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Flatland: A Romance of Many Dimensions ......................................................................................................1

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

19. How, though the Sphere shewed me other mysteries of Spaceland, I still desired more; and what came of it

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

If my poor Flatland friend retained the vigour of mind which he enjoyed when he began to compose these

Memoirs, I should not now need to represent him in this preface, in which he desires, firstly, to return his

thanks to his readers and critics in Spaceland, whose appreciation has, with unexpected celerity, required a

second edition of his work; secondly, to apologize for certain errors and misprints (for which, however, he is

not entirely responsible); and, thirdly, to explain one or two misconceptions. But he is not the Square he once

was. Years of imprisonment, and the still heavier burden of general incredulity and mockery, have combined

with the natural decay of old age to erase from his mind many of the thoughts and notions, and much also of

the terminology, which he acquired during his short stay in Spaceland. He has, therefore, requested me to

reply in his behalf to two special objections, one of an intellectual, the other of a moral nature.

The first objection is, that a Flatlander, seeing a Line, sees something that must be THICK to the eye as well

as LONG to the eye (otherwise it would not be visible, if it had not some thickness); and consequently he

ought (it is argued) to acknowledge that his countrymen are not only long and broad, but also (though

doubtless in a very slight degree) THICK or HIGH. This objection is plausible, and, to Spacelanders, almost

irresistible, so that, I confess, when I first heard it, I knew not what to reply. But my poor old friend's answer

"I admit," said he when I mentioned to him this objection "I admit the truth of your critic's facts, but I

deny his conclusions. It is true that we have really in Flatland a Third unrecognized Dimension called 'height',

just as it is also true that you have really in Spaceland a Fourth unrecognized Dimension, called by no name

at present, but which I will call 'extraheight'. But we can no more take cognizance of our 'height' than you

can of your 'extraheight'. Even I who have been in Spaceland, and have had the privilege of

understanding for twentyfour hours the meaning of 'height' even I cannot now comprehend it, nor realize

it by the sense of sight or by any process of reason; I can but apprehend it by faith.

"The reason is obvious. Dimension implies direction, implies measurement, implies the more and the less.

Now, all our lines are EQUALLY and INFINITESIMALLY thick (or high, whichever you like);

consequently, there is nothing in them to lead our minds to the conception of that Dimension. No 'delicate

micrometer' as has been suggested by one too hasty Spaceland critic would in the least avail us; for we

should not know WHAT TO MEASURE, NOR IN WHAT DIRECTION. When we see a Line, we see

something that is long and BRIGHT; BRIGHTNESS, as well as length, is necessary to the existence of a

Line; if the brightness vanishes, the Line is extinguished. Hence, all my Flatland friends when I talk to

them about the unrecognized Dimension which is somehow visible in a Line say, 'Ah, you mean

BRIGHTNESS': and when I reply, 'No, I mean a real Dimension', they at once retort, 'Then measure it, or tell

us in what direction it extends'; and this silences me, for I can do neither. Only yesterday, when the Chief

Circle (in other words our High Priest) came to inspect the State Prison and paid me his seventh annual visit,

and when for the seventh time he put me the question, 'Was I any better?' I tried to prove to him that he was

'high', as well as long and broad, although he did not know it. But what was his reply? 'You say I am "high";

measure my "highness" and I will believe you.' What could I do? How could I meet his challenge? I was

"Does this still seem strange to you? Then put yourself in a similar position. Suppose a person of the Fourth

Dimension, condescending to visit you, were to say, 'Whenever you open your eyes, you see a Plane (which

is of Two Dimensions) and you INFER a Solid (which is of Three); but in reality you also see (though you do

not recognize) a Fourth Dimension, which is not colour nor brightness nor anything of the kind, but a true

Dimension, although I cannot point out to you its direction, nor can you possibly measure it.' What would

you say to such a visitor? Would not you have him locked up? Well, that is my fate: and it is as natural for us

Flatlanders to lock up a Square for preaching the Third Dimension, as it is for you Spacelanders to lock up a

Cube for preaching the Fourth. Alas, how strong a family likeness runs through blind and persecuting

humanity in all Dimensions! Points, Lines, Squares, Cubes, ExtraCubes we are all liable to the same

errors, all alike the Slaves of our respective Dimensional prejudices, as one of your Spaceland poets has said

of his critics on this matter has induced him to insert in his dialogue with the Sphere, certain remarks which

have a bearing on the point in question, and which he had previously omitted as being tedious and

On this point the defence of the Square seems to me to be impregnable. I wish I could say that his answer to

the second (or moral) objection was equally clear and cogent. It has been objected that he is a womanhater;

and as this objection has been vehemently urged by those whom Nature's decree has constituted the

somewhat larger half of the Spaceland race, I should like to remove it, so far as I can honestly do so. But the

Square is so unaccustomed to the use of the moral terminology of Spaceland that I should be doing him an

injustice if I were literally to transcribe his defence against this charge. Acting, therefore, as his interpreter

and summarizer, I gather that in the course of an imprisonment of seven years he has himself modified his

own personal views, both as regards Women and as regards the Isosceles or Lower Classes. Personally, he

now inclines to the opinion of the Sphere that the Straight Lines are in many important respects superior to

the Circles. But, writing as a Historian, he has identified himself (perhaps too closely) with the views

generally adopted by Flatland, and (as he has been informed) even by Spaceland, Historians; in whose pages

(until very recent times) the destinies of Women and of the masses of mankind have seldom been deemed

In a still more obscure passage he now desires to disavow the Circular or aristocratic tendencies with which

some critics have naturally credited him. While doing justice to the intellectual power with which a few

Circles have for many generations maintained their supremacy over immense multitudes of their countrymen,

he believes that the facts of Flatland, speaking for themselves without comment on his part, declare that

Revolutions cannot always be suppressed by slaughter, and that Nature, in sentencing the Circles to

infecundity, has condemned them to ultimate failure "and herein," he says, "I see a fulfilment of the great

Law of all worlds, that while the wisdom of Man thinks it is working one thing, the wisdom of Nature

constrains it to work another, and quite a different and far better thing." For the rest, he begs his readers not to

suppose that every minute detail in the daily life of Flatland must needs correspond to some other detail in

Spaceland; and yet he hopes that, taken as a whole, his work may prove suggestive as well as amusing, to

those Spacelanders of moderate and modest minds who speaking of that which is of the highest

importance, but lies beyond experience decline to say on the one hand, "This can never be," and on the

I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers,

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other

figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the

power of rising above or sinking below it, very much like shadows only hard and with luminous edges

and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should

have said "my universe": but now my mind has been opened to higher views of things.

In such a country, you will perceive at once that it is impossible that there should be anything of what you

call a "solid" kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles,

Squares, and other figures, moving about as I have described them. On the contrary, we could see nothing of

the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to

us, except Straight Lines; and the necessity of this I will speedily demonstrate.

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

But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and

more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more

oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are,

as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become,

The same thing would happen if you were to treat in the same way a Triangle, or Square, or any other figure

cut out of pasteboard. As soon as you look at it with your eye on the edge on the table, you will find that it

ceases to appear to you a figure, and that it becomes in appearance a straight line. Take for example an

equilateral Triangle who represents with us a Tradesman of the respectable class. Fig. 1 represents the

Tradesman as you would see him while you were bending over him from above; figs. 2 and 3 represent the

Tradesman, as you would see him if your eye were close to the level, or all but on the level of the table; and if

your eye were quite on the level of the table (and that is how we see him in Flatland) you would see nothing

When I was in Spaceland I heard that your sailors have very similar experiences while they traverse your seas

and discern some distant island or coast lying on the horizon. The faroff land may have bays, forelands,

angles in and out to any number and extent; yet at a distance you see none of these (unless indeed your sun

shines bright upon them revealing the projections and retirements by means of light and shade), nothing but a

Well, that is just what we see when one of our triangular or other acquaintances comes toward us in Flatland.

As there is neither sun with us, nor any light of such a kind as to make shadows, we have none of the helps to

the sight that you have in Spaceland. If our friend comes closer to us we see his line becomes larger; if he

leaves us it becomes smaller: but still he looks like a straight line; be he a Triangle, Square, Pentagon,

You may perhaps ask how under these disadvantageous circumstances we are able to distinguish our friends

from one another: but the answer to this very natural question will be more fitly and easily given when I

come to describe the inhabitants of Flatland. For the present let me defer this subject, and say a word or two

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

There being no sun nor other heavenly bodies, it is impossible for us to determine the North in the usual way;

but we have a method of our own. By a Law of Nature with us, there is a constant attraction to the South;

and, although in temperate climates this is very slight so that even a Woman in reasonable health can

journey several furlongs northward without much difficulty yet the hampering effect of the southward

attraction is quite sufficient to serve as a compass in most parts of our earth. Moreover, the rain (which falls

at stated intervals) coming always from the North, is an additional assistance; and in the towns we have the

guidance of the houses, which of course have their sidewalls running for the most part North and South, so

that the roofs may keep off the rain from the North. In the country, where there are no houses, the trunks of

the trees serve as some sort of guide. Altogether, we have not so much difficulty as might be expected in

Yet in our more temperate regions, in which the southward attraction is hardly felt, walking sometimes in a

perfectly desolate plain where there have been no houses nor trees to guide me, I have been occasionally

compelled to remain stationary for hours together, waiting till the rain came before continuing my journey.

On the weak and aged, and especially on delicate Females, the force of attraction tells much more heavily

than on the robust of the Male Sex, so that it is a point of breeding, if you meet a Lady in the street, always to

give her the North side of the way by no means an easy thing to do always at short notice when you are in

rude health and in a climate where it is difficult to tell your North from your South.

Windows there are none in our houses: for the light comes to us alike in our homes and out of them, by day

and by night, equally at all times and in all places, whence we know not. It was in old days, with our learned

men, an interesting and oftinvestigated question, "What is the origin of light?" and the solution of it has

been repeatedly attempted, with no other result than to crowd our lunatic asylums with the wouldbe solvers.

Hence, after fruitless attempts to suppress such investigations indirectly by making them liable to a heavy tax,

the Legislature, in comparatively recent times, absolutely prohibited them. I alas, I alone in Flatland

know now only too well the true solution of this mysterious problem; but my knowledge cannot be made

intelligible to a single one of my countrymen; and I am mocked at I, the sole possessor of the truths of

Space and of the theory of the introduction of Light from the world of three Dimensions as if I were the

maddest of the mad! But a truce to these painful digressions: let me return to our houses.

The most common form for the construction of a house is fivesided or pentagonal, as in the annexed figure.

The two Northern sides RO, OF, constitute the roof, and for the most part have no doors; on the East is a

small door for the Women; on the West a much larger one for the Men; the South side or floor is usually

Square and triangular houses are not allowed, and for this reason. The angles of a Square (and still more those

of an equilateral Triangle), being much more pointed than those of a Pentagon, and the lines of inanimate

objects (such as houses) being dimmer than the lines of Men and Women, it follows that there is no little

danger lest the points of a square or triangular house residence might do serious injury to an inconsiderate or

perhaps absentminded traveller suddenly therefore, running against them: and as early as the eleventh

century of our era, triangular houses were universally forbidden by Law, the only exceptions being

fortifications, powdermagazines, barracks, and other state buildings, which it is not desirable that the

At this period, square houses were still everywhere permitted, though discouraged by a special tax. But, about

three centuries afterwards, the Law decided that in all towns containing a population above ten thousand, the

angle of a Pentagon was the smallest houseangle that could be allowed consistently with the public safety.

The good sense of the community has seconded the efforts of the Legislature; and now, even in the country,

the pentagonal construction has superseded every other. It is only now and then in some very remote and

backward agricultural district that an antiquarian may still discover a square house.

The greatest length or breadth of a full grown inhabitant of Flatland may be estimated at about eleven of your

Our Soldiers and Lowest Classes of Workmen are Triangles with two equal sides, each about eleven inches

long, and a base or third side so short (often not exceeding half an inch) that they form at their vertices a very

sharp and formidable angle. Indeed when their bases are of the most degraded type (not more than the eighth

part of an inch in size), they can hardly be distinguished from Straight Lines or Women; so extremely pointed

are their vertices. With us, as with you, these Triangles are distinguished from others by being called

Our Professional Men and Gentlemen are Squares (to which class I myself belong) and FiveSided Figures

Next above these come the Nobility, of whom there are several degrees, beginning at SixSided Figures, or

Hexagons, and from thence rising in the number of their sides till they receive the honourable title of

Polygonal, or manysided. Finally when the number of the sides becomes so numerous, and the sides

themselves so small, that the figure cannot be distinguished from a circle, he is included in the Circular or

It is a Law of Nature with us that a male child shall have one more side than his father, so that each

generation shall rise (as a rule) one step in the scale of development and nobility. Thus the son of a Square is

But this rule applies not always to the Tradesmen, and still less often to the Soldiers, and to the Workmen;

who indeed can hardly be said to deserve the name of human Figures, since they have not all their sides

equal. With them therefore the Law of Nature does not hold; and the son of an Isosceles (i.e. a Triangle with

two sides equal) remains Isosceles still. Nevertheless, all hope is not shut out, even from the Isosceles, that

his posterity may ultimately rise above his degraded condition. For, after a long series of military successes,

or diligent and skilful labours, it is generally found that the more intelligent among the Artisan and Soldier

classes manifest a slight increase of their third side or base, and a shrinkage of the two other sides.

Intermarriages (arranged by the Priests) between the sons and daughters of these more intellectual members

of the lower classes generally result in an offspring approximating still more to the type of the EqualSided

Rarely in proportion to the vast numbers of Isosceles births is a genuine and certifiable EqualSided

Triangle produced a Spaceland critic may ask: "Is not the procreation of a Square Son a certificate from

Nature herself, proving the Equalsidedness of the Father?" I reply that no Lady of any position will marry

an uncertified Triangle. Square offspring has sometimes resulted from a slightly Irregular Triangle; but in

almost every such case the Irregularity of the first generation is visited on the third; which either fails to attain

the Pentagonal rank, or relapses to the Triangular.] Such a birth requires, as its antecedents, not only a series

of carefully arranged intermarriages, but also a long, continued exercise of frugality and selfcontrol on the

part of the wouldbe ancestors of the coming Equilateral, and a patient, systematic, and continuous

The birth of a True Equilateral Triangle from Isosceles parents is the subject of rejoicing in our country for

many furlongs around. After a strict examination conducted by the Sanitary and Social Board, the infant, if

certified as Regular, is with solemn ceremonial admitted into the class of Equilaterals. He is then immediately

taken from his proud yet sorrowing parents and adopted by some childless Equilateral, who is bound by oath

never to permit the child henceforth to enter his former home or so much as to look upon his relations again,

for fear lest the freshly developed organism may, by force of unconscious imitation, fall back again into his

The occasional emergence of an Equilateral from the ranks of his serfborn ancestors is welcomed, not only

by the poor serfs themselves, as a gleam of light and hope shed upon the monotonous squalor of their

existence, but also by the Aristocracy at large; for all the higher classes are well aware that these rare

phenomena, while they do little or nothing to vulgarize their own privileges, serve as a most useful barrier

Had the acuteangled rabble been all, without exception, absolutely destitute of hope and of ambition, they

might have found leaders in some of their many seditious outbreaks, so able as to render their superior

numbers and strength too much even for the wisdom of the Circles. But a wise ordinance of Nature has

decreed that, in proportion as the workingclasses increase in intelligence, knowledge, and all virtue, in that

same proportion their acute angle (which makes them physically terrible) shall increase also and approximate

to the comparatively harmless angle of the Equilateral Triangle. Thus, in the most brutal and formidable of

the soldier class creatures almost on a level with women in their lack of intelligence it is found that, as

they wax in the mental ability necessary to employ their tremendous penetrating power to advantage, so do

How admirable is this Law of Compensation! And how perfect a proof of the natural fitness and, I may

almost say, the divine origin of the aristocratic constitution of the States in Flatland! By a judicious use of

this Law of Nature, the Polygons and Circles are almost always able to stifle sedition in its very cradle, taking

advantage of the irrepressible and boundless hopefulness of the human mind. Art also comes to the aid of

Law and Order. It is generally found possible by a little artificial compression or expansion on the part of

the State physicians to make some of the more intelligent leaders of a rebellion perfectly Regular, and to

admit them at once into the privileged classes; a much larger number, who are still below the standard,

allured by the prospect of being ultimately ennobled, are induced to enter the State Hospitals, where they are

kept in honourable confinement for life; one or two alone of the more obstinate, foolish, and hopelessly

Then the wretched rabble of the Isosceles, planless and leaderless, are either transfixed without resistance by

the small body of their brethren whom the Chief Circle keeps in pay for emergencies of this kind; or else

more often, by means of jealousies and suspicions skilfully fomented among them by the Circular party, they

are stirred to mutual warfare, and perish by one another's angles. No less than one hundred and twenty

rebellions are recorded in our annals, besides minor outbreaks numbered at two hundred and thirtyfive; and

If our highly pointed Triangles of the Soldier class are formidable, it may be readily inferred that far more

formidable are our Women. For if a Soldier is a wedge, a Woman is a needle; being, so to speak, ALL point,

at least at the two extremities. Add to this the power of making herself practically invisible at will, and you

will perceive that a Female, in Flatland, is a creature by no means to be trifled with.

But here, perhaps, some of my younger Readers may ask HOW a woman in Flatland can make herself

invisible. This ought, I think, to be apparent without any explanation. However, a few words will make it

Place a needle on a table. Then, with your eye on the level of the table, look at it sideways, and you see the

whole length of it; but look at it endways, and you see nothing but a point, it has become practically

invisible. Just so is it with one of our Women. When her side is turned towards us, we see her as a straight

line; when the end containing her eye or mouth for with us these two organs are identical is the part

that meets our eye, then we see nothing but a highly lustrous point; but when the back is presented to our

view, then being only sublustrous, and, indeed, almost as dim as an inanimate object her hinder

The dangers to which we are exposed from our Women must now be manifest to the meanest capacity in

Spaceland. If even the angle of a respectable Triangle in the middle class is not without its dangers; if to run

against a Working Man involves a gash; if collision with an officer of the military class necessitates a serious

wound; if a mere touch from the vertex of a Private Soldier brings with it danger of death; what can it be

to run against a Woman, except absolute and immediate destruction? And when a Woman is invisible, or

visible only as a dim sublustrous point, how difficult must it be, even for the most cautious, always to avoid

Many are the enactments made at different times in the different States of Flatland, in order to minimize this

peril; and in the Southern and less temperate climates where the force of gravitation is greater, and human

beings more liable to casual and involuntary motions, the Laws concerning Women are naturally much more

stringent. But a general view of the Code may be obtained from the following summary:

1. Every house shall have one entrance in the Eastern side, for the use of Females only; by which all females

shall enter "in a becoming and respectful manner" and not by the Men's some of your Priestly circles have in

the same way a separate entrance for Villagers, Farmers and Teachers of Board Schools (`Spectator', Sept.

2. No Female shall walk in any public place without continually keeping up her Peacecry, under penalty of

3. Any Female, duly certified to be suffering from St. Vitus's Dance, fits, chronic cold accompanied by

violent sneezing, or any disease necessitating involuntary motions, shall be instantly destroyed.

In some of the States there is an additional Law forbidding Females, under penalty of death, from walking or

standing in any public place without moving their backs constantly from right to left so as to indicate their

presence to those behind them; others oblige a Woman, when travelling, to be followed by one of her sons, or

servants, or by her husband; others confine Women altogether to their houses except during the religious

festivals. But it has been found by the wisest of our Circles or Statesmen that the multiplication of restrictions

on Females tends not only to the debilitation and diminution of the race, but also to the increase of domestic

murders to such an extent that a State loses more than it gains by a too prohibitive Code.

For whenever the temper of the Women is thus exasperated by confinement at home or hampering

regulations abroad, they are apt to vent their spleen upon their husbands and children; and in the less

temperate climates the whole male population of a village has been sometimes destroyed in one or two hours

of simultaneous female outbreak. Hence the Three Laws, mentioned above, suffice for the better regulated

After all, our principal safeguard is found, not in Legislature, but in the interests of the Women themselves.

For, although they can inflict instantaneous death by a retrograde movement, yet unless they can at once

disengage their stinging extremity from the struggling body of their victim, their own frail bodies are liable to

The power of Fashion is also on our side. I pointed out that in some less civilized States no female is suffered

to stand in any public place without swaying her back from right to left. This practice has been universal

among ladies of any pretensions to breeding in all wellgoverned States, as far back as the memory of

Figures can reach. It is considered a disgrace to any State that legislation should have to enforce what ought

to be, and is in every respectable female, a natural instinct. The rhythmical and, if I may so say,

wellmodulated undulation of the back in our ladies of Circular rank is envied and imitated by the wife of a

common Equilateral, who can achieve nothing beyond a mere monotonous swing, like the ticking of a

pendulum; and the regular tick of the Equilateral is no less admired and copied by the wife of the progressive

and aspiring Isosceles, in the females of whose family no "backmotion" of any kind has become as yet a

necessity of life. Hence, in every family of position and consideration, "back motion" is as prevalent as time

itself; and the husbands and sons in these households enjoy immunity at least from invisible attacks.

Not that it must be for a moment supposed that our Women are destitute of affection. But unfortunately the

passion of the moment predominates, in the Frail Sex, over every other consideration. This is, of course, a

necessity arising from their unfortunate conformation. For as they have no pretensions to an angle, being

inferior in this respect to the very lowest of the Isosceles, they are consequently wholly devoid of

brainpower, and have neither reflection, judgment nor forethought, and hardly any memory. Hence, in their

fits of fury, they remember no claims and recognize no distinctions. I have actually known a case where a

Woman has exterminated her whole household, and half an hour afterwards, when her rage was over and the

fragments swept away, has asked what has become of her husband and her children.

Obviously then a Woman is not to be irritated as long as she is in a position where she can turn round. When

you have them in their apartments which are constructed with a view to denying them that power you

can say and do what you like; for they are then wholly impotent for mischief, and will not remember a few

minutes hence the incident for which they may be at this moment threatening you with death, nor the

promises which you may have found it necessary to make in order to pacify their fury.

On the whole we get on pretty smoothly in our domestic relations, except in the lower strata of the Military

Classes. There the want of tact and discretion on the part of the husbands produces at times indescribable

disasters. Relying too much on the offensive weapons of their acute angles instead of the defensive organs of

good sense and seasonable simulation, these reckless creatures too often neglect the prescribed construction

of the women's apartments, or irritate their wives by illadvised expressions out of doors, which they refuse

immediately to retract. Moreover a blunt and stolid regard for literal truth indisposes them to make those

lavish promises by which the more judicious Circle can in a moment pacify his consort. The result is

massacre; not, however, without its advantages, as it eliminates the more brutal and troublesome of the

Isosceles; and by many of our Circles the destructiveness of the Thinner Sex is regarded as one among many

providential arrangements for suppressing redundant population, and nipping Revolution in the bud.

Yet even in our best regulated and most approximately Circular families I cannot say that the ideal of family

life is so high as with you in Spaceland. There is peace, in so far as the absence of slaughter may be called by

that name, but there is necessarily little harmony of tastes or pursuits; and the cautious wisdom of the Circles

has ensured safety at the cost of domestic comfort. In every Circular or Polygonal household it has been a

habit from time immemorial and now has become a kind of instinct among the women of our higher

classes that the mothers and daughters should constantly keep their eyes and mouths towards their

husband and his male friends; and for a lady in a family of distinction to turn her back upon her husband

would be regarded as a kind of portent, involving loss of STATUS. But, as I shall soon shew, this custom,

In the house of the Working Man or respectable Tradesman where the wife is allowed to turn her back

upon her husband, while pursuing her household avocations there are at least intervals of quiet, when the

wife is neither seen nor heard, except for the humming sound of the continuous Peacecry; but in the homes

of the upper classes there is too often no peace. There the voluble mouth and bright penetrating eye are ever

directed towards the Master of the household; and light itself is not more persistent than the stream of

feminine discourse. The tact and skill which suffice to avert a Woman's sting are unequal to the task of

stopping a Woman's mouth; and as the wife has absolutely nothing to say, and absolutely no constraint of wit,

sense, or conscience to prevent her from saying it, not a few cynics have been found to aver that they prefer

the danger of the deathdealing but inaudible sting to the safe sonorousness of a Woman's other end.

To my readers in Spaceland the condition of our Women may seem truly deplorable, and so indeed it is. A

Male of the lowest type of the Isosceles may look forward to some improvement of his angle, and to the

ultimate elevation of the whole of his degraded caste; but no Woman can entertain such hopes for her sex.

"Once a Woman, always a Woman" is a Decree of Nature; and the very Laws of Evolution seem suspended

in her disfavour. Yet at least we can admire the wise Prearrangement which has ordained that, as they have no

hopes, so they shall have no memory to recall, and no forethought to anticipate, the miseries and humiliations

which are at once a necessity of their existence and the basis of the constitution of Flatland.

You, who are blessed with shade as well as light, you, who are gifted with two eyes, endowed with a

knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually SEE an

angle, and contemplate the complete circumference of a circle in the happy region of the Three Dimensions

how shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one

Recall what I told you above. All beings in Flatland, animate or inanimate, no matter what their form, present

TO OUR VIEW the same, or nearly the same, appearance, viz. that of a straight Line. How then can one be

The answer is threefold. The first means of recognition is the sense of hearing; which with us is far more

highly developed than with you, and which enables us not only to distinguish by the voice our personal

friends, but even to discriminate between different classes, at least so far as concerns the three lowest orders,

the Equilateral, the Square, and the Pentagon for of the Isosceles I take no account. But as we ascend in

the social scale, the process of discriminating and being discriminated by hearing increases in difficulty,

partly because voices are assimilated, partly because the faculty of voicediscrimination is a plebeian virtue

not much developed among the Aristocracy. And wherever there is any danger of imposture we cannot trust

to this method. Amongst our lowest orders, the vocal organs are developed to a degree more than

correspondent with those of hearing, so that an Isosceles can easily feign the voice of a Polygon, and, with

some training, that of a Circle himself. A second method is therefore more commonly resorted to.

FEELING is, among our Women and lower classes about our upper classes I shall speak presently the

principal test of recognition, at all events between strangers, and when the question is, not as to the

individual, but as to the class. What therefore "introduction" is among the higher classes in Spaceland, that

the process of "feeling" is with us. "Permit me to ask you to feel and be felt by my friend Mr. Soandso"

is still, among the more oldfashioned of our country gentlemen in districts remote from towns, the

customary formula for a Flatland introduction. But in the towns, and among men of business, the words "be

felt by" are omitted and the sentence is abbreviated to, "Let me ask you to feel Mr. Soandso"; although it is

assumed, of course, that the "feeling" is to be reciprocal. Among our still more modern and dashing young

gentlemen who are extremely averse to superfluous effort and supremely indifferent to the purity of their

native language the formula is still further curtailed by the use of "to feel" in a technical sense, meaning,

"to recommendforthepurposesoffeelingandbeingfelt"; and at this moment the "slang" of polite or

fast society in the upper classes sanctions such a barbarism as "Mr. Smith, permit me to feel Mr. Jones."

Let not my Reader however suppose that "feeling" is with us the tedious process that it would be with you, or

that we find it necessary to feel right round all the sides of every individual before we determine the class to

which he belongs. Long practice and training, begun in the schools and continued in the experience of daily

life, enable us to discriminate at once by the sense of touch, between the angles of an equalsided Triangle,

Square, and Pentagon; and I need not say that the brainless vertex of an acuteangled Isosceles is obvious to

the dullest touch. It is therefore not necessary, as a rule, to do more than feel a single angle of an individual;

and this, once ascertained, tells us the class of the person whom we are addressing, unless indeed he belongs

to the higher sections of the nobility. There the difficulty is much greater. Even a Master of Arts in our

University of Wentbridge has been known to confuse a tensided with a twelvesided Polygon; and there is

hardly a Doctor of Science in or out of that famous University who could pretend to decide promptly and

unhesitatingly between a twentysided and a twentyfour sided member of the Aristocracy.

Those of my readers who recall the extracts I gave above from the Legislative code concerning Women, will

readily perceive that the process of introduction by contact requires some care and discretion. Otherwise the

angles might inflict on the unwary Feeler irreparable injury. It is essential for the safety of the Feeler that the

Felt should stand perfectly still. A start, a fidgety shifting of the position, yes, even a violent sneeze, has been

known before now to prove fatal to the incautious, and to nip in the bud many a promising friendship.

Especially is this true among the lower classes of the Triangles. With them, the eye is situated so far from

their vertex that they can scarcely take cognizance of what goes on at that extremity of their frame. They are,

moreover, of a rough coarse nature, not sensitive to the delicate touch of the highly organized Polygon. What

wonder then if an involuntary toss of the head has ere now deprived the State of a valuable life!

I have heard that my excellent Grandfather one of the least irregular of his unhappy Isosceles class, who

indeed obtained, shortly before his decease, four out of seven votes from the Sanitary and Social Board for

passing him into the class of the Equalsided often deplored, with a tear in his venerable eye, a

miscarriage of this kind, which had occured to his greatgreatgreatGrandfather, a respectable Working

Man with an angle or brain of 59 degrees 30 minutes. According to his account, my unfortunate Ancestor,

being afflicted with rheumatism, and in the act of being felt by a Polygon, by one sudden start accidentally

transfixed the Great Man through the diagonal; and thereby, partly in consequence of his long imprisonment

and degradation, and partly because of the moral shock which pervaded the whole of my Ancestor's relations,

threw back our family a degree and a half in their ascent towards better things. The result was that in the next

generation the family brain was registered at only 58 degrees, and not till the lapse of five generations was

the lost ground recovered, the full 60 degrees attained, and the Ascent from the Isosceles finally achieved.

And all this series of calamities from one little accident in the process of Feeling.

At this point I think I hear some of my better educated readers exclaim, "How could you in Flatland know

anything about angles and degrees, or minutes? We can SEE an angle, because we, in the region of Space,

can see two straight lines inclined to one another; but you, who can see nothing but one straight line at a time,

or at all events only a number of bits of straight lines all in one straight line how can you ever discern any

I answer that though we cannot SEE angles, we can INFER them, and this with great precision. Our sense of

touch, stimulated by necessity, and developed by long training, enables us to distinguish angles far more

accurately than your sense of sight, when unaided by a rule or measure of angles. Nor must I omit to explain

that we have great natural helps. It is with us a Law of Nature that the brain of the Isosceles class shall begin

at half a degree, or thirty minutes, and shall increase (if it increases at all) by half a degree in every

generation; until the goal of 60 degrees is reached, when the condition of serfdom is quitted, and the freeman

Consequently, Nature herself supplies us with an ascending scale or Alphabet of angles for half a degree up

to 60 degrees, Specimens of which are placed in every Elementary School throughout the land. Owing to

occasional retrogressions, to still more frequent moral and intellectual stagnation, and to the extraordinary

fecundity of the Criminal and Vagabond Classes, there is always a vast superfluity of individuals of the half

degree and single degree class, and a fair abundance of Specimens up to 10 degrees. These are absolutely

destitute of civic rights; and a great number of them, not having even intelligence enough for the purposes of

warfare, are devoted by the States to the service of education. Fettered immovably so as to remove all

possibility of danger, they are placed in the class rooms of our Infant Schools, and there they are utilized by

the Board of Education for the purpose of imparting to the offspring of the Middle Classes that tact and

In some States the Specimens are occasionally fed and suffered to exist for several years; but in the more

temperate and better regulated regions, it is found in the long run more advantageous for the educational

interests of the young, to dispense with food, and to renew the Specimens every month which is about the

average duration of the foodless existence of the Criminal class. In the cheaper schools, what is gained by the

longer existence of the Specimen is lost, partly in the expenditure for food, and partly in the diminished

accuracy of the angles, which are impaired after a few weeks of constant "feeling". Nor must we forget to

add, in enumerating the advantages of the more expensive system, that it tends, though slightly yet

perceptibly, to the diminution of the redundant Isosceles population an object which every statesman in

Flatland constantly keeps in view. On the whole therefore although I am not ignorant that, in many

popularly elected School Boards, there is a reaction in favour of "the cheap system" as it is called I am

myself disposed to think that this is one of the many cases in which expense is the truest economy.

But I must not allow questions of School Board politics to divert me from my subject. Enough has been said,

I trust, to shew that Recognition by Feeling is not so tedious or indecisive a process as might have been

supposed; and it is obviously more trustworthy than Recognition by hearing. Still there remains, as has been

pointed out above, the objection that this method is not without danger. For this reason many in the Middle

and Lower classes, and all without exception in the Polygonal and Circular orders, prefer a third method, the

I am about to appear very inconsistent. In previous sections I have said that all figures in Flatland present the

appearance of a straight line; and it was added or implied, that it is consequently impossible to distinguish by

the visual organ between individuals of different classes: yet now I am about to explain to my Spaceland

If however the Reader will take the trouble to refer to the passage in which Recognition by Feeling is stated

to be universal, he will find this qualification "among the lower classes". It is only among the higher

That this power exists in any regions and for any classes is the result of Fog; which prevails during the

greater part of the year in all parts save the torrid zones. That which is with you in Spaceland an unmixed

evil, blotting out the landscape, depressing the spirits, and enfeebling the health, is by us recognized as a

blessing scarcely inferior to air itself, and as the Nurse of arts and Parent of sciences. But let me explain my

If Fog were nonexistent, all lines would appear equally and indistinguishably clear; and this is actually the

case in those unhappy countries in which the atmosphere is perfectly dry and transparent. But wherever there

is a rich supply of Fog objects that are at a distance, say of three feet, are appreciably dimmer than those at a

distance of two feet eleven inches; and the result is that by careful and constant experimental observation of

comparative dimness and clearness, we are enabled to infer with great exactness the configuration of the

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

Suppose I see two individuals approaching whose rank I wish to ascertain. They are, we will suppose, a

Merchant and a Physician, or in other words, an Equilateral Triangle and a Pentagon: how am I to distinguish

It will be obvious, to every child in Spaceland who has touched the threshold of Geometrical Studies, that, if I

can bring my eye so that its glance may bisect an angle (A) of the approaching stranger, my view will lie as it

were evenly between his two sides that are next to me (viz. CA and AB), so that I shall contemplate the two

Now in the case of (1) the Merchant, what shall I see? I shall see a straight line DAE, in which the middle

point (A) will be very bright because it is nearest to me; but on either side the line will shade away RAPIDLY

INTO DIMNESS, because the sides AC and AB RECEDE RAPIDLY INTO THE FOG and what appear to

On the other hand in the case of (2) the Physician, though I shall here also see a line (D'A'E') with a bright

centre (A'), yet it will shade away LESS RAPIDLY into dimness, because the sides (A'C', A'B') RECEDE

LESS RAPIDLY INTO THE FOG: and what appear to me the Physician's extremities, viz. D' and E', will not

The Reader will probably understand from these two instances how after a very long training

supplemented by constant experience it is possible for the welleducated classes among us to discriminate

with fair accuracy between the middle and lowest orders, by the sense of sight. If my Spaceland Patrons have

grasped this general conception, so far as to conceive the possibility of it and not to reject my account as

altogether incredible I shall have attained all I can reasonably expect. Were I to attempt further details I

should only perplex. Yet for the sake of the young and inexperienced, who may perchance infer from the

two simple instances I have given above, of the manner in which I should recognize my Father and my Sons

that Recognition by sight is an easy affair, it may be needful to point out that in actual life most of the

If for example, when my Father, the Triangle, approaches me, he happens to present his side to me instead of

his angle, then, until I have asked him to rotate, or until I have edged my eye round him, I am for the moment

doubtful whether he may not be a Straight Line, or, in other words, a Woman. Again, when I am in the

company of one of my two hexagonal Grandsons, contemplating one of his sides (AB) full front, it will be

evident from the accompanying diagram that I shall see one whole line (AB) in comparative brightness

(shading off hardly at all at the ends) and two smaller lines (CA and BD) dim throughout and shading away

But I must not give way to the temptation of enlarging on these topics. The meanest mathematician in

Spaceland will readily believe me when I assert that the problems of life, which present themselves to the

welleducated when they are themselves in motion, rotating, advancing or retreating, and at the same time

attempting to discriminate by the sense of sight between a number of Polygons of high rank moving in

different directions, as for example in a ballroom or conversazione must be of a nature to task the

angularity of the most intellectual, and amply justify the rich endowments of the Learned Professors of

Geometry, both Static and Kinetic, in the illustrious University of Wentbridge, where the Science and Art of

Sight Recognition are regularly taught to large classes of the ELITE of the States.

It is only a few of the scions of our noblest and wealthiest houses, who are able to give the time and money

necessary for the thorough prosecution of this noble and valuable Art. Even to me, a Mathematician of no

mean standing, and the Grandfather of two most hopeful and perfectly regular Hexagons, to find myself in

the midst of a crowd of rotating Polygons of the higher classes, is occasionally very perplexing. And of

course to a common Tradesman, or Serf, such a sight is almost as unintelligible as it would be to you, my

In such a crowd you could see on all sides of you nothing but a Line, apparently straight, but of which the

parts would vary irregularly and perpetually in brightness or dimness. Even if you had completed your third

year in the Pentagonal and Hexagonal classes in the University, and were perfect in the theory of the subject,

you would still find that there was need of many years of experience, before you could move in a fashionable

crowd without jostling against your betters, whom it is against etiquette to ask to "feel", and who, by their

superior culture and breeding, know all about your movements, while you know very little or nothing about

theirs. In a word, to comport oneself with perfect propriety in Polygonal society, one ought to be a Polygon

It is astonishing how much the Art or I may almost call it instinct of Sight Recognition is developed by

the habitual practice of it and by the avoidance of the custom of "Feeling". Just as, with you, the deaf and

dumb, if once allowed to gesticulate and to use the handalphabet, will never acquire the more difficult but

far more valuable art of lipspeech and lipreading, so it is with us as regards "Seeing" and "Feeling". None

For this reason, among our Higher Classes, "Feeling" is discouraged or absolutely forbidden. From the cradle

their children, instead of going to the Public Elementary schools (where the art of Feeling is taught), are sent

to higher Seminaries of an exclusive character; and at our illustrious University, to "feel" is regarded as a

most serious fault, involving Rustication for the first offence, and Expulsion for the second.

But among the lower classes the art of Sight Recognition is regarded as an unattainable luxury. A common

Tradesman cannot afford to let his son spend a third of his life in abstract studies. The children of the poor are

therefore allowed to "feel" from their earliest years, and they gain thereby a precocity and an early vivacity

which contrast at first most favourably with the inert, undeveloped, and listless behaviour of the

halfinstructed youths of the Polygonal class; but when the latter have at last completed their University

course, and are prepared to put their theory into practice, the change that comes over them may almost be

described as a new birth, and in every art, science, and social pursuit they rapidly overtake and distance their

Only a few of the Polygonal Class fail to pass the Final Test or Leaving Examination at the University. The

condition of the unsuccessful minority is truly pitiable. Rejected from the higher class, they are also despised

by the lower. They have neither the matured and systematically trained powers of the Polygonal Bachelors

and Masters of Arts, nor yet the native precocity and mercurial versatility of the youthful Tradesman. The

professions, the public services, are closed against them; and though in most States they are not actually

debarred from marriage, yet they have the greatest difficulty in forming suitable alliances, as experience

shews that the offspring of such unfortunate and illendowed parents is generally itself unfortunate, if not

It is from these specimens of the refuse of our Nobility that the great Tumults and Seditions of past ages have

generally derived their leaders; and so great is the mischief thence arising that an increasing minority of our

more progressive Statesmen are of opinion that true mercy would dictate their entire suppression, by enacting

that all who fail to pass the Final Examination of the University should be either imprisoned for life, or

But I find myself digressing into the subject of Irregularities, a matter of such vital interest that it demands a

Throughout the previous pages I have been assuming what perhaps should have been laid down at the

beginning as a distinct and fundamental proposition that every human being in Flatland is a Regular

Figure, that is to say of regular construction. By this I mean that a Woman must not only be a line, but a

straight line; that an Artisan or Soldier must have two of his sides equal; that Tradesmen must have three

sides equal; Lawyers (of which class I am a humble member), four sides equal, and generally, that in every

The size of the sides would of course depend upon the age of the individual. A Female at birth would be

about an inch long, while a tall adult Woman might extend to a foot. As to the Males of every class, it may be

roughly said that the length of an adult's sides, when added together, is two feet or a little more. But the size

of our sides is not under consideration. I am speaking of the EQUALITY of sides, and it does not need much

reflection to see that the whole of the social life in Flatland rests upon the fundamental fact that Nature wills

If our sides were unequal our angles might be unequal. Instead of its being sufficient to feel, or estimate by

sight, a single angle in order to determine the form of an individual, it would be necessary to ascertain each

angle by the experiment of Feeling. But life would be too short for such a tedious grouping. The whole

science and art of Sight Recognition would at once perish; Feeling, so far as it is an art, would not long

survive; intercourse would become perilous or impossible; there would be an end to all confidence, all

forethought; no one would be safe in making the most simple social arrangements; in a word, civilization

Am I going too fast to carry my Readers with me to these obvious conclusions? Surely a moment's reflection,

and a single instance from common life, must convince every one that our whole social system is based upon

Regularity, or Equality of Angles. You meet, for example, two or three Tradesmen in the street, whom you

recognize at once to be Tradesmen by a glance at their angles and rapidly bedimmed sides, and you ask them

to step into your house to lunch. This you do at present with perfect confidence, because everyone knows to

an inch or two the area occupied by an adult Triangle: but imagine that your Tradesman drags behind his

regular and respectable vertex, a parallelogram of twelve or thirteen inches in diagonal: what are you to

But I am insulting the intelligence of my Readers by accumulating details which must be patent to everyone

who enjoys the advantages of a Residence in Spaceland. Obviously the measurements of a single angle would

no longer be sufficient under such portentous circumstances; one's whole life would be taken up in feeling or

surveying the perimeter of one's acquaintances. Already the difficulties of avoiding a collision in a crowd are

enough to tax the sagacity of even a welleducated Square; but if no one could calculate the Regularity of a

single figure in the company, all would be chaos and confusion, and the slightest panic would cause serious

injuries, or if there happened to be any Women or Soldiers present perhaps considerable loss of life.

Expediency therefore concurs with Nature in stamping the seal of its approval upon Regularity of

conformation: nor has the Law been backward in seconding their efforts. "Irregularity of Figure" means with

us the same as, or more than, a combination of moral obliquity and criminality with you, and is treated

accordingly. There are not wanting, it is true, some promulgators of paradoxes who maintain that there is no

necessary connection between geometrical and moral Irregularity. "The Irregular", they say, "is from his birth

scouted by his own parents, derided by his brothers and sisters, neglected by the domestics, scorned and

suspected by society, and excluded from all posts of responsibility, trust, and useful activity. His every

movement is jealously watched by the police till he comes of age and presents himself for inspection; then he

is either destroyed, if he is found to exceed the fixed margin of deviation, or else immured in a Government

Office as a clerk of the seventh class; prevented from marriage; forced to drudge at an uninteresting

occupation for a miserable stipend; obliged to live and board at the office, and to take even his vacation under

close supervision; what wonder that human nature, even in the best and purest, is embittered and perverted by

All this very plausible reasoning does not convince me, as it has not convinced the wisest of our Statesmen,

that our ancestors erred in laying it down as an axiom of policy that the toleration of Irregularity is

incompatible with the safety of the State. Doubtless, the life of an Irregular is hard; but the interests of the

Greater Number require that it shall be hard. If a man with a triangular front and a polygonal back were

allowed to exist and to propagate a still more Irregular posterity, what would become of the arts of life? Are

the houses and doors and churches in Flatland to be altered in order to accommodate such monsters? Are our

ticketcollectors to be required to measure every man's perimeter before they allow him to enter a theatre or

to take his place in a lecture room? Is an Irregular to be exempted from the militia? And if not, how is he to

be prevented from carrying desolation into the ranks of his comrades? Again, what irresistible temptations to

fraudulent impostures must needs beset such a creature! How easy for him to enter a shop with his polygonal

front foremost, and to order goods to any extent from a confiding tradesman! Let the advocates of a falsely

called Philanthropy plead as they may for the abrogation of the Irregular Penal Laws, I for my part have

never known an Irregular who was not also what Nature evidently intended him to be a hypocrite, a

misanthropist, and, up to the limits of his power, a perpetrator of all manner of mischief.

Not that I should be disposed to recommend (at present) the extreme measures adopted by some States, where

an infant whose angle deviates by half a degree from the correct angularity is summarily destroyed at birth.

Some of our highest and ablest men, men of real genius, have during their earliest days laboured under

deviations as great as, or even greater than, fortyfive minutes: and the loss of their precious lives would

have been an irreparable injury to the State. The art of healing also has achieved some of its most glorious

triumphs in the compressions, extensions, trepannings, colligations, and other surgical or diaetetic operations

by which Irregularity has been partly or wholly cured. Advocating therefore a VIA MEDIA, I would lay

down no fixed or absolute line of demarcation; but at the period when the frame is just beginning to set, and

when the Medical Board has reported that recovery is improbable, I would suggest that the Irregular offspring

If my Readers have followed me with any attention up to this point, they will not be surprised to hear that life

is somewhat dull in Flatland. I do not, of course, mean that there are not battles, conspiracies, tumults,

factions, and all those other phenomena which are supposed to make History interesting; nor would I deny

that the strange mixture of the problems of life and the problems of Mathematics, continually inducing

conjecture and giving the opportunity of immediate verification, imparts to our existence a zest which you in

Spaceland can hardly comprehend. I speak now from the aesthetic and artistic point of view when I say that

How can it be otherwise, when all one's prospect, all one's landscapes, historical pieces, portraits, flowers,

still life, are nothing but a single line, with no varieties except degrees of brightness and obscurity?

It was not always thus. Colour, if Tradition speaks the truth, once for the space of half a dozen centuries or

more, threw a transient splendour over the lives of our ancestors in the remotest ages. Some private individual

a Pentagon whose name is variously reported having casually discovered the constituents of the

simpler colours and a rudimentary method of painting, is said to have begun decorating first his house, then

his slaves, then his Father, his Sons, and Grandsons, lastly himself. The convenience as well as the beauty of

the results commended themselves to all. Wherever Chromatistes, for by that name the most trustworthy

authorities concur in calling him, turned his variegated frame, there he at once excited attention, and

attracted respect. No one now needed to "feel" him; no one mistook his front for his back; all his movements

were readily ascertained by his neighbours without the slightest strain on their powers of calculation; no one

jostled him, or failed to make way for him; his voice was saved the labour of that exhausting utterance by

which we colourless Squares and Pentagons are often forced to proclaim our individuality when we move

The fashion spread like wildfire. Before a week was over, every Square and Triangle in the district had

copied the example of Chromatistes, and only a few of the more conservative Pentagons still held out. A

month or two found even the Dodecagons infected with the innovation. A year had not elapsed before the

habit had spread to all but the very highest of the Nobility. Needless to say, the custom soon made its way

from the district of Chromatistes to surrounding regions; and within two generations no one in all Flatland

Here Nature herself appeared to erect a barrier, and to plead against extending the innovation to these two

classes. "Distinction of sides is intended by Nature to imply distinction of colours" such was the sophism

which in those days flew from mouth to mouth, converting whole towns at a time to the new culture. But

manifestly to our Priests and Women this adage did not apply. The latter had only one side, and therefore

plurally and pedantically speaking NO SIDES. The former if at least they would assert their claim to

be really and truly Circles, and not mere highclass Polygons with an infinitely large number of

infinitesimally small sides were in the habit of boasting (what Women confessed and deplored) that they

also had no sides, being blessed with a perimeter of one line, or, in other words, a Circumference. Hence it

came to pass that these two Classes could see no force in the socalled axiom about "Distinction of Sides

implying Distinction of Colour"; and when all others had succumbed to the fascinations of corporal

decoration, the Priests and the Women alone still remained pure from the pollution of paint.

Immoral, licentious, anarchical, unscientific call them by what names you will yet, from an aesthetic

point of view, those ancient days of the Colour Revolt were the glorious childhood of Art in Flatland a

childhood, alas, that never ripened into manhood, nor even reached the blossom of youth. To live was then in

itself a delight, because living implied seeing. Even at a small party, the company was a pleasure to behold;

the richly varied hues of the assembly in a church or theatre are said to have more than once proved too

distracting for our greatest teachers and actors; but most ravishing of all is said to have been the unspeakable

The sight of a line of battle of twenty thousand Isosceles suddenly facing about, and exchanging the sombre

black of their bases for the orange and purple of the two sides including their acute angle; the militia of the

Equilateral Triangles tricoloured in red, white, and blue; the mauve, ultramarine, gamboge, and burnt umber

of the Square artillerymen rapidly rotating near their vermilion guns; the dashing and flashing of the

fivecoloured and sixcoloured Pentagons and Hexagons careering across the field in their offices of

surgeons, geometricians and aidesdecamp all these may well have been sufficient to render credible the

famous story how an illustrious Circle, overcome by the artistic beauty of the forces under his command,

threw aside his marshal's baton and his royal crown, exclaiming that he henceforth exchanged them for the

artist's pencil. How great and glorious the sensuous development of these days must have been is in part

indicated by the very language and vocabulary of the period. The commonest utterances of the commonest

citizens in the time of the Colour Revolt seem to have been suffused with a richer tinge of word or thought;

and to that era we are even now indebted for our finest poetry and for whatever rhythm still remains in the

The Art of Sight Recognition, being no longer needed, was no longer practised; and the studies of Geometry,

Statics, Kinetics, and other kindred subjects, came soon to be considered superfluous, and fell into disrespect

and neglect even at our University. The inferior Art of Feeling speedily experienced the same fate at our

Elementary Schools. Then the Isosceles classes, asserting that the Specimens were no longer used nor

needed, and refusing to pay the customary tribute from the Criminal classes to the service of Education,

waxed daily more numerous and more insolent on the strength of their immunity from the old burden which

had formerly exercised the twofold wholesome effect of at once taming their brutal nature and thinning their

Year by year the Soldiers and Artisans began more vehemently to assert and with increasing truth that

there was no great difference between them and the very highest class of Polygons, now that they were raised

to an equality with the latter, and enabled to grapple with all the difficulties and solve all the problems of life,

whether Statical or Kinetical, by the simple process of Colour Recognition. Not content with the natural

neglect into which Sight Recognition was falling, they began boldly to demand the legal prohibition of all

"monopolizing and aristocratic Arts" and the consequent abolition of all endowments for the studies of Sight

Recognition, Mathematics, and Feeling. Soon, they began to insist that inasmuch as Colour, which was a

second Nature, had destroyed the need of aristocratic distinctions, the Law should follow in the same path,

and that henceforth all individuals and all classes should be recognized as absolutely equal and entitled to

Finding the higher Orders wavering and undecided, the leaders of the Revolution advanced still further in

their requirements, and at last demanded that all classes alike, the Priests and the Women not excepted,

should do homage to Colour by submitting to be painted. When it was objected that Priests and Women had

no sides, they retorted that Nature and Expediency concurred in dictating that the front half of every human

being (that is to say, the half containing his eye and mouth) should be distinguishable from his hinder half.

They therefore brought before a general and extraordinary Assembly of all the States of Flatland a Bill

proposing that in every Woman the half containing the eye and mouth should be coloured red, and the other

half green. The Priests were to be painted in the same way, red being applied to that semicircle in which the

eye and mouth formed the middle point; while the other or hinder semicircle was to be coloured green.

There was no little cunning in this proposal, which indeed emanated not from any Isosceles for no being

so degraded would have had angularity enough to appreciate, much less to devise, such a model of statecraft

but from an Irregular Circle who, instead of being destroyed in his childhood, was reserved by a foolish

indulgence to bring desolation on his country and destruction on myriads of his followers.

On the one hand the proposition was calculated to bring the Women in all classes over to the side of the

Chromatic Innovation. For by assigning to the Women the same two colours as were assigned to the Priests,

the Revolutionists thereby ensured that, in certain positions, every Woman would appear like a Priest, and be

treated with corresponding respect and deference a prospect that could not fail to attract the Female Sex in

But by some of my Readers the possibility of the identical appearance of Priests and Women, under the new

Imagine a woman duly decorated, according to the new Code; with the front half (i.e. the half containing eye

and mouth) red, and with the hinder half green. Look at her from one side. Obviously you will see a straight

Now imagine a Priest, whose mouth is at M, and whose front semicircle (AMB) is consequently coloured red,

while his hinder semicircle is green; so that the diameter AB divides the green from the red. If you

contemplate the Great Man so as to have your eye in the same straight line as his dividing diameter (AB),

what you will see will be a straight line (CBD), of which ONE HALF (CB) WILL BE RED, AND THE

OTHER (BD) GREEN. The whole line (CD) will be rather shorter perhaps than that of a fullsized Woman,

and will shade off more rapidly towards its extremities; but the identity of the colours would give you an

immediate impression of identity of Class, making you neglectful of other details. Bear in mind the decay of

Sight Recognition which threatened society at the time of the Colour Revolt; add too the certainty that

Women would speedily learn to shade off their extremities so as to imitate the Circles; it must then be surely

obvious to you, my dear Reader, that the Colour Bill placed us under a great danger of confounding a Priest

How attractive this prospect must have been to the Frail Sex may readily be imagined. They anticipated with

delight the confusion that would ensue. At home they might hear political and ecclesiastical secrets intended

not for them but for their husbands and brothers, and might even issue commands in the name of a priestly

Circle; out of doors the striking combination of red and green, without addition of any other colours, would

be sure to lead the common people into endless mistakes, and the Women would gain whatever the Circles

lost, in the deference of the passers by. As for the scandal that would befall the Circular Class if the frivolous

and unseemly conduct of the Women were imputed to them, and as to the consequent subversion of the

Constitution, the Female Sex could not be expected to give a thought to these considerations. Even in the

households of the Circles, the Women were all in favour of the Universal Colour Bill.

The second object aimed at by the Bill was the gradual demoralization of the Circles themselves. In the

general intellectual decay they still preserved their pristine clearness and strength of understanding. From

their earliest childhood, familiarized in their Circular households with the total absence of Colour, the Nobles

alone preserved the Sacred Art of Sight Recognition, with all the advantages that result from that admirable

training of the intellect. Hence, up to the date of the introduction of the Universal Colour Bill, the Circles had

not only held their own, but even increased their lead of the other classes by abstinence from the popular

Now therefore the artful Irregular whom I described above as the real author of this diabolical Bill,

determined at one blow to lower the status of the Hierarchy by forcing them to submit to the pollution of

Colour, and at the same time to destroy their domestic opportunities of training in the Art of Sight

Recognition, so as to enfeeble their intellects by depriving them of their pure and colourless homes. Once

subjected to the chromatic taint, every parental and every childish Circle would demoralize each other. Only

in discerning between the Father and the Mother would the Circular infant find problems for the exercise of

its understanding problems too often likely to be corrupted by maternal impostures with the result of

shaking the child's faith in all logical conclusions. Thus by degrees the intellectual lustre of the Priestly Order

would wane, and the road would then lie open for a total destruction of all Aristocratic Legislature and for the

The agitation for the Universal Colour Bill continued for three years; and up to the last moment of that period

A whole army of Polygons, who turned out to fight as private soldiers, was utterly annihilated by a superior

force of Isosceles Triangles the Squares and Pentagons meanwhile remaining neutral. Worse than all,

some of the ablest Circles fell a prey to conjugal fury. Infuriated by political animosity, the wives in many a

noble household wearied their lords with prayers to give up their opposition to the Colour Bill; and some,

finding their entreaties fruitless, fell on and slaughtered their innocent children and husband, perishing

themselves in the act of carnage. It is recorded that during that triennial agitation no less than twentythree

Great indeed was the peril. It seemed as though the Priests had no choice between submission and

extermination; when suddenly the course of events was completely changed by one of those picturesque

incidents which Statesmen ought never to neglect, often to anticipate, and sometimes perhaps to originate,

because of the absurdly disproportionate power with which they appeal to the sympathies of the populace.

It happened that an Isosceles of a low type, with a brain little if at all above four degrees accidentally

dabbling in the colours of some Tradesman whose shop he had plundered painted himself, or caused

himself to be painted (for the story varies) with the twelve colours of a Dodecagon. Going into the Market

Place he accosted in a feigned voice a maiden, the orphan daughter of a noble Polygon, whose affection in

former days he had sought in vain; and by a series of deceptions aided, on the one side, by a string of

lucky accidents too long to relate, and on the other, by an almost inconceivable fatuity and neglect of

ordinary precautions on the part of the relations of the bride he succeeded in consummating the marriage.

The unhappy girl committed suicide on discovering the fraud to which she had been subjected.

When the news of this catastrophe spread from State to State the minds of the Women were violently

agitated. Sympathy with the miserable victim and anticipations of similar deceptions for themselves, their

sisters, and their daughters, made them now regard the Colour Bill in an entirely new aspect. Not a few

openly avowed themselves converted to antagonism; the rest needed only a slight stimulus to make a similar

avowal. Seizing this favourable opportunity, the Circles hastily convened an extraordinary Assembly of the

States; and besides the usual guard of Convicts, they secured the attendance of a large number of reactionary

Amidst an unprecedented concourse, the Chief Circle of those days by name Pantocyclus arose to find

himself hissed and hooted by a hundred and twenty thousand Isosceles. But he secured silence by declaring

that henceforth the Circles would enter on a policy of Concession; yielding to the wishes of the majority, they

would accept the Colour Bill. The uproar being at once converted to applause, he invited Chromatistes, the

leader of the Sedition, into the centre of the hall, to receive in the name of his followers the submission of the

Hierarchy. Then followed a speech, a masterpiece of rhetoric, which occupied nearly a day in the delivery,

With a grave appearance of impartiality he declared that as they were now finally committing themselves to

Reform or Innovation, it was desirable that they should take one last view of the perimeter of the whole

subject, its defects as well as its advantages. Gradually introducing the mention of the dangers to the

Tradesmen, the Professional Classes and the Gentlemen, he silenced the rising murmurs of the Isosceles by

reminding them that, in spite of all these defects, he was willing to accept the Bill if it was approved by the

majority. But it was manifest that all, except the Isosceles, were moved by his words and were either neutral

Turning now to the Workmen he asserted that their interests must not be neglected, and that, if they intended

to accept the Colour Bill, they ought at least to do so with full view of the consequences. Many of them, he

said, were on the point of being admitted to the class of the Regular Triangles; others anticipated for their

children a distinction they could not hope for themselves. That honourable ambition would now have to be

sacrificed. With the universal adoption of Colour, all distinctions would cease; Regularity would be confused

with Irregularity; development would give place to retrogression; the Workman would in a few generations

be degraded to the level of the Military, or even the Convict Class; political power would be in the hands of

the greatest number, that is to say the Criminal Classes, who were already more numerous than the Workmen,

and would soon outnumber all the other Classes put together when the usual Compensative Laws of Nature

A subdued murmur of assent ran through the ranks of the Artisans, and Chromatistes, in alarm, attempted to

step forward and address them. But he found himself encompassed with guards and forced to remain silent

while the Chief Circle in a few impassioned words made a final appeal to the Women, exclaiming that, if the

Colour Bill passed, no marriage would henceforth be safe, no woman's honour secure; fraud, deception,

hypocrisy would pervade every household; domestic bliss would share the fate of the Constitution and pass to

At these words, which were the preconcerted signal for action, the Isosceles Convicts fell on and transfixed

the wretched Chromatistes; the Regular Classes, opening their ranks, made way for a band of Women who,

under direction of the Circles, moved, back foremost, invisibly and unerringly upon the unconscious soldiers;

the Artisans, imitating the example of their betters, also opened their ranks. Meantime bands of Convicts

The battle, or rather carnage, was of short duration. Under the skillful generalship of the Circles almost every

Woman's charge was fatal and very many extracted their sting uninjured, ready for a second slaughter. But no

second blow was needed; the rabble of the Isosceles did the rest of the business for themselves. Surprised,

leaderless, attacked in front by invisible foes, and finding egress cut off by the Convicts behind them, they

at once after their manner lost all presence of mind, and raised the cry of "treachery". This sealed their

fate. Every Isosceles now saw and felt a foe in every other. In half an hour not one of that vast multitude was

living; and the fragments of seven score thousand of the Criminal Class slain by one another's angles attested

The Circles delayed not to push their victory to the uttermost. The Working Men they spared but decimated.

The Militia of the Equilaterals was at once called out; and every Triangle suspected of Irregularity on

reasonable grounds, was destroyed by Court Martial, without the formality of exact measurement by the

Social Board. The homes of the Military and Artisan classes were inspected in a course of visitations

extending through upwards of a year; and during that period every town, village, and hamlet was

systematically purged of that excess of the lower orders which had been brought about by the neglect to pay

the tribute of Criminals to the Schools and University, and by the violation of the other natural Laws of the

Needless to say that henceforth the use of Colour was abolished, and its possession prohibited. Even the

utterance of any word denoting Colour, except by the Circles or by qualified scientific teachers, was punished

by a severe penalty. Only at our University in some of the very highest and most esoteric classes which I

myself have never been privileged to attend it is understood that the sparing use of Colour is still

sanctioned for the purpose of illustrating some of the deeper problems of mathematics. But of this I can only

Elsewhere in Flatland, Colour is now nonexistent. The art of making it is known to only one living person,

the Chief Circle for the time being; and by him it is handed down on his deathbed to none but his Successor.

One manufactory alone produces it; and, lest the secret should be betrayed, the Workmen are annually

consumed, and fresh ones introduced. So great is the terror with which even now our Aristocracy looks back

It is high time that I should pass from these brief and discursive notes about things in Flatland to the central

event of this book, my initiation into the mysteries of Space. THAT is my subject; all that has gone before is

For this reason I must omit many matters of which the explanation would not, I flatter myself, be without

interest for my Readers: as for example, our method of propelling and stopping ourselves, although destitute

of feet; the means by which we give fixity to structures of wood, stone, or brick, although of course we have

no hands, nor can we lay foundations as you can, nor avail ourselves of the lateral pressure of the earth; the

manner in which the rain originates in the intervals between our various zones, so that the northern regions do

not intercept the moisture from falling on the southern; the nature of our hills and mines, our trees and

vegetables, our seasons and harvests; our Alphabet and method of writing, adapted to our linear tablets; these

and a hundred other details of our physical existence I must pass over, nor do I mention them now except to

indicate to my readers that their omission proceeds not from forgetfulness on the part of the author, but from

Yet before I proceed to my legitimate subject some few final remarks will no doubt be expected by my

Readers upon those pillars and mainstays of the Constitution of Flatland, the controllers of our conduct and

shapers of our destiny, the objects of universal homage and almost of adoration: need I say that I mean our

When I call them Priests, let me not be understood as meaning no more than the term denotes with you. With

us, our Priests are Administrators of all Business, Art, and Science; Directors of Trade, Commerce,

Generalship, Architecture, Engineering, Education, Statesmanship, Legislature, Morality, Theology; doing

nothing themselves, they are the Causes of everything worth doing, that is done by others.

Although popularly everyone called a Circle is deemed a Circle, yet among the better educated Classes it is

known that no Circle is really a Circle, but only a Polygon with a very large number of very small sides. As

the number of the sides increases, a Polygon approximates to a Circle; and, when the number is very great

indeed, say for example three or four hundred, it is extremely difficult for the most delicate touch to feel any

polygonal angles. Let me say rather, it WOULD be difficult: for, as I have shown above, Recognition by

Feeling is unknown among the highest society, and to FEEL a Circle would be considered a most audacious

insult. This habit of abstention from Feeling in the best society enables a Circle the more easily to sustain the

veil of mystery in which, from his earliest years, he is wont to enwrap the exact nature of his Perimeter or

Circumference. Three feet being the average Perimeter it follows that, in a Polygon of three hundred sides

each side will be no more than the hundredth part of a foot in length, or little more than the tenth part of an

inch; and in a Polygon of six or seven hundred sides the sides are little larger than the diameter of a

Spaceland pinhead. It is always assumed, by courtesy, that the Chief Circle for the time being has ten

The ascent of the posterity of the Circles in the social scale is not restricted, as it is among the lower Regular

classes, by the Law of Nature which limits the increase of sides to one in each generation. If it were so, the

number of sides in a Circle would be a mere question of pedigree and arithmetic, and the four hundred and

ninetyseventh descendant of an Equilateral Triangle would necessarily be a Polygon with five hundred

sides. But this is not the case. Nature's Law prescribes two antagonistic decrees affecting Circular

propagation; first, that as the race climbs higher in the scale of development, so development shall proceed at

an accelerated pace; second, that in the same proportion, the race shall become less fertile. Consequently in

the home of a Polygon of four or five hundred sides it is rare to find a son; more than one is never seen. On

the other hand the son of a fivehundredsided Polygon has been known to possess five hundred and fifty, or

Art also steps in to help the process of the higher Evolution. Our physicians have discovered that the small

and tender sides of an infant Polygon of the higher class can be fractured, and his whole frame reset, with

such exactness that a Polygon of two or three hundred sides sometimes by no means always, for the

process is attended with serious risk but sometimes overleaps two or three hundred generations, and as it

were doubles at a stroke, the number of his progenitors and the nobility of his descent.

Many a promising child is sacrificed in this way. Scarcely one out of ten survives. Yet so strong is the

parental ambition among those Polygons who are, as it were, on the fringe of the Circular class, that it is very

rare to find a Nobleman of that position in society, who has neglected to place his firstborn in the Circular

One year determines success or failure. At the end of that time the child has, in all probability, added one

more to the tombstones that crowd the NeoTherapeutic Cemetery; but on rare occasions a glad procession

bears back the little one to his exultant parents, no longer a Polygon, but a Circle, at least by courtesy: and a

single instance of so blessed a result induces multitudes of Polygonal parents to submit to similar domestic

As to the doctrine of the Circles it may briefly be summed up in a single maxim, "Attend to your

Configuration." Whether political, ecclesiastical, or moral, all their teaching has for its object the

improvement of individual and collective Configuration with special reference of course to the

It is the merit of the Circles that they have effectually suppressed those ancient heresies which led men to

waste energy and sympathy in the vain belief that conduct depends upon will, effort, training, encouragement,

praise, or anything else but Configuration. It was Pantocyclus the illustrious Circle mentioned above, as

the queller of the Colour Revolt who first convinced mankind that Configuration makes the man; that if,

for example, you are born an Isosceles with two uneven sides, you will assuredly go wrong unless you have

them made even for which purpose you must go to the Isosceles Hospital; similarly, if you are a Triangle,

or Square, or even a Polygon, born with any Irregularity, you must be taken to one of the Regular Hospitals to

have your disease cured; otherwise you will end your days in the State Prison or by the angle of the State

All faults or defects, from the slightest misconduct to the most flagitious crime, Pantocyclus attributed to

some deviation from perfect Regularity in the bodily figure, caused perhaps (if not congenital) by some

collision in a crowd; by neglect to take exercise, or by taking too much of it; or even by a sudden change of

temperature, resulting in a shrinkage or expansion in some too susceptible part of the frame. Therefore,

concluded that illustrious Philosopher, neither good conduct nor bad conduct is a fit subject, in any sober

estimation, for either praise or blame. For why should you praise, for example, the integrity of a Square who

faithfully defends the interests of his client, when you ought in reality rather to admire the exact precision of

his right angles? Or again, why blame a lying, thievish Isosceles when you ought rather to deplore the

Theoretically, this doctrine is unquestionable; but it has practical drawbacks. In dealing with an Isosceles, if a

rascal pleads that he cannot help stealing because of his unevenness, you reply that for that very reason,

because he cannot help being a nuisance to his neighbours, you, the Magistrate, cannot help sentencing him

to be consumed and there's an end of the matter. But in little domestic difficulties, where the penalty of

consumption, or death, is out of the question, this theory of Configuration sometimes comes in awkwardly;

and I must confess that occasionally when one of my own Hexagonal Grandsons pleads as an excuse for his

disobedience that a sudden change of the temperature has been too much for his Perimeter, and that I ought to

lay the blame not on him but on his Configuration, which can only be strengthened by abundance of the

choicest sweetmeats, I neither see my way logically to reject, nor practically to accept, his conclusions.

For my own part, I find it best to assume that a good sound scolding or castigation has some latent and

strengthening influence on my Grandson's Configuration; though I own that I have no grounds for thinking

so. At all events I am not alone in my way of extricating myself from this dilemma; for I find that many of

the highest Circles, sitting as Judges in law courts, use praise and blame towards Regular and Irregular

Figures; and in their homes I know by experience that, when scolding their children, they speak about "right"

or "wrong" as vehemently and passionately as if they believed that these names represented real existences,

Constantly carrying out their policy of making Configuration the leading idea in every mind, the Circles

reverse the nature of that Commandment which in Spaceland regulates the relations between parents and

children. With you, children are taught to honour their parents; with us next to the Circles, who are the

chief object of universal homage a man is taught to honour his Grandson, if he has one; or, if not, his Son.

By "honour", however, is by no means meant "indulgence", but a reverent regard for their highest interests:

and the Circles teach that the duty of fathers is to subordinate their own interests to those of posterity, thereby

advancing the welfare of the whole State as well as that of their own immediate descendants.

The weak point in the system of the Circles if a humble Square may venture to speak of anything Circular

as containing any element of weakness appears to me to be found in their relations with Women.

As it is of the utmost importance for Society that Irregular births should be discouraged, it follows that no

Woman who has any Irregularities in her ancestry is a fit partner for one who desires that his posterity should

Now the Irregularity of a Male is a matter of measurement; but as all Women are straight, and therefore

visibly Regular so to speak, one has to devise some other means of ascertaining what I may call their

invisible Irregularity, that is to say their potential Irregularities as regards possible offspring. This is effected

by carefullykept pedigrees, which are preserved and supervised by the State; and without a certified

Now it might have been supposed that a Circle proud of his ancestry and regardful for a posterity which

might possibly issue hereafter in a Chief Circle would be more careful than any other to choose a wife

who had no blot on her escutcheon. But it is not so. The care in choosing a Regular wife appears to diminish

as one rises in the social scale. Nothing would induce an aspiring Isosceles, who had hopes of generating an

Equilateral Son, to take a wife who reckoned a single Irregularity among her Ancestors; a Square or

Pentagon, who is confident that his family is steadily on the rise, does not inquire above the fivehundredth

generation; a Hexagon or Dodecagon is even more careless of the wife's pedigree; but a Circle has been

known deliberately to take a wife who has had an Irregular GreatGrandfather, and all because of some slight

superiority of lustre, or because of the charms of a low voice which, with us, even more than you, is

Such illjudged marriages are, as might be expected, barren, if they do not result in positive Irregularity or in

diminution of sides; but none of these evils have hitherto proved sufficiently deterrent. The loss of a few sides

in a highlydeveloped Polygon is not easily noticed, and is sometimes compensated by a successful operation

in the NeoTherapeutic Gymnasium, as I have described above; and the Circles are too much disposed to

acquiesce in infecundity as a Law of the superior development. Yet, if this evil be not arrested, the gradual

diminution of the Circular class may soon become more rapid, and the time may be not far distant when, the

race being no longer able to produce a Chief Circle, the Constitution of Flatland must fall.

One other word of warning suggests itself to me, though I cannot so easily mention a remedy; and this also

refers to our relations with Women. About three hundred years ago, it was decreed by the Chief Circle that,

since women are deficient in Reason but abundant in Emotion, they ought no longer to be treated as rational,

nor receive any mental education. The consequence was that they were no longer taught to read, nor even to

master Arithmetic enough to enable them to count the angles of their husband or children; and hence they

sensibly declined during each generation in intellectual power. And this system of female noneducation or

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

For the consequence is that, as things now are, we Males have to lead a kind of bilingual, and I may almost

say bimental, existence. With Women, we speak of "love", "duty", "right", "wrong", "pity", "hope", and

other irrational and emotional conceptions, which have no existence, and the fiction of which has no object

except to control feminine exuberances; but among ourselves, and in our books, we have an entirely different

vocabulary and I may almost say, idiom. "Love" then becomes "the anticipation of benefits"; "duty" becomes

"necessity" or "fitness"; and other words are correspondingly transmuted. Moreover, among Women, we use

language implying the utmost deference for their Sex; and they fully believe that the Chief Circle Himself is

not more devoutly adored by us than they are: but behind their backs they are both regarded and spoken of

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

Now my humble fear is that this double training, in language as well as in thought, imposes somewhat too

heavy a burden upon the young, especially when, at the age of three years old, they are taken from the

maternal care and taught to unlearn the old language except for the purpose of repeating it in the presence

of their Mothers and Nurses and to learn the vocabulary and idiom of science. Already methinks I discern

a weakness in the grasp of mathematical truth at the present time as compared with the more robust intellect

of our ancestors three hundred years ago. I say nothing of the possible danger if a Woman should ever

surreptitiously learn to read and convey to her Sex the result of her perusal of a single popular volume; nor of

the possibility that the indiscretion or disobedience of some infant Male might reveal to a Mother the secrets

of the logical dialect. On the simple ground of the enfeebling of the Male intellect, I rest this humble appeal

It was the last day but one of the 1999th year of our era, and the first day of the Long Vacation. Having

amused myself till a late hour with my favourite recreation of Geometry, I had retired to rest with an

I saw before me a vast multitude of small Straight Lines (which I naturally assumed to be Women)

interspersed with other Beings still smaller and of the nature of lustrous points all moving to and fro in

one and the same Straight Line, and, as nearly as I could judge, with the same velocity.

A noise of confused, multitudinous chirping or twittering issued from them at intervals as long as they were

Approaching one of the largest of what I thought to be Women, I accosted her, but received no answer. A

second and a third appeal on my part were equally ineffectual. Losing patience at what appeared to me

intolerable rudeness, I brought my mouth into a position full in front of her mouth so as to intercept her

motion, and loudly repeated my question, "Woman, what signifies this concourse, and this strange and

confused chirping, and this monotonous motion to and fro in one and the same Straight Line?"

"I am no Woman," replied the small Line. "I am the Monarch of the world. But thou, whence intrudest thou

into my realm of Lineland?" Receiving this abrupt reply, I begged pardon if I had in any way startled or

molested his Royal Highness; and describing myself as a stranger I besought the King to give me some

account of his dominions. But I had the greatest possible difficulty in obtaining any information on points

that really interested me; for the Monarch could not refrain from constantly assuming that whatever was

familiar to him must also be known to me and that I was simulating ignorance in jest. However, by

It seemed that this poor ignorant Monarch as he called himself was persuaded that the Straight Line

which he called his Kingdom, and in which he passed his existence, constituted the whole of the world, and

indeed the whole of Space. Not being able either to move or to see, save in his Straight Line, he had no

conception of anything out of it. Though he had heard my voice when I first addressed him, the sounds had

come to him in a manner so contrary to his experience that he had made no answer, "seeing no man", as he

expressed it, "and hearing a voice as it were from my own intestines." Until the moment when I placed my

mouth in his World, he had neither seen me, nor heard anything except confused sounds beating against

what I called his side, but what he called his INSIDE or STOMACH; nor had he even now the least

conception of the region from which I had come. Outside his World, or Line, all was a blank to him; nay, not

His subjects of whom the small Lines were men and the Points Women were all alike confined in

motion and eyesight to that single Straight Line, which was their World. It need scarcely be added that the

whole of their horizon was limited to a Point; nor could any one ever see anything but a Point. Man, woman,

child, thing each was a Point to the eye of a Linelander. Only by the sound of the voice could sex or age

be distinguished. Moreover, as each individual occupied the whole of the narrow path, so to speak, which

constituted his Universe, and no one could move to the right or left to make way for passers by, it followed

that no Linelander could ever pass another. Once neighbours, always neighbours. Neighbourhood with them

was like marriage with us. Neighbours remained neighbours till death did them part.

Such a life, with all vision limited to a Point, and all motion to a Straight Line, seemed to me inexpressibly

dreary; and I was surprised to note the vivacity and cheerfulness of the King. Wondering whether it was

possible, amid circumstances so unfavourable to domestic relations, to enjoy the pleasures of conjugal union,

I hesitated for some time to question his Royal Highness on so delicate a subject; but at last I plunged into it

by abruptly inquiring as to the health of his family. "My wives and children," he replied, "are well and

Staggered at this answer for in the immediate proximity of the Monarch (as I had noted in my dream

before I entered Lineland) there were none but Men I ventured to reply, "Pardon me, but I cannot imagine

how your Royal Highness can at any time either see or approach their Majesties, when there are at least half a

dozen intervening individuals, whom you can neither see through, nor pass by? Is it possible that in Lineland

"How can you ask so absurd a question?" replied the Monarch. "If it were indeed as you suggest, the

Universe would soon be depopulated. No, no; neighbourhood is needless for the union of hearts; and the birth

of children is too important a matter to have been allowed to depend upon such an accident as proximity. You

cannot be ignorant of this. Yet since you are pleased to affect ignorance, I will instruct you as if you were the

veriest baby in Lineland. Know, then, that marriages are consummated by means of the faculty of sound and

"You are of course aware that every Man has two mouths or voices as well as two eyes a bass at one

and a tenor at the other of his extremities. I should not mention this, but that I have been unable to distinguish

your tenor in the course of our conversation." I replied that I had but one voice, and that I had not been aware

that his Royal Highness had two. "That confirms my impression," said the King, "that you are not a Man, but

a feminine Monstrosity with a bass voice, and an utterly uneducated ear. But to continue.

"Nature having herself ordained that every Man should wed two wives " "Why two?" asked I. "You carry

your affected simplicity too far", he cried. "How can there be a completely harmonious union without the

combination of the Four in One, viz. the Bass and Tenor of the Man and the Soprano and Contralto of the two

Women?" "But supposing," said I, "that a man should prefer one wife or three?" "It is impossible," he said;

"it is as inconceivable as that two and one should make five, or that the human eye should see a Straight

"Once in the middle of each week a Law of Nature compels us to move to and fro with a rhythmic motion of

more than usual violence, which continues for the time you would take to count a hundred and one. In the

midst of this choral dance, at the fiftyfirst pulsation, the inhabitants of the Universe pause in full career, and

each individual sends forth his richest, fullest, sweetest strain. It is in this decisive moment that all our

marriages are made. So exquisite is the adaptation of Bass to Treble, of Tenor to Contralto, that oftentimes

the Loved Ones, though twenty thousand leagues away, recognize at once the responsive note of their

destined Lover; and, penetrating the paltry obstacles of distance, Love unites the three. The marriage in that

instant consummated results in a threefold Male and Female offspring which takes its place in Lineland."

"Bassvoiced Monstrosity! yes," replied the King. "How else could the balance of the Sexes be maintained, if

two girls were not born for every boy? Would you ignore the very Alphabet of Nature?" He ceased,

speechless for fury; and some time elapsed before I could induce him to resume his narrative.

"You will not, of course, suppose that every bachelor among us finds his mates at the first wooing in this

universal Marriage Chorus. On the contrary, the process is by most of us many times repeated. Few are the

hearts whose happy lot it is at once to recognize in each other's voices the partner intended for them by

Providence, and to fly into a reciprocal and perfectly harmonious embrace. With most of us the courtship is

of long duration. The Wooer's voices may perhaps accord with one of the future wives, but not with both; or

not, at first, with either; or the Soprano and Contralto may not quite harmonize. In such cases Nature has

provided that every weekly Chorus shall bring the three Lovers into closer harmony. Each trial of voice, each

fresh discovery of discord, almost imperceptibly induces the less perfect to modify his or her vocal utterance

so as to approximate to the more perfect. And after many trials and many approximations, the result is at last

achieved. There comes a day at last, when, while the wonted Marriage Chorus goes forth from universal

Lineland, the three faroff Lovers suddenly find themselves in exact harmony, and, before they are awake,

the wedded Triplet is rapt vocally into a duplicate embrace; and Nature rejoices over one more marriage and

Thinking that it was time to bring down the Monarch from his raptures to the level of common sense, I

determined to endeavour to open up to him some glimpses of the truth, that is to say of the nature of things in

Flatland. So I began thus: "How does your Royal Highness distinguish the shapes and positions of his

subjects? I for my part noticed by the sense of sight, before I entered your Kingdom, that some of your people

are Lines and others Points, and that some of the Lines are larger " "You speak of an impossibility,"

interrupted the King; "you must have seen a vision; for to detect the difference between a Line and a Point by

the sense of sight is, as every one knows, in the nature of things, impossible; but it can be detected by the

sense of hearing, and by the same means my shape can be exactly ascertained. Behold me I am a Line, the

longest in Lineland, over six inches of Space " "Of Length", I ventured to suggest. "Fool," said he, "Space

I apologized; but he continued scornfully, "Since you are impervious to argument, you shall hear with your

ears how by means of my two voices I reveal my shape to my Wives, who are at this moment six thousand

miles seventy yards two feet eight inches away, the one to the North, the other to the South. Listen, I call to

He chirruped, and then complacently continued: "My wives at this moment receiving the sound of one of my

voices, closely followed by the other, and perceiving that the latter reaches them after an interval in which

sound can traverse 6.457 inches, infer that one of my mouths is 6.457 inches further from them than the other,

and accordingly know my shape to be 6.457 inches. But you will of course understand that my wives do not

make this calculation every time they hear my two voices. They made it, once for all, before we were

married. But they COULD make it at any time. And in the same way I can estimate the shape of any of my

"But how," said I, "if a Man feigns a Woman's voice with one of his two voices, or so disguises his Southern

voice that it cannot be recognized as the echo of the Northern? May not such deceptions cause great

inconvenience? And have you no means of checking frauds of this kind by commanding your neighbouring

subjects to feel one another?" This of course was a very stupid question, for feeling could not have answered

the purpose; but I asked with the view of irritating the Monarch, and I succeeded perfectly.

"What!" cried he in horror, "explain your meaning." "Feel, touch, come into contact," I replied. "If you mean

by FEELING," said the King, "approaching so close as to leave no space between two individuals, know,

Stranger, that this offence is punishable in my dominions by death. And the reason is obvious. The frail form

of a Woman, being liable to be shattered by such an approximation, must be preserved by the State; but since

Women cannot be distinguished by the sense of sight from Men, the Law ordains universally that neither

Man nor Woman shall be approached so closely as to destroy the interval between the approximator and the

"And indeed what possible purpose would be served by this illegal and unnatural excess of approximation

which you call TOUCHING, when all the ends of so brutal and coarse a process are attained at once more

easily and more exactly by the sense of hearing? As to your suggested danger of deception, it is nonexistent:

for the Voice, being the essence of one's Being, cannot be thus changed at will. But come, suppose that I had

the power of passing through solid things, so that I could penetrate my subjects, one after another, even to the

number of a billion, verifying the size and distance of each by the sense of FEELING: how much time and

energy would be wasted in this clumsy and inaccurate method! Whereas now, in one moment of audition, I

take as it were the census and statistics, local, corporeal, mental and spiritual, of every living being in

So saying he paused and listened, as if in an ecstasy, to a sound which seemed to me no better than a tiny

"Truly," replied I, "your sense of hearing serves you in good stead, and fills up many of your deficiencies.

But permit me to point out that your life in Lineland must be deplorably dull. To see nothing but a Point! Not

even to be able to contemplate a Straight Line! Nay, not even to know what a Straight Line is! To see, yet be

cut off from those Linear prospects which are vouchsafed to us in Flatland! Better surely to have no sense of

sight at all than to see so little! I grant you I have not your discriminative faculty of hearing; for the concert of

all Lineland which gives you such intense pleasure, is to me no better than a multitudinous twittering or

chirping. But at least I can discern, by sight, a Line from a Point. And let me prove it. Just before I came into

your kingdom, I saw you dancing from left to right, and then from right to left, with Seven Men and a

Woman in your immediate proximity on the left, and eight Men and two Women on your right. Is not this

"It is correct," said the King, "so far as the numbers and sexes are concerned, though I know not what you

mean by 'right' and 'left'. But I deny that you saw these things. For how could you see the Line, that is to say

the inside, of any Man? But you must have heard these things, and then dreamed that you saw them. And let

me ask what you mean by those words 'left' and 'right'. I suppose it is your way of saying Northward and

"Not so," replied I; "besides your motion of Northward and Southward, there is another motion which I call

I. Well, yes. Out of YOUR World. Out of YOUR Space. For your Space is not the true Space. True Space is a

KING. If you cannot indicate this motion from left to right by yourself moving in it, then I beg you to

I. If you cannot tell your right side from your left, I fear that no words of mine can make my meaning clear to

I. Alas! How shall I make it clear? When you move straight on, does it not sometimes occur to you that you

COULD move in some other way, turning your eye round so as to look in the direction towards which your

side is now fronting? In other words, instead of always moving in the direction of one of your extremities, do

KING. Never. And what do you mean? How can a man's inside "front" in any direction? Or how can a man

I. Well then, since words cannot explain the matter, I will try deeds, and will move gradually out of Lineland

At the word I began to move my body out of Lineland. As long as any part of me remained in his dominion

and in his view, the King kept exclaiming, "I see you, I see you still; you are not moving." But when I had at

last moved myself out of his Line, he cried in his shrillest voice, "She is vanished; she is dead." "I am not

dead," replied I; "I am simply out of Lineland, that is to say, out of the Straight Line which you call Space,

and in the true Space, where I can see things as they are. And at this moment I can see your Line, or side

or inside as you are pleased to call it; and I can see also the Men and Women on the North and South of you,

whom I will now enumerate, describing their order, their size, and the interval between each."

When I had done this at great length, I cried triumphantly, "Does that at last convince you?" And, with that, I

But the Monarch replied, "If you were a Man of sense though, as you appear to have only one voice I

have little doubt you are not a Man but a Woman but, if you had a particle of sense, you would listen to

reason. You ask me to believe that there is another Line besides that which my senses indicate, and another

motion besides that of which I am daily conscious. I, in return, ask you to describe in words or indicate by

motion that other Line of which you speak. Instead of moving, you merely exercise some magic art of

vanishing and returning to sight; and instead of any lucid description of your new World, you simply tell me

the numbers and sizes of some forty of my retinue, facts known to any child in my capital. Can anything be

more irrational or audacious? Acknowledge your folly or depart from my dominions."

Furious at his perversity, and especially indignant that he professed to be ignorant of my sex, I retorted in no

measured terms, "Besotted Being! You think yourself the perfection of existence, while you are in reality the

most imperfect and imbecile. You profess to see, whereas you can see nothing but a Point! You plume

yourself on inferring the existence of a Straight Line; but I CAN SEE Straight Lines, and infer the existence

of Angles, Triangles, Squares, Pentagons, Hexagons, and even Circles. Why waste more words? Suffice it

that I am the completion of your incomplete self. You are a Line, but I am a Line of Lines, called in my

country a Square: and even I, infinitely superior though I am to you, am of little account among the great

nobles of Flatland, whence I have come to visit you, in the hope of enlightening your ignorance."

Hearing these words the King advanced towards me with a menacing cry as if to pierce me through the

diagonal; and in that same moment there arose from myriads of his subjects a multitudinous warcry,

increasing in vehemence till at last methought it rivalled the roar of an army of a hundred thousand Isosceles,

and the artillery of a thousand Pentagons. Spellbound and motionless, I could neither speak nor move to

avert the impending destruction; and still the noise grew louder, and the King came closer, when I awoke to

It was the last day of the 1999th year of our era. The pattering of the rain had long ago announced nightfall;

and I was sitting in the company of my wife, musing on the events of the past and the prospects of the

any change of attitude such as you in Spaceland signify by that word; for as we have no feet, we can no more

"sit" nor "stand" (in your sense of the word) than one of your soles or flounders.

Nevertheless, we perfectly well recognize the different mental states of volition implied in "lying", "sitting",

and "standing", which are to some extent indicated to a beholder by a slight increase of lustre corresponding

My four Sons and two orphan Grandchildren had retired to their several apartments; and my wife alone

I was rapt in thought, pondering in my mind some words that had casually issued from the mouth of my

youngest Grandson, a most promising young Hexagon of unusual brilliancy and perfect angularity. His

uncles and I had been giving him his usual practical lesson in Sight Recognition, turning ourselves upon our

centres, now rapidly, now more slowly, and questioning him as to our positions; and his answers had been so

satisfactory that I had been induced to reward him by giving him a few hints on Arithmetic, as applied to

Taking nine Squares, each an inch every way, I had put them together so as to make one large Square, with a

side of three inches, and I had hence proved to my little Grandson that though it was impossible for us to

SEE the inside of the Square yet we might ascertain the number of square inches in a Square by simply

squaring the number of inches in the side: "and thus," said I, "we know that 3^2, or 9, represents the number

The little Hexagon meditated on this a while and then said to me; "But you have been teaching me to raise

numbers to the third power: I suppose 3^3 must mean something in Geometry; what does it mean?" "Nothing

at all," replied I, "not at least in Geometry; for Geometry has only Two Dimensions." And then I began to

shew the boy how a Point by moving through a length of three inches makes a Line of three inches, which

may be represented by 3; and how a Line of three inches, moving parallel to itself through a length of three

inches, makes a Square of three inches every way, which may be represented by 3^2.

Upon this, my Grandson, again returning to his former suggestion, took me up rather suddenly and

exclaimed, "Well, then, if a Point by moving three inches, makes a Line of three inches represented by 3; and

if a straight Line of three inches, moving parallel to itself, makes a Square of three inches every way,

represented by 3^2; it must be that a Square of three inches every way, moving somehow parallel to itself

(but I don't see how) must make Something else (but I don't see what) of three inches every way and this

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

So my Grandson had disappeared in disgrace; and there I sat by my Wife's side, endeavouring to form a

retrospect of the year 1999 and of the possibilities of the year 2000, but not quite able to shake off the

thoughts suggested by the prattle of my bright little Hexagon. Only a few sands now remained in the

halfhour glass. Rousing myself from my reverie I turned the glass Northward for the last time in the old

Straightway I became conscious of a Presence in the room, and a chilling breath thrilled through my very

being. "He is no such thing," cried my Wife, "and you are breaking the Commandments in thus dishonouring

your own Grandson." But I took no notice of her. Looking round in every direction I could see nothing; yet

still I FELT a Presence, and shivered as the cold whisper came again. I started up. "What is the matter?" said

my Wife, "there is no draught; what are you looking for? There is nothing." There was nothing; and I

resumed my seat, again exclaiming, "The boy is a fool, I say; 3^3 can have no meaning in Geometry." At

once there came a distinctly audible reply, "The boy is not a fool; and 3^3 has an obvious Geometrical

My Wife as well as myself heard the words, although she did not understand their meaning, and both of us

sprang forward in the direction of the sound. What was our horror when we saw before us a Figure! At the

first glance it appeared to be a Woman, seen sideways; but a moment's observation shewed me that the

extremities passed into dimness too rapidly to represent one of the Female Sex; and I should have thought it a

Circle, only that it seemed to change its size in a manner impossible for a Circle or for any regular Figure of

But my Wife had not my experience, nor the coolness necessary to note these characteristics. With the usual

hastiness and unreasoning jealousy of her Sex, she flew at once to the conclusion that a Woman had entered

the house through some small aperture. "How comes this person here?" she exclaimed, "you promised me,

my dear, that there should be no ventilators in our new house." "Nor are there any," said I; "but what makes

you think that the stranger is a Woman? I see by my power of Sight Recognition " "Oh, I have no

patience with your Sight Recognition," replied she, "'Feeling is believing' and 'A Straight Line to the touch is

worth a Circle to the sight'" two Proverbs, very common with the Frailer Sex in Flatland.

"Well," said I, for I was afraid of irritating her, "if it must be so, demand an introduction." Assuming her most

gracious manner, my Wife advanced towards the Stranger, "Permit me, Madam, to feel and be felt by "

then, suddenly recoiling, "Oh! it is not a Woman, and there are no angles either, not a trace of one. Can it be

"I am indeed, in a certain sense a Circle," replied the Voice, "and a more perfect Circle than any in Flatland;

but to speak more accurately, I am many Circles in one." Then he added more mildly, "I have a message, dear

Madam, to your husband, which I must not deliver in your presence; and, if you would suffer us to retire for a

few minutes " But my Wife would not listen to the proposal that our august Visitor should so

incommode himself, and assuring the Circle that the hour of her own retirement had long passed, with many

reiterated apologies for her recent indiscretion, she at last retreated to her apartment.

I glanced at the halfhour glass. The last sands had fallen. The third Millennium had begun.

As soon as the sound of the Peacecry of my departing Wife had died away, I began to approach the Stranger

with the intention of taking a nearer view and of bidding him be seated: but his appearance struck me dumb

and motionless with astonishment. Without the slightest symptoms of angularity he nevertheless varied every

instant with gradations of size and brightness scarcely possible for any Figure within the scope of my

experience. The thought flashed across me that I might have before me a burglar or cutthroat, some

monstrous Irregular Isosceles, who, by feigning the voice of a Circle, had obtained admission somehow into

In a sittingroom, the absence of Fog (and the season happened to be remarkably dry), made it difficult for

me to trust to Sight Recognition, especially at the short distance at which I was standing. Desperate with fear,

I rushed forward with an unceremonious, "You must permit me, Sir " and felt him. My Wife was right.

There was not the trace of an angle, not the slightest roughness or inequality: never in my life had I met with

a more perfect Circle. He remained motionless while I walked round him, beginning from his eye and

returning to it again. Circular he was throughout, a perfectly satisfactory Circle; there could not be a doubt of

it. Then followed a dialogue, which I will endeavour to set down as near as I can recollect it, omitting only

some of my profuse apologies for I was covered with shame and humiliation that I, a Square, should have

been guilty of the impertinence of feeling a Circle. It was commenced by the Stranger with some impatience

STRANGER. Have you felt me enough by this time? Are you not introduced to me yet?

I. Most illustrious Sir, excuse my awkwardness, which arises not from ignorance of the usages of polite

society, but from a little surprise and nervousness, consequent on this somewhat unexpected visit. And I

beseech you to reveal my indiscretion to no one, and especially not to my Wife. But before your Lordship

enters into further communications, would he deign to satisfy the curiosity of one who would gladly know

I. Pardon me, my Lord, but is not your Lordship already in Space, your Lordship and his humble servant,

STRANGER. Exactly: you see you do not even know what Space is. You think it is of Two Dimensions

I. Your Lordship is pleased to be merry. We also speak of length and height, or breadth and thickness, thus

I. Would your Lordship indicate or explain to me in what direction is the Third Dimension, unknown to me?

STRANGER. I mean nothing of the kind. I mean a direction in which you cannot look, because you have no

I. Pardon me, my Lord, a moment's inspection will convince your Lordship that I have a perfect luminary at

STRANGER. Yes: but in order to see into Space you ought to have an eye, not on your Perimeter, but on

your side, that is, on what you would probably call your inside; but we in Spaceland should call it your side.

STRANGER. I am in no jesting humour. I tell you that I come from Space, or, since you will not understand

what Space means, from the Land of Three Dimensions whence I but lately looked down upon your Plane

which you call Space forsooth. From that position of advantage I discerned all that you speak of as SOLID

(by which you mean "enclosed on four sides"), your houses, your churches, your very chests and safes, yes

When I descended here, I saw your four Sons, the Pentagons, each in his apartment, and your two Grandsons

the Hexagons; I saw your youngest Hexagon remain a while with you and then retire to his room, leaving you

and your Wife alone. I saw your Isosceles servants, three in number, in the kitchen at supper, and the little

STRANGER. Not so. Your roof, as you know very well, has been recently repaired, and has no aperture by

which even a Woman could penetrate. I tell you I come from Space. Are you not convinced by what I have

I. Your Lordship must be aware that such facts touching the belongings of his humble servant might be easily

ascertained by any one in the neighbourhood possessing your Lordship's ample means of obtaining

STRANGER. (TO HIMSELF.) What must I do? Stay; one more argument suggests itself to me. When you

see a Straight Line your wife, for example how many Dimensions do you attribute to her?

I. Your Lordship would treat me as if I were one of the vulgar who, being ignorant of Mathematics, suppose

that a Woman is really a Straight Line, and only of One Dimension. No, no, my Lord; we Squares are better

advised, and are as well aware as your Lordship that a Woman, though popularly called a Straight Line, is,

really and scientifically, a very thin Parallelogram, possessing Two Dimensions, like the rest of us, viz.,

STRANGER. But the very fact that a Line is visible implies that it possesses yet another Dimension.

I. My Lord, I have just acknowledged that a Woman is broad as well as long. We see her length, we infer her

STRANGER. You do not understand me. I mean that when you see a Woman, you ought besides

inferring her breadth to see her length, and to SEE what we call her HEIGHT; although that last

Dimension is infinitesimal in your country. If a Line were mere length without "height", it would cease to

I. I must indeed confess that I do not in the least understand your Lordship. When we in Flatland see a Line,

we see length and BRIGHTNESS. If the brightness disappears, the Line is extinguished, and, as you say,

ceases to occupy Space. But am I to suppose that your Lordship gives to brightness the title of a Dimension,

STRANGER. No, indeed. By "height" I mean a Dimension like your length: only, with you, "height" is not

I. My Lord, your assertion is easily put to the test. You say I have a Third Dimension, which you call

"height". Now, Dimension implies direction and measurement. Do but measure my "height", or merely

indicate to me the direction in which my "height" extends, and I will become your convert. Otherwise, your

STRANGER. (TO HIMSELF.) I can do neither. How shall I convince him? Surely a plain statement of facts

You are living on a Plane. What you style Flatland is the vast level surface of what I may call a fluid, on, or

in, the top of which you and your countrymen move about, without rising above it or falling below it.

I am not a plane Figure, but a Solid. You call me a Circle; but in reality I am not a Circle, but an infinite

number of Circles, of size varying from a Point to a Circle of thirteen inches in diameter, one placed on the

top of the other. When I cut through your plane as I am now doing, I make in your plane a section which you,

very rightly, call a Circle. For even a Sphere which is my proper name in my own country if he

manifest himself at all to an inhabitant of Flatland must needs manifest himself as a Circle.

Do you not remember for I, who see all things, discerned last night the phantasmal vision of Lineland

written upon your brain do you not remember, I say, how, when you entered the realm of Lineland, you

were compelled to manifest yourself to the King, not as a Square, but as a Line, because that Linear Realm

had not Dimensions enough to represent the whole of you, but only a slice or section of you? In precisely the

same way, your country of Two Dimensions is not spacious enough to represent me, a being of Three, but

The diminished brightness of your eye indicates incredulity. But now prepare to receive proof positive of the

truth of my assertions. You cannot indeed see more than one of my sections, or Circles, at a time; for you

have no power to raise your eye out of the plane of Flatland; but you can at least see that, as I rise in Space,

so my sections become smaller. See now, I will rise; and the effect upon your eye will be that my Circle will

There was no "rising" that I could see; but he diminished and finally vanished. I winked once or twice to

make sure that I was not dreaming. But it was no dream. For from the depths of nowhere came forth a hollow

voice close to my heart it seemed "Am I quite gone? Are you convinced now? Well, now I will

gradually return to Flatland and you shall see my section become larger and larger."

Every reader in Spaceland will easily understand that my mysterious Guest was speaking the language of

truth and even of simplicity. But to me, proficient though I was in Flatland Mathematics, it was by no means

a simple matter. The rough diagram given above will make it clear to any Spaceland child that the Sphere,

ascending in the three positions indicated there, must needs have manifested himself to me, or to any

Flatlander, as a Circle, at first of full size, then small, and at last very small indeed, approaching to a Point.

But to me, although I saw the facts before me, the causes were as dark as ever. All that I could comprehend

was, that the Circle had made himself smaller and vanished, and that he had now reappeared and was rapidly

When he regained his original size, he heaved a deep sigh; for he perceived by my silence that I had

altogether failed to comprehend him. And indeed I was now inclining to the belief that he must be no Circle

at all, but some extremely clever juggler; or else that the old wives' tales were true, and that after all there

After a long pause he muttered to himself, "One resource alone remains, if I am not to resort to action. I must

try the method of Analogy." Then followed a still longer silence, after which he continued our dialogue.

SPHERE. Tell me, Mr. Mathematician; if a Point moves Northward, and leaves a luminous wake, what name

SPHERE. Now conceive the Northward straight Line moving parallel to itself, East and West, so that every

point in it leaves behind it the wake of a straight Line. What name will you give to the Figure thereby

formed? We will suppose that it moves through a distance equal to the original straight Line. What name,

SPHERE. Now stretch your imagination a little, and conceive a Square in Flatland, moving parallel to itself

If it moved Northward, the Southern points in the Square would have to move through the positions

I mean that every Point in you for you are a Square and will serve the purpose of my illustration every

Point in you, that is to say in what you call your inside, is to pass upwards through Space in such a way that

no Point shall pass through the position previously occupied by any other Point; but each Point shall describe

a straight Line of its own. This is all in accordance with Analogy; surely it must be clear to you.

Restraining my impatience for I was now under a strong temptation to rush blindly at my Visitor and to

precipitate him into Space, or out of Flatland, anywhere, so that I could get rid of him I replied:

"And what may be the nature of the Figure which I am to shape out by this motion which you are pleased to

denote by the word 'upward'? I presume it is describable in the language of Flatland."

SPHERE. Oh, certainly. It is all plain and simple, and in strict accordance with Analogy only, by the way,

you must not speak of the result as being a Figure, but as a Solid. But I will describe it to you. Or rather not I,

We began with a single Point, which of course being itself a Point has only ONE terminal Point.

Now you can give yourself the answer to your own question: 1, 2, 4, are evidently in Geometrical

I. And has this Creature sides, as well as angles or what you call "terminal Points"?

SPHERE. Of course; and all according to Analogy. But, by the way, not what YOU call sides, but what WE

I. And how many solids or sides will appertain to this Being whom I am to generate by the motion of my

SPHERE. How can you ask? And you a mathematician! The side of anything is always, if I may so say, one

Dimension behind the thing. Consequently, as there is no Dimension behind a Point, a Point has 0 sides; a

Line, if I may say, has 2 sides (for the Points of a Line may be called by courtesy, its sides); a Square has 4

SPHERE. Exactly. Then you see you have answered your own question. The Cube which you will generate

will be bounded by six sides, that is to say, six of your insides. You see it all now, eh?

"Monster," I shrieked, "be thou juggler, enchanter, dream, or devil, no more will I endure thy mockeries.

Either thou or I must perish." And saying these words I precipitated myself upon him.

It was in vain. I brought my hardest right angle into violent collision with the Stranger, pressing on him with

a force sufficient to have destroyed any ordinary Circle: but I could feel him slowly and unarrestably slipping

from my contact; no edging to the right nor to the left, but moving somehow out of the world, and vanishing

SPHERE. Why will you refuse to listen to reason? I had hoped to find in you as being a man of sense and

an accomplished mathematician a fit apostle for the Gospel of the Three Dimensions, which I am allowed

to preach once only in a thousand years: but now I know not how to convince you. Stay, I have it. Deeds, and

I have told you I can see from my position in Space the inside of all things that you consider closed. For

example, I see in yonder cupboard near which you are standing, several of what you call boxes (but like

everything else in Flatland, they have no tops nor bottoms) full of money; I see also two tablets of accounts. I

am about to descend into that cupboard and to bring you one of those tablets. I saw you lock the cupboard

half an hour ago, and I know you have the key in your possession. But I descend from Space; the doors, you

see, remain unmoved. Now I am in the cupboard and am taking the tablet. Now I have it. Now I ascend with

I rushed to the closet and dashed the door open. One of the tablets was gone. With a mocking laugh, the

Stranger appeared in the other corner of the room, and at the same time the tablet appeared upon the floor. I

I groaned with horror, doubting whether I was not out of my senses; but the Stranger continued: "Surely you

must now see that my explanation, and no other, suits the phenomena. What you call Solid things are really

superficial; what you call Space is really nothing but a great Plane. I am in Space, and look down upon the

insides of the things of which you only see the outsides. You could leave this Plane yourself, if you could but

summon up the necessary volition. A slight upward or downward motion would enable you to see all that I

"The higher I mount, and the further I go from your Plane, the more I can see, though of course I see it on a

smaller scale. For example, I am ascending; now I can see your neighbour the Hexagon and his family in

their several apartments; now I see the inside of the Theatre, ten doors off, from which the audience is only

just departing; and on the other side a Circle in his study, sitting at his books. Now I shall come back to you.

And, as a crowning proof, what do you say to my giving you a touch, just the least touch, in your stomach? It

will not seriously injure you, and the slight pain you may suffer cannot be compared with the mental benefit

Before I could utter a word of remonstrance, I felt a shooting pain in my inside, and a demoniacal laugh

seemed to issue from within me. A moment afterwards the sharp agony had ceased, leaving nothing but a dull

ache behind, and the Stranger began to reappear, saying, as he gradually increased in size, "There, I have not

hurt you much, have I? If you are not convinced now, I don't know what will convince you. What say you?"

My resolution was taken. It seemed intolerable that I should endure existence subject to the arbitrary

visitations of a Magician who could thus play tricks with one's very stomach. If only I could in any way

Once more I dashed my hardest angle against him, at the same time alarming the whole household by my

cries for aid. I believe, at the moment of my onset, the Stranger had sunk below our Plane, and really found

difficulty in rising. In any case he remained motionless, while I, hearing, as I thought, the sound of some help

approaching, pressed against him with redoubled vigour, and continued to shout for assistance.

A convulsive shudder ran through the Sphere. "This must not be," I thought I heard him say: "either he must

listen to reason, or I must have recourse to the last resource of civilization." Then, addressing me in a louder

tone, he hurriedly exclaimed, "Listen: no stranger must witness what you have witnessed. Send your Wife

back at once, before she enters the apartment. The Gospel of Three Dimensions must not be thus frustrated.

Not thus must the fruits of one thousand years of waiting be thrown away. I hear her coming. Back! back!

Away from me, or you must go with me whither you know not into the Land of Three Dimensions!"

"Fool! Madman! Irregular!" I exclaimed; "never will I release thee; thou shalt pay the penalty of thine

"Ha! Is it come to this?" thundered the Stranger: "then meet your fate: out of your Plane you go. Once, twice,

An unspeakable horror seized me. There was a darkness; then a dizzy, sickening sensation of sight that was

not like seeing; I saw a Line that was no Line; Space that was not Space: I was myself, and not myself. When

I could find voice, I shrieked aloud in agony, "Either this is madness or it is Hell." "It is neither," calmly

replied the voice of the Sphere, "it is Knowledge; it is Three Dimensions: open your eye once again and try to

I looked, and, behold, a new world! There stood before me, visibly incorporate, all that I had before inferred,

conjectured, dreamed, of perfect Circular beauty. What seemed the centre of the Stranger's form lay open to

my view: yet I could see no heart, nor lungs, nor arteries, only a beautiful harmonious Something for

which I had no words; but you, my Readers in Spaceland, would call it the surface of the Sphere.

Prostrating myself mentally before my Guide, I cried, "How is it, O divine ideal of consummate loveliness

and wisdom that I see thy inside, and yet cannot discern thy heart, thy lungs, thy arteries, thy liver?" "What

you think you see, you see not," he replied; "it is not given to you, nor to any other Being to behold my

internal parts. I am of a different order of Beings from those in Flatland. Were I a Circle, you could discern

my intestines, but I am a Being, composed as I told you before, of many Circles, the Many in the One, called

in this country a Sphere. And, just as the outside of a Cube is a Square, so the outside of a Sphere presents the

Bewildered though I was by my Teacher's enigmatic utterance, I no longer chafed against it, but worshipped

him in silent adoration. He continued, with more mildness in his voice. "Distress not yourself if you cannot at

first understand the deeper mysteries of Spaceland. By degrees they will dawn upon you. Let us begin by

casting back a glance at the region whence you came. Return with me a while to the plains of Flatland, and I

will shew you that which you have often reasoned and thought about, but never seen with the sense of sight

a visible angle." "Impossible!" I cried; but, the Sphere leading the way, I followed as if in a dream, till

once more his voice arrested me: "Look yonder, and behold your own Pentagonal house, and all its inmates."

I looked below, and saw with my physical eye all that domestic individuality which I had hitherto merely

inferred with the understanding. And how poor and shadowy was the inferred conjecture in comparison with

the reality which I now beheld! My four Sons calmly asleep in the NorthWestern rooms, my two orphan

Grandsons to the South; the Servants, the Butler, my Daughter, all in their several apartments. Only my

affectionate Wife, alarmed by my continued absence, had quitted her room and was roving up and down in

the Hall, anxiously awaiting my return. Also the Page, aroused by my cries, had left his room, somewhere in

a faint, was prying into the cabinet in my study. All this I could now SEE, not merely infer; and as we came

nearer and nearer, I could discern even the contents of my cabinet, and the two chests of gold, and the tablets

Touched by my Wife's distress, I would have sprung downward to reassure her, but I found myself incapable

of motion. "Trouble not yourself about your Wife," said my Guide: "she will not be long left in anxiety;

Once more I felt myself rising through space. It was even as the Sphere had said. The further we receded

from the object we beheld, the larger became the field of vision. My native city, with the interior of every

house and every creature therein, lay open to my view in miniature. We mounted higher, and lo, the secrets of

the earth, the depths of mines and inmost caverns of the hills, were bared before me.

Awestruck at the sight of the mysteries of the earth, thus unveiled before my unworthy eye, I said to my

Companion, "Behold, I am become as a God. For the wise men in our country say that to see all things, or as

they express it, OMNIVIDENCE, is the attribute of God alone." There was something of scorn in the voice of

my Teacher as he made answer: "Is it so indeed? Then the very pickpockets and cutthroats of my country

are to be worshipped by your wise men as being Gods: for there is not one of them that does not see as much

SPHERE. I do not know. But, if a pickpocket or a cutthroat of our country can see everything that is in

your country, surely that is no reason why the pickpocket or cutthroat should be accepted by you as a God.

This omnividence, as you call it it is not a common word in Spaceland does it make you more just,

more merciful, less selfish, more loving? Not in the least. Then how does it make you more divine?

I. "More merciful, more loving!" But these are the qualities of women! And we know that a Circle is a higher

Being than a Straight Line, in so far as knowledge and wisdom are more to be esteemed than mere affection.

SPHERE. It is not for me to classify human faculties according to merit. Yet many of the best and wisest in

Spaceland think more of the affections than of the understanding, more of your despised Straight Lines than

of your belauded Circles. But enough of this. Look yonder. Do you know that building?

I looked, and afar off I saw an immense Polygonal structure, in which I recognized the General Assembly

Hall of the States of Flatland, surrounded by dense lines of Pentagonal buildings at right angles to each other,

which I knew to be streets; and I perceived that I was approaching the great Metropolis.

"Here we descend," said my Guide. It was now morning, the first hour of the first day of the two thousandth

year of our era. Acting, as was their wont, in strict accordance with precedent, the highest Circles of the realm

were meeting in solemn conclave, as they had met on the first hour of the first day of the year 1000, and also

The minutes of the previous meetings were now read by one whom I at once recognized as my brother, a

perfectly Symmetrical Square, and the Chief Clerk of the High Council. It was found recorded on each

occasion that: "Whereas the States had been troubled by divers illintentioned persons pretending to have

received revelations from another World, and professing to produce demonstrations whereby they had

instigated to frenzy both themselves and others, it had been for this cause unanimously resolved by the Grand

Council that on the first day of each millenary, special injunctions be sent to the Prefects in the several

districts of Flatland, to make strict search for such misguided persons, and without formality of mathematical

examination, to destroy all such as were Isosceles of any degree, to scourge and imprison any regular

Triangle, to cause any Square or Pentagon to be sent to the district Asylum, and to arrest any one of higher

rank, sending him straightway to the Capital to be examined and judged by the Council."

"You hear your fate," said the Sphere to me, while the Council was passing for the third time the formal

resolution. "Death or imprisonment awaits the Apostle of the Gospel of Three Dimensions." "Not so," replied

I, "the matter is now so clear to me, the nature of real space so palpable, that methinks I could make a child

understand it. Permit me but to descend at this moment and enlighten them." "Not yet," said my Guide, "the

time will come for that. Meantime I must perform my mission. Stay thou there in thy place." Saying these

words, he leaped with great dexterity into the sea (if I may so call it) of Flatland, right in the midst of the ring

of Counsellors. "I come," cried he, "to proclaim that there is a land of Three Dimensions."

I could see many of the younger Counsellors start back in manifest horror, as the Sphere's circular section

widened before them. But on a sign from the presiding Circle who shewed not the slightest alarm or

surprise six Isosceles of a low type from six different quarters rushed upon the Sphere. "We have him,"

"My Lords," said the President to the Junior Circles of the Council, "there is not the slightest need for

surprise; the secret archives, to which I alone have access, tell me that a similar occurrence happened on the

last two millennial commencements. You will, of course, say nothing of these trifles outside the Cabinet."

Raising his voice, he now summoned the guards. "Arrest the policemen; gag them. You know your duty."

After he had consigned to their fate the wretched policemen illfated and unwilling witnesses of a

Statesecret which they were not to be permitted to reveal he again addressed the Counsellors. "My

Lords, the business of the Council being concluded, I have only to wish you a happy New Year." Before

departing, he expressed, at some length, to the Clerk, my excellent but most unfortunate brother, his sincere

regret that, in accordance with precedent and for the sake of secrecy, he must condemn him to perpetual

imprisonment, but added his satisfaction that, unless some mention were made by him of that day's incident,

When I saw my poor brother led away to imprisonment, I attempted to leap down into the Council Chamber,

desiring to intercede on his behalf, or at least bid him farewell. But I found that I had no motion of my own. I

absolutely depended on the volition of my Guide, who said in gloomy tones, "Heed not thy brother; haply

Once more we ascended into space. "Hitherto," said the Sphere, "I have shewn you naught save Plane Figures

and their interiors. Now I must introduce you to Solids, and reveal to you the plan upon which they are

constructed. Behold this multitude of moveable square cards. See, I put one on another, not, as you supposed,

Northward of the other, but ON the other. Now a second, now a third. See, I am building up a Solid by a

multitude of Squares parallel to one another. Now the Solid is complete, being as high as it is long and broad,

"Pardon me, my Lord," replied I; "but to my eye the appearance is as of an Irregular Figure whose inside is

laid open to the view; in other words, methinks I see no Solid, but a Plane such as we infer in Flatland; only

of an Irregularity which betokens some monstrous criminal, so that the very sight of it is painful to my eyes."

"True," said the Sphere, "it appears to you a Plane, because you are not accustomed to light and shade and

perspective; just as in Flatland a Hexagon would appear a Straight Line to one who has not the Art of Sight

Recognition. But in reality it is a Solid, as you shall learn by the sense of Feeling."

He then introduced me to the Cube, and I found that this marvellous Being was indeed no Plane, but a Solid;

and that he was endowed with six plane sides and eight terminal points called solid angles; and I remembered

the saying of the Sphere that just such a Creature as this would be formed by a Square moving, in Space,

parallel to himself: and I rejoiced to think that so insignificant a Creature as I could in some sense be called

But still I could not fully understand the meaning of what my Teacher had told me concerning "light" and

"shade" and "perspective"; and I did not hesitate to put my difficulties before him.

Were I to give the Sphere's explanation of these matters, succinct and clear though it was, it would be tedious

to an inhabitant of Space, who knows these things already. Suffice it, that by his lucid statements, and by

changing the position of objects and lights, and by allowing me to feel the several objects and even his own

sacred Person, he at last made all things clear to me, so that I could now readily distinguish between a Circle

This was the Climax, the Paradise, of my strange eventful History. Henceforth I have to relate the story of my

miserable Fall: most miserable, yet surely most undeserved! For why should the thirst for knowledge be

aroused, only to be disappointed and punished? My volition shrinks from the painful task of recalling my

humiliation; yet, like a second Prometheus, I will endure this and worse, if by any means I may arouse in the

interiors of Plane and Solid Humanity a spirit of rebellion against the Conceit which would limit our

Dimensions to Two or Three or any number short of Infinity. Away then with all personal considerations! Let

me continue to the end, as I began, without further digressions or anticipations, pursuing the plain path of

dispassionate History. The exact facts, the exact words, and they are burnt in upon my brain, shall be

set down without alteration of an iota; and let my Readers judge between me and Destiny.

The Sphere would willingly have continued his lessons by indoctrinating me in the conformation of all

regular Solids, Cylinders, Cones, Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons, and Spheres: but I

ventured to interrupt him. Not that I was wearied of knowledge. On the contrary, I thirsted for yet deeper and

"Pardon me," said I, "O Thou Whom I must no longer address as the Perfection of all Beauty; but let me beg

SPHERE. Whence this illtimed impertinent request? And what mean you by saying that I am no longer the

I. My Lord, your own wisdom has taught me to aspire to One even more great, more beautiful, and more

closely approximate to Perfection than yourself. As you yourself, superior to all Flatland forms, combine

many Circles in One, so doubtless there is One above you who combines many Spheres in One Supreme

Existence, surpassing even the Solids of Spaceland. And even as we, who are now in Space, look down on

Flatland and see the insides of all things, so of a certainty there is yet above us some higher, purer region,

whither thou dost surely purpose to lead me O Thou Whom I shall always call, everywhere and in all

Dimensions, my Priest, Philosopher, and Friend some yet more spacious Space, some more dimensionable

Dimensionality, from the vantageground of which we shall look down together upon the revealed insides of

Solid things, and where thine own intestines, and those of thy kindred Spheres, will lie exposed to the view of

the poor wandering exile from Flatland, to whom so much has already been vouchsafed.

SPHERE. Pooh! Stuff! Enough of this trifling! The time is short, and much remains to be done before you are

fit to proclaim the Gospel of Three Dimensions to your blind benighted countrymen in Flatland.

I. Nay, gracious Teacher, deny me not what I know it is in thy power to perform. Grant me but one glimpse

of thine interior, and I am satisfied for ever, remaining henceforth thy docile pupil, thy unemancipable slave,

ready to receive all thy teachings and to feed upon the words that fall from thy lips.

SPHERE. Well, then, to content and silence you, let me say at once, I would shew you what you wish if I

could; but I cannot. Would you have me turn my stomach inside out to oblige you?

I. But my Lord has shewn me the intestines of all my countrymen in the Land of Two Dimensions by taking

me with him into the Land of Three. What therefore more easy than now to take his servant on a second

journey into the blessed region of the Fourth Dimension, where I shall look down with him once more upon

this land of Three Dimensions, and see the inside of every threedimensioned house, the secrets of the solid

earth, the treasures of the mines in Spaceland, and the intestines of every solid living creature, even of the

SPHERE. Not I. There is no such land. The very idea of it is utterly inconceivable.

I. Not inconceivable, my Lord, to me, and therefore still less inconceivable to my Master. Nay, I despair not

that, even here, in this region of Three Dimensions, your Lordship's art may make the Fourth Dimension

visible to me; just as in the Land of Two Dimensions my Teacher's skill would fain have opened the eyes of

his blind servant to the invisible presence of a Third Dimension, though I saw it not.

Let me recall the past. Was I not taught below that when I saw a Line and inferred a Plane, I in reality saw a

Third unrecognized Dimension, not the same as brightness, called "height"? And does it not now follow that,

in this region, when I see a Plane and infer a Solid, I really see a Fourth unrecognized Dimension, not the

same as colour, but existent, though infinitesimal and incapable of measurement?

I. Your Lordship tempts his servant to see whether he remembers the revelations imparted to him. Trifle not

with me, my Lord; I crave, I thirst, for more knowledge. Doubtless we cannot SEE that other higher

Spaceland now, because we we have no eye in our stomachs. But, just as there WAS the realm of Flatland,

though that poor puny Lineland Monarch could neither turn to left nor right to discern it, and just as there

WAS close at hand, and touching my frame, the land of Three Dimensions, though I, blind senseless wretch,

had no power to touch it, no eye in my interior to discern it, so of a surety there is a Fourth Dimension, which

my Lord perceives with the inner eye of thought. And that it must exist my Lord himself has taught me. Or

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

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

In Three Dimensions, did not a moving Square produce did not this eye of mine behold it that blessed

And in Four Dimensions shall not a moving Cube alas, for Analogy, and alas for the Progress of Truth, if

it be not so shall not, I say, the motion of a divine Cube result in a still more divine Organization with

Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not this a Geometrical Progression? Is not this

Again, was I not taught by my Lord that as in a Line there are TWO bounding Points, and in a Square there

are FOUR bounding Lines, so in a Cube there must be SIX bounding Squares? Behold once more the

confirming Series, 2, 4, 6: is not this an Arithmetical Progression? And consequently does it not of necessity

follow that the more divine offspring of the divine Cube in the Land of Four Dimensions, must have 8

bounding Cubes: and is not this also, as my Lord has taught me to believe, "strictly according to Analogy"?

O, my Lord, my Lord, behold, I cast myself in faith upon conjecture, not knowing the facts; and I appeal to

your Lordship to confirm or deny my logical anticipations. If I am wrong, I yield, and will no longer demand

I ask therefore, is it, or is it not, the fact, that ere now your countrymen also have witnessed the descent of

Beings of a higher order than their own, entering closed rooms, even as your Lordship entered mine, without

the opening of doors or windows, and appearing and vanishing at will? On the reply to this question I am

ready to stake everything. Deny it, and I am henceforth silent. Only vouchsafe an answer.

SPHERE. (AFTER A PAUSE). It is reported so. But men are divided in opinion as to the facts. And even

granting the facts, they explain them in different ways. And in any case, however great may be the number of

different explanations, no one has adopted or suggested the theory of a Fourth Dimension. Therefore, pray

I. I was certain of it. I was certain that my anticipations would be fulfilled. And now have patience with me

and answer me yet one more question, best of Teachers! Those who have thus appeared no one knows

whence and have returned no one knows whither have they also contracted their sections and

vanished somehow into that more Spacious Space, whither I now entreat you to conduct me?

SPHERE (MOODILY). They have vanished, certainly if they ever appeared. But most people say that

these visions arose from the thought you will not understand me from the brain; from the perturbed

I. Say they so? Oh, believe them not. Or if it indeed be so, that this other Space is really Thoughtland, then

take me to that blessed Region where I in Thought shall see the insides of all solid things. There, before my

ravished eye, a Cube, moving in some altogether new direction, but strictly according to Analogy, so as to

make every particle of his interior pass through a new kind of Space, with a wake of its own shall create a

still more perfect perfection than himself, with sixteen terminal Extrasolid angles, and Eight solid Cubes for

his Perimeter. And once there, shall we stay our upward course? In that blessed region of Four Dimensions,

shall we linger on the threshold of the Fifth, and not enter therein? Ah, no! Let us rather resolve that our

ambition shall soar with our corporal ascent. Then, yielding to our intellectual onset, the gates of the Sixth

How long I should have continued I know not. In vain did the Sphere, in his voice of thunder, reiterate his

command of silence, and threaten me with the direst penalties if I persisted. Nothing could stem the flood of

my ecstatic aspirations. Perhaps I was to blame; but indeed I was intoxicated with the recent draughts of

Truth to which he himself had introduced me. However, the end was not long in coming. My words were cut

short by a crash outside, and a simultaneous crash inside me, which impelled me through space with a

velocity that precluded speech. Down! down! down! I was rapidly descending; and I knew that return to

Flatland was my doom. One glimpse, one last and nevertobeforgotten glimpse I had of that dull level

wilderness which was now to become my Universe again spread out before my eye. Then a darkness.

Then a final, allconsummating thunderpeal; and, when I came to myself, I was once more a common

creeping Square, in my Study at home, listening to the PeaceCry of my approaching Wife.

Although I had less than a minute for reflection, I felt, by a kind of instinct, that I must conceal my

experiences from my Wife. Not that I apprehended, at the moment, any danger from her divulging my secret,

but I knew that to any Woman in Flatland the narrative of my adventures must needs be unintelligible. So I

endeavoured to reassure her by some story, invented for the occasion, that I had accidentally fallen through

The Southward attraction in our country is so slight that even to a Woman my tale necessarily appeared

extraordinary and wellnigh incredible; but my Wife, whose good sense far exceeds that of the average of her

Sex, and who perceived that I was unusually excited, did not argue with me on the subject, but insisted that I

was ill and required repose. I was glad of an excuse for retiring to my chamber to think quietly over what had

happened. When I was at last by myself, a drowsy sensation fell on me; but before my eyes closed I

endeavoured to reproduce the Third Dimension, and especially the process by which a Cube is constructed

through the motion of a Square. It was not so clear as I could have wished; but I remembered that it must be

"Upward, and yet not Northward", and I determined steadfastly to retain these words as the clue which, if

firmly grasped, could not fail to guide me to the solution. So mechanically repeating, like a charm, the words,

During my slumber I had a dream. I thought I was once more by the side of the Sphere, whose lustrous hue

betokened that he had exchanged his wrath against me for perfect placability. We were moving together

towards a bright but infinitesimally small Point, to which my Master directed my attention. As we

approached, methought there issued from it a slight humming noise as from one of your Spaceland

bluebottles, only less resonant by far, so slight indeed that even in the perfect stillness of the Vacuum through

which we soared, the sound reached not our ears till we checked our flight at a distance from it of something

"Look yonder," said my Guide, "in Flatland thou hast lived; of Lineland thou hast received a vision; thou hast

soared with me to the heights of Spaceland; now, in order to complete the range of thy experience, I conduct

thee downward to the lowest depth of existence, even to the realm of Pointland, the Abyss of No dimensions.

"Behold yon miserable creature. That Point is a Being like ourselves, but confined to the nondimensional

Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception;

he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance

even of the number Two; nor has he a thought of Plurality; for he is himself his One and All, being really

Nothing. Yet mark his perfect selfcontentment, and hence learn this lesson, that to be selfcontented is to be

vile and ignorant, and that to aspire is better than to be blindly and impotently happy. Now listen."

He ceased; and there arose from the little buzzing creature a tiny, low, monotonous, but distinct tinkling, as

from one of your Spaceland phonographs, from which I caught these words, "Infinite beatitude of existence!

"What," said I, "does the puny creature mean by 'it'?" "He means himself," said the Sphere: "have you not

noticed before now, that babies and babyish people who cannot distinguish themselves from the world, speak

"It fills all Space," continued the little soliloquizing Creature, "and what It fills, It is. What It thinks, that It

utters; and what It utters, that It hears; and It itself is Thinker, Utterer, Hearer, Thought, Word, Audition; it is

"Can you not startle the little thing out of its complacency?" said I. "Tell it what it really is, as you told me;

reveal to it the narrow limitations of Pointland, and lead it up to something higher." "That is no easy task,"

"Silence, silence, contemptible Creature. You call yourself the All in All, but you are the Nothing: your

socalled Universe is a mere speck in a Line, and a Line is a mere shadow as compared with " "Hush,

hush, you have said enough," interrupted the Sphere, "now listen, and mark the effect of your harangue on the

The lustre of the Monarch, who beamed more brightly than ever upon hearing my words, shewed clearly that

he retained his complacency; and I had hardly ceased when he took up his strain again. "Ah, the joy, ah, the

joy of Thought! What can It not achieve by thinking! Its own Thought coming to Itself, suggestive of Its

disparagement, thereby to enhance Its happiness! Sweet rebellion stirred up to result in triumph! Ah, the

"You see," said my Teacher, "how little your words have done. So far as the Monarch understands them at

all, he accepts them as his own for he cannot conceive of any other except himself and plumes himself

upon the variety of 'Its Thought' as an instance of creative Power. Let us leave this God of Pointland to the

ignorant fruition of his omnipresence and omniscience: nothing that you or I can do can rescue him from his

After this, as we floated gently back to Flatland, I could hear the mild voice of my Companion pointing the

moral of my vision, and stimulating me to aspire, and to teach others to aspire. He had been angered at first

he confessed by my ambition to soar to Dimensions above the Third; but, since then, he had received

fresh insight, and he was not too proud to acknowledge his error to a Pupil. Then he proceeded to initiate me

into mysteries yet higher than those I had witnessed, shewing me how to construct ExtraSolids by the

motion of Solids, and Double ExtraSolids by the motion of ExtraSolids, and all "strictly according to

Analogy", all by methods so simple, so easy, as to be patent even to the Female Sex.

I awoke rejoicing, and began to reflect on the glorious career before me. I would go forth, methought, at

once, and evangelize the whole of Flatland. Even to Women and Soldiers should the Gospel of Three

Just as I had decided on the plan of my operations, I heard the sound of many voices in the street

commanding silence. Then followed a louder voice. It was a herald's proclamation. Listening attentively, I

recognized the words of the Resolution of the Council, enjoining the arrest, imprisonment, or execution of

any one who should pervert the minds of the people by delusions, and by professing to have received

I reflected. This danger was not to be trifled with. It would be better to avoid it by omitting all mention of my

Revelation, and by proceeding on the path of Demonstration which after all, seemed so simple and so

conclusive that nothing would be lost by discarding the former means. "Upward, not Northward" was the

clue to the whole proof. It had seemed to me fairly clear before I fell asleep; and when I first awoke, fresh

from my dream, it had appeared as patent as Arithmetic; but somehow it did not seem to me quite so obvious

now. Though my Wife entered the room opportunely just at that moment, I decided, after we had exchanged a

My Pentagonal Sons were men of character and standing, and physicians of no mean reputation, but not great

in mathematics, and, in that respect, unfit for my purpose. But it occurred to me that a young and docile

Hexagon, with a mathematical turn, would be a most suitable pupil. Why therefore not make my first

experiment with my little precocious Grandson, whose casual remarks on the meaning of 3^3 had met with

the approval of the Sphere? Discussing the matter with him, a mere boy, I should be in perfect safety; for he

would know nothing of the Proclamation of the Council; whereas I could not feel sure that my Sons so

greatly did their patriotism and reverence for the Circles predominate over mere blind affection might not

feel compelled to hand me over to the Prefect, if they found me seriously maintaining the seditious heresy of

But the first thing to be done was to satisfy in some way the curiosity of my Wife, who naturally wished to

know something of the reasons for which the Circle had desired that mysterious interview, and of the means

by which he had entered the house. Without entering into the details of the elaborate account I gave her,

an account, I fear, not quite so consistent with truth as my Readers in Spaceland might desire, I must be

content with saying that I succeeded at last in persuading her to return quietly to her household duties without

eliciting from me any reference to the World of Three Dimensions. This done, I immediately sent for my

Grandson; for, to confess the truth, I felt that all that I had seen and heard was in some strange way slipping

away from me, like the image of a halfgrasped, tantalizing dream, and I longed to essay my skill in making

When my Grandson entered the room I carefully secured the door. Then, sitting down by his side and taking

our mathematical tablets, or, as you would call them, Lines I told him we would resume the lesson of

yesterday. I taught him once more how a Point by motion in One Dimension produces a Line, and how a

straight Line in Two Dimensions produces a Square. After this, forcing a laugh, I said, "And now, you scamp,

you wanted to make me believe that a Square may in the same way by motion 'Upward, not Northward'

produce another figure, a sort of extra Square in Three Dimensions. Say that again, you young rascal."

At this moment we heard once more the herald's "O yes! O yes!" outside in the street proclaiming the

Resolution of the Council. Young though he was, my Grandson who was unusually intelligent for his age,

and bred up in perfect reverence for the authority of the Circles took in the situation with an acuteness for

which I was quite unprepared. He remained silent till the last words of the Proclamation had died away, and

then, bursting into tears, "Dear Grandpapa," he said, "that was only my fun, and of course I meant nothing at

all by it; and we did not know anything then about the new Law; and I don't think I said anything about the

Third Dimension; and I am sure I did not say one word about 'Upward, not Northward', for that would be

such nonsense, you know. How could a thing move Upward, and not Northward? Upward and not

Northward! Even if I were a baby, I could not be so absurd as that. How silly it is! Ha! ha! ha!"

"Not at all silly," said I, losing my temper; "here for example, I take this Square," and, at the word, I grasped

a moveable Square, which was lying at hand "and I move it, you see, not Northward but yes, I move it

Upward that is to say, not Northward, but I move it somewhere not exactly like this, but somehow "

Here I brought my sentence to an inane conclusion, shaking the Square about in a purposeless manner, much

to the amusement of my Grandson, who burst out laughing louder than ever, and declared that I was not

teaching him, but joking with him; and so saying he unlocked the door and ran out of the room. Thus ended

My failure with my Grandson did not encourage me to communicate my secret to others of my household;

yet neither was I led by it to despair of success. Only I saw that I must not wholly rely on the catchphrase,

"Upward, not Northward", but must rather endeavour to seek a demonstration by setting before the public a

clear view of the whole subject; and for this purpose it seemed necessary to resort to writing.

So I devoted several months in privacy to the composition of a treatise on the mysteries of Three Dimensions.

Only, with the view of evading the Law, if possible, I spoke not of a physical Dimension, but of a

Thoughtland whence, in theory, a Figure could look down upon Flatland and see simultaneously the insides

of all things, and where it was possible that there might be supposed to exist a Figure environed, as it were,

with six Squares, and containing eight terminal Points. But in writing this book I found myself sadly

hampered by the impossibility of drawing such diagrams as were necessary for my purpose; for of course, in

our country of Flatland, there are no tablets but Lines, and no diagrams but Lines, all in one straight Line and

only distinguishable by difference of size and brightness; so that, when I had finished my treatise (which I

entitled, "Through Flatland to Thoughtland") I could not feel certain that many would understand my

Meanwhile my life was under a cloud. All pleasures palled upon me; all sights tantalized and tempted me to

outspoken treason, because I could not but compare what I saw in Two Dimensions with what it really was if

seen in Three, and could hardly refrain from making my comparisons aloud. I neglected my clients and my

own business to give myself to the contemplation of the mysteries which I had once beheld, yet which I could

impart to no one, and found daily more difficult to reproduce even before my own mental vision.

One day, about eleven months after my return from Spaceland, I tried to see a Cube with my eye closed, but

failed; and though I succeeded afterwards, I was not then quite certain (nor have I been ever afterwards) that I

had exactly realized the original. This made me more melancholy than before, and determined me to take

some step; yet what, I knew not. I felt that I would have been willing to sacrifice my life for the Cause, if

thereby I could have produced conviction. But if I could not convince my Grandson, how could I convince

And yet at times my spirit was too strong for me, and I gave vent to dangerous utterances. Already I was

considered heterodox if not treasonable, and I was keenly alive to the danger of my position; nevertheless I

could not at times refrain from bursting out into suspicious or halfseditious utterances, even among the

highest Polygonal and Circular society. When, for example, the question arose about the treatment of those

lunatics who said that they had received the power of seeing the insides of things, I would quote the saying of

an ancient Circle, who declared that prophets and inspired people are always considered by the majority to be

mad; and I could not help occasionally dropping such expressions as "the eye that discerns the interiors of

things", and "the allseeing land"; once or twice I even let fall the forbidden terms "the Third and Fourth

Dimensions". At last, to complete a series of minor indiscretions, at a meeting of our Local Speculative

Society held at the palace of the Prefect himself, some extremely silly person having read an elaborate

paper exhibiting the precise reasons why Providence has limited the number of Dimensions to Two, and why

the attribute of omnividence is assigned to the Supreme alone I so far forgot myself as to give an exact

account of the whole of my voyage with the Sphere into Space, and to the Assembly Hall in our Metropolis,

and then to Space again, and of my return home, and of everything that I had seen and heard in fact or vision.

At first, indeed, I pretended that I was describing the imaginary experiences of a fictitious person; but my

enthusiasm soon forced me to throw off all disguise, and finally, in a fervent peroration, I exhorted all my

hearers to divest themselves of prejudice and to become believers in the Third Dimension.

Next morning, standing in the very place where but a very few months ago the Sphere had stood in my

company, I was allowed to begin and to continue my narration unquestioned and uninterrupted. But from the

first I foresaw my fate; for the President, noting that a guard of the better sort of Policemen was in

attendance, of angularity little, if at all, under 55 degrees, ordered them to be relieved before I began my

defence, by an inferior class of 2 or 3 degrees. I knew only too well what that meant. I was to be executed or

imprisoned, and my story was to be kept secret from the world by the simultaneous destruction of the

officials who had heard it; and, this being the case, the President desired to substitute the cheaper for the more

After I had concluded my defence, the President, perhaps perceiving that some of the junior Circles had been

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

2. Whether I could by any diagrams or descriptions (other than the enumeration of imaginary sides and

I declared that I could say nothing more, and that I must commit myself to the Truth, whose cause would

The President replied that he quite concurred in my sentiment, and that I could not do better. I must be

sentenced to perpetual imprisonment; but if the Truth intended that I should emerge from prison and

evangelize the world, the Truth might be trusted to bring that result to pass. Meanwhile I should be subjected

to no discomfort that was not necessary to preclude escape, and, unless I forfeited the privilege by

misconduct, I should be occasionally permitted to see my brother who had preceded me to my prison.

Seven years have elapsed and I am still a prisoner, and if I except the occasional visits of my brother

debarred from all companionship save that of my jailers. My brother is one of the best of Squares, just,

sensible, cheerful, and not without fraternal affection; yet I confess that my weekly interviews, at least in one

respect, cause me the bitterest pain. He was present when the Sphere manifested himself in the Council

Chamber; he saw the Sphere's changing sections; he heard the explanation of the phenomena then given to

the Circles. Since that time, scarcely a week has passed during seven whole years, without his hearing from

me a repetition of the part I played in that manifestation, together with ample descriptions of all the

phenomena in Spaceland, and the arguments for the existence of Solid things derivable from Analogy. Yet

I take shame to be forced to confess it my brother has not yet grasped the nature of the Third Dimension,

Hence I am absolutely destitute of converts, and, for aught that I can see, the millennial Revelation has been

made to me for nothing. Prometheus up in Spaceland was bound for bringing down fire for mortals, but I

poor Flatland Prometheus lie here in prison for bringing down nothing to my countrymen. Yet I exist in

the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity

in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited

That is the hope of my brighter moments. Alas, it is not always so. Heavily weighs on me at times the

burdensome reflection that I cannot honestly say I am confident as to the exact shape of the onceseen,

oftregretted Cube; and in my nightly visions the mysterious precept, "Upward, not Northward", haunts me

like a souldevouring Sphinx. It is part of the martyrdom which I endure for the cause of the Truth that there

are seasons of mental weakness, when Cubes and Spheres flit away into the background of scarcepossible

existences; when the Land of Three Dimensions seems almost as visionary as the Land of One or None; nay,

when even this hard wall that bars me from my freedom, these very tablets on which I am writing, and all the

substantial realities of Flatland itself, appear no better than the offspring of a diseased imagination, or the