion in the infinite world.*
Out of the numerous psychological attempts to investigate the fourth dimension I shall dwell also on the book by Johan van Manen, Some Occult Experiences.**
This book contains a remarkable drawing of a four-dimensional body, which the author 'saw' by his inner vision. This interesting experience is described by van Manen in the following way:

When residing and touring in the North of England, several years ago, I talked and lectured several times on the fourth dimension. One day after having retired to bed, I lay fully awake, thinking out some problem connected with this subject. I tried to visualize or think out the shape of a fourth-dimensional cube, which I imagined to be the simplest fourth-dimensional shape. To my great astonishment I saw plainly before me first a fourth-dimensional globe and afterwards a fourth-dimensional cube, and learned only then from this object lesson that the globe is the simplest body, and not the cube, as the third-dimensional analogy ought to have told me beforehand. The remarkable thing was that the definite endeavour to see the one thing made me see the other. I saw the forms as before me in the air (though the room was dark), and behind the forms I saw clearly a rift in the curtains through which a glimmer of light filtered into the room. This was a case in which I can clearly fix the impression that the objects seen were outside my head. In most of the other cases I could not say so definitely, as they partake of a dual character, being almost equally felt as outside and inside the brain.
I forgo the attempt to describe the fourth-dimensional cube as to its form. Mathematical description would be possible, but would at the same time disintegrate the real impression in its totality. The fourth-dimensional globe can be better described. It was an ordinary three-dimensional globe, out of which on each side, beginning at its vertical circumference, bent tapering horns proceeded, which, with a circular bend, united their points above the globe from which they started.

* A. Einstein's book on relativity, which has since appeared, makes it possible to become better acquainted with the scientific (physical) treatment of this question.
** Some Occult Experiences described by Johan van Manen and annotated by C. W. Leadbeater, Theosophical Publishing House, Adyar, Madras, India, 1913.

So three circles are formed, the lower one representing the initial globe, the upper one representing empty space, and the greater circle circumscribing the whole. If it be now understood that the upper circle [empty space] does not exist and the lower (small) circle is identical with the outer (large) circle, the impression will have been conveyed, at least to some extent. . .I have always been easily able to recall this globe, to recall the cube is far more difficult, and I have to concentrate to get it back.
I have in a like manner had rare visions of fifth-and sixth-dimensional figures. At least I have felt as if the figures I saw were fifth- and sixth-dimensional. In these matters the greatest caution is necessary. I am aware that I have come into contact with these things as far as the physical brain allows it, without denying that beyond what the brain has caught there was something further, felt at the time, which was not handed on The sixth-dimensional figure I cannot describe. All I remember of it is that it gave me at the time an impression in form of what we might call diversity in unity, or synthesis in differentiation The fifth-dimensional vision is best described, or rather hinted at, by saying that it looked like an Alpine relief map, with the singularity that all mountain peaks and the whole landscape represented in the map were one mountain,* or again, in other words, as if all the mountains had one single base. This was the difference between the fifth and sixth, and in the fifth the excrescences were in one sense exteriorized and yet rested in the same unit; but in the sixth they were differentiated but not exteriorized, they were only in different ways identical with the same base, which was their whole.

In a note to these remarkable pages C. W. Leadbeater says:

Striking as the drawing is [of a four-dimensional figure made by van Manen] its value lies chiefly in its suggestiveness to those who have once seen that which it represents. One can hardly hope that it will convey a clear idea of the reality to those who have never seen it. It is difficult to get an animal to understand a picture - apparently because he is incapable of grasping the idea that perspective on a flat surface is intended to represent objects which he knows only as solid The average man is in exactly the same position with regard to any drawing or model which is intended to

* See Jacob Boehme's story, quoted by James, of a harp of many strings, of which each string is a separate instrument

suggest to him the idea of the fourth dimension; and so, clever and suggestive as it is, I doubt whether it will be of much help to the average reader.
The man who has seen the reality might well be helped by this to bring into his ordinary life a flash of that higher consciousness; and in that case perhaps he might be able to supply, in his thought, what must necessarily be lacking in the physical-plane drawing.
For my part I may say that the true meaning of van Manen's 'vision' is hard even to appreciate with the means at our disposal. When I saw in his book the drawing reproduced here, I at once understood and felt all that it means. But I disagreed somewhat with van Manen in the interpretation of this drawing. He writes:
We may also call the total impression that of a ring. I think it was then [looking at the drawing] that I understood for the first time that so-called fourth-dimensional sight is sight with reference to a space-conception arising from the visual perception of density.
In spite of all its caution, this remark seems to me dangerous, for it creates the possibility of the same mistake which has stopped Hinton in many things. This mistake consists in the possibility of constructing a certain pseudo-fourth dimension which, in actual fact, lies entirely in three dimensions. In my opinion the figure is full of motion. The whole figure seems to me moving, as though constantly arising in the meeting point of the sharp ends, spreading out from there and being re-absorbed there. But I shall not analyse and examine van Manen's experience now, leaving this to the readers who have had similar experiences.
As regards van Manen's descriptions of his observations of the 'fifth' and the 'sixth' dimensions, it seems to me that nothing in them justifies the supposition that they refer to a domain higher and more complex than the four-dimensional world.
In my opinion all this is no more than observations of the domain of the fourth dimension. But the remarkable thing in them is their similarity to the experiences of some mystics, especially those of Jacob Boehme. Moreover, the method of objectlesson is very interesting, i.e. those two images which van Manen saw and from the comparison of which he drew his conclusions.

Tertium Organum

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