Journey to the Land of the Fourth Dimension

by Gaston de Pawlowski

  The effects of the Great War on Pawlowski’s sense of humor probably never wore off entirely, but they were gradually ameliorated, and his spirits were doubtless raised considerably when he married Marguerite Mangin in 1921. He published few books thereafter, although his journalistic activities continued apace; his most prominent production in volume form, with the exception of the augmented Voyage, was Ma voiture de course [My Racing Car] (1923), which appeared in a pioneering series of “romans de sport” [sports novels].

  Pawlowski suffered a fatal heart attack at his home in Paris on February 2, 1933, and was buried in the Père Lachaise cemetery. His vast and various book collection was sold off in 1938, along with much of his voluminous correspondence, which he had carefully hoarded; unfortunately, the items were sold piecemeal and the collection dispersed.

  The La Boétie edition of Voyage added some confusion to Pawlowski’s bibliography by rendering his by-line on the cover and spine as “G. de Pawlowsky,” although the title-page has the correct spelling. That is the edition from which I have taken this translation, although it contains several other obvious typographical errors, and may well have others that are less easily detectable and corrigible.

  The text inevitably presents certain awkward problems to a translator, many of which reflect Pawlowski’s own difficulties in trying to broach and examine ideas to which “three-dimensional language” is unsuited. For instance, the translation of the word pays in the title as “land,” although perfectly orthodox, is clearly misleading, “land” being an essentially three-dimensional as well as a sociologically-loaded concept. Had he so wished, however, Pawlowski could have used a vaguer or more refined term, and he presumably chose not to in order to illustrate the difficulty of adapting three-dimensional terms to his purpose; I have, therefore, done likewise, not only in that instance but others.

  Brian Stableford

  JOURNEY TO THE LAND OF

  THE FOURTH DIMENSION

  I. The Silent Soul

  Having arrived in the land of the fourth dimension some time ago, I find it strangely awkward, as I begin to write my anticipated memoirs, to translate them into ordinary language—the vocabulary of which is, of course, conceived according to the givens of three-dimensional space.

  No words exist capable of defining precisely the bizarre impressions that one senses when one elevates oneself permanently above the world of habitual sensations. The vision of the fourth dimension reveals entirely new horizons to us. It completes our comprehension of the world; it permits the realization of a definitive synthesis of our items of knowledge; it justifies all of them, even though they seem contradictory, and one understands that it confers a totality upon ideas which partial expressions cannot contain. The fact of enunciating an idea by means of words in common usage limits one to the preliminary assumption of three-dimensional space. Now, although we know that the three geometrical dimensions—length, breadth and height1—can always be contained in an idea, those three dimensions, by contrast, can never suffice wholly to construct a quality, be it a curve in space or a reasoning of the mind. Neither numbers nor words constructed in three dimensions can take account of that difference between the container and the contained, between idea and matter, between art and science, which is not measurable in quantities—and which, for want of a better term, we call the fourth dimension.

  It is not at all astonishing that, taking the part for the whole, I should use the words fourth dimension in the course of this story to describe the continuous ensemble of phenomena, incorporating into that ensemble what it is convenient to call “the three dimensions of Euclidean geometry”. In spite of its imperfect name, one should not, in fact, consider the fourth dimension as a fourth measurement added to three others, but rather as a Platonic fashion of understanding the universe,2 without there being any need for him to dissent from Aristotle on this point: as a means of escape, permitting the comprehension of things in their eternal and immutable aspect, and a liberation from modification of quantity in order to attain the quality of facts.

  I know that I could, in writing these notes, have recourse—as some philosophers do—to a conventional vocabulary, coining obscure words to mask the insufficiency of current language, but that would only serve to push the difficulty back without resolving it. I therefore prefer to recount these memories of my journeys in the land of the fourth dimension in the ways they presented themselves to my mind, without literary pretension, naively and in disorder, hoping for the reader’s indulgence, and will be happy if I can merely evoke in his mind a few dormant ideas that no one, in our world, has yet bothered to awaken.

  To begin with, despite the difficulties of vocabulary, and especially the impossibility of my classifying chronologically future memories that escape any notion of time, I shall attempt to retrace the mental path which, little by little and step by step, led me to the land of the fourth dimension.

  Before anything else, it is necessary to establish that the process of being transposed—“transported” is the wrong word—to the land of the fourth dimension immediately overturns the common notions we have of time and space. Naturally, therefore, it is by means of small observations contradicting these common notions that the attention is gradually attracted to the possibility of the great voyage that our mind may accomplish. These contradictions are frequent, in everyday life as well as in the opportunities of the loftiest scientific research.

  Because presentiments make us afraid when they come true, we prefer to explain the leaps of our heart in terms of passionate causes rather than the obscure aspirations of the race, and, when we speak of the exact sciences, we avoid as subversive all indiscreet questions regarding the impossibility of explaining a curved line, parallelism, movement and, in general, everything that surrounds us.

  Time, without the space that expresses it, is inaccessible to us, and space can only be explained to our senses in terms of the time we take to traverse it. By virtue of a sort of natural slothfulness, however, our mind avoids and dissimulates these contradictions, as if they constituted a veritable mortal danger.

  In fact, it is necessary to recognize that, in the present state of our civilization, few minds can support without danger the abrupt destruction, or even the dissociation, of notions of time and space. These notions are so indispensable to us that we immediately feel terror and madness brushing our minds when we relieve ourselves momentarily of these two traditional crutches, which allow us to take our initial steps safely.

  We feel, however, that we are perpetually surrounded by an immense unknown. We occupy a strange and ill-defined location between the sensible world and our consciousness; we remain timidly curled up in the depths of a ship that carries us wherever the waves of an unknown sea dictate, and we declare ourselves satisfied if our location remains subjectively much the same, between the four walls of our cabin. If, however, we were to take it into our heads to emerge briefly from our retreat and courageously direct our eyes outside, it would be easy to understand that nothing is less safe than our perilous situation in the ensemble of phenomena and ideas.

  Could there be anything more uncertain, in fact, than the notion of time that appears to us to be fundamental? Certain undeniable facts of psychic notification, of future prediction, would be worthy of being courageously envisaged by science, if science were not terrified by the idea of emerging momentarily from its petty domain of known relationships, in which ideas are formulated like the steps of a minuet. We accept historical knowledge of the past as something perfectly natural, but is it not evident that the past, of which we are so sure, does not presently exist, and that nothing, in consequence, can permit us to prove its existence? We use, as a basis for that proof, objects that subsist and personal memories, although we know perfectly well that this material evidence and these intellectual memories are, in the final analysis, only present vibrations.

  The future seems to us unknown, because we believe that we have no material vision of it. This is, however, a crude and
superficial reasoning that is limited in its range once we understand that the world as it appears to us is only luminous because we have eyes, sonorous because we have ears, and solid because we can touch it—that it is only formed, in reality, of different, obscure and mute vibrations, immaterial in the absolute sense of the word. The past is made of nothing but present vibrations; why, I ask you, could the future, which is contained in those same vibrations, not be known in a fashion just as certain, if we had a true understanding of the totality of motion,3 in accordance with which the entire universe would be seemingly modified for our sensibility?

  When one has arrived in the land of the fourth dimension, when one is liberated forever from the notions of space and time, it is with this intelligence that one thinks and reflects. By virtue of that, one finds oneself confounded with the entire universe, with pretended past events. Everything, henceforth, is a world of forms and immobile and innumerable qualities, which are, in a way, merely the harmonious lines of the same masterpiece.

  One can, of course, discern in this world, as in everyday life, different points of existence and link up events that connect them, but it is useless, for that purpose, to appeal to the habitual notion of time. Events are outlined in the manner of geometrical figures—or, better still, the contours of a marble statue. Nothing can have, properly speaking, a beginning or an end. Nothing subsists any longer but harmonious symbols. One understands then how poor and inexpressive words such as Journey to the Land of the Fourth Dimension are. In this intellectually superior state, journey signifies nothing, and the expression fourth dimension itself is nothing but the manifestation of a synthetic state rather than the analysis of a new quality.

  As soon as one has arrived in this world of pure ideas, every expression of ordinary language becomes negative. The mind no longer operates with anything but the universality of things; its ideas are all possible, without any possible reaction. The silent soul is no longer disturbed by the noises of the world; they are no longer anything but conventional points, incapable of embracing the immortal unknown idea of the mundane, and confusing all eyes with that mysterious veil we call time.

  These general notions of the relative existence of time were not, however, those which first appeared to me most clearly. I only understood the whole of their strange scope when, having already arrived in the land of the fourth dimension, I was able to know simultaneously what had happened in ages past and what would happen in centuries to come. The overturning of the habitual idea that one has of space, the abstraction of distances that I succeeded in realizing progressively, the discovery I made of the Flat House with two exits, and the fashion in which I traversed the Horizontal Staircase, permitted me for the first time conclusively to abandon our three-dimensional world and to travel in all tranquility into the unknown.

  II. The Untied Ribbon

  The first obstacle that one encounters, when one first ventures into the land of the fourth dimension, is the ancestral resistance of the body, conceived in three dimensions. The mind adapts itself quite naturally to the abstractions of space and time, but the body seems, at first, to be incapable of escaping apparent material necessity. Curiously, however, the first facts that pointed out the road to the fourth dimension for me were purely material. They demonstrated to me, with adequate evidence, how close we are, without being aware of it, to the conception of the fourth dimension—which, for a long time, has justly preoccupied all those who have devoted themselves to the study of transcendental geometry.

  I knew that an attempt had already been made to take account of the curious abilities of a medium, explaining them by the existence of the fourth dimension. This medium tied genuine bow-knots in an extended cord whose extremities were held by trustworthy individuals. I knew, too, that it had been explained that the theorems of Lobatchevsky, Riemann, Helmholtz and Beltrami are the sole logical bases of any true theory of parallelism.4 I did not, however, have the opportunity to establish for myself the possibility of similar experimental demonstrations until the day when, desirous of conserving a few letters that I had, I decided to tie a ribbon around a little box—which, I was told, had come from India. Once the knot was tied, I remembered that I had forgotten to place one letter in the box and, instinctively, while thinking about something else, I opened the box, put the letter in, and closed it again.

  Only then did I notice that I had forgotten to untie the knot.

  I reviewed the facts carefully, and was forced to admit, by virtue of the wax seal, that the knot I had made, and which absolutely prevented the opening of the box, had not been touched. The object undeniably avoided the ordinary rules of our three-dimensional space.

  I remembered then that Félix Klein had demonstrated that knots cannot subsist in a four-dimensional space and I understood that the box I had before my eyes had been constructed outside any Euclidean law—that the curious object must have been conceived in India and materialized in France without the necessity to transport it materially.

  Needless to say, after that extraordinary adventure I sought by every possible means to find a rational explanation for it. I had doubtless been the victim of a simple hallucination, and there was nothing to prove that the stray letter was actually inside. I opened the box again, this time untying the ligature. The letter was indeed there! Perhaps I had put it there before the first closure? But a little bit of wax had fallen on the forgotten envelope when I closed the box for the first time, providing indubitable confirmation of my memory. Materially, the fact was impossible to admit. Materially, however, I was obliged to concede its reality. I confess that the certainty was, at first, infinitely painful for me, for it overturned the fundamental notions without which our mind goes astray and is set adrift.

  Nothing is easier to accept, in fact, than the existence of unknown and invisible forces situated inside us, which can be externalized to provoke phenomena that are only surprising in appearance. Everything can thus be explained with the utmost simplicity. In haunted houses, for example, we always find some unbalanced young woman in the neighborhood, whose nervous force, unwittingly externalized, is sufficient to produce the strangest phenomena. From there to thinking that there are unutilized forces dormant within us, more powerful than all the machines in the world, is only a single step. A day will come when we shall understand that there exists within every human being a path of progress much surer and much easier than the external path that science is presently attempting to follow.

  It is necessary to say, though, that all these phenomena, still mysterious because they are unknown, do not overturn anything in our habitual vision of the world. No one doubts that there are fluids other than electricity, but that never upsets the notion of cause-and-effect that forms the basis of our reasoning, and it is only when the relationship of succession seems to us to be inverted that our reason totters.

  What mysterious intervention had been able to overturn the relationship of succession in the events of which I have conserved such a precise memory? I could not account for it in a plausible fashion at first, because it proved impossible to repeat the adventure as I wished. My traditional attention had been awakened; it was always necessary for me to untie the ligature to open the box.

  I thought it, therefore, prudent not to advertise such an absurd incident—but I conserved the memory that had impressed me vividly. It was, for me, the first certain indication of the existence of a four-dimensional space in which a ligature could not subsist, nor a locked room remain closed, but I only understood much later how our traditional ideas of succession in time could be modified, and how that succession might become void on the day when, thanks to the intervention of the fourth dimension, all facts become, in a sense, simultaneous: detached from any historical relationship of cause and effect, distinguished from one another only by their qualities.

  III. The Innumerable Diligence

  Some time after the adventure of the Hindu box, the existence of the fourth dimension was revealed to me in a more precise fashion by s
ome observations that I made concerning the possible abstraction of distances.

  I have always been somewhat distrustful of spiritual experiments, particularly reported legends of Asia. It is necessary to recognize, however, that Orientals often appear to have realized the suppression of space in a practical fashion and that evidence in this regard is abundant. Arabs, as everyone knows, can communicate over very long distances without recourse to the telegraph. De Lesseps witnessed it on the occasion of the concession of the Suez canal,5 and it is equally well-known that Hindu ambassadors congratulated the Queen of England in London on a victory that her troops in the Orient were achieving at that moment. Have not trustworthy witnesses similarly reported, with telling details, how a Hindu can appear aboard a vessel that had quit the land several days before, deliver a message and disappear, his presence in India being established immediately afterwards? But these are simple materializations at a distance, which will doubtless obtain rational and scientific explanation one day.