Science and the problem of the fourth dimension. The address of Prof. N. A. Oumoff before the Mendeleevskian Convention in 1911—"The Characteristic Traits and Problems of Contemporary Scientific Thought." The new physics. The electro-magnetic theory. The principle of relativity. The works of Einstein and Minkowsky. Simultaneous existence of the past and the future. The Eternal Now. Van Manen's book about occult experiences. The drawing of a four-dimensional figure.
SPEAKING generally with regard to the problems propounded in the foregoing chapters—those of time, space, and the higher dimensions—it is impossible not to dwell once more upon the relation of science to these problems. To many persons the relation of "exact science" to these questions which undoubtedly constitute the most important problem now engaging human thought appears highly enigmatical.
If it is important why does not science deal with it? And why, on the contrary, does science repeat the old, contradictory affirmations, pretending not to know or not to notice an entire series of theories and hypotheses advanced?
Science should be the investigation of the unknown. Why, therefore, is it not anxious to investigate this unknown, which has been in process of revelation for a long time—which soon will cease to be the unknown?
It is possible to answer this question only by acknowledging that unfortunately official, academic science is doing but a small part of what it should be doing in regard to the investigation of the new and unknown. For the most part, it is only teaching that which has already become the commonplace of the independent thinker; or still worse, has already become antiquated and rejected as valueless.
So it is the more pleasant to remark that even in science may sometimes be discerned an aspiration toward the search of new horizons of thought; or, to put it differently, not always and not in all the academic routine, with its obligatory repetition of an endless number of commonplaces, has the love of knowledge and the power of independent thinking been crowded out.
Although timidly and tentatively, science, through its boldest representatives, in the last few decades has after all been touching upon the problems of higher dimensions, and in such cases has arrived at results almost identical with those propounded in the preceding chapters.
In December, 1911, the second Mendeleevskian Convention 1 was opened by the address of Prof. N. A. Oumoff, dedicated to the problems of time and higher dimensions under the title, The Characteristic Traits and Problems of Contemporary Natural-Scientific Thought.
The address of Prof. Oumoff, though not altogether outspoken, was nevertheless an event of great importance in the history of the development of exact science, and some time it will doubtless be recognized as an unusually bold and brilliant attempt to come forward and proclaim absolutely new ideas which practically renounce all positivism: and in the very citadel of positivism which the Mendeleevskian Convention represents.
But inertia and routine of course did their work. Prof. Oumoff's address was heard along with the other addresses, was printed in the Proceedings of the Convention, and there rested, without producing at all the impression of an exploded bomb that it should have produced had the listeners been more in a position to appreciate its true meaning and significance, and—more important—had they the desire to do so.
In this diminution of its significance the reserves and limitations which Prof. Oumoff himself made in his address assisted to a degree, as did the title, in failing to express its substance and general tendency, which was to show that science goes now in a new direction, and one which is not in reality—i.e., that the new direction goes against science.
Professor Oumoff died in 1916, and I am unwilling to impose upon him thoughts which he did not share. I talked with him in January, 1912, and from our conversation I saw that he was stopping half way, as it were, between the ideas of the fourth dimension approximating those expressed by me in the first edition of Tertium Organum and those physical theories which still admit motion as an independent fact. What I wish to convey is that Prof. Oumoff, admitting time as being the fourth dimension of space, did not regard motion as the illusion of our consciousness, but recognized the reality of motion in the world, as a fact independent of us and of our psyche.
I speak of this, because later I shall quote extracts from Prof. Oumoff's paper, choosing generally those places containing the ideas almost identical with the thoughts expressed in the preceding chapters.
That part of the address which pictures the evolution of modern physics from the atom to the electron I shall omit, because this seems to me somewhat artificially united to those ideas upon which I wish to dwell, and is not inwardly connected with them at all.
From my standpoint it is immaterial whether we make the foundation of matter the atom or the electron. I believe that at the foundation of matter lies illusion, or, in other words, a form of perception. And the consistent development of those ideas of higher space which Prof. Oumoff made the basis of his address leads, in my opinion, to the negation of motion; just as the consistent development of the ideas of mathematical physics has led to the negation of matter as substance.
Having mentioned electrons, I may add that there is a method whereby modern scientific ideas and the data of the psychological method may be reconciled; namely, by the aid of the very ancient systems of the Kabala, Alchemy and so forth, which establish the foundation of the material world in four principles or elements, of which the first two—fire and water—correspond to the positive and negative electrons of modern physics.
But in such case the electrons must be regarded, not simply as electro-magnetic units, but as principles, i.e., as two opposite aspects or phases constituting the world.
Prof. Oumoff's address is interesting and remarkable in that he stands already on the very threshold of metaphysics, and he is perhaps hindered from entering only by a lingering faith in the value of the positivistic method, which dies when the new watch-words of science are declared.
The introductory word to our forthcoming labors [says Prof. Oumoff] it will be most proper to dedicate to the excursions of scientific thought in its search for the image of the world. The necessity for scientific research along this path will become clear if we will turn to the covenants of our high priests of science. These covenants convey the deep motives of active service to natural science and to men. It is useful to express them in our time, wherein thought is preeminently directed to the questions of the organization of life. Let us remember the credo of the natural scientist:
To establish the authority of man over energy, time and space:
To know the architecture of the universe, and in this knowledge to find a basis of creative foresight. This foresight inspires confidence that natural science continuing the great and responsible work of creation in the fields of nature which it has already made its own, will not fail to enter a new field adapted to the enlarged necessities of mankind.
This new nature has become a vital necessity of personal and public activity. But its grandeur and power summon the mind as it were to tranquillity.
The demand for stability in the household and the brevity of the personal experience in comparison with the evolution of the earth lead men to faith, and create in them an image of the durability of the surrounding order of things not for the present only, but for the future. The pioneers of natural science do not enjoy such a serene point of view, and to this circumstance the natural sciences are indebted for their continuous development. I venture to lift the brilliant and familiar veil and throw open the sanctuaries of scientific thought, now poised upon the summit of two contrasted contemplations of the world.
The steersman of science shall be ceaselessly vigilant, despite the felicity of his voyage; above him shall invariably shine the stars by which he finds his way upon the ocean of the unknown.
At the time in which we are living now the constellations in the skies of our science have changed, and a new star has flashed out, having no equal to itself in brightness.
Persistent scientific investigation has expanded the volume of the knowable to dimensions which could scarcely be imagined only a short time—fifteen or twenty years—ago. Number remains, as before, the lawmaker of nature, but, being capable of representation, it has escaped from that mode of contemplating the world which regarded as possible its representation by mechanical models.
This augmentation of knowledge gives a sufficient number of images for the construction of the world, but they destroy its architecture as that is known to us, and create as it were a new order, extending far, in its free lines, beyond the limits not only of the old visible world, but even beyond the fundamental forms of our thinking.
I have now to lead you to the summits from which open the perspectives that are re-forming the very basis of our understanding of the world.
The ascent to them amid the ruins of classical physics is attended with no small difficulty, and I ask in advance your indulgence and shall exercise all my efforts to simplify and shorten our path as far as possible.
Prof. Oumoff proceeds to picture the evolution of form "from the atom to the electron," from materialistic and mechanistic ideas about the universe to the electro-magnetic theory.
The axioms of mechanics are only fragments, and their application may be compared to the judgment concerning the contents of an entire chapter by means of a single sentence.
Therefore it is not strange that the attempt of the mechanistic explanation of the properties of the electro-magnetic ether by the aid of axioms in which these properties were either denied or one-sidedly predetermined was doomed to failure. . . .
The mechanistic contemplation of the world appeared as one-sided. . . . In the image of the world, unity was not in evidence. The electro-magnetic world could not remain as something quite alien, unrelated to matter. The material mode of contemplating the world, with its fixed formula, had no sufficient flexibility to bring about unification through it and its principles. There remained only one way out—to sacrifice one of the worlds—the material, the mechanistic, or the electro-magnetic. It was necessary to find sufficient foundations for decision on the one side or on the other. These were not slow to appear.
The consequent development of physics is a process against matter, which ended with its expulsion. But along with this negative activity has gone the creative work of the reformation of electro-magnetic symbolics; it was forced to become adequate to express the properties of the material world: its atomic structure, inertia, radiation and absorption of energy, electromagnetic phenomena. . . .
. . . On the horizon of scientific thought was arising the electronic theory of matter.
Through electrical corpuscles was opening the connection between matter and vacuum. . . .
. . . The idea of a special substratum filling the vacuum—ether—became superfluous.
. . . Light and heat are born by the motion of electrons. They are the suns of microcosms.
. . . The universe consists of positive and negative corpuscles, bound by electro-magnetic fields.
Matter disappeared; its variety was replaced by a system of mutually related electric corpuscles and instead of the accustomed material world one deeply different—the electro-magnetic world—is envisaging itself to us....
But the recognition of the electro-magnetic world did not annihilate many unsolved problems and difficulties, and the necessity for a generalizing system was felt.
In our difficult ascent we have reached the point [according to Prof. Oumoff] at which the road divides. One stretches horizontally to that plane which has been pictured, another goes to the high summit which is already visible, and the grade is not steep.
Let us look about us at the point which we have reached. It is very dangerous; not one theory only has suffered wreck there. It is the more dangerous that its subtlety is covered by the mask of simplicity. Its basis is the experimental attempts which gave a negative answer to the researches of careful and skilled experimenters.
Prof. Oumoff shows the contradictions which were the outcome of certain experiments. The necessity to explain these contradictions served as the incentive to the discovery of the unifying principle: this was the principle of relativity.
The deductions of Lorentz, which were made in 1909, and which in general had in view electro-optical phenomena only, gave the impetus to the promulgation 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 it is difficult to discern its all-important significance. It asserts that the laws of phenomena in the system of bodies for the observer who is connected with it, will be the same, whether this system is at rest, or is moving uniformly and rectilinearly.
Hence it follows that the observer cannot detect by the aid of the phenomena which are proceeding in the system of bodies with which he is connected, whether this system has a uniform translational motion or not.
Thus we cannot detect from any phenomena proceeding on the earth, its translational motion in space.
The principle of relativity includes the observing intellect within itself, which is a circumstance of extraordinary significance. The intellect is connected with a complex physical instrument—the nervous system. This principle therefore gives directions concerning things proceeding in moving bodies, not only in relation to physical and chemical phenomena, but also in relation to the phenomena of life and therefore to the quests of man. It is remarkable as an example of a thesis, founded upon strictly scientific experiment, in a purely physical region, which erects a bridge between two worlds usually regarded as quite distinct.
Prof. Oumoff gives examples of the explanation of complex phenomena by the aid of the principle of relativity.
He shows further how the most enigmatical problems of life are explained from the standpoint of the electro-magnetic theory and the principle of relativity, and he comes at last to that which is the most interesting to us.
Time is involved in all spatial measurements. 1 We cannot define the geometrical form of a solid moving in relation to us; we are always defining its kinematical form. Therefore our spatial measurements are in reality proceeding not in a three-dimensional manifold, i.e., having three dimensions, of height, length and width, like this hall; but in a four-dimensional manifold: the first three dimensions we can represent by the divisions of a tape-measure upon which are marked feet, yards, or some other measure of length; the fourth dimension we will represent by the film of a cinematograph upon which each point corresponds to a new phase of the world's phenomena. The distances between the points of this film are measured by a clock going indifferently with this or that velocity. One observer will measure the distance between two points by a year—another by a hundred years. The transition from one point to another of this film corresponds to our concept of the flow of time. This fourth dimension we will call, therefore, time. The film of a cinematograph can replace the reel of any tape-measure, and contrariwise. The ingenious mathematician, Minkowsky, who died too young, proved that all these four dimensions are equivalent. How shall we comprehend this? Persons who arrive in St. Petersburg from Moscow have passed through Tver. They are not at this station (Tver) any longer, but nevertheless it continues to exist. In the same manner, that moment of time corresponding to some event which has already passed—the beginning of life on earth, for example—has not disappeared, it exists still. It is not outlived by the universe, but only by the earth. The place of this event is defined by a certain point in the four-dimensional universe and this point existed, is existing, and will exist; now through it, through this station passed by the earth, passes another wanderer. Time does not flow, any more than space flows. It is we who are flowing, wanderers in a four-dimensional universe. Time is just the same measurement of space as is length, breadth and height. Having changed them in the expression of some law of nature we are returning to the identical law.
These new concepts are embodied by Minkowsky in an elegant mathematical theory; we shall not enter the magnificent temple erected by his genius, from which proceeds this voice:
"In nature all is given: for her the past and future do not exist; she is the eternal present; she has no limits, either of space or of time. Changes are proceeding in individuals and correspond to their displacements upon world-ways in a four-dimensional eternal and limitless manifold. These concepts in the region of philosophical thought will produce a revolution considerably greater than that caused by the displacement of the earth from the centre of the universe by Copernicus." From the times of Newton to those of natural science, more brilliant perspectives have never opened up. Is not the power of natural science proclaimed in the transition from the undoubted experimental fact—the impossibility of the absolute motion of the earth—to a problem of the soul! A contemporary philosopher exclaimed in his confusion, "beyond truth and falsehood."
When the cult of a new God is born his word is not perfectly understood; the true meaning only becomes clear after the lapse of time. I think that this is true also as regards the principle of relativity. The elimination of anthropomorphism from scientific conceptions was of enormous service to science. On the same path stands the principle of relativity showing the dependence of our observations on general conditions of phenomena.
The electro-magnetic theory of the world (and the principle of relativity) explains only those phenomena the place of which is defined by that part of the universe which is occupied by matter; the rest of it, which presents itself to our senses as a vacuum remains as yet beyond the reach of science. But at the shores of the material world is changelessly dashing the surf of new energy from that deep ocean empty for our senses, but not for our reason.
Is not this dualism of matter and vacuum the anthropomorphism of science, and the last one? Let us put the fundamental question: What part of the universe is filled by matter? Let us surround our planetary system with a sphere the radius of which is equal to half of the distance from the sun to the nearest stars: the length of this radius is traversed by a light-ray in one and a half years. The volume of this sphere let us take as the volume of the world. Let us now describe, with the sun as a centre, another, lesser sphere with a radius equal to the distance of our sun to the outermost planet. I admit that the matter of our world, collected in one place, will not take more than one-tenth of the volume of the planetary sphere: Ii think that this figure is considerably exaggerated. After calculations of volume it will appear that in our world the volume occupied by the matter will be related to the volume of the vacuum as the figure 1 to the number represented by the figure 3 with 13 zeros. This relation is equivalent to the relation of one second to one million years.
According to the calculations of Lord Kelvin, the density of matter corresponding to such a relation would be less than the density of water by ten thousand million times, i.e., it would be in an extreme degree of rarefaction. . . .
Prof. Oumoff gives the example of such a number of balls as correspond to the number of seconds in one million years. Upon one of these balls (corresponding to the matter in the universe) is written all that we know, because all that we know is related to matter. And matter is only one ball among millions and millions of "balls of vacuum."
This is his conclusion; says he:
Matter represents a highly improbable fact in the universe. This event came into existence because small probability does not mean impossibility. But where, and in what manner, are realized more probable events? Is it not in the domain of radiant energy?
The theory of probability includes the immense part of the universe—the vacuum—in the world of becoming. We know that radiant energy possesses the preponderating mass. Among the different phenomena in the world of inter-crossing rays, out of elements attracting one another are not the tiny fragments born which by their congregation compose our material world? Is not the vacuum the laboratory matter? The material world corresponds to that limited horizon which is open to a man who has come out into a field. To his senses life is teeming only within the limits of this horizon; outside of it for the senses of man there is only a vacuum.
I do not desire to start a polemic about those thoughts in Prof. Oumoff's address with which I do not agree. Yet I shall mention and enumerate the questions which in my opinion are raised by the incompatibility of certain principles.
The contrast between the vacuum and the material world sounds almost naive after the just quoted words of Minkowsky concerning the necessity of a transfer of attention, on the part of science, from purely physical problems to questions of consciousness. Moreover I do not see any fundamental difference between the material, the mechanical, and the electro-magnetic universe. All this is three-dimensional. In the electro-magnetic universe there is as yet no true transition to the fourth dimension. And Prof. Oumoff makes only one clear attempt to bind the electro-magnetic world with the higher dimensions. He says:
That sheet of paper, written in electro-magnetic symbols, with which we covered the vacuum, it is possible to regard as billions of separate superimposed sheets, but of which each one represents the field of one small electric quantity or charge.
But this is all. The rest is just as three-dimensional as the theory of atoms and the ether.
"We are present at the funeral of the old physics," says Prof. Oumoff, and this is true. But the old physics is losing itself and disappears not in the electro-magnetic theory, but in the idea of a new dimension of space which up to the present has been called time and motion.
Truly, the new physics will be that in which there will be no motion, i.e., there will be no dualism of rest and motion, and no dualism of matter and vacuum.
Understanding the universe as thought and consciousness we completely divorce ourselves from the idea of a vacuum. And from this standpoint is explained the small probability of matter to which Prof. Oumoff referred. Matter, i.e., everything finite, is an illusion in an infinite world. 1
Among many attempts at the psychological investigation of the fourth dimension I shall note one in the book by Johan Van Manen, Some Occult Experiences.
In this book is a remarkable drawing of a four-dimensional figure which the author "saw" by means of his inner vision. This interesting experience Van Manen describes 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 problems connected with this subject. I tried to visualize or think out the shape of a four-dimensional cube, which I imagined to be the simplest four-dimensional shape. To my great astonishment I saw plainly before me first a four-dimensional globe and afterwards a four-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 endeavor 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 forego 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. The effect is best indicated by circumscribing the numeral 8 by a circle. So three circles are formed, the lower one representing the initial globe, the upper one representing empty space, and the greater circle circumbscribing the whole. If it be now understood that the upper circle 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 the 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 the sixth, that in the fifth the excrescences were in one sense exteriorized and yet rooted 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.
C. W. Leadbeater on a note to these remarkable pages says:
Striking as this drawing is, 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 suggest to him the idea of the fourth dimension; and so, clever and suggestive as this 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 he might perhaps 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 difficult even to appreciate with the means at our disposal. After seeing the drawing in his book I at once felt and understood all that it means, but I disagree somewhat with the author in the interpretation of his drawing. He says:
"We may also call the total impression that of a ring. I think it was then 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."
This remark though very cautions seems to me dangerous, because it creates the possibility of the same mistake which stopped Hinton in many things and which I partly repeated in the first edition of the book The Fourth Dimension. 1 This mistake consists in the possibility of the construction of some pseudo fourth dimension, which lies in reality completely in three dimensions. In my opinion there is very much of motion in the figure. The entire figure appears to me as a moving one, continuously generating itself, as though it were at the point of contact of the acute ends, coming from there and involving back there. But I shall not analyze and comment upon Van Manen's experience now, leaving it to readers who have had similar experiences.
So far as Van Manen's descriptions of his observations of the "fifth" and "sixth" dimensions are concerned, it seems to me that nothing in them warrants the supposition that they are related to any region higher or more complex than the four-dimensional world. In my opinion all these are just observations of the region of the fourth dimension. But the similarity to the experience of certain mystics is very remarkable in them, especially those of Jacob Boehme. Moreover the method of object-lesson is very interesting—i.e., those two images which Van Manen saw and from the comparison of which he deduced his conclusions.
125:1 A convention of Russian scientists, named in honor of the famous Russian chemist, Prof. Mendeleeyeff. Transl.
129:1 Italicized by me. P. Ouspensky.
133:1 The works on Relativity by Dr. A. Einstein make possible a more thorough acquaintance with the scientific (physical) treatment of this subject.
135:1 One of P. D. Ouspensky's books. Transl.
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