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diff --git a/201-0.txt b/201-0.txt new file mode 100644 index 0000000..2670239 --- /dev/null +++ b/201-0.txt @@ -0,0 +1,4218 @@ +The Project Gutenberg eBook of Flatland: A Romance of Many Dimensions, by Edwin A. Abbot + +This eBook is for the use of anyone anywhere in the United States and +most other parts of the world at no cost and with almost no restrictions +whatsoever. You may copy it, give it away or re-use it under the terms +of the Project Gutenberg License included with this eBook or online at +www.gutenberg.org. If you are not located in the United States, you +will have to check the laws of the country where you are located before +using this eBook. + +Title: Flatland: + A Romance of Many Dimensions + +Author: Edwin A. Abbot + +Release Date: January, 1995 [eBook #201] +[Most recently updated: June 26, 2022] + +Language: English + +Character set encoding: UTF-8 + + +*** START OF THE PROJECT GUTENBERG EBOOK FLATLAND *** + + + + +Flatland: A Romance of Many Dimensions + +Edwin A. Abbott (1838-1926. English scholar, theologian, and writer.) + + + + ----------------------------------------------------------------- + | "O day and night, but this is wondrous strange" | + | ______ | + | / / /| ------ / /| /| / /-. | + | /---- / /__| / / /__| / | / / / | + | / /___ / | / /___ / | / |/ /__.-' | + | | + | No Dimensions One Dimension | + | . A ROMANCE OF MANY DIMENSIONS ----- | + | POINTLAND LINELAND | + | | + | Two Dimensions Three Dimensions | + | ___ __ | + | | | /__/| | + | |___| |__|/ | + | FLATLAND SPACELAND | + | "Fie, fie, how franticly I square my talk!" | + ----------------------------------------------------------------- + +With Illustrations by the Author, A SQUARE (Edwin A. Abbott) + + + + + + + To + The Inhabitants of SPACE IN GENERAL + And H. C. IN PARTICULAR + This Work is Dedicated + By a Humble Native of Flatland + In the Hope that + Even as he was Initiated into the Mysteries + Of THREE Dimensions + Having been previously conversant + With ONLY TWO + So the Citizens of that Celestial Region + May aspire yet higher and higher + To the Secrets of FOUR FIVE OR EVEN SIX Dimensions + Thereby contributing + To the Enlargement of THE IMAGINATION + And the possible Development + Of that most rare and excellent Gift of MODESTY + Among the Superior Races + Of SOLID HUMANITY + + + + + + +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, firstly, to return +his thanks to his readers and critics in Spaceland, whose appreciation +has, with unexpected celerity, required a second edition of his work; +secondly, to apologize for certain errors and misprints (for which, +however, he is not entirely responsible); and, thirdly, to explain one +or two misconceptions. But he is not the Square he once was. Years of +imprisonment, and the still heavier burden of general incredulity and +mockery, have combined with the natural decay of old age to erase from +his mind many of the thoughts and notions, and much also of the +terminology, which he acquired during his short stay in Spaceland. He +has, therefore, requested me to reply in his behalf to two special +objections, one of an intellectual, the other of a moral nature. + +The first objection is, that a Flatlander, seeing a Line, sees +something that must be THICK to the eye as well as LONG to the eye +(otherwise it would not be visible, if it had not some thickness); and +consequently he ought (it is argued) to acknowledge that his countrymen +are not only long and broad, but also (though doubtless in a very +slight degree) THICK or HIGH. This objection is plausible, and, to +Spacelanders, almost irresistible, so that, I confess, when I first +heard it, I knew not what to reply. But my poor old friend's answer +appears to me completely to meet it. + +"I admit," said he--when I mentioned to him this objection--"I admit +the truth of your critic's facts, but I deny his conclusions. It is +true that we have really in Flatland a Third unrecognized Dimension +called 'height', just as it is also true that you have really in +Spaceland a Fourth unrecognized Dimension, called by no name at +present, but which I will call 'extra-height'. But we can no more take +cognizance of our 'height' than you can of your 'extra-height'. Even +I--who have been in Spaceland, and have had the privilege of +understanding for twenty-four hours the meaning of 'height'--even I +cannot now comprehend it, nor realize it by the sense of sight or by +any process of reason; I can but apprehend it by faith. + +"The reason is obvious. Dimension implies direction, implies +measurement, implies the more and the less. Now, all our lines are +EQUALLY and INFINITESIMALLY thick (or high, whichever you like); +consequently, there is nothing in them to lead our minds to the +conception of that Dimension. No 'delicate micrometer'--as has been +suggested by one too hasty Spaceland critic--would in the least avail +us; for we should not know WHAT TO MEASURE, NOR IN WHAT DIRECTION. +When we see a Line, we see something that is long and BRIGHT; +BRIGHTNESS, as well as length, is necessary to the existence of a Line; +if the brightness vanishes, the Line is extinguished. Hence, all my +Flatland friends--when I talk to them about the unrecognized Dimension +which is somehow visible in a Line--say, 'Ah, you mean BRIGHTNESS': +and when I reply, 'No, I mean a real Dimension', they at once retort, +'Then measure it, or tell us in what direction it extends'; and this +silences me, for I can do neither. Only yesterday, when the Chief +Circle (in other words our High Priest) came to inspect the State +Prison and paid me his seventh annual visit, and when for the seventh +time he put me the question, 'Was I any better?' I tried to prove to +him that he was 'high', as well as long and broad, although he did not +know it. But what was his reply? 'You say I am "high"; measure my +"high-ness" and I will believe you.' What could I do? How could I +meet his challenge? I was crushed; and he left the room triumphant. + +"Does this still seem strange to you? Then put yourself in a similar +position. Suppose a person of the Fourth Dimension, condescending to +visit you, were to say, 'Whenever you open your eyes, you see a Plane +(which is of Two Dimensions) and you INFER a Solid (which is of Three); +but in reality you also see (though you do not recognize) a Fourth +Dimension, which is not colour nor brightness nor anything of the kind, +but a true Dimension, although I cannot point out to you its direction, +nor can you possibly measure it.' What would you say to such a +visitor? Would not you have him locked up? Well, that is my fate: and +it is as natural for us Flatlanders to lock up a Square for preaching +the Third Dimension, as it is for you Spacelanders to lock up a Cube +for preaching the Fourth. Alas, how strong a family likeness runs +through blind and persecuting humanity in all Dimensions! Points, +Lines, Squares, Cubes, Extra-Cubes--we are all liable to the same +errors, all alike the Slaves of our respective Dimensional prejudices, +as one of your Spaceland poets has said-- + + 'One touch of Nature makes all worlds akin'." + +[Note: The Author desires me to add, that the misconception of some of +his critics on this matter has induced him to insert in his dialogue +with the Sphere, certain remarks which have a bearing on the point in +question, and which he had previously omitted as being tedious and +unnecessary.] + +On this point the defence of the Square seems to me to be impregnable. +I wish I could say that his answer to the second (or moral) objection +was equally clear and cogent. It has been objected that he is a +woman-hater; and as this objection has been vehemently urged by those +whom Nature's decree has constituted the somewhat larger half of the +Spaceland race, I should like to remove it, so far as I can honestly do +so. But the Square is so unaccustomed to the use of the moral +terminology of Spaceland that I should be doing him an injustice if I +were literally to transcribe his defence against this charge. Acting, +therefore, as his interpreter and summarizer, I gather that in the +course of an imprisonment of seven years he has himself modified his +own personal views, both as regards Women and as regards the Isosceles +or Lower Classes. Personally, he now inclines to the opinion of the +Sphere that the Straight Lines are in many important respects superior +to the Circles. But, writing as a Historian, he has identified himself +(perhaps too closely) with the views generally adopted by Flatland, and +(as he has been informed) even by Spaceland, Historians; in whose pages +(until very recent times) the destinies of Women and of the masses of +mankind have seldom been deemed worthy of mention and never of careful +consideration. + +In a still more obscure passage he now desires to disavow the Circular +or aristocratic tendencies with which some critics have naturally +credited him. While doing justice to the intellectual power with which +a few Circles have for many generations maintained their supremacy over +immense multitudes of their countrymen, he believes that the facts of +Flatland, speaking for themselves without comment on his part, declare +that Revolutions cannot always be suppressed by slaughter, and that +Nature, in sentencing the Circles to infecundity, has condemned them to +ultimate failure--"and herein," he says, "I see a fulfilment of the +great Law of all worlds, that while the wisdom of Man thinks it is +working one thing, the wisdom of Nature constrains it to work another, +and quite a different and far better thing." For the rest, he begs his +readers not to suppose that every minute detail in the daily life of +Flatland must needs correspond to some other detail in Spaceland; and +yet he hopes that, taken as a whole, his work may prove suggestive as +well as amusing, to those Spacelanders of moderate and modest minds +who--speaking of that which is of the highest importance, but lies +beyond experience--decline to say on the one hand, "This can never be," +and on the other hand, "It must needs be precisely thus, and we know +all about it." + + + + + + +CONTENTS: + + + +PART I: THIS WORLD + +Section + + 1. Of the Nature of Flatland + 2. Of the Climate and Houses in Flatland + 3. Concerning the Inhabitants of Flatland + 4. Concerning the Women + 5. Of our Methods of Recognizing one another + 6. Of Recognition by Sight + 7. Concerning Irregular Figures + 8. Of the Ancient Practice of Painting + 9. Of the Universal Colour Bill + 10. Of the Suppression of the Chromatic Sedition + 11. Concerning our Priests + 12. Of the Doctrine of our Priests + +PART II: OTHER WORLDS + + 13. How I had a Vision of Lineland + 14. How I vainly tried to explain the nature of Flatland + 15. Concerning a Stranger from Spaceland + 16. How the Stranger vainly endeavoured to reveal to me + in words the mysteries of Spaceland + 17. How the Sphere, having in vain tried words, + resorted to deeds + 18. How I came to Spaceland, and what I saw there + 19. How, though the Sphere shewed me other mysteries + of Spaceland, I still desired more; and what came of it + 20. How the Sphere encouraged me in a Vision + 21. How I tried to teach the Theory of Three Dimensions + to my Grandson, and with what success + 22. How I then tried to diffuse the Theory + of Three Dimensions by other means, and of the result + + + + + + +PART I: THIS WORLD + +"Be patient, for the world is broad and wide." + + + + + + +Section 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 and with luminous edges--and you will then have a +pretty correct notion of my country and countrymen. Alas, a few years +ago, I should have said "my universe": but now my mind has been opened +to higher views of things. + +In such a country, you will perceive at once that it is impossible that +there should be anything of what you call a "solid" kind; but I dare +say you will suppose that we could at least distinguish by sight the +Triangles, Squares, and other figures, moving about as I have described +them. On the contrary, we could see nothing of the kind, not at least +so as to distinguish one figure from another. Nothing was visible, nor +could be visible, to us, except Straight Lines; and the necessity of +this I will speedily demonstrate. + +Place a penny on the middle of one of your tables in Space; and leaning +over it, look down upon it. It will appear a circle. + +But now, drawing back to the edge of the table, gradually lower your +eye (thus bringing yourself more and more into the condition of the +inhabitants of Flatland), and you will find the penny becoming more and +more oval to your view, and at last when you have placed your eye +exactly on the edge of the table (so that you are, as it were, actually +a Flatlander) the penny will then have ceased to appear oval at all, +and will have become, so far as you can see, a straight line. + +The same thing would happen if you were to treat in the same way a +Triangle, or Square, or any other figure cut out of pasteboard. As +soon as you look at it with your eye on the edge on the table, you will +find that it ceases to appear to you a figure, and that it becomes in +appearance a straight line. Take for example an equilateral +Triangle--who represents with us a Tradesman of the respectable class. +Fig. 1 represents the Tradesman as you would see him while you were +bending over him from above; figs. 2 and 3 represent the Tradesman, as +you would see him if your eye were close to the level, or all but on +the level of the table; and if your eye were quite on the level of the +table (and that is how we see him in Flatland) you would see nothing +but a straight line. + + +[Illustration 1] + +[ASCII approximation follows] + + + (1) __________ (2) ___________ (3) _________ + \ / --__ __-- --- + \ / - + \/ + + +When I was in Spaceland I heard that your sailors have very similar +experiences while they traverse your seas and discern some distant +island or coast lying on the horizon. The far-off land may have bays, +forelands, angles in and out to any number and extent; yet at a +distance you see none of these (unless indeed your sun shines bright +upon them revealing the projections and retirements by means of light +and shade), nothing but a grey unbroken line upon the water. + +Well, that is just what we see when one of our triangular or other +acquaintances comes toward us in Flatland. As there is neither sun +with us, nor any light of such a kind as to make shadows, we have none +of the helps to the sight that you have in Spaceland. If our friend +comes closer to us we see his line becomes larger; if he leaves us it +becomes smaller: but still he looks like a straight line; be he a +Triangle, Square, Pentagon, Hexagon, Circle, what you will--a straight +Line he looks and nothing else. + +You may perhaps ask how under these disadvantageous circumstances we +are able to distinguish our friends from one another: but the answer to +this very natural question will be more fitly and easily given when I +come to describe the inhabitants of Flatland. For the present let me +defer this subject, and say a word or two about the climate and houses +in our country. + + + + +Section 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 effect of the +southward attraction is quite sufficient to serve as a compass in most +parts of our earth. Moreover, the rain (which falls at stated +intervals) coming always from the North, is an additional assistance; +and in the towns we have the guidance of the houses, which of course +have their side-walls running for the most part North and South, so +that the roofs may keep off the rain from the North. In the country, +where there are no houses, the trunks of the trees serve as some sort +of guide. Altogether, we have not so much difficulty as might be +expected in determining our bearings. + +Yet in our more temperate regions, in which the southward attraction is +hardly felt, walking sometimes in a perfectly desolate plain where +there have been no houses nor trees to guide me, I have been +occasionally compelled to remain stationary for hours together, waiting +till the rain came before continuing my journey. On the weak and aged, +and especially on delicate Females, the force of attraction tells much +more heavily than on the robust of the Male Sex, so that it is a point +of breeding, if you meet a Lady in the street, always to give her the +North side of the way--by no means an easy thing to do always at short +notice when you are in rude health and in a climate where it is +difficult to tell your North from your South. + +Windows there are none in our houses: for the light comes to us alike +in our homes and out of them, by day and by night, equally at all times +and in all places, whence we know not. It was in old days, with our +learned men, an interesting and oft-investigated question, "What is the +origin of light?" and the solution of it has been repeatedly attempted, +with no other result than to crowd our lunatic asylums with the +would-be solvers. Hence, after fruitless attempts to suppress such +investigations indirectly by making them liable to a heavy tax, the +Legislature, in comparatively recent times, absolutely prohibited them. +I--alas, I alone in Flatland--know now only too well the true solution +of this mysterious problem; but my knowledge cannot be made +intelligible to a single one of my countrymen; and I am mocked at--I, +the sole possessor of the truths of Space and of the theory of the +introduction of Light from the world of three Dimensions--as if I were +the maddest of the mad! But a truce to these painful digressions: let +me return to our houses. + +The most common form for the construction of a house is five-sided or +pentagonal, as in the annexed figure. The two Northern sides RO, OF, +constitute the roof, and for the most part have no doors; on the East +is a small door for the Women; on the West a much larger one for the +Men; the South side or floor is usually doorless. + +Square and triangular houses are not allowed, and for this reason. The +angles of a Square (and still more those of an equilateral Triangle), +being much more pointed than those of a Pentagon, and the lines of +inanimate objects (such as houses) being dimmer than the lines of Men +and Women, it follows that there is no little danger lest the points of +a square or triangular house residence might do serious injury to an +inconsiderate or perhaps absent-minded traveller suddenly therefore, +running against them: and as early as the eleventh century of our era, +triangular houses were universally forbidden by Law, the only +exceptions being fortifications, powder-magazines, barracks, and other +state buildings, which it is not desirable that the general public +should approach without circumspection. + + +[Illustration 2] + +[ASCII approximation follows] + + + O + /\ + / \ + / \ + / \ + / \ + R/ \F + \_ / + _/ + Men's door _ Women's door + _ / + \____________/ + A B + + +At this period, square houses were still everywhere permitted, though +discouraged by a special tax. But, about three centuries afterwards, +the Law decided that in all towns containing a population above ten +thousand, the angle of a Pentagon was the smallest house-angle that +could be allowed consistently with the public safety. The good sense +of the community has seconded the efforts of the Legislature; and now, +even in the country, the pentagonal construction has superseded every +other. It is only now and then in some very remote and backward +agricultural district that an antiquarian may still discover a square +house. + + + + +Section 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 Classes 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 more than the eighth part of an inch in size), +they can hardly be distinguished from Straight Lines or Women; so +extremely pointed are their vertices. With us, as with you, these +Triangles are distinguished from others by being called Isosceles; and +by this name I shall refer to them in the following pages. + +Our Middle Class consists of Equilateral or Equal-Sided Triangles. + +Our Professional Men and Gentlemen are Squares (to which class I myself +belong) and Five-Sided Figures or Pentagons. + +Next above these come the Nobility, of whom there are several degrees, +beginning at Six-Sided Figures, or Hexagons, and from thence rising in +the number of their sides till they receive the honourable title of +Polygonal, or many-sided. Finally when the number of the sides becomes +so numerous, and the sides themselves so small, that the figure cannot +be distinguished from a circle, he is included in the Circular or +Priestly order; and this is the highest class of all. + +It is a Law of Nature with us that a male child shall have one more +side than his father, so that each generation shall rise (as a rule) +one step in the scale of development and nobility. Thus the son of a +Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on. + +But this rule applies not always to the Tradesmen, and still less often +to the Soldiers, and to the Workmen; who indeed can hardly be said to +deserve the name of human Figures, since they have not all their sides +equal. With them therefore the Law of Nature does not hold; and the +son of an Isosceles (i.e. a Triangle with two sides equal) remains +Isosceles still. Nevertheless, all hope is not shut out, even from the +Isosceles, that his posterity may ultimately rise above his degraded +condition. For, after a long series of military successes, or diligent +and skilful labours, it is generally found that the more intelligent +among the Artisan and Soldier classes manifest a slight increase of +their third side or base, and a shrinkage of the two other sides. +Intermarriages (arranged by the Priests) between the sons and daughters +of these more intellectual members of the lower classes generally +result in an offspring approximating still more to the type of the +Equal-Sided Triangle. + +Rarely--in proportion to the vast numbers of Isosceles births--is a +genuine and certifiable Equal-Sided Triangle produced from Isosceles +parents. [Note: "What need of a certificate?" a Spaceland critic may +ask: "Is not the procreation of a Square Son a certificate from Nature +herself, proving the Equal-sidedness of the Father?" I reply that no +Lady of any position will marry an uncertified Triangle. Square +offspring has sometimes resulted from a slightly Irregular Triangle; +but in almost every such case the Irregularity of the first generation +is visited on the third; which either fails to attain the Pentagonal +rank, or relapses to the Triangular.] Such a birth requires, as its +antecedents, not only a series of carefully arranged intermarriages, +but also a long, continued exercise of frugality and self-control on +the part of the would-be ancestors of the coming Equilateral, and a +patient, systematic, and continuous development of the Isosceles +intellect through many generations. + +The birth of a True Equilateral Triangle from Isosceles parents is the +subject of rejoicing in our country for many furlongs around. After a +strict examination conducted by the Sanitary and Social Board, the +infant, if certified as Regular, is with solemn ceremonial admitted +into the class of Equilaterals. He is then immediately taken from his +proud yet sorrowing parents and adopted by some childless Equilateral, +who is bound by oath never to permit the child henceforth to enter his +former home or so much as to look upon his relations again, for fear +lest the freshly developed organism may, by force of unconscious +imitation, fall back again into his hereditary level. + +The occasional emergence of an Equilateral from the ranks of his +serf-born ancestors is welcomed, not only by the poor serfs themselves, +as a gleam of light and hope shed upon the monotonous squalor of their +existence, but also by the Aristocracy at large; for all the higher +classes are well aware that these rare phenomena, while they do little +or nothing to vulgarize their own privileges, serve as a most useful +barrier against revolution from below. + +Had the acute-angled rabble been all, without exception, absolutely +destitute of hope and of ambition, they might have found leaders in +some of their many seditious outbreaks, so able as to render their +superior numbers and strength too much even for the wisdom of the +Circles. But a wise ordinance of Nature has decreed that, in +proportion as the working-classes increase in intelligence, knowledge, +and all virtue, in that same proportion their acute angle (which makes +them physically terrible) shall increase also and approximate to the +comparatively harmless angle of the Equilateral Triangle. Thus, in the +most brutal and formidable of the soldier class--creatures almost on a +level with women in their lack of intelligence--it is found that, as +they wax in the mental ability necessary to employ their tremendous +penetrating power to advantage, so do they wane in the power of +penetration itself. + +How admirable is this Law of Compensation! And how perfect a proof of +the natural fitness and, I may almost say, the divine origin of the +aristocratic constitution of the States in Flatland! By a judicious +use of this Law of Nature, the Polygons and Circles are almost always +able to stifle sedition in its very cradle, taking advantage of the +irrepressible and boundless hopefulness of the human mind. Art also +comes to the aid of Law and Order. It is generally found possible--by +a little artificial compression or expansion on the part of the State +physicians--to make some of the more intelligent leaders of a rebellion +perfectly Regular, and to admit them at once into the privileged +classes; a much larger number, who are still below the standard, +allured by the prospect of being ultimately ennobled, are induced to +enter the State Hospitals, where they are kept in honourable +confinement for life; one or two alone of the more obstinate, foolish, +and hopelessly irregular are led to execution. + +Then the wretched rabble of the Isosceles, planless and leaderless, are +either transfixed without resistance by the small body of their +brethren whom the Chief Circle keeps in pay for emergencies of this +kind; or else more often, by means of jealousies and suspicions +skilfully fomented among them by the Circular party, they are stirred +to mutual warfare, and perish by one another's angles. No less than +one hundred and twenty rebellions are recorded in our annals, besides +minor outbreaks numbered at two hundred and thirty-five; and they have +all ended thus. + + + + +Section 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 make herself invisible. This ought, I think, to be +apparent without any explanation. However, a few words will make it +clear to the most unreflecting. + +Place a needle on a table. Then, with your eye on the level of the +table, look at it side-ways, and you see the whole length of it; but +look at it end-ways, and you see nothing but a point, it has become +practically invisible. Just so is it with one of our Women. When her +side is turned towards us, we see her as a straight line; when the end +containing her eye or mouth--for with us these two organs are +identical--is the part that meets our eye, then we see nothing but a +highly lustrous point; but when the back is presented to our view, +then--being only sub-lustrous, and, indeed, almost as dim as an +inanimate object--her hinder extremity serves her as a kind of +Invisible Cap. + +The dangers to which we are exposed from our Women must now be manifest +to the meanest capacity in Spaceland. If even the angle of a +respectable Triangle in the middle class is not without its dangers; if +to run against a Working Man involves a gash; if collision with an +officer of the military class necessitates a serious wound; if a mere +touch from the vertex of a Private Soldier brings with it danger of +death;--what can it be to run against a Woman, except absolute and +immediate destruction? And when a Woman is invisible, or visible only +as a dim sub-lustrous point, how difficult must it be, even for the +most cautious, always to avoid collision! + +Many are the enactments made at different times in the different States +of Flatland, in order to minimize this peril; and in the Southern and +less temperate climates where the force of gravitation is greater, and +human beings more liable to casual and involuntary motions, the Laws +concerning Women are naturally much more stringent. But a general view +of the Code may be obtained from the following summary:-- + + +1. Every house shall have one entrance in the Eastern side, for the +use of Females only; by which all females shall enter "in a becoming +and respectful manner" and not by the Men's or Western door. [Note: +When I was in Spaceland I understood that some of your Priestly circles +have in the same way a separate entrance for Villagers, Farmers and +Teachers of Board Schools (`Spectator', Sept. 1884, p. 1255) that they +may "approach in a becoming and respectful manner."] + +2. No Female shall walk in any public place without continually +keeping up her Peace-cry, under penalty of death. + +3. Any Female, duly certified to be suffering from St. Vitus's Dance, +fits, chronic cold accompanied by violent sneezing, or any disease +necessitating involuntary motions, shall be instantly destroyed. + + +In some of the States there is an additional Law forbidding Females, +under penalty of death, from walking or standing in any public place +without moving their backs constantly from right to left so as to +indicate their presence to those behind them; others oblige a Woman, +when travelling, to be followed by one of her sons, or servants, or by +her husband; others confine Women altogether to their houses except +during the religious festivals. But it has been found by the wisest of +our Circles or Statesmen that the multiplication of restrictions on +Females tends not only to the debilitation and diminution of the race, +but also to the increase of domestic murders to such an extent that a +State loses more than it gains by a too prohibitive Code. + +For whenever the temper of the Women is thus exasperated by confinement +at home or hampering regulations abroad, they are apt to vent their +spleen upon their husbands and children; and in the less temperate +climates the whole male population of a village has been sometimes +destroyed in one or two hours of simultaneous female outbreak. Hence +the Three Laws, mentioned above, suffice for the better regulated +States, and may be accepted as a rough exemplification of our Female +Code. + +After all, our principal safeguard is found, not in Legislature, but in +the interests of the Women themselves. For, although they can inflict +instantaneous death by a retrograde movement, yet unless they can at +once disengage their stinging extremity from the struggling body of +their victim, their own frail bodies are liable to be shattered. + +The power of Fashion is also on our side. I pointed out that in some +less civilized States no female is suffered to stand in any public +place without swaying her back from right to left. This practice has +been universal among ladies of any pretensions to breeding in all +well-governed States, as far back as the memory of Figures can reach. +It is considered a disgrace to any State that legislation should have +to enforce what ought to be, and is in every respectable female, a +natural instinct. The rhythmical and, if I may so say, well-modulated +undulation of the back in our ladies of Circular rank is envied and +imitated by the wife of a common Equilateral, who can achieve nothing +beyond a mere monotonous swing, like the ticking of a pendulum; and the +regular tick of the Equilateral is no less admired and copied by the +wife of the progressive and aspiring Isosceles, in the females of whose +family no "back-motion" of any kind has become as yet a necessity of +life. Hence, in every family of position and consideration, "back +motion" is as prevalent as time itself; and the husbands and sons in +these households enjoy immunity at least from invisible attacks. + +Not that it must be for a moment supposed that our Women are destitute +of affection. But unfortunately the passion of the moment +predominates, in the Frail Sex, over every other consideration. This +is, of course, a necessity arising from their unfortunate conformation. +For as they have no pretensions to an angle, being inferior in this +respect to the very lowest of the Isosceles, they are consequently +wholly devoid of brain-power, and have neither reflection, judgment nor +forethought, and hardly any memory. Hence, in their fits of fury, they +remember no claims and recognize no distinctions. I have actually +known a case where a Woman has exterminated her whole household, and +half an hour afterwards, when her rage was over and the fragments swept +away, has asked what has become of her husband and her children. + +Obviously then a Woman is not to be irritated as long as she is in a +position where she can turn round. When you have them in their +apartments--which are constructed with a view to denying them that +power--you can say and do what you like; for they are then wholly +impotent for mischief, and will not remember a few minutes hence the +incident for which they may be at this moment threatening you with +death, nor the promises which you may have found it necessary to make +in order to pacify their fury. + +On the whole we get on pretty smoothly in our domestic relations, +except in the lower strata of the Military Classes. There the want of +tact and discretion on the part of the husbands produces at times +indescribable disasters. Relying too much on the offensive weapons of +their acute angles instead of the defensive organs of good sense and +seasonable simulation, these reckless creatures too often neglect the +prescribed construction of the women's apartments, or irritate their +wives by ill-advised expressions out of doors, which they refuse +immediately to retract. Moreover a blunt and stolid regard for literal +truth indisposes them to make those lavish promises by which the more +judicious Circle can in a moment pacify his consort. The result is +massacre; not, however, without its advantages, as it eliminates the +more brutal and troublesome of the Isosceles; and by many of our +Circles the destructiveness of the Thinner Sex is regarded as one among +many providential arrangements for suppressing redundant population, +and nipping Revolution in the bud. + +Yet even in our best regulated and most approximately Circular families +I cannot say that the ideal of family life is so high as with you in +Spaceland. There is peace, in so far as the absence of slaughter may +be called by that name, but there is necessarily little harmony of +tastes or pursuits; and the cautious wisdom of the Circles has ensured +safety at the cost of domestic comfort. In every Circular or Polygonal +household it has been a habit from time immemorial--and now has become +a kind of instinct among the women of our higher classes--that the +mothers and daughters should constantly keep their eyes and mouths +towards their husband and his male friends; and for a lady in a family +of distinction to turn her back upon her husband would be regarded as a +kind of portent, involving loss of STATUS. But, as I shall soon shew, +this custom, though it has the advantage of safety, is not without its +disadvantages. + +In the house of the Working Man or respectable Tradesman--where the +wife is allowed to turn her back upon her husband, while pursuing her +household avocations--there are at least intervals of quiet, when the +wife is neither seen nor heard, except for the humming sound of the +continuous Peace-cry; but in the homes of the upper classes there is +too often no peace. There the voluble mouth and bright penetrating eye +are ever directed towards the Master of the household; and light itself +is not more persistent than the stream of feminine discourse. The tact +and skill which suffice to avert a Woman's sting are unequal to the +task of stopping a Woman's mouth; and as the wife has absolutely +nothing to say, and absolutely no constraint of wit, sense, or +conscience to prevent her from saying it, not a few cynics have been +found to aver that they prefer the danger of the death-dealing but +inaudible sting to the safe sonorousness of a Woman's other end. + +To my readers in Spaceland the condition of our Women may seem truly +deplorable, and so indeed it is. A Male of the lowest type of the +Isosceles may look forward to some improvement of his angle, and to the +ultimate elevation of the whole of his degraded caste; but no Woman can +entertain such hopes for her sex. "Once a Woman, always a Woman" is a +Decree of Nature; and the very Laws of Evolution seem suspended in her +disfavour. Yet at least we can admire the wise Prearrangement which +has ordained that, as they have no hopes, so they shall have no memory +to recall, and no forethought to anticipate, the miseries and +humiliations which are at once a necessity of their existence and the +basis of the constitution of Flatland. + + + + +Section 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 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, animate or +inanimate, no matter what their form, present TO OUR VIEW the same, or +nearly the same, appearance, viz. that of a straight Line. How then +can one be distinguished from another, where all appear the same? + +The answer is threefold. The first means of recognition is the sense +of hearing; which with us is far more highly developed than with you, +and which enables us not only to distinguish by the voice our personal +friends, but even to discriminate between different classes, at least +so far as concerns the three lowest orders, the Equilateral, the +Square, and the Pentagon--for of the Isosceles I take no account. But +as we ascend in the social scale, the process of discriminating and +being discriminated by hearing increases in difficulty, partly because +voices are assimilated, partly because the faculty of +voice-discrimination is a plebeian virtue not much developed among the +Aristocracy. And wherever there is any danger of imposture we cannot +trust to this method. Amongst our lowest orders, the vocal organs are +developed to a degree more than correspondent with those of hearing, so +that an Isosceles can easily feign the voice of a Polygon, and, with +some training, that of a Circle himself. A second method is therefore +more commonly resorted to. + +FEELING is, among our Women and lower classes--about our upper classes +I shall speak presently--the principal test of recognition, at all +events between strangers, and when the question is, not as to the +individual, but as to the class. What therefore "introduction" is +among the higher classes in Spaceland, that the process of "feeling" is +with us. "Permit me to ask you to feel and be felt by my friend Mr. +So-and-so"--is still, among the more old-fashioned of our country +gentlemen in districts remote from towns, the customary formula for a +Flatland introduction. But in the towns, and among men of business, +the words "be felt by" are omitted and the sentence is abbreviated to, +"Let me ask you to feel Mr. So-and-so"; although it is assumed, of +course, that the "feeling" is to be reciprocal. Among our still more +modern and dashing young gentlemen--who are extremely averse to +superfluous effort and supremely indifferent to the purity of their +native language--the formula is still further curtailed by the use of +"to feel" in a technical sense, meaning, "to +recommend-for-the-purposes-of-feeling-and-being-felt"; and at this +moment the "slang" of polite or fast society in the upper classes +sanctions such a barbarism as "Mr. Smith, permit me to feel Mr. Jones." + +Let not my Reader however suppose that "feeling" is with us the tedious +process that it would be with you, or that we find it necessary to feel +right round all the sides of every individual before we determine the +class to which he belongs. Long practice and training, begun in the +schools and continued in the experience of daily life, enable us to +discriminate at once by the sense of touch, between the angles of an +equal-sided Triangle, Square, and Pentagon; and I need not say that the +brainless vertex of an acute-angled Isosceles is obvious to the dullest +touch. It is therefore not necessary, as a rule, to do more than feel +a single angle of an individual; and this, once ascertained, tells us +the class of the person whom we are addressing, unless indeed he +belongs to the higher sections of the nobility. There the difficulty +is much greater. Even a Master of Arts in our University of Wentbridge +has been known to confuse a ten-sided with a twelve-sided Polygon; and +there is hardly a Doctor of Science in or out of that famous University +who could pretend to decide promptly and unhesitatingly between a +twenty-sided and a twenty-four sided member of the Aristocracy. + +Those of my readers who recall the extracts I gave above from the +Legislative code concerning Women, will readily perceive that the +process of introduction by contact requires some care and discretion. +Otherwise the angles might inflict on the unwary Feeler irreparable +injury. It is essential for the safety of the Feeler that the Felt +should stand perfectly still. A start, a fidgety shifting of the +position, yes, even a violent sneeze, has been known before now to +prove fatal to the incautious, and to nip in the bud many a promising +friendship. Especially is this true among the lower classes of the +Triangles. With them, the eye is situated so far from their vertex +that they can scarcely take cognizance of what goes on at that +extremity of their frame. They are, moreover, of a rough coarse +nature, not sensitive to the delicate touch of the highly organized +Polygon. What wonder then if an involuntary toss of the head has ere +now deprived the State of a valuable life! + +I have heard that my excellent Grandfather--one of the least irregular +of his unhappy Isosceles class, who indeed obtained, shortly before his +decease, four out of seven votes from the Sanitary and Social Board for +passing him into the class of the Equal-sided--often deplored, with a +tear in his venerable eye, a miscarriage of this kind, which had +occured to his great-great-great-Grandfather, a respectable Working Man +with an angle or brain of 59 degrees 30 minutes. According to his +account, my unfortunate Ancestor, being afflicted with rheumatism, and +in the act of being felt by a Polygon, by one sudden start accidentally +transfixed the Great Man through the diagonal; and thereby, partly in +consequence of his long imprisonment and degradation, and partly +because of the moral shock which pervaded the whole of my Ancestor's +relations, threw back our family a degree and a half in their ascent +towards better things. The result was that in the next generation the +family brain was registered at only 58 degrees, and not till the lapse +of five generations was the lost ground recovered, the full 60 degrees +attained, and the Ascent from the Isosceles finally achieved. And all +this series of calamities from one little accident in the process of +Feeling. + +At this point I think I hear some of my better educated readers +exclaim, "How could you in Flatland know anything about angles and +degrees, or minutes? We can SEE an angle, because we, in the region of +Space, can see two straight lines inclined to one another; but you, who +can see nothing but one straight line at a time, or at all events only +a number of bits of straight lines all in one straight line--how can +you ever discern any angle, and much less register angles of different +sizes?" + +I answer that though we cannot SEE angles, we can INFER them, and this +with great precision. Our sense of touch, stimulated by necessity, and +developed by long training, enables us to distinguish angles far more +accurately than your sense of sight, when unaided by a rule or measure +of angles. Nor must I omit to explain that we have great natural +helps. It is with us a Law of Nature that the brain of the Isosceles +class shall begin at half a degree, or thirty minutes, and shall +increase (if it increases at all) by half a degree in every generation; +until the goal of 60 degrees is reached, when the condition of serfdom +is quitted, and the freeman enters the class of Regulars. + +Consequently, Nature herself supplies us with an ascending scale or +Alphabet of angles for half a degree up to 60 degrees, Specimens of +which are placed in every Elementary School throughout the land. Owing +to occasional retrogressions, to still more frequent moral and +intellectual stagnation, and to the extraordinary fecundity of the +Criminal and Vagabond Classes, there is always a vast superfluity of +individuals of the half degree and single degree class, and a fair +abundance of Specimens up to 10 degrees. These are absolutely +destitute of civic rights; and a great number of them, not having even +intelligence enough for the purposes of warfare, are devoted by the +States to the service of education. Fettered immovably so as to remove +all possibility of danger, they are placed in the class rooms of our +Infant Schools, and there they are utilized by the Board of Education +for the purpose of imparting to the offspring of the Middle Classes +that tact and intelligence of which these wretched creatures themselves +are utterly devoid. + +In some States the Specimens are occasionally fed and suffered to exist +for several years; but in the more temperate and better regulated +regions, it is found in the long run more advantageous for the +educational interests of the young, to dispense with food, and to renew +the Specimens every month--which is about the average duration of the +foodless existence of the Criminal class. In the cheaper schools, what +is gained by the longer existence of the Specimen is lost, partly in +the expenditure for food, and partly in the diminished accuracy of the +angles, which are impaired after a few weeks of constant "feeling". +Nor must we forget to add, in enumerating the advantages of the more +expensive system, that it tends, though slightly yet perceptibly, to +the diminution of the redundant Isosceles population--an object which +every statesman in Flatland constantly keeps in view. On the whole +therefore--although I am not ignorant that, in many popularly elected +School Boards, there is a reaction in favour of "the cheap system" as +it is called--I am myself disposed to think that this is one of the +many cases in which expense is the truest economy. + +But I must not allow questions of School Board politics to divert me +from my subject. Enough has been said, I trust, to shew that +Recognition by Feeling is not so tedious or indecisive a process as +might have been supposed; and it is obviously more trustworthy than +Recognition by hearing. Still there remains, as has been pointed out +above, the objection that this method is not without danger. For this +reason many in the Middle and Lower classes, and all without exception +in the Polygonal and Circular orders, prefer a third method, the +description of which shall be reserved for the next section. + + + + +Section 6. Of Recognition by Sight + + + +I am about to appear very inconsistent. In 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 Feeling is stated to be universal, he will find +this qualification--"among the lower classes". It is only among the +higher classes and in our temperate climates that Sight Recognition is +practised. + +That this power exists in any regions and for any classes is the result +of Fog; which prevails during the greater part of the year in all parts +save the torrid zones. That which is with you in Spaceland an unmixed +evil, blotting out the landscape, depressing the spirits, and +enfeebling the health, is by us recognized as a blessing scarcely +inferior to air itself, and as the Nurse of arts and Parent of +sciences. But let me explain my meaning, without further eulogies on +this beneficent Element. + +If Fog were non-existent, all lines would appear equally and +indistinguishably clear; and this is actually the case in those unhappy +countries in which the atmosphere is perfectly dry and transparent. +But wherever there is a rich supply of Fog objects that are at a +distance, say of three feet, are appreciably dimmer than those at a +distance of two feet eleven inches; and the result is that by careful +and constant experimental observation of comparative dimness and +clearness, we are enabled to infer with great exactness the +configuration of the object observed. + +An instance will do more than a volume of generalities to make my +meaning clear. + +Suppose I see two individuals approaching whose rank I wish to +ascertain. They are, we will suppose, a Merchant and a Physician, or +in other words, an Equilateral Triangle and a Pentagon: how am I to +distinguish them? + + +[Illustration 3] + +[ASCII approximation follows] + + + C (1) + |\ - _ D + | \ ||- _ + | \ || - _ + | <--- >|| -----------+(> Eye-glance + ___C' (2) | / A|| _ - + ___--- \ - _D' | / ||_ - + __--- \ || - _ |/ _ - E + | \ || - _ B + | \ || - _ + | Eye-glance \ || - _ + | <----------- A'>|| ------------------------+(> + | / || _ - + | / || _ - + |__ / || _ - + ---___ / || _ - + ---___/ _ -E' + B' + + +It will be obvious, to every child in Spaceland who has touched the +threshold of Geometrical Studies, that, if I can bring my eye so that +its glance may bisect an angle (A) of the approaching stranger, my view +will lie as it were evenly between his two sides that are next to me +(viz. CA and AB), so that I shall contemplate the two impartially, and +both will appear of the same size. + +Now in the case of (1) the Merchant, what shall I see? I shall see a +straight line DAE, in which the middle point (A) will be very bright +because it is nearest to me; but on either side the line will shade +away RAPIDLY INTO DIMNESS, because the sides AC and AB RECEDE RAPIDLY +INTO THE FOG and what appear to me as the Merchant's extremities, viz. +D and E, will be VERY DIM INDEED. + +On the other hand in the case of (2) the Physician, though I shall here +also see a line (D'A'E') with a bright centre (A'), yet it will shade +away LESS RAPIDLY into dimness, because the sides (A'C', A'B') RECEDE +LESS RAPIDLY INTO THE FOG: and what appear to me the Physician's +extremities, viz. D' and E', will not be NOT SO DIM as the extremities +of the Merchant. + +The Reader will probably understand from these two instances how--after +a very long training supplemented by constant experience--it is +possible for the well-educated classes among us to discriminate with +fair accuracy between the middle and lowest orders, by the sense of +sight. If my Spaceland Patrons have grasped this general conception, +so far as to conceive the possibility of it and not to reject my +account as altogether incredible--I shall have attained all I can +reasonably expect. Were I to attempt further details I should only +perplex. Yet for the sake of the young and inexperienced, who may +perchance infer--from the two simple instances I have given above, of +the manner in which I should recognize my Father and my Sons--that +Recognition by sight is an easy affair, it may be needful to point out +that in actual life most of the problems of Sight Recognition are far +more subtle and complex. + +If for example, when my Father, the Triangle, approaches me, he happens +to present his side to me instead of his angle, then, until I have +asked him to rotate, or until I have edged my eye round him, I am for +the moment doubtful whether he may not be a Straight Line, or, in other +words, a Woman. Again, when I am in the company of one of my two +hexagonal Grandsons, contemplating one of his sides (AB) full front, it +will be evident from the accompanying diagram that I shall see one +whole line (AB) in comparative brightness (shading off hardly at all at +the ends) and two smaller lines (CA and BD) dim throughout and shading +away into greater dimness towards the extremities C and D. + + +[Illustration 4] + +[ASCII approximation follows] + + + /\ - _ C + / \ || _ + / \ || - _ + / \|| - _ + | A || - _ + | || -+(> (Eye) + | B || _ - + \ /|| _ - + \ / || _ - + \ / || - + \/ _ - D + + +But I must not give way to the temptation of enlarging on these topics. +The meanest mathematician in Spaceland will readily believe me when I +assert that the problems of life, which present themselves to the +well-educated--when they are themselves in motion, rotating, advancing +or retreating, and at the same time attempting to discriminate by the +sense of sight between a number of Polygons of high rank moving in +different directions, as for example in a ball-room or +conversazione--must be of a nature to task the angularity of the most +intellectual, and amply justify the rich endowments of the Learned +Professors of Geometry, both Static and Kinetic, in the illustrious +University of Wentbridge, where the Science and Art of Sight +Recognition are regularly taught to large classes of the ELITE of the +States. + +It is only a few of the scions of our noblest and wealthiest houses, +who are able to give the time and money necessary for the thorough +prosecution of this noble and valuable Art. Even to me, a +Mathematician of no mean standing, and the Grandfather of two most +hopeful and perfectly regular Hexagons, to find myself in the midst of +a crowd of rotating Polygons of the higher classes, is occasionally +very perplexing. And of course to a common Tradesman, or Serf, such a +sight is almost as unintelligible as it would be to you, my Reader, +were you suddenly transported into our country. + +In such a crowd you could see on all sides of you nothing but a Line, +apparently straight, but of which the parts would vary irregularly and +perpetually in brightness or dimness. Even if you had completed your +third year in the Pentagonal and Hexagonal classes in the University, +and were perfect in the theory of the subject, you would still find +that there was need of many years of experience, before you could move +in a fashionable crowd without jostling against your betters, whom it +is against etiquette to ask to "feel", and who, by their superior +culture and breeding, know all about your movements, while you know +very little or nothing about theirs. In a word, to comport oneself +with perfect propriety in Polygonal society, one ought to be a Polygon +oneself. Such at least is the painful teaching of my experience. + +It is astonishing how much the Art--or I may almost call it +instinct--of Sight Recognition is developed by the habitual practice of +it and by the avoidance of the custom of "Feeling". Just as, with you, +the deaf and dumb, if once allowed to gesticulate and to use the +hand-alphabet, will never acquire the more difficult but far more +valuable art of lipspeech and lip-reading, so it is with us as regards +"Seeing" and "Feeling". None who in early life resort to "Feeling" +will ever learn "Seeing" in perfection. + +For this reason, among our Higher Classes, "Feeling" is discouraged or +absolutely forbidden. From the cradle their children, instead of going +to the Public Elementary schools (where the art of Feeling is taught), +are sent to higher Seminaries of an exclusive character; and at our +illustrious University, to "feel" is regarded as a most serious fault, +involving Rustication for the first offence, and Expulsion for the +second. + +But among the lower classes the art of Sight Recognition is regarded as +an unattainable luxury. A common Tradesman cannot afford to let his +son spend a third of his life in abstract studies. The children of the +poor are therefore allowed to "feel" from their earliest years, and +they gain thereby a precocity and an early vivacity which contrast at +first most favourably with the inert, undeveloped, and listless +behaviour of the half-instructed youths of the Polygonal class; but +when the latter have at last completed their University course, and are +prepared to put their theory into practice, the change that comes over +them may almost be described as a new birth, and in every art, science, +and social pursuit they rapidly overtake and distance their Triangular +competitors. + +Only a few of the Polygonal Class fail to pass the Final Test or +Leaving Examination at the University. The condition of the +unsuccessful minority is truly pitiable. Rejected from the higher +class, they are also despised by the lower. They have neither the +matured and systematically trained powers of the Polygonal Bachelors +and Masters of Arts, nor yet the native precocity and mercurial +versatility of the youthful Tradesman. The professions, the public +services, are closed against them; and though in most States they are +not actually debarred from marriage, yet they have the greatest +difficulty in forming suitable alliances, as experience shews that the +offspring of such unfortunate and ill-endowed parents is generally +itself unfortunate, if not positively Irregular. + +It is from these specimens of the refuse of our Nobility that the great +Tumults and Seditions of past ages have generally derived their +leaders; and so great is the mischief thence arising that an increasing +minority of our more progressive Statesmen are of opinion that true +mercy would dictate their entire suppression, by enacting that all who +fail to pass the Final Examination of the University should be either +imprisoned for life, or extinguished by a painless death. + +But I find myself digressing into the subject of Irregularities, a +matter of such vital interest that it demands a separate section. + + + + +Section 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 generally, that in every Polygon, all the sides must +be equal. + +The size of the sides would of course depend upon the age of the +individual. A Female at birth would be about an inch long, while a +tall adult Woman might extend to a foot. As to the Males of every +class, it may be roughly said that the length of an adult's sides, when +added together, is two feet or a little more. But the size of our +sides is not under consideration. I am speaking of the EQUALITY of +sides, and it does not need much reflection to see that the whole of +the social life in Flatland rests upon the fundamental fact that Nature +wills all Figures to have their sides equal. + +If our sides were unequal our angles might be unequal. Instead of its +being sufficient to feel, or estimate by sight, a single angle in order +to determine the form of an individual, it would be necessary to +ascertain each angle by the experiment of Feeling. But life would be +too short for such a tedious grouping. The whole science and art of +Sight Recognition would at once perish; Feeling, so far as it is an +art, would not long survive; intercourse would become perilous or +impossible; there would be an end to all confidence, all forethought; +no one would be safe in making the most simple social arrangements; in +a word, civilization would relapse into barbarism. + +Am I going too fast to carry my Readers with me to these obvious +conclusions? Surely a moment's reflection, and a single instance from +common life, must convince every one that our whole social system is +based upon Regularity, or Equality of Angles. You meet, for example, +two or three Tradesmen in the street, whom you recognize at once to be +Tradesmen by a glance at their angles and rapidly bedimmed sides, and +you ask them to step into your house to lunch. This you do at present +with perfect confidence, because everyone knows to an inch or two the +area occupied by an adult Triangle: but imagine that your Tradesman +drags behind his regular and respectable vertex, a parallelogram of +twelve or thirteen inches in diagonal:--what are you to do with such a +monster sticking fast in your house door? + +But I am insulting the intelligence of my Readers by accumulating +details which must be patent to everyone who enjoys the advantages of a +Residence in Spaceland. Obviously the measurements of a single angle +would no longer be sufficient under such portentous circumstances; +one's whole life would be taken up in feeling or surveying the +perimeter of one's acquaintances. Already the difficulties of avoiding +a collision in a crowd are enough to tax the sagacity of even a +well-educated Square; but if no one could calculate the Regularity of a +single figure in the company, all would be chaos and confusion, and the +slightest panic would cause serious injuries, or--if there happened to +be any Women or Soldiers present--perhaps considerable loss of life. + +Expediency therefore concurs with Nature in stamping the seal of its +approval upon Regularity of conformation: nor has the Law been +backward in seconding their efforts. "Irregularity of Figure" means +with us the same as, or more than, a combination of moral obliquity and +criminality with you, and is treated accordingly. There are not +wanting, it is true, some promulgators of paradoxes who maintain that +there is no necessary connection between geometrical and moral +Irregularity. "The Irregular", they say, "is from his birth scouted by +his own parents, derided by his brothers and sisters, neglected by the +domestics, scorned and suspected by society, and excluded from all +posts of responsibility, trust, and useful activity. His every +movement is jealously watched by the police till he comes of age and +presents himself for inspection; then he is either destroyed, if he is +found to exceed the fixed margin of deviation, or else immured in a +Government Office as a clerk of the seventh class; prevented from +marriage; forced to drudge at an uninteresting occupation for a +miserable stipend; obliged to live and board at the office, and to take +even his vacation under close supervision; what wonder that human +nature, even in the best and purest, is embittered and perverted by +such surroundings!" + +All this very plausible reasoning does not convince me, as it has not +convinced the wisest of our Statesmen, that our ancestors erred in +laying it down as an axiom of policy that the toleration of +Irregularity is incompatible with the safety of the State. Doubtless, +the life of an Irregular is hard; but the interests of the Greater +Number require that it shall be hard. If a man with a triangular front +and a polygonal back were allowed to exist and to propagate a still +more Irregular posterity, what would become of the arts of life? Are +the houses and doors and churches in Flatland to be altered in order to +accommodate such monsters? Are our ticket-collectors to be required to +measure every man's perimeter before they allow him to enter a theatre +or to take his place in a lecture room? Is an Irregular to be exempted +from the militia? And if not, how is he to be prevented from carrying +desolation into the ranks of his comrades? Again, what irresistible +temptations to fraudulent impostures must needs beset such a creature! +How easy for him to enter a shop with his polygonal front foremost, and +to order goods to any extent from a confiding tradesman! Let the +advocates of a falsely called Philanthropy plead as they may for the +abrogation of the Irregular Penal Laws, I for my part have never known +an Irregular who was not also what Nature evidently intended him to +be--a hypocrite, a misanthropist, and, up to the limits of his power, a +perpetrator of all manner of mischief. + +Not that I should be disposed to recommend (at present) the extreme +measures adopted by some States, where an infant whose angle deviates +by half a degree from the correct angularity is summarily destroyed at +birth. Some of our highest and ablest men, men of real genius, have +during their earliest days laboured under deviations as great as, or +even greater than, forty-five minutes: and the loss of their precious +lives would have been an irreparable injury to the State. The art of +healing also has achieved some of its most glorious triumphs in the +compressions, extensions, trepannings, colligations, and other surgical +or diaetetic operations by which Irregularity has been partly or wholly +cured. Advocating therefore a VIA MEDIA, I would lay down no fixed or +absolute line of demarcation; but at the period when the frame is just +beginning to set, and when the Medical Board has reported that recovery +is improbable, I would suggest that the Irregular offspring be +painlessly and mercifully consumed. + + + + +Section 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 the opportunity +of immediate verification, imparts to our existence a zest which you in +Spaceland can hardly comprehend. I speak now from the aesthetic and +artistic point of view when I say that life with us is dull; +aesthetically and artistically, very dull indeed. + +How can it be otherwise, when all one's prospect, all one's landscapes, +historical pieces, portraits, flowers, still life, are nothing but a +single line, with no varieties except degrees of brightness and +obscurity? + +It was not always thus. Colour, if Tradition speaks the truth, once +for the space of half a dozen centuries or more, threw a transient +splendour over the lives of our ancestors in the remotest ages. Some +private individual--a Pentagon whose name is variously reported--having +casually discovered the constituents of the simpler colours and a +rudimentary method of painting, is said to have begun decorating first +his house, then his slaves, then his Father, his Sons, and Grandsons, +lastly himself. The convenience as well as the beauty of the results +commended themselves to all. Wherever Chromatistes,--for by that name +the most trustworthy authorities concur in calling him,--turned his +variegated frame, there he at once excited attention, and attracted +respect. No one now needed to "feel" him; no one mistook his front for +his back; all his movements were readily ascertained by his neighbours +without the slightest strain on their powers of calculation; no one +jostled him, or failed to make way for him; his voice was saved the +labour of that exhausting utterance by which we colourless Squares and +Pentagons are often forced to proclaim our individuality when we move +amid a crowd of ignorant Isosceles. + +The fashion spread like wildfire. Before a week was over, every Square +and Triangle in the district had copied the example of Chromatistes, +and only a few of the more conservative Pentagons still held out. A +month or two found even the Dodecagons infected with the innovation. A +year had not elapsed before the habit had spread to all but the very +highest of the Nobility. Needless to say, the custom soon made its way +from the district of Chromatistes to surrounding regions; and within +two generations no one in all Flatland was colourless except the Women +and the Priests. + +Here Nature herself appeared to erect a barrier, and to plead against +extending the innovation to these two classes. Many-sidedness was +almost essential as a pretext for the Innovators. "Distinction of +sides is intended by Nature to imply distinction of colours"--such was +the sophism which in those days flew from mouth to mouth, converting +whole towns at a time to the new culture. But manifestly to our +Priests and Women this adage did not apply. The latter had only one +side, and therefore--plurally and pedantically speaking--NO SIDES. The +former--if at least they would assert their claim to be really and +truly Circles, and not mere high-class Polygons with an infinitely +large number of infinitesimally small sides--were in the habit of +boasting (what Women confessed and deplored) that they also had no +sides, being blessed with a perimeter of one line, or, in other words, +a Circumference. Hence it came to pass that these two Classes could +see no force in the so-called axiom about "Distinction of Sides +implying Distinction of Colour"; and when all others had succumbed to +the fascinations of corporal decoration, the Priests and the Women +alone still remained pure from the pollution of paint. + +Immoral, licentious, anarchical, unscientific--call them by what names +you will--yet, from an aesthetic point of view, those ancient days of +the Colour Revolt were the glorious childhood of Art in Flatland--a +childhood, alas, that never ripened into manhood, nor even reached the +blossom of youth. To live was then in itself a delight, because living +implied seeing. Even at a small party, the company was a pleasure to +behold; the richly varied hues of the assembly in a church or theatre +are said to have more than once proved too distracting for our greatest +teachers and actors; but most ravishing of all is said to have been the +unspeakable magnificence of a military review. + +The sight of a line of battle of twenty thousand Isosceles suddenly +facing about, and exchanging the sombre black of their bases for the +orange and purple of the two sides including their acute angle; the +militia of the Equilateral Triangles tricoloured in red, white, and +blue; the mauve, ultra-marine, gamboge, and burnt umber of the Square +artillerymen rapidly rotating near their vermilion guns; the dashing +and flashing of the five-coloured and six-coloured Pentagons and +Hexagons careering across the field in their offices of surgeons, +geometricians and aides-de-camp--all these may well have been +sufficient to render credible the famous story how an illustrious +Circle, overcome by the artistic beauty of the forces under his +command, threw aside his marshal's baton and his royal crown, +exclaiming that he henceforth exchanged them for the artist's pencil. +How great and glorious the sensuous development of these days must have +been is in part indicated by the very language and vocabulary of the +period. The commonest utterances of the commonest citizens in the time +of the Colour Revolt seem to have been suffused with a richer tinge of +word or thought; and to that era we are even now indebted for our +finest poetry and for whatever rhythm still remains in the more +scientific utterance of these modern days. + + + + +Section 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 refusing to pay the customary tribute from the +Criminal classes to the service of Education, waxed daily more numerous +and more insolent on the strength of their immunity from the old burden +which had formerly exercised the twofold wholesome effect of at once +taming their brutal nature and thinning their excessive numbers. + +Year by year the Soldiers and Artisans began more vehemently to +assert--and with increasing truth--that there was no great difference +between them and the very highest class of Polygons, now that they were +raised to an equality with the latter, and enabled to grapple with all +the difficulties and solve all the problems of life, whether Statical +or Kinetical, by the simple process of Colour Recognition. Not content +with the natural neglect into which Sight Recognition was falling, they +began boldly to demand the legal prohibition of all "monopolizing and +aristocratic Arts" and the consequent abolition of all endowments for +the studies of Sight Recognition, Mathematics, and Feeling. Soon, they +began to insist that inasmuch as Colour, which was a second Nature, had +destroyed the need of aristocratic distinctions, the Law should follow +in the same path, and that henceforth all individuals and all classes +should be recognized as absolutely equal and entitled to equal rights. + +Finding the higher Orders wavering and undecided, the leaders of the +Revolution advanced still further in their requirements, and at last +demanded that all classes alike, the Priests and the Women not +excepted, should do homage to Colour by submitting to be painted. When +it was objected that Priests and Women had no sides, they retorted that +Nature and Expediency concurred in dictating that the front half of +every human being (that is to say, the half containing his eye and +mouth) should be distinguishable from his hinder half. They therefore +brought before a general and extraordinary Assembly of all the States +of Flatland a Bill proposing that in every Woman the half containing +the eye and mouth should be coloured red, and the other half green. +The Priests were to be painted in the same way, red being applied to +that semicircle in which the eye and mouth formed the middle point; +while the other or hinder semicircle was to be coloured green. + +There was no little cunning in this proposal, which indeed emanated not +from any Isosceles--for no being so degraded would have had angularity +enough to appreciate, much less to devise, such a model of +state-craft--but from an Irregular Circle who, instead of being +destroyed in his childhood, was reserved by a foolish indulgence to +bring desolation on his country and destruction on myriads of his +followers. + +On the one hand the proposition was calculated to bring the Women in +all classes over to the side of the Chromatic Innovation. For by +assigning to the Women the same two colours as were assigned to the +Priests, the Revolutionists thereby ensured that, in certain positions, +every Woman would appear like a Priest, and be treated with +corresponding respect and deference--a prospect that could not fail to +attract the Female Sex in a mass. + +But by some of my Readers the possibility of the identical appearance +of Priests and Women, under the new Legislation, may not be recognized; +if so, a word or two will make it obvious. + +Imagine a woman duly decorated, according to the new Code; with the +front half (i.e. the half containing eye and mouth) red, and with the +hinder half green. Look at her from one side. Obviously you will see +a straight line, HALF RED, HALF GREEN. + + +[Illustration 5] + +[ASCII approximation follows] + +[for simplicity's sake, the circle is approximated as an octogon] + + + M + _____ + / \ - C_ + / \|| - _ + | || - _ + A|- - - - - - -||B- - - - - -_-+(> (Eye) + | || _ - + \ /||_ - + \ _____ / - D + + +Now imagine a Priest, whose mouth is at M, and whose front semicircle +(AMB) is consequently coloured red, while his hinder semicircle is +green; so that the diameter AB divides the green from the red. If you +contemplate the Great Man so as to have your eye in the same straight +line as his dividing diameter (AB), what you will see will be a +straight line (CBD), of which ONE HALF (CB) WILL BE RED, AND THE OTHER +(BD) GREEN. The whole line (CD) will be rather shorter perhaps than +that of a full-sized Woman, and will shade off more rapidly towards its +extremities; but the identity of the colours would give you an +immediate impression of identity of Class, making you neglectful of +other details. Bear in mind the decay of Sight Recognition which +threatened society at the time of the Colour Revolt; add too the +certainty that Women would speedily learn to shade off their +extremities so as to imitate the Circles; it must then be surely +obvious to you, my dear Reader, that the Colour Bill placed us under a +great danger of confounding a Priest with a young Woman. + +How attractive this prospect must have been to the Frail Sex may +readily be imagined. They anticipated with delight the confusion that +would ensue. At home they might hear political and ecclesiastical +secrets intended not for them but for their husbands and brothers, and +might even issue commands in the name of a priestly Circle; out of +doors the striking combination of red and green, without addition of +any other colours, would be sure to lead the common people into endless +mistakes, and the Women would gain whatever the Circles lost, in the +deference of the passers by. As for the scandal that would befall the +Circular Class if the frivolous and unseemly conduct of the Women were +imputed to them, and as to the consequent subversion of the +Constitution, the Female Sex could not be expected to give a thought to +these considerations. Even in the households of the Circles, the Women +were all in favour of the Universal Colour Bill. + +The second object aimed at by the Bill was the gradual demoralization +of the Circles themselves. In the general intellectual decay they +still preserved their pristine clearness and strength of understanding. +From their earliest childhood, familiarized in their Circular +households with the total absence of Colour, the Nobles alone preserved +the Sacred Art of Sight Recognition, with all the advantages that +result from that admirable training of the intellect. Hence, up to the +date of the introduction of the Universal Colour Bill, the Circles had +not only held their own, but even increased their lead of the other +classes by abstinence from the popular fashion. + +Now therefore the artful Irregular whom I described above as the real +author of this diabolical Bill, determined at one blow to lower the +status of the Hierarchy by forcing them to submit to the pollution of +Colour, and at the same time to destroy their domestic opportunities of +training in the Art of Sight Recognition, so as to enfeeble their +intellects by depriving them of their pure and colourless homes. Once +subjected to the chromatic taint, every parental and every childish +Circle would demoralize each other. Only in discerning between the +Father and the Mother would the Circular infant find problems for the +exercise of its understanding--problems too often likely to be +corrupted by maternal impostures with the result of shaking the child's +faith in all logical conclusions. Thus by degrees the intellectual +lustre of the Priestly Order would wane, and the road would then lie +open for a total destruction of all Aristocratic Legislature and for +the subversion of our Privileged Classes. + + + + +Section 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 household wearied their +lords with prayers to give up their opposition to the Colour Bill; and +some, finding their entreaties fruitless, fell on and slaughtered their +innocent children and husband, perishing themselves in the act of +carnage. It is recorded that during that triennial agitation no less +than twenty-three Circles perished in domestic discord. + +Great indeed was the peril. It seemed as though the Priests had no +choice between submission and extermination; when suddenly the course +of events was completely changed by one of those picturesque incidents +which Statesmen ought never to neglect, often to anticipate, and +sometimes perhaps to originate, because of the absurdly +disproportionate power with which they appeal to the sympathies of the +populace. + +It happened that an Isosceles of a low type, with a brain little if at +all above four degrees--accidentally dabbling in the colours of some +Tradesman whose shop he had plundered--painted himself, or caused +himself to be painted (for the story varies) with the twelve colours of +a Dodecagon. Going into the Market Place he accosted in a feigned +voice a maiden, the orphan daughter of a noble Polygon, whose affection +in former days he had sought in vain; and by a series of +deceptions--aided, on the one side, by a string of lucky accidents too +long to relate, and on the other, by an almost inconceivable fatuity +and neglect of ordinary precautions on the part of the relations of the +bride--he succeeded in consummating the marriage. The unhappy girl +committed suicide on discovering the fraud to which she had been +subjected. + +When the news of this catastrophe spread from State to State the minds +of the Women were violently agitated. Sympathy with the miserable +victim and anticipations of similar deceptions for themselves, their +sisters, and their daughters, made them now regard the Colour Bill in +an entirely new aspect. Not a few openly avowed themselves converted +to antagonism; the rest needed only a slight stimulus to make a similar +avowal. Seizing this favourable opportunity, the Circles hastily +convened an extraordinary Assembly of the States; and besides the usual +guard of Convicts, they secured the attendance of a large number of +reactionary Women. + +Amidst an unprecedented concourse, the Chief Circle of those days--by +name Pantocyclus--arose to find himself hissed and hooted by a hundred +and twenty thousand Isosceles. But he secured silence by declaring +that henceforth the Circles would enter on a policy of Concession; +yielding to the wishes of the majority, they would accept the Colour +Bill. The uproar being at once converted to applause, he invited +Chromatistes, the leader of the Sedition, into the centre of the hall, +to receive in the name of his followers the submission of the +Hierarchy. Then followed a speech, a masterpiece of rhetoric, which +occupied nearly a day in the delivery, and to which no summary can do +justice. + +With a grave appearance of impartiality he declared that as they were +now finally committing themselves to Reform or Innovation, it was +desirable that they should take one last view of the perimeter of the +whole subject, its defects as well as its advantages. Gradually +introducing the mention of the dangers to the Tradesmen, the +Professional Classes and the Gentlemen, he silenced the rising murmurs +of the Isosceles by reminding them that, in spite of all these defects, +he was willing to accept the Bill if it was approved by the majority. +But it was manifest that all, except the Isosceles, were moved by his +words and were either neutral or averse to the Bill. + +Turning now to the Workmen he asserted that their interests must not be +neglected, and that, if they intended to accept the Colour Bill, they +ought at least to do so with full view of the consequences. Many of +them, he said, were on the point of being admitted to the class of the +Regular Triangles; others anticipated for their children a distinction +they could not hope for themselves. That honourable ambition would now +have to be sacrificed. With the universal adoption of Colour, all +distinctions would cease; Regularity would be confused with +Irregularity; development would give place to retrogression; the +Workman would in a few generations be degraded to the level of the +Military, or even the Convict Class; political power would be in the +hands of the greatest number, that is to say the Criminal Classes, who +were already more numerous than the Workmen, and would soon out-number +all the other Classes put together when the usual Compensative Laws of +Nature were violated. + +A subdued murmur of assent ran through the ranks of the Artisans, and +Chromatistes, in alarm, attempted to step forward and address them. +But he found himself encompassed with guards and forced to remain +silent while the Chief Circle in a few impassioned words made a final +appeal to the Women, exclaiming that, if the Colour Bill passed, no +marriage would henceforth be safe, no woman's honour secure; fraud, +deception, hypocrisy would pervade every household; domestic bliss +would share the fate of the Constitution and pass to speedy perdition. +"Sooner than this," he cried, "Come death." + +At these words, which were the preconcerted signal for action, the +Isosceles Convicts fell on and transfixed the wretched Chromatistes; +the Regular Classes, opening their ranks, made way for a band of Women +who, under direction of the Circles, moved, back foremost, invisibly +and unerringly upon the unconscious soldiers; the Artisans, imitating +the example of their betters, also opened their ranks. Meantime bands +of Convicts occupied every entrance with an impenetrable phalanx. + +The battle, or rather carnage, was of short duration. Under the +skillful generalship of the Circles almost every Woman's charge was +fatal and very many extracted their sting uninjured, ready for a second +slaughter. But no second blow was needed; the rabble of the Isosceles +did the rest of the business for themselves. Surprised, leader-less, +attacked in front by invisible foes, and finding egress cut off by the +Convicts behind them, they at once--after their manner--lost all +presence of mind, and raised the cry of "treachery". This sealed their +fate. Every Isosceles now saw and felt a foe in every other. In half +an hour not one of that vast multitude was living; and the fragments of +seven score thousand of the Criminal Class slain by one another's +angles attested the triumph of Order. + +The Circles delayed not to push their victory to the uttermost. The +Working Men they spared but decimated. The Militia of the Equilaterals +was at once called out; and every Triangle suspected of Irregularity on +reasonable grounds, was destroyed by Court Martial, without the +formality of exact measurement by the Social Board. The homes of the +Military and Artisan classes were inspected in a course of visitations +extending through upwards of a year; and during that period every town, +village, and hamlet was systematically purged of that excess of the +lower orders which had been brought about by the neglect to pay the +tribute of Criminals to the Schools and University, and by the +violation of the other natural Laws of the Constitution of Flatland. +Thus the balance of classes was again restored. + +Needless to say that henceforth the use of Colour was abolished, and +its possession prohibited. Even the utterance of any word denoting +Colour, except by the Circles or by qualified scientific teachers, was +punished by a severe penalty. Only at our University in some of the +very highest and most esoteric classes--which I myself have never been +privileged to attend--it is understood that the sparing use of Colour +is still sanctioned for the purpose of illustrating some of the deeper +problems of mathematics. But of this I can only speak from hearsay. + +Elsewhere in Flatland, Colour is now non-existent. The art of making +it is known to only one living person, the Chief Circle for the time +being; and by him it is handed down on his death-bed to none but his +Successor. One manufactory alone produces it; and, lest the secret +should be betrayed, the Workmen are annually consumed, and fresh ones +introduced. So great is the terror with which even now our Aristocracy +looks back to the far-distant days of the agitation for the Universal +Colour Bill. + + + + +Section 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 structures of +wood, stone, or brick, although of course we have no hands, nor can we +lay foundations as you can, nor avail ourselves of the lateral pressure +of the earth; the manner in which the rain originates in the intervals +between our various zones, so that the northern regions do not +intercept the moisture from falling on the southern; the nature of our +hills and mines, our trees and vegetables, our seasons and harvests; +our Alphabet and method of writing, adapted to our linear tablets; +these and a hundred other details of our physical existence I must pass +over, nor do I mention them now except to indicate to my readers that +their omission proceeds not from forgetfulness on the part of the +author, but from his regard for the time of the Reader. + +Yet before I proceed to my legitimate subject some few final remarks +will no doubt be expected by my Readers upon those pillars and +mainstays of the Constitution of Flatland, the controllers of our +conduct and shapers of our destiny, the objects of universal homage and +almost of adoration: need I say that I mean our Circles or Priests? + +When I call them Priests, let me not be understood as meaning no more +than the term denotes with you. With us, our Priests are +Administrators of all Business, Art, and Science; Directors of Trade, +Commerce, Generalship, Architecture, Engineering, Education, +Statesmanship, Legislature, Morality, Theology; doing nothing +themselves, they are the Causes of everything worth doing, that is done +by others. + +Although popularly everyone called a Circle is deemed a Circle, yet +among the better educated Classes it is known that no Circle is really +a Circle, but only a Polygon with a very large number of very small +sides. As the number of the sides increases, a Polygon approximates to +a Circle; and, when the number is very great indeed, say for example +three or four hundred, it is extremely difficult for the most delicate +touch to feel any polygonal angles. Let me say rather, it WOULD be +difficult: for, as I have shown above, Recognition by Feeling is +unknown among the highest society, and to FEEL a Circle would be +considered a most audacious insult. This habit of abstention from +Feeling in the best society enables a Circle the more easily to sustain +the veil of mystery in which, from his earliest years, he is wont to +enwrap the exact nature of his Perimeter or Circumference. Three feet +being the average Perimeter it follows that, in a Polygon of three +hundred sides each side will be no more than the hundredth part of a +foot in length, or little more than the tenth part of an inch; and in a +Polygon of six or seven hundred sides the sides are little larger than +the diameter of a Spaceland pin-head. It is always assumed, by +courtesy, that the Chief Circle for the time being has ten thousand +sides. + +The ascent of the posterity of the Circles in the social scale is not +restricted, as it is among the lower Regular classes, by the Law of +Nature which limits the increase of sides to one in each generation. +If it were so, the number of sides in a Circle would be a mere question +of pedigree and arithmetic, and the four hundred and ninety-seventh +descendant of an Equilateral Triangle would necessarily be a Polygon +with five hundred sides. But this is not the case. Nature's Law +prescribes two antagonistic decrees affecting Circular propagation; +first, that as the race climbs higher in the scale of development, so +development shall proceed at an accelerated pace; second, that in the +same proportion, the race shall become less fertile. Consequently in +the home of a Polygon of four or five hundred sides it is rare to find +a son; more than one is never seen. On the other hand the son of a +five-hundred-sided Polygon has been known to possess five hundred and +fifty, or even six hundred sides. + +Art also steps in to help the process of the higher Evolution. Our +physicians have discovered that the small and tender sides of an infant +Polygon of the higher class can be fractured, and his whole frame +re-set, with such exactness that a Polygon of two or three hundred +sides sometimes--by no means always, for the process is attended with +serious risk--but sometimes overleaps two or three hundred generations, +and as it were doubles at a stroke, the number of his progenitors and +the nobility of his descent. + +Many a promising child is sacrificed in this way. Scarcely one out of +ten survives. Yet so strong is the parental ambition among those +Polygons who are, as it were, on the fringe of the Circular class, that +it is very rare to find a Nobleman of that position in society, who has +neglected to place his first-born in the Circular Neo-Therapeutic +Gymnasium before he has attained the age of a month. + +One year determines success or failure. At the end of that time the +child has, in all probability, added one more to the tombstones that +crowd the Neo-Therapeutic Cemetery; but on rare occasions a glad +procession bears back the little one to his exultant parents, no longer +a Polygon, but a Circle, at least by courtesy: and a single instance of +so blessed a result induces multitudes of Polygonal parents to submit +to similar domestic sacrifices, which have a dissimilar issue. + + + + +Section 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 sympathy in +the vain belief that conduct depends upon will, effort, training, +encouragement, praise, or anything else but Configuration. It was +Pantocyclus--the illustrious Circle mentioned above, as the queller of +the Colour Revolt--who first convinced mankind that Configuration makes +the man; that if, for example, you are born an Isosceles with two +uneven sides, you will assuredly go wrong unless you have them made +even--for which purpose you must go to the Isosceles Hospital; +similarly, if you are a Triangle, or Square, or even a Polygon, born +with any Irregularity, you must be taken to one of the Regular +Hospitals to have your disease cured; otherwise you will end your days +in the State Prison or by the angle of the State Executioner. + +All faults or defects, from the slightest misconduct to the most +flagitious crime, Pantocyclus attributed to some deviation from perfect +Regularity in the bodily figure, caused perhaps (if not congenital) by +some collision in a crowd; by neglect to take exercise, or by taking +too much of it; or even by a sudden change of temperature, resulting in +a shrinkage or expansion in some too susceptible part of the frame. +Therefore, concluded that illustrious Philosopher, neither good conduct +nor bad conduct is a fit subject, in any sober estimation, for either +praise or blame. For why should you praise, for example, the integrity +of a Square who faithfully defends the interests of his client, when +you ought in reality rather to admire the exact precision of his right +angles? Or again, why blame a lying, thievish Isosceles when you ought +rather to deplore the incurable inequality of his sides? + +Theoretically, this doctrine is unquestionable; but it has practical +drawbacks. In dealing with an Isosceles, if a rascal pleads that he +cannot help stealing because of his unevenness, you reply that for that +very reason, because he cannot help being a nuisance to his neighbours, +you, the Magistrate, cannot help sentencing him to be consumed--and +there's an end of the matter. But in little domestic difficulties, +where the penalty of consumption, or death, is out of the question, +this theory of Configuration sometimes comes in awkwardly; and I must +confess that occasionally when one of my own Hexagonal Grandsons pleads +as an excuse for his disobedience that a sudden change of the +temperature has been too much for his Perimeter, and that I ought to +lay the blame not on him but on his Configuration, which can only be +strengthened by abundance of the choicest sweetmeats, I neither see my +way logically to reject, nor practically to accept, his conclusions. + +For my own part, I find it best to assume that a good sound scolding or +castigation has some latent and strengthening influence on my +Grandson's Configuration; though I own that I have no grounds for +thinking so. At all events I am not alone in my way of extricating +myself from this dilemma; for I find that many of the highest Circles, +sitting as Judges in law courts, use praise and blame towards Regular +and Irregular Figures; and in their homes I know by experience that, +when scolding their children, they speak about "right" or "wrong" as +vehemently and passionately as if they believed that these names +represented real existences, and that a human Figure is really capable +of choosing between them. + +Constantly carrying out their policy of making Configuration the +leading idea in every mind, the Circles reverse the nature of that +Commandment which in Spaceland regulates the relations between parents +and children. With you, children are taught to honour their parents; +with us--next to the Circles, who are the chief object of universal +homage--a man is taught to honour his Grandson, if he has one; or, if +not, his Son. By "honour", however, is by no means meant "indulgence", +but a reverent regard for their highest interests: and the Circles +teach that the duty of fathers is to subordinate their own interests to +those of posterity, thereby advancing the welfare of the whole State as +well as that of their own immediate descendants. + +The weak point in the system of the Circles--if a humble Square may +venture to speak of anything Circular as containing any element of +weakness--appears to me to be found in their relations with Women. + +As it is of the utmost importance for Society that Irregular births +should be discouraged, it follows that no Woman who has any +Irregularities in her ancestry is a fit partner for one who desires +that his posterity should rise by regular degrees in the social scale. + +Now the Irregularity of a Male is a matter of measurement; but as all +Women are straight, and therefore visibly Regular so to speak, one has +to devise some other means of ascertaining what I may call their +invisible Irregularity, that is to say their potential Irregularities +as regards possible offspring. This is effected by carefully-kept +pedigrees, which are preserved and supervised by the State; and without +a certified pedigree no Woman is allowed to marry. + +Now it might have been supposed that a Circle--proud of his ancestry +and regardful for a posterity which might possibly issue hereafter in a +Chief Circle--would be more careful than any other to choose a wife who +had no blot on her escutcheon. But it is not so. The care in choosing +a Regular wife appears to diminish as one rises in the social scale. +Nothing would induce an aspiring Isosceles, who had hopes of generating +an Equilateral Son, to take a wife who reckoned a single Irregularity +among her Ancestors; a Square or Pentagon, who is confident that his +family is steadily on the rise, does not inquire above the +five-hundredth generation; a Hexagon or Dodecagon is even more careless +of the wife's pedigree; but a Circle has been known deliberately to +take a wife who has had an Irregular Great-Grandfather, and all because +of some slight superiority of lustre, or because of the charms of a low +voice--which, with us, even more than you, is thought "an excellent +thing in Woman". + +Such ill-judged marriages are, as might be expected, barren, if they do +not result in positive Irregularity or in diminution of sides; but none +of these evils have hitherto proved sufficiently deterrent. The loss +of a few sides in a highly-developed Polygon is not easily noticed, and +is sometimes compensated by a successful operation in the +Neo-Therapeutic Gymnasium, as I have described above; and the Circles +are too much disposed to acquiesce in infecundity as a Law of the +superior development. Yet, if this evil be not arrested, the gradual +diminution of the Circular class may soon become more rapid, and the +time may be not far distant when, the race being no longer able to +produce a Chief Circle, the Constitution of Flatland must fall. + +One other word of warning suggests itself to me, though I cannot so +easily mention a remedy; and this also refers to our relations with +Women. About three hundred years ago, it was decreed by the Chief +Circle that, since women are deficient in Reason but abundant in +Emotion, they ought no longer to be treated as rational, nor receive +any mental education. The consequence was that they were no longer +taught to read, nor even to master Arithmetic enough to enable them to +count the angles of their husband or children; and hence they sensibly +declined during each generation in intellectual power. And this system +of female non-education or quietism still prevails. + +My fear is that, with the best intentions, this policy has been carried +so far as to react injuriously on the Male Sex. + +For the consequence is that, as things now are, we Males have to lead a +kind of bi-lingual, and I may almost say bi-mental, existence. With +Women, we speak of "love", "duty", "right", "wrong", "pity", "hope", +and other irrational and emotional conceptions, which have no +existence, and the fiction of which has no object except to control +feminine exuberances; but among ourselves, and in our books, we have an +entirely different vocabulary and I may almost say, idiom. "Love" then +becomes "the anticipation of benefits"; "duty" becomes "necessity" or +"fitness"; and other words are correspondingly transmuted. Moreover, +among Women, we use language implying the utmost deference for their +Sex; and they fully believe that the Chief Circle Himself is not more +devoutly adored by us than they are: but behind their backs they are +both regarded and spoken of--by all except the very young--as being +little better than "mindless organisms". + +Our Theology also in the Women's chambers is entirely different from +our Theology elsewhere. + +Now my humble fear is that this double training, in language as well as +in thought, imposes somewhat too heavy a burden upon the young, +especially when, at the age of three years old, they are taken from the +maternal care and taught to unlearn the old language--except for the +purpose of repeating it in the presence of their Mothers and +Nurses--and to learn the vocabulary and idiom of science. Already +methinks I discern a weakness in the grasp of mathematical truth at the +present time as compared with the more robust intellect of our +ancestors three hundred years ago. I say nothing of the possible +danger if a Woman should ever surreptitiously learn to read and convey +to her Sex the result of her perusal of a single popular volume; nor of +the possibility that the indiscretion or disobedience of some infant +Male might reveal to a Mother the secrets of the logical dialect. On +the simple ground of the enfeebling of the Male intellect, I rest this +humble appeal to the highest Authorities to reconsider the regulations +of Female education. + + + + + + +PART II: OTHER WORLDS + +"O brave new worlds, that have such people in them!" + + + + + + +Section 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, and, as nearly as I could judge, with +the same velocity. + +A noise of confused, multitudinous chirping or twittering issued from +them at intervals as long as they were moving; but sometimes they +ceased from motion, and then all was silence. + +Approaching one of the largest of what I thought to be Women, I +accosted her, but received no answer. A second and a third appeal on +my part were equally ineffectual. Losing patience at what appeared to +me intolerable rudeness, I brought my mouth into a position full in +front of her mouth so as to intercept her motion, and loudly repeated +my question, "Woman, what signifies this concourse, and this strange +and confused chirping, and this monotonous motion to and fro in one and +the same Straight Line?" + + +[Illustration 6] + +[ASCII approximation follows] + + + My view of Lineland + + --------- + | | + | Myself| + | | + My eye o-------- + + + Women A boy Men The KING Men A boy Women + + + + + - --- -- -- -- -- (>----<) -- -- -- -- --- - + + + + + ^ ^ + The KING'S eyes + much larger than the reality + shewing that HIS MAJESTY + could see nothing but a point. + + +"I am no Woman," replied the small Line. "I am the Monarch of the +world. But thou, whence intrudest thou into my realm of Lineland?" +Receiving this abrupt reply, I begged pardon if I had in any way +startled or molested his Royal Highness; and describing myself as a +stranger I besought the King to give me some account of his dominions. +But I had the greatest possible difficulty in obtaining any information +on points that really interested me; for the Monarch could not refrain +from constantly assuming that whatever was familiar to him must also be +known to me and that I was simulating ignorance in jest. However, by +persevering questions I elicited the following facts: + +It seemed that this poor ignorant Monarch--as he called himself--was +persuaded that the Straight Line which he called his Kingdom, and in +which he passed his existence, constituted the whole of the world, and +indeed the whole of Space. Not being able either to move or to see, +save in his Straight Line, he had no conception of anything out of it. +Though he had heard my voice when I first addressed him, the sounds had +come to him in a manner so contrary to his experience that he had made +no answer, "seeing no man", as he expressed it, "and hearing a voice as +it were from my own intestines." Until the moment when I placed my +mouth in his World, he had neither seen me, nor heard anything except +confused sounds beating against--what I called his side, but what he +called his INSIDE or STOMACH; nor had he even now the least conception +of the region from which I had come. Outside his World, or Line, all +was a blank to him; nay, not even a blank, for a blank implies Space; +say, rather, all was non-existent. + +His subjects--of whom the small Lines were men and the Points +Women--were all alike confined in motion and eye-sight to that single +Straight Line, which was their World. It need scarcely be added that +the whole of their horizon was limited to a Point; nor could any one +ever see anything but a Point. Man, woman, child, thing--each was a +Point to the eye of a Linelander. Only by the sound of the voice could +sex or age be distinguished. Moreover, as each individual occupied the +whole of the narrow path, so to speak, which constituted his Universe, +and no one could move to the right or left to make way for passers by, +it followed that no Linelander could ever pass another. Once +neighbours, always neighbours. Neighbourhood with them was like +marriage with us. Neighbours remained neighbours till death did them +part. + +Such a life, with all vision limited to a Point, and all motion to a +Straight Line, seemed to me inexpressibly dreary; and I was surprised +to note the vivacity and cheerfulness of the King. Wondering whether +it was possible, amid circumstances so unfavourable to domestic +relations, to enjoy the pleasures of conjugal union, I hesitated for +some time to question his Royal Highness on so delicate a subject; but +at last I plunged into it by abruptly inquiring as to the health of his +family. "My wives and children," he replied, "are well and happy." + +Staggered at this answer--for in the immediate proximity of the Monarch +(as I had noted in my dream before I entered Lineland) there were none +but Men--I ventured to reply, "Pardon me, but I cannot imagine how your +Royal Highness can at any time either see or approach their Majesties, +when there are at least half a dozen intervening individuals, whom you +can neither see through, nor pass by? Is it possible that in Lineland +proximity is not necessary for marriage and for the generation of +children?" + +"How can you ask so absurd a question?" replied the Monarch. "If it +were indeed as you suggest, the Universe would soon be depopulated. +No, no; neighbourhood is needless for the union of hearts; and the +birth of children is too important a matter to have been allowed to +depend upon such an accident as proximity. You cannot be ignorant of +this. Yet since you are pleased to affect ignorance, I will instruct +you as if you were the veriest baby in Lineland. Know, then, that +marriages are consummated by means of the faculty of sound and the +sense of hearing. + +"You are of course aware that every Man has two mouths or voices--as +well as two eyes--a bass at one and a tenor at the other of his +extremities. I should not mention this, but that I have been unable to +distinguish your tenor in the course of our conversation." I replied +that I had but one voice, and that I had not been aware that his Royal +Highness had two. "That confirms my impression," said the King, "that +you are not a Man, but a feminine Monstrosity with a bass voice, and an +utterly uneducated ear. But to continue. + +"Nature having herself ordained that every Man should wed two wives--" +"Why two?" asked I. "You carry your affected simplicity too far", he +cried. "How can there be a completely harmonious union without the +combination of the Four in One, viz. the Bass and Tenor of the Man and +the Soprano and Contralto of the two Women?" "But supposing," said I, +"that a man should prefer one wife or three?" "It is impossible," he +said; "it is as inconceivable as that two and one should make five, or +that the human eye should see a Straight Line." I would have +interrupted him; but he proceeded as follows: + +"Once in the middle of each week a Law of Nature compels us to move to +and fro with a rhythmic motion of more than usual violence, which +continues for the time you would take to count a hundred and one. In +the midst of this choral dance, at the fifty-first pulsation, the +inhabitants of the Universe pause in full career, and each individual +sends forth his richest, fullest, sweetest strain. It is in this +decisive moment that all our marriages are made. So exquisite is the +adaptation of Bass to Treble, of Tenor to Contralto, that oftentimes +the Loved Ones, though twenty thousand leagues away, recognize at once +the responsive note of their destined Lover; and, penetrating the +paltry obstacles of distance, Love unites the three. The marriage in +that instant consummated results in a threefold Male and Female +offspring which takes its place in Lineland." + +"What! Always threefold?" said I. "Must one wife then always have +twins?" + +"Bass-voiced Monstrosity! yes," replied the King. "How else could the +balance of the Sexes be maintained, if two girls were not born for +every boy? Would you ignore the very Alphabet of Nature?" He ceased, +speechless for fury; and some time elapsed before I could induce him to +resume his narrative. + +"You will not, of course, suppose that every bachelor among us finds +his mates at the first wooing in this universal Marriage Chorus. On +the contrary, the process is by most of us many times repeated. Few +are the hearts whose happy lot it is at once to recognize in each +other's voices the partner intended for them by Providence, and to fly +into a reciprocal and perfectly harmonious embrace. With most of us +the courtship is of long duration. The Wooer's voices may perhaps +accord with one of the future wives, but not with both; or not, at +first, with either; or the Soprano and Contralto may not quite +harmonize. In such cases Nature has provided that every weekly Chorus +shall bring the three Lovers into closer harmony. Each trial of voice, +each fresh discovery of discord, almost imperceptibly induces the less +perfect to modify his or her vocal utterance so as to approximate to +the more perfect. And after many trials and many approximations, the +result is at last achieved. There comes a day at last, when, while the +wonted Marriage Chorus goes forth from universal Lineland, the three +far-off Lovers suddenly find themselves in exact harmony, and, before +they are awake, the wedded Triplet is rapt vocally into a duplicate +embrace; and Nature rejoices over one more marriage and over three more +births." + + + + +Section 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 speak of an impossibility," interrupted the King; +"you must have seen a vision; for to detect the difference between a +Line and a Point by the sense of sight is, as every one knows, in the +nature of things, impossible; but it can be detected by the sense of +hearing, and by the same means my shape can be exactly ascertained. +Behold me--I am a Line, the longest in Lineland, over six inches of +Space--" "Of Length", I ventured to suggest. "Fool," said he, "Space +is Length. Interrupt me again, and I have done." + +I apologized; but he continued scornfully, "Since you are impervious to +argument, you shall hear with your ears how by means of my two voices I +reveal my shape to my Wives, who are at this moment six thousand miles +seventy yards two feet eight inches away, the one to the North, the +other to the South. Listen, I call to them." + +He chirruped, and then complacently continued: "My wives at this +moment receiving the sound of one of my voices, closely followed by the +other, and perceiving that the latter reaches them after an interval in +which sound can traverse 6.457 inches, infer that one of my mouths is +6.457 inches further from them than the other, and accordingly know my +shape to be 6.457 inches. But you will of course understand that my +wives do not make this calculation every time they hear my two voices. +They made it, once for all, before we were married. But they COULD +make it at any time. And in the same way I can estimate the shape of +any of my Male subjects by the sense of sound." + +"But how," said I, "if a Man feigns a Woman's voice with one of his two +voices, or so disguises his Southern voice that it cannot be recognized +as the echo of the Northern? May not such deceptions cause great +inconvenience? And have you no means of checking frauds of this kind +by commanding your neighbouring subjects to feel one another?" This of +course was a very stupid question, for feeling could not have answered +the purpose; but I asked with the view of irritating the Monarch, and I +succeeded perfectly. + +"What!" cried he in horror, "explain your meaning." "Feel, touch, come +into contact," I replied. "If you mean by FEELING," said the King, +"approaching so close as to leave no space between two individuals, +know, Stranger, that this offence is punishable in my dominions by +death. And the reason is obvious. The frail form of a Woman, being +liable to be shattered by such an approximation, must be preserved by +the State; but since Women cannot be distinguished by the sense of +sight from Men, the Law ordains universally that neither Man nor Woman +shall be approached so closely as to destroy the interval between the +approximator and the approximated. + +"And indeed what possible purpose would be served by this illegal and +unnatural excess of approximation which you call TOUCHING, when all the +ends of so brutal and coarse a process are attained at once more easily +and more exactly by the sense of hearing? As to your suggested danger +of deception, it is non-existent: for the Voice, being the essence of +one's Being, cannot be thus changed at will. But come, suppose that I +had the power of passing through solid things, so that I could +penetrate my subjects, one after another, even to the number of a +billion, verifying the size and distance of each by the sense of +FEELING: how much time and energy would be wasted in this clumsy and +inaccurate method! Whereas now, in one moment of audition, I take as +it were the census and statistics, local, corporeal, mental and +spiritual, of every living being in Lineland. Hark, only hark!" + +So saying he paused and listened, as if in an ecstasy, to a sound which +seemed to me no better than a tiny chirping from an innumerable +multitude of lilliputian grasshoppers. + +"Truly," replied I, "your sense of hearing serves you in good stead, +and fills up many of your deficiencies. But permit me to point out +that your life in Lineland must be deplorably dull. To see nothing but +a Point! Not even to be able to contemplate a Straight Line! Nay, not +even to know what a Straight Line is! To see, yet be cut off from +those Linear prospects which are vouchsafed to us in Flatland! Better +surely to have no sense of sight at all than to see so little! I grant +you I have not your discriminative faculty of hearing; for the concert +of all Lineland which gives you such intense pleasure, is to me no +better than a multitudinous twittering or chirping. But at least I can +discern, by sight, a Line from a Point. And let me prove it. Just +before I came into your kingdom, I saw you dancing from left to right, +and then from right to left, with Seven Men and a Woman in your +immediate proximity on the left, and eight Men and two Women on your +right. Is not this correct?" + +"It is correct," said the King, "so far as the numbers and sexes are +concerned, though I know not what you mean by 'right' and 'left'. But +I deny that you saw these things. For how could you see the Line, that +is to say the inside, of any Man? But you must have heard these +things, and then dreamed that you saw them. And let me ask what you +mean by those words 'left' and 'right'. I suppose it is your way of +saying Northward and Southward." + +"Not so," replied I; "besides your motion of Northward and Southward, +there is another motion which I call from right to left." + +KING. Exhibit to me, if you please, this motion from left to right. + +I. Nay, that I cannot do, unless you could step out of your Line +altogether. + +KING. Out of my Line? Do you mean out of the world? Out of Space? + +I. Well, yes. Out of YOUR World. Out of YOUR Space. For your Space +is not the true Space. True Space is a Plane; but your Space is only a +Line. + +KING. If you cannot indicate this motion from left to right by +yourself moving in it, then I beg you to describe it to me in words. + +I. If you cannot tell your right side from your left, I fear that no +words of mine can make my meaning clear to you. But surely you cannot +be ignorant of so simple a distinction. + +KING. I do not in the least understand you. + +I. Alas! How shall I make it clear? When you move straight on, does +it not sometimes occur to you that you COULD move in some other way, +turning your eye round so as to look in the direction towards which +your side is now fronting? In other words, instead of always moving in +the direction of one of your extremities, do you never feel a desire to +move in the direction, so to speak, of your side? + +KING. Never. And what do you mean? How can a man's inside "front" in +any direction? Or how can a man move in the direction of his inside? + +I. Well then, since words cannot explain the matter, I will try deeds, +and will move gradually out of Lineland in the direction which I desire +to indicate to you. + +At the word I began to move my body out of Lineland. As long as any +part of me remained in his dominion and in his view, the King kept +exclaiming, "I see you, I see you still; you are not moving." But when +I had at last moved myself out of his Line, he cried in his shrillest +voice, "She is vanished; she is dead." "I am not dead," replied I; "I +am simply out of Lineland, that is to say, out of the Straight Line +which you call Space, and in the true Space, where I can see things as +they are. And at this moment I can see your Line, or side--or inside +as you are pleased to call it; and I can see also the Men and Women on +the North and South of you, whom I will now enumerate, describing their +order, their size, and the interval between each." + + +[Illustration 7] + +[ASCII approximation follows] + + + My body just before I disappeared + +---------+ + |\ \ \ \ \| + |\ \ \ \ \| + |\ \ \ \ \| + Lineland ----> |\ \ \ \ \| The King + --------------------+---------+--------------======== + + +When I had done this at great length, I cried triumphantly, "Does that +at last convince you?" And, with that, I once more entered Lineland, +taking up the same position as before. + +But the Monarch replied, "If you were a Man of sense--though, as you +appear to have only one voice I have little doubt you are not a Man but +a Woman--but, if you had a particle of sense, you would listen to +reason. You ask me to believe that there is another Line besides that +which my senses indicate, and another motion besides that of which I am +daily conscious. I, in return, ask you to describe in words or +indicate by motion that other Line of which you speak. Instead of +moving, you merely exercise some magic art of vanishing and returning +to sight; and instead of any lucid description of your new World, you +simply tell me the numbers and sizes of some forty of my retinue, facts +known to any child in my capital. Can anything be more irrational or +audacious? Acknowledge your folly or depart from my dominions." + +Furious at his perversity, and especially indignant that he professed +to be ignorant of my sex, I retorted in no measured terms, "Besotted +Being! You think yourself the perfection of existence, while you are +in reality the most imperfect and imbecile. You profess to see, +whereas you can see nothing but a Point! You plume yourself on +inferring the existence of a Straight Line; but I CAN SEE Straight +Lines, and infer the existence of Angles, Triangles, Squares, +Pentagons, Hexagons, and even Circles. Why waste more words? Suffice +it that I am the completion of your incomplete self. You are a Line, +but I am a Line of Lines, called in my country a Square: and even I, +infinitely superior though I am to you, am of little account among the +great nobles of Flatland, whence I have come to visit you, in the hope +of enlightening your ignorance." + +Hearing these words the King advanced towards me with a menacing cry as +if to pierce me through the diagonal; and in that same moment there +arose from myriads of his subjects a multitudinous war-cry, increasing +in vehemence till at last methought it rivalled the roar of an army of +a hundred thousand Isosceles, and the artillery of a thousand +Pentagons. Spell-bound and motionless, I could neither speak nor move +to avert the impending destruction; and still the noise grew louder, +and the King came closer, when I awoke to find the breakfast-bell +recalling me to the realities of Flatland. + + + + +Section 15. Concerning a Stranger from Spaceland + + + +From dreams I proceed to facts. + +It was the last day of the 1999th year of our era. The pattering of +the rain had long ago announced nightfall; and I was sitting 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. + +[Note: 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 of the word) +than one of your soles or flounders. + +Nevertheless, we perfectly well recognize the different mental states +of volition implied in "lying", "sitting", and "standing", which are to +some extent indicated to a beholder by a slight increase of lustre +corresponding to the increase of volition. + +But on this, and a thousand other kindred subjects, time forbids me to +dwell.] + +My four Sons and two orphan Grandchildren had retired to their several +apartments; and my wife alone remained with me to see the old +Millennium out and the new one in. + +I was rapt in thought, pondering in my mind some words that had +casually issued from the mouth of my youngest Grandson, a most +promising young Hexagon of unusual brilliancy and perfect angularity. +His uncles and I had been giving him his usual practical lesson in +Sight Recognition, turning ourselves upon our centres, now rapidly, now +more slowly, and questioning him as to our positions; and his answers +had been so satisfactory that I had been induced to reward him by +giving him a few hints on Arithmetic, as applied to Geometry. + +Taking nine Squares, each an inch every way, I had put them together so +as to make one large Square, with a side of three inches, and I had +hence proved to my little Grandson that--though it was impossible for +us to SEE the inside of the Square--yet we might ascertain the number +of square inches in a Square by simply squaring the number of inches in +the side: "and thus," said I, "we know that 3^2, or 9, represents the +number of square inches in a Square whose side is 3 inches long." + +The little Hexagon meditated on this a while and then said to me; "But +you have been teaching me to raise numbers to the third power: I +suppose 3^3 must mean something in Geometry; what does it mean?" +"Nothing at all," replied I, "not at least in Geometry; for Geometry +has only Two Dimensions." And then I began to shew the boy how a Point +by moving through a length of three inches makes a Line of three +inches, which may be represented by 3; and how a Line of three inches, +moving parallel to itself through a length of three inches, makes a +Square of three inches every way, which may be represented by 3^2. + +Upon this, my Grandson, again returning to his former suggestion, took +me up rather suddenly and exclaimed, "Well, then, if a Point by moving +three inches, makes a Line of three inches represented by 3; and if a +straight Line of three inches, moving parallel to itself, makes a +Square of three inches every way, represented by 3^2; it must be that a +Square of three inches every way, moving somehow parallel to itself +(but I don't see how) must make Something else (but I don't see what) +of three inches every way--and this must be represented by 3^3." + +"Go to bed," said I, a little ruffled by this interruption: "if you +would talk less nonsense, you would remember more sense." + +So my Grandson had disappeared in disgrace; and there I sat by my +Wife's side, endeavouring to form a retrospect of the year 1999 and of +the possibilities of the year 2000, but not quite able to shake off the +thoughts suggested by the prattle of my bright little Hexagon. Only a +few sands now remained in the half-hour glass. Rousing myself from my +reverie I turned the glass Northward for the last time in the old +Millennium; and in the act, I exclaimed aloud, "The boy is a fool." + +Straightway I became conscious of a Presence in the room, and a +chilling breath thrilled through my very being. "He is no such thing," +cried my Wife, "and you are breaking the Commandments in thus +dishonouring your own Grandson." But I took no notice of her. Looking +round in every direction I could see nothing; yet still I FELT a +Presence, and shivered as the cold whisper came again. I started up. +"What is the matter?" said my Wife, "there is no draught; what are you +looking for? There is nothing." There was nothing; and I resumed my +seat, again exclaiming, "The boy is a fool, I say; 3^3 can have no +meaning in Geometry." At once there came a distinctly audible reply, +"The boy is not a fool; and 3^3 has an obvious Geometrical meaning." + +My Wife as well as myself heard the words, although she did not +understand their meaning, and both of us sprang forward in the +direction of the sound. What was our horror when we saw before us a +Figure! At the first glance it appeared to be a Woman, seen sideways; +but a moment's observation shewed me that the extremities passed into +dimness too rapidly to represent one of the Female Sex; and I should +have thought it a Circle, only that it seemed to change its size in a +manner impossible for a Circle or for any regular Figure of which I had +had experience. + +But my Wife had not my experience, nor the coolness necessary to note +these characteristics. With the usual hastiness and unreasoning +jealousy of her Sex, she flew at once to the conclusion that a Woman +had entered the house through some small aperture. "How comes this +person here?" she exclaimed, "you promised me, my dear, that there +should be no ventilators in our new house." "Nor are there any," said +I; "but what makes you think that the stranger is a Woman? I see by my +power of Sight Recognition----" "Oh, I have no patience with your Sight +Recognition," replied she, "'Feeling is believing' and 'A Straight Line +to the touch is worth a Circle to the sight'"--two Proverbs, very +common with the Frailer Sex in Flatland. + +"Well," said I, for I was afraid of irritating her, "if it must be so, +demand an introduction." Assuming her most gracious manner, my Wife +advanced towards the Stranger, "Permit me, Madam, to feel and be felt +by----" then, suddenly recoiling, "Oh! it is not a Woman, and there +are no angles either, not a trace of one. Can it be that I have so +misbehaved to a perfect Circle?" + +"I am indeed, in a certain sense a Circle," replied the Voice, "and a +more perfect Circle than any in Flatland; but to speak more accurately, +I am many Circles in one." Then he added more mildly, "I have a +message, dear Madam, to your husband, which I must not deliver in your +presence; and, if you would suffer us to retire for a few minutes----" +But my Wife would not listen to the proposal that our august Visitor +should so incommode himself, and assuring the Circle that the hour of +her own retirement had long passed, with many reiterated apologies for +her recent indiscretion, she at last retreated to her apartment. + +I glanced at the half-hour glass. The last sands had fallen. The +third Millennium had begun. + + + + +Section 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 gradations 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 burglar or cut-throat, some monstrous Irregular Isosceles, +who, by feigning the voice of a Circle, had obtained admission somehow +into the house, and was now preparing to stab me with his acute angle. + +In a sitting-room, the absence of Fog (and the season happened to be +remarkably dry), made it difficult for me to trust to Sight +Recognition, especially at the short distance at which I was standing. +Desperate with fear, I rushed forward with an unceremonious, "You must +permit me, Sir--" and felt him. My Wife was right. There was not the +trace of an angle, not the slightest roughness or inequality: never in +my life had I met with a more perfect Circle. He remained motionless +while I walked round him, beginning from his eye and returning to it +again. Circular he was throughout, a perfectly satisfactory Circle; +there could not be a doubt of it. Then followed a dialogue, which I +will endeavour to set down as near as I can recollect it, omitting only +some of my profuse apologies--for I was covered with shame and +humiliation that I, a Square, should have been guilty of the +impertinence of feeling a Circle. It was commenced by the Stranger +with some impatience at the lengthiness of my introductory process. + +STRANGER. Have you felt me enough by this time? Are you not +introduced to me yet? + +I. Most illustrious Sir, excuse my awkwardness, which arises not from +ignorance of the usages of polite society, but from a little surprise +and nervousness, consequent on this somewhat unexpected visit. And I +beseech you to reveal my indiscretion to no one, and especially not to +my Wife. But before your Lordship enters into further communications, +would he deign to satisfy the curiosity of one who would gladly know +whence his Visitor came? + +STRANGER. From Space, from Space, Sir: whence else? + +I. Pardon me, my Lord, but is not your Lordship already in Space, your +Lordship and his humble servant, even at this moment? + +STRANGER. Pooh! what do you know of Space? Define Space. + +I. Space, my Lord, is height and breadth indefinitely prolonged. + +STRANGER. Exactly: you see you do not even know what Space is. You +think it is of Two Dimensions only; but I have come to announce to you +a Third--height, breadth, and length. + +I. Your Lordship is pleased to be merry. We also speak of length and +height, or breadth and thickness, thus denoting Two Dimensions by four +names. + +STRANGER. But I mean not only three names, but Three Dimensions. + +I. Would your Lordship indicate or explain to me in what direction is +the Third Dimension, unknown to me? + +STRANGER. I came from it. It is up above and down below. + +I. My Lord means seemingly that it is Northward and Southward. + +STRANGER. I mean nothing of the kind. I mean a direction in which you +cannot look, because you have no eye in your side. + +I. Pardon me, my Lord, a moment's inspection will convince your +Lordship that I have a perfect luminary at the juncture of two of my +sides. + +STRANGER. Yes: but in order to see into Space you ought to have an +eye, not on your Perimeter, but on your side, that is, on what you +would probably call your inside; but we in Spaceland should call it +your side. + +I. An eye in my inside! An eye in my stomach! Your Lordship jests. + +STRANGER. I am in no jesting humour. I tell you that I come from +Space, or, since you will not understand what Space means, from the +Land of Three Dimensions whence I but lately looked down upon your +Plane which you call Space forsooth. From that position of advantage I +discerned all that you speak of as SOLID (by which you mean "enclosed +on four sides"), your houses, your churches, your very chests and +safes, yes even your insides and stomachs, all lying open and exposed +to my view. + +I. Such assertions are easily made, my Lord. + +STRANGER. But not easily proved, you mean. But I mean to prove mine. + +When I descended here, I saw your four Sons, the Pentagons, each in his +apartment, and your two Grandsons the Hexagons; I saw your youngest +Hexagon remain a while with you and then retire to his room, leaving +you and your Wife alone. I saw your Isosceles servants, three in +number, in the kitchen at supper, and the little Page in the scullery. +Then I came here, and how do you think I came? + +I. Through the roof, I suppose. + +STRANGER. Not so. Your roof, as you know very well, has been recently +repaired, and has no aperture by which even a Woman could penetrate. I +tell you I come from Space. Are you not convinced by what I have told +you of your children and household? + +I. Your Lordship must be aware that such facts touching the belongings +of his humble servant might be easily ascertained by any one in the +neighbourhood possessing your Lordship's ample means of obtaining +information. + +STRANGER. (TO HIMSELF.) What must I do? Stay; one more argument +suggests itself to me. When you see a Straight Line--your wife, for +example--how many Dimensions do you attribute to her? + +I. Your Lordship would treat me as if I were one of the vulgar who, +being ignorant of Mathematics, suppose that a Woman is really a +Straight Line, and only of One Dimension. No, no, my Lord; we Squares +are better advised, and are as well aware as your Lordship that a +Woman, though popularly called a Straight Line, is, really and +scientifically, a very thin Parallelogram, possessing Two Dimensions, +like the rest of us, viz., length and breadth (or thickness). + +STRANGER. But the very fact that a Line is visible implies that it +possesses yet another Dimension. + +I. My Lord, I have just acknowledged that a Woman is broad as well as +long. We see her length, we infer her breadth; which, though very +slight, is capable of measurement. + +STRANGER. You do not understand me. I mean that when you see a Woman, +you ought--besides inferring her breadth--to see her length, and to SEE +what we call her HEIGHT; although that last Dimension is infinitesimal +in your country. If a Line were mere length without "height", it would +cease to occupy Space and would become invisible. Surely you must +recognize this? + +I. I must indeed confess that I do not in the least understand your +Lordship. When we in Flatland see a Line, we see length and +BRIGHTNESS. If the brightness disappears, the Line is extinguished, +and, as you say, ceases to occupy Space. But am I to suppose that your +Lordship gives to brightness the title of a Dimension, and that what we +call "bright" you call "high"? + +STRANGER. No, indeed. By "height" I mean a Dimension like your +length: only, with you, "height" is not so easily perceptible, being +extremely small. + +I. My Lord, your assertion is easily put to the test. You say I have +a Third Dimension, which you call "height". Now, Dimension implies +direction and measurement. Do but measure my "height", or merely +indicate to me the direction in which my "height" extends, and I will +become your convert. Otherwise, your Lordship's own understanding must +hold me excused. + +STRANGER. (TO HIMSELF.) I can do neither. How shall I convince him? +Surely a plain statement of facts followed by ocular demonstration +ought to suffice. --Now, Sir; listen to me. + +You are living on a Plane. What you style Flatland is the vast level +surface of what I may call a fluid, on, or in, the top of which you and +your countrymen move about, without rising above it or falling below it. + +I am not a plane Figure, but a Solid. You call me a Circle; but in +reality I am not a Circle, but an infinite number of Circles, of size +varying from a Point to a Circle of thirteen inches in diameter, one +placed on the top of the other. When I cut through your plane as I am +now doing, I make in your plane a section which you, very rightly, call +a Circle. For even a Sphere--which is my proper name in my own +country--if he manifest himself at all to an inhabitant of +Flatland--must needs manifest himself as a Circle. + +Do you not remember--for I, who see all things, discerned last night +the phantasmal vision of Lineland written upon your brain--do you not +remember, I say, how, when you entered the realm of Lineland, you were +compelled to manifest yourself to the King, not as a Square, but as a +Line, because that Linear Realm had not Dimensions enough to represent +the whole of you, but only a slice or section of you? In precisely the +same way, your country of Two Dimensions is not spacious enough to +represent me, a being of Three, but can only exhibit a slice or section +of me, which is what you call a Circle. + +The diminished brightness of your eye indicates incredulity. But now +prepare to receive proof positive of the truth of my assertions. You +cannot indeed see more than one of my sections, or Circles, at a time; +for you have no power to raise your eye out of the plane of Flatland; +but you can at least see that, as I rise in Space, so my sections +become smaller. See now, I will rise; and the effect upon your eye +will be that my Circle will become smaller and smaller till it dwindles +to a point and finally vanishes. + + +[Illustration 8] + +[ASCII approximation follows] + + + The Sphere on the + point of vanishing + (2) __-----__ + The Sphere with The Sphere rising / \ (3) + his section __-----__ / \ + at full size / \ | | + __-----__ / \ | | + / \ | | | | + / __ - __ \ | | \ / My + | -- -- | | __ --- __ | \ __ __ / Eye + --|-----------------|----\--__-------__--/------------===----------+(> + | -- __ __ -- | \ __ --- __ / + \ - / ----- + \ __ __ / + ----- + + +There was no "rising" that I could see; but he diminished and finally +vanished. I winked once or twice to make sure that I was not dreaming. +But it was no dream. For from the depths of nowhere came forth a +hollow voice--close to my heart it seemed--"Am I quite gone? Are you +convinced now? Well, now I will gradually return to Flatland and you +shall see my section become larger and larger." + +Every reader in Spaceland will easily understand that my mysterious +Guest was speaking the language of truth and even of simplicity. But +to me, proficient though I was in Flatland Mathematics, it was by no +means a simple matter. The rough diagram given above will make it +clear to any Spaceland child that the Sphere, ascending in the three +positions indicated there, must needs have manifested himself to me, or +to any Flatlander, as a Circle, at first of full size, then small, and +at last very small indeed, approaching to a Point. But to me, although +I saw the facts before me, the causes were as dark as ever. All that I +could comprehend was, that the Circle had made himself smaller and +vanished, and that he had now reappeared and was rapidly making himself +larger. + +When he regained his original size, he heaved a deep sigh; for he +perceived by my silence that I had altogether failed to comprehend him. +And indeed I was now inclining to the belief that he must be no Circle +at all, but some extremely clever juggler; or else that the old wives' +tales were true, and that after all there were such people as +Enchanters and Magicians. + +After a long pause he muttered to himself, "One resource alone remains, +if I am not to resort to action. I must try the method of Analogy." +Then followed a still longer silence, after which he continued our +dialogue. + +SPHERE. Tell me, Mr. Mathematician; if a Point moves Northward, and +leaves a luminous wake, what name would you give to the wake? + +I. A straight Line. + +SPHERE. And a straight Line has how many extremities? + +I. Two. + +SPHERE. Now conceive the Northward straight Line moving parallel to +itself, East and West, so that every point in it leaves behind it the +wake of a straight Line. What name will you give to the Figure thereby +formed? We will suppose that it moves through a distance equal to the +original straight Line. --What name, I say? + +I. A Square. + +SPHERE. And how many sides has a Square? How many angles? + +I. Four sides and four angles. + +SPHERE. Now stretch your imagination a little, and conceive a Square +in Flatland, moving parallel to itself upward. + +I. What? Northward? + +SPHERE. No, not Northward; upward; out of Flatland altogether. + +If it moved Northward, the Southern points in the Square would have to +move through the positions previously occupied by the Northern points. +But that is not my meaning. + +I mean that every Point in you--for you are a Square and will serve the +purpose of my illustration--every Point in you, that is to say in what +you call your inside, is to pass upwards through Space in such a way +that no Point shall pass through the position previously occupied by +any other Point; but each Point shall describe a straight Line of its +own. This is all in accordance with Analogy; surely it must be clear +to you. + +Restraining my impatience--for I was now under a strong temptation to +rush blindly at my Visitor and to precipitate him into Space, or out of +Flatland, anywhere, so that I could get rid of him--I replied:-- + +"And what may be the nature of the Figure which I am to shape out by +this motion which you are pleased to denote by the word 'upward'? I +presume it is describable in the language of Flatland." + +SPHERE. Oh, certainly. It is all plain and simple, and in strict +accordance with Analogy--only, by the way, you must not speak of the +result as being a Figure, but as a Solid. But I will describe it to +you. Or rather not I, but Analogy. + +We began with a single Point, which of course--being itself a +Point--has only ONE terminal Point. + +One Point produces a Line with TWO terminal Points. + +One Line produces a Square with FOUR terminal Points. + +Now you can give yourself the answer to your own question: 1, 2, 4, +are evidently in Geometrical Progression. What is the next number? + +I. Eight. + +SPHERE. Exactly. The one Square produces a SOMETHING-WHICH- +YOU-DO-NOT-AS-YET-KNOW-A-NAME-FOR-BUT-WHICH-WE-CALL-A-CUBE with EIGHT +terminal Points. Now are you convinced? + +I. And has this Creature sides, as well as angles or what you call +"terminal Points"? + +SPHERE. Of course; and all according to Analogy. But, by the way, not +what YOU call sides, but what WE call sides. You would call them +SOLIDS. + +I. And how many solids or sides will appertain to this Being whom I am +to generate by the motion of my inside in an "upward" direction, and +whom you call a Cube? + +SPHERE. How can you ask? And you a mathematician! The side of +anything is always, if I may so say, one Dimension behind the thing. +Consequently, as there is no Dimension behind a Point, a Point has 0 +sides; a Line, if I may say, has 2 sides (for the Points of a Line may +be called by courtesy, its sides); a Square has 4 sides; 0, 2, 4; what +Progression do you call that? + +I. Arithmetical. + +SPHERE. And what is the next number? + +I. Six. + +SPHERE. Exactly. Then you see you have answered your own question. +The Cube which you will generate will be bounded by six sides, that is +to say, six of your insides. You see it all now, eh? + +"Monster," I shrieked, "be thou juggler, enchanter, dream, or devil, no +more will I endure thy mockeries. Either thou or I must perish." And +saying these words I precipitated myself upon him. + + + + +Section 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; no edging to the right nor to +the left, but moving somehow out of the world, and vanishing to +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 man of sense and an accomplished mathematician--a +fit apostle for the Gospel of the Three Dimensions, which I am allowed +to preach once only in a thousand years: but now I know not how to +convince you. Stay, I have it. Deeds, and not words, shall proclaim +the truth. Listen, my friend. + +I have told you I can see from my position in Space the inside of all +things that you consider closed. For example, I see in yonder cupboard +near which you are standing, several of what you call boxes (but like +everything else in Flatland, they have no tops nor bottoms) full of +money; I see also two tablets of accounts. I am about to descend into +that cupboard and to bring you one of those tablets. I saw you lock +the cupboard half an hour ago, and I know you have the key in your +possession. But I descend from Space; the doors, you see, remain +unmoved. Now I am in the cupboard and am taking the tablet. Now I +have it. Now I ascend with it. + +I rushed to the closet and dashed the door open. One of the tablets +was gone. With a mocking laugh, the Stranger appeared in the other +corner of the room, and at the same time the tablet appeared upon the +floor. I took it up. There could be no doubt--it was the missing +tablet. + +I groaned with horror, doubting whether I was not out of my senses; but +the Stranger continued: "Surely you must now see that my explanation, +and no other, suits the phenomena. What you call Solid things are +really superficial; what you call Space is really nothing but a great +Plane. I am in Space, and look down upon the insides of the things of +which you only see the outsides. You could leave this Plane yourself, +if you could but summon up the necessary volition. A slight upward or +downward motion would enable you to see all that I can see. + +"The higher I mount, and the further I go from your Plane, the more I +can see, though of course I see it on a smaller scale. For example, I +am ascending; now I can see your neighbour the Hexagon and his family +in their several apartments; now I see the inside of the Theatre, ten +doors off, from which the audience is only just departing; and on the +other side a Circle in his study, sitting at his books. Now I shall +come back to you. And, as a crowning proof, what do you say to my +giving you a touch, just the least touch, in your stomach? It will not +seriously injure you, and the slight pain you may suffer cannot be +compared with the mental benefit you will receive." + +Before I could utter a word of remonstrance, I felt a shooting pain in +my inside, and a demoniacal laugh seemed to issue from within me. A +moment afterwards the sharp agony had ceased, leaving nothing but a +dull ache behind, and the Stranger began to reappear, saying, as he +gradually increased in size, "There, I have not hurt you much, have I? +If you are not convinced now, I don't know what will convince you. +What say you?" + +My resolution was taken. It seemed intolerable that I should endure +existence subject to the arbitrary visitations of a Magician who could +thus play tricks with one's very stomach. If only I could in any way +manage to pin him against the wall till help came! + +Once more I dashed my hardest angle against him, at the same time +alarming the whole household by my cries for aid. I believe, at the +moment of my onset, the Stranger had sunk below our Plane, and really +found difficulty in rising. In any case he remained motionless, while +I, hearing, as I thought, the sound of some help approaching, pressed +against him with redoubled vigour, and continued to shout for +assistance. + +A convulsive shudder ran through the Sphere. "This must not be," I +thought I heard him say: "either he must listen to reason, or I must +have recourse to the last resource of civilization." Then, addressing +me in a louder tone, he hurriedly exclaimed, "Listen: no stranger must +witness what you have witnessed. Send your Wife back at once, before +she enters the apartment. The Gospel of Three Dimensions must not be +thus frustrated. Not thus must the fruits of one thousand years of +waiting be thrown away. I hear her coming. Back! back! Away from me, +or you must go with me--whither you know not--into the Land of Three +Dimensions!" + +"Fool! Madman! Irregular!" I exclaimed; "never will I release thee; +thou shalt pay the penalty of thine impostures." + +"Ha! Is it come to this?" thundered the Stranger: "then meet your +fate: out of your Plane you go. Once, twice, thrice! 'Tis done!" + + + + +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 +incorporate, all that I had before inferred, 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. + +Prostrating myself mentally before my Guide, I cried, "How is it, O +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." + +Bewildered 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. Return with me a while to the plains of +Flatland, and I will shew you that which you have 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." + +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 orphan 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. + + +[Illustration 9] + +[ASCII approximation follows] + + + /\ + / |My \ + / <> |Study \ + /______ | ___ \ + / <> My Sons\ \|The \ + /______/ \ Page / \ + N / <> \ / My \ + ^ /______/ THE HALL \ Bedroom \ + | \ <> My\ / + | \____| /\Wife's / + W--+--E \ My Wife / Apartment/ + | ------- /\ --- \ WOMEN'S DOOR + | MEN'S DOOR \My Daughter + | /\ --== \ / The Scullion + S \ My Grandsons \ -==# \/ The Footman + \___ ___ _ _/ \-=#|/ The Butler + \ <> | <> | |THE CELLAR \ / + \____|____|_|____________/ + + ###===--- ---===### + Policeman Policeman + + +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 be long 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 lo, the secrets of the earth, the +depths of mines and inmost caverns of the hills, were bared before me. + +Awestruck 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 pick-pockets 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 besides Gods? + +SPHERE. I do not know. But, if a pick-pocket or a cut-throat of our +country can see everything that is in your country, surely that is no +reason why the pick-pocket 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? + +I. "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, in so far 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 +recognized 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 +their wont, 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 1000, and also on the first hour of +the first day of the year 0. + +The minutes of the previous meetings were now read by one whom I at +once recognized 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 straightway 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 methinks 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. Meantime I must +perform my mission. Stay thou there in thy place." Saying these +words, he leaped with great dexterity into the sea (if I may so call +it) of Flatland, right in the midst of the ring of Counsellors. "I +come," cried he, "to proclaim that there is a land of Three Dimensions." + +I could see many of the younger Counsellors start back in manifest +horror, as the Sphere's circular section widened before them. But on a +sign from the presiding Circle--who shewed not the slightest alarm or +surprise--six Isosceles of a low 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 guards. "Arrest the policemen; +gag them. You know your duty." After he had consigned to their fate +the wretched policemen--ill-fated and unwilling witnesses of a +State-secret which they were not to be permitted to reveal--he again +addressed the Counsellors. "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 length, 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 shewed me other mysteries + of Spaceland, 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; haply thou shalt have ample +time hereafter to condole with him. Follow me." + + +[Illustration 10] + +[ASCII approximation follows] + + + (1) (2) + __________ __________ + |\ |\ | \ + | \ | \ | \ + | \ ____|____\ | \ + | | | | | | + |_____|____| | | | + \ | \ | \ | + \ | \ | \ | + \|_________\| \ __________| + + +Once more we ascended into space. "Hitherto," said the Sphere, "I have +shewn you naught save Plane 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 moveable 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 of +an Irregular Figure whose inside is laid open to the view; in other +words, methinks I see no Solid, but a Plane 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 Plane, 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 Plane, but a Solid; and that he was endowed with +six plane 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. + +But 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. Suffice 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 Plane 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 Plane 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 dispassionate 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 conformation of all regular Solids, Cylinders, Cones, +Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons, and Spheres: but I +ventured to interrupt him. Not that I was wearied of knowledge. On +the contrary, I thirsted for yet deeper and fuller draughts 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? And 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 +Spaceland. 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 vouchsafed. + +SPHERE. Pooh! 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 countrymen in Flatland. + +I. 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 +unemancipable 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 at once, I +would shew 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 shewn 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 mines in Spaceland, 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. Not inconceivable, my Lord, to me, and therefore still less +inconceivable to my Master. Nay, I despair not that, even here, in +this region of Three Dimensions, your Lordship's art may make the +Fourth Dimension visible to me; just as in the Land of Two Dimensions +my Teacher's skill would fain have opened the eyes of his blind servant +to the invisible presence of a Third Dimension, though I saw it not. + +Let me recall the past. Was I not taught below that when I saw a Line +and inferred a Plane, I in reality saw a Third unrecognized Dimension, +not the same as brightness, called "height"? And does it not now +follow that, in this region, when I see a Plane and infer a Solid, I +really see a Fourth unrecognized Dimension, not the same as colour, but +existent, though infinitesimal and incapable of measurement? + +And besides this, there is the Argument from Analogy of Figures. + +SPHERE. Analogy! Nonsense: what analogy? + +I. Your Lordship tempts his servant to see whether he remembers the +revelations imparted to him. Trifle not with me, my Lord; I crave, I +thirst, for more knowledge. Doubtless we cannot SEE that other higher +Spaceland now, because we we have no eye in our stomachs. But, just as +there WAS the realm of Flatland, 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 eye in +my interior to discern it, so of a surety there is a Fourth Dimension, +which my Lord perceives with the inner eye of thought. 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 Organization with +SIXTEEN terminal points? + +Behold the infallible confirmation of the Series, 2, 4, 8, 16: 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, 2, 4, 6: 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 +8 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 facts; 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. Deny it, and I am henceforth silent. Only vouchsafe 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. 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, whither 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 Thoughtland, 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 command of silence, and threaten me with the direst +penalties if I persisted. Nothing could stem the flood of my ecstatic +aspirations. Perhaps I was to blame; but indeed I was intoxicated with +the recent draughts 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-consummating thunder-peal; 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 + + + +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 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 endeavoured 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 placability. We were moving together +towards a bright but infinitesimally small Point, to which my Master +directed my attention. As we approached, methought there issued from +it a slight humming noise as from one of your Spaceland bluebottles, +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 Flatland thou hast lived; of Lineland +thou hast received a vision; thou hast soared with me to the heights of +Spaceland; now, in order to complete the range of thy experience, I +conduct thee downward to the lowest depth of existence, even to the +realm of Pointland, the Abyss of No dimensions. + +"Behold yon 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 Spaceland +phonographs, from which I caught these words, "Infinite beatitude 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, Utterer, Hearer, +Thought, Word, Audition; it is the One, and yet the All in All. Ah, +the happiness ah, 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 Pointland, 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 Pointland." + +The lustre of the Monarch, who beamed more brightly than ever upon +hearing my words, shewed 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 Pointland 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, shewing 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. + + + + +Section 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 Resolution of the Council, enjoining the +arrest, imprisonment, or execution of any one 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 opportunely just at that moment, I +decided, after we had exchanged 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 3^3 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 the 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 Spaceland 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 that I had seen and heard was in some strange way +slipping away from me, like the image of a half-grasped, tantalizing +dream, and I longed to essay 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 herald's "O yes! O 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 Grandpapa," 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! Ha! ha! ha!" + +"Not at all silly," said I, losing my temper; "here for example, I take +this Square," and, at the word, I grasped a moveable 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. + + + + +Section 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 mysteries of Three Dimensions. Only, with the view of evading +the Law, if possible, I spoke not of a physical Dimension, but of a +Thoughtland whence, in theory, a Figure could look down upon Flatland +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 Flatland, 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 Flatland to +Thoughtland") I could not feel certain that many would understand my +meaning. + +Meanwhile my life was under a cloud. All pleasures palled upon me; all +sights tantalized 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 Spaceland, 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 realized 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 +treasonable, and I was keenly alive to the danger 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. When, 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. + +Need 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 Policemen was in attendance, of angularity little, if at +all, under 55 degrees, ordered them to be relieved before I began my +defence, by an inferior class of 2 or 3 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 except +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 +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 +Spaceland, 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 aught that I can +see, the millennial Revelation has been made to me for nothing. +Prometheus up in Spaceland was bound for bringing down fire for +mortals, but I--poor Flatland 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. +Heavily 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 + ----------------------------------------------------------------- + | THE END of | + | ______ | + | / / /| ------ / /| /| / /-. | + | /---- / /__| / / /__| / | / / / | + | / /___ / | / /___ / | / |/ /__.-' | + | | + | The baseless fabric of my vision | + | Melted into air into thin air | + | Such stuff as dreams are made of | + ----------------------------------------------------------------- + + + + +*** END OF THE PROJECT GUTENBERG EBOOK FLATLAND *** + +Updated editions will replace the previous one--the old editions will +be renamed. + +Creating the works from print editions not protected by U.S. copyright +law means that no one owns a United States copyright in these works, +so the Foundation (and you!) can copy and distribute it in the +United States without permission and without paying copyright +royalties. 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