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by A Square, sm. 410., 1884

FLATLAND

A Romance of Many Dimensions

FLATLAND

A Romance of Many Dimensions

With Illustrations by the Author, A SQUARE

" Fie, fie, how franticly 1 square my talk!'

LONDON SEELEY &f Co., 46, 47 &r 48, ESSEX STREET, STRAND

(Late 15/54 FLEET STREET) 1884

LONDON :

R. CLAY, SONS, AND TAYLOR,

BREAD STREET HILL.

To

The Inhabitants of SPACE IN GENERAL And H. C. IN PARTICULAR

This Work is Dedicated By a Humble Native of Flatland

In the Hope that Even as he was Initiated into the Mysteries

Of THREE Dimensions Having been previously conversant

With ONLY Two So the Citizens of that Celestial Region

May aspire yet higher and higher To the Secrets of FOUR FIVE OR EVEN Six Dimensions

Thereby contributing To the Enlargement of THE IMAGINATION

And the possible Development

Of that most rare and excellent Gift of MODESTY

Among the Superior Races

Of SOLID HUMANITY

CONTENTS

PART I

THIS WORLD

Section

1 Of the Nature of Flatland

2 Of the Climate and Houses in Flatland

3 Concerning the Inhabitants of Flatland

4 Concerning the Women

5 Of our Methods of Recognizing one another

6 Of Recognition by Sight

7 Concerning Irregular Figures

8 Of the Ancient Practice of Painting

9 Of the Universal Colour Bill

10 Of the Suppression of the Chromatic Sedition

1 1 Concerning our Priests

12 Of the Doctrine of our Priests

viii Contents

Section

13 How 1 had a Vision of Lineland

14 How in my Vision I endeavoured to explain the nature of Flatland, but

could not

15 Concerning a Stranger from Spaceland

1 6 How the Stranger vainly endeavoured to reveal to me in words the mysteries

of Spaceland

1 7 How the Sphere, having in vain tried words ; resorted to deeds

1 8 How I came to Spaceland and what I saw there

19 How, though the Sphere showed me other mysteries of Spaceland, I still

desired more ; and what came of it

20 How the Sphere encouraged me in a Vision

2 1 How I tried to teach the Theory of Three Dimensions to my Grandson, and

with what success

22 How I then tried to diffuse the Theory of Three Dimensions by other means,

and of the result

PART 1

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

FLATLAND

PART I THIS WORLD

§ i. Of the Nature of Flat land.

I CALL our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows only hard and with luminous edges and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said " my universe " : but now my mind has been opened to higher views of things.

In such a country, you will perceive at once that it is impossible that there should be anything of what you. call a " solid " kind ; but I dare say you will suppose that we could at least distinguish by sight the Triangles Squares and other figures moving about as I have described them. On the contrary, we could see nothing of the kind, not at least so as to

4 Flatland

distinguish one figure from another. Nothing was visible, nor could be visible, to us, except straight Lines; and the necessity of this I will speedily demonstrate.

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

But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view ; and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatland citizen) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line. The same thing would happen if you were to treat in the same way a Triangle, or Square, or any other figure cut out of pasteboard. As soon as you look at it with your eye on the edge of the table, you will find that it ceases to appear to you a figure, and that it becomes in appear- ance a straight line. Take for example an equilateral Triangle who represents with us a Tradesman of the respectable class. Fig. I represents the Tradesman as you would see him

while you were bending over him from above ;

•(2)

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

(3)

if your eye were quite on the level of the table

(and that is how we see him in Flatland) you would see nothing but a straight line.

When I was in Spaceland I heard that your sailors have very similar experiences while they traverse your seas and discern some distant island

Flatland 5

or coast lying on the horizon. The far-off land may have bays, forelands, angles in and out to any number and extent ; yet at a distance you see none of these (unless indeed your sun shines bright upon them revealing the projections and retirements by means of light and shade), nothing but a grey unbroken line upon the water.

Well, that is just what we see when one of our triangular or other acquaintances comes towards 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 close to us we see his line becomes larger ; if he leaves us it becomes smaller : but still he looks like a straight line ; be he a Triangle, Square, Pentagon, Hexagon, Circle, what you will a straight Line he looks and nothing else.

You may perhaps ask how under these disadvantageous circumstances we are able to distinguish our friends from one another: but the answer to this very natural question will be more fitly and easily given when I come to describe the inhabitants of Flatland. For the present let me defer this subject, and say a word or two about the climate and houses in our country.

§ 2. Of the climate ana houses in Flatland.

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

There being no sun nor other heavenly bodies, it is impossible for us to determine the North in the usual way ; but we have a method of our own. By a Law of Nature with us, there is a constant attraction to the South ; and, although in temperate climates this is very slight so that even a Woman in reasonable health can journey several furlongs northward without much difficulty yet the hampering effect of the southward attraction is quite sufficient to serve as a compass in most parts of our earth. Moreover

6 Flatland

the rain (which falls at stated intervals) coming always from the North, is an additional assistance ; and in the towns we have the guidance of the houses, which of course have their side-walls running for the most part North and South, so that the roofs may keep off the rain from the North. In the country, where there are no houses, the trunks of the trees serve as some sort of guide. Altogether, we have not so much difficulty as might be expected in determining our bearings.

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

Windows there are none in our houses: for the light comes to us alike in our homes and out of them, by day and by night, equally at all times and in all places, whence we know not. It was in old days, with our learned men, an interesting and oft-investigated question, What is the origin of light ; and the solution of it has been repeatedly attempted, with no other result than to crowd our lunatic asylums with the would-be solvers. Hence, after fruitless attempts to suppress such investigations indirectly by making them liable to a heavy tax, the Legislature, in comparatively recent times, absolutely prohibited them. I, alas I alone in Flatland know now only too well the true solution of this mysterious problem ; but my knowledge cannot be made intelligible to a single one of my countrymen ; and I am mocked at I,

Flatland

the sole possessor of the truths of Space and of the theory of the introduction of Light from the world of Three Dimensions as if I were the maddest of the mad ! But a truce to these painful digressions : let me return to our houses.

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

Square and triangular houses are not allowed, and for this reason. The angles of a Square (and still more those of an equilateral Triangle) being much more pointed than those

of a Pentagon, and the lines of inanimate objects (such as houses) being dimmer than the lines of Men and Women, it follows that there is no little danger lest the points of a square or triangular house residence might do serious injury to an inconsiderate or perhaps absent- minded traveller suddenly running against them : and therefore, as early as the eleventh century of our era, triangular houses were universally forbidden by Law, the only exceptions being fortifications, powder-magazines, barracks, and other state buildings, which it is not desirable that the general public should approach without circumspection.

At this period, square houses were still everywhere permitted, though discouraged by a special tax. But, about three centuries afterwards, the Law decided that in all towns containing a population above ten thousand, the angle of a Pentagon was the smallest house-angle that could be

8 Flatland

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.

§ 3. Concerning the Inhabitants of Flatland.

The greatest length or breadth of a full-grown inhabitant of Flatland may be estimated at about eleven of ryour inches. Twelve inches may be regarded as a maximum.

Our Women are Straight Lines.

Our Soldiers and Lowest Classes of Workmen are Triangles with two equal sides, each about eleven inches long, and a base or third side so short (often not exceeding half an inch) that they form at their vertices a very sharp and formidable angle. Indeed when their bases are of the most degraded type (not more than the eighth part of an inch in size), they can hardly be distinguished from Straight Lines or Women ; so extremely pointed are their vertices. With us, as with you, these Triangles are distinguished from others by being called Isosceles ; and by this name I shall refer to them in the following pages.

Our Middle Class consists of Equilateral or Equal-sided Triangles.

Our Professional Men and Gentlemen are Squares (to which class I myself belong) and Five-sided figures or Pentagons.

Next above these come the Nobility, of whom there are several degrees, beginning at Six-sided Figures, or Hexagons, and from thence rising in the number of their sides till they receive the honourable title of Polygonal, or many-sided. Finally when the number of the sides becomes so numerous, and the sides themselves so small, that the figure cannot be distinguished from a circle, he is included in the Circular or Priestly order ; and this is the highest class of all.

It is a Law of Nature with us that a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility. Thus the son of a Square is a Pentagon ; the son of a Pentagon, a Hexagon ; and so on.

But this rule applies not always to the Tradesmen, and still less often to the Soldiers, and to the Workmen; who indeed can hardly be said to deserve the name of human Figures, since they have not all their sides equal. With them therefore the Law of Nature does not hold ; and the son of an Isosceles (i.e. a Triangle with two sides equal) remains Isosceles still. Nevertheless, all hope is not shut out, even from the Isosceles, that his posterity may ultimately rise : above his degraded condition. For, after a long series of military successes, or diligent and skilful labours, it is generally found that the more intelligent among the Artisan and Soldier classes manifest a slight increase of their third side or base, and a shrinkage of the two other sides. Intermarriages (arranged by the^ Priests) between the sons and daughters of these more intellectual members of the lower classes generally result in an offspring approxi- mating still more to the type of the Equal-sided Triangle.

Rarely in proportion to the vast number of Isosceles births— is a genuine and certifiable Equal-sided Triangle produced from Isosceles parents.1 Such a birth requires, as its antecedents, not only a series of carefully arranged intermarriages, but also a long-continued exercise of frugality and self-control on the part of the would-be ancestors of the coming Equilateral, and a patient, systematic, and continuous development of the Isosceles intellect through many generations.

1 " What need of a certificate?" a Spaceland critic may ask : " Is not the procreation of a Square Son a certificate from Nature herself, proving the Equal-sidedness of the Father ? " 1 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.

B

io Flat land

The birth of a True Equilateral Triangle from Isosceles parents is the subject of rejoicing in our country for many furlongs round. After a strict eximination conducted by the Sanitary and Social Board, the infant, if certified as Regular, is with solemn ceremonial admitted into the class of Equilaterals. He is then immediately taken from his proud yet sorrowing parents and adopted by some childless Equilateral, who is bound by oath never to permit the child henceforth to enter his former home or so much as to look upon his relations again, for fear lest the freshly developed organism may, by force of unconscious imitation, fall back again into his hereditary level.

The occasional emergence of an Isosceles from the ranks of his serf- born ancestors, is welcomed not only by the poor serfs themselves, as a gleam of light and hope shed upon the monotonous squalor of their existence, but also by the Aristocracy at large ; for all the higher classes are well aware that these rare phenomena, while they do little or nothing to vulgarise their own privileges, serve as a most useful barrier against revolution from below.

Had the acute-angled rabble been all, without exception, absolutely destitute of hope and of ambition, they might have found leaders in some of their many seditious outbreaks, so able as to render their superior numbers and strength too much even for the wisdom of the Circles. But a wise ordinance of Nature has decreed that, in proportion as the working-classes increase in intelligence, knowledge, and all virtue, in that same proportion their acute angle (which makes them physically terrible) shall increase also and approximate to the harmless angle of the Equilateral Triangle. Thus, in the most brutal and formidable of the soldier class creatures almost on a level with women in their lack of intelligence it is found that, as they wax in the mental ability necessary to employ their tremendous penetrating power to advantage, so do they wane in the power of penetration itself.

1 1

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 ulti- mately ennobled, are induced to enter the State Hospitals, where they are kept in honourable confinement for life ; one or two alone of the more obstinate, foolish, and hopelessly irregular are led to execution.

Then the wretched rabble of the Isosceles, planless and leaderless, are either transfixed without resistance by the small body of their brethren whom the Chief Circle keeps in pay for emergencies of this kind ; or else more often, by means of jealousies and suspicions skilfully fomented among them by the Circular party, they are stirred to mutual warfare, and perish by one another's angles. No less than one hundred and twenty rebellions are recorded in our annals, besides minor outbreaks numbered at two hundred and thirty-five ; and they have all ended thus.

§ 4. Concerning the Women.

If our highly pointed Triangles of the Soldier class are formidable, it may be readily inferred that far more formidable are our Women. For, if a Soldier is a wedge, a Woman is a needle ; being, so to speak, all point, at least at the two extremities. Add to this the power of making herself practically invisible at will, and you will perceive that a Female,

in Flatland, is a creature by no means to be trifled with.

B 2

1 2 Flatland

But here, perhaps, some of my younger Readers may ask how a woman in Flatland can make herself invisible. This ought, I think, to be apparent without any explanation. However, a few words will make it clear to the most unreflecting.

Place a needle on a table. Then, with your eye on the level of the table, look at it side-ways, and you see the whole length of it ; but look at it end-ways, and you see nothing but a point : it has become practically invisible. Just so is it with one of our Women. When her side is turned towards us, we see her as a straight line ; when the end containing her eye or mouth for with us these two organs are identical is the part that meets our eye, then we see nothing but a highly lustrous point ; but when the back is presented to our view, then being only sub-lustrous, and, indeed, almost as dim as an inanimate object her hinder extremity serves her as a kind of Invisible Cap.

The dangers to which we are exposed from our Women must now be manifest to the meanest capacity in Spaceland. If even the angle of a respectable Triangle in the middle class is not without its dangers ; if to run against a Working Man involves a gash ; if collision with an Officer of the military class necessitates a serious wound ; if a mere touch from the vertex of a Private Soldier brings with it danger of death ; what can it be to run against a Woman, except absolute and immediate destruction ? And when a Woman is invisible, or visible only as a dim sub-lustrous point, how difficult must it be, even for the most cautious, always to avoid collision !

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

Flatland 1 3

1. Every house shall have one entrance in the Eastern side, for the use of Females only ; by which all females shall enter " in a becoming and respectful manner " * and not by the Men's or Western door.

2. No Female shall walk in any public place without continually keeping up her Peace-cry, under penalty of death.

3. Any Female, duly certified to be suffering from St. Vitus's Dance, fits, chronic cold accompanied by violent sneezing, or any disease necessitating involuntary motions, shall be instantly destroyed.

In some of the States there is an additional Law forbidding Females, under penalty of death, from walking or standing in any public place without moving their backs constantly from right to left so as to indicate their presence to those 'behind them ; others oblige a Woman, when travelling, to be followed by one of her sons, or servants, or by her husband ; others confine Women altogether to their houses except during the religious festivals. But it has been found by the wisest of our Circles or Statesmen that the multiplication of restrictions on Females tends not only to the debilitation and diminution of the race, but also to the increase of domestic murders to such an extent that a State loses more than it gains by a too prohibitive Code.

For whenever the temper of the Women is thus exasperated by con- finement at home or hampering regulations abroad, they are apt to vent their spleen upon their husbands and children ; and in the less temperate climates the whole male population of a village has been sometimes destroyed in one or two hours of simultaneous female outbreak. Hence the Three Laws, mentioned above, suffice for the better regulated States, and may be accepted as a rough exemplification of our Female Code.

After all, our principal safeguard is found, not in Legislature, but in

1 When I was in Spaceland I understood that some of your Priestly Circles have in the same way a separate entrance for Villagers, Fanners, and Teachers of Board Schools (Spectator, Sept. 1884, p. 1255) that they may "approach in a becoming and respectful manner."

14 Flat land

the interests of the Women themselves. For, although they can inflict instantaneous death by a retrograde movement, yet unless they can at once disengage their stinging extremity from the struggling body of their victim, their own frail bodies are liable to be shattered.

The power of Fashion is also on our side. I pointed out that in some less civilised States no female is suffered to stand in any public place with- out swaying her back from right to left. This practice has been universal among ladies of any pretensions to breeding in all well-governed States, as far back as the memory of Figures can reach. It is considered a disgrace to any State that legislation should have to enforce what ought to be, and is in every respectable female, a natural instinct. The rhythmical and, if I may so say, well-modulated undulation of the back in our ladies of Circular rank is envied and imitated by the wife of a common Equilateral, who can achieve nothing beyond a mere monotonous swing, like the ticking of a pendulum ; and the regular tick of the Equilateral is no less admired and copied by the wife of the progressive and aspiring Isosceles, in the females of whose family no " back-motion " of any kind has become as yet a necessity of life. Hence, in every family of position and consideration, " back motion " is as prevalent as time itself ; and the husbands and sons in these households enjoy immunity at least from invisible attacks.

Not that it must be for a moment supposed that our Women are destitute of affection. But unfortunately the passion of the moment predominates, in the Frail Sex, over every other consideration. This is, of course, a necessity arising from their unfortunate conformation. For as they have no pretensions to an angle, being inferior in this respect to the very lowest of the, Isosceles, they are consequently wholly devoid of brain-power, and have neither reflection, judgment nor forethought, and hardly any memory. Hence, in their fits of fury, they remember no claims and recognise no distinctions. I have actually known a case where a Woman has exterminated her whole household, and half an hour

Flat land 15

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 thtir 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 simulations, these reckless creatures too often neglect the prescribed construction of the Women's apartments, or irritate their wives by ill-advised expressions out of doors, which they refuse immediately to retract. Moreover a blunt and stolid regard for literal truth indisposes them to make those lavish promises by which the more judicious Circle can in a moment pacify his consort. The result is massacre ; not however without its advantages, as it eliminates the more brutal and troublesome of the Isosceles ; and by many of our Circles the destructiveness of the Thinner Sex is regarded as one among many providential arrangements for suppressing redundant population, and nipping Revolution in the bud.

Yet even in our best regulated and most approximately circular families I cannot say that the ideal of family life is so high as with you in Spaceland. There is peace, in so far as the absence of slaughter may be called by that name, but there is necessarily little harmony of tastes or pursuits ; and the cautious wisdom of the Circles has ensured safety at the cost of domestic

1 6 Flat land

comfort. In every Circular or Polygonal household it has been a habit from time immemorial and has now become a kind of instinct among the women of our higher classes that the mothers and daughters should constantly keep their eyes and mouths towards their husband and his male friends ; and for a lady in a family of distinction to turn her back upon her husband would be regarded as a kind of portent, involving loss of status. But, as I shall soon shew, this custom, though it has the advantage of safety, is not without its disadvantages.

In the house of the Working Man or respectable Tradesman where the wife is allowed to turn her back upon her husband, while pursuing her household avocations there are at least intervals of quiet, when the wife is neither seen nor heard, except for the humming sound of the continuous Peace-cry ; but in the homes of the upper classes there is too often no peace. There the voluble mouth and bright penetrating eye are ever directed towards the Master of the household ; and light itself is not more persistent than the stream of feminine discourse. The tact and skill which suffice to avert a Woman's sting are unequal to the task of stopping a Woman's mouth ; and as the wife has absolutely nothing to say, and absolutely no constraint of wit, sense, or conscience to prevent her from saying it, not a few cynics have been found to aver that they prefer the danger of the death-dealing but inaudible sting to the safe sonorousness of a Woman's other end.

To my readers in Spaceland the condition of our Women may seem truly deplorable, and so indeed it is. A Male of the lowest type of the Isosceles may look forward to some improvement of his angle, and to the ultimate elevation of the whole of his degraded caste ; but no Woman can entertain such hopes for her sex. " Once a Woman, always a Woman" is a Decree of Nature ; and the very Laws of Evolution seem suspended in her disfavour. Yet at least we can admire the wise Prearrangement which has ordained that, as they have no hopes, so they shall have no memory to

Flat land 1 7

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.

§ 5. Of our methods of recognizing one another.

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

Recall what I told you above. All beings in Flatland, animate or inanimate, no matter what their form, present to our view the same, or nearly the same, appearance, viz. that of a straight Line. How then can one be distinguished from another, where all appear the same ?

The answer is threefold. The first means of recognition is the sense of hearing ; which with us is far more highly developed than with you, and which enables us not only to distinguish by the voice our personal friends, but even to discriminate between different classes, at least so far as concerns the three lowest orders, the Equilateral, the Square, and the Pentagon for of the Isosceles I take no account. But as we ascend in the social scale, the process of discriminating and being discriminated by hearing increases in difficulty, partly because voices are assimilated, partly because the faculty of voice-discrimination is a plebeian virtue not much developed among the Aristocracy. And wherever there is any danger of imposture we cannot trust to this method. Amongst our lowest orders, the vocal organs are developed to a degree more than correspondent with those of hearing, so that an Isosceles can easily feign the voice of a

i8 Flat land

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

Feeling is, among our Women and lower classes about our upper classes I shall speak presently the principal test of recognition, at all events between strangers, and when the question is, not as to the individual, but as to the class. What therefore " introduction" is among the higher classes in Spaceland, that the process of " feeling " is with us. " Permit me to ask you to feel and be felt by my friend Mr. So-and-so " is still, among the more old-fashioned of our country gentlemen in districts remote from towns, the customary formula for a Flatland introduction. But in the towns, and among men of business, the words " be felt by " are omitted and the sentence is abbreviated to, " Let me ask you to feel Mr. So-and- so " ; although it is assumed, of course, that the " feeling " is to be recipro- cal. Among our still more modern and dashing young gentlemen who are extremely averse to superfluous effort and supremely indifferent to the purity of their native language the formula is still further curtailed by the use of "to feel" in a technical sense, meaning, "to recommend-for-the purposes-of-feeling-and-being-felt " ; and at this moment the " slang " of polite or fast society in the upper classes sanctions such a barbarism as " Mr. Smith, permit me to feel you Mr. Jones."

Let not my Reader however suppose that " feeling " is with us the tedious process that it would be with you.or that we find it necessary to feel right round all the sides of every individual before we determine the class to which he belongs. Long practice and training, begun in the schools and continued in the experience of daily life, enable us to discriminate at once by the sense of touch, between the angles of an equal-sided Triangle, Square, and Pentagon ; and I need not say that the brainless vertex of an acute-angled Isosceles is obvious to the dullest touch. It is therefore not necessary, as a rule, to do more than feel a single angle of any individual ; and this, once ascertained, tells us the class of the person whom we are

Flat land 19

addressing, unless indeed he belongs to the higher sections of the nobility. There the difficulty is much greater. Even a Master of Arts in our University of Wentbridge has been known to confuse a ten-sided with a twelve-sided Polygon ; and there is hardly a Doctor of Science in or out of that famous University who could pretend to decide promptly and unhesitatingly between a twenty-sided and a twenty-four sided member of the Aristocracy.

Those of my readers who recall the extracts I gave above from the Legislative code concerning Women, will readily perceive that the process of introduction by contact requires some care and discretion. Otherwise the angles might inflict on the unwary Feeler irreparable injury. It is essential for the safety of the Feeler that the Felt should stand perfectly still. A start, a fidgety shifting of the position, yes, even a violent sneeze, has been known before now to prove fatal to the incau- tious, and to nip in the bud many a promising friendship. Especially is this true among the lower classes of the Triangles. With them, the eye is situated so far from their vertex that they can scarcely take cognizance of what goes on at that extremity of their frame. They are moreover of a rough coarse nature, not sensitive to the delicate touch of the highly organized Polygon. What wonder then if an involuntary toss of the head has ere now deprived the State of a valuable life !

I have heard that my excellent Grandfather one of the least irregular of his unhappy Isosceles class, who indeed obtained, shortly before his decease, four out of seven votes from the Sanitary and Social Board for passing him into the class of the Equal-sided often deplored with a tear in his venerable eye, a miscarriage of this kind, which had occurred to his great-great-great- Grand father, a respectable Working Man with an angle or brain of 59° 30'. 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

2O Flatland

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°, and not till the lapse of five generations was the lost ground recovered, the full 60° attained, and the Ascent from the Isosceles finally achieved. And all this series of calamities from one little accident in the process of Feeling.

At this point I think I hear some of my better educated readers exclaim, " How could you in Flatland know anything about angles and degrees, or minutes ? We can see an angle, because we in the region of Space, can see two straight lines inclined to one another ; but you, who can see nothing but one straight line at a time, or at all events only a number of bits of straight lines all in one straight line, how can you ever discern any angle, and much less register angles of different sizes ? "

I answer that though we cannot see angles, we can infer them, and this with great precision. Our sense of touch, stimulated by necessity, and developed by long training, enables us to distinguish angles far more accurately than your sense of sight, when unaided by a rule or measure of angles. Nor must I omit to explain that we have great natural helps. It is with us a Law of Nature that the brain of the Isosceles class shall begin at half a degree, or thirty minutes, and shall increase (if it increases at all) by half a degree in every generation ; until the goal of 60° is reached, when the condition of serfdom is quitted, and the freeman enters the class of Regulars.

Consequently, Nature herself supplies us with an ascending scale or Alphabet of angles for half a degree up to 60°, Specimens of which are placed in every Elementary School throughout the land. Owing to occasional retrogressions, to still more frequent moral and intellectual

Flat land 2 1

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°. These are absolutely destitute of civic rights ; and a great number of them, not having even intelligence enough for the purposes of warfare, are devoted by the States to the service of education. Fettered immovably so as to remove all possibility of danger, they are placed in the class rooms of our Infant Schools, and there they are utilized by the Board of Education for the purpose of imparting to the offspring of the Middle Classes that tact and intelligence of which these wretched creatures themselves are utterly devoid.

In some states the Specimens are occasionally fed and suffered to exist for several years ; but in the more temperate and better regulated regions, it is found in the long run more advantageous for the educational interests of the young, to dispense with food, and to renew the Specimens every month, which is about the average duration of the foodless existence of the Criminal class. In the cheaper schools, what is gained by the longer existence of the Specimens 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 show that Recognition

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Flatland

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 remain, as has been pointed out above, the objection that this method is not without danger. ' For this reason many in the Middle and Lower classes, and all without exception in the Polygonal and Circular orders, prefer a third method, the description of which shall be reserved for the next section.

§ 6. Of Recognition by Sight.

I am about to appear very inconsistent. In previous sections I have said that all figures in Flatland present the appearance of a straight line ; and it was added or implied, that it is consequently impossible to distin- guish by the visual organ between individuals of different classes : yet now I am about to explain to my Spaceland Critics how we are able to recognize one another by the sense of sight.

If however the Reader will take the trouble to refer to the passage