Journey to the Land of the Fourth Dimension

by Gaston de Pawlowski

  Is not the insurmountable margin that prevents Achilles from reaching the tortoise always that infinity which never arises spontaneously in the continuous life of our consciousness, but which surges forth immediately as soon as a mathematician proposes the completion of a formula?

  We have asked explicitly what the suppositions might be of an observer in a world of two dimensions, seeing a square sign elongate into a diamond and then reduce to infinity, without suspecting that it is turning in the third dimension. Our impressions are analogous, in our three-dimensional world; in the Lorentz transformation, a primitive round body (or very nearly round, since the movement of the Earth already affects the relationship of the circumference to the diameter) becomes oval as it gathers speed, then infinitely flat when its velocity attains that of light. Has this sign too “rotated” in a new dimension?

  Yes, if we are permitted that rudimentary image; it has vanished into Einstein’s fourth dimension—which is to say, into time—not forgetting that the infinite loss is comprised, thanks to the constant Interval, of an infinite gain in energy, mass and density.57

  At 300,000 kilometers a second, the dilatation of time towards infinity will always be removed by a fraction.

  Evidently, I hasten to say, such a compensation of infinities is scarcely in the mind of a pure mathematician. All that I want to retain is the single fact of limiting time, energy, mass, at a velocity of 300,000 kilometers a second, sufficiently to bring forth the purely negative notion of infinity, without, moreover, permitting its attainment, since a fraction of a second, however minimal it might be, will always separate us from the conclusive disappearance of time.

  Does time no longer exist at the speed of light?

  It still exists in infinitely small quantity, since the speed is conceived in terms of a space and time according to our measurement.

  At 300,000 kilometers a second, time no longer exists, save for infinitely small fractions of seconds and kilometers, but those fractions suffice for Achilles never to catch up with the tortoise—by which I mean the integral and continuous conception of the universe.

  This simple observation cannot diminish in the least the extraordinary practical value of Einstein’s theories and the rare penetration of mathematical symbols designed to enlighten a new era in the study of the physical world.

  But if, as we believe, the fourth dimension must be—in the domain of pure quality and outside that of number—the living and mysterious unknown element that, by the union of opposites, explains and completes the universe, there is not now and never will be a mathematical symbol that can express it to us.

  Einstein’s space-time has no psychological quality.

  Art, in this respect, opens up to us a domain that is vaster and more replete with promise.

  In becoming a function of space and its fourth dimension, Einstein’s mathematical time is transformed into space-time. It loses all its psychological and physiological qualities; it is no longer, for us, an idea complete in itself, a succession in the natural order. Following the rhythm of our reasoning, it is no longer permissible for consciousness to take itself as a system of reference.

  For the philosopher who knows that all living reality is in consciousness and that mathematical symbols, like those of language, only represent it approximately, rather like a delegate representing his constituency, Einstein’s theories, useful as they appear, are only a new mathematical prison in which the mind might fall dangerously asleep in a false certainty.

  If the mind is to remain free, it will therefore find it necessary to resume the dolorous road of doubt—that doubt which, for want of a better word, we call humor, which is the pride of an independent mind.

  The uncertain and dolorous highway of Art serves our journey better than the prison of mathematical certainty.

  “Certainty” undoubtedly receives a better welcome from the crowd, which always dreams of immediate applications, but let us not forget this: the less useful something is immediately, the more serviceable it will be at length. That is the entire history of Art, whose range is in direct relation to its immediate uselessness.

  Civilization is a work of art—a well-regulated comedy.

  Let no one be mistaken, in fact: alongside the mathematical library where the symbolic measurements of life are crystallized out, art, since the origin of the world, has pursued its mysterious and patient synthesis of qualities—without our being aware of it, since our everyday life as civilized beings is already literature.

  Our current ideas are inspired by the literary novel or by that other work of the imagination that we call history; our gestures are suggested by the examples of morality or the fine arts, magical formulas giving their prestige to rightness just as hypotheses serve as the basis for scientific equations in medicine. Civilization is, first and foremost, a work of art, a well-regulated comedy, and an intelligent man cannot avoid occasionally having the very clear sensation that he is, first and foremost, an actor forced to play a role on Earth that he has not scripted.

  Let us not complain. It is by means of this progress in the artificial that the superior world of qualities gradually separates itself out, and that the imperceptible operation of the synthesis of life, linearity, space and movement becomes immobile and eternal thanks to Art—a synthesis that allows us, better than mathematical analysis, finally to attain what we call the fourth dimension.

  Art is anterior to man. It is already found in the groupings of matter…

  It is necessary not to forget, moreover, that art is anterior to the appearance of man. It already exists in the most humble groupings of matter, in the life of crystals as in the prodigious transmutations of matter effected by those alchemists of genius, plants.

  Even before spontaneous generation—impossible only in pasteurized milieu—became manifest everywhere, abundant and miraculous, matter already grouped itself in the form of living beings, as the osmotic growths described by Stéphane Leduc prove, with their elegant plant-like silhouettes.58 Since the appearance of matter, in fact—for want of any way to go further back—everything in nature has been choice, rational preference, research in form, line and harmony, pursuit of imponderable quality. Everything is alive, in a word, and the first manifestations of art appear to us in the primal groupings of matter.

  Every living being comes from a living being; nothing is more natural if one is prepared to admit that matter is alive and that its sensibility and its mobility are what engender all living beings—without it being possible, as the evolutionists would like to do, to establish a hierarchy between its children and to declare, for example, that a Protamoeba primitiva, a simple blob of protoplasm, a vague living nucleus in the Ocean, displays an ingenuity superior to that of a carnivorous plant or a crystal that nourishes itself, repairs itself, grows and reproduces.59

  …and in the formidable intra-atomic activity.

  The admirable discoveries of Gustave Le Bon concerning the dissociation of matter (too often attributed in the past to Becquerel and today to Einstein) have acquainted us with the potential grandeur of intra-atomic energy.60

  A bronze sphere weighing a gram, with a radius of three millimeters, rotating with an equatorial velocity of 100,000 kilometers a second (the velocity of dissociated particles) would have an active force equal to the work furnished by 1510 locomotives of 50 horse-power. At the speed of light, which is closely approximated by the β particles of radium, that force surpasses 1,800 billion kilograms—and if that velocity is a speed limit, as Einstein proposes, that would similarly be the supreme value of the intra-atomic energy.61

  Let us take note, in passing, that, as in the gyroscope, a certain velocity is necessary to the stability of the atom and that it begins to dissociate when its velocity of rotation falls below a certain critical point. Perhaps it will be confirmed one day that life and thought are due to the deceleration and dissociation of an atom; let us hope, for the sake of our pride, that this dissociation is as slow and graceful as that of a milligram of
musk, which, according to Berthelot, releases the innumerable particles of its perfume for 100,000 years before vanishing.62

  Science ignores of progress in quality.

  Science begins, as we have seen, by measuring in metrical symbols, thus to understand the energy of matter better, but it tells us nothing and never will be able to tell us anything about the prodigious intelligence that impels matter to group itself into ever-superior aesthetic forms, to transmute its “simple” bodies and to form beings therefrom that we call living in a more specific sense. This ardor for improvement, this choice of qualities, science ignores completely (for there is no better way of putting it) when it is a matter of extracting a human moral, for all that is imponderable remains foreign to it.

  The fourth dimension represents the artistic side of life.

  It is, therefore, to a fourth dimension that the concern reverts of completing our knowledge of the Universe, of symbolizing that domain of Art—immense, active, imponderable, immeasurable and mysterious—that we cannot remove from a general conception of the Universe without omitting that which constitutes the Universe’s reason for existence, its evolution and its end.

  The certainty that we mentioned above? But it is entirely contained in the subtle, mysterious, moving and continuous art of Life, in that Fourth Dimension, so close to us, which blinds us and prevents us from grasping it. The consoling illusion? It is, on the contrary, in the mirror-play of mathematics, even while the mirror-play dazzles us by interweaving and deforming, before the enraptured spectator, the luminous rays of the rotating lighthouse illuminated by Einstein.

  The fourth dimension is the sensation of the invisible in the presence of the visible.

  The fourth dimension? Shall we understand, one day, that it is our only axis of reference, the touchstone that permits us immediately to recognize as sublime a masterpiece that we do not know, and which contradicts our sensory experience: the counselor that suggests to us the against in the presence of the for and permits us to judge equitably between the visible and the invisible. Shall we ever understand, in a word, what our consciousness is, sprung from the depths of the ages, completing and explaining the universe: an internal and impartial sense judging the other senses and their hypotheses; a sense that a poet does not hesitate to call the sense of the divine, and which a humorist calls, perhaps more simply, common sense.

  The objective quest for certainty is nothing but facile cowardice. Let us not expect anything save from ourselves.

  The term “common sense” will doubtless shock those who see elevated philosophical research or great scientific discoveries as the only means of attaining the Absolute and expend all their personal efforts upon it; that is what explains, moreover, why these reaches and discoveries always enthuse ordinary people.

  How much more flattering the term “the sense of the divine” is to their mental sloth! One sole cry—Deus, ecce Deus!—and by the same token, our consciousness has covered, as by a single cry: Vive Un Tel… or the sound of a military march, sufficient to discharge us from the care and responsibility of thought.63

  Simple common sense, on the contrary, falls back to reality, towards that humble everyday labor of thought which, by means of successive choices, slowly pursues the interminable road of progress! Having nothing to await—neither external prodigies nor divine intervention—knowing that all revelation is within us and can only come from us: what a crushing responsibility for the human mind, but what a sublime mission too!

  Our external constructions, made in our image, are useful…

  Since human beings came into existence, their principal occupation has been to discharge, at least in part, this heavy responsibility, by materializing around them the self-knowledge that they have been able to acquire and constructing the world in their own image. Without that anthropomorphic procedure, we hasten to say, no progress of the human mind would be possible and we could not conceive any model at all of the universe. Consciousness, devoted to itself, remains mute; it is necessary that it reflects itself in words, images, symbols, formulas or hypotheses in order to act, and the purely qualitative fourth dimension only expresses itself in contact with the three quantitative dimensions of our relative world.

  Without the primitive hypotheses of our senses, without their personal interpretation, the external world would be neither resistant, nor sonorous, nor colored; there would be nothing but a collection of indiscernible movements and vibrations. Without the scientific hypothesis, no image of the world would be possible, just as a reasoning unordered by words would be impossible.

  …provided that we do not take them for absolute objective certainties.

  It remains no less true that these successive hypotheses, indispensable as they are, are only provisional and that the mistake of taking them for definitive certainties, immobilizes and considerably slows down the progress of ideas. While admiring them with all our heart, our duty is therefore to denounce their relativity, to demonstrate their limits and always to suggest new possibilities to the human mind.

  This task is that of humorist when it is a matter of fixing the limits of a hypothesis by means of the absurd; it is that of the poet when it is a matter of proposing new aspects of imponderable quality.

  It is this double task that we have attempted to realize in this book, solely with recourse to the symbols of Art.

  Now, we live surrounded by reassuring idols.

  We are the slaves of our creations.

  We have shown above what a danger is posed to the movement of ideas by the mental paralysis that is false mathematical certainty, and we know how joyfully man complaisantly mires himself in the unity of the number that presents him with his own image—but this anthropomorphism is by no means specific to science, for we see the human Narcissus marveling at his creations at every step, and taking his portrait, caricature or shadow for objective, reassuring and certain models. We live, therefore, surrounded by idols in human form, like primitive savages.

  Our houses, our furniture, our household objects, our machines and our scientific instruments are made in the image of man, with hair, arms, feet, arteries, bones, muscles, nerves and even senses. If we construct an automobile, for example, we conceive it, save for the wheels, in the image of a man, with an electrical nervous system, a respiration, a digestion, muscles, a bone-structure, arms that touch the ground, legs that propel, eyes and a voice. If we construct a moral entity such as the State, we similarly conceive it in the image of a man, with a brain, muscles, a digestive apparatus and a skeleton, which would be perfect if we did not then proceed, after the fashion of fetishists, to adore the idol that we have created and submit ourselves to its illusory superior powers.

  We live, to put it bluntly, religiously, and are pusillanimously happy to serve the innumerable masters that we have given ourselves.

  Without being aware of it, we become the slaves of our creatures, and, believing our lives to be transitory, we aspire to attach ourselves desperately to more durable creations of which we are the authors.

  What a familial tenderness is maintained today by the movable property we possess, instead of the immovable property of old, and how many affections would be able to resist the admirable evangelical advice to “Sell all that you have, give the money to the poor and follow me?”

  Which is the civilization that could similarly resist the destruction of its material and moral monuments, residues of the past?

  The human mind is almost always satisfied with received precepts, established order and respected customs. Infinitely rare are its movements of independence and originality. In social matters, this dependence on idols is such that man, having come to that pass—as we have seen—willingly believes in the existence of a superior being: the Animal-State, and allows himself to become gradually less differentiated, like a mere specialized cell, like a cogwheel of the enormous organism that grips him.

  Without refusing to recognize the material utility of these idols, the benefits of life in society and the
useful hypotheses of scientists, it seems that the time has come to render to man his sovereignty and to turn his mind, not towards the world of his creations—which is to say, the world below—but towards the source from which all his ideas come—which is to say, all the intuitions that permit him, every day, to make progress, by proposing new and more elevated goals.

  The most formidable and the most comfortable of our creations is that which we have made of God.

  In this respect, however, one last obstacle arises, the most formidable of all: that of the internal idol, that of the divinity. As if by some mental cowardice, man, who is pleased to live among his creations, experiences an invincible sloth when it is a matter of elevating himself above his condition and understanding. It seems more convenient to him to create a Being superior to him, charged with all that he has not yet attained and which represents for him the unknown. And his humility, like his devotion, is similarly nothing but the evident mark of idleness or weakness, a sloth so extensive that man has preferred to bring God down to Earth rather than go towards Him.

  On the day our Father dies, it will be necessary for us to take His place.

  It has sometimes been observed that a man only becomes a man on the day his father dies. However old, active or independent he might be, it is on that day alone that he experiences a distressing sense of emptiness above him. He is now the responsible leader who marches ahead and who masks the unknown for those who follow him. No guide will any longer return in a bad situation to offer him a hand; he remains alone in life, facing the horizon over which death looms.