Flatland by Edwin A. Abbott

1884

 To The Inhabitance 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 Enlargment of THE IMAGINATION And the possible Development Of that most and excellent Gift of MODESTY Among the Superior Races Of SOLID HUMANITY

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FLATLAND

PART 1

THIS WORLD

SECTION 1 Of the Nature of Flatland

I call our world Flatland, not because we call it so, but to make itsnature clearer to you, my happy readers, who are privileged to live inSpace. 

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remainingfixed in their places, move freely about, on or in the surface, butwithout the power of rising above or sinking below it, very much likeshadows--only hard with luminous edges--and you will then have a prettycorrect notion of my country and countrymen. Alas, a few years ago, Ishould have said "my universe:" but now my mind has been opened tohigher views of things. 

In such a country, you will perceive at once that it is impossible thatthere should be anything of what you call a "solid" kind; but I daresay you will suppose that we could at least distinguish by sight theTriangles, Squares, and other figures, moving about as I have describedthem. On the contrary, we could see nothing of the kind, not at leastso as to distinguish one figure from another. Nothing was visible, norcould be visible, to us, except Straight Lines; and the necessity ofthis I will speedily demonstrate. 

Place a penny on the middle of one of your tables in Space; and leaningover it, look down upon it. It will appear a circle. 

But now, drawing back to the edge of the table, gradually lower youreye (thus bringing yourself more and more into the condition of theinhabitants of Flatland), and you will find the penny becoming more andmore oval to your view, and at last when you have placed your eyeexactly on the edge of the table (so that you are, as it were, actuallya 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 aTriangle, or a Square, or any other figure cut out from pasteboard. Assoon as you look at it with your eye on the edge of the table, you willfind that it ceases to appear to you as a figure, and that it becomesin appearance a straight line. Take for example an equilateralTriangle--who represents with us a Tradesman of the respectable class. Figure 1 represents the Tradesman as you would see him while you werebending over him from above; figures 2 and 3 represent the Tradesman, as you would see him if your eye were close to the level, or all but onthe level of the table; and if your eye were quite on the level of thetable (and that is how we see him in Flatland) you would see nothingbut a straight line. 

When I was in Spaceland I heard that your sailors have very similarexperiences while they traverse your seas and discern some distantisland 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 adistance you see none of these (unless indeed your sun shines brightupon them revealing the projections and retirements by means of lightand shade), nothing but a grey unbroken line upon the water. 

Well, that is just what we see when one of our triangular or otheracquaintances comes towards us in Flatland. As there is neither sunwith us, nor any light of such a kind as to make shadows, we have noneof the helps to the sight that you have in Spaceland. If our friendcomes closer to us we see his line becomes larger; if he leaves us itbecomes smaller; but still he looks like a straight line; be he aTriangle, Square, Pentagon, Hexagon, Circle, what you will--a straightLine he looks and nothing else. 

You may perhaps ask how under these disadvantagous circumstances we areable to distinguish our friends from one another: but the answer tothis very natural question will be more fitly and easily given when Icome to describe the inhabitants of Flatland. For the present let medefer this subject, and say a word or two about the climate and housesin our country. 

SECTION 2 Of the Climate and Houses in Flatland

As with you, so also with us, there are four points of the compassNorth, South, East, and West. 

There being no sun nor other heavenly bodies, it is impossible for usto determine the North in the usual way; but we have a method of ourown. By a Law of Nature with us, there is a constant attraction to theSouth; and, although in temperate climates this is very slight--so thateven a Woman in reasonable health can journey several furlongsnorthward without much difficulty--yet the hampering effort of thesouthward attraction is quite sufficient to serve as a compass in mostparts of our earth. Moreover, the rain (which falls at statedintervals) coming always from the North, is an additional assistance;and in the towns we have the guidance of the houses, which of coursehave their side-walls running for the most part North and South, sothat 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 sortof guide. Altogether, we have not so much difficulty as might beexpected in determining our bearings. 

Yet in our more temperate regions, in which the southward attraction ishardly felt, walking sometimes in a perfectly desolate plain wherethere have been no houses nor trees to guide me, I have beenoccasionally compelled to remain stationary for hours together, waitingtill the rain came before continuing my journey. On the weak and aged, and especially on delicate Females, the force of attraction tells muchmore heavily than on the robust of the Male Sex, so that it is a pointof breeding, if you meet a Lady on the street, always to give her theNorth side of the way--by no means an easy thing to do always at shortnotice when you are in rude health and in a climate where it isdifficult to tell your North from your South. 

Windows there are none in our houses: for the light comes to us alikein our homes and out of them, by day and by night, equally at all timesand in all places, whence we know not. It was in old days, with ourlearned men, an interesting and oft-investigate question, "What is theorigin of light?" and the solution of it has been repeatedly attempted, with no other result than to crowd our lunatic asylums with thewould-be solvers. Hence, after fruitless attempts to suppress suchinvestigations indirectly by making them liable to a heavy tax, theLegislature, in comparatively recent times, absolutely prohibited them. I--alas, I alone in Flatland--know now only too well the true solutionof this mysterious problem; but my knowledge cannot be madeintelligible 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 theintroduction of Light from the world of three Dimensions--as if I werethe maddest of the mad! But a truce to these painful digressions: letme return to our homes. 

The most common form for the construction of a house is five-sided orpentagonal, as in the annexed figure. The two Northern sides RO, OF, constitute the roof, and for the most part have no doors; on the Eastis a small door for the Women; on the West a much larger one for theMen; the South side or floor is usually doorless. 

Square and triangular houses are not allowed, and for this reason. Theangles of a Square (and still more those of an equilateral Triangle, )being much more pointed than those of a Pentagon, and the lines ofinanimate objects (such as houses) being dimmer than the lines of Menand Women, it follows that there is no little danger lest the points ofa square of triangular house residence might do serious injury to aninconsiderate or perhaps absentminded traveller suddenly runningagainst them: and therefore, as early as the eleventh century of ourera, triangular houses were universally forbidden by Law, the onlyexceptions being fortifications, powder-magazines, barracks, and otherstate buildings, which is not desirable that the general public shouldapproach without circumspection. 

At this period, square houses were still everywhere permitted, thoughdiscouraged by a special tax. But, about three centuries afterwards, the Law decided that in all towns containing a population above tenthousand, the angle of a Pentagon was the smallest house-angle thatcould be allowed consistently with the public safety. The good senseof the community has seconded the efforts of the Legislature; and now, even in the country, the pentagonal construction has superseded everyother. It is only now and then in some very remote and backwardagricultural district that an antiquarian may still discover a squarehouse. 

SECTION 3 Concerning the Inhabitants of Flatland

The greatest length or breadth of a full grown inhabitant of Flatlandmay be estimated at about eleven of your inches. Twelve inches may beregarded as a maximum. 

Our Women are Straight Lines. 

Our Soldiers and Lowest Class of Workmen are Triangles with two equalsides, 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 avery sharp and formidable angle. Indeed when their bases are of themost degraded type (not more than the eighth part of an inch in size), they can hardly be distinguished from Straight lines or Women; soextremely pointed are their vertices. With us, as with you, theseTriangles are distinguished from others by being called Isosceles; andby 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 myselfbelong) 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 inthe number of their sides till they receive the honourable title ofPolygonal, or many-Sided. Finally when the number of the sides becomesso numerous, and the sides themselves so small, that the figure cannotbe distinguished from a circle, he is included in the Circular orPriestly order; and this is the highest class of all. 

It is a Law of Nature with us that a male child shall have one moreside 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 aSquare is a Pentagon; the son of a Pentagon, a Hexagon; and so on. 

But this rule applies not always to the Tradesman, and still less oftento the Soldiers, and to the Workmen; who indeed can hardly be said todeserve the name of human Figures, since they have not all their sidesequal. With them therefore the Law of Nature does not hold; and theson of an Isosceles (i. E. A Triangle with two sides equal) remainsIsosceles still. Nevertheless, all hope is not such out, even from theIsosceles, that his posterity may ultimately rise above his degradedcondition. For, after a long series of military successes, or diligentand skillful labours, it is generally found that the more intelligentamong the Artisan and Soldier classes manifest a slight increase oftheir third side or base, and a shrinkage of the two other sides. Intermarriages (arranged by the Priests) between the sons and daughtersof these more intellectual members of the lower classes generallyresult in an offspring approximating still more to the type of theEqual-Sided Triangle. 

Rarely--in proportion to the vast numbers of Isosceles births--is agenuine and certifiable Equal-Sided Triangle produced from Isoscelesparents (footnote 1). Such a birth requires, as its antecedents, notonly a series of carefully arranged intermarriages, but also along-continued exercise of frugality and self-control on the part ofthe would-be ancestors of the coming Equilateral, and a patient, systematic, and continuous development of the Isosceles intellectthrough many generations. 

The birth of a True Equilateral Triangle from Isosceles parents is thesubject of rejoicing in our country for many furlongs round. After astrict examination conducted by the Sanitary and Social Board, theinfant, if certified as Regular, is with solemn ceremonial admittedinto the class of Equilaterals. He is then immediately taken from hisproud yet sorrowing parents and adopted by some childless Equilateral, who is bound by oath never to permit the child henceforth to enter hisformer home or so much as to look upon his relations again, for fearlest the freshly developed organism may, by force of unconsciousimitation, fall back again into his hereditary level. 

The occasional emergence of an Equilateral from the ranks of hisserf-born ancestors is welcomed, not only by the poor serfs themselves, as a gleam of light and hope shed upon the monotonous squalor of theirexistence, but also by the Aristocracy at large; for all the higherclasses are well aware that these rare phenomena, while they do littleor nothing to vulgarize their own privileges, serve as almost usefulbarrier against revolution from below. 

Had the acute-angled rabble been all, without exception, absolutelydestitute of hope and of ambition, they might have found leaders insome of their many seditious outbreaks, so able as to render theirsuperior numbers and strength too much even for the wisdom of theCircles. But a wise ordinance of Nature has decreed that in proportionas the working-classes increase in intelligence, knowledge, and allvirtue, in that same proportion their acute angle (which makes themphysically terrible) shall increase also and approximate to theircomparatively harmless angle of the Equilateral Triangle. Thus, in themost brutal and formidable off the soldier class--creatures almost on alevel with women in their lack of intelligence--it is found that, asthey wax in the mental ability necessary to employ their tremendouspenetrating power to advantage, so do they wane in the power ofpenetration itself. 

How admirable is the Law of Compensation! And how perfect a proof ofthe natural fitness and, I may almost say, the divine origin of thearistocratic constitution of the States of Flatland! By a judicioususe of this Law of Nature, the Polygons and Circles are almost alwaysable to stifle sedition in its very cradle, taking advantage of theirrepressible and boundless hopefulness of the human mind. Art alsocomes to the aid of Law and Order. It is generally found possible--bya little artificial compression or expansion on the part of the Statephysicians--to make some of the more intelligent leaders of a rebellionperfectly Regular, and to admit them at once into the privilegedclasses; a much larger number, who are still below the standard, allured by the prospect of being ultimately ennobled, are induced toenter the State Hospitals, where they are kept in honourableconfinement for life; one or two alone of the most obstinate, foolish, and hopelessly irregular are led to execution. 

Then the wretched rabble of the Isosceles, planless and leaderless, areeither transfixed without resistance by the small body of theirbrethren whom the Chief Circle keeps in pay for emergencies of thiskind; or else more often, by means of jealousies and suspiciousskillfully fomented among them by the Circular party, they are stirredto mutual warfare, and perish by one another's angles. No less thanone hundred and twenty rebellions are recorded in our annals, besidesminor outbreaks numbered at two hundred and thirty-five; and they haveall ended thus. 

Footnote 1. "What need of a certificate?" a Spaceland critic may ask:"Is not the procreation of a Square Son a certificate from Natureherself, proving the Equal-sidedness of the Father?" I reply that noLady of any position will mary an uncertified Triangle. Squareoffspring has sometimes resulted from a slightly Irregular Triangle;but in almost every such case the Irregularity of the first generationis visited on the third; which either fails to attain the Pentagonalrank, or relapses to the Triangular. 

SECTION 4 Concerning the Women

If our highly pointed Triangles of the Soldier class are formidable, itmay 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, ALLpoint, at least at the two extremities. Add to this the power ofmaking herself practically invisible at will, and you will perceivethat a Female, in Flatland, is a creature by no means to be trifledwith. 

But here, perhaps, some of my younger Readers may ask HOW a woman inFlatland can make herself invisible. This ought, I think, to beapparent without any explanation. However, a few words will make itclear to the most unreflecting. 

Place a needle on the table. Then, with your eye on the level of thetable, look at it side-ways, and you see the whole length of it; butlook at it end-ways, and you see nothing but a point, it has becomepractically invisible. Just so is it with one of our Women. When herside is turned towards us, we see her as a straight line; when the endcontaining her eye or mouth--for with us these two organs areidentical--is the part that meets our eye, then we see nothing but ahighly lustrous point; but when the back is presented to our view, then--being only sub-lustrous, and, indeed, almost as dim as aninanimate object--her hinder extremity serves her as a kind ofInvisible Cap. 

The dangers to which we are exposed from our Women must now be manifestto the meanest capacity of Spaceland. If even the angle of arespectable Triangle in the middle class is not without its dangers; ifto run against a Working Man involves a gash; if collision with anOfficer of the military class necessitates a serious wound; if a meretouch from the vertex of a Private Soldier brings with it danger ofdeath;--what can it be to run against a woman, except absolute andimmediate destruction? And when a Woman is invisible, or visible onlyas a dim sub-lustrous point, how difficult must it be, even for themost cautious, always to avoid collision!

Many are the enactments made at different times in the different Statesof Flatland, in order to minimize this peril; and in the Southern andless temperate climates, where the force of gravitation is greater, andhuman beings more liable to casual and involuntary motions, the Lawsconcerning Women are naturally much more stringent. But a general viewof the Code may be obtained from the following summary:--

1. Every house shall have one entrance on the Eastern side, for theuse of Females only; by which all females shall enter "in a becomingand respectful manner" (footnote 1) and not by the Men's or Westerndoor. 

2. No Female shall walk in any public place without continuallykeeping 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 diseasenecessitating 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 placewithout moving their backs constantly from right to left so as toindicate their presence to those behind them; other oblige a Woman, when travelling, to be followed by one of her sons, or servants, or byher husband; others confine Women altogether in their houses exceptduring the religious festivals. But it has been found by the wisest ofour Circles or Statesmen that the multiplication of restrictions onFemales tends not only to the debilitation and diminution of the race, but also to the increase of domestic murders to such an extent that aState loses more than it gains by a too prohibitive Code. 

For whenever the temper of the Women is thus exasperated by confinementat home or hampering regulations abroad, they are apt to vent theirspleen upon their husbands and children; and in the less temperateclimates the whole male population of a village has been sometimesdestroyed in one or two hours of a simultaneous female outbreak. Hencethe Three Laws, mentioned above, suffice for the better regulatedStates, and may be accepted as a rough exemplification of our FemaleCode. 

After all, our principal safeguard is found, not in Legislature, but inthe interests of the Women themselves. For, although they can inflictinstantaneous death by a retrograde movement, yet unless they can atonce disengage their stinging extremity from the struggling body oftheir victim, their own frail bodies are liable to be shattered. 

The power of Fashion is also on our side. I pointed out that in someless civilized States no female is suffered to stand in any publicplace without swaying her back from right to left. This practice hasbeen universal among ladies of any pretensions to breeding in allwell-governed States, as far back as the memory of Figures can reach. It is considered a disgrace to any state that legislation should haveto enforce what ought to be, and is in every respectable female, anatural instinct. The rhythmical and, if I may so say, well-modulatedundulation of the back in our ladies of Circular rank is envied andimitated by the wife of a common Equilateral, who can achieve nothingbeyond a mere monotonous swing, like the ticking of a pendulum; and theregular tick of the Equilateral is no less admired and copied by thewife of the progressive and aspiring Isosceles, in the females of whosefamily no "back-motion" of any kind has become as yet a necessity oflife. Hence, in every family of position and consideration, "backmotion" is as prevalent as time itself; and the husbands and sons inthese households enjoy immunity at least from invisible attacks. 

Not that it must be for a moment supposed that our Women are destituteof affection. But unfortunately the passion of the momentpredominates, in the Frail Sex, over every other consideration. Thisis, of course, a necessity arising from their unfortunate conformation. For as they have no pretensions to an angle, being inferior in thisrespect to the very lowest of the Isosceles, they are consequentlywholly devoid of brainpower, and have neither reflection, judgment norforethought, and hardly any memory. Hence, in their fits of fury, theyremember no claims and recognize no distinctions. I have actuallyknown a case where a Woman has exterminated her whole household, andhalf an hour afterwards, when her rage was over and the fragments sweptaway, has asked what has become of her husband and children. 

Obviously then a Woman is not to be irritated as long as she is in aposition where she can turn round. When you have them in theirapartments--which are constructed with a view to denying them thatpower--you can say and do what you like; for they are then whollyimpotent for mischief, and will not remember a few minutes hence theincident for which they may be at this moment threatening you withdeath, nor the promises which you may have found it necessary to makein order to pacify their fury. 

On the whole we got on pretty smoothly in our domestic relations, except in the lower strata of the Military Classes. There the want oftact and discretion on the part of the husbands produces at timesindescribable disasters. Relying too much on the offensive weapons oftheir acute angles instead of the defensive organs of good sense andseasonable simulations, these reckless creatures too often neglect theprescribed construction of the women's apartments, or irritate theirwives by ill-advised expressions out of doors, which they refuseimmediately to retract. Moreover a blunt and stolid regard for literaltruth indisposes them to make those lavish promises by which the morejudicious Circle can in a moment pacify his consort. The result ismassacre; not, however, without its advantages, as it eliminates themore brutal and troublesome of the Isosceles; and by many of ourCircles the destructiveness of the Thinner Sex is regarded as one amongmany providential arrangements for suppressing redundant population, and nipping Revolution in the bud. 

Yet even in our best regulated and most approximately Circular familiesI cannot say that the ideal of family life is so high as with you inSpaceland. There is peace, in so far as the absence of slaughter maybe called by that name, but there is necessarily little harmony oftastes or pursuits; and the cautious wisdom of the Circles has ensuredsafety at the cost of domestic comfort. In every Circular or Polygonalhousehold it has been a habit from time immemorial--and now has becomea kind of instinct among the women of our higher classes--that themothers and daughters should constantly keep their eyes and mouthstowards their husband and his male friends; and for a lady in a familyof distinction to turn her back upon her husband would be regarded as akind of portent, involving loss of STATUS. But, as I shall soon shew, this custom, though it has the advantage of safety, is not withoutdisadvantages. 

In the house of the Working Man or respectable Tradesman--where thewife is allowed to turn her back upon her husband, while pursuing herhousehold avocations--there are at least intervals of quiet, when thewife is neither seen nor heard, except for the humming sound of thecontinuous Peace-cry; but in the homes of the upper classes there istoo often no peace. There the voluble mouth and bright penetrating eyeare ever directed toward the Master of the household; and light itselfis not more persistent than the stream of Feminine discourse. The tactand skill which suffice to avert a Woman's sting are unequal to thetask of stopping a Woman's mouth; and as the wife has absolutelynothing to say, and absolutely no constraint of wit, sense, orconscience to prevent her from saying it, not a few cynics have beenfound to aver that they prefer the danger of the death-dealing butinaudible sting to the safe sonorousness of a Woman's other end. 

To my readers in Spaceland the condition of our Women may seen trulydeplorable, and so indeed it is. A Male of the lowest type of theIsosceles may look forward to some improvement of his angle, and to theultimate elevation of the whole of his degraded caste; but no Woman canentertain such hopes for her sex. "Once a Woman, always a Woman" is aDecree of Nature; and the very Laws of Evolution seem suspended in herdisfavour. Yet at least we can admire the wise Prearrangement whichhas ordained that, as they have no hopes, so they shall have no memoryto recall, and no forethought to anticipate, the miseries andhumiliations which are at once a necessity of their existence and thebasis 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 giftedwith two eyes, endowed with a knowledge of perspective, and charmedwith the enjoyment of various colours, you, who can actually SEE anangle, and contemplate the complete circumference of a Circle in thehappy region of the Three Dimensions--how shall I make it clear to youthe extreme difficulty which we in Flatland experience in recognizingone another's configuration?

Recall what I told you above. All beings in Flatland, animate andinanimate, no matter what their form, present TO OUR VIEW the same, ornearly the same, appearance, viz. That of a straight Line. How thencan one be distinguished from another, where all appear the same?

The answer is threefold. The first means of recognition is the senseof hearing; which with us is far more highly developed than with you, and which enables us not only to distinguish by the voice of ourpersonal 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 the Isosceles I take no account. Butas we ascend the social scale, the process of discriminating and beingdiscriminated by hearing increases in difficulty, partly because voicesare assimilated, partly because the faculty of voice-discrimination isa plebeian virtue not much developed among the Aristocracy. Andwherever there is any danger of imposture we cannot trust to thismethod. Amongst our lowest orders, the vocal organs are developed to adegree more than correspondent with those of hearing, so that anIsosceles can easily feign the voice of a Polygon, and, with sometraining, that of a Circle himself. A second method is therefore morecommonly resorted to. 

FEELING is, among our Women and lower classes--about our upper classesI shall speak presently--the principal test of recognition, at allevents between strangers, and when the question is, not as to theindividual, but as to the class. What therefore "introduction" isamong the higher classes in Spaceland, that the process of "feeling" iswith 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 countrygentlemen in districts remote from towns, the customary formula for aFlatland 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, ofcourse, that the "feeling" is to be reciprocal. Among our still moremodern and dashing young gentlemen--who are extremely averse tosuperfluous effort and supremely indifferent to the purity of theirnative language--the formula is still further curtailed by the use of"to feel" in a technical sense, meaning, "torecommend-for-the-purposes-of-feeling-and-being-felt"; and at thismoment the "slang" of polite or fast society in the upper classessanctions such a barbarism as "Mr. Smith, permit me to feel Mr. Jones. "

Let not my Reader however suppose that "feeling" is with us the tediousprocess that it would be with you, or that we find it necessary to feelright round all the sides of every individual before we determine theclass to which he belongs. Long practice and training, begun in theschools and continued in the experience of daily life, enable us todiscriminate at once by the sense of touch, between the angles of anequal-sided Triangle, Square, and Pentagon; and I need not say that thebrainless vertex of an acute-angled Isosceles is obvious to the dullesttouch. It is therefore not necessary, as a rule, to do more than feela single angle of an individual; and this, once ascertained, tells usthe class of the person whom we are addressing, unless indeed hebelongs to the higher sections of the nobility. There the difficultyis much greater. Even a Master of Arts in our University of Wentbridgehas been known to confuse a ten-sided with a twelve-sided Polygon; andthere is hardly a Doctor of Science in or out of that famous Universitywho could pretend to decide promptly and unhesitatingly between atwenty-sided and a twenty-four sided member of the Aristocracy. 

Those of my readers who recall the extracts I gave above from theLegislative code concerning Women, will readily perceive that theprocess of introduction by contact requires some care and discretion. Otherwise the angles might inflict on the unwary Feeling irreparableinjury. It is essential for the safety of the Feeler that the Feltshould stand perfectly still. A start, a fidgety shifting of theposition, yes, even a violent sneeze, has been known before now toprove fatal to the incautious, and to nip in the bud many a promisingfriendship. Especially is this true among the lower classes of theTriangles. With them, the eye is situated so far from their vertexthat they can scarcely take cognizance of what goes on at thatextremity of their frame. They are, moreover, of a rough coarsenature, not sensitive to the delicate touch of the highly organizedPolygon. What wonder then if an involuntary toss of the head has erenow deprived the State of a valuable life!

I have heard that my excellent Grandfather--one of the least irregularof his unhappy Isosceles class, who indeed obtained, shortly before hisdecease, four out of seven votes from the Sanitary and Social Board forpassing him into the class of the Equal-sided--often deplored, with atear in his venerable eye, a miscarriage of this kind, which hadoccurred to his great-great-great-Grandfather, a respectable WorkingMan with an angle or brain of 59 degrees 30 minutes. According to hisaccount, my unfortunately Ancestor, being afflicted with rheumatism, and in the act of being felt by a Polygon, by one sudden startaccidentally transfixed the Great Man through the diagonal and thereby, partly in consequence of his long imprisonment and degradation, andpartly because of the moral shock which pervaded the whole of myAncestor's relations, threw back our family a degree and a half intheir ascent towards better things. The result was that in the nextgeneration the family brain was registered at only 58 degrees, and nottill the lapse of five generations was the lost ground recovered, thefull 60 degrees attained, and the Ascent from the Isosceles finallyachieved. And all this series of calamities from one little accidentin the process of Feeling. 

As this point I think I hear some of my better educated readersexclaim, "How could you in Flatland know anything about angles anddegrees, or minutes? We SEE an angle, because we, in the region ofSpace, can see two straight lines inclined to one another; but you, whocan see nothing but on straight line at a time, or at all events only anumber of bits of straight lines all in one straight line, --how can youever discern an angle, and much less register angles of differentsizes?"

I answer that though we cannot SEE angles, we can INFER them, and thiswith great precision. Our sense of touch, stimulated by necessity, anddeveloped by long training, enables us to distinguish angles far moreaccurately than your sense of sight, when unaided by a rule or measureof angles. Nor must I omit to explain that we have great naturalhelps. It is with us a Law of Nature that the brain of the Isoscelesclass shall begin at half a degree, or thirty minutes, and shallincrease (if it increases at all) by half a degree in every generationuntil the goal of 60 degrees is reached, when the condition of serfdomis quitted, and the freeman enters the class of Regulars. 

Consequently, Nature herself supplies us with an ascending scale orAlphabet of angles for half a degree up to 60 degrees, Specimen ofwhich are placed in every Elementary School throughout the land. Owingto occasional retrogressions, to still more frequent moral andintellectual stagnation, and to the extraordinary fecundity of theCriminal and Vagabond classes, there is always a vast superfluity ofindividuals of the half degree and single degree class, and a fairabundance of Specimens up to 10 degrees. These are absolutelydestitute of civil rights; and a great number of them, not having evenintelligence enough for the purposes of warfare, are devoted by theStates to the service of education. Fettered immovably so as to removeall possibility of danger, they are placed in the classrooms of ourInfant Schools, and there they are utilized by the Board of Educationfor the purpose of imparting to the offspring of the Middle Classes thetact and intelligence which these wretched creatures themselves areutterly devoid. 

In some States the Specimens are occasionally fed and suffered to existfor several years; but in the more temperate and better regulatedregions, it is found in the long run more advantageous for theeducational interests of the young, to dispense with food, and to renewthe Specimens every month--which is about the average duration of thefoodless existence of the Criminal class. In the cheaper schools, whatis gained by the longer existence of the Specimen is lost, partly inthe expenditure for food, and partly in the diminished accuracy of theangles, which are impaired after a few weeks of constant "feeling. " Normust we forget to add, in enumerating the advantages of the moreexpensive system, that it tends, though slightly yet perceptibly, tothe diminution of the redundant Isosceles population--an object whichevery statesman in Flatland constantly keeps in view. On the wholetherefore--although I am not ignorant that, in many popularly electedSchool Boards, there is a reaction in favour of "the cheap system" asit is called--I am myself disposed to think that this is one of themany cases in which expense is the truest economy. 

But I must not allow questions of School Board politics to divert mefrom my subject. Enough has been said, I trust, to shew thatRecognition by Feeling is not so tedious or indecisive a process asmight have been supposed; and it is obviously more trustworthy thanRecognition by hearing. Still there remains, as has been pointed outabove, the objection that this method is not without danger. For thisreason many in the Middle and Lower classes, and all without exceptionin the Polygonal and Circular orders, prefer a third method, thedescription of which shall be reserved for the next section. 

SECTION 6 Of Recognition by Sight

I am about to appear very inconsistent. In the previous sections Ihave said that all figures in Flatland present the appearance of astraight line; and it was added or implied, that it is consequentlyimpossible to distinguish by the visual organ between individuals ofdifferent classes: yet now I am about to explain to my Spacelandcritics 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 inwhich Recognition by Feeling is stated to be universal, he will findthis qualification--"among the lower classes. " It is only among thehigher classes and in our more temperate climates that SightRecognition is practised. 

That this power exists in any regions and for any classes is the resultof Fog; which prevails during the greater part of the year in all partssave the torrid zones. That which is with you in Spaceland an unmixedevil, blotting out the landscape, depressing the spirits, andenfeebling the health, is by us recognized as a blessing scarcelyinferior to air itself, and as the Nurse of arts and Parent ofsciences. But let me explain my meaning, without further eulogies onthis beneficent Element. 

If Fog were non-existent, all lines would appear equally andindistinguishably clear; and this is actually the case in those unhappycountries in which the atmosphere is perfectly dry and transparent. But wherever there is a rich supply of Fog, objects that are at adistance, say of three feet, are appreciably dimmer than those at thedistance of two feet eleven inches; and the result is that by carefuland constant experimental observation of comparative dimness andclearness, we are enabled to infer with great exactness theconfiguration of the object observed. 

An instance will do more than a volume of generalities to make mymeaning clear. 

Suppose I see two individuals approaching whose rank I wish toascertain. They are, we will suppose, a Merchant and a Physician, orin other words, an Equilateral Triangle and a Pentagon; how am I todistinguish them?

It will be obvious, to every child in Spaceland who has touched thethreshold of Geometrical Studies, that, if I can bring my eye so thatits glance may bisect an angle (A) of the approaching stranger, my viewwill lie as it were evenly between the two sides that are next to me(viz. CA and AB), so that I shall contemplate the two impartially, andboth will appear of the same size. 

Now in the case of (1) the Merchant, what shall I see? I shall see astraight line DAE, in which the middle point (A) will be very brightbecause it is nearest to me; but on either side the line will shadeaway RAPIDLY TO DIMNESS, because the sides AC and AB RECEDE RAPIDLYINTO 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 herealso see a line (D'A'E') with a bright centre (A'), yet it will shadeaway LESS RAPIDLY to dimness, because the sides (A'C', A'B') RECEDELESS RAPIDLY INTO THE FOG: and what appear to me the Physician'sextremities, viz. D' and E', will not be NOT SO DIM as the extremitiesof the Merchant. 

The Reader will probably understand from these two instances how--aftera very long training supplemented by constant experience--it ispossible for the well-educated classes among us to discriminate withfair accuracy between the middle and lowest orders, by the sense ofsight. If my Spaceland Patrons have grasped this general conception, so far as to conceive the possibility of it and not to reject myaccount as altogether incredible--I shall have attained all I canreasonably expect. Were I to attempt further details I should onlyperplex. Yet for the sake of the young and inexperienced, who mayperchance infer--from the two simple instances I have given above, ofthe manner in which I should recognize my Father and my Sons--thatRecognition by sight is an easy affair, it may be needful to point outthat in actual life most of the problems of Sight Recognition are farmore subtle and complex. 

If for example, when my Father, the Triangle, approaches me, he happensto present his side to me instead of his angle, then, until I haveasked him to rotate, or until I have edged my eye around him, I am forthe moment doubtful whether he may not be a Straight Line, or, in otherwords, a Woman. Again, when I am in the company of one of my twohexagonal Grandsons, contemplating one of his sides (AB) full front, itwill be evident from the accompanying diagram that I shall see onewhole line (AB) in comparative brightness (shading off hardly at all atthe ends) and two smaller lines (CA and BD) dim throughout and shadingaway into greater dimness towards the extremities C and 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 Iassert that the problems of life, which present themselves to thewell-educated--when they are themselves in motion, rotating, advancingor retreating, and at the same time attempting to discriminate by thesense of sight between a number of Polygons of high rank moving indifferent directions, as for example in a ball-room orconversazione--must be of a nature to task the angularity of the mostintellectual, and amply justify the rich endowments of the LearnedProfessors of Geometry, both Static and Kinetic, in the illustriousUniversity of Wentbridge, where the Science and Art of SightRecognition are regularly taught to large classes of the ELITE of theStates. 

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 thoroughprosecution of this noble and valuable Art. Even to me, aMathematician of no mean standing, and the Grandfather of two mosthopeful and perfectly regular Hexagons, to find myself in the midst ofa crowd of rotating Polygons of the higher classes, is occasionallyvery perplexing. And of course to a common Tradesman, or Serf, such asight is almost as unintelligible as it would be to you, my Reader, were you suddenly transported to my 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 andperpetually in brightness or dimness. Even if you had completed yourthird year in the Pentagonal and Hexagonal classes in the University, and were perfect in the theory of the subject, you would still findthere was need of many years of experience, before you could move in afashionable crowd without jostling against your betters, whom it isagainst etiquette to ask to "feel, " and who, by their superior cultureand breeding, know all about your movements, while you know very littleor nothing about theirs. In a word, to comport oneself with perfectpropriety 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 itinstinct--of Sight Recognition is developed by the habitual practice ofit 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 thehand-alphabet, will never acquire the more difficult but far morevaluable art of lip-speech and lip-reading, so it is with us as regards"Seeing" and "Feeling. " None who in early life resort to "Feeling" willever learn "Seeing" in perfection. 

For this reason, among our Higher Classes, "Feeling" is discouraged orabsolutely forbidden. From the cradle their children, instead of goingto the Public Elementary schools (where the art of Feeling is taught, )are sent to higher Seminaries of an exclusive character; and at ourillustrious University, to "feel" is regarded as a most serious fault, involving Rustication for the first offence, and Expulsion for thesecond. 

But among the lower classes the art of Sight Recognition is regarded asan unattainable luxury. A common Tradesman cannot afford to let hisson spend a third of his life in abstract studies. The children of thepoor are therefore allowed to "feel" from their earliest years, andthey gain thereby a precocity and an early vivacity which contrast atfirst most favourably with the inert, undeveloped, and listlessbehaviour of the half-instructed youths of the Polygonal class; butwhen the latter have at last completed their University course, and areprepared to put their theory into practice, the change that comes overthem may almost be described as a new birth, and in every art, science, and social pursuit they rapidly overtake and distance their Triangularcompetitors. 

Only a few of the Polygonal Class fail to pass the Final Test orLeaving Examination at the University. The condition of theunsuccessful minority is truly pitiable. Rejected from the higherclass, they are also despised by the lower. They have neither thematured and systematically trained powers of the Polygonal Bachelorsand Masters of Arts, nor yet the native precocity and mercurialversatility of the youthful Tradesman. The professions, the publicservices, are closed against them, and though in most States they arenot actually debarred from marriage, yet they have the greatestdifficulty in forming suitable alliances, as experience shews that theoffspring of such unfortunate and ill-endowed parents is generallyitself unfortunate, if not positively Irregular. 

It is from these specimens of the refuse of our Nobility that the greatTumults and Seditions of past ages have generally derived theirleaders; and so great is the mischief thence arising that an increasingminority of our more progressive Statesmen are of opinion that truemercy would dictate their entire suppression, by enacting that all whofail to pass the Final Examination of the University should be eitherimprisoned for life, or extinguished by a painless death. 

But I find myself digressing into the subject of Irregularities, amatter 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 shouldhave been laid down at the beginning as a distinct and fundamentalproposition--that every human being in Flatland is a Regular Figure, that is to say of regular construction. By this I mean that a Womanmust not only be a line, but a straight line; that an Artisan orSoldier must have two of his sides equal; that Tradesmen must havethree sides equal; Lawyers (of which class I am a humble member), foursides equal, and, generally, that in every Polygon, all the sides mustbe equal. 

The sizes of the sides would of course depend upon the age of theindividual. A Female at birth would be about an inch long, while atall adult Woman might extend to a foot. As to the Males of everyclass, it may be roughly said that the length of an adult's size, whenadded together, is two feet or a little more. But the size of oursides is not under consideration. I am speaking of the EQUALITY ofsides, and it does not need much reflection to see that the whole ofthe social life in Flatland rests upon the fundamental fact that Naturewills all Figures to have their sides equal. 

If our sides were unequal our angles might be unequal. Instead of itsbeing sufficient to feel, or estimate by sight, a single angle in orderto determine the form of an individual, it would be necessary toascertain each angle by the experiment of Feeling. But life would betoo short for such a tedious groping. The whole science and art ofSight Recognition would at once perish; Feeling, so far as it is anart, would not long survive; intercourse would become perilous orimpossible; there would be an end to all confidence, all forethought;no one would be safe in making the most simple social arrangements; ina word, civilization might relapse into barbarism. 

Am I going too fast to carry my Readers with me to these obviousconclusions? Surely a moment's reflection, and a single instance fromcommon life, must convince every one that our social system is basedupon Regularity, or Equality of Angles. You meet, for example, two orthree Tradesmen in the street, whom your recognize at once to beTradesman by a glance at their angles and rapidly bedimmed sides, andyou ask them to step into your house to lunch. This you do at presentwith perfect confidence, because everyone knows to an inch or two thearea occupied by an adult Triangle: but imagine that your Tradesmandrags behind his regular and respectable vertex, a parallelogram oftwelve or thirteen inches in diagonal:--what are you to do with such amonster sticking fast in your house door?

But I am insulting the intelligence of my Readers by accumulatingdetails which must be patent to everyone who enjoys the advantages of aResidence in Spaceland. Obviously the measurements of a single anglewould no longer be sufficient under such portentous circumstances;one's whole life would be taken up in feeling or surveying theperimeter of one's acquaintances. Already the difficulties of avoidinga collision in a crowd are enough to tax the sagacity of even awell-educated Square; but if no one could calculate the Regularity of asingle figure in the company, all would be chaos and confusion, and theslightest panic would cause serious injuries, or--if there happened tobe any Women or Soldiers present--perhaps considerable loss of life. 

Expediency therefore concurs with Nature in stamping the seal of itsapproval upon Regularity of conformation: nor has the Law beenbackward in seconding their efforts. "Irregularity of Figure" meanswith us the same as, or more than, a combination of moral obliquity andcriminality with you, and is treated accordingly. There are notwanting, it is true, some promulgators of paradoxes who maintain thatthere is no necessary connection between geometrical and moralIrregularity. "The Irregular, " they say, "is from his birth scouted byhis own parents, derided by his brothers and sisters, neglected by thedomestics, scorned and suspected by society, and excluded from allposts of responsibility, trust, and useful activity. His everymovement is jealously watched by the police till he comes of age andpresents himself for inspection; then he is either destroyed, if he isfound to exceed the fixed margin of deviation, at an uninterestingoccupation for a miserable stipend; obliged to live and board at theoffice, and to take even his vacation under close supervision; whatwonder that human nature, even in the best and purest, is embitteredand perverted by such surroundings!"

All this very plausible reasoning does not convince me, as it has notconvinced the wisest of our Statesmen, that our ancestors erred inlaying it down as an axiom of policy that the toleration ofIrregularity is incompatible with the safety of the State. Doubtless, the life of an Irregular is hard; but the interests of the GreaterNumber require that it shall be hard. If a man with a triangular frontand a polygonal back were allowed to exist and to propagate a stillmore Irregular posterity, what would become of the arts of life? Arethe houses and doors and churches in Flatland to be altered in order toaccommodate such monsters? Are our ticket-collectors to be required tomeasure 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 exemptedfrom the militia? And if not, how is he to be prevented from carryingdesolation into the ranks of his comrades? Again, what irresistibletemptations to fraudulent impostures must needs beset such a creature!How easy for him to enter a shop with his polygonal front foremost, andto order goods to any extent from a confiding tradesman! Let theadvocates of a falsely called Philanthropy plead as they may for theabrogation of the Irregular Penal Laws, I for my part have never knownan Irregular who was not also what Nature evidently intended him tobe--a hypocrite, a misanthropist, and, up to the limits of his power, aperpetrator of all manner of mischief. 

Not that I should be disposed to recommend (at present) the extrememeasures adopted by some States, where an infant whose angle deviatesby half a degree from the correct angularity is summarily destroyed atbirth. Some of our highest and ablest men, men of real genius, haveduring their earliest days laboured under deviations as great as, oreven greater than forty-five minutes: and the loss of their preciouslives would have been an irreparable injury to the State. The art ofhealing also has achieved some of its most glorious triumphs in thecompressions, extensions, trepannings, colligations, and other surgicalor diaetetic operations by which Irregularity has been partly or whollycured. Advocating therefore a VIA MEDIA, I would lay down no fixed orabsolute line of demarcation; but at the period when the frame is justbeginning to set, and when the Medical Board has reported that recoveryis improbably, I would suggest that the Irregular offspring bepainlessly 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 inFlatland. I do not, of course, mean that there are not battles, conspiracies, tumults, factions, and all those other phenomena whichare supposed to make History interesting; nor would I deny that thestrange mixture of the problems of life and the problems ofMathematics, continually inducing conjecture and giving an opportunityof immediate verification, imparts to our existence a zest which you inSpaceland can hardly comprehend. I speak now from the aesthetic andartistic 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 asingle line, with no varieties except degrees of brightness andobscurity?

It was not always thus. Colour, if Tradition speaks the truth, oncefor the space of half a dozen centuries or more, threw a transientsplendour over the lives of our ancestors in the remotest ages. Someprivate individual--a Pentagon whose name is variously reported--havingcasually discovered the constituents of the simpler colours and arudimentary method of painting, is said to have begun by decoratingfirst his house, then his slaves, then his Father, his Sons, andGrandsons, lastly himself. The convenience as well as the beauty ofthe results commended themselves to all. Wherever Chromatistes, --forby that name the most trustworthy authorities concur in callinghim, --turned his variegated frame, there he at once excited attention, and attracted respect. No one now needed to "feel" him; no one mistookhis front for his back; all his movements were readily ascertained byhis neighbours without the slightest strain on their powers ofcalculation; no one jostled him, or failed to make way for him; hisvoice was saved the labour of that exhausting utterance by which wecolourless Squares and Pentagons are often forced to proclaim ourindividuality when we move amid a crowd of ignorant Isosceles. 

The fashion spread like wildfire. Before a week was over, every Squareand Triangle in the district had copied the example of Chromatistes, and only a few of the more conservative Pentagons still held out. Amonth or two found even the Dodecagons infected with the innovation. Ayear had not elapsed before the habit had spread to all but the veryhighest of the Nobility. Needless to say, the custom soon made its wayfrom the district of Chromatistes to surrounding regions; and withintwo generations no one in all Flatland was colourless except the Womenand the Priests. 

Here Nature herself appeared to erect a barrier, and to plead againstextending the innovations to these two classes. Many-sidedness wasalmost essential as a pretext for the Innovators. "Distinction ofsides is intended by Nature to imply distinction of colours"--such wasthe sophism which in those days flew from mouth to mouth, convertingwhole towns at a time to a new culture. But manifestly to our Priestsand Women this adage did not apply. The latter had only one side, andtherefore--plurally and pedantically speaking--NO SIDES. Theformer--if at least they would assert their claim to be readily andtruly Circles, and not mere high-class Polygons, with an infinitelylarge number of infinitesimally small sides--were in the habit ofboasting (what Women confessed and deplored) that they also had nosides, being blessed with a perimeter of only one line, or, in otherwords, a Circumference. Hence it came to pass that these two Classescould see no force in the so-called axiom about "Distinction of Sidesimplying Distinction of Colour;" and when all others had succumbed tothe fascinations of corporal decoration, the Priests and the Womenalone still remained pure from the pollution of paint. 

Immoral, licentious, anarchical, unscientific--call them by what namesyou will--yet, from an aesthetic point of view, those ancient days ofthe Colour Revolt were the glorious childhood of Art in Flatland--achildhood, alas, that never ripened into manhood, nor even reached theblossom of youth. To live then in itself a delight, because livingimplied seeing. Even at a small party, the company was a pleasure tobehold; the richly varied hues of the assembly in a church or theatreare said to have more than once proved too distracting from ourgreatest teachers and actors; but most ravishing of all is said to havebeen the unspeakable magnificence of a military review. 

The sight of a line of battle of twenty thousand Isosceles suddenlyfacing about, and exchanging the sombre black of their bases for theorange of the two sides including their acute angle; the militia of theEquilateral Triangles tricoloured in red, white, and blue; the mauve, ultra-marine, gamboge, and burnt umber of the Square artillerymenrapidly rotating near their vermillion guns; the dashing and flashingof the five-coloured and six-coloured Pentagons and Hexagons careeringacross the field in their offices of surgeons, geometricians andaides-de-camp--all these may well have been sufficient to rendercredible the famous story how an illustrious Circle, overcome by theartistic beauty of the forces under his command, threw aside hismarshal's baton and his royal crown, exclaiming that he henceforthexchanged them for the artist's pencil. How great and glorious thesensuous development of these days must have been is in part indicatedby the very language and vocabulary of the period. The commonestutterances of the commonest citizens in the time of the Colour Revoltseem to have been suffused with a richer tinge of word or thought; andto that era we are even now indebted for our finest poetry and forwhatever rhythm still remains in the more scientific utterance of thosemodern 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 longerpractised; and the studies of Geometry, Statics, Kinetics, and otherkindred subjects, came soon to be considered superfluous, and fell intodisrespect and neglect even at our University. The inferior Art ofFeeling speedily experienced the same fate at our Elementary Schools. Then the Isosceles classes, asserting that the Specimens were no longerused nor needed, and refusing to pay the customary tribute from theCriminal classes to the service of Education, waxed daily more numerousand more insolent on the strength of their immunity from the old burdenwhich had formerly exercised the twofold wholesome effect of at oncetaming their brutal nature and thinning their excessive numbers. 

Year by year the Soldiers and Artisans began more vehemently toassert--and with increasing truth--that there was no great differencebetween them and the very highest class of Polygons, now that they wereraised to an equality with the latter, and enabled to grapple with allthe difficulties and solve all the problems of life, whether Staticalor Kinetical, by the simple process of Colour Recognition. Not contentwith the natural neglect into which Sight Recognition was falling, theybegan boldly to demand the legal prohibition of all "monopolizing andaristocratic Arts" and the consequent abolition of all endowments forthe studies of Sight Recognition, Mathematics, and Feeling. Soon, theybegan to insist that inasmuch as Colour, which was a second Nature, haddestroyed the need of aristocratic distinctions, the Law should followin the same path, and that henceforth all individuals and all classesshould be recognized as absolutely equal and entitled to equal rights. 

Finding the higher Orders wavering and undecided, the leaders of theRevolution advanced still further in their requirements, and at lastdemanded that all classes alike, the Priests and the Women notexcepted, should do homage to Colour by submitting to be painted. Whenit was objected that Priests and Women had no sides, they retorted thatNature and Expediency concurred in dictating that the front half ofevery human being (that is to say, the half containing his eye andmouth) should be distinguishable from his hinder half. They thereforebrought before a general and extraordinary Assembly of all the Statesof Flatland a Bill proposing that in every Woman the half containingthe 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 tothat 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 notfrom any Isosceles--for no being so degraded would have angularityenough to appreciate, much less to devise, such a model ofstate-craft--but from an Irregular Circle who, instead of beingdestroyed in his childhood, was reserved by a foolish indulgence tobring desolation on his country and destruction on myriads of followers. 

On the one hand the proposition was calculated to bring the Women inall classes over to the side of the Chromatic Innovation. For byassigning to the Women the same two colours as were assigned to thePriests, the Revolutionists thereby ensured that, in certain positions, every Woman would appear as a Priest, and be treated with correspondingrespect and deference--a prospect that could not fail to attract theFemale Sex in a mass. 

But by some of my Readers the possibility of the identical appearanceof Priests and Women, under a 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 thefront half (i. E. , the half containing the eye and mouth) red, and withthe hinder half green. Look at her from one side. Obviously you willsee a straight line, HALF RED, HALF GREEN. 

Now imagine a Priest, whose mouth is at M, and whose front semicircle(AMB) is consequently coloured red, while his hinder semicircle isgreen; so that the diameter AB divides the green from the red. If youcontemplate the Great Man so as to have your eye in the same straightline as his dividing diameter (AB), what you will see will be astraight line (CBD), of which ONE HALF (CB) WILL BE RED, AND THE OTHER(BD) GREEN. The whole line (CD) will be rather shorter perhaps thanthat of a full-sized Woman, and will shade off more rapidly towards itsextremities; but the identity of the colours would give you animmediate impression of identity in Class, making you neglectful ofother details. Bear in mind the decay of Sight Recognition whichthreatened society at the time of the Colour revolt; add too thecertainty that Woman would speedily learn to shade off theirextremities so as to imitate the Circles; it must then be surelyobvious to you, my dear Reader, that the Colour Bill placed us under agreat danger of confounding a Priest with a young Woman. 

How attractive this prospect must have been to the Frail Sex mayreadily be imagined. They anticipated with delight the confusion thatwould ensue. At home they might hear political and ecclesiasticalsecrets intended not for them but for their husbands and brothers, andmight even issue some commands in the name of a priestly Circle; out ofdoors the striking combination of red and green without addition of anyother colours, would be sure to lead the common people into endlessmistakes, and the Woman would gain whatever the Circles lost, in thedeference of the passers by. As for the scandal that would befall theCircular Class if the frivolous and unseemly conduct of the Women wereimputed to them, and as to the consequent subversion of theConstitution, the Female Sex could not be expected to give a thought tothese considerations. Even in the households of the Circles, the Womenwere all in favour of the Universal Colour Bill. 

The second object aimed at by the Bill was the gradual demoralizationof the Circles themselves. In the general intellectual decay theystill preserved their pristine clearness and strength of understanding. From their earliest childhood, familiarized in their Circularhouseholds with the total absence of Colour, the Nobles alone preservedthe Sacred Art of Sight Recognition, with all the advantages thatresult from that admirable training of the intellect. Hence, up to thedate of the introduction of the Universal Colour Bill, the Circles hadnot only held their own, but even increased their lead of the otherclasses by abstinence from the popular fashion. 

Now therefore the artful Irregular whom I described above as the realauthor of this diabolical Bill, determined at one blow to lower thestatus of the Hierarchy by forcing them to submit to the pollution ofColour, and at the same time to destroy their domestic opportunities oftraining in the Art of Sight Recognition, so as to enfeeble theirintellects by depriving them of their pure and colourless homes. Oncesubjected to the chromatic taint, every parental and every childishCircle would demoralize each other. Only in discerning between theFather and the Mother would the Circular infant find problems for theexercise of his understanding--problems too often likely to becorrupted by maternal impostures with the result of shaking the child'sfaith in all logical conclusions. Thus by degrees the intellectuallustre of the Priestly Order would wane, and the road would then lieopen for a total destruction of all Aristocratic Legislature and forthe 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 Anarchywere 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--theSquares and Pentagons meanwhile remaining neutral. 

Worse than all, some of the ablest Circles fell a prey to conjugalfury. Infuriated by political animosity, the wives in many a noblehousehold wearied their lords with prayers to give up their oppositionto the Colour Bill; and some, finding their entreaties fruitless, fellon and slaughtered their innocent children and husband, perishingthemselves in the act of carnage. It is recorded that during thattriennial agitation no less than twenty-three Circles perished indomestic discord. 

Great indeed was the peril. It seemed as though the Priests had nochoice between submission and extermination; when suddenly the courseof events was completely changed by one of those picturesque incidentswhich Statesmen ought never to neglect, often to anticipate, andsometimes perhaps to originate, because of the absurdlydisproportionate power with which they appeal to the sympathies of thepopulace. 

It happened that an Isosceles of a low type, with a brain little if atall above four degrees--accidentally dabbling in the colours of someTradesman whose shop he had plundered--painted himself, or causedhimself to be painted (for the story varies) with the twelve colours ofa Dodecagon. Going into the Market Place he accosted in a feignedvoice a maiden, the orphan daughter of a noble Polygon, whose affectionin former days he had sought in vain; and by a series ofdeceptions--aided, on the one side, by a string of lucky accidents toolong to relate, and, on the other, by an almost inconceivable fatuityand neglect of ordinary precautions on the part of the relations of thebride--he succeeded in consummating the marriage. The unhappy girlcommitted suicide on discovering the fraud to which she had beensubjected. 

When the news of this catastrophe spread from State to State the mindsof the Women were violently agitated. Sympathy with the miserablevictim and anticipations of similar deceptions for themselves, theirsisters, and their daughters, made them now regard the Colour Bill inan entirely new aspect. Not a few openly avowed themselves convertedto antagonism; the rest needed only a slight stimulus to make a similaravowal. Seizing this favourable opportunity, the Circles hastilyconvened an extraordinary Assembly of the States; and besides the usualguard of Convicts, they secured the attendance of a large number ofreactionary Women. 

Amidst an unprecedented concourse, the Chief Circle of those days--byname Pantocyclus--arose to find himself hissed and hooted by a hundredand twenty thousand Isosceles. But he secured silence by declaringthat henceforth the Circles would enter on a policy of Concession;yielding to the wishes of the majority, they would accept the ColourBill. The uproar being at once converted to applause, he invitedChromatistes, the leader of the Sedition, into the centre of the hall, to receive in the name of his followers the submission of theHierarchy. Then followed a speech, a masterpiece of rhetoric, whichoccupied nearly a day in the delivery, and to which no summary can dojustice. 

With a grave appearance of impartiality he declared that as they werenow finally committing themselves to Reform or Innovation, it wasdesirable that they should take one last view of the perimeter of thewhole subject, its defects as well as its advantages. Graduallyintroduction the mention of the dangers to the Tradesmen, theProfessional Classes and the Gentlemen, he silenced the rising murmursof 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 hiswords and were either neutral or averse to the Bill. 

Turning now to the Workmen he asserted that their interests must not beneglected, and that, if they intended to accept the Colour Bill, theyought at least to do so with full view of the consequences. Many ofthem, he said, were on the point of being admitted to the class of theRegular Triangles; others anticipated for their children a distinctionthey could not hope for themselves. That honourable ambition would nothave to be sacrificed. With the universal adoption of Colour, alldistinctions would cease; Regularity would be confused withIrregularity; development would give place to retrogression; theWorkman would in a few generations be degraded to the level of theMilitary, or even the Convict Class; political power would be in thehands of the greatest number, that is to say the Criminal Classes, whowere already more numerous than the Workmen, and would soon out-numberall the other Classes put together when the usual Compensative Laws ofNature were violated. 

A subdued murmur of assent ran through the ranks of the Artisans, andChromatistes, in alarm, attempted to step forward and address them. But he found himself encompassed with guards and forced to remainsilent while the Chief Circle in a few impassioned words made a finalappeal to the Women, exclaiming that, if the Colour Bill passed, nomarriage would henceforth be safe, no woman's honour secure; fraud, deception, hypocrisy would pervade every household; domestic blisswould 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, theIsosceles Convicts fell on and transfixed the wretched Chromatistes;the Regular Classes, opening their ranks, made way for a band of Womenwho, under direction of the Circles, moved back foremost, invisibly andunerringly upon the unconscious soldiers; the Artisans, imitating theexample of their betters, also opened their ranks. Meantime bands ofConvicts occupied every entrance with an impenetrable phalanx. 

The battle, or rather carnage, was of short duration. Under theskillful generalship of the Circles almost every Woman's charge wasfatal and very many extracted their sting uninjured, ready for a secondslaughter. But no second blow was needed; the rabble of the Isoscelesdid the rest of the business for themselves. Surprised, leader-less, attacked in front by invisible foes, and finding egress cut off by theConvicts behind them, they at once--after their manner--lost allpresence of mind, and raised the cry of "treachery. " This sealed theirfate. Every Isosceles now saw and felt a foe in every other. In halfan hour not one of that vast multitude was living; and the fragments ofseven score thousand of the Criminal Class slain by one another'sangles attested the triumph of Order. 

The Circles delayed not to push their victory to the uttermost. TheWorking Men they spared but decimated. The Militia of the Equilateralswas at once called out, and every Triangle suspected of Irregularity onreasonable grounds, was destroyed by Court Martial, without theformality of exact measurement by the Social Board. The homes of theMilitary and Artisan classes were inspected in a course of visitationextending through upwards of a year; and during that period every town, village, and hamlet was systematically purged of that excess of thelower orders which had been brought about by the neglect to pay thetribute of Criminals to the Schools and University, and by theviolation of other natural Laws of the Constitution of Flatland. Thusthe balance of classes was again restored. 

Needless to say that henceforth the use of Colour was abolished, andits possession prohibited. Even the utterance of any word denotingColour, except by the Circles or by qualified scientific teachers, waspunished by a severe penalty. Only at our University in some of thevery highest and most esoteric classes--which I myself have never beenprivileged to attend--it is understood that the sparing use of Colouris still sanctioned for the purpose of illustrating some of the deeperproblems of mathematics. But of this I can only speak from hearsay. 

Elsewhere in Flatland, Colour is now non-existent. The art of makingit is known to only one living person, the Chief Circle for the timebeing; and by him it is handed down on his death-bed to none but hisSuccessor. One manufactory alone produces it; and, lest the secretshould be betrayed, the Workmen are annually consumed, and fresh onesintroduced. So great is the terror with which even now our Aristocracylooks back to the far-distant days of the agitation for the UniversalColour Bill. 

SECTION 11 Concerning our Priests

It is high time that I should pass from these brief and discursivenotes about things in Flatland to the central event of this book, myinitiation into the mysteries of Space. THAT is my subject; all thathas gone before is merely preface. 

For this reason I must omit many matters of which the explanation wouldnot, I flatter myself, be without interest for my Readers: as forexample, our method of propelling and stopping ourselves, althoughdestitute of feet; the means by which we give fixity to structures ofwood, stone, or brick, although of course we have no hands, nor can welay foundations as you can, nor avail ourselves of the lateral pressureof the earth; the manner in which the rain originates in the intervalsbetween our various zones, so that the northern regions do notintercept the moisture falling on the southern; the nature of our hillsand mines, our trees and vegetables, our seasons and harvests; ourAlphabet and method of writing, adapted to our linear tablets; theseand 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 theiromission proceeds not from forgetfulness on the part of the author, butfrom his regard for the time of the Reader. 

Yet before I proceed to my legitimate subject some few final remarkswill no doubt be expected by my Readers upon these pillars andmainstays of the Constitution of Flatland, the controllers of ourconduct and shapers of our destiny, the objects of universal homage andalmost 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 morethan the term denotes with you. With us, our Priests areAdministrators of all Business, Art, and Science; Directors of Trade, Commerce, Generalship, Architecture, Engineering, Education, Statesmanship, Legislature, Morality, Theology; doing nothingthemselves, they are the Causes of everything worth doing, that is doneby others. 

Although popularly everyone called a Circle is deemed a Circle, yetamong the better educated Classes it is known that no Circle is reallya Circle, but only a Polygon with a very large number of very smallsides. As the number of the sides increases, a Polygon approximates toa Circle; and, when the number is very great indeed, say for examplethree or four hundred, it is extremely difficult for the most delicatetouch to feel any polygonal angles. Let me say rather it WOULD bedifficult: for, as I have shown above, Recognition by Feeling isunknown among the highest society, and to FEEL a Circle would beconsidered a most audacious insult. This habit of abstention fromFeeling in the best society enables a Circle the more easily to sustainthe veil of mystery in which, from his earliest years, he is wont toenwrap the exact nature of his Perimeter or Circumference. Three feetbeing the average Perimeter it follows that, in a Polygon of threehundred sides each side will be no more than the hundredth part of afoot in length, or little more than the tenth part of an inch; and in aPolygon of six or seven hundred sides the sides are little larger thanthe diameter of a Spaceland pin-head. It is always assumed, bycourtesy, that the Chief Circle for the time being has ten thousandsides. 

The ascent of the posterity of the Circles in the social scale is notrestricted, as it is among the lower Regular classes, by the Law ofNature which limits the increase of sides to one in each generation. If it were so, the number of sides in the Circle would be a merequestion of pedigree and arithmetic, and the four hundred andninety-seventh descendant of an Equilateral Triangle would necessarilybe a polygon with five hundred sides. But this is not the case. Nature's Law prescribes two antagonistic decrees affecting Circularpropagation; first, that as the race climbs higher in the scale ofdevelopment, so development shall proceed at an accelerated pace;second, that in the same proportion, the race shall become lessfertile. Consequently in the home of a Polygon of four or five hundredsides it is rare to find a son; more than one is never seen. On theother hand the son of a five-hundred-sided Polygon has been known topossess five hundred and fifty, or even six hundred sides. 

Art also steps in to help the process of higher Evolution. Ourphysicians have discovered that the small and tender sides of an infantPolygon of the higher class can be fractured, and his whole framere-set, with such exactness that a Polygon of two or three hundredsides sometimes--by no means always, for the process is attended withserious risk--but sometimes overleaps two or three hundred generations, and as it were double at a stroke, the number of his progenitors andthe nobility of his descent. 

Many a promising child is sacrificed in this way. Scarcely one out often survives. Yet so strong is the parental ambition among thosePolygons who are, as it were, on the fringe of the Circular class, thatit is very rare to find the Nobleman of that position in society, whohas neglected to place his first-born in the Circular Neo-TherapeuticGymnasium before he has attained the age of a month. 

One year determines success or failure. At the end of that time thechild has, in all probability, added one more to the tombstones thatcrowd the Neo-Therapeutic Cemetery; but on rare occasional a gladprocession bears back the little one to his exultant parents, no longera Polygon, but a Circle, at least by courtesy: and a single instanceof so blessed a result induces multitudes of Polygonal parents tosubmit to similar domestic sacrifice, 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 asingle maxim, "Attend to your Configuration. " Whether political, ecclesiastical, or moral, all their teaching has for its object theimprovement of individual and collective Configuration--with specialreference of course to the Configuration of the Circles, to which allother objects are subordinated. 

It is the merit of the Circles that they have effectually suppressedthose ancient heresies which led men to waste energy and sympathy inthe vain belief that conduct depends upon will, effort, training, encouragement, praise, or anything else but Configuration. It wasPantocyclus--the illustrious Circle mentioned above, as the queller ofthe Colour Revolt--who first convinced mankind that Configuration makesthe man; that if, for example, you are born an Isosceles with twouneven sides, you will assuredly go wrong unless you have them madeeven--for which purpose you must go to the Isosceles Hospital;similarly, if you are a Triangle, or Square, or even a Polygon, bornwith any Irregularity, you must be taken to one of the RegularHospitals to have your disease cured; otherwise you will end your daysin the State Prison or by the angle of the State Executioner. 

All faults or defects, from the slightest misconduct to the mostflagitious crime, Pantocyclus attributed to some deviation from perfectRegularity in the bodily figure, caused perhaps (if not congenital) bysome collision in a crowd; by neglect to take exercise, or by takingtoo much of it; or even by a sudden change of temperature, resulting ina shrinkage or expansion in some too susceptible part of the frame. Therefore, concluded that illustrious Philosopher, neither good conductnor bad conduct is a fit subject, in any sober estimation, for eitherpraise or blame. For why should you praise, for example, the integrityof a Square who faithfully defends the interests of his client, whenyou ought in reality rather to admire the exact precision of his rightangles? Or again, why blame a lying, thievish Isosceles, when youought rather to deplore the incurable inequality of his sides?

Theoretically, this doctrine is unquestionable; but it has practicaldrawbacks. In dealing with an Isosceles, if a rascal pleads that hecannot help stealing because of his unevenness, you reply that for thatvery reason, because he cannot help being a nuisance to his neighbours, you, the Magistrate, cannot help sentencing him to be consumed--andthere's an end of the matter. But in little domestic difficulties, when the penalty of consumption, or death, is out of the question, thistheory of Configuration sometimes comes in awkwardly; and I mustconfess that occasionally when one of my own Hexagonal Grandsons pleadsas an excuse for his disobedience that a sudden change of temperaturehas been too much for his Perimeter, and that I ought to lay the blamenot on him but on his Configuration, which can only be strengthened byabundance of the choicest sweetmeats, I neither see my way logically toreject, nor practically to accept, his conclusions. 

For my own part, I find it best to assume that a good sound scolding orcastigation has some latent and strengthening influence on myGrandson's Configuration; though I own that I have no grounds forthinking so. At all events I am not alone in my way of extricatingmyself from this dilemma; for I find that many of the highest Circles, sitting as Judges in law courts, use praise and blame towards Regularand Irregular Figures; and in their homes I know by experience that, when scolding their children, they speak about "right" and "wrong" asvehemently and passionately as if they believe that these namesrepresented real existence, and that a human Figure is really capableof choosing between them. 

Constantly carrying out their policy of making Configuration theleading idea in every mind, the Circles reverse the nature of thatCommandment which in Spaceland regulates the relations between parentsand children. With you, children are taught to honour their parents;with us--next to the Circles, who are the chief object of universalhomage--a man is taught to honour his Grandson, if he has one; or, ifnot, his Son. By "honour, " however, is by no means mean "indulgence, "but a reverent regard for their highest interests: and the Circlesteach that the duty of fathers is to subordinate their own interests tothose of posterity, thereby advancing the welfare of the whole State aswell as that of their own immediate descendants. 

The weak point in the system of the Circles--if a humble Square mayventure to speak of anything Circular as containing any element ofweakness--appears to me to be found in their relations with Women. 

As it is of the utmost importance for Society that Irregular birthsshould be discouraged, it follows that no Woman who has anyIrregularities in her ancestry is a fit partner for one who desiresthat his posterity should rise by regular degrees in the social scale. 

Now the Irregularity of a Male is a matter of measurement; but as allWomen are straight, and therefore visibly Regular so to speak, one hasto device some other means of ascertaining what I may call theirinvisible Irregularity, that is to say their potential Irregularitiesas regards possible offspring. This is effected by carefully-keptpedigrees, which are preserved and supervised by the State; and withouta certified pedigree no Woman is allowed to marry. 

Now it might have been supposed the a Circle--proud of his ancestry andregardful for a posterity which might possibly issue hereafter in aChief Circle--would be more careful than any other to choose a wife whohad no blot on her escutcheon. But it is not so. The care in choosinga Regular wife appears to diminish as one rises in the social scale. Nothing would induce an aspiring Isosceles, who has hopes of generatingan Equilateral Son, to take a wife who reckoned a single Irregularityamong her Ancestors; a Square or Pentagon, who is confident that hisfamily is steadily on the rise, does not inquire above thefive-hundredth generation; a Hexagon or Dodecagon is even more carelessof the wife's pedigree; but a Circle has been known deliberately totake a wife who has had an Irregular Great-Grandfather, and all becauseof some slight superiority of lustre, or because of the charms of a lowvoice--which, with us, even more than with you, is thought "anexcellent thing in a Woman. "

Such ill-judged marriages are, as might be expected, barren, if they donot result in positive Irregularity or in diminution of sides; but noneof these evils have hitherto provided sufficiently deterrent. The lossof a few sides in a highly-developed Polygon is not easily noticed, andis sometimes compensated by a successful operation in theNeo-Therapeutic Gymnasium, as I have described above; and the Circlesare too much disposed to acquiesce in infecundity as a law of thesuperior development. Yet, if this evil be not arrested, the gradualdiminution of the Circular class may soon become more rapid, and thetime may not be far distant when, the race being no longer able toproduce a Chief Circle, the Constitution of Flatland must fall. 

One other word of warning suggest itself to me, though I cannot soeasily mention a remedy; and this also refers to our relations withWomen. About three hundred years ago, it was decreed by the ChiefCircle that, since women are deficient in Reason but abundant inEmotion, they ought no longer to be treated as rational, nor receiveany mental education. The consequence was that they were no longertaught to read, nor even to master Arithmetic enough to enable them tocount the angles of their husband or children; and hence they sensiblydeclined during each generation in intellectual power. And this systemof female non-education or quietism still prevails. 

My fear is that, with the best intentions, this policy has been carriedso far as to react injuriously on the Male Sex. 

For the consequence is that, as things now are, we Males have to lead akind of bi-lingual, and I may almost say bimental, existence. WithWomen, we speak of "love, " "duty, " "right, " "wrong, " "pity, " "hope, "and other irrational and emotional conceptions, which have noexistence, and the fiction of which has no object except to controlfeminine exuberances; but among ourselves, and in our books, we have anentirely different vocabulary and I may also say, idiom. "Love" thembecomes "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 theirSex; and they fully believe that the Chief Circle Himself is not moredevoutly adored by us than they are: but behind their backs they areboth regarded and spoken of--by all but the very young--as being littlebetter than "mindless organisms. "

Our Theology also in the Women's chambers is entirely different fromour Theology elsewhere. 

Now my humble fear is that this double training, in language as well asin thought, imposes somewhat too heavy a burden upon the young, especially when, at the age of three years old, they are taken from thematernal care and taught to unlearn the old language--except for thepurpose of repeating it in the presence of the Mothers and Nurses--andto learn the vocabulary and idiom of science. Already methinks Idiscern a weakness in the grasp of mathematical truth at the presenttime as compared with the more robust intellect of our ancestors threehundred years ago. I say nothing of the possible danger if a Womanshould ever surreptitiously learn to read and convey to her Sex theresult of her perusal of a single popular volume; nor of thepossibility that the indiscretion or disobedience of some infant Malemight reveal to a Mother the secrets of the logical dialect. On thesimple ground of the enfeebling of the male intellect, I rest thishumble appeal to the highest Authorities to reconsider the regulationsof 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 thefirst day of the Long Vacation. Having amused myself till a late hourwith my favourite recreation of Geometry, I had retired to rest with anunsolved problem in my mind. In the night I had a dream. 

I saw before me a vast multitude of small Straight Lines (which Inaturally assumed to be Women) interspersed with other Beings stillsmaller and of the nature of lustrous points--all moving to and fro inone and the same Straight Line, and, as nearly as I could judge, withthe same velocity. 

A noise of confused, multitudinous chirping or twittering issued fromthem at intervals as long as they were moving; but sometimes theyceased from motion, and then all was silence. 

Approaching one of the largest of what I thought to be Women, Iaccosted her, but received no answer. A second and third appeal on mypart were equally ineffectual. Losing patience at what appeared to meintolerable rudeness, I brought my mouth to a position full in front ofher mouth so as to intercept her motion, and loudly repeated myquestion, "Woman, what signifies this concourse, and this strange andconfused chirping, and this monotonous motion to and fro in one and thesame Straight Line?"

"I am no Woman, " replied the small Line: "I am the Monarch of theworld. But thou, whence intrudest thou into my realm of Lineland?"Receiving this abrupt reply, I begged pardon if I had in any waystartled or molested his Royal Highness; and describing myself as astranger I besought the King to give me some account of his dominions. But I had the greatest possible difficulty in obtaining any informationon points that really interested me; for the Monarch could not refrainfrom constantly assuming that whatever was familiar to him must also beknown to me and that I was simulating ignorance in jest. However, bypreserving questions I elicited the following facts:

It seemed that this poor ignorant Monarch--as he called himself--waspersuaded that the Straight Line which he called his Kingdom, and inwhich he passed his existence, constituted the whole of the world, andindeed 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 hadcome to him in a manner so contrary to his experience that he had madeno answer, "seeing no man, " as he expressed it, "and hearing a voice asit were from my own intestines. " Until the moment when I placed mymouth in his World, he had neither seen me, nor heard anything exceptconfused sounds beating against, what I called his side, but what hecalled his INSIDE or STOMACH; nor had he even now the least conceptionof the region from which I had come. Outside his World, or Line, allwas 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 PointsWomen--were all alike confined in motion and eyesight to that singleStraight Line, which was their World. It need scarcely be added thatthe whole of their horizon was limited to a Point; nor could any oneever see anything but a Point. Man, woman, child, thing--each as aPoint to the eye of a Linelander. Only by the sound of the voice couldsex or age be distinguished. Moreover, as each individual occupied thewhole 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. Onceneighbours, always neighbours. Neighbourhood with them was likemarriage with us. Neighbours remained neighbours till death did thempart. 

Such a life, with all vision limited to a Point, and all motion to aStraight Line, seemed to me inexpressibly dreary; and I was surprisedto note that vivacity and cheerfulness of the King. Wondering whetherit was possible, amid circumstances so unfavourable to domesticrelations, to enjoy the pleasures of conjugal union, I hesitated forsome time to question his Royal Highness on so delicate a subject; butat last I plunged into it by abruptly inquiring as to the health of hisfamily. "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 nonebut Men--I ventured to reply, "Pardon me, but I cannot imagine how yourRoyal Highness can at any time either see or approach their Majesties, when there at least half a dozen intervening individuals, whom you canneither see through, nor pass by? Is it possible that in Linelandproximity is not necessary for marriage and for the generation ofchildren?"

"How can you ask so absurd a question?" replied the Monarch. "If itwere indeed as you suggest, the Universe would soon be depopulated. No, no; neighbourhood is needless for the union of hearts; and thebirth of children is too important a matter to have been allowed todepend upon such an accident as proximity. You cannot be ignorant ofthis. Yet since you are pleased to affect ignorance, I will instructyou as if you were the veriest baby in Lineland. Know, then, thatmarriages are consummated by means of the faculty of sound and thesense of hearing. 

"You are of course aware that every Man has two mouths or voices--aswell as two eyes--a bass at one and a tenor at the other of hisextremities. I should not mention this, but that I have been unable todistinguish your tenor in the course of our conversation. " I repliedthat I had but one voice, and that I had not been aware that his RoyalHighness had two. "That confirms my impression, " said the King, "thatyou are not a Man, but a feminine Monstrosity with a bass voice, and anutterly 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, " hecried. "How can there be a completely harmonious union without thecombination of the Four in One, viz. The Bass and Tenor of the Man andthe Soprano and Contralto of the two Women?" "But supposing, " said I, "that a man should prefer one wife or three?" "It is impossible, " hesaid; "it is as inconceivable as that two and one should make five, orthat the human eye should see a Straight Line. " I would haveinterrupted him; but he proceeded as follows:

"Once in the middle of each week a Law of Nature compels us to move toand fro with a rhythmic motion of more than usual violence, whichcontinues for the time you would take to count a hundred and one. Inthe midst of this choral dance, at the fifty-first pulsation, theinhabitants of the Universe pause in full career, and each individualsends forth his richest, fullest, sweetest strain. It is in thisdecisive moment that all our marriages are made. So exquisite is theadaptation of Bass and Treble, of Tenor to Contralto, that oftentimesthe Loved Ones, though twenty thousand leagues away, recognize at oncethe responsive note of their destined Lover; and, penetrating thepaltry obstacles of distance, Love unites the three. The marriage inthat instance consummated results in a threefold Male and Femaleoffspring which takes its place in Lineland. "

"What! Always threefold?" said I. "Must one wife then always havetwins?"

"Bass-voice Monstrosity! yes, " replied the King. "How else could thebalance of the Sexes be maintained, if two girls were not born forevery boy? Would you ignore the very Alphabet of Nature?" He ceased, speechless for fury; and some time elapsed before I could induce him toresume his narrative. 

"You will not, of course, suppose that every bachelor among us findshis mates at the first wooing in this universal Marriage Chorus. Onthe contrary, the process is by most of us many times repeated. Feware the hearts whose happy lot is at once to recognize in each other'svoice the partner intended for them by Providence, and to fly into areciprocal and perfectly harmonious embrace. With most of us thecourtship is of long duration. The Wooer's voices may perhaps accordwith one of the future wives, but not with both; or not, at first, witheither; or the Soprano and Contralto may not quite harmonize. In suchcases Nature has provided that every weekly Chorus shall bring thethree Lovers into closer harmony. Each trial of voice, each freshdiscovery of discord, almost imperceptibly induces the less perfect tomodify his or her vocal utterance so as to approximate to the moreperfect. And after many trials and many approximations, the result isat last achieved. There comes a day at last when, while the wontedMarriage Chorus goes forth from universal Lineland, the three far-offLovers suddenly find themselves in exact harmony, and, before they areaware, the wedded Triplet is rapt vocally into a duplicate embrace; andNature 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 rapturesto the level of common sense, I determined to endeavour to open up tohim some glimpses of the truth, that is to say of the nature of thingsin Flatland. So I began thus: "How does your Royal Highnessdistinguish the shapes and positions of his subjects? I for my partnoticed by the sense of sight, before I entered your Kingdom, that someof your people are lines and others Points; and that some of the linesare larger--" "You speak of an impossibility, " interrupted the King;"you must have seen a vision; for to detect the difference between aLine and a Point by the sense of sight is, as every one knows, in thenature of things, impossible; but it can be detected by the sense ofhearing, and by the same means my shape can be exactly ascertained. Behold me--I am a Line, the longest in Lineland, over six inches ofSpace--" "Of Length, " I ventured to suggest. "Fool, " said he, "Spaceis Length. Interrupt me again, and I have done. "

I apologized; but he continued scornfully, "Since you are impervious toargument, you shall hear with your ears how by means of my two voices Ireveal my shape to my Wives, who are at this moment six thousand milesseventy yards two feet eight inches away, the one to the North, theother to the South. Listen, I call to them. "

He chirruped, and then complacently continued: "My wives at thismoment receiving the sound of one of my voice, closely followed by theother, and perceiving that the latter reaches them after an interval inwhich sound can traverse 6. 457 inches, infer that one of my mouths is6. 457 inches further from them than the other, and accordingly know myshape to be 6. 457 inches. But you will of course understand that mywives do not make this calculation every time they hear my two voices. They made it, once for all, before we were married. But they COULDmake it at any time. And in the same way I can estimate the shape ofany 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 twovoices, or so disguises his Southern voice that it cannot be recognizedas the echo of the Northern? May not such deceptions cause greatinconvenience? And have you no means of checking frauds of this kindby commanding your neighbouring subjects to feel one another?" This ofcourse was a very stupid question, for feeling could not have answeredthe purpose; but I asked with the view of irritating the Monarch, and Isucceeded perfectly. 

"What!" cried he in horror, "explain your meaning. " "Feel, touch, comeinto 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 bydeath. And the reason is obvious. The frail form of a Woman, beingliable to be shattered by such an approximation, must be preserved bythe State; but since Women cannot be distinguished by the sense ofsight from Men, the Law ordains universally that neither Man nor Womanshall be approached so closely as to destroy the interval between theapproximator and the approximated. 

"And indeed what possible purpose would be served by this illegal andunnatural excess of approximation which you call TOUCHING, when all theends of so brutal and course a process are attained at once more easilyand more exactly by the sense of hearing? As to your suggested dangerof deception, it is non-existent: for the Voice, being the essence ofone's Being, cannot be thus changed at will. But come, suppose that Ihad the power of passing through solid things, so that I couldpenetrate my subjects, one after another, even to the number of abillion, verifying the size and distance of each by the sense ofFEELING: How much time and energy would be wasted in this clumsy andinaccurate method! Whereas now, in one moment of audition, I take asit were the census and statistics, local, corporeal, mental andspiritual, of every living being in Lineland. Hark, only hark!"

So saying he paused and listened, as if in an ecstasy, to a sound whichseemed to me no better than a tiny chirping from an innumerablemultitude 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 outthat your life in Lineland must be deplorably dull. To see nothing buta Point! Not even to be able to contemplate a Straight Line! Nay, noteven to know what a Straight Line is! To see, yet to be cut off fromthose Linear prospects which are vouchsafed to us in Flatland! Bettersurely to have no sense of sight at all than to see so little! I grantyou I have not your discriminative faculty of hearing; for the concertof all Lineland which gives you such intense pleasure, is to me nobetter than a multitudinous twittering or chirping. But at least I candiscern, by sight, a Line from a Point. And let me prove it. Justbefore 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 yourimmediate proximity on the left, and eight Men and two Women on yourright. Is not this correct?"

"It is correct, " said the King, "so far as the numbers and sexes areconcerned, though I know not what you mean by 'right' and 'left. ' But Ideny that you saw these things. For how could you see the Line, thatis to say the inside, of any Man? But you must have heard thesethings, and then dreamed that you saw them. And let me ask what youmean by those words 'left' and 'right. ' I suppose it is your way ofsaying 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 Linealtogether. 

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 Spaceis not the true Space. True Space is a Plane; but your Space is only aLine. 

King. If you cannot indicate this motion from left to right byyourself 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 nowords of mine can make my meaning clearer to you. But surely youcannot 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, doesit 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 whichyour side is now fronting? In other words, instead of always moving inthe direction of one of your extremities, do you never feel a desire tomove in the direction, so to speak, of your side?

King. Never. And what do you mean? How can a man's inside "front" inany 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 desireto indicate to you. 

At the word I began to move my body out of Lineland. As long as anypart of me remained in his dominion and in his view, the King keptexclaiming, "I see you, I see you still; you are not moving. " But whenI had at last moved myself out of his Line, he cried in his shrillestvoice, "She is vanished; she is dead. " "I am not dead, " replied I; "Iam simply out of Lineland, that is to say, out of the Straight Linewhich you call Space, and in the true Space, where I can see things asthey are. And at this moment I can see your Line, or side--or insideas you are pleased to call it; and I can see also the Men and Women onthe North and South of you, whom I will now enumerate, describing theirorder, their size, and the interval between each. "

When I had done this at great length, I cried triumphantly, "Does thatat 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 youappear to have only one voice I have little doubt you are not a Man buta Woman--but, if you had a particle of sense, you would listen toreason. You ask me to believe that there is another Line besides thatwhich my senses indicate, and another motion besides that of which I amdaily conscious. I, in return, ask you to describe in words orindicate by motion that other Line of which you speak. Instead ofmoving, you merely exercise some magic art of vanishing and returningto sight; and instead of any lucid description of your new World, yousimply tell me the numbers and sizes of some forty of my retinue, factsknown to any child in my capital. Can anything be more irrational oraudacious? Acknowledge your folly or depart from my dominions. "

Furious at his perversity, and especially indignant that he professedto be ignorant of my sex, I retorted in no measured terms, "BesottedBeing! You think yourself the perfection of existence, while you arein reality the most imperfect and imbecile. You profess to see, whereas you see nothing but a Point! You plume yourself on inferringthe existence of a Straight Line; but I CAN SEE Straight Lines, andinfer the existence of Angles, Triangles, Squares, Pentagons, Hexagons, and even Circles. Why waste more words? Suffice it that I am thecompletion of your incomplete self. You are a Line, but I am a Line ofLines called in my country a Square: and even I, infinitely superiorthough I am to you, am of little account among the great nobles ofFlatland, whence I have come to visit you, in the hope of enlighteningyour ignorance. "

Hearing these words the King advanced towards me with a menacing cry asif to pierce me through the diagonal; and in that same movement therearose from myriads of his subjects a multitudinous war-cry, increasingin vehemence till at last methought it rivalled the roar of an army ofa hundred thousand Isosceles, and the artillery of a thousandPentagons. Spell-bound and motionless, I could neither speak nor moveto avert the impending destruction; and still the noise grew louder, and the King came closer, when I awoke to find the breakfast-bellrecalling 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 our 1999th year of our era. The patterning ofthe rain had long ago announced nightfall; and I was sitting (footnote3) in the company of my wife, musing on the events of the past and theprospects of the coming year, the coming century, the coming Millennium. 

My four Sons and two orphan Grandchildren had retired to their severalapartments; and my wife alone remained with me to see the oldMillennium out and the new one in. 

I was rapt in thought, pondering in my mind some words that hadcasually issued from the mouth of my youngest Grandson, a mostpromising young Hexagon of unusual brilliancy and perfect angularity. His uncles and I had been giving him his usual practical lesson inSight Recognition, turning ourselves upon our centres, now rapidly, nowmore slowly, and questioning him as to our positions; and his answershad been so satisfactory that I had been induced to reward him bygiving him a few hints on Arithmetic, as applied to Geometry. 

Taking nine Squares, each an inch every way, I had put them together soas to make one large Square, with a side of three inches, and I hadhence proved to my little Grandson that--though it was impossible forus to SEE the inside of the Square--yet we might ascertain the numberof square inches in a Square by simply squaring the number of inches inthe side: "and thus, " said I, "we know that three-to-the-second, ornine, represents the number of square inches in a Square whose side isthree inches long. "

The little Hexagon meditated on this a while and then said to me; "Butyou have been teaching me to raise numbers to the third power: Isuppose three-to-the-third must mean something in Geometry; what doesit mean?" "Nothing at all, " replied I, "not at least in Geometry; forGeometry has only Two Dimensions. " And then I began to shew the boyhow a Point by moving through a length of three inches makes a Line ofthree inches, which may be represented by three; and how a Line ofthree inches, moving parallel to itself through a length of threeinches, makes a Square of three inches every way, which may berepresented by three-to-the-second. Xxx Upon this, my Grandson, againreturning to his former suggestion, took me up rather suddenly andexclaimed, "Well, then, if a Point by moving three inches, makes a Lineof three inches represented by three; and if a straight Line of threeinches, moving parallel to itself, makes a Square of three inches everyway, represented by three-to-the-second; it must be that a Square ofthree inches every way, moving somehow parallel to itself (but I don'tsee how) must make Something else (but I don't see what) of threeinches every way--and this must be represented by three-to-the-third. "

"Go to bed, " said I, a little ruffled by this interruption: "if youwould talk less nonsense, you would remember more sense. "

So my Grandson had disappeared in disgrace; and there I sat by myWife's side, endeavouring to form a retrospect of the year 1999 and ofthe possibilities of the year 2000; but not quite able to shake of thethoughts suggested by the prattle of my bright little Hexagon. Only afew sands now remained in the half-hour glass. Rousing myself from myreverie I turned the glass Northward for the last time in the oldMillennium; and in the act, I exclaimed aloud, "The boy is a fool. "

Straightway I became conscious of a Presence in the room, and achilling breath thrilled through my very being. "He is no such thing, "cried my Wife, "and you are breaking the Commandments in thusdishonouring your own Grandson. " But I took no notice of her. Lookingaround in every direction I could see nothing; yet still I FELT aPresence, and shivered as the cold whisper came again. I started up. "What is the matter?" said my Wife, "there is no draught; what are youlooking for? There is nothing. " There was nothing; and I resumed myseat, again exclaiming, "The boy is a fool, I say; three-to-the-thirdcan have no meaning in Geometry. " At once there came a distinctlyaudible reply, "The boy is not a fool; and three-to-the-third has anobvious Geometrical meaning. "

My Wife as well as myself heard the words, although she did notunderstand their meaning, and both of us sprang forward in thedirection of the sound. What was our horror when we saw before us aFigure! At the first glance it appeared to be a Woman, seen sideways;but a moment's observation shewed me that the extremities passed intodimness too rapidly to represent one of the Female Sex; and I shouldhave thought it a Circle, only that it seemed to change its size in amanner impossible for a Circle or for any regular Figure of which I hadhad experience. 

But my Wife had not my experience, nor the coolness necessary to notethese characteristics. With the usual hastiness and unreasoningjealousy of her Sex, she flew at once to the conclusion that a Womanhad entered the house through some small aperture. "How comes thisperson here?" she exclaimed, "you promised me, my dear, that thereshould be no ventilators in our new house. " "Nor are they any, " saidI; "but what makes you think that the stranger is a Woman? I see by mypower 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 aCircle to the sight'"--two Proverbs, very common with the Frailer Sexin 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 Wifeadvanced towards the Stranger, "Permit me, Madam to feel and be feltby--" then, suddenly recoiling, "Oh! it is not a Woman, and there areno angles either, not a trace of one. Can it be that I have somisbehaved to a perfect Circle?"

"I am indeed, in a certain sense a Circle, " replied the Voice, "and amore perfect Circle than any in Flatland; but to speak more accurately, I am many Circles in one. " Then he added more mildly, "I have amessage, dear Madam, to your husband, which I must not deliver in yourpresence; and, if you would suffer us to retire for a few minutes--"But my wife would not listen to the proposal that our august Visitorshould so incommode himself, and assuring the Circle that the hour ofher own retirement had long passed, with many reiterated apologies forher recent indiscretion, she at last retreated to her apartment. 

I glanced at the half-hour glass. The last sands had fallen. Thethird Millennium had begun. 

Footnote 3. When I say "sitting, " of course I do not mean any changeof attitude such as you in Spaceland signify by that word; for as wehave no feet, we can no more "sit" nor "stand" (in your sense of theword) than one of your soles or flounders. 

Nevertheless, we perfectly well recognize the different mental statesof volition implied by "lying, " "sitting, " and "standing, " which are tosome extent indicated to a beholder by a slight increase of lustrecorresponding to the increase of volition. 

But on this, and a thousand other kindred subjects, time forbids me todwell. 

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 diedaway, I began to approach the Stranger with the intention of taking anearer view and of bidding him be seated: but his appearance struck medumb and motionless with astonishment. Without the slightest symptomsof angularity he nevertheless varied every instant with graduations ofsize and brightness scarcely possible for any Figure within the scopeof my experience. The thought flashed across me that I might havebefore me a burglar or cut-throat, some monstrous Irregular Isosceles, who, by feigning the voice of a Circle, had obtained admission somehowinto 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 beremarkably dry), made it difficult for me to trust to SightRecognition, especially at the short distance at which I was standing. Desperate with fear, I rushed forward with an unceremonious, "You mustpermit me, Sir--" and felt him. My Wife was right. There was not thetrace of an angle, not the slightest roughness or inequality: never inmy life had I met with a more perfect Circle. He remained motionlesswhile I walked around him, beginning from his eye and returning to itagain. Circular he was throughout, a perfectly satisfactory Circle;there could not be a doubt of it. Then followed a dialogue, which Iwill endeavour to set down as near as I can recollect it, omitting onlysome of my profuse apologies--for I was covered with shame andhumiliation that I, a Square, should have been guilty of theimpertinence of feeling a Circle. It was commenced by the Strangerwith some impatience at the lengthiness of my introductory process. 

Stranger. Have you felt me enough by this time? Are you notintroduced to me yet?

I. Most illustrious Sir, excuse my awkwardness, which arises not fromignorance of the usages of polite society, but from a little surpriseand nervousness, consequent on this somewhat unexpected visit. And Ibeseech you to reveal my indiscretion to no one, and especially not tomy Wife. But before your Lordship enters into further communications, would he deign to satisfy the curiosity of one who would gladly knowwhence his visitor came?

Stranger. From Space, from Space, Sir: whence else?

I. Pardon me, my Lord, but is not your Lordship already in Space, yourLordship 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. Youthink it is of Two Dimensions only; but I have come to announce to youa Third--height, breadth, and length. 

I. Your Lordship is pleased to be merry. We also speak of length andheight, or breadth and thickness, thus denoting Two Dimensions by fournames. 

Stranger. But I mean not only three names, but Three Dimensions. 

I. Would your Lordship indicate or explain to me in what direction isthe 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 youcannot look, because you have no eye in your side. 

I. Pardon me, my Lord, a moment's inspection will convince yourLordship that I have a perfectly luminary at the juncture of my twosides. 

Stranger: Yes: but in order to see into Space you ought to have aneye, not on your Perimeter, but on your side, that is, on what youwould probably call your inside; but we in Spaceland should call ityour 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 fromSpace, or, since you will not understand what Space means, from theLand of Three Dimensions whence I but lately looked down upon yourPlane which you call Space forsooth. From that position of advantage Idiscerned all that you speak of as SOLID (by which you mean "enclosedon four sides"), your houses, your churches, your very chests andsafes, yes even your insides and stomachs, all lying open and exposedto 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 hisapartment, and your two Grandsons the Hexagons; I saw your youngestHexagon remain a while with you and then retire to his room, leavingyou and your Wife alone. I saw your Isosceles servants, three innumber, 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. 

Strange. Not so. Your roof, as you know very well, has been recentlyrepaired, and has no aperture by which even a Woman could penetrate. Itell you I come from Space. Are you not convinced by what I have toldyou of your children and household?

I. Your Lordship must be aware that such facts touching the belongingsof his humble servant might be easily ascertained by any one of theneighbourhood possessing your Lordship's ample means of information. 

Stranger. (TO HIMSELF. ) What must I do? Stay; one more argumentsuggests itself to me. When you see a Straight Line-- your wife, forexample--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 aStraight Line, and only of One Dimension. No, no, my Lord; we Squaresare better advised, and are as well aware of your Lordship that aWoman, though popularly called a Straight Line, is, really andscientifically, 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 itpossesses yet another Dimension. 

I. My Lord, I have just acknowledged that a Woman is broad as well aslong. We see her length, we infer her breadth; which, though veryslight, 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 SEEwhat we call her HEIGHT; although the last Dimension is infinitesimalin your country. If a Line were mere length without "height, " it wouldcease to occupy Space and would become invisible. Surely you mustrecognize this?

I. I must indeed confess that I do not in the least understand yourLordship. When we in Flatland see a Line, we see length andBRIGHTNESS. If the brightness disappears, the Line is extinguished, and, as you say, ceases to occupy Space. But am I to suppose that yourLordship gives the brightness the title of a Dimension, and that whatwe call "bright" you call "high"?

Stranger. No, indeed. By "height" I mean a Dimension like yourlength: only, with you, "height" is not so easily perceptible, beingextremely small. 

I. My Lord, your assertion is easily put to the test. You say I havea Third Dimension, which you call "height. " Now, Dimension impliesdirection and measurement. Do but measure my "height, " or merelyindicate to me the direction in which my "height" extends, and I willbecome your convert. Otherwise, your Lordship's own understand musthold me excused. 

Stranger. (TO HIMSELF. ) I can do neither. How shall I convince him?Surely a plain statement of facts followed by ocular demonstrationought to suffice. --Now, Sir; listen to me. 

You are living on a Plane. What you style Flatland is the vast levelsurface of what I may call a fluid, or in, the top of which you andyour countrymen move about, without rising above or falling below it. 

I am not a plane Figure, but a Solid. You call me a Circle; but inreality I am not a Circle, but an infinite number of Circles, of sizevarying from a Point to a Circle of thirteen inches in diameter, oneplaced on the top of the other. When I cut through your plane as I amnow doing, I make in your plane a section which you, very rightly, calla Circle. For even a Sphere--which is my proper name in my owncountry--if he manifest himself at all to an inhabitant ofFlatland--must needs manifest himself as a Circle. 

Do you not remember--for I, who see all things, discerned last nightthe phantasmal vision of Lineland written upon your brain--do you notremember, I say, how when you entered the realm of Lineland, you werecompelled to manifest yourself to the King, not as a Square, but as aLine, because that Linear Realm had not Dimensions enough to representthe whole of you, but only a slice or section of you? In precisely thesame way, your country of Two Dimensions is not spacious enough torepresent me, a being of Three, but can only exhibit a slice or sectionof me, which is what you call a Circle. 

The diminished brightness of your eye indicates incredulity. But nowprepare to receive proof positive of the truth of my assertions. Youcannot 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 sectionsbecome smaller. See now, I will rise; and the effect upon your eyewill be that my Circle will become smaller and smaller till it dwindlesto a point and finally vanishes. 

There was no "rising" that I could see; but he diminished and finallyvanished. 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 ahollow voice--close to my heart it seemed--"Am I quite gone? Are youconvinced now? Well, now I will gradually return to Flatland and youshall see my section become larger and larger. "

Every reader in Spaceland will easily understand that my mysteriousGuest was speaking the language of truth and even of simplicity. Butto me, proficient though I was in Flatland Mathematics, it was by nomeans a simple matter. The rough diagram given above will make itclear to any Spaceland child that the Sphere, ascending in the threepositions indicated there, must needs have manifested himself to me, orto any Flatlander, as a Circle, at first of full size, then small, andat last very small indeed, approaching to a Point. But to me, althoughI saw the facts before me, the causes were as dark as ever. All that Icould comprehend was, that the Circle had made himself smaller andvanished, and that he had now re-appeared and was rapidly makinghimself larger. 

When he regained his original size, he heaved a deep sigh; for heperceived 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 Circleat all, but some extremely clever juggler; or else that the old wives'tales were true, and that after all there were such people asEnchanters 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 ourdialogue. 

Sphere. Tell me, Mr. Mathematician; if a Point moves Northward, andleaves 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 toitself, East and West, so that every point in it leaves behind it thewake of a straight Line. What name will you give to the Figure therebyformed? We will suppose that it moves through a distance equal to theoriginal 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 Squarein 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 tomove 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 thepurpose of my illustration--every Point in you, that is to say in whatyou call your inside, is to pass upwards through Space in such a waythat no Point shall pass through the position previously occupied byany other Point; but each Point shall describe a straight Line of itsown. This is all in accordance with Analogy; surely it must be clearto you. 

Restraining my impatience--for I was now under a strong temptation torush blindly at my Visitor and to precipitate him into Space, or out ofFlatland, 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 bythis motion which you are pleased to denote by the word 'upward'? Ipresume it is describable in the language of Flatland. "

Sphere. Oh, certainly. It is all plain and simple, and in strictaccordance with Analogy--only, by the way, you must not speak of theresult as being a Figure, but as a Solid. But I will describe it toyou. Or rather not I, but Analogy. 

We began with a single Point, which of course--being itself aPoint--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 EIGHTterminal 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, notwhat YOU call sides, but what WE call sides. You would call themSOLIDS. 

I. And how many solids or sides will appertain to this Being whom I amto generate by the motion of my inside in an "upward" direction, andwhom you call a Cube?

Sphere. How can you ask? And you a mathematician! The side ofanything is always, if I may so say, one Dimension behind the thing. Consequently, as there is no Dimension behind a Point, a Point has 0sides; a Line, if I may so say, has 2 sides (for the points of a Linemay 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 isto say, six of your insides. You see it all now, eh?

"Monster, " I shrieked, "be thou juggler, enchanter, dream, or devil, nomore will I endure thy mockeries. Either thou or I must perish. " Andsaying these words I precipitated myself upon him. 

SECTION 17 How the Sphere, having in vain tried words, resorted todeeds

It was in vain. I brought my hardest right angle into violentcollision with the Stranger, pressing on him with a force sufficient tohave destroyed any ordinary Circle: but I could feel him slowly andunarrestably slipping from my contact; not edging to the right nor tothe left, but moving somehow out of the world, and vanishing intonothing. Soon there was a blank. But still I heard the Intruder'svoice. 

Sphere. Why will you refuse to listen to reason? I had hoped to findin you--as being a man of sense and an accomplished mathematician--afit apostle for the Gospel of the Three Dimensions, which I am allowedto preach once only in a thousand years: but now I know not how toconvince you. Stay, I have it. Deeds, and not words, shall proclaimthe truth. Listen, my friend. 

I have told you I can see from my position in Space the inside of allthings that you consider closed. For example, I see in yonder cupboardnear which you are standing, several of what you call boxes (but likeeverything else in Flatland, they have no tops or bottom) full ofmoney; I see also two tablets of accounts. I am about to descend intothat cupboard and to bring you one of those tablets. I saw you lockthe cupboard half an hour ago, and I know you have the key in yourpossession. But I descend from Space; the doors, you see, remainunmoved. Now I am in the cupboard and am taking the tablet. Now Ihave it. Now I ascend with it. 

I rushed to the closet and dashed the door open. One of the tabletswas gone. With a mocking laugh, the Stranger appeared in the othercorner of the room, and at the same time the tablet appeared upon thefloor. I took it up. There could be no doubt--it was the missingtablet. 

I groaned with horror, doubting whether I was not out of my sense; butthe Stranger continued: "Surely you must now see that my explanation, and no other, suits the phenomena. What you call Solid things arereally superficial; what you call Space is really nothing but a greatPlane. I am in Space, and look down upon the insides of the things ofwhich you only see the outsides. You could leave the Plane yourself, if you could but summon up the necessary volition. A slight upward ordownward 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 Ican see, though of course I see it on a smaller scale. For example, Iam ascending; now I can see your neighbour the Hexagon and his familyin their several apartments; now I see the inside of the Theatre, tendoors off, from which the audience is only just departing; and on theother side a Circle in his study, sitting at his books. Now I shallcome back to you. And, as a crowning proof, what do you say to mygiving you a touch, just the least touch, in your stomach? It will notseriously injure you, and the slight pain you may suffer cannot becompared with the mental benefit you will receive. "

Before I could utter a word of remonstrance, I felt a shooting pain inmy inside, and a demoniacal laugh seemed to issue from within me. Amoment afterwards the sharp agony had ceased, leaving nothing but adull ache behind, and the Stranger began to reappear, saying, as hegradually 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 endureexistence subject to the arbitrary visitations of a Magician who couldthus play tricks with one's very stomach. If only I could in any waymanage to pin him against the wall till help came!

Once more I dashed my hardest angle against him, at the same timealarming the whole household by my cries for aid. I believe, at themoment of my onset, the Stranger had sunk below our Plane, and reallyfound difficulty in rising. In any case he remained motionless, whileI, hearing, as I thought, the sound of some help approaching, pressedagainst him with redoubled vigor, and continued to shout for assistance. 

A convulsive shudder ran through the Sphere. "This must not be, " Ithought I heard him say: "either he must listen to reason, or I musthave recourse to the last resource of civilization. " Then, addressingme in a louder tone, he hurriedly exclaimed, "Listen: no stranger mustwitness what you have witnessed. Send your Wife back at once, beforeshe enters the apartment. The Gospel of Three Dimensions must not bethus frustrated. Not thus must the fruits of one thousand years ofwaiting be thrown away. I hear her coming. Back! back! Away from me, or you must go with me--wither you know not--into the Land of ThreeDimensions!"

"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 yourfate: 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 Linethat was no Line; Space that was not Space: I was myself, and notmyself. When I could find voice, I shrieked loud in agony, "Eitherthis is madness or it is Hell. " "It is neither, " calmly replied thevoice of the Sphere, "it is Knowledge; it is Three Dimensions: openyour eye once again and try to look steadily. "

I looked, and, behold, a new world! There stood before me, visiblyincorporate, all that I had before inferred, conjectured, dreamed, ofperfect Circular beauty. What seemed the centre of the Stranger's formlay open to my view: yet I could see no heart, lungs, nor arteries, only a beautiful harmonious Something--for which I had no words; butyou, my Readers in Spaceland, would call it the surface of the Sphere. 

Prostrating myself mentally before my Guide, I cried, "How is it, Odivine 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 giving toyou, nor to any other Being, to behold my internal parts. I am of adifferent order of Beings from those in Flatland. Were I a Circle, youcould discern my intestines, but I am a Being, composed as I told youbefore, of many Circles, the Many in the One, called in this country aSphere. And, just as the outside of a Cube is a Square, so the outsideof a Sphere represents the appearance of a Circle. "

Bewildered though I was by my Teacher's enigmatic utterance, I nolonger chafed against it, but worshipped him in silent adoration. Hecontinued, with more mildness in his voice. "Distress not yourself ifyou cannot at first understand the deeper mysteries of Spaceland. Bydegrees they will dawn upon you. Let us begin by casting back a glanceat the region whence you came. Return with me a while to the plains ofFlatland and I will shew you that which you have often reasoned andthought about, but never seen with the sense of sight--a visibleangle. " "Impossible!" I cried; but, the Sphere leading the way, Ifollowed as if in a dream, till once more his voice arrested me: "Lookyonder, and behold your own Pentagonal house, and all its inmates. "

I looked below, and saw with my physical eye all that domesticindividuality which I had hitherto merely inferred with theunderstanding. And how poor and shadowy was the inferred conjecture incomparison with the reality which I now behold! My four Sons calmlyasleep in the North-Western rooms, my two orphan Grandsons to theSouth; the Servants, the Butler, my Daughter, all in their severalapartments. Only my affectionate Wife, alarmed by my continuedabsence, had quitted her room and was roving up and down in the Hall, anxiously awaiting my return. Also the Page, aroused by my cries, hadleft his room, and under pretext of ascertaining whether I had fallensomewhere in a faint, was prying into the cabinet in my study. Allthis I could now SEE, not merely infer; and as we came nearer andnearer, I could discern even the contents of my cabinet, and the twochests of gold, and the tablets of which the Sphere had made mention. 

Touched by my Wife's distress, I would have sprung downward to reassureher, but I found myself incapable of motion. "Trouble not yourselfabout 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 theSphere had said. The further we receded from the object we beheld, thelarger became the field of vision. My native city, with the interiorof every house and every creature therein, lay open to my view inminiature. We mounted higher, and lo, the secrets of the earth, thedepths of the mines and inmost caverns of the hills, were bared beforeme. 

Awestruck at the sight of the mysteries of the earth, thus unveiledbefore my unworthy eye, I said to my Companion, "Behold, I am become asa God. For the wise men in our country say that to see all things, oras they express it, OMNIVIDENCE, is the attribute of God alone. " Therewas something of scorn in the voice of my Teacher as he made answer:"it is so indeed? Then the very pick-pockets and cut-throats of mycountry are to be worshipped by your wise men as being Gods: for thereis not one of them that does not see as much as you see now. But trustme, 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 ourcountry can see everything that is in your country, surely that is noreason why the pick-pocket or cut-throat should be accepted by you as aGod. This omnividence, as you call it--it is not a common word inSpaceland--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 ofwomen! And we know that a Circle is a higher Being than a StraightLine, in so far as knowledge and wisdom are more to be esteemed thanmere affection. 

Sphere. It is not for me to classify human faculties according tomerit. Yet many of the best and wisest in Spaceland think more of theaffections than of the understand, more of your despised Straight Linesthan of your belauded Circles. But enough of this. Look yonder. Doyou know that building?

I looked, and afar off I saw an immense Polygonal structure, in which Irecognized the General Assembly Hall of the States of Flatland, surrounded by dense lines of Pentagonal buildings at right angles toeach other, which I knew to be streets; and I perceived that I wasapproaching the great Metropolis. 

"Here we descend, " said my Guide. It was now morning, the first hourof the first day of the two thousandth year of our era. Acting, as wastheir wont, in strict accordance with precedent, the highest Circles ofthe realm were meeting in solemn conclave, as they had met on the firsthour of the first day of the year 1000, and also on the first hour ofthe first day of the year 0. 

The minutes of the previous meetings were now read by one whom I atonce recognized as my brother, a perfectly Symmetrical Square, and theChief Clerk of the High Council. It was found recorded on eachoccasion that: "Whereas the States had been troubled by diversill-intentioned persons pretending to have received revelations fromanother World, and professing to produce demonstrations whereby theyhad instigated to frenzy both themselves and others, it had been forthis cause unanimously resolved by the Grand Council that on the firstday of each millenary, special injunctions be sent to the Prefects inthe several districts of Flatland, to make strict search for suchmisguided persons, and without formality of mathematical examination, to destroy all such as were Isosceles of any degree, to scourge andimprison any regular Triangle, to cause any Square or Pentagon to besent to the district Asylum, and to arrest any one of higher rank, sending him straightway to the Capital to be examined and judged by theCouncil. "

"You hear your fate, " said the Sphere to me, while the Council waspassing for the third time the formal resolution. "Death orimprisonment awaits the Apostle of the Gospel of Three Dimensions. ""Not so, " replied I, "the matter is now so clear to me, the nature ofreal space so palpable, that methinks I could make a child understandit. Permit me but to descend at this moment and enlighten them. " "Notyet, " said my Guide, "the time will come for that. Meantime I mustperform 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) ofFlatland, right in the midst of the ring of Counsellors. "I come, "said he, "to proclaim that there is a land of Three Dimensions. "

I could see many of the younger Counsellors start back in manifesthorror, as the Sphere's circular section widened before them. But on asign from the presiding Circle--who shewed not the slightest alarm orsurprise--six Isosceles of a low type from six different quartersrushed upon the Sphere. "We have him, " they cried; "No; yes; we havehim 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, towhich I alone have access, tell me that a similar occurrence happenedon the last two millennial commencements. You will, of course, saynothing 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 fatethe wretched policemen--ill-fated and unwilling witnesses of aState-secret which they were not to be permitted to reveal--he againaddressed the Counsellors. "My Lords, the business of the Councilbeing concluded, I have only to wish you a happy New Year. " Beforedeparting, he expressed, at some length, to the Clerk, my excellent butmost unfortunate brother, his sincere regret that, in accordance withprecedent and for the sake of secrecy, he must condemn him to perpetualimprisonment, but added his satisfaction that, unless some mention weremade 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 desire more; and what came of it

When I saw my poor brother led away to imprisonment, I attempted toleap down into the Council Chamber, desiring to intercede on hisbehalf, or at least bid him farewell. But I found that I had no motionof my own. I absolutely depended on the volition of my Guide, who saidin gloomy tones, "Heed not thy brother; haply thou shalt have ampletime hereafter to condole with him. Follow me. "

Once more we ascended into space. "Hitherto, " said the Sphere, "I haveshewn you naught save Plane Figures and their interiors. Now I mustintroduce you to Solids, and reveal to you the plan upon which they areconstructed. Behold this multitude of moveable square cards. See, Iput one on another, not, as you supposed, Northward of the other, butON the other. Now a second, now a third. See, I am building up aSolid by a multitude of Squares parallel to one another. Now the Solidis complete, being as high as it is long and broad, and we call it aCube. "

"Pardon me, my Lord, " replied I; "but to my eye the appearance is as ofan Irregular Figure whose inside is laid open to view; in other words, methinks I see no Solid, but a Plane such as we infer in Flatland; onlyof an Irregularity which betokens some monstrous criminal, so that thevery sight of it is painful to my eyes. "

"True, " said the Sphere; "it appears to you a Plane, because you arenot accustomed to light and shade and perspective; just as in Flatlanda Hexagon would appear a Straight Line to one who has not the Art ofSight Recognition. But in reality it is a Solid, as you shall learn bythe sense of Feeling. "

He then introduced me to the Cube, and I found that this marvellousBeing was indeed no Plane, but a Solid; and that he was endowed withsix plane sides and eight terminal points called solid angles; and Iremembered the saying of the Sphere that just such a Creature as thiswould be formed by the Square moving, in Space, parallel to himself:and I rejoiced to think that so insignificant a Creature as I could insome sense be called the Progenitor of so illustrious an offspring. 

But still I could not fully understand the meaning of what my Teacherhad told me concerning "light" and "shade" and "perspective"; and I didnot hesitate to put my difficulties before him. 

Were I to give the Sphere's explanation of these matters, succinct andclear though it was, it would be tedious to an inhabitant of Space, whoknows these things already. Suffice it, that by his lucid statements, and by changing the position of objects and lights, and by allowing meto feel the several objects and even his own sacred Person, he at lastmade all things clear to me, so that I could now readily distinguishbetween 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:--mostmiserable, yet surely most undeserved! For why should the thirst forknowledge be aroused, only to be disappointed and punished? Myvolition shrinks from the painful task of recalling my humiliation;yet, like a second Prometheus, I will endure this and worse, if by anymeans I may arouse in the interiors of Plane and Solid Humanity aspirit of rebellion against the Conceit which would limit ourDimensions to Two or Three or any number short of Infinity. Away thenwith all personal considerations! Let me continue to the end, as Ibegan, without further digressions or anticipations, pursuing the plainpath of dispassionate History. The exact facts, the exact words, --andthey are burnt in upon my brain, --shall be set down without alterationof an iota; and let my Readers judge between me and Destiny. 

The Sphere would willingly have continued his lessons by indoctrinatingme in the conformation of all regular Solids, Cylinders, Cones, Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons, and Spheres: but Iventured to interrupt him. Not that I was wearied of knowledge. Onthe contrary, I thirsted for yet deeper and fuller draughts than he wasoffering to me. 

"Pardon me, " said I, "O Thou Whom I must no longer address as thePerfection of all Beauty; but let me beg thee to vouchsafe thy servanta sight of thine interior. "

Sphere. My what?

I. Thine interior: thy stomach, thy intestines. 

Sphere. Whence this ill-timed impertinent request? And what mean youby 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 moregreat, more beautiful, and more closely approximate to Perfection thanyourself. As you yourself, superior to all Flatland forms, combinemany Circles in One, so doubtless there is One above you who combinesmany Spheres in One Supreme Existence, surpassing even the Solids ofSpaceland. And even as we, who are now in Space, look down on Flatlandand see the insides of all things, so of a certainty there is yet aboveus some higher, purer region, whither thou dost surely purpose to leadme--O Thou Whom I shall always call, everywhere and in all Dimensions, my Priest, Philosopher, and Friend--some yet more spacious Space, somemore dimensionable Dimensionality, from the vantage-ground of which weshall look down together upon the revealed insides of Solid things, andwhere thine own intestines, and those of thy kindred Spheres, will lieexposed to the view of the poor wandering exile from Flatland, to whomso 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 Gospelof Three Dimensions to your blind benighted countrymen in Flatland. 

I. Nay, gracious Teacher, deny me not what I know it is in thy powerto reform. Grant me but one glimpse of thine interior, and I amsatisfied for ever, remaining henceforth thy docile pupil, thyunemancipable slave, ready to receive all thy teachings and to feed uponthe words that fall from thy lips. 

Sphere. Well, then, to content and silence you, let me say at once, Iwould shew you what you wish if I could; but I cannot. Would you haveme turn my stomach inside out to oblige you?

I. But my Lord has shewn me the intestines of all my countrymen in theLand 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 secondjourney into the blessed region of the Fourth Dimension, where I shalllook down with him once more upon this land of Three Dimensions, andsee the inside of every three-dimensioned house, the secrets of thesolid earth, the treasures of the mines of Spaceland, and theintestines of every solid living creature, even the noble and adorableSpheres. 

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 utterlyinconceivable. 

I. Not inconceivable, my Lord, to me, and therefore still lessinconceivable to my Master. Nay, I despair not that, even here, inthis region of Three Dimensions, your Lordship's art may make theFourth Dimension visible to me; just as in the Land of Two Dimensionsmy Teacher's skill would fain have opened the eyes of his blind servantto 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 Lineand inferred a Plane, I in reality saw a Third unrecognized Dimension, not the same as brightness, called "height"? And does it not nowfollow that, in this region, when I see a Plane and infer a Solid, Ireally see a Fourth unrecognized Dimension, not the same as colour, butexistent, 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 therevelations imparted to him. Trifle not with me, my Lord; I crave, Ithirst, for more knowledge. Doubtless we cannot SEE that other higherSpaceland now, because we have no eye in our stomachs. But, just asthere WAS the realm of Flatland, though that poor puny Lineland Monarchcould neither turn to left nor right to discern it, and just as thereWAS 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 inmy 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 itmust exist my Lord himself has taught me. Or can he have forgottenwhat he himself imparted to his servant?

In One Dimension, did not a moving Point produce a Line with TWOterminal points?

In Two Dimensions, did not a moving Line produce a Square with FOURterminal points?

In Three Dimensions, did not a moving Square produce--did not this eyeof mine behold it--that blessed Being, a Cube, with EIGHT terminalpoints?

And in Four Dimensions shall not a moving Cube--alas, for Analogy, andalas for the Progress of Truth, if it be not so--shall not, I say, themotion of a divine Cube result in a still more divine Organization withSIXTEEN terminal points?

Behold the infallible confirmation of the Series, 2, 4, 8, 16: is notthis a Geometrical Progression? Is not this--if I might quote myLord's own words--"strictly according to Analogy"?

Again, was I not taught by my Lord that as in a Line there are TWObounding Points, and in a Square there are FOUR bounding Lines, so in aCube there must be SIX bounding Squares? Behold once more theconfirming Series, 2, 4, 6: is not this an Arithmetical Progression?And consequently does it not of necessity follow that the more divineoffspring of the divine Cube in the Land of Four Dimensions, must have8 bounding Cubes: and is not this also, as my Lord has taught me tobelieve, "strictly according to Analogy"? O, my Lord, my Lord, behold, I cast myself in faith upon conjecture, not knowing the facts; and Iappeal 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 yourcountrymen also have witnessed the descent of Beings of a higher orderthan their own, entering closed rooms, even as your Lordship enteredmine, without the opening of doors or windows, and appearing andvanishing at will? On the reply to this question I am ready to stakeeverything. Deny it, and I am henceforth silent. Only vouchsafe ananswer. 

Sphere (AFTER A PAUSE). It is reported so. But men are divided inopinion as to the facts. And even granting the facts, they explainthem in different ways. And in any case, however great may be thenumber of different explanations, no one has adopted or suggested thetheory of a Fourth Dimension. Therefore, pray have done with thistrifling, and let us return to business. 

I. I was certain of it. I was certain that my anticipations would befulfilled. And now have patience with me and answer me yet one morequestion, best of Teachers! Those who have thus appeared--no one knowswhence--and have returned--no one knows whither--have they alsocontracted their sections and vanished somehow into that more SpaciousSpace, whither I now entreat you to conduct me?

Sphere (MOODILY). They have vanished, certainly--if they everappeared. But most people say that these visions arose from thethought--you will not understand me--from the brain; from the perturbedangularity of the Seer. 

I. Say they so? Oh, believe them not. Or if it indeed be so, thatthis other Space is really Thoughtland, then take me to that blessedRegion where I in Thought shall see the insides of all solid things. There, before my ravished eye, a Cube moving in some altogether newdirection, but strictly according to Analogy, so as to make everyparticle of his interior pass through a new kind of Space, with a wakeof its own--shall create a still more perfect perfection than himself, with sixteen terminal Extra-solid angles, and Eight solid Cubes for hisPerimeter. And once there, shall we stay our upward course? In thatblessed region of Four Dimensions, shall we linger at the threshold ofthe Fifth, and not enter therein? Ah, no! Let us rather resolve thatour ambition shall soar with our corporal ascent. Then, yielding toour intellectual onset, the gates of the Six 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 threatenme with the direst penalties if I persisted. Nothing could stem theflood of my ecstatic aspirations. Perhaps I was to blame; but indeed Iwas intoxicated with the recent draughts of Truth to which he himselfhad introduced me. However, the end was not long in coming. My wordswere 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 toFlatland was my doom. One glimpse, one last and never-to-be-forgottenglimpse I had of that dull level wilderness--which was now to become myUniverse again--spread out before my eye. Then a darkness. Then afinal, all-consummating thunder-peal; and, when I came to myself, I wasonce more a common creeping Square, in my Study at home, listening tothe 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 ofinstinct, that I must conceal my experiences from my Wife. Not that Iapprehended, at the moment, any danger from her divulging my secret, but I knew that to any Woman in Flatland the narrative of my adventuresmust needs be unintelligible. So I endeavoured to reassure her by somestory, invented for the occasion, that I had accidentally fallenthrough the trap-door of the cellar, and had there lain stunned. 

The Southward attraction in our country is so slight that even to aWoman my tale necessarily appeared extraordinary and well-nighincredible; but my Wife, whose good sense far exceeds that of theaverage of her Sex, and who perceived that I was unusually excited, didnot argue with me on the subject, but insisted that I was ill andrequired repose. I was glad of an excuse for retiring to my chamber tothink quietly over what had happened. When I was at last by myself, adrowsy sensation fell on me; but before my eyes closed I endeavoured toreproduce the Third Dimension, and especially the process by which aCube is constructed through the motion of a Square. It was not soclear as I could have wished; but I remembered that it must be "Upward, and yet not Northward, " and I determined steadfastly to retain thesewords as the clue which, if firmly grasped, could not fail to guide meto 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 sideof the Sphere, whose lustrous hue betokened that he had exchanged hiswrath against me for perfectly placability. We were moving togethertowards a bright but infinitesimally small Point, to which my Masterdirected my attention. As we approached, methought there issued fromit a slight humming noise as from one of your Spaceland bluebottles, only less resonant by far, so slight indeed that even in the perfectstillness of the Vacuum through which we soared, the sound reached notour ears till we checked our flight at a distance from it of somethingunder twenty human diagonals. 

"Look yonder, " said my Guide, "in Flatland thou hast lived; of Linelandthou hast received a vision; thou hast soared with me to the heights ofSpaceland; now, in order to complete the range of thy experience, Iconduct thee downward to the lowest depth of existence, even to therealm 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 noexperience of them; he has no cognizance even of the number Two; norhas he a thought of Plurality; for he is himself his One and All, beingreally Nothing. Yet mark his perfect self-contentment, and hence learnhis lesson, that to be self-contented is to be vile and ignorant, andthat to aspire is better than to be blindly and impotently happy. Nowlisten. "

He ceased; and there arose from the little buzzing creature a tiny, low, monotonous, but distinct tinkling, as from one of your Spacelandphonographs, from which I caught these words, "Infinite beatitude ofexistence! It is; and there is nothing else beside It. "

"What, " said I, "does the puny creature mean by 'it'?" "He meanshimself, " said the Sphere: "have you not noticed before now, thatbabies and babyish people who cannot distinguish themselves from theworld, speak of themselves in the Third Person? But hush!"

"It fills all Space, " continued the little soliloquizing Creature, "andwhat It fills, It is. What It thinks, that It utters; and what Itutters, 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 narrowlimitations of Pointland, and lead it up to something higher. " "That isno easy task, " said my Master; "try you. "

Hereon, raising by voice to the uttermost, I addressed the Point asfollows:

"Silence, silence, contemptible Creature. You call yourself the All inAll, but you are the Nothing: your so-called Universe is a mere speckin a Line, and a Line is a mere shadow as compared with--" "Hush, hush, you have said enough, " interrupted the Sphere, "now listen, and markthe effect of your harangue on the King of Pointland. "

The lustre of the Monarch, who beamed more brightly than ever uponhearing my words, shewed clearly that he retained his complacency; andI 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 ownThought coming to Itself, suggestive of its disparagement, thereby toenhance Its happiness! Sweet rebellion stirred up to result intriumph! Ah, the divine creative power of the All in One! Ah, thejoy, the joy of Being!"

"You see, " said my Teacher, "how little your words have done. So faras the Monarch understand them at all, he accepts them as his own--forhe cannot conceive of any other except himself--and plumes himself uponthe variety of 'Its Thought' as an instance of creative Power. Let usleave this God of Pointland to the ignorant fruition of hisomnipresence and omniscience: nothing that you or I can do can rescuehim from his self-satisfaction. "

After this, as we floated gently back to Flatland, I could hear themild voice of my Companion pointing the moral of my vision, andstimulating me to aspire, and to teach others to aspire. He had beenangered at first--he confessed--by my ambition to soar to Dimensionsabove the Third; but, since then, he had received fresh insight, and hewas not too proud to acknowledge his error to a Pupil. Then heproceeded to initiate me into mysteries yet higher than those I hadwitnessed, shewing me how to construct Extra-Solids by the motion ofSolids, and Double Extra-Solids by the motion of Extra-Solids, and all"strictly according to Analogy, " all by methods so simple, so easy, asto 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 beforeme. I would go forth, methought, at once, and evangelize the whole ofFlatland. Even to Women and Soldiers should the Gospel of ThreeDimensions be proclaimed. I would begin with my Wife. 

Just as I had decided on the plan of my operations, I heard the soundof many voices in the street commanding silence. Then followed alouder voice. It was a herald's proclamation. Listening attentively, I recognized the words of the Resolution of the Council, enjoining thearrest, imprisonment, or execution of any one who should pervert theminds of people by delusions, and by professing to have receivedrevelations from another World. 

I reflected. This danger was not to be trifled with. It would bebetter to avoid it by omitting all mention of my Revelation, and byproceeding on the path of Demonstration--which after all, seemed sosimple and so conclusive that nothing would be lost by discarding theformer means. "Upward, not Northward"--was the clue to the wholeproof. It had seemed to me fairly clear before I fell asleep; and whenI first awoke, fresh from my dream, it had appeared as patent asArithmetic; but somehow it did not seem to me quite so obvious now. Though my Wife entered the room opportunely at just that moment, Idecided, after we had exchanged a few words of commonplaceconversation, not to begin with her. 

My Pentagonal Sons were men of character and standing, and physiciansof no mean reputation, but not great in mathematics, and, in thatrespect, unfit for my purpose. But it occurred to me that a young anddocile Hexagon, with a mathematical turn, would be a most suitablepupil. Why therefore not make my first experiment with my littleprecocious Grandson, whose casual remarks on the meaning ofthree-to-the-third had met with the approval of the Sphere? Discussingthe matter with him, a mere boy, I should be in perfect safety; for hewould know nothing of the Proclamation of the Council; whereas I couldnot feel sure that my Sons--so greatly did their patriotism andreverence for the Circles predominate over mere blind affection--mightnot feel compelled to hand me over to the Prefect, if they found meseriously maintaining the seditious heresy of the Third Dimension. 

But the first thing to be done was to satisfy in some way the curiosityof my Wife, who naturally wished to know something of the reasons forwhich the Circle had desired that mysterious interview, and of themeans by which he had entered the house. Without entering into thedetails of the elaborate account I gave her, --an account, I fear, notquite so consistent with truth as my Readers in Spaceland mightdesire, --I must be content with saying that I succeeded at last inpersuading her to return quietly to her household duties withouteliciting from me any reference to the World of Three Dimensions. Thisdone, I immediately sent for my Grandson; for, to confess the truth, Ifelt that all that I had seen and heard was in some strange wayslipping away from me, like the image of a half-grasped, tantalizingdream, 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, asyou would call them, Lines--I told him we would resume the lesson ofyesterday. I taught him once more how a Point by motion in OneDimension produces a Line, and how a straight Line in Two Dimensionsproduces a Square. After this, forcing a laugh, I said, "And now, youscamp, you wanted to make believe that a Square may in the same way bymotion 'Upward, not Northward' produce another figure, a sort of extrasquare in Three Dimensions. Say that again, you young rascal. "

At this moment we heard once more the herald's "O yes! O yes!" outsidein the street proclaiming the REsolution of the Council. Young thoughhe was, my Grandson--who was unusually intelligent for his age, andbred up in perfect reverence for the authority of the Circles--took inthe situation with an acuteness for which I was quite unprepared. Heremained silent till the last words of the Proclamation had died away, and then, bursting into tears, "Dear Grandpapa, " he said, "that wasonly my fun, and of course I meant nothing at all by it; and we did notknow anything then about the new Law; and I don't think I said anythingabout 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 notNorthward! 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 takethis Square, " and, at the word, I grasped a moveable Square, which waslying at hand--"and I move it, you see, not Northward but--yes, I moveit Upward--that is to say, Northward but I move it somewhere--notexactly like this, but somehow--" Here I brought my sentence to aninane conclusion, shaking the Square about in a purposeless manner, much to the amusement of my Grandson, who burst out laughing louderthan ever, and declared that I was not teaching him, but joking withhim; and so saying he unlocked the door and ran out of the room. Thusended my first attempt to convert a pupil to the Gospel of ThreeDimensions. 

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 mysecret to others of my household; yet neither was I led by it todespair of success. Only I saw that I must not wholly rely on thecatch-phrase, "Upward, not Northward, " but must rather endeavour toseek a demonstration by setting before the public a clear view of thewhole subject; and for this purpose it seemed necessary to resort towriting. 

So I devoted several months in privacy to the composition of a treatiseon the mysteries of Three Dimensions. Only, with the view of evadingthe Law, if possible, I spoke not of a physical Dimension, but of aThoughtland whence, in theory, a Figure could look down upon Flatlandand see simultaneously the insides of all things, and where it waspossible that there might be supposed to exist a Figure environed, asit were, with six Squares, and containing eight terminal Points. Butin writing this book I found myself sadly hampered by the impossibilityof drawing such diagrams as were necessary for my purpose: for ofcourse, in our country of Flatland, there are no tablets but Lines, andno diagrams but Lines, all in one straight Line and onlydistinguishable by difference of size and brightness; so that, when Ihad finished my treatise (which I entitled, "Through Flatland toThoughtland") I could not feel certain that many would understand mymeaning. 

Meanwhile my wife was under a cloud. All pleasures palled upon me; allsights tantalized and tempted me to outspoken treason, because I couldnot compare what I saw in Two Dimensions with what it really was ifseen in Three, and could hardly refrain from making my comparisonsaloud. I neglected my clients and my own business to give myself tothe contemplation of the mysteries which I had once beheld, yet which Icould impart to no one, and found daily more difficult to reproduceeven before my own mental vision. One day, about eleven months aftermy return from Spaceland, I tried to see a Cube with my eye closed, butfailed; and though I succeeded afterwards, I was not then quite certain(nor have I been ever afterwards) that I had exactly realized theoriginal. This made me more melancholy than before, and determined meto take some step; yet what, I knew not. I felt that I would have beenwilling to sacrifice my life for the Cause, if thereby I could haveproduced conviction. But if I could not convince my Grandson, howcould 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 todangerous utterances. Already I was considered heterodox if nottreasonable, and I was keenly alive to the danger of my position;nevertheless I could not at times refrain from bursting out intosuspicious or half-seditious utterances, even among the highestPolygonal or Circular society. When, for example, the question aroseabout the treatment of those lunatics who said that they had receivedthe power of seeing the insides of things, I would quote the saying ofan ancient Circle, who declared that prophets and inspired people arealways considered by the majority to be mad; and I could not helpoccasionally dropping such expressions as "the eye that discerns theinteriors of things, " and "the all-seeing land"; once or twice I evenlet fall the forbidden terms "the Third and Fourth Dimensions. " Atlast, to complete a series of minor indiscretions, at a meeting of ourLocal Speculative Society held at the palace of the Prefecthimself, --some extremely silly person having read an elaborate paperexhibiting the precise reasons why Providence has limited the number ofDimensions to Two, and why the attribute of omnividence is assigned tothe Supreme alone--I so far forgot myself as to give an exact accountof the whole of my voyage with the Sphere into Space, and to theAssembly Hall in our Metropolis, and then to Space again, and of myreturn home, and of everything that I had seen and heard in fact orvision. At first, indeed, I pretended that I was describing theimaginary experiences of a fictitious person; but my enthusiasm soonforced me to throw off all disguise, and finally, in a ferventperoration, I exhorted all my hearers to divest themselves of prejudiceand 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 monthsago the Sphere had stood in my company, I was allowed to begin and tocontinue my narration unquestioned and uninterrupted. But from thefirst I foresaw my fate; for the President, noting that a guard of thebetter sort of Policemen was in attendance, of angularity little, if atall, under 55 degrees, ordered them to be relieved before I began mydefence, by an inferior class of 2 or 3 degrees. I knew only too wellwhat that meant. I was to be executed or imprisoned, and my story wasto be kept secret from the world by the simultaneous destruction of theofficials who had heard it; and, this being the case, the Presidentdesired to substitute the cheaper for the more expensive victims. 

After I had concluded my defence, the President, perhaps perceivingthat some of the junior Circles had been moved by evident earnestness, asked me two questions:--

1. Whether I could indicate the direction which I meant when I usedthe words "Upward, not Northward"?

2. Whether I could by any diagrams or descriptions (other than theenumeration of imaginary sides and angles) indicate the Figure I waspleased to call a Cube?

I declared that I could say nothing more, and that I must commit myselfto the Truth, whose cause would surely prevail in the end. 

The President replied that he quite concurred in my sentiment, and thatI could not do better. I must be sentenced to perpetual imprisonment;but if the Truth intended that I should emerge from prison andevangelize the world, the Truth might be trusted to bring that resultto pass. Meanwhile I should be subjected to no discomfort that was notnecessary to preclude escape, and, unless I forfeited the privilege bymisconduct, I should be occasionally permitted to see my brother whohad preceded me to my prison. 

Seven years have elapsed and I am still a prisoner, and--if I exceptthe occasional visits of my brother--debarred from all companionshipsave that of my jailers. My brother is one of the best of Squares, just sensible, cheerful, and not without fraternal affection; yet Iconfess that my weekly interviews, at least in one respect, cause methe bitterest pain. He was present when the Sphere manifested himselfin the Council Chamber; he saw the Sphere's changing sections; he heardthe explanation of the phenomena then give to the Circles. Since thattime, scarcely a week has passed during seven whole years, without hishearing from me a repetition of the part I played in thatmanifestation, together with ample descriptions of all the phenomena inSpaceland, and the arguments for the existence of Solid thingsderivable from Analogy. Yet--I take shame to be forced to confessit--my brother has not yet grasped the nature of Three Dimensions, andfrankly avows his disbelief in the existence of a Sphere. 

Hence I am absolutely destitute of converts, and, for aught that I cansee, the millennial Revelation has been made to me for nothing. Prometheus up in Spaceland was bound for bringing down fire formortals, but I--poor Flatland Prometheus--lie here in prison forbringing down nothing to my countrymen. Yet I existing the hope thatthese memoirs, in some manner, I know not how, may find their way tothe minds of humanity in Some Dimension, and may stir up a race ofrebels who shall refuse to be confined to limited Dimensionality. 

That is the hope of my brighter moments. Alas, it is not always so. Heavily weights on me at times the burdensome reflection that I cannothonestly 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 ispart of the martyrdom which I endure for the cause of Truth that thereare seasons of mental weakness, when Cubes and Spheres flit away intothe background of scarce-possible existences; when the Land of ThreeDimensions seems almost as visionary as the Land of One or None; nay, when even this hard wall that bars me from my freedom, these verytablets on which I am writing, and all the substantial realities ofFlatland itself, appear no better than the offspring of a diseasedimagination, or the baseless fabric of a dream. 

***

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

If my poor Flatland friend retained the vigour of mind which he enjoyedwhen he began to compose these Memoirs, I should not now need torepresent him in this preface, in which he desires, fully, to returnhis thanks to his readers and critics in Spaceland, whose appreciationhas, with unexpected celerity, required a second edition of this work;secondly, to apologize for certain errors and misprints (for which, however, he is not entirely responsible); and, thirdly, to explain onor two misconceptions. But he is not the Square he once was. Years ofimprisonment, and the still heavier burden of general incredulity andmockery, have combined with the thoughts and notions, and much also ofthe terminology, which he acquired during his short stay in spaceland. He has, therefore, requested me to reply in his behalf to two specialobjections, one of an intellectual, the other of a moral nature. 

The first objection is, that a Flatlander, seeing a Line, seessomething 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); andconsequently he ought (it is argued) to acknowledge that his countrymenare not only long and broad, but also (though doubtless to a veryslight degree) THICK or HIGH. This objection is plausible, and, toSpacelanders, almost irresistible, so that, I confess, when I firstheard it, I knew not what to reply. But my poor old friend's answerappears to me completely to meet it. 

"I admit, " said he--when I mentioned to him this objection--"I admitthe truth of your critic's facts, but I deny his conclusions. It istrue that we have really in Flatland a Third unrecognized Dimensioncalled 'height, ' just as it also is true that you have really inSpaceland a Fourth unrecognized Dimension, called by no name atpresent, but which I will call 'extra-height. ' But we can no more takecognizance of our 'height' than you can of your 'extra-height. ' EvenI--who have been in Spaceland, and have had the privilege ofunderstanding for twenty-four hours the meaning of 'height'--even Icannot now comprehend it, nor realize it by the sense of sight or byany process of reason; I can but apprehend it by faith. 

"The reason is obvious. Dimension implies direction, impliesmeasurement, implies the more and the less. Now, all our lines areEQUALLY and INFINITESIMALLY thick (or high, whichever you like);consequently, there is nothing in them to lead our minds to theconception of that Dimension. No 'delicate micrometer'--as has beensuggested by one too hasty Spaceland critic--would in the least availus; 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 myFlatland friends--when I talk to them about the unrecognized Dimensionwhich is somehow visible in a Line--say, 'Ah, you mean BRIGHTNESS': andwhen I reply, 'No, I mean a real Dimension, ' they at once retort, 'Thenmeasure it, or tell us in what direction it extends'; and this silencesme, for I can do neither. Only yesterday, when the Chief Circle (inother words our High Priest) came to inspect the State Prison and paidme his seventh annual visit, and when for the seventh time he put methe 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. Butwhat was his reply? 'You say I am "high"; measure my "high-ness" and Iwill 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 similarposition. Suppose a person of the Fourth Dimension, condescending tovisit 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 FourthDimension, 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 asnatural for us Flatlanders to lock up a Square for preaching the ThirdDimension, as it is for you Spacelanders to lock up a Cube forpreaching the Fourth. Alas, how strong a family likeness runs throughblind and persecuting humanity in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes--we are all liable to the same errors, allalike the Slaves of our respective Dimensional prejudices, as one ofour Spaceland poets has said--

 'One touch of Nature makes all worlds akin. '" (footnote 1)

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) objectionwas equally clear and cogent. It has been objected that he is awoman-hater; and as this objection has been vehemently urged by thosewhom Nature's decree has constituted the somewhat larger half of theSpaceland race, I should like to remove it, so far as I can honestly doso. But the Square is so unaccustomed to the use of the moralterminology of Spaceland that I should be doing him an injustice if Iwere literally to transcribe his defence against this charge. Acting, therefore, as his interpreter and summarizer, I gather that in thecourse of an imprisonment of seven years he has himself modified hisown personal views, both as regards Women and as regards the Isoscelesor Lower Classes. Personally, he now inclines to the opinion of theSphere (see page 86) that the Straight Lines are in many importantrespects superior to the Circles. But, writing as a Historian, he hasidentified himself (perhaps too closely) with the views generallyadopted by Flatland, and (as he has been informed) even by Spaceland, Historians; in whose pages (until very recent times) the destinies ofWomen and of the masses of mankind have seldom been deemed worthy ofmention and never of careful consideration. 

In a still more obscure passage he now desires to disavow the Circularor aristocratic tendencies with which some critics have naturallycredited him. While doing justice to the intellectual power with whicha few Circles have for many generations maintained their supremacy overimmense multitudes of their countrymen, he believes that the facts ofFlatland, speaking for themselves without comment on his part, declarethat Revolutions cannot always be suppressed by slaughter, and thatNature, in sentencing the Circles to infecundity, has condemned them toultimate failure--"and herein, " he says, "I see a fulfilment of thegreat Law of all worlds, that while the wisdom of Man thinks it isworking one thing, the wisdom of Nature constrains it to work another, and quite a different and far better thing. " For the rest, he begs hisreaders not to suppose that every minute detail in the daily life ofFlatland must needs correspond to some other detail in Spaceland; andyet he hopes that, taken as a whole, his work may prove suggestive aswell as amusing, to those Spacelanders of moderate and modest mindswho--speaking of that which is of the highest importance, but liesbeyond 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 knowall about it. "

Footnote 1. The Author desires me to add, that the misconceptions ofsome of his critics on this matter has induced him to insert (on pp. 74 and 92) in his dialogue with the Sphere, certain remarks which havea bearing on the point in question and which he had previously omittedas being tedious and unnecessary.