Journey to the Land of the Fourth Dimension

by Gaston de Pawlowski

  The idea of instantaneity is equivalent, for us, to that of nothing, and we cannot, for the most powerful reasons, support the idea that I have already mentioned, of a possible inversion of the order of succession in the development of a fact or an idea—and yet, many banal observations ought to demonstrate to us how puerile and inexact this way of envisaging things is.

  In a dream, for example, when an external noise or an odd sensation disturbs our sleep, we immediately conjure up a long and complicated story that justifies and precedes the abrupt sensation. We dream that, after interminable preparations, we have set forth on a journey; that after a journey lasting hours, all of whose details are still in our memory, we arrive at its goal; that a catastrophe awaits us, and is taking us by surprise. It is evident, however, that the catastrophe has preceded our historical justification, even though we do not hesitate to consider it as the final moment of our dream. We suppose, in brief, a vain genesis of instantaneous four-dimensional ideas in imitation of the genesis of three-dimensional phenomena.

  This need for preparation is found, to some extent, everywhere, even in very serious matters of scientific or artistic research that have nothing in common with dreams. Consider, in fact, what happens when a scientist makes a great discovery or a writer senses the emergence of an idea of genius. In such a case, the first concern of the inventor is not to recognize that the idea has come to him from an unknown source, that it has suggested itself to him involuntarily, but, on the contrary, to justify his discovery with reasoning invented after the fact.

  With the best will in the world, the scientist will construct in all its elements, step by step, the pretended method that led him to make his discovery. Quite sincerely, he does not perceive that he is only justifying an involuntary intuition by means of the subsequent experiments, and that, in reality, he did not play any voluntary part in that instantaneous intuition.

  The writer does the same when he tries to explain afterwards what his intentions were in conceiving a work of genius. In reality, the man, however knowledgeable he might be, does not know himself and is merely the humble servant of his immobile four-dimensional intelligence, beneath which he moves in an incomplete and transitory three-dimensional space.

  Everything, in temporal terms, in subject to illusion. The duration of human life, sufficient from our point of view, is insignificant if one compares it to that of the stars, prodigious if one sets it beside that of inferior creatures, which are born, reproduce and die within a few seconds.

  It is similarly worth pointing out that in the life of a man of genius, the truly creative act seems to occur within the short space of a few seconds. The rest is merely a matter of tuning, interminable variation and adaptation to vulgar prejudices constructed in three dimensions. In general, it is in the early years of their life that men of talent really conceive the ideas that will later make their intellectual fortune, and tomorrow’s great man is only the fortunate inheritor of yesterday’s wealthy child.

  The duration of our actions, long and complicated as they may seem, is infinitely multiplied by the material difficulties of action or expression in a three-dimensional world. It often happens that a simple glance exchanged between two passers-by who do not know one another replaces years of communal life or complete intimacy, and the minds understand one another in an instant better than they would through the medium of their bodies in an interval of three long years.

  We necessarily attribute a temporal duration to these intellectual flashes of total four-dimensional comprehension and, fugitive as they are, we suppose that they must last at least a few seconds. Even that duration is non-existent, however, for there is no possible duration in the world of four dimensions, and, in consequence, no necessary succession in actions that are, in sum, as simultaneous as all the distinct parts of a marble statue.

  It was this apparently complex, but quite simple, notion that permitted me to explain, for the first time, the three little journeys that I had been able to make to the land of the fourth dimension.

  These journeys were accomplished, if I might put it thus, on the spot, in depth and in an instantaneous fashion, in spite of all the difficulties—and I must observe once again that the words are unfortunately lacking for me to describe, in a language conceived in three dimensions, the admirable simplicity of these journeys without displacement: these extensive instantaneous excursions, which, however—to employ current language—comprised long and curious episodes. The first ones were devoid of much interest, but they surprised me by their strange novelty.

  One day, therefore, without any apparent reason—I might almost say disinterestedly—I found myself in Paris, having gone past the Gare du Nord and the Gare de l’Est, in a little deserted square of provincial appearance where the Gare du Midi was.9

  I cannot describe the strange impression made on me by that seemingly-abandoned building with the high roofs and walls of stone and brick, all of whose windows were closed and whose façade bore, in banal letters of gilded zinc, the simple words: Gare du Midi. Behind the building there was no railway, no movement.

  By virtue of what materialization of ideas was this unnecessary and absurd station there, and why had the crossroads of memory erected it for me on this Parisian site? I did not even attempt to explain it to myself, and the more interesting journeys that I made thereafter soon erased this insignificant encounter from my mind.

  VII. The Flat House

  I have indicated in the preceding chapter how I was led to conceive that the development of the sciences is not effected, as is commonly believed, by deduction, but that, on the contrary, all the discoveries made by the human mind were due to the intuition of certain thinkers, whose conceptions often qualified as fantasies, although the recording savants subsequently appropriated them by verifying them.

  It is to poets, to the imaginative, that the privilege has belonged since the origin of the world of discovering the secrets of nature, because that discovery is, in the final analysis, entirely internal, and its experimental verification nothing but a vain simulacrum. In failing to recognize the profound truth of certain poetic inventions, scientists have not neglected to reduce the domain of possible discovery, and one cannot stress too heavily the facility with which they set aside from their preoccupations certain problems whose existence is nevertheless undeniable. It hardly matters to Euclidean geometers that they give a ridiculous definition of parallelism: “two lines that only meet at infinity.” They are content to smile when their approach to the squaring of the circle is criticized and they declare themselves satisfied when they have represented space and time as a succession of points occupied one after another by a moving object. Only definite quantities interest them, although such quantities are nothing but the reflection to infinity of the same unity; continuity escapes them and quality is, for them, a word devoid of meaning. Only quality and continuity, however, can permit us to rise above the commonplace world and glimpse, beyond pretended scientific certainties, the definitive certainty that never changes.

  It is by this means, continually increasing our mental faculties, that infinity and eternity are eventually revealed within a moment, of which it is sufficient to increase the power, whether in a past or in a future, in which eternity is nothing but a pure mirage.

  It was doubtless under the influence of sharp memories encountered at certain moments in my thoughts that it was possible for me thus to accomplish my first instantaneous journeys to the land of the fourth dimension.

  The discovery I made of the Gare du Midi situated in the heart of Paris beside the Gares du Nord and de l’Est was not, for me, the first revelation of the possible existence of “places in the world”—as we used to say—distinct from the ones that one normally sees, coexistent in the fourth dimension.

  I remember, for example, a certain green room of which I established the undeniable existence during my childhood, which was situated exactly in between the final bedroom looking out from the façade of an old provincial château an
d the large room that came immediately afterwards and which occupied the entire wing of the château.

  On reflection, adopting the ordinary three-dimensional point of view, that room had no door to the central corridor that served all the rooms, and its existence was geometrically impossible. It is no less true that no detail of the furniture of the green room, in the Empire style, was unknown to me, and I remember, even today, the periodic but entirely clear impressions I had of it. Moreover, that did not astonish me for many years, for it was customary to abandon certain rooms that were never used and to consecrate them permanently to memories of other times, In Paris, one cannot conceive of the existence of these forgotten rooms, but it seems perfectly natural in the provinces. It was that very fact that prevented me from taking a more particular interest in the green room during that period of my life. It is for that reason, too, that I only record the fact as a memory, without wishing to draw any other consequence from it.

  Similarly, I only want to cite for form’s sake the existence of an abandoned house that I discovered one day in the forest of Fougères, in which I went with some astonishment though rooms that were not constructed geometrically, whose vertically-arranged floors only comprised a single one internally. Since then, I have understood that these constructions are only explicable by the existence of four-dimensional space—but that did not become evident to me until the day when I discovered, in a quarter of Paris previously inaccessible to me and situated outside the habitual vision of three dimensions, an extraordinary flat house with two doors, one of which let out into the Place de la Concorde and the other on to the Terrasse de Saint-Germain. I have necessarily to employ the absurd expression flat house because I cannot find any words in our language capable of describing that house—which, in three-dimensional vision, would have been invisible in profile, whose facades could only be perceived at an angle, and whose entrance and exit were confused, distinguished only by the clearly-differentiated places in the world of three dimensions to which they led.

  It is no less true that, after an initial atavistic revolt of my entire being, it was possible for me to pass through—in every sense of the phrase and quite naturally—the marvelous domain that was offered to me. Furthermore, it was not even a mater of personal displacement: the space seemed to come to me. This was not the “levitation” about which so much has been said, nor mental transport at a distance; it was something infinitely more simple than all that: a dissolution of the universe, unexpected and definitive. My immobility was analogous to that of the geometrical axis of a wheel rotating at top speed. I displaced myself while remaining still. My movements were only movements relative to myself. I benefited from them according to my desire, without contributing the least effort thereto.

  According to every appearance, this reconstruction of the world was due to the power of my internal memories, which completed themselves and exteriorized themselves with a force that can only derive from the working of a highly-developed visual memory. The second door opened on to the Terrase de Saint-Germain, but it was quite evident that, had my desire been modified, it might have opened somewhere else entirely.

  Needless to say, the habitual preoccupations of modern life soon appeared to me to be infinitely paltry and pointless. The idea that thousands of men had been able to live in the world until then without benefiting from its complete vision seemed implausible to me. How long would that be the case? It did not take me long to understand that the question did not even make sense and that, from the viewpoint of the fourth dimension, the world cannot have a beginning or an end, properly speaking.

  Nothing prevented me from achieving the same displacement—to employ the common expression—that I had succeeded in effectuating in space, by means of the fourth dimension, in time as well. I was thus permitted to enter into a relationship with that which had been and that which must be, all the while remaining motionless in the eyes of the vulgar, who have no understanding of the extreme mobility of the motionless philosopher and my power to explore, solely according to the caprices of my will, what are commonly known as future ages.

  VIII. The Transmutation of Atoms of Time

  It was, therefore, by displacements in space that the existence of the land of the fourth dimension was first revealed to me. Once again, I do not know how to explain these displacements by borrowing terms from a contemporary language constructed in three dimensions. I am forced, in spite of everything, to employ sketchy images, to have recourse to old expressions believed to be the preserve of alchemy, to describe an incident that is, however, quite simple and which should not be surprising, however unfamiliar one might be with the unity of viewpoint that characterizes the fourth dimension.

  Just as one has recourse to the atomic theory to provide an adequate image of chemical combinations, I too am constrained to have recourse to an analogous hypothesis to explain in a rough fashion the displacements that one effects in the land of the fourth dimension; this imperfect explanation goes like this:

  Whereas in displacement in three dimensions, the atoms forming a body are pushed back and replaced by other atoms composing another body, in the same way that a ship displaces the sea-water, displacement in the land of the fourth dimension is made by means of what was once called a transmutation.

  The world of the fourth dimension being continuous, no movement, in the vulgar sense of the word can be produced there as in the mobile world of three dimensions. A displacement is therefore made by an exchange of qualities between neighboring atoms, and—to employ the same gross image as before—when a ship is displaced, it is the atoms of water in front of it that mutate into the atoms of the ship while, behind it, the atoms of the ship mutate into atoms of water.

  This, if properly understood, is only an image of the most primitive sort, designed to explain, in the language of three dimensions, a procedure of displacement that has no Euclidean character in the continuous world of four dimensions. It is, indeed, necessary to repeat that the atoms are only a convenient hypothesis. They do not exist in reality; there are only different qualities in a single physical continuum.

  The atom is a conception of the mind, which isolates matter with all its attributes and all its qualities. The mind conceives the atom in its own image, thus extracting it from a complete and unique four-dimensional world, and it is an illusion of the senses that reflects the atom to infinity, as if by means of multiple mirrors, into the various appearances of an incomplete world of three dimensions. As soon as one is transposed into the land of the fourth dimension, movement, as we understand it, no longer exists; there are only changes in quality, and we remain motionless, in the vulgar sense of the word.

  The same rough comparison permits a glimpse of the similar displacement in time that occurs when one is transposed into the land of the fourth dimension. In the same way that we suppose atoms in juxtaposition to explain space, we imagine, in order to justify time, a succession of moments that are, in a way, the atoms of time. Here, as with displacement in space, displacement in time is effectuated by means of a transmutation of the atoms of time—moments, that is—under the action of that philosopher’s stone, the atom or, better still, the monad that is our mind. Again, it is quite evident that this is no more than a convenient hypothesis, and that, in reality, time is not composed of distinct moments but is a continuum whose quality alone can be modified.

  When one has arrived in the land of the fourth dimension, these truths appear much simpler that all our scientific explanations of the three-dimensional world, and it is very difficult to envisage, without a certain amount of pity, the extreme ignorance of men of our time—by which I mean of our quality. It seems to me, however, that it should be easy for them to observe the strange opposition that there is between what everyday language calls force and matter, mind and body, quality and quantity—which is to say, between the world seen in four dimensions or only in three.

  As they admire for the first time a new verity or an esthetic masterpiece that did not exist before
, men often declare that the truth or the masterpiece is superior to everything that existed before, but do not ask themselves where that strange revelation can have come from. They freely repeat the assertion that observation and experience alone have formed their minds and bodies, but are not surprised abruptly to find themselves in the realm of knowledge when a new fact contradicts all that pretended acquired experience.

  Art, in itself, is a perpetual contradiction of science. It proves to us that there is, over and above ourselves, a world of qualities on which we depend, that we know directly, and which permits us to judge in an instant the greater or lesser value of an artistic symbol conceived in three dimensions.

  Without the existence of the veritable four-dimensional world known to our minds outside any idea of time and space, the evolution of species would be inexplicable, progress a nonsense, and art a folly. One cannot imitate a model that does not yet exist, and, without a model, the three-dimensional world would remain inert.

  The men of today, bound by prejudice to three-dimensional space and, by the same token, to the division of a single movement into successive points in time, are in a situation not unlike that of an insect wandering indefinitely over a statue, which experiences its contours as a succession of events and never contemplates the whole. When one knows how to disengage oneself forever from that traditional inferiority, it seems, on the contrary, that one is abruptly established in the situation of an artist who admires the totality of the statue, sees it entire in a single moment and takes pity on the awkward insect which feverishly pursues its obscure route from one grain of marble to the next.