 Part 2, sections 18 to 20, of Flatland. This LibriVox recording is in the public domain. Recording by Ruth Golding. Flatland, a romance of many dimensions, by Edwin Abbott Abbott. Part 2, section 18, how I came to Spaceland and what I saw there. An unspeakable horror seized me. There was a darkness, then a dizzy, sickening sensation of sight that was not like seeing. I saw a line that was no line, space that was not space. I was myself, and not myself. When I could find voice, I shrieked aloud in agony, Either this is madness, or it is hell. It is neither, calmly replied, the voice of the sphere. It is knowledge. It is three dimensions. Open your eye once again, and try to look steadily. I looked, and behold, a new world. There stood before me, visibly in corporate, all that I had before in third, conjectured, dreamed, of perfect circular beauty. What seemed the centre of the stranger's form lay open to my view. Yet I could see no heart, nor lungs, nor arteries, only a beautiful, harmonious something for which I had no words. But you, my readers in Spaceland, would call it the surface of the sphere. Seeing myself mentally before my guide, I cried, How is it, oh divine, ideal of consummate loveliness and wisdom, that I see thy inside, and yet cannot discern thy heart, thy lungs, thy arteries, thy liver? What you think you see, you see not, he replied. It is not given to you, nor to any other being, to behold my internal parts. I am of a different order of beings from those in flatland. Were I a circle, you could discern my intestines, but I am a being composed, as I told you before, of many circles, the many in the one, called in this country a sphere, and just as the outside of a cube is a square, so the outside of a sphere presents the appearance of a circle. But though I was, by my teacher's enigmatic utterance, I no longer chafed against it, but worshipped him in silent adoration. He continued with more mildness in his voice, Distress not yourself, if you cannot at first understand the deeper mysteries of Spaceland. By degrees they will dawn upon you. Let us begin by casting back a glance at the region whence you came. Open with me a while to the plains of flatland, and I will show you that which you have so often reasoned and thought about, but never seen with the sense of sight, a visible angle. Impossible! I cried, but the sphere leading the way I followed as if in a dream till once more his voice arrested me. Look yonder, and behold your own pentagonal house and all its inmates. Readers note the following paragraph refers to a detailed diagram. The diagram shows the points of the compass with north at the top. Next to this there is a large equal-sided pentagon sitting on a horizontal base. Centrally placed on the lower left edge of the pentagon there is an opening labelled men's door, the size of the opening being about a quarter of the length of that edge. This door leads into a large central space labelled the hall, which is otherwise surrounded by rooms. The position of these rooms will now be described. Clockwise from the northern point the upper right edge is divided equally between two rooms labelled in order my study and my bedroom. The left hand wall of the study runs vertically down from the northern point and the right hand wall is parallel to the lower right edge of the pentagon. The study has a door into the hall and there is an isosceles triangle inside labelled the page. Clearing a wall with the study is my rhomboid shaped bedroom, the right hand wall of which is the top quarter of the lower right hand edge of the pentagon. It shares a wall and communicating door with the room to the south labelled my wife's apartment. About three-tenths down the lower right edge there is a narrow opening labelled women's door. This leads into a long narrow room labelled my wife's apartment. This room has doorways into my bedroom above, into the hall to the left and into the room to the south also long and narrow where a straight line is marked my daughter. The only door from my daughter's room is into my wife's apartment. Clearing clockwise down the lower right edge of the pentagon the next room is a long and wide room with two openings into the hall. Inside are three isosceles triangles of varying acuteness. The uppermost and most acute is labelled the scullion, the next and middle-sized is labelled the footman, and the lowest and least acute is labelled the butler. At the bottom right point of the pentagon a large corner room is labelled the cellar and has a door into the hall. Along the left half of the bottom or southern edge there are two small rooms each with a door into the hall and each with a hexagon inside labelled my grandsons. Continuing clockwise up the left side of the pentagon between the men's door and the northern point there are four small rooms. Each of these rooms labelled my sons has a pentagon inside it and a door into the hall. In the middle of the central hall is a straight line labelled my wife. Outside the pentagon one at each end of the bottom or southern edge are two very acute isosceles triangles each labelled policeman. I looked below and saw with my physical eye all that domestic individuality which I had hitherto merely inferred with the understanding and how poor and shadowy was the inferred conjecture in comparison with the reality which I now beheld. My four sons calmly asleep in the north-western rooms, my two often grandsons to the south, the servants, the butler, my daughter, all in their several apartments. Only my affectionate wife alarmed by my continued absence had quitted her room and was roving up and down in the hall anxiously awaiting my return. Also the page aroused by my cries had left his room and under pretext of ascertaining whether I had fallen somewhere in a faint was prying into the cabinet in my study. All this I could now see, not merely infer. And as we came nearer and nearer I could discern even the contents of my cabinet and the two chests of gold and the tablets of which the sphere had made mention. Touched by my wife's distress I would have sprung downward to reassure her, but I found myself incapable of motion. "'Trouble not yourself about your wife,' said my guide. She will not belong left in anxiety. Meantime let us take a survey of flatland.' Once more I felt myself rising through space. It was even as the sphere had said. The further we receded from the object we beheld, the larger became the field of vision. My native city, with the interior of every house and every creature therein, lay open to my view in miniature. We mounted higher, and low, the secrets of the earth, the depths of mines and inmost caverns of the hills were bared before me. Orstruck at the sight of the mysteries of the earth thus unveiled before my unworthy eye, I said to my companion, Behold, I am become as a God! For the wise men in our country say that to see all things, or as they express it, Omnividence, is the attribute of God alone.' There was something of scorn in the voice of my teacher, as he made answer. "'Is it so, indeed? Then the very pickpockets and cut-throats of my country are to be worshipped by your wise men as being gods. For there is not one of them that does not see as much as you see now. But, trust me, your wise men are wrong. I, then, is Omnividence the attribute of others beside gods? Sphere, I do not know. But if a pickpocket or a cut-throat of our country can see everything that is in your country, surely that is no reason why the pickpocket or cut-throat should be accepted by you as a God. This Omnividence, as you call it, it is not a common word in Spaceland. Does it make you more just, more merciful, less selfish, more loving? Not in the least. Then how does it make you more divine? More merciful, more loving. But these are the qualities of women. And we know that a circle is a higher being than a straight line, insofar as knowledge and wisdom are more to be esteemed than mere affection. Sphere, it is not for me to classify human faculties according to merit, yet many of the best and wisest in Spaceland think more of the affections than of the understanding. More of your despised, straight lines than of your belauded circles. But enough of this. Look yonder. Do you know that building? I looked, and afar off I saw an immense polygonal structure in which I recognised the General Assembly Hall of the States of Flatland surrounded by dense lines of pentagonal buildings at right angles to each other, which I knew to be streets. And I perceived that I was approaching the Great Metropolis. Here we descend," said my guide. It was now morning, the first hour of the first day of the two-thousandth year of our era. Acting as was there won't in strict accordance with precedent, the highest circles of the realm were meeting in solemn conclave, as they had met on the first hour of the first day of the year one-thousand, and also on the first hour of the first day of the year nought. The minutes of the previous meetings were now read by one whom I at once recognised as my brother, a perfectly symmetrical square, and the chief clerk of the High Council. It was found recorded on each occasion that, whereas the States had been troubled by divers' ill-intentioned persons pretending to have received revelations from another world, and professing to produce demonstrations whereby they had instigated to frenzy both themselves and others, it had been for this cause unanimously resolved by the Grand Council that on the first day of each millenary special injunctions be sent to the prefects in the several districts of Flatland to make strict search for such misguided persons, and without formality of mathematical examination to destroy all such as were isosceles of any degree, to scourge and imprison any regular triangle, to cause any square or pentagon to be sent to the district asylum, and to arrest any one of higher rank, sending him straight way to the capital to be examined and judged by the Council. You hear your fate, said the Sphere to me, while the Council was passing for the third time the formal resolution. Death or imprisonment awaits the Apostle of the Gospel of three dimensions. Not so, replied I, the matter is now so clear to me, the nature of real space so palpable that me thinks I could make a child understand it. Permit me but to descend at this moment and enlighten them. Not yet, said my guide, the time will come for that. In time I must perform my mission. Stay thou there in thy place. Saying these words, he leapt with great dexterity into the sea, if I may say, call it, of Flatland, right in the midst of the Ring of Councillors. I come, cried he, to proclaim that there is a land of three dimensions. I could see many of the younger Councillors start back in manifest horror as the Sphere's circular section widened before them. But on a sign from the presiding circle, who showed not the slightest alarm or surprise, six isosceles of a lone type from six different quarters rushed upon the Sphere. We have him! they cried. No! Yes! We have him still! He's going! He's gone! My lords, said the President, to the junior circles of the Council. There is not the slightest need for surprise, the secret archives to which I alone have access, tell me that a similar occurrence happened on the last two millennial commencements. You will, of course, say nothing of these trifles outside the Cabinet. Raising his voice, he now summoned the Guard. Arrest the policeman, gag them, you know your duty. After he had consigned to their fate the wretched policeman, ill-fated and unwilling witnesses of a state secret which they were not to be permitted to reveal, he again addressed the Councillors. My lords, the business of the Council being concluded, I have only to wish you a happy new year. Before departing, he expressed at some lengths to the clerk, my excellent but most unfortunate brother, his sincere regret that, in accordance with precedent, and for the sake of secrecy, he must condemn him to perpetual imprisonment, but added his satisfaction that, unless some mention were made by him of that day's incident, his life would be spared. Section 19 How, though the sphere showed me other mysteries of space-land, I still desired more, and what came of it. When I saw my poor brother led away to imprisonment, I attempted to leap down into the Council Chamber, desiring to intercede on his behalf, or at least bid him farewell. But I found that I had no motion of my own. I absolutely depended on the volition of my guide, who said in gloomy tones, Heed not, thy brother, happily thou shalt have ample time hereafter to condol with him. Follow me. Readers note, the following paragraph makes reference to a diagram. Diagram one shows a three-dimensional cube, with visible edges drawn and hidden edges dotted, giving it a three-dimensional appearance. Typical shading makes it appear that the cube is made up of many layers. Diagram two shows the same figure, but all lines indicating perspective are missing, with the effect that it no longer appears to be solid, but looks like a two-dimensional, irregular, hexagonal figure. End of Readers note. Once more we ascended into space. Here the two," said the Sphere, I have shown you not save plain figures and their interiors. Now I must introduce you to solids, and reveal to you the plan upon which they are constructed. Behold this multitude of movable square cards. See I put one on another, not as you supposed northward of the other, but on the other. Now a second, now a third. See I am building up a solid by a multitude of squares parallel to one another. Now the solid is complete, being as high as it is long and broad, and we call it a cube. Pardon me, my lord," replied I, but to my eye the appearance is as often a regular figure whose inside is laid open to the view. In other words, me thinks I see no solid, but a plain such as we infer in Flatland, only of an irregularity which betokens some monstrous criminal, so that the very sight of it is painful to my eyes. "'True,' said the Sphere, it appears to you a plain, because you are not accustomed to light and shade and perspective. Just as in Flatland a hexagon would appear a straight line to one who has not the art of sight recognition. But in reality it is a solid, as you shall learn by the sense of feeling. He then introduced me to the cube, and I found that this marvellous being was indeed no plain but a solid, and that he was endowed with six plain sides and eight terminal points called solid angles. And I remembered the saying of the Sphere that just such a creature as this would be formed by a square moving in space parallel to himself. And I rejoiced to think that so insignificant a creature as I could in some sense be called the progenitor of so illustrious an offspring. And still I could not fully understand the meaning of what my teacher had told me concerning light and shade and perspective. And I did not hesitate to put my difficulties before him. Were I to give the Sphere's explanation of these matters, succinct and clear though it was, it would be tedious to an inhabitant of space who knows these things already. Place it that by his lucid statements and by changing the position of objects and lights, and by allowing me to feel the several objects and even his own sacred person, he at last made all things clear to me, so that I could now readily distinguish between a circle and a sphere, a plain figure and a solid. This was the climax, the paradise of my strange eventful history. Henceforth I have to relate the story of my miserable fall, most miserable, yet surely most undeserved, for why should the thirst for knowledge be aroused only to be disappointed and punished? My volition shrinks from the painful task of recalling my humiliation, yet like a second Prometheus I will endure this, and worse, if by any means I may arouse in the interiors of plain and solid humanity a spirit of rebellion against the conceit which would limit our dimensions to two, or three, or any number short of infinity. Away then with all personal considerations, let me continue to the end as I began, without further digressions or anticipations, pursuing the plain path of dispassion at history. The exact facts, the exact words, and they are burnt in upon my brain, shall be set down without alteration of an iota, and let my readers judge between me and destiny. The sphere would willingly have continued his lessons by indoctrinating me in the confirmation of all regular solids, cylinders, cones, pyramids, pentahedrons, hexahedrons, dodecahedrons, and spheres, but I ventured to interrupt him. Not that I was weary of knowledge, on the contrary I thirsted for yet deeper and fuller drafts than he was offering to me. Pardon me, said I, O thou whom I must no longer address as the perfection of all beauty, but let me beg thee to vouchsafe thy servant a sight of thine interior. Sphere, my what? I, thine interior, thy stomach, thy intestines. Sphere, whence this ill-timed impertinent request? Then what mean you by saying that I am no longer the perfection of all beauty? I, my lord, your own wisdom has taught me to aspire to one even more great, more beautiful, and more closely approximate to perfection than yourself. As you yourself, superior to all flatland forms, combine many circles in one, so doubtless there is one above you who combines many spheres in one supreme existence, surpassing even the solids of space-land. And even as we, who are now in space, look down on flatland and see the insides of all things, so of a certainty there is yet above us some higher, purer region, whither thou dost surely purpose to lead me, o thou whom I shall always call everywhere and in all dimensions, my priest, philosopher, and friend, some yet more spacious space, some more dimensionable dimensionality, from the vantage ground of which we shall look down together upon the revealed insides of solid things, and where thine own intestines and those of thy kindred spheres will lie exposed to the view of the poor wandering exile from flatland, to whom so much has already been thou to save it. Sphere. Oh! Stuff! Enough of this trifling! The time is short, and much remains to be done before you are fit to proclaim the Gospel of three dimensions to your blind, benighted countryman in flatland. Nay, gracious teacher, deny me not what I know it is in thy power to perform, grant me but one glimpse of thine interior, and I am satisfied for ever, remaining henceforth thy docile pupil, thy unimansible slave, ready to receive all thy teachings and to feed upon the words that fall from thy lips. Sphere. Well, then, to content and silence you, let me say it once. I would show you what you wish if I could, but I cannot. Would you have me turn my stomach inside out to oblige you? I. But my Lord has shown me the intestines of all my countrymen in the land of two dimensions by taking me with him into the land of three. What therefore more easy than now to take his servant on a second journey into the blessed region of the fourth dimension, where I shall look down with him once more upon this land of three dimensions, and see the inside of every three-dimensioned house, the secrets of the solid earth, the treasures of the minds in space-land, and the intestines of every solid living creature, even of the noble and adorable spheres. Sphere. But where is this land of four dimensions? I. I know not, but doubtless my teacher knows. Sphere. Not I. There is no such land. The very idea of it is utterly inconceivable. I. Your Lordship tempts his servant to see whether he remembers the revelations imparted to him. Tryful not with me, my Lord. I crave. I thirst for more knowledge. Doubtless we cannot see that other higher space-land now, because we have no I in our stomachs. But just as there was the realm of flat land, though that poor puny-lineland monarch could neither turn to left nor right to discern it, and just as there was, close at hand and touching my frame, the land of three dimensions, though I, blind, senseless wretch, had no power to touch it, no I in my interior to discern it, so of a surety there is a fourth dimension which my Lord perceives with the inner eye of thoughts. And that it must exist my Lord himself has taught me, or can he have forgotten what he himself imparted to his servant. In one dimension did not a moving point produce a line with two terminal points. In two dimensions did not a moving line produce a square with four terminal points. In three dimensions did not a moving square produce did not this eye of mine behold it that blessed being a cube with eight terminal points. And in four dimensions shall not a moving cube, alas for analogy and alas for the progress of truth if it be not so, shall not I say the motion of a divine cube result in a still more divine organisation with sixteen terminal points? Behold the infallible confirmation of the series two, four, eight, sixteen. Is not this a geometrical progression? Is not this, if I might quote my Lord's own words, strictly according to analogy? Again was I not taught by my Lord that as in a line there are two bounding points, and in a square there are four bounding lines, so in a cube there must be six bounding squares. Behold once more the confirming series two, four, six, is not this an arithmetical progression? And consequently does it not of necessity follow that the more divine offspring of the divine cube in the land of four dimensions must have eight bounding cubes? And is not this also as my Lord has taught me to believe strictly according to analogy? O my Lord, my Lord, behold, I cast myself in faith upon conjecture, not knowing the fact, and I appeal to your lordship to confirm or deny my logical anticipations. If I am wrong I yield, and will no longer demand a fourth dimension, but if I am right my Lord will listen to reason. I ask therefore is it, or is it not the fact, that ere now your countrymen also have witnessed the descent of beings of a higher order than their own, entering closed rooms, even as your lordship entered mine, without the opening of doors or windows, and appearing and vanishing at will? On the reply to this question I am ready to stake everything. I deny it, and I am henceforth silent. Only that safe an answer." Sphere after a pause. It is reported so. But men are divided in opinion as to the facts, and even granting the facts they explain them in different ways, and in any case however great may be the number of different explanations no one has adopted or suggested the theory of a fourth dimension. Therefore pray have done with this trifling, and let us return to business. I was certain of it. I was certain that my anticipations would be fulfilled, and now have patience with me and answer me yet one more question, best of teachers. Those who have thus appeared no one knows whence, and have returned no one knows whither. Have they also contracted their sections, and vanished somehow into that more spacious space, with which I now entreat you to conduct me? Sphere moodily. They have vanished certainly, if they ever appeared. But most people say that these visions arose from the thought. You will not understand me, from the brain, from the perturbed angularity of the seer. I say they so? Oh, believe them not, or if it indeed be so that this other space is really thought-land, then take me to that blessed region where I in thought shall see the insides of all solid things. There, before my ravished eye, a cube, moving in some altogether new direction, but strictly according to analogy, so as to make every particle of his interior pass through a new kind of space with a wake of its own, shall create a still more perfect perfection than himself, with sixteen terminal extra solid angles, and eight solid cubes for his perimeter. And once there shall we stay our upward course? In that blessed region of four dimensions shall we linger on the threshold of the fifth, and not enter therein? Ah, no! Let us rather resolve that our ambition shall soar with our corporal ascent. Then yielding to our intellectual onset the gates of the sixth dimension shall fly open. After that a seventh, and then an eighth. How long I should have continued, I know not. In vain did the sphere in his voice of thunder reiterate his commands of silence, and threaten me with the direst penalties if I persisted. Everything could stem the flood of my ecstatic aspirations. Perhaps I was to blame, but indeed I was intoxicated with the recent drafts of truth to which he himself had introduced me. However, the end was not long in coming. My words were cut short by a crash outside, and a simultaneous crash inside me, which impelled me through space, with a velocity that precluded speech, down, down, down. I was rapidly descending, and I knew that return to flatland was my doom. One glimpse, one last, and never to be forgotten glimpse I had of that dull level wilderness which was now to become my universe again, spread out before my eye. Then a darkness, then a final, all-consumating thunder-peel, and when I came to myself I was once more a common creeping square in my study at home, listening to the peace cry of my approaching wife. Section 20 How the Sphere Encouraged Me in a Vision So I had less than a minute for reflection, I felt, by a kind of instinct, that I must conceal my experiences from my wife. Not that I apprehended at the moment any danger from her divulging my secret, but I knew that to any woman in flatland the narrative of my adventures must needs be unintelligible. So I endeavored to reassure her by some story, invented for the occasion, that I had accidentally fallen through the trap-door of the cellar, and had their lane stunned. The southward attraction in our country is so slight that even to a woman my tale necessarily appeared extraordinary and well-nigh incredible. But my wife, whose good sense far exceeds that of the average of her sex, and who perceived that I was unusually excited, did not argue with me on the subject, but insisted that I was ill and required repose. I was glad of an excuse for retiring to my chamber to think quietly over what had happened. When I was at last by myself a drowsy sensation fell on me. But before my eyes closed I endeavored to reproduce the third dimension, and especially the process by which a cube is constructed through the motion of a square. It was not so clear as I could have wished, but I remembered that it must be upward, and yet not northward. And I determined steadfastly to retain these words as the clue which if firmly grasped could not fail to guide me to the solution. So mechanically repeating like a charm the words upward yet not northward, I fell into a sound refreshing sleep. During my slumber I had a dream. I thought I was once more by the side of the sphere whose lustrous hue betokened that he had exchanged his wrath against me for perfect plaqueability. We were moving together towards a bright but infinitesimally small point to which my master directed my attention. As we approached me sought there issued from it a slight humming noise, as from one of your space-land blue-bottles, only less resonant by far, so slight indeed that even in the perfect stillness of the vacuum through which we soared the sound reached not our ears till we checked our flight at a distance from it of something under twenty human diagonals. Look yonder, said my guide, in flat land thou hast lived, of line-land thou hast received a vision, thou hast soared with me to the heights of space-land, now in order to complete the range of thy experience I conduct thee downward to the lowest depths of existence, even to the realm of point-land the abyss of no dimensions. Behold, your miserable creature, that point is a being like ourselves but confined to the non-dimensional gulf. He is himself his own world, his own universe. Of any other than himself he can form no conception. He knows not length nor breadth nor height, for he has had no experience of them. He has no cognizance even of the number two, nor has he a thought of plurality, for he is himself his one and all, being really nothing. Yet mark his perfect self-contentment, and hence learn this lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy. Now listen. He ceased, and there arose from the little buzzing creature a tiny, low, monotonous but distinct tinkling, as from one of your space-land phonographs, from which I caught these words. Infinite be-attitude of existence. It is, and there is none else beside it. What, said I, does the puny creature mean by it? He means himself, said the Sphere, have you not noticed before now, that babies and babyish people who cannot distinguish themselves from the world speak of themselves in the third person? But hush! It fills all space, continued the little soliloquizing creature, and what it fills it is, what it thinks that it utters, and what it utters that it hears, and it itself is thinker, uttererer, hearer, thought, word, audition. It is the one, and yet the all in all, are the happiness, are the happiness of being, can you not startle the little thing out of its complacency? said I. Tell it what it really is, as you told me, reveal to it the narrow limitations of point-land, and lead it up to something higher. That is no easy task, said my master, try you. Hereon raising my voice to the uttermost I addressed the point as follows. Silence, silence, contemptible creature! You call yourself the all in all, but you are the nothing. Your so-called universe is a mere speck in a line, and a line is a mere shadow as compared with hush, hush, you have said enough, interrupted the Sphere. Now listen, and mark the effect of your harangue on the king of point-land. The luster of the monarch, who beamed more brightly than ever upon hearing my words, showed clearly that he retained his complacency, and I had hardly ceased when he took up his strain again. Ah, the joy, ah, the joy of thought! What can it not achieve by thinking? Its own thought coming to itself, suggestive of its disparagement thereby to enhance its happiness. Sweet rebellion stirred up to result in triumph. Ah, the divine creative power of the all in one! Ah, the joy, the joy of being! You see, said my teacher, how little your words have done! So far as the monarch understands them at all, he accepts them as his own. For he cannot conceive of any other except himself, and plumes himself upon the variety of its thought as an instance of creative power. Let us leave this God of point-land to the ignorant fruition of his omnipresence and omniscience. Nothing that you or I can do can rescue him from his self-satisfaction. After this, as we floated gently back to flatland, I could hear the mild voice of my companion pointing the moral of my vision, and stimulating me to aspire, and to teach others to aspire. He had been angered at first, he confessed by my ambition to soar to dimensions above the third, but since then he had received fresh insight, and he was not too proud to acknowledge his error to a pupil. Then he proceeded to initiate me into mysteries yet higher than those I had witnessed, showing me how to construct extra solids by the motion of solids, and double extra solids by the motion of extra solids, and all strictly according to analogy. All by methods so simple, so easy, as to be patent even to the female sex. I tried to teach the theory of three dimensions to my grandson, and with what success. I woke rejoicing, and began to reflect on the glorious career before me. I would go forth, me thought, at once, and evangelise the whole of flatland. Even to women and soldiers should the gospel of three dimensions be proclaimed, I would begin with my wife. Just as I had decided on the plan of my operations, I heard the sound of many voices in the street commanding silence. Then followed a louder voice. It was a herald's proclamation. Listening attentively, I recognised the words of the resolution of the council, in joining the arrest, imprisonment, or execution of anyone who should pervert the minds of the people by delusions, and by professing to have received revelations from another world. I reflected. This danger was not to be trifled with. It would be better to avoid it by omitting all mention of my revelation, and by proceeding on the path of demonstration, which, after all, seemed so simple and so conclusive, that nothing would be lost by discarding the former means. Upward, not northward, was the clue to the whole proof. It had seemed to me fairly clear before I fell asleep, and when I first awoke, fresh from my dream, it had appeared as patent as arithmetic. But somehow it did not seem to me quite so obvious now. Though my wife entered the room opportunally just at that moment, I decided, after we had interchanged a few words of commonplace conversation, not to begin with her. My pentagonal sons were men of character and standing, and physicians of no mean reputation, but not great in mathematics, and in that respect unfit for my purpose. But it occurred to me that a young and docile hexagon with a mathematical turn would be a most suitable pupil. Why therefore not make my first experiment with my little precocious grandson, whose casual remarks on the meaning of three cubed had met with the approval of the sphere? Discussing the matter with him, a mere boy, I should be in perfect safety, for he would know nothing of the proclamation of the council, whereas I could not feel sure that my sons, so greatly did their patriotism and reverence for the circles predominate over mere blind affection, might not feel compelled to hand me over to the prefect if they found me seriously maintaining the seditious heresy of the third dimension. But the first thing to be done was to satisfy in some way the curiosity of my wife, who naturally wished to know something of the reasons for which the circle had desired that mysterious interview, and of the means by which he had entered our house. Without entering into the details of the elaborate account I gave her, an account I fear not quite so consistent with truth as my readers in space-land might desire. I must be content with saying that I succeeded at last in persuading her to return quietly to her household duties without eliciting from me any reference to the world of three dimensions. This done I immediately sent for my grandson, for, to confess the truth, I felt that all I had seen and heard was in some strange way slipping away from me, like the image of a half-grasp tantalizing dream, and I longed to assay my skill in making a first disciple. When my grandson entered the room I carefully secured the door, then, sitting down by his side and taking our mathematical tablets, or as you would call them, lines, I told him we would resume the lesson of yesterday. I taught him once more how a point by motion in one dimension produces a line, and how a straight line in two dimensions produces a square. After this, forcing a laugh, I said, and now you scamp! You wanted to make me believe that a square may in the same way by motion, upward, not northward, produce another figure, a sort of extra square in three dimensions. Say that again, you young rascal. At this moment we heard once more the heralds, oh yes, oh yes, outside in the street, proclaiming the resolution of the council. Young though he was, my grandson, who was unusually intelligent for his age, and bred up in perfect reverence for the authority of the circles, took in the situation with an acuteness for which I was quite unprepared. He remained silent till the last words of the proclamation had died away, and then, bursting into tears, dear grand-papa, he said, that was only my fun, and of course I meant nothing at all by it, and we did not know anything then about the new law, and I don't think I said anything about the third dimension, and I am sure I did not say one word about upward, not northward, for that would be such nonsense, you know. How could a thing move upward and not northward? Upward and not northward, even if I were a baby I could not be so absurd as that. How silly it is! Not at all silly, said I, losing my temper. Here for example I take this square, and at the word I grasped a movable square which was lying at hand. And I move it, you see, not northward, but yes, I move it upward, that is to say, not northward, but I move it somewhere, not exactly like this, but somehow. Here I brought my sentence to an inane conclusion, shaking the square about in a purposeless manner, much to the amusement of my grandson, who burst out laughing louder than ever, and declared that I was not teaching him, but joking with him, and so saying, he unlocked the door and ran out of the room. Thus ended my first attempt to convert a pupil to the gospel of three dimensions. How I then tried to diffuse the theory of three dimensions by other means, and of the result. My failure with my grandson did not encourage me to communicate my secret to others of my household. Yet neither was I led by it to despair of success. Only I saw that I must not wholly rely on the catchphrase upward, not northward, but must rather endeavour to seek a demonstration by setting before the public a clear view of the whole subject, and for this purpose it seemed necessary to resort to writing. So I devoted several months in privacy to the composition of a treatise on the mysteries of three dimensions. Only with the view of evading the law, if possible, I spoke not of a physical dimension, but of a thought-land, when in theory a figure could look down upon flat land, and see simultaneously the insides of all things, and where it was possible that there might be supposed to exist a figure environed as it were with six squares, and containing eight terminal points. But in writing this book I found myself sadly hampered by the impossibility of drawing such diagrams as were necessary for my purpose. For of course in our country of flat land there are no tablets but lines, and no diagrams but lines, all in one straight line, and only distinguishable by difference of size and brightness. So that when I had finished my treatise, which I entitled through flat land to thought-land, I could not feel certain that many would understand my meaning. Meanwhile my life was under a cloud, all pleasures pawled upon me, all sights tantalised and tempted me to outspoken treason, because I could not but compare what I saw in two dimensions with what it really was, if seen in three, and could hardly refrain from making my comparisons aloud. I neglected my clients and my own business to give myself to the contemplation of the mysteries which I had once beheld, yet which I could impart to no one, and found daily more difficult to reproduce, even before my own mental vision. One day, about eleven months after my return from space-land, I tried to see a cube with my eye closed, but failed. And though I succeeded afterwards, I was not then quite certain, nor have I been ever afterwards, that I had exactly realised the original. This made me more melancholy than before, and determined me to take some step, yet what I knew not. I felt that I would have been willing to sacrifice my life for the cause, if thereby I could have produced conviction. But if I could not convince my grandson, how could I convince the highest and most developed circles in the land? And yet, at times, my spirit was too strong for me, and I gave vent to dangerous utterances. Already I was considered heterodox, if not reasonable, and I was keenly alive to the dangers of my position. Nevertheless, I could not at times refrain from bursting out into suspicious or half-seditious utterances, even among the highest polygonal and circular society. Even for example, the question arose about the treatment of those lunatics who said that they had received the power of seeing the insides of things. I would quote the saying of an ancient circle, who declared that prophets and inspired people are always considered by the majority to be mad. And I could not help occasionally dropping such expressions as the eye that discerns the interiors of things, and the all-seeing land. Once or twice, I even let fall the forbidden terms, the third and fourth dimensions. At last, to complete a series of minor indiscretions, at a meeting of our local speculative society, held at the palace of the prefect himself, some extremely silly person having read an elaborate paper, exhibiting the precise reasons why providence has limited the number of dimensions to two, and why the attribute of omnividence is assigned to the supreme alone, I so far forgot myself, as to give an exact account of the whole of my voyage with the sphere into space, and to the assembly-hall in our metropolis, and then to space again, and of my return home, and of everything that I had seen and heard in fact or vision. At first, indeed, I pretended that I was describing the imaginary experiences of a fictitious person, but my enthusiasm soon forced me to throw off all disguise, and finally, in a fervent peroration, I exhorted all my hearers to divest themselves of prejudice, and to become believers in the third dimension. And I say that I was at once arrested and taken before the council. Next morning, standing in the very place where, but a very few months ago, the sphere had stood in my company, I was allowed to begin and to continue my narration unquestioned and uninterrupted. But from the first I foresaw my fate. For the president, noting that a guard of the better sort of policeman was in attendance, of angularity little, if at all, under fifty-five degrees, ordered them to be relieved, before I began my defence, by an inferior class of two or three degrees. I knew only too well what that meant. I was to be executed or imprisoned, and my story was to be kept secret from the world by the simultaneous destruction of the officials who had heard it. And this being the case, the president desired to substitute the cheaper for the more expensive victims. After I had concluded my defence, the president, perhaps perceiving that some of the junior circles had been moved by my evident earnestness, asked me two questions. 1. Whether I could indicate the direction which I meant, when I used the words upward, not northward. 2. Whether I could by any diagrams or descriptions, other than the enumeration of imaginary sides and angles, indicate the figure I was pleased to call a cube. I declared that I could say nothing more, and that I must commit myself to the truth whose cause would surely prevail in the end. The president replied that he quite concurred in my sentiment, and that I could not do better. I must be sentenced to perpetual imprisonment. But if the truth intended that I should emerge from prison and evangelize the world, the truth might be trusted to bring that result to pass. Meanwhile I should be subjected to no discomfort that was not necessary to preclude escape, and unless I forfeited the privilege by misconduct, I should be occasionally permitted to see my brother, who had preceded me to my prison. Seven years have elapsed, and I am still a prisoner, and if I accept the occasional visits of my brother, debarred from all companionship, save that of my jailers. My brother is one of the best of squares, just, sensible, cheerful, and not without fraternal affection. Yet I must confess that my weekly interviews, at least in one respect, cause me the bitterest pain. He was present when the sphere manifested himself in the council chamber. He saw the sphere's changing sections. He heard the explanation of the phenomena then given to the circles. Since that time, scarcely a week has passed during seven whole years without his hearing from me a repetition of the part I played in that manifestation, together with ample descriptions of all the phenomena in space-land, and the arguments for the existence of solid things derivable from analogy. Yet I take shame to be forced to confess it. My brother has not yet grasped the nature of the third dimension, and frankly avows his disbelief in the existence of a sphere. Hence I am absolutely destitute of converts, and, for ought that I can see, the millennial revelation has been made to me for nothing. Prometheus up in space-land was bound for bringing down fire for mortals, but I, poor, flat-land Prometheus, lie here in prison for bringing down nothing to my countrymen. Yet I exist in the hope that these memoirs in some manner, I know not how, may find their way to the minds of humanity in some dimension, and may stir up a race of rebels who shall refuse to be confined to limited dimensionality. That is the hope of my brighter moments, alas it is not always so. Clearly weighs on me at times the burdensome reflection that I cannot honestly say I am confident as to the exact shape of the once-seen, oft-regretted cube. And in my nightly visions the mysterious precept, upward, not northward, haunts me, like a soul-devouring sphinx. It is part of the martyrdom which I endure for the cause of the truth that there are seasons of mental weakness when cubes and spheres flit away into the background of scarce possible existences, when the land of three dimensions seems almost as visionary as the land of one or none. Nay, when even this hard wall that bars me from my freedom, these very tablets on which I am writing, and all the substantial realities of flatland itself, appear no better than the offspring of a diseased imagination, or the baseless fabric of a dream. The End of Flatland A Romance of Many Dimensions by Edwin Abbott Abbott Read by Ruth Golding October 2008