Flatland: A Romance of Many Dimensions

Edwin A. Abbott (1838-1926. English scholar, theologian, and writer. )

 ----------------------------------------------------------------- | "O day and night, but this is wondrous strange" | | ______ | | / / /| ------ / /| /| / /-. | | /---- / /__| / / /__| / | / / / | | / /___ / | / /___ / | / |/ /__. -' | | | | No Dimensions One Dimension | | . A ROMANCE OF MANY DIMENSIONS ----- | | POINTLAND LINELAND | | | | Two Dimensions Three Dimensions | | ___ __ | | | | /__/| | | |___| |__|/ | | FLATLAND SPACELAND | | "Fie, fie, how franticly I square my talk!" | -----------------------------------------------------------------

With Illustrations by the Author, A SQUARE (Edwin A. Abbott)

 To The Inhabitants of SPACE IN GENERAL And H. C. IN PARTICULAR This Work is Dedicated By a Humble Native of Flatland In the Hope that Even as he was Initiated into the Mysteries Of THREE Dimensions Having been previously conversant With ONLY TWO So the Citizens of that Celestial Region May aspire yet higher and higher To the Secrets of FOUR FIVE OR EVEN SIX Dimensions Thereby contributing To the Enlargement of THE IMAGINATION And the possible Development Of that most rare and excellent Gift of MODESTY Among the Superior Races Of SOLID HUMANITY

Preface to the Second and Revised Edition, 1884. 

By the Editor

If my poor Flatland friend retained the vigour of mind which he enjoyedwhen he began to compose these Memoirs, I should not now need torepresent him in this preface, in which he desires, firstly, to returnhis thanks to his readers and critics in Spaceland, whose appreciationhas, with unexpected celerity, required a second edition of his work;secondly, to apologize for certain errors and misprints (for which, however, he is not entirely responsible); and, thirdly, to explain oneor 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 natural decay of old age to erase fromhis mind many of the thoughts and notions, and much also of theterminology, which he acquired during his short stay in Spaceland. Hehas, 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 in 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 is also 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':and when I reply, 'No, I mean a real Dimension', they at once retort, 'Then measure it, or tell us in what direction it extends'; and thissilences me, for I can do neither. Only yesterday, when the ChiefCircle (in other words our High Priest) came to inspect the StatePrison and paid me his seventh annual visit, and when for the seventhtime he put me the question, 'Was I any better?' I tried to prove tohim that he was 'high', as well as long and broad, although he did notknow it. But what was his reply? 'You say I am "high"; measure my"high-ness" and I will believe you. ' What could I do? How could Imeet 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 avisitor? Would not you have him locked up? Well, that is my fate: andit is as natural for us Flatlanders to lock up a Square for preachingthe Third Dimension, as it is for you Spacelanders to lock up a Cubefor preaching the Fourth. Alas, how strong a family likeness runsthrough blind and persecuting humanity in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes--we are all liable to the sameerrors, all alike the Slaves of our respective Dimensional prejudices, as one of your Spaceland poets has said--

 'One touch of Nature makes all worlds akin'. "

[Note: The Author desires me to add, that the misconception of some ofhis critics on this matter has induced him to insert in his dialoguewith the Sphere, certain remarks which have a bearing on the point inquestion, and which he had previously omitted as being tedious andunnecessary. ]

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 that the Straight Lines are in many important respects superiorto the Circles. But, writing as a Historian, he has identified himself(perhaps too closely) with the views generally adopted by Flatland, and(as he has been informed) even by Spaceland, Historians; in whose pages(until very recent times) the destinies of Women and of the masses ofmankind have seldom been deemed worthy of mention and never of carefulconsideration. 

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. "

CONTENTS:

PART I: THIS WORLD

Section

 1. Of the Nature of Flatland 2. Of the Climate and Houses in Flatland 3. Concerning the Inhabitants of Flatland 4. Concerning the Women 5. Of our Methods of Recognizing one another 6. Of Recognition by Sight 7. Concerning Irregular Figures 8. Of the Ancient Practice of Painting 9. Of the Universal Colour Bill 10. Of the Suppression of the Chromatic Sedition 11. Concerning our Priests 12. Of the Doctrine of our Priests

PART II: OTHER WORLDS

 13. How I had a Vision of Lineland 14. How I vainly tried to explain the nature of Flatland 15. Concerning a Stranger from Spaceland 16. How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland 17. How the Sphere, having in vain tried words, resorted to deeds 18. How I came to Spaceland, and what I saw there 19. How, though the Sphere shewed me other mysteries of Spaceland, I still desired more; and what came of it 20. How the Sphere encouraged me in a Vision 21. How I tried to teach the Theory of Three Dimensions to my Grandson, and with what success 22. How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result

PART I: THIS WORLD

"Be patient, for the world is broad and wide. "

Section 1. Of the Nature of Flatland

I call our world Flatland, not because we call it so, but to make 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 and with luminous edges--and you will then have apretty correct notion of my country and countrymen. Alas, a few yearsago, I should have said "my universe": but now my mind has been openedto higher 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 Square, or any other figure cut out of pasteboard. Assoon as you look at it with your eye on the edge on the table, you willfind that it ceases to appear to you a figure, and that it becomes inappearance a straight line. Take for example an equilateralTriangle--who represents with us a Tradesman of the respectable class. Fig. 1 represents the Tradesman as you would see him while you werebending over him from above; figs. 2 and 3 represent the Tradesman, asyou 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. 

[Illustration 1]

[ASCII approximation follows]

 (1) __________ (2) ___________ (3) _________ \ / --__ __-- --- \ / - \/

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 toward 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 disadvantageous circumstances weare able 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 effect 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 in 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-investigated 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 houses. 

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 or triangular house residence might do serious injury to aninconsiderate or perhaps absent-minded traveller suddenly therefore, running against them: and as early as the eleventh century of our era, triangular houses were universally forbidden by Law, the onlyexceptions being fortifications, powder-magazines, barracks, and otherstate buildings, which it is not desirable that the general publicshould approach without circumspection. 

[Illustration 2]

[ASCII approximation follows]

 O /\ / \ / \ / \ / \ R/ \F \_ / _/ Men's door _ Women's door _ / \____________/ A B

At this period, square houses were still everywhere permitted, 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 Classes 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 Tradesmen, 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 shut out, even from theIsosceles, that his posterity may ultimately rise above his degradedcondition. For, after a long series of military successes, or diligentand skilful 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. [Note: "What need of a certificate?" a Spaceland critic mayask: "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 marry 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. ] Such a birth requires, as itsantecedents, not only a series of carefully arranged intermarriages, but also a long, continued exercise of frugality and self-control onthe part of the would-be ancestors of the coming Equilateral, and apatient, systematic, and continuous development of the Isoscelesintellect through many generations. 

The birth of a True Equilateral Triangle from Isosceles parents is thesubject of rejoicing in our country for many furlongs around. 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 a most 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, inproportion as the working-classes increase in intelligence, knowledge, and all virtue, in that same proportion their acute angle (which makesthem physically terrible) shall increase also and approximate to thecomparatively harmless angle of the Equilateral Triangle. Thus, in themost brutal and formidable of 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 this 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 in 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 more 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 suspicionsskilfully 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. 

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 ifa 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 a 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 in 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 in the Eastern side, for theuse of Females only; by which all females shall enter "in a becomingand respectful manner" and not by the Men's or Western door. [Note:When I was in Spaceland I understood that some of your Priestly circleshave in the same way a separate entrance for Villagers, Farmers andTeachers of Board Schools (`Spectator', Sept. 1884, p. 1255) that theymay "approach in a becoming and respectful manner. "]

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; others oblige a Woman, when travelling, to be followed by one of her sons, or servants, or byher husband; others confine Women altogether to 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 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 brain-power, 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 her 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 get 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 simulation, 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 without itsdisadvantages. 

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 towards 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 seem 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 clear to you theextreme difficulty which we in Flatland experience in recognizing oneanother's configuration?

Recall what I told you above. All beings in Flatland, animate orinanimate, 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 our personalfriends, but even to discriminate between different classes, at leastso far as concerns the three lowest orders, the Equilateral, theSquare, and the Pentagon--for of the Isosceles I take no account. Butas we ascend in the social scale, the process of discriminating andbeing discriminated by hearing increases in difficulty, partly becausevoices are assimilated, partly because the faculty ofvoice-discrimination is a plebeian virtue not much developed among theAristocracy. And wherever there is any danger of imposture we cannottrust to this method. Amongst our lowest orders, the vocal organs aredeveloped to a degree more than correspondent with those of hearing, sothat an Isosceles can easily feign the voice of a Polygon, and, withsome training, that of a Circle himself. A second method is thereforemore commonly 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 Feeler 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 hadoccured to his great-great-great-Grandfather, a respectable Working Manwith an angle or brain of 59 degrees 30 minutes. According to hisaccount, my unfortunate Ancestor, being afflicted with rheumatism, andin the act of being felt by a Polygon, by one sudden start accidentallytransfixed the Great Man through the diagonal; and thereby, partly inconsequence of his long imprisonment and degradation, and partlybecause of the moral shock which pervaded the whole of my Ancestor'srelations, threw back our family a degree and a half in their ascenttowards better things. The result was that in the next generation thefamily brain was registered at only 58 degrees, and not till the lapseof five generations was the lost ground recovered, the full 60 degreesattained, and the Ascent from the Isosceles finally achieved. And allthis series of calamities from one little accident in the process ofFeeling. 

At 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 can SEE an angle, because we, in the region ofSpace, can see two straight lines inclined to one another; but you, whocan see nothing but one straight line at a time, or at all events onlya number of bits of straight lines all in one straight line--how canyou ever discern any 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 generation;until 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, Specimens 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 civic 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 class rooms of ourInfant Schools, and there they are utilized by the Board of Educationfor the purpose of imparting to the offspring of the Middle Classesthat tact and intelligence of which these wretched creatures themselvesare utterly 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". Nor must 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 previous sections I havesaid that all figures in Flatland present the appearance of a straightline; and it was added or implied, that it is consequently impossibleto distinguish by the visual organ between individuals of differentclasses: yet now I am about to explain to my Spaceland critics how weare 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 temperate climates that Sight Recognition ispractised. 

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 adistance 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?

[Illustration 3]

[ASCII approximation follows]

 C (1) |\ - _ D | \ ||- _ | \ || - _ | || -----------+(> Eye-glance ___C' (2) | / A|| _ - ___--- \ - _D' | / ||_ - __--- \ || - _ |/ _ - E | \ || - _ B | \ || - _ | Eye-glance \ || - _ | ---- | -- __ __ -- | \ __ --- __ / \ - / ----- \ __ __ / -----

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 reappeared and was rapidly making himselflarger. 

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 say, has 2 sides (for the Points of a Line maybe called by courtesy, its sides); a Square has 4 sides; 0, 2, 4; whatProgression 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 to deeds

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; no edging to the right nor tothe left, but moving somehow out of the world, and vanishing tonothing. 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 nor bottoms) 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 senses; 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 this 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 vigour, and continued to shout forassistance. 

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--whither 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 aloud 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, nor lungs, norarteries, only a beautiful harmonious Something--for which I had nowords; but you, my Readers in Spaceland, would call it the surface ofthe 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 given 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 presents 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 beheld! 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. 

[Illustration 9]

[ASCII approximation follows]

 /\ / |My \ / |Study \ /______ | ___ \ / My Sons\ \|The \ /______/ \ Page / \ N / \ / My \ ^ /______/ THE HALL \ Bedroom \ | \ My\ / | \____| /\Wife's / W--+--E \ My Wife / Apartment/ | ------- /\ --- \ WOMEN'S DOOR | MEN'S DOOR \My Daughter | /\ --== \ / The Scullion S \ My Grandsons \ -==# \/ The Footman \___ ___ _ _/ \-=#|/ The Butler \ | | |THE CELLAR \ / \____|____|_|____________/

 ###===--- ---===### Policeman Policeman

Touched by my Wife's distress, I would have sprung downward to 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 mines and inmost caverns of the hills, were bared before me. 

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:"Is it 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 understanding, more of your despised StraightLines than of your belauded Circles. But enough of this. Look yonder. Do you know that building?

I looked, and afar off I saw an immense Polygonal structure, in which 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 thesewords, he leaped with great dexterity into the sea (if I may so callit) of Flatland, right in the midst of the ring of Counsellors. "Icome, " cried 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 desired 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. "

[Illustration 10]

[ASCII approximation follows]

 (1) (2) __________ __________ |\ |\ | \ | \ | \ | \ | \ ____|____\ | \ | | | | | | |_____|____| | | | \ | \ | \ | \ | \ | \ | \|_________\| \ __________|

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 the view; in otherwords, methinks I see no Solid, but a Plane such as we infer inFlatland; only of an Irregularity which betokens some monstrouscriminal, so that the very 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 a Square moving, in Space, parallel to himself: andI rejoiced to think that so insignificant a Creature as I could in somesense 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 perform. 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 feedupon the 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 in Spaceland, and theintestines of every solid living creature, even of the noble andadorable Spheres. 

SPHERE. But where is this land of Four Dimensions?

I. I know not: but doubtless my Teacher knows. 

SPHERE. Not I. There is no such land. The very idea of it is 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 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 I appeal to your Lordship to confirm or denymy logical anticipations. If I am wrong, I yield, and will no longerdemand a fourth Dimension; but, if I am right, my Lord will listen toreason. 

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 on 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 Sixth Dimension shall flyopen; after that a Seventh, and then an Eighth-- How long I should havecontinued I know not. In vain did the Sphere, in his voice of thunder, reiterate his command of silence, and threaten me with the direstpenalties if I persisted. Nothing could stem the flood of my ecstaticaspirations. Perhaps I was to blame; but indeed I was intoxicated withthe recent draughts of Truth to which he himself had introduced me. However, the end was not long in coming. My words were cut short by acrash outside, and a simultaneous crash inside me, which impelled methrough space with a velocity that precluded speech. Down! down! down!I was rapidly descending; and I knew that return to Flatland was mydoom. One glimpse, one last and never-to-be-forgotten glimpse I had ofthat dull level wilderness--which was now to become my Universeagain--spread out before my eye. Then a darkness. Then a final, all-consummating thunder-peal; and, when I came to myself, I was oncemore a common creeping Square, in my Study at home, listening to thePeace-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 perfect 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 learnthis 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 none 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. " "Thatis no easy task, " said my Master; "try you. "

Hereon, raising my 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, andmark the 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 in triumph!Ah, the divine creative power of the All in One! Ah, the joy, the joyof Being!"

"You see, " said my Teacher, "how little your words have done. So faras the Monarch understands 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 the 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 just at 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 of 3^3 had metwith the approval of the Sphere? Discussing the matter with him, amere boy, I should be in perfect safety; for he would know nothing ofthe Proclamation of the Council; whereas I could not feel sure that mySons--so greatly did their patriotism and reverence for the Circlespredominate over mere blind affection--might not feel compelled to handme over to the Prefect, if they found me seriously maintaining theseditious 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 me believe that a Square may in the same wayby motion 'Upward, not Northward' produce another figure, a sort ofextra Square 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, not 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 life was under a cloud. All pleasures palled upon me; allsights tantalized and tempted me to outspoken treason, because I couldnot but 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 after my return from Spaceland, I tried tosee a Cube with my eye closed, but failed; and though I succeededafterwards, I was not then quite certain (nor have I been everafterwards) that I had exactly realized the original. This made memore melancholy than before, and determined me to take some step; yetwhat, I knew not. I felt that I would have been willing to sacrificemy life for the Cause, if thereby I could have produced conviction. But if I could not convince my Grandson, how could I convince thehighest 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 and 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 my evidentearnestness, 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 given 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 the Third Dimension, and frankly avows his disbelief in the existence of a Sphere. 

Hence I am absolutely destitute of converts, and, for aught that I 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 exist in 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 weighs 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 the Truth thatthere are seasons of mental weakness, when Cubes and Spheres flit awayinto the background of scarce-possible existences; when the Land ofThree Dimensions seems almost as visionary as the Land of One or None;nay, when even this hard wall that bars me from my freedom, these 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. 

 THE END of FLATLAND ----------------------------------------------------------------- | THE END of | | ______ | | / / /| ------ / /| /| / /-. | | /---- / /__| / / /__| / | / / / | | / /___ / | / /___ / | / |/ /__. -' | | | | The baseless fabric of my vision | | Melted into air into thin air | | Such stuff as dreams are made of | -----------------------------------------------------------------