Flatland: A Romance Of Many Dimensions - free ebook by Edwin Abbott Abbott

PART I THIS WORLD

“Be patient, for the world is broad and wide.”...

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§ 1 Of the Nature of Flatland

I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space. Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard with luminous edges—and you will then have a pretty correct

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§ 2 Of the Climate and Houses in Flatland

As with you, so also with us, there are four points of the compass North, South, East, and West. There being no sun nor other heavenly bodies, it is impossible for us to determine the North in the usual way; but we have a method of our own. By a Law of Nature with us, there is a constant attraction to the South; and, although in temperate climates this is very slight—so that even a Woman in reasonable health can journey several furlongs northward without much difficulty—yet the hampering effort

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§ 3 Concerning the Inhabitants of Flatland

The greatest length or breadth of a full grown inhabitant of Flatland may be estimated at about eleven of your inches. Twelve inches may be regarded as a maximum. Our Women are Straight Lines. Our Soldiers and Lowest Class of Workmen are Triangles with two equal sides, each about eleven inches long, and a base or third side so short (often not exceeding half an inch) that they form at their vertices a very sharp and formidable angle. Indeed when their bases are of the most degraded type (not mor

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§ 4 Concerning the Women

If our highly pointed Triangles of the Soldier class are formidable, it may be readily inferred that far more formidable are our Women. For, if a Soldier is a wedge, a Woman is a needle; being, so to speak, all point, at least at the two extremities. Add to this the power of making herself practically invisible at will, and you will perceive that a Female, in Flatland, is a creature by no means to be trifled with. But here, perhaps, some of my younger Readers may ask HOW a woman in Flatland can

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§ 5 Of our Methods of Recognizing one another

You, who are blessed with shade as well as light, you, who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually see an angle, and contemplate the complete circumference of a Circle in the happy region of the Three Dimensions—how shall I make it clear to you the extreme difficulty which we in Flatland experience in recognizing one another’s configuration? Recall what I told you above. All beings in Flatland, an

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§ 6 Of Recognition by Sight

I am about to appear very inconsistent. In the previous sections I have said that all figures in Flatland present the appearance of a straight line; and it was added or implied, that it is consequently impossible to distinguish by the visual organ between individuals of different classes: yet now I am about to explain to my Spaceland critics how we are able to recognize one another by the sense of sight. If however the Reader will take the trouble to refer to the passage in which Recognition by

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§ 7 Concerning Irregular Figures

Throughout the previous pages I have been assuming—what perhaps should have been laid down at the beginning as a distinct and fundamental proposition—that every human being in Flatland is a Regular Figure, that is to say of regular construction. By this I mean that a Woman must not only be a line, but a straight line; that an Artisan or Soldier must have two of his sides equal; that Tradesmen must have three sides equal; Lawyers (of which class I am a humble member), four sides equal, and, gener

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§ 8 Of the Ancient Practice of Painting

If my Readers have followed me with any attention up to this point, they will not be surprised to hear that life is somewhat dull in Flatland. I do not, of course, mean that there are not battles, conspiracies, tumults, factions, and all those other phenomena which are supposed to make History interesting; nor would I deny that the strange mixture of the problems of life and the problems of Mathematics, continually inducing conjecture and giving an opportunity of immediate verification, imparts

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§ 9 Of the Universal Colour Bill

But meanwhile the intellectual Arts were fast decaying. The Art of Sight Recognition, being no longer needed, was no longer practised; and the studies of Geometry, Statics, Kinetics, and other kindred subjects, came soon to be considered superfluous, and fell into disrespect and neglect even at our University. The inferior Art of Feeling speedily experienced the same fate at our Elementary Schools. Then the Isosceles classes, asserting that the Specimens were no longer used nor needed, and refus

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§ 10 Of the Suppression of the Chromatic Sedition

The agitation for the Universal Colour Bill continued for three years; and up to the last moment of that period it seemed as though Anarchy were destined to triumph. A whole army of Polygons, who turned out to fight as private soldiers, was utterly annihilated by a superior force of Isosceles Triangles—the Squares and Pentagons meanwhile remaining neutral. Worse than all, some of the ablest Circles fell a prey to conjugal fury. Infuriated by political animosity, the wives in many a noble househo

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§ 11 Concerning our Priests

It is high time that I should pass from these brief and discursive notes about things in Flatland to the central event of this book, my initiation into the mysteries of Space. That is my subject; all that has gone before is merely preface. For this reason I must omit many matters of which the explanation would not, I flatter myself, be without interest for my Readers: as for example, our method of propelling and stopping ourselves, although destitute of feet; the means by which we give fixity to

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§ 12 Of the Doctrine of our Priests

As to the doctrine of the Circles it may briefly be summed up in a single maxim, “Attend to your Configuration.” Whether political, ecclesiastical, or moral, all their teaching has for its object the improvement of individual and collective Configuration—with special reference of course to the Configuration of the Circles, to which all other objects are subordinated. It is the merit of the Circles that they have effectually suppressed those ancient heresies which led men to waste energy and symp

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PART II OTHER WORLDS

“O brave new worlds, That have such people in them!”...

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§ 13 How I had a Vision of Lineland

It was the last day but one of the 1999th year of our era, and the first day of the Long Vacation. Having amused myself till a late hour with my favourite recreation of Geometry, I had retired to rest with an unsolved problem in my mind. In the night I had a dream. I saw before me a vast multitude of small Straight Lines (which I naturally assumed to be Women) interspersed with other Beings still smaller and of the nature of lustrous points—all moving to and fro in one and the same Straight Line

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§ 14 How I vainly tried to explain the nature of Flatland

Thinking that it was time to bring down the Monarch from his raptures to the level of common sense, I determined to endeavour to open up to him some glimpses of the truth, that is to say of the nature of things in Flatland. So I began thus: “How does your Royal Highness distinguish the shapes and positions of his subjects? I for my part noticed by the sense of sight, before I entered your Kingdom, that some of your people are lines and others Points; and that some of the lines are larger—” “You

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§ 15 Concerning a Stranger from Spaceland

From dreams I proceed to facts. It was the last day of our 1999th year of our era. The patterning of the rain had long ago announced nightfall; and I was sitting [1] in the company of my wife, musing on the events of the past and the prospects of the coming year, the coming century, the coming Millennium. [1] When I say “sitting,” of course I do not mean any change of attitude such as you in Spaceland signify by that word; for as we have no feet, we can no more “sit” nor “stand” (in your sense o

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§ 16 How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland

As soon as the sound of the Peace-cry of my departing Wife had died away, I began to approach the Stranger with the intention of taking a nearer view and of bidding him be seated: but his appearance struck me dumb and motionless with astonishment. Without the slightest symptoms of angularity he nevertheless varied every instant with graduations of size and brightness scarcely possible for any Figure within the scope of my experience. The thought flashed across me that I might have before me a bu

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§ 17 How the Sphere, having in vain tried words, resorted to deeds

It was in vain. I brought my hardest right angle into violent collision with the Stranger, pressing on him with a force sufficient to have destroyed any ordinary Circle: but I could feel him slowly and unarrestably slipping from my contact; not edging to the right nor to the left, but moving somehow out of the world, and vanishing into nothing. Soon there was a blank. But still I heard the Intruder’s voice. Sphere . Why will you refuse to listen to reason? I had hoped to find in you—as being a m

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§ 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 loud 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

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§ 19 How, though the Sphere shewed me other mysteries of Spaceland, I still desire 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; haply thou shalt have ample time hereafter to condole with him. Follow me.” Once more we ascended into space. “Hitherto,” said the Sphere, “I have shewn you naught save Plane Figures an

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§ 20 How the Sphere encouraged me in a Vision.

Although 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 endeavoured to reassure her by some story, invented for the occasion, that I had accidentally fallen through the trap-door of the cellar, and had there lain stunned. The Southward att

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§ 21 How I tried to teach the Theory of Three Dimensions to my Grandson, and with what success

I awoke rejoicing, and began to reflect on the glorious career before me. I would go forth, methought, at once, and evangelize 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 recognized the words of the Resoluti

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§ 22 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 catch-phrase, “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 mysteri

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PREFACE TO THE SECOND AND REVISED EDITION, 1884. BY THE EDITOR

If my poor Flatland friend retained the vigour of mind which he enjoyed when he began to compose these Memoirs, I should not now need to represent him in this preface, in which he desires, fully, to return his thanks to his readers and critics in Spaceland, whose appreciation has, with unexpected celerity, required a second edition of this work; secondly, to apologize for certain errors and misprints (for which, however, he is not entirely responsible); and, thirdly, to explain one or two miscon

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