Classic Audiobook Collection - Flatland - A Romance of Many Dimensions by Edwin Abbott Abbott ~ Full Audiobook [scifi]

Episode Date: April 3, 2023

Flatland - A Romance of Many Dimensions by Edwin Abbott Abbott audiobook. Genre: scifi In the perfectly ordered world of Flatland, everything and everyone is a geometric shape, and your place in society is literally defined by the number of sides you have. A Square, a respectable middle-class professional, lives a predictable life governed by rigid rules, sharp prejudices, and an unquestioned faith in the dimensions he can see. But on the eve of the centennial celebration, his routine is interrupted by unsettling encounters that hint at realities beyond length and width. When a mysterious visitor from a higher dimension appears, the Square is drawn into a mind-bending journey that challenges his understanding of space, logic, and even the limits of imagination. As he struggles to communicate what he has learned to a society terrified of the unknown, Flatland becomes both a playful mathematical thought experiment and a pointed satire of social hierarchy, conformity, and intellectual censorship. By blending wit with wonder, Edwin Abbott Abbott crafts a story that invites listeners to reconsider how easily 'common sense' can become a cage - and how daring it is to see the world from a different angle. For ad-free listening try our premium subscription Chapters (Approximate) (00:00:00) Chapter 1 (00:22:55) Chapter 2 (00:50:48) Chapter 3 (01:15:58) Chapter 4 (01:46:01) Chapter 5 (02:06:29) Chapter 6 (02:34:13) Chapter 7 (03:10:04) Chapter 8 (03:54:33) Chapter 9 Learn more about your ad choices. Visit megaphone.fm/adchoices

Flatland, a romance of many dimensions by Edwin Abbott Abbott. To the inhabitants of space in general, and H.C. in particular, this work is dedicated by a humble native of Flatland, in the hope that even as he was initiated into the mysteries of three dimensions, having been previously conversant with only two, so the citizens of that celestial region may aspire yet higher and higher to the secrets of four, five or even six dimensions, thereby contributing to the enlargement of the imagination, and the possible development of that most rare and excellent gift of modesty among the superior races of solid humanity. Part 1. This World

Be patient for the world is broad and wide. Section 1 of the nature of Flatland I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in space. Imagine a vast sheet of paper, on which straight lines, triangles, squares, pentagons, hexagons and other figures, instead of remaining fixed in their places, move freely about on or in the surface, but without the power of rising above or sinking below it, very much like shadows, only hard and with luminous edges,

and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said my universe, but now my mind has been opened to higher views of things. In such a country, you will perceive at once, once that it is impossible that there should be anything of what you call a solid kind. But I dare say you will suppose that we could at least distinguish by sight the triangles, squares and other figures moving about as I have described them. On the contrary, we could see nothing of the kind,

not at least so as to distinguish one figure from another. Nothing was visible nor could be visible to us except straight lines and the necessity of this I will speedily demonstrate place a penny on the middle of one of your tables in space

and leaning over it look down upon it it will appear a circle but now drawing back to the edge of the table gradually lower your eye thus bringing yourself more and more into the condition of the inhabitants of flatland,

and you will find the penny becoming more and more oval to your view, and at last, when you have placed your eye exactly on the edge of the table, so that you are, as it were, actually a 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 appearance a straight line. Take, for example, an equilateral triangle, who represents with us a tradesman of the respectable class.

Figure 1 represents the tradesman as you would see him while you were bending over him from above. Reader's note, figure 1 is a downward pointing triangle with all sides equal. End of reader's note. Figures 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. reader's note. Figure 2 shows a much flatter downward pointing triangle, with the top edge much longer than the other two sides, which are of equal length. Figure 3 is flatter still, barely identifiable as a triangle at all. End of reader's note. And if your eye were quite on the level of the table, and that is how we see him in flatland, you would see nothing but a straight line. When I was in space land, I heard that your sailors have very similar experiences

while they traverse your seas and discern some distant island or coast lying on the horizon. The far-off land may have bays, fallants, 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 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. Section 2 of the climate and houses in Flatland. As with you, so also with us, there are four points of the compass, north, south, east and west.

There being no sun, nor other heavenly bodies, it is impossible for us to determine the north in the usual way, but we have a method of our own. By a law of nature with us, there is a constant attraction to the south, and although in temperate climates this is very slight, so that even a woman in reasonable health can journey several furlongs northward without much difficulty,

yet the hampering effect of the southward attraction is quite sufficient to serve as a compass in most parts of our earth. Moreover, the rain, which falls at stated intervals, coming always from the north, is an additional assistance. And in the towns we have the guidance of the houses, which of course have their side walls running for the most part north and south, so that the roofs may keep off the rain from the north. In the country where there are no houses, the trunks of the trees serve as some sort of guide. Altogether, we have not so much difficulty as might be expected in determining our bearings. Yet in our more temperate regions, in which the southward attraction is hardly felt, walking sometimes in a perfectly desolate plain where there have been no houses nor trees to guide me,

I have been occasionally compelled to remain stationary for hours together, waiting till the rain came before continuing my journey. On the week 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 yourself. 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, quents we know not.

It was, in old days with our learned men, an interesting and often investigated question, what is the origin of light, and the solution of it has been repeatedly attempted, with no other result than to crowd our lunatic asylums with the would-be solvers. Hence, after fruitless attempts to suppress such investigations indirectly by making them liable to a heavy tax, The legislature, in comparatively recent times, absolutely prohibited them. I, alas, I alone in Flatland, know now only too well the true solution of this mysterious problem. But my knowledge cannot be made intelligible to a single one of my countrymen.

And I am mocked at! I, the sole possessor of the truths of space, and of the theory of the introduction of light from the world of three dimensions, as if I were the maddest of the mad! But a truce to these painful digressions let me return to our houses. The most common form for the construction of a house is five-sided or pentagonal, as in the annexed figure. Reader's note,

The figure shows a pentagon slightly skewed to the right, with two sides marked R-O and O-F, forming a point marked O to the north. The left or western side which has a large opening marked men's door is marked A-R. The right or eastern side which has a small opening marked women's door is marked B-F. The base or southern side is marked A-B. End of reader's note. The two northern sides R-O-O-F, 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 11th 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 allowed consistently with the public safety. The good sense of the community has seconded the efforts of the legislature,

and now, even in the country, the pentagonal construction has superseded every other. It is only now and then in some very remote and backward agricultural district that an antiquarian may still discover a square house. section three concerning the inhabitants of flatland the greatest length or breadth of a full-grown inhabitant of flatland may be estimated at about eleven of your inches twelve inches may be regarded as a maximum our women are straight lines our soldiers and lowest classes of workmen are triangles with two equal size 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 eighths 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 skillful labours, it is generally found that the more intelligent among the artisan and soldier classes manifest a slight increase of their third side or base and a shrinkage of the two other sides. Intermarriages, arranged by the priests, between the sons and daughters of these more intellectual members of the lower classes, generally result in an offspring approximating still more to the type of the equal-sided triangle. Rarely, in proportion to the vast number of Isosceles' births,

is a genuine and certifiable equal-sided triangle produced from Isosceles parents. Footnote. What need of a certificate, a spaceland critic may ask? Is not the procreation of a square son a certificate from nature herself, proving the equal-sidedness of the father? I reply that no lady of any position will marry an uncertified triangle. square offspring has sometimes resulted from a slightly irregular triangle, but in almost every such case, the irregularity of the first generation is visited on the third, which either fails to attain the pentagonal rank or relapses to the triangular.

End of footnote. Such a birth requires, as its antecedents, not only a series of carefully arranged intermarriages, but also a long-continued exercise of frugality and self-control on the part of the would-be ancestors of the coming equilateral, and a patient, systematic and continuous development of the Isosceles intellect through many generations. The birth of a true equilateral triangle from Isosceles parents is the subject of rejoicing in our country for many furlongs round. 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 or,

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 surf-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. 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 classings. A much larger number, who are still below the standard, allured by the prospect of being ultimately ennobled, are induced to enter the state hospitals, where they are kept in honourable confinement for life. One or two alone of the more obstinate, foolish and hopelessly irregular are led to execution. Then the wretched rabble of the isosceles, planless and leaderless, are either transfixed without resistance by the small body of their brethren,

whom the chief circle keeps in pay for emergencies of this kind, or else more often, by means of jealousies and suspicions, skillfully fermented among them by the circular party, they are stirred to mutual warfare and perish by one another's angles. No less than 120 rebellions are recorded in our annals, besides minor outbreaks numbered at 235, and they have all ended thus. End of Part 1, Section 3, recording by Ruth Golding. Part 1, Sections 4 to 5, of Flatland.

This Librivox recording is in the public domain, recording by Ruth Golding. Flatland, a romance of many dimensions, by Edwin Abbott Abbott. Part 1, Section 4, concerning the women. If our highly pointed triangles of the soldier class are formidable, it may be readily inferred that far more formidable are our women. For if a soldier is a wedge, a woman is a needle, being, so to speak, all point, at least at the two extremities. Add to this the power of making herself practically invisible,

at will, and you will perceive that a female in Flatland is a creature by no means to be trifled with. But here, perhaps, some of my younger readers may ask how a woman in Flatland can make herself invisible. This ought, I think, to be apparent without any explanation. However, a few words will make it clear to the most unreflecting. Place a needle on a table. Then, with your own. 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 hindr 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 space-land. 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 minimise this peril, and in the southern and less temperate climates, where the force of gravitation is greater and human beings more liable to casual,

and involuntary motions, the laws concerning women are naturally much more stringent. But a general view of the code may be obtained from the following summary. 1. Every house shall have one entrance in the eastern side for the use of females only, by which all females shall enter in a becoming and respectful manner, and not by the men's or western door. footnote when i was in spaceland i understood that some of your priestly circles have in the same way a separate entrance for villagers farmers and teachers of board schools spectator september eighteen eighty four page one two five five that they may approach in a becoming and respectful manner end a footnote two 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. Baitis's dance, fits, chronic cold

accompanied by violent sneezing, or any disease necessitating involuntary emotions, shall be instantly destroyed. In some of the states there is an additional law forbidding females under penalty of death from walking or standing in any public place without moving their backs constantly from right to left, so as to indicate their presence to those behind them. Others oblige a woman, when travelling, to be followed by one of her sons or servants, or by her husband. Others confine women altogether to their houses, except during the religious festivals. But it has been found by the wisest of our circles or statesmen that the multiplication of restrictions on females tends not only to the debilitation and diminution of the race, but also to the increase of domestic murders, to such an extent that a state loses more than it gains by a too prohibitive code. For whenever the temper of the women is thus exasperated by confinement at home or hampering regulations abroad,

they are apt to vent their spleen upon their husbands and children, and in the less temperate climates, the whole male population of a village has been sometimes destroyed in one or two hours of simultaneous female outbreak. Hence, the three laws mentioned above suffice for the better regulated states, and may be accepted as a rough exemplification of our female code. After all, our principal safeguard is found not in legislature, but in the interests of the women themselves. For although they can inflict instantaneous death by a retrograde movement, yet unless they can at once disengage their stinging extremity from the struggling body of their victim, their own frail bodies are liable to be shattered.

The power of fashion is also on our side. I pointed out that in some less civilised states, no female is suffered to stand in any public place without swaying her back from right to left. This practice has been universal among ladies of any pretensions to breeding in all well-governed states, as far back as the memory of figures can reach. It is considered a discreet.

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 say so, 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 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 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, insofar 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 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 show, 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 elevations.

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 seems suspended in her disfavor. Yet at least we can admire the wise prearrangement, which has ordained that, as they have no hopes, so they shall have no memory to recall, and no forethought to anticipate the miseries and humiliations which are at once a necessity of their existence, and the basis of the Constitution of Flatland.

Section 5 of our methods of recognising 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 recognising one another's configurations? Recall what I told you above. All beings in Flatland, animate or inanimate, no matter what you,

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 imposter, we cannot trust to this method. Amongst our lowest orders, the vocal organs are developed to a degree more than correspondent with those of hearing, so that an isosceles can easily feign the voice of a polygon, and with some training that of a circle himself. A second method is therefore more commonly resorted to. Feeling is, among our women and lower classes, about our upper classes I shall speak presently, the principal test of recognition, at all events between strangers, and when the question is,

not as to the individual but as to the class. What, therefore, introduction is among the higher classes in spaceland, that the process of feeling is with us? Permit me to ask you to feel and be felt by my friend Mr. So-and-so, is, still among the more old-fashioned of our country gentlemen in district's remote from towns, the customary formula for a flatland introduction. But in the terms and among men of business, the words be felt by are omitted, and the sentence is abbreviated to, Let me ask you to feel Mr. So-and-so, although it is assumed, of course, that the feeling is to be reciprocal.

Among our still more modern and dashing young gentlemen, who are extremely averse to superfluous effort, and supremely indifferent to the purity of their native language, the formula is still. further curtailed by the use of to feel in a technical sense, meaning to recommend for the purposes of feeling and being felt. And at this moment the slang of polite or fast society in the upper classes sanctions such a barbarism as, Mr. Smith, permit me to feel 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 addressing, unless, indeed, he belongs to the higher sections of the nobility. There the difficulty is much greater. Even a Master of Arts in our University of Wentbridge has been known to confuse a ten-sided with a twelve-sided polygon,

and there is hardly a doctor of science in or out of that famous university who could pretend to decide promptly and unhesitatingly between a twenty-sided and a twenty-four-sided member of the aristocracy. Those of my readers who recall the extracts I gave above from the legislative code concerning women will readily perceive that the process of introduction by contact requires some care and discretion. Otherwise the angles might inflict on the unwary feeler irreparable injury. It is essential for the safety of the feeler that the felt should stand perfectly still. A start, a fidgety shifting of the position, yes, even a violent sneeze, has been known before now to prove fatal to the incautious.

and to nip in the bud many a promising friendship. Especially is this true among the lower classes of the triangles. With them, the eye is situated so far from their vertex that they can scarcely take cognizance of what goes on at that extremity of their frame. They are, moreover, of a rough coarse nature, not sensitive to the delicate touch of the highly organised polygon. What wonder, then, if an invertebrose, voluntary toss of the head, as 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-grandfather, a respectable working man with an angle or brain of 59 degrees 30 minutes. According to his account, my unfortunate ancestor, being afflicted with rheumatism and in the act of being felt by a polygon, by one sudden start, accidentally transfixed the great man

through the diagonal, and thereby, partly in consequence of his law. imprisonment and degradation, and partly because of the moral shock which pervaded the whole of my ancestors' 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 three, 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 30 minutes,

and shall increase, if it increases at all, by half a degree in every generation, until the goal of 60 degrees is reached, when the condition of serfdom is quitted, and the freeman enters the class of regulars. Consequently, nature herself supplies us with an ascending scale or alphabet of angles for half a degree up to 60 degrees, specimens of which are placed in every elementary school throughout the land. owing to occasional retrogressions, to still more frequent moral and intellectual stagnation, and to the extraordinary fecundity of the criminal and vagabond classes,

there is always a vast superfluity of individuals of the half-degree and single-degree class, and a fair abundance of specimens up to ten 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 state to the service of education. Fettered immovably, so as to remove all possibility of danger, they are placed in the classrooms of our infant schools, and there they are utilised 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 isos.

population, an object which every statesman in flatland constantly keeps in view. On the whole, therefore, although I'm 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 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. End of Part 1, Section 5, Recording by Ruth Golding. Part 1, Sections 6 and 7 of Flatland. This Librivox recording is in the public domain, recording by Ruth Golding Flatland A Romance of Many Dimensions by Edwin Abbott Abbott

Part 1, Section 6 Of Recognition by Sight I am about to appear very inconsistent In previous sections I have said that all figures in Flatland present the appearance of a straight line and it was added or implied

that it is consequently impossible to distinguish by the visual organ between individuals of different classes. Yet now I am about to explain to my spaceland critics how we are able to recognise one another by the sense of sight. If, however, the reader will take the trouble to refer to the passage in which recognition by feeling is stated to be universal, he will find this qualification, among the lower classes. It is only among the higher classes, and in our more temperate climates, that site recognition is practiced.

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 infebling the health, is by us recognised as a blessing scarcely inferior to air itself, and as the nurse of arts and parent of sciences. But let me explain my meaning without further eulogies on this beneficent element. If fog were non-existent, all lines would appear equally and indistinguishably clear. And this is actually the case in those unhappy countries in which the atmosphere is perfectly dry and transparent.

But wherever there is a rich supply of fog, objects that are at a distance, say, of three feet, are appreciably dimmer than those at a distance of two feet eleven inches. And the result is that by careful and constant experimental observation of comparative dimness and clearness, we are enabled to infer with great exactness the configuration of the object observed. An instance will do more than a volume of generalities

to make my meaning clear. Suppose I see two individuals approaching whose rank I wish to ascertain. They are, we will, suppose, a merchant and a physician, or, in other words, an equilateral triangle and a pentagon. How am I to distinguish them? Reader's note, the following part paragraph makes reference to an accompanying diagram. Diagram 1 is a rightward pointing equilateral

triangle. The vertical left-hand side of which is marked B-C, the other two sides being marked B-A and C-A. Dotted lines are drawn from B and C to a point further to the right to form an isosceles triangle. The far right-hand point of this triangle represents the eye of the observer, and a horizontal dotted arrow pointing left from it indicates his eye glance. A broad vertical line, D-A-E, is drawn to indicate what the observer sees. D-A-E is bright at the centre and darkens sharply towards its ends. End of reader's note. 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, C.A. and A.B. So that I shall contemplate the two impartially, and both will appear of the same size. Now in the case of one, the merchant, what shall I see? I shall see a straight line, D-A-E, 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 A-C and A-B recede rapidly into the fog, and what appear to me as the merchant's extremities, Viz D and E, will be very dim indeed. Readers note.

The following paragraph makes reference to an accompanying diagram. Diagram 2 is a regular pentagon sitting on a horizontal base with C1 at the apex, A1 at middle right, and B1 at lower right. Longer dotted lines are drawn out towards the right, upwards from B1 and downwards from C1 to form an irregular pentagon. The far right-hand point of the extended pentagon represents the eye of the observer, and a dotted arrow pointing from it towards the centre of the lower left edge of the pentagon indicates his eye glance. Again, a broad line D1A1E1 parallel to the lower left edge of the pentagon is drawn to indicate what the observer sees.

D1A1E1 is bright at the centre of the centre of the centre of the centre of the centre of the centre of recognise, and darkens very gradually towards its ends. End of reader's note. On the other hand, in the case of two, the physician, though I shall here also see a line, D1, A1, E1, with a bright centre, A1, yet it will shade away less rapidly into dimness because the sides A1C1, A1B1,

recede less rapidly into the fog. and what appear to me the physician's extremities, this D-1 and E-1, will be not so dim as the extremities of the merchant. The reader will probably understand from these two instances how, after a very long training supplemented by constant experience, it is possible for the well-educated classes among us to discriminate with fair accuracy

between the middle and lowest orders by the sense of sight. If my spaceland patrons have grasped this general conception so far as to conceive the possibility of it, and not to reject my account as altogether incredible, I shall have attained all I can reasonably expect. Were I to attempt further details, I should only perplex. Yet, for the sake of the young and inexperienced, who may perchance infer, from the two simple instances I have given above, of the manner in which I should

recognise my father and my sons, that recognition by sight is an easy affair, it may be needful to point out that in actual life most of the problems of sight recognition are far more subtle and complex. If, for example, when my father, the triangle, approaches me, he happens to present his side to me, me instead of his angle, then until I have asked him to rotate, or until I have edged my eye around him, I am for the moment doubtful whether he may not be a straight line, or, in other words, a woman. Reader's note, the following paragraph makes reference to an accompanying diagram. The diagram shows a hexagon with points at top and bottom. The vertical right-hand side is marked A.B. Dotted lines are drawn downward from the topmost and upward from the bottommost points of the

hexagon and extended to the right until they meet, forming an irregular pentagon. The far right hand point of the pentagon represents the eye of the observer. The line A-B is extended to where it meets the dotted lines to form a broad vertical line C-A-B-D. The middle portion of this line, is bright, and the outer portions darken towards C and D. End of reader's note. Again, when I'm in the company of one of my two hexagonal grandsons, contemplating one of his sides, A.B. full front. It will be evident from the accompanying diagram that I shall see one whole line, A. B, in comparative brightness, shading off hardly at all at the ends, and two

smaller lines, C. A. and B. D. D. D. D. D. M. M. M.? Shading away into greater dimness toward the extremities, C and D. But I must not give way to the temptation of enlarging on these topics. The meanest mathematician in spaceland will readily believe me when I assert that the problems of life, which present themselves to the well-educated, when they are themselves in motion, rotating, advancing or retreating, and at the same time attempting to discriminate by the sense of sight between a number of polygons of high rank moving in different directions, as, for example, in a 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 science 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, defined myself in the midst of a crowd of rotating polygons of the higher classes is occasionally very perplexing. And of course to a common tradesman

or serf, such a sight is almost as unintelligible as it would be to you, my reader, were you suddenly transported into our country. In such a crowd you could see on all sides of you nothing but a line apparently straight, but of which the parts would vary irregularly and perpetually in brightness or dimness. Even if you had completed your third year in the pentagonal and hexagonal classes in the university, and were perfect in the theory of the subject, you would still find that there was need of many years of experience before you could move in a fashionable crowd without jostling against your bettors, whom it is against etiquette to ask to feel, and who, by their superior culture and breeding know all about your movements, while you know very little or nothing

about theirs. In a word, to comport oneself with perfect propriety in polygonal society, one ought to be a polygon oneself. Such, at least, is the painful teaching of my experience. It is astonishing how much the art, or I may almost call it instinct, of sight recognition, is developed by the habitual practice of it, and by the avoidance of the custom of feeling. Just as with you, the deaf and dumb, if once allowed to gesticulate and to use the hand alphabet, will never acquire the more difficult but far more valuable art of lip speech and lip reading, so it is with us as regards seeing and feeling. None who in early life resort to feeling will ever learn seeing in perfection.

For this reason, among our higher classes, feeling is discouraged or absolutely forbidden. From the cradle, their children, instead of going to the public elementary schools, where the art of feeling is taught, are sent to hire 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 favourable. with the inert, undeveloped, and listless behaviour of the half-instructed youths of the polygonal class. But when the latter have at last completed their university course, and are prepared to put their theory into practice, the change that comes over them may almost be described as a new birth, and in every art, science and social pursuit, they rapidly overtake and distance their triangular competitors. Only a few of the polygonal class fail to pass the final test or leaving examination at the university. The condition of the unsuccessful minority is truly pitiable. Rejected from the higher class, they are also despised by the lower.

They have neither the matured and systematically trained powers of the polygonal bachelor's and masters of arts, nor yet the native precocity and mercurial versatility of the useful tradesmen. 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 shows that the offspring of such unfortunate and ill-indowed parents is generally itself unfortunate, if not positively irregular. It is from these specimens of the refuse of our nobility

that the great tumults and seditions of past ages have generally derived their leaders, and so great is the mischief thence arising that an increasing minority of our more progressive statesmen are of opinion that true mercy would dictate their entire suppression by enacting that all who fail to pass the final examination of the university should be either imprisoned for life or extinguished by a painless death. But I find myself digressing into the subject of irregularities,

a matter of such vital interest that it demands a separate section. Section 7 of irregular figures Throughout the previous pages I have been assuming what perhaps should have been laid down at the beginning as a distinct and fundamental proposition, that every human being in Flatland is a regular figure, that is to say, of regular construction. By this I mean that a woman must not only be a line, but a straight line. That an artisan or soldier must have two of his sides equal, that tradesmen must have three sides equal,

lawyers, of which class I am a humble member, four sides equal, and generally that in every polygon all the sides must be equal. The size of the sides would of course depend upon the age of the individual. A female at birth would be about an inch long, while a tall adult woman might extend to a foot. As to the males of every class, it may be roughly said that the length of an adult's sides, when added together, is three feet or a little more. But the size of our sides is not under consideration. I am speaking of the equality of sides. And it does not need much reflection to see that the whole of the social life in Flatland

rests upon the fundamental fact that nature wills all figures to have their sides equal. If our sides were unequal, our angles would 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 groping. The whole science and art of sight recognition would at once perish. Feeling, so far as it is an art, would not long survive. Intercourse would become perilous or impossible.

There would be an end to all confidence, all forethought. No one would be safe in making the most simple social arrangements. In a word, civilization would relapse into barbarism. Am I going too fast to carry my readers with me to these obvious conclusions? surely a moment's reflection and a single instance from common life must convince everyone 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 recognise 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 12 or 13 inches in diagonal. What are you to do with such a monster sticking fast in your house door? But I am insulting the intelligence of my readers

by accumulating details which must be patent to everyone who enjoys the advantages of a residence in spaceland. Obviously, the measurements of a single angle would no longer be sufficient under such portentous circumstances. One's whole life would be taken up in feeling or surveying the perimeter of one's acquaintances. Already, the difficulties of avoiding a collision in a crowd are enough to tax the sagacity of even, in a well-educated square. But if no one could calculate the regularity of a single figure in the company, all would be chaos and confusion, and the slightest panic would cause serious injuries, or, if there happened to be any women or soldiers present, perhaps considerable loss of life. Expediency therefore concurs with nature in stamping the seal of its approval upon regularity

of confirmation, 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 births 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.

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 vocation under close supervision. What wonder that human nature, even in the the best and purest is embittered and perverted by such surroundings. All this very plausible reasoning does not convince me, as it has not convinced the wisest of our statesman, that our ancestors erred in laying it down as an axiom of policy

that the toleration of irregularity is incompatible with the safety of the state. Doubtless the life of an irregular is hard, but the interests of the greater number require that it shall be hard. If a man with a triangular front and a polygonal back were allowed to exist and to propagate a still more irregular posterity, what would become of the arts of life? Are the houses and doors and churches in Flatland to be altered in order to accommodate such monsters?

Are our ticket collectors to be required to measure every man's perimeter? before they allow him to enter a theatre or to take his place in a lecture room? Is an irregular to be exempted from the militia? And if not, how is he to be prevented from carrying desolation into the ranks of his comrades? Again, what irresistible temptations to fraudulent impostures must needs beset such a creature? How easy for him to enter a shop with his polygonal front-form? 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 in 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 45 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, tripanings, colligations, and other surgical, or dietetic operations by which irregularity has been partly or wholly cured. Advocating, therefore, a fear media, I would lay down no fixed or absolute line of demarcation. But at the period when the frame is just beginning to set, and when the medical board has reported that recovery is improbable, I would suggest that the irregular offspring be painlessly and mercifully consumed.

End of Section 7. Recording by Ruth Golding. Part 1, Section 8 to 10 of Flatland. This Librivox recording is in the public domain. Recording by Ruth Golding. Flatland, a romance of many dimensions by Edwin Abbott Abbott. Part 1, Section 8, of the ancient practice of painting. If my readers have followed me with any attention up to this point,

they will not be surprised to hear that life is somewhat dull in flatland. I do not, of course, mean that there are not battles, conspiracies, tumults, factions, and all those other phenomena which are supposed to make history interesting. Nor would I deny that the strange mixture of the problems of life and the problems of mathematics, continually inducing conjecture and giving the opportunity of immediate verification, in parts to our existence a zest which you in spaceland can hardly comprehend. I speak now from the aesthetic and artistic point of view when I say that life with us is dull, aesthetically and artistically very dull indeed.

How can it be otherwise when all one's prospect, all one's landscapes, historical pieces, portraits, flowers, still life, are nothing but a single line, with no varieties except degrees of brightness and obscurity. It was not always thus. Color, if tradition speaks the truth, once, for the space of half a dozen centuries or more, threw a transient charm upon 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 by decorating first his house, then his slaves, then his father, his sons and grandsons, lastly himself. The convenience, as well as the beauty of the results, commended themselves to all. Wherever Chromatistes,

for by that name the most trustworthy authorities concur in calling him, turned his variegated frame, there he at once excited attention and attracted respect. No one now needed to feel him. No one mistook his front for his back. All his movements were readily ascertained by his neighbours without the slightest strain on their powers of calculation. No one jostled him or failed to make way for him.

His voice was saved the labour of that exhausting utterance by which we colourless squares and pentagons are often forced to proclaim our individuality when we move amid a crowd of ignorant isosceles. The fashions 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 dodecatans 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 customs soon made its way from the district of Cromatisties to surrounding regions, and within two generations no one in all flatland was colourless except the women and the priests. Here nature herself appeared to erect a barrier and to plead against extending the innovation to these two classes. many-sidedness was almost essential as a pretext for the innovators. Distinction of sides is intended by nature to imply distinction of colours, such was the sophism which in those days flew from mouth to mouth, converting whole towns at a time to the new culture. But manifestly to our priests and women this adage did not apply.

The latter had only one side, and therefore, plurally and pettison. identically speaking, no sides. The former, if at least they would assert their claim to be really and truly circles, and not mere high-class polygons with an infinitely large number of infinitesimally small sides, were in the habit of boasting what women confessed and deplored, that they also had no sides, being blessed with a perimeter of one line, or, in other words, a circumference. Hence it came to pass that these two classes could see no force in the so-called axiom about distinction of sides implying distinction of colour. And when all others had succumbed to the fascinations of corporal decoration, the priests and the women alone still remained pure

from the pollution of paint. Immoral, licentious, anarchical, unscientific, call them by what names you will, yet, from an aesthetic point of view, those ancient days of the colour revolt with a glorious childhood of art in Flatland. A childhood, alas, that never ripened into manhood, nor even reached the blossom of youth. To live was then in itself a delight, because living implied seeing. Even at a small party the company was a pleasure to behold, The richly varied hues of the assembly in a church or theatre are said to have more than once proved too distracting for our greatest teachers and actors.

But most ravishing of all is said to have been the unspeakable magnificence of a military review. The sight of a line of battle of 20,000 isosceles suddenly facing about, and exchanging the sombre black of their bases for the orange and purple of the two sides in general. including their acute angle. The militia of the equilateral triangles

tri-coloured in red, white and blue. The mauve, ultramarine, gamboge and burnt umber of the square artillerymen rapidly rotating near their familian guns. The dashing and flashing of the five-coloured and six-coloured pentagons and hexagons careering across the field in their offices of surgeons, geometricians and aide-de-cant.

All these may well have. been sufficient to render credible the famous story, how an illustrious circle, overcome by the artistic beauty of the forces under his command, threw aside his marshal's baton and his royal crown, exclaiming that he henceforth exchanged them for the artist's pencil. How great and glorious the sensuous development of these days must have been is in part indicated by the very language and vocabulary of the period. The commonest utterances of the commonest citizens in the time of the colour revolt seem to have been suffused with a richer tinge of word or thought.

And to that era we are even now indebted for our finest poetry and for whatever rhythm still remains in the more scientific utterance of these modern days. Section 9 of the Universal Color Bill But meanwhile the intellectual arts were fast decaying. The art of sight recognition, being no longer needed, was no longer practiced, and the studies of geometry, statics, kinetics, and other kindred subjects came soon to be considered superfluous, and fell into disrepute and neglect even as. our university. The inferior art of feeling speedily experienced the same fate at our elementary schools.

Then the isosceles classes, asserting that the specimens were no longer used nor needed, and refusing to pay the customary tribute from the criminal classes to the service of education, waxed daily more numerous and more insolent on the strength of their immunity from the old burden, which, had formerly exercised the twofold wholesome effect of at once taming their brutal nature and thinning their excessive numbers. Year by year, the soldiers and artisans began more vehemently to assert, and with increasing truth, that there was no great difference between them and the very highest class of polygons, now that they were raised to inequality with the latter, and enabled to grapple with all the difficulties and solve all the problems of life, whether statical and 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 monopolising and aristocratic arts, and the consequent abolition of all endowments for the studies of site 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 recognised as absolutely equal and entitled to equal rights. Finding the higher orders wavering and undecided, the leaders of the revolution advanced still further in their requirements, and at last demanded that all classes alike, the priests and the women not accepted, 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 a mass. But by some of my readers, the possibility of the identical appearance, of priests and women under the new legislation may not be recognised. If so, a word or two will make it obvious. Imagine a woman duly decorated according to the new code, with the front half, i.e. the half containing eye and mouth red, and with the hinder half green. Look at her from one side. Obviously, you will see a straight line, half red, half green. Reader's note, the following paragraph makes reference to an accompanying diagram. The diagram shows a circle or priestly figure.

If it is visualised as a clock face, 12 o'clock is marked M for the priest's mouth. 3 o'clock is marked B and 9 o'clock is marked A. The diameter A-B is drawn as a dotted line. and is extended outside the circle rightwards to a point which represents the position of the observer. Dotted lines are drawn downward and rightward from M towards this point and upward and rightward from 6 o'clock to this point. A broad vertical line, C, B, D, is drawn between the dotted lines to indicate what the observer sees.

CBD is bright at the centre and darkens sharply towards its ends. End of reader's note. Now imagine a priest whose mouth is at M and whose front semicircle, AM, 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, A.B. What you will see will be a straight line, C. B, D, of which one half, C.B, will be red, and the other B.D, green. The whole line, C.D, will be rather shorter, perhaps, than that of a full-sized woman, and will shade off. more rapidly towards its extremities, but the identity of the colours would give you an immediate

impression of identity, if not class, making you neglectful of other details. Bear in mind the decay of sight recognition which threatened society at the time of the colour revolt, add, too, the certainty that women would speedily learn to shade off their extremities so as to imitate the circles. It must then be surely obvious to you, my dear reader, that the colour bill placed us under a great danger of confounding a priest with a young woman. How attractive this prospect must have been to the frail sex

may readily be imagined. They anticipated with delight the confusion that would ensue. At home they might hear political and political and ecclesiastical secrets, intended not for them but for their husbands and brothers, and might even issue command 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 consequence 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, familiarised 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 Color Bill, the circles had not only held their own,

but even increased their lead of other classes by abstinence from the popular fashion. Now, therefore, the artful irregular, whom I described above, as the real author of this diabolical bill, determined at one blow to lower the status of the hierarchy, by forcing them to submit to the pollution of colour. and at the same time to destroy their domestic opportunities of training in the art of sight recognition so as to enfeeble their intellects by depriving them of their pure and colourless homes Once subjected to the chromatic taint, every parental and every childish circle would demoralise 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 intellectuals, the intellectuals. luster of the priestly order would wane, and the road would then lie open for a total destruction of all aristocratic legislature, and for the subversion of our privileged classes. Section 10 of the suppression of the chromatic sedition. The agitation for the Universal Colour Bill continued for three years, and up to the last moment of that period, it seemed as though anarchy were destined to triumph. A whole army of polygons, who turned out to fight as private soldiers, was utterly annihilated by a superior force of Isosceles triangles, the squares

and pentagons meanwhile remaining neutral. Worse than all, some of the ablest circles fell a prey to conjugal fury. Infuriated by political animosity, the wives in many a noble household wearied their lords with prayers to give up their opposition to the colour bill, and some, finding their entreaties fruitless, fell on and slaughtered their innocent children and husbands, perishing themselves in the act of carnage. It is recorded that during that triennial agitation, no less than 23 circles perished in domestic discord. Great indeed was the peril. It seemed as though the priests had no choice between submission and extermination, when suddenly the course of events was completely changed,

by one of those picturesque incidents which statesmen ought never to neglect, often to anticipate, and sometimes perhaps to originate, because of the absurdly disproportionate power with which they appeal to the sympathies of the populace. It happened that an isosceles of a low type, with a brain, little if at all, above four degrees, accidentally dabbling in the colours of some tradesmen whose shop he had plundered, painted himself, or caused himself to be painted, for the story varies, with the twelve colours of a dodecahedron. Going into the marketplace, 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 subject. When the news of this catastrophe spread from state to state, the minds of the women were violently agitated. Sympathy with the miserable victim and anticipations of similar deceptions for themselves,

their sisters and their daughters, made them now regard the colour bill in an entirely new aspect. Not a few openly avowed themselves converted to antagonism. the rest needed only a slight stimulus to make a similar avowal. Seizing this favourable opportunity, the circles hastily convened an extraordinary assembly of the States, and besides the usual guard of convicts, they secured the attendance of a large number of reactionary women. Amidst an unprecedented concourse,

the chief circle of those days, by name Pantosyclos, arose to find himself his, 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 Chromatistis, the leader of the sedition, into the centre of the hall, to receive, in the name of his followers,

the submission of the hierarchy. then followed a speech, a masterpiece of rhetoric, which occupied nearly a day in the delivery, and to which no summary can do justice. With a grave appearance of impartiality, he declared that as they were now finally committing themselves to reform or innovation, it was desirable that they should take one last view of the perimeter of the whole subject, its defects as well as its advantages. Gradually introducing the mention of the dangers to the tradesmen, the professional classes and the gentlemen, he silenced the rising murmurs of the isosceles by reminding them that, in spite of all these defects, he was willing to accept the bill if it was approved by the majority. But it was manifest that all, except the isosceles, were moved by his words,

and were either neutral or averse to the bill. turning now to the workmen he asserted that their interests must not be neglected and that if they intended to accept the colour bill they ought at least to do so with a 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 workmen would, in a few generations, be degraded to the level of the military,

or even the convict class. Political power would be in the hand. 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 were violated. A subdued murmur of assent ran through the ranks of the artisans, and Chromatistis, in alarm, attempted to step forward and address them. But he found himself encompassed with guards, and forced to remain silent. silent, while the chief circle, in a few impassioned words, made a final appeal to the women,

exclaiming that, if the colour bill passed, no marriage would henceforth be safe, no woman's honour secure. Fraud, deception, hypocrisy would pervade every household. Domestic bliss would share the fate of the Constitution, and pass to speedy perdition. Sooner than this, he cried, come death. At these words, which were the preconcerted signal for action, the Isosceles convicts fell on and transfixed the wretched chromatistes. The regular classes opening their ranks made way for a band of women, who, under direction of the circles, moved back foremost,

invisibly and unerringly upon the unconscious soldiers. The artisans, imitating the example of their betters, also opened their ranks. Meantime, bands of convicts occupied every entrance with an impenetrable phalanx. The battle, or rather carnage, was of short duration. Under the skilful 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 triumph of order. The circles delayed not to push their victory to the uttermost. The working men they spared but desecere. The militia of the equilateral's 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 other natural laws of the constitution of flatland.

Thus the balance of classes was again restored. Needless to say that henceforth the use of colour was abolished and its possession, prohibited. Even the utterance of any word denoting colour, except by the circles or by qualified scientific teachers, was punished by a severe penalty. Only at our university, in some of the very highest and most esoteric classes, which I myself have never been privileged to attend, it is understood that the sparing use of colour is still sanctioned, for the purpose of illustrating some of the deeper problems of mathematics. But of this I can only speak from hearsay. Elsewhere in Flatland's colour is now non-existent. The art of making it is known to only one

living person, the chief circle for the time being, and by him it is handed down on his 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 to the far distant days of the agitation for the Universal Color Bill. End of Section 10, recording by Ruth Golding. Part 1, Sections 11 and 12 of Flatland. This Librevox recording is in the part.

public domain. Recording by Ruth Golding. Flatland, a romance of many dimensions, by Edwin Abbott Abbott, Part 1, Section 11, concerning our priests. It is high time that I should pass from these brief and discursive notes about things in Flatland to the central event of this book, my initiation into the mysteries of space. That is my subject. All that has gone before is merely preface. For this reason, I must omit many matters of which the explanation would not, I flatter myself, be without interest for my readers. As, for example, our method of propelling and stopping ourselves, although destitute of feet. The means by which we give fixity to structures of wood, stone or brick,

although, of course, we have no hands, nor can we lay foundations as you can, nor avail ourselves of the lateral pressure of the earth. The manner in which the rain originates in the intervals between our various zones, so that the northern regions do not intercept the moisture from falling on the southern. The nature of our hills and mines, our trees and vegetables, our seasons and harvests. our alphabet and method of writing adapted to our linear tablets. These and a hundred other details of our physical existence I must pass over, nor do I mention them now except to indicate to my readers that their omission proceeds not from forgetfulness on the part of the author, but from his regard for the time of the reader.

Yet before I proceed to my legitimate subject, some few final remarks will no doubt be expected by my readers upon those pillars and mainstays of the constitution of Flapland, the controllers of our conduct and shapers of our destiny, the objects of universal homage and almost of adoration, need I say, that I mean our circles or priests. When I call them priests, let me not be understood as meaning no more than the term denotes with you. With us, our priests are administrators of all business, art and science, directors of trade, commerce, generalship, architecture, engineering, education, statesmanship, legislature, morality, theology.

Doing nothing themselves, they are the causes of everything worth doing that is done by others. Although popularly everyone called a circle is deemed a circle, yet among the better educated classes, it is known that no circle is really a circle, but only a polygon with a very large number of very small sides. In proportion to the number of the sides, the polygon approximates to a circle. And when the number is very great,

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 300 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 10,000 sides. The ascent of the posterity of the circles in the social scale

is not restricted, as it is among the lower regular classes, by the law of nature which limits the increase of sides to one in each generation. If it were so, the number of the number of the number of, of sides in a circle would be a mere question of pedigree and arithmetic, and the 497th descendant of an equilateral triangle would necessarily be a polygon with 500 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 sun, more than one is never seen. On the other hand, the sun of a five hundred-sided polygon has been known to possess 550 or even 600 sides. Art also steps in to help the process of the higher evolution. Our physicians have discovered that the small and tender sides of an infant polygon of the higher class

can be fractured and his whole frame 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 the, that position in society who has neglected to place his firstborn son in the circular, neotherapeutic gymnasium before he has attained the age of a month. One year determined 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 sacrifices which have a dissimilar issue. Section 12 of the doctrine of our priests. As to the doctrine of the circles, it may briefly be summed up in a single single, maxim, attend to your configuration. Whether political, ecclesiastical or moral, all their teaching has

for its object the improvement of individual and collective configuration, with special reference, of course, to the configuration of the circles, to which all other objects are subordinated. It is the merit of the circles that they have effectually suppressed those ancient heresies which led men to waste energy and sympathy in the vain belief that conduct depends upon will, effort, training, encouragement, praise, or anything else but configuration. It was Pantocyclos, the illustrious circle mentioned above as the queller of the color of oat, who first convinced mankind that configuration makes the man, that if, for example, you are born an isosceles with two two,

uneven sides, you will assuredly go wrong unless you have them made even, for which purpose you must go to the Isosceles Hospital. Similarly, if you are a triangle or square, or even a polygon born with any irregularity, you must be taken to one of the regular hospitals to have your disease cured. Otherwise, you will end your days in the state prison, or by the angle of the state executioner. or defects, from the slightest misconduct to the most flagitious crime, pentocyclos 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 rectangles?

or again why blame a lying thievish isosceles when you ought rather to deplore the incurable inequality of his sides? Theoretically this doctrine is unquestionable, but it has practical drawbacks. In dealing with an isosceles, if a rascal pleads that he cannot help stealing because of his unevenness, you reply that for that very reason, because he cannot help, because he cannot help, 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, whether 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 castigating, has some latent and strengthening influence on my grandson's configuration, though I own that I have no grounds for thinking so.

At all events I am not alone in my way of extricating myself from this dilemma, for I find that many of the highest circles, sitting as judges in law courts, use praise and blame towards regular and irregular figures. And in their homes, I know by experience that, when scolding their children, they speak about right or wrong as vehemently and passionately as if they believed that these names represented real existences, and that a human figure is really capable of choosing between them. Consistently carrying out their policy of making configuration

the leading idea in every mind, the circles reverse the nature of that commandment which in spaceland regulates the relations between parents and children. with you children are taught to honour their parents with us next to the circles who are the chief object of universal homage a man is taught to honour his grandson if he has one or if not his son by honour however is by no means meant indulgence but a reverent regard for their highest interests and the circles teach that the duty of fathers is to subordinate their own interests to those of posterity, thereby advancing the welfare of the whole state, as well as that of their own immediate descendants.

The weak point in the system of the circles, if a humble square may venture to speak of anything circular as containing any element of weakness, appears to me to be found in their relations with women. As it is of the utmost importance for society that irregular births should be discouraged. It follows that no woman who has any irregularities in her ancestry is a fit partner for one who desires that his posterity should rise by regular degrees in the social scale.

Now, the irregularity of a male is a matter of measurement, but as all women are straight and therefore visibly regular, so to speak, one has to devise some other means of ascertaining what I may call their invisible, visible irregularity. That is to say, their potential irregularities as regards possible offspring. This is effected by carefully kept pedigrees, which are preserved and supervised by the state, and without a certified pedigree, no woman is allowed to marry. Now it might have been supposed that a circle, proud of his ancestry and regardful for a posterity which might possibly issue her after in a chief circle, would be more careful than any other

to choose a wife who had no blot on her escutcheon. But it is not so. The care in choosing a regular wife appears to diminish as one rises in the social scale. Nothing would induce an aspiring isosceles who had hopes of generating an equilateral son to take a wife who reckoned a single irregularity among her ancestors. A square or pentagon, who is confident that his family is steadily on the rise, does not inquire above the five hundredth generation. A hexagon, or dodecahedron, is even more careless of the wife's pedigree. But a circle has been known deliberately to take a wife who has had an irregular great-grandfather, and all because of some slight superiority of lustre, or because of the charms of a low voice, which, with us, even more

than with you, is thought, an excellent thing in woman. Such ill-judged marriages are, as might be expected, barren if they do not result in positive irregularity or in diminution of sides. But none of these evils have hitherto proved sufficiently deterrent. the loss of a few sides in a highly developed polygon is not easily noticed and is sometimes compensated by a successful operation in the 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 not be far distant when, the race being no longer able to produce a chief circle, the constitution of Flatland must fall. One other word of warnings suggest itself to me, though I cannot so easily mention a remedy,

and this also refers to our relations with women. About 300 years ago, it was decreed by the chief circle that, since women are deficient in reason but abundant in emotion, they ought no longer to be treated as rational, nor receive any mental education. The consequence was that they were no longer taught to read, nor even to master arithmetic, enough to enable them to count the angles of their husband or children.

And hence they sensibly declined during each generation in intellectual power, and this system of female non-education or quietism still prevails. My fear is that with the best intentions, this policy has been carried so far as to react injuriously on the male sex. For the consequence is that, as things now are, we males have to lead a kind of bilingual, and I may almost say, bi-mental existence. With the 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 our us than they are. But behind their backs, they are both regarded and spoken of by all except the very young, as being little better than mindless organisms. Our theology also in the women's chambers is entirely different from our theology elsewhere. Now, my humble fear is that this double

training in language as well as in thought imposes somewhat too heavy a burden upon the young, especially when at the age of three years old they are taken from the maternal care and taught to unlearn the old language except for the purpose of repeating it in the presence of their mothers and nurses and to learn the vocabulary and idiom of science already methinks i discern a weakness in the grasp of mathematical truth at the present time as compared with the more robust intellect of our ancestors three hundred years ago i say nothing of the possible danger if a woman should ever surreptitiously learn to read, and convey to her sex the result of her perusal of a single popular volume, nor of the possibility that the indiscretion or disobedience of some infant male might reveal to a mother the secrets of the logical dialect. On the simple ground of the enfeebling of the male intellect, I rest this humble appeal to the

highest authorities to reconsider the regulations of female education. End of Section 12 and of Part 1. Recording by Ruth Golding. Part 2, Section 13 and 14 of Flatland. This Librivox recording is in the public domain, recording by Ruth Golding. Flatland, a romance of many dimensions by Edwin Abbott Abbott. Part 2. Other Worlds O brave new worlds that have such people in them!

Section 13 How I Had a Vision of Line Land It was the last day but one of the 1999th year of our era and the first day of the long vacation. Having amused myself till a late hour with my favourite recreation of geometry, I had retired to rest with an unsolved problem in my mind. In the night I had a dream. Reader's note, the following paragraph makes reference to a diagram.

The diagram is headed, My View of Lineland. Beneath this title and centrally placed is a square, labeled myself. Under that, from left to right on a horizontal plane, are four dots, labeled women, a short dash, labeled a boy, six longer dashes marked men, then, directly below myself, a thick dash labeled the king with an eye looking out from either end. Under the eyes is written, the king's eyes much larger than the reality, showing that his majesty could see nothing but a point. The horizontal line then continues towards the right, with seven dashes marked men, one dash marked a boy, and seven dots marked women.

End of reader's note. I saw before me a vast multitude of small straight lines, which I naturally assumed to be women, interspersed with other beings, still smaller, and of the nature of lustrous points, all moving to and fro in one and the same straight line, and, as nearly as I could judge, with the same velocity. A noise of confused, multitudinous chirping or twittering issued from them at intervals as long as they were moving, but sometimes they ceased from motion, and then all was silence. Approaching one of the largest of what I thought to be women, I accosted her, but received no answer. a second and 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 persevering questions, I elicited the following facts. It seemed that this poor ignorant monarch, as he called himself, was persuaded that the straight line which he called his kingdom, and in which he passed his existence, constituted the whole of the world, and indeed the whole of space. Not being able either to move or to see, save in his straight line, he had no

conception of anything out of it. Though he had heard my voice when I first addressed him, the sounds had come to him in a manner so contrary to his experience that he had made no answer, seeing no man, as he expressed it, and hearing a voice, as it were, from my own intestines. Until the moment when I placed my mouth in his world, he had neither seen me nor heard anything except confused sounds, beating against what I called his side, but what he called his inside or stomach. nor had he even now the least conception of the region from which i had come outside his world or line all was a blank to him nay not even a blank for a blank implies space say rather all was non-existent his subjects of whom the small lions were men and the points women were all alike confined in motion and i sands 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 anyone ever see anything but a point. Man, woman, child, thing, each was a point to the eye of a limelander. Only by the sound of the voice

could sex or age be distinguished. Moreover, as each, Each individual occupied the whole of the narrow paths, 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 subject. But at last I plunged into it by abruptly inquiring as to the health of his family. My wives and children, he replied, are well and happy. Staggered at this answer, for in the immediate proximity of the monarch, as I had noted in my dream before I entered Lainland, there were none but men, I ventured to reply, pardon me, but I cannot imagine how, your Royal Highness,

can at any time either see or approach their majesties when there are at least half a dozen intervening individuals whom you can neither see through nor pass by. Is it possible that in lineland proximity is not necessary for marriage and for the generation of children? How can you ask so absurd a question? replied the monarch. If it were indeed as you suggest, the universe would soon be depopulated. No, no, neighbourhood is needless for the union of hearts. And the birth of children is too important a matter to have been allowed to depend on 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 limeland. know then that marriages are consummated by means of the faculty of sound and the sense of hearing. You are, of course, aware that every man has two mouths or voices as well as two eyes, a base 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 base voice and an utterly uneducated ear. But, to continue. Nature herself having ordained that every man should wed two wives, why too? asked Lerner, asked Lerner, 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? Fizz 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 impossible, he said, it is a It is as inconceivable as that two and one should make five, or that the human eye should

see a straight line. I would have interrupted him, but he proceeded as follows. Once in the middle of each week, a law of nature compels us to move to and fro with a rhythmic motion of more than usual violence, which continues for the time you would take to count a hundred and one. In the midst of this choral dance, at the 51st 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 base to treble, of tenor to contralto, that oftentimes the loved ones, though twenty thousand leagues away, recognise at once the responsive note of their destined lover, and penetrating the paltry obstacles of distance, love unites the three. The marriage in that instant consummated results in a threefold male and female offspring, which takes its place in lineland. "'What, always threefold?' said I. "'Must one wife then always have twins?' "'Base-voice monstrosity!

"'Yes!' replied the king. "'How else could the balance of the sexes be maintained "'if two girls were not born for every boy? "'Would you ignore the very alphabet of nature?' "'He ceased, speechless for fury, "'and some time elapsed before I could induce him to resume his narrative. "'You will not, of course, suppose that every bachelor among us "'finds his mates at the first wooing in this,

universal marriage chorus? On the contrary, the process is by most of us many times repeated. Few are the hearts whose happy lot it is at once to recognize in each other's voices the partner intended for them by Providence, and to fly into a reciprocal and perfectly harmonious embrace. With most of us, the courtship is of long duration. The wooer's voices may perhaps accord with one of the future wives, but not with both. or not at first with either, or the soprano and contralto may not quite harmonize. In such cases, nature has provided that every weekly chorus shall bring the three lovers into closer harmony. Each trial of voice, each fresh discovery of discord, almost imperceptibly induces the less perfect

to modify his or her vocal utterance, so as to approximate to the more perfect. And after many trials and many approximations, the result is at last achieved. There comes a day at last, when, while the wonted marriage chorus goes forth from universal lineland, the three far-off lovers suddenly find themselves in exact harmony. And before they are aware, the wedded triplet is rapt, vocally, into a duplicate embrace. and nature rejoices over one more marriage and over three more births. Section 14, how I vainly tried to explain the nature of Flatland. Thinking that it was time to bring down the monarch from his raptures to the level of common sense,

I determined to endeavour to open up to him some glimpses of the truth, that is to say, of the nature of things in Flatland. So I began thus. How does your Royal Highness distinguish the shapes and positions of his subjects? I, for my part, noticed by the sense of sight, before I entered your kingdom, that some of your people are lines and others' points, and that some of the lines are larger— "'You speak of an impossibility!' interrupted the King.

"'You must have seen a vision, for to detect the difference between a line and a point by the sense of sight is, as everyone knows, in the nature of things, impossible. But it can be detected by the sense of hearing, and by the same means my shape can be exactly ascertained. Behold me, I am a line, the longest in lineland, over six inches of space. "'Of length,' I ventured to suggest. "'Fool!' said he. "'Space is length. "'Interrupt me again, and I have done.'

"'I apologised, but he continued scornfully, "'since you are impervious to argument, "'you shall hear with your ears "'how by means of my two voices "'I reveal my shape to my wives, "'who are at this moment six thousand miles, "'seventy yards, two feet, eight inches away, the one to the north, the other to the south.

Listen, I call to them. He chirruped, and then complacently continued, My wives at this moment receiving the sound of one of my voices, closely followed by the other, and perceiving that the latter reaches them after an interval in which sound can traverse 6.457 inches, infer that one of my mouths is 6.457. inches further from them than the other, and accordingly know my shape to be 6.457 inches.

But you will, of course, understand that my wives do not make this calculation every time they hear my two voices. They made it once for all before we were married. But they could make it at any time. And in the same way, I can estimate the shape of any of my male subjects by the sense of sound. "'But how,' said I, "'if a man feigns a woman's voice with one of his two voices, "'or so disguises his southern voice "'that it cannot be recognised 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, No, 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 for a man, the law ordains universally that neither man nor woman shall be approached so closely as to destroy the interval between the approach. and the approximator and the approximated. And indeed what possible purpose would be served by this

illegal and unnatural excess of approximation which you call touching, when all the ends of so brutal and coarse a process are attained at once more easily and more exactly by the sense of hearing. As to your suggested danger of deception, it is non-existent, for the voice, being the essence of one's being, cannot be thus changed at will. But come, suppose that I had the power of passing through solid things, so that I could penetrate my subjects one after another, even to the number of a billion, verifying the size and distance of each by the sense of feeling, how much time and energy would be wasted in this clumsy and inaccurate method,

whereas now, in one moment of audition, I take, as it were, the census and statistics, local, corporal, mental, and spiritual, of every living being in Lionland. Hark! Only hark! So saying, he paused and listened, as if, in an ecstasy, to a sound which seemed to me no better than a tiny chirping

from an innumerable multitude of Lilliputian grasshoppers. truly replied i your sense of hearing serves you in good stead and fills up many of your deficiencies but permit me to point out that your life in lineland must be deplorably dull to see nothing but a point not even to be able to contemplate a straight line nay not even to know what a straight line is to see yet to be cut off from those linear prospects which are vouched safety to us in flatland. Better, surely, to have no sense of sight at all than to see so little. I grant you I have not your discriminative faculty of hearing, for the concert of all lineland which gives you such intense pleasure is to me no better than a multitudinous twittering or chirping.

But at least I can discern by sight a line from a point, and let me prove it. "'Just before I came into your kingdom, I saw you dancing from left to right, and then from right to left, with seven men and a woman, in your immediate proximity on the left, and eight men and two women on your right. Is not this correct?' "'It is correct,' said the king, so far as the numbers and sexes are concerned, though I know not what you mean by right and left. "'But I deny that you saw these things.' "'for how could you see the line, that is to say, the inside of any man?

"'But you must have heard these things and then dreamed that you saw them. "'And let me ask what you mean by those words left and right. "'I suppose it is your way of saying northward and southward.' "'Not so,' replied I. "'Besides your motion of northward and southward, "'there is another motion which I call from right to left.' King, Exhibit to me, if you please, this motion from left to right. I. Nay, that I cannot do, unless you could step out of your line altogether.

King, out of my line? Do you mean out of the world? Out of space? I, well, yes, out of your world, out of your space. For your space is not the true space. True space is a plane. but your space is only a line. King, if you cannot indicate this motion from left to right by yourself moving in it, then I beg you to describe it to me in words. I, if you cannot tell your right side from my left, I fear that no words of mine can make my meaning clear to you,

but surely you cannot be ignorant of so simple a distinction. King, I do not in the least understand. you? I. Alas, how shall I make it clear? When you move straight on, does it not sometimes occur to you that you could move in some other way? Turning your eye round so as to look in the direction to which your side is now fronting? In other words, instead of always moving in the direction of one of your extremities, do you never feel a desire to move in the direction, so to speak, of your side?

King. Never. And what do you mean? How can a man's inside front in any direction? Or how can a man move in the direction of his inside? Aye. Well then, since words cannot explain the matter, I will try deeds and will move gradually out of line land in the direction which I desire to indicate to you. reader's note the following paragraph makes reference to a diagram the diagram shows a horizontal line at the left is marked lineland with an arrow pointing rightward at the right on the line is a broad dash labelled the king in the centre on the line is a horizontally shaded square over which is written my body just before i disappeared end of reader's note At the word, I began to move my body out of limeland. 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'm not dead, replied I. I am simply out of limeland, 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 also see 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 this at last convince you? And with that I once more entered Lineland, taking up the same position as before. But the monarch replied, If you were a man of sense, though, as you appear to have only one voice, I have little doubt you are not a man but a woman. But if you had a particle of sense, you would listen to reason.

You ask me to believe that there is another line besides that which my senses indicate, and another motion besides that of which I am daily conscious. I, in return, ask you to describe in words, or indicate by motion, that other line of which you speak. Instead of moving, you merely exercise some magic art of vanishing and returning to sight. and instead of any lucid description of your new world, you simply tell me the numbers and sizes of some forty of my retinue, facts known to any child in my capital. Can anything be more irrational or audacious? Acknowledge your folly, or depart from my dominions. Furious at his perversity, and especially indignant that he professed to be ignorant of my sex, I retorted in no measured terms, Besotted being, you think yourself the perfection of existence, while you are in reality the most imperfect and imbecile. You profess to see, whereas you can see nothing but a point.

You plume yourself on inferring the existence of a straight line, but I can see straight lines, and infer the existence of angles, triangles, squares, pentagons, hexagons, and even circles. "'Why waste more words? "'Suffice it that I am the completion of your incomplete self. "'You are a line, but I am a line of lines, "'called in my country a square. "'And even I, infinitely superior, though I am to you, "'am of little account among the great nobles of Flatland, "'whence I have come to visit you,

"'in the hope of enlightening your ignorance.' "'Hearing these words, the king advanced to, towards me with a menacing cry, as if to pierce me through the diagonal. And in that same moment there arose from myriads of his subjects a multitudinous war-cry, increasing in vehemence, till at last me thought it rivaled the roar of an army of a hundred thousand isosceles and the artillery of a thousand pentagons. Spell-bound and motionless, I could neither speak nor move to avert the impending destruction. and still the noise grew louder and the king came closer when I awoke to find the breakfast bell

recalling me to the realities of Flatland. End of Section 14. Recording by Ruth Golding. Part 2, Sections 15 to 17 of Flatland. This Libri-Box recording is in the public domain, recording by Ruth Golding. Flatland, a romance of many. Dimensions by Edwin Abbott Abbott. Part 2, Section 15, concerning a stranger from spaceland. From dreams I proceed to facts. It was the last day of the 1919th year of our era.

The pattering of the rain had long ago announced nightfall, and I was sitting in the company of my wife, musing on the events of the past and the prospects of the coming year, the country of the coming year, the coming century, the coming millennium. Footnote. When I say sitting, of course, I do not mean any change of attitude such as you in spaceland signify by that word, for as we have no feet, we can no more sit, nor stand, in your sense of the word, than one of your souls or flounders. Nevertheless, we perfectly well recognise 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 luster corresponding to the increase of volition. But on this and a thousand other kindred subjects, time forbids me to dwell. End of footnote. My four sons and two orphan grandchildren had retired to their several apartments, and my wife alone remained with me to see the old millennium out, and the new one in. I was rapt in thought, pondering in my mind some words that had casually issued from the mouth of my youngest grandson, a most promising young hexagon of unusual brilliancy and perfect angularity. His uncles and I had been giving him his usual practical lesson in sight recognition, turning ourselves upon our centres, now rapidly, now more slowly, and questioning him as to our positions. and his answers had been so satisfactory

that I had been induced to reward him by giving him a few hints on arithmetic as applied to geometry. Taking nine squares each an inch every way, I had put them together so as to make one large square with a side of three inches. And I had hence proved to my little grandson that, though it was impossible for us to see the inside of the square,

yet we might ascertain the number of square inches in a square by simply squaring the number of inches in the side and thus said i we know that three squared or nine represents the number of square inches in a square whose side is three inches long the little hexagon meditated on this a while and then said to me but you have been teaching me to raise numbers to the third power i suppose three cubed 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 show the boy how a point by moving through a length of three inches makes a line of three inches which may be represented by three 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 three squared. 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 three, and if a straight line of three inches moving parallel to its makes a square of three inches every way represented by three squared. It must be that a square of three inches every way, moving somehow parallel to itself, but I don't see how, must make a something else, but I don't see what, of three inches every way, and this must be represented by three cubed. Go to bed, said I, a little ruffled by his interruption. if you would talk less nonsense you would remember more sense so my grandson had disappeared in disgrace and there i sat by my wife's side endeavouring to form a retrospect of the year nineteen ninety nine and of the possibilities of the year two thousand but not quite able to shake off the thoughts suggested by the prattle of my bright little hexagon only a few sands now remained in the half-hour glass

rousing myself from my reverie, I turned the glass northward for the last time in the old millennium, and in the act I exclaimed aloud, "'The boy is a fool!' Straightway I became conscious of a presence in the room, and a chilling breath thrilled through my very being. "'He is no such thing,' cried my wife, "'and you are breaking the commandments in thus dishonouring your own grandson.' but I took no notice of her.

Looking round in every direction I could see nothing, yet still I felt a presence, and shivered as the cold whisper came again. I started up. "'What is the matter?' said my wife. "'There is no draught. What are you looking for? There is nothing.'

There was nothing, and I resumed my seat, again exclaiming, "'The boy is a fool, I say. "'Three cubed can have no meaning in geometry.' "'At once there came a distinctly audible reply. "'The boy is not a fool, "'and three-cubed has an obvious geometrical meaning.

"'My wife, as well as myself, heard the words, "'although she did not understand their meaning, "'and both of us sprang forward in the direction of the sound. "'What was our hot, when we saw before us a figure. At the first glance it appeared to be a woman seen sideways, but a moment's observation showed me that the extremities passed into dimness too rapidly to represent one of the female sex.

And I should have thought it a circle, only that it seemed to change its size in a manner impossible for a circle, or for any regular figure of which I had had experience. But my wife had not my experience, nor the coolness necessary to note these characteristics. With the usual hastiness and unreasoning jealousy of her sex, she flew at once to the conclusion that a woman had entered the house through some small aperture. "'How comes this person here?' she exclaimed. "'You promised me, my dear, that there should be no ventilators in our new house.'

"'Nor are there any,' said I. "'But what makes you think that the stranger is a woman?' "'I see by my power of sight recognition. "'Oh, I have no patience with your sight recognition,' replied she. "'Feeling is believing, and a straight line to the touch is worth a circle to the sight. "'Two proverbs very common with the frailess ex in Flatland.' "'Well,' said I, "'for I was afraid of irritating her.

"'If it must be so, demand an introduction.' Assuming her most gracious manner, my wife advanced towards the stranger. Permit me, madam, to feel and be felt by, then suddenly recoiling, Oh, it is not a woman, and there are no angles either, not a trace of one. Can it be that I have so misbehaved to a perfect circle? I am indeed, in a 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 for her own retirement had long passed, with many reiterated apologies for her recent indiscretion, she had last retreated to her apartment.

I glanced at the half-hour glass. The last sands had fallen. The second millennium had begun. Section 16. How the stranger vainly endeavoured to reveal to me in words the mysteries of spaceland. As soon as the sound of my wife's retreating footsteps 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 the house, and was now preparing to stab me with his acute angle. In a sitting-room, the absence of fog, and the season happened to be remarkably dry, made it difficult for me to trust to sight recognition, especially at the sitting-room. 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, "'emitting only some of my profuse apologies, "'for I was covered with shame and humiliation

"'that I, a square, "'should have been guilty of the impertinence of feeling a circle. "'It was commenced by the stranger, with some impatience at the lengthiness of my introductory process. "'Stranger, have you felt me enough by this time? Are you not introduced to me yet?' "'I, most illustrious, sir, excuse my awkwardness, which arises not from ignorance of the usages of polite society,

but from a little surprise and nervousness, consequent on this somewhat unexpected visit. And I beseech you to reveal my indiscretion to, to know one, and especially not to my wife. But before your lordship enters into further communications, would he deign to satisfy the curiosity of one who would gladly know whence his visitor came? Stranger, From space! From space, sir! Whence else? I, pardon me, my lord, but is not your lordship already in space? Your lordship and his humble servant even at this moment?

Stranger. What do you know of space? Define space. Aye. Space, my lord, is height and breadth, indefinitely prolonged. Stranger. Exactly.

You see, you do not even know what space is. You think it is of two dimensions only, but I have come to announce to you a third. height, breadth and length. I. Your lordship is pleased to be merry. We also speak of length and height, or breadth and thickness, thus denoting two dimensions by four names. Stranger, but I mean not only three names, but three dimensions. I. Would your lordship indicate or explain to me in what direction is?

the third dimension, unknown to me? Stranger, I came from it. It is up above and down below. I, my lord, means seemingly that it is northward and southward. Stranger, I mean nothing of the kind. I mean a direction in which you cannot look, because you have no eye in your side. I, pardon me, my lord, a moment's in inspection will convince your lordship that I have a perfect luminary at the juncture of two of my sides. Stranger, yes, but in order to see into space, you ought to have an eye not on your perimeter, but on your side. That is on what you would probably call your inside, but we in spaceland should call it your side.

I. An eye in my inside, an eye in my stomach, your lordship jests. Stranger, I am in no jesting humour. I tell you that I come from space, or, since you will not understand what space means, from the land of three dimensions. whence I but lately looked down upon your plane which you call space forsooth. From that position of advantage I discerned all that you speak of as solid, by which you mean enclosed on four sides, your houses, your churches, your very chests and safes. Yes, even your insides and stomachs, all lying open and exposed to my view. I. Such assertions are easily made, my lord. Stranger, but not easily proved, you mean, but I mean to prove mine.

When I descended here, I saw your four sons, the pentagons, each in his apartment, and your two grandsons, the hexagons. I saw your youngest hexagon remain a while with you, and then retire to his room, leaving you and your wife alone. I saw your Isosceles servants, three in number, in the kitchen at supper, and the little page in the scullery. Then I came here, and how do you think I came? I, through the roof, I suppose. Stranger, not so. Your roof, as you know very well, has been recently repaired, and has no aperture by which even a woman could penetrate.

I tell you I come from space. Are you not convinced by what I have told you of your children and household? Aye, your lordship must be aware that such facts touching the belongings of his humble servant might be easily ascertained by anyone in the neighbourhood, possessing your lordship's ample means of obtaining information. Stranger, how shall I convince him? Surely a plain statement of facts, followed by ocular demonstration, ought to suffice. Now, sir, listen to me. You are living on a plane.

What you style flatland is the vast level surface of what I may call a fluid, on or in the top of which you and your countrymen move about, without rising above it or falling below it. I am not a plain 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 13 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 limeland written upon your brain, do you not remember, I say, how when you entered the realm of realm of lineland, you are compelled to manifest yourself to the king not as a square but as a line,

because that linear realm had not dimensions enough to represent the whole of you, but only a slice or section of you? In precisely the same way, your country of two dimensions is not spacious enough to represent me, a being of three, but can only exhibit a slice or section of me, which is what you call a circle. The diminished brightness of your eye indicates incredulity, but now prepare to receive proof positive of the truth of my assertions. You cannot indeed see more than one of my sections or circles at a time, for you have no power to raise your eye out of the plain of flatland, but you can at least see that as I rise in space,

so my section becomes smaller see now i will rise and the effect upon your eye will be that my circle will become smaller and smaller till it dwindles to a point and finally vanishes reader's note the following paragraph makes reference to a diagram the diagram shows a horizontal line cutting the line there are three spheres the first or leftmost is half a bar, and half below the line, with its equator drawn at the level of the line to indicate the sphere's solid nature. Over it is written, the sphere with his section at full size. The second or central sphere is positioned about five sixths above the line and one sixth below, with a circumference drawn at the level of the line. This is labelled two, the sphere rising. the third or right-hand sphere is nearly all above the line with just a sliver below the circumference being drawn at the level of the line this is labelled three the sphere on the point of vanishing

at the right-hand end of the line there is an eye marked my eye looking towards the left end of reader's note there was no rising that i could see but he didn't know 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 a full size, then small, and at last very small indeed, approaching to a point. But to me, although I saw the facts before me, the causes were as dark as ever, all that I could comprehend was that the circle had made himself smaller and vanished, and that he had now reappeared and was rapidly making himself larger. When he had regained his original sighs, he heaved a deep sigh,

for he perceived by my silence that I had altogether failed to comprehend him. And indeed, I was now inclining to the belief that he must be no circle at all, but some extremely clever juggler, or else that the old wives' tales were true, and that after all there were such people as enchanters and magic.

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 lumines, wake. What name would you give to the wake? I. A straight line. Sphere. And a straight line has

how many extremities? I, two. Sphere. Now conceive the northward straight line, moving parallel to itself, east and west, so that every point in it leaves behind it, the wake of a straight line. What name will you give to the figure thereby formed? We will suppose that it moves through a distance equal to the original straight line. What name, I say. I, a square. Sphere. And how many sides has a square, and how many angles?

I. Four sides and four angles. Sphere. Now, stretch your imagination a little and conceive a square in flatland moving parallel to itself upward. I. What? Northward. Sphere. No, not northward, upward. Out of flatland altogether. If it moved northward, the southern point in the square would have to move through the positions previously occupied by the northern points, but that is not my meaning. I mean that every point in you, for you are a square and will serve the purpose of my illustration, every point in you, that is to say in what you call your inside, is to pass upwards through space in such a way that no way that no way. 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. "'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 upwards? I presume it is describable in the language of Flatland.' "'Sphere.' "'Oh, certainly. It is all plain and simple, and in strict accordance with analogy. Only, by the way, you must not speak of the result as being a figure, but as a solid.

But I will describe it to you, or rather not I, but analogy. We began with a single point, which, of course, being itself a point, has only one terminal point. One point produces a line with two terminal points. One line produces a square, with four terminal points. Now you can yourself give the answer to your own question. 1, 2, 4 are evidently in geometrical progression. What is the next number? I. 8.

Sphere. Exactly. The 1 square produces a something which you do not as yet know a name for, but which we call a cube, with 8 terminal points. Now are you convinced? Aye. And has this creature sides as well as angles or what you call term? terminal points?

Sphere. Of course, and all according to analogy. But, by the way, not what you call sides, but what we call sides. You would call them solids. Aye, and how many solids or sides will appertain to this being whom I am to generate by the motion of my inside in an upward direction, and whom you call a cube? Sphere. How can you ask? And you a mathematician? A 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 naught sides. A line, if I may so say, has two sides, for the points of a line may be called by courtesy its sides. A square has four sides. A square has four sides. sides, 0, 2, 4, what progression do you call that? I, arismetical.

Sphere. And what is the next number? I, 6. Sphere, exactly. Then you see, you have answered your own question. The cube which you will generate will be bounded by six sides, that is to say six of your insides. You see it all now, eh? Monster, I shrieked. Be thou juggler, enchanter, dream or devil,

no more will I endure thy mockeries. Either thou or I must perish. And saying these words, I precipitated myself upon him. Section 17. How the sphere, having in vain tried words, resorted to deeds. It was in vain. I brought my hardest right angle into violent collision with the stranger, pressing on him with a force sufficient to have destroyed any ordinary circle,

but I could feel him slowly and unarrestably slipping from my contact, not edging to the right nor to the left, but moving somehow out of the world and vanishing to nothing. Soon there was a blank, but I saw, still heard the intruder's voice. Svir, why will you refuse to listen to reason? I had hoped to finding you, as being a man of sense and an accomplished mathematician, a fit apostle for the gospel of the three dimensions, which I am allowed to preach once

only in a thousand years. But now I know not how to convince you. Stay, I have it. Deeds and not words shall proclaim the truth. Listen, my friend. I have told you I can see from my position in space the inside of all things that you consider closed. For example, I see in yonder cupboard near which you are standing several of what you call boxes, but like everything else in Flatland they have no tops nor bottoms, full of money. I also see two tablets of accounts. I'm about to descend into that cupboard and to bring you one of those tablets. I saw you lock the cupboard half an hour ago, and I know you have the key in your possession,

but I descend from space. The doors, you see, remain unmoved. Now I am in the cupboard, and am taking the tablet. Now I have it. Now I ascend with it. I rushed to the closet and dashed the door open. One of the tablets was gone. With a mocking laugh, the stranger appeared in the other corner of the room, and at the same time the tablet appeared upon the floor. I took it up. There could be no doubt it was the missing tablet.

I groaned with horror, doubting whether I was not out of my senses, but the stranger continued, Surely you must now see that my explanation and no other, suit the phenomena. What you call solid things are really superficial. What you call space is really nothing but a great plane. I am in space and look down upon the insides of the things of which you only see the outsides. You could leave this plane yourself, if you could but summon up the necessary volition. A slight upward or downward motion would enable you to see all that I can see. The higher I mount and the further I go from your plane, the more I can see, though of course I see

it on a smaller scale. For example, I am ascending. Now I can see your neighbor the hexagon and his family in their several apartments. Now I see the inside of the the theatre ten doors off, from which the audience is only just departing, and on the other side a circle in his study sitting at his books. Now I shall come back to you, and as a crowning proof, what do you say to my giving you a touch, just the least touch, in your stomach? It will not seriously injure you, and the slight pain you may suffer cannot be compared with the mental benefit you will receive? Before I could utter a word of remonstrance, I felt a shooting pain in my inside, and a demoniacal laugh seemed to issue from within me. A moment afterwards,

the sharp agony had ceased, leaving nothing but a dull ache behind, and the stranger began to reappear, saying, as he gradually increased in size, "'There, I have not hurt you much, have I?' If you are not convinced now, I don't know what will convince you. What say you? My resolution was taken. It seemed intolerable that I should endure existence subject to the arbitrary visitations of a magician who could thus play tricks with one's very stomach. If only I could in any way manage to pin him against the wall till help came.

Once more I dashed by hardest angle against him. 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 figure, and continued to shout for assistance. A convulsive shudder ran through the state. fear. 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 civilisation. Then, addressing me in a louder tone, he hurriedly

exclaimed, listen. No stranger must witness what you have witnessed. Send your wife back at once before she enters the apartment. The gospel of three dimensions must not be thus frustrated. "'Not thus must the fruits of one thousand years of waiting be thrown away. "'I hear her coming, back, back, away from me, "'or you must go with me, whither you know not, "'into the land of three dimensions.' "'Fool, madman, irregular!' I exclaimed. "'Never will I release thee.

"'Thou shalt pay the penalty of thine impostures.' "'Hah! Is it come to this?' Thundered the stranger. Then meet your fate. Out of your plane you go. Once, twice, thrice, tis done. End of Section 17, recording by Ruth Golding. Part 2, Sections 18 to 20 of Flatland.

This Librivox recording is in the public domain. Recording by Ruth Golding. Flatland, a romance of many dimensions by Edwin Abbott Abbott. Part 2, Section 18, How I Came to Space Land and What I Saw There. An unspeakable horror seized me. There was a darkness, then a dizzy, sickening sensation of sight that was not like seeing. I saw a line that was no line, space that was not space. I was myself and not myself. When I could find voice, I shrieked aloud in agony.

Either this is madness, or it is hell. It is neither, calmly replied the voice of the sphere. It is knowledge. It is three dimensions. Open your eye once again and try to look steadily. I looked, and behold, a new world. There stood before me, Visibly incorporate all that I had before inferred, conjectured, dreamed, of perfect circular beauty. What seemed the centre of the stranger's form lay open to my view.

Yet I could see no heart, nor lungs, nor arteries, only a beautiful, harmonious, something, for which I had no words. But you, my readers in Space Land, would call it the surface of the sphere. Prostrating myself mentally before my guide, I cried, How is it, oh, divine ideal of consummate loveliness and wisdom, that I see thy inside, and yet cannot discern thy heart, thy lungs, thy arteries, thy liver? What you think you see, you see not,

he replied, "'It is not given to you nor to any other being to behold my internal parts. I am of a different order of beings from those in flatland. Were I a circle, you could discern my intestines, but I am a being composed, as I told you before, of many circles, the many in the one, called in this country a sphere, and just as the outside of a cube is a square, so the outside of a sphere presents the appearance of a circle. Bewildered though I was, by my teacher's enigmatic utterance, I no longer chafed against it, but worshipped him in silent adoration. He continued with more mildness in his voice.

Distress not yourself if you cannot at first understand the deeper mysteries of spaceland. By degrees they will dawn upon you. let us begin by casting back a glance at the region whence you came return with me a while to the plains of flatland and i will show you that which you have so 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 reader's note the following paragraph refers to a detailed diagram the diagram shows the points of the compass with north at the top next to this there is a large equal side pentagon sitting on a horizontal base. Centurally placed on the lower left edge of the pentagon there is an opening labelled men's door, the size of the opening being about a quarter of the length of that edge. This door leads into a large central space labeled the hall, which is

otherwise surrounded by rooms. The position of these rooms will now be described. clockwise from the northern point the upper right edge is divided equally between two rooms labelled in order my study and my bedroom the left-hand wall of the study runs vertically down from the northern point

and the right-hand wall is parallel to the lower right edge of the pentagon the study has a door into the hall and there is an isosceles triangle inside labelled the page. Sharing a wall with the study is my rhomboid-shaped bedroom, the right-hand wall of which is the top quarter of the lower right-hand edge of the Pentagon.

It shares a wall and communicating door with the room to the south, labelled my wife's apartment. About three-tenths down the lower right edge, there is a narrow opening labelled women's door, This leads into a long, narrow room labelled my wife's apartment. This room has doorways into my bedroom above, into the hall to the left, and into the room to the south, also long and narrow,

where a straight line is marked my daughter. The only door from my daughter's room is into my wife's apartment. Continuing clockwise down the lower right edge of the page, the next room is a long and wide room with two openings into the hall. Inside are three isosceles triangles of varying acuteness. The uppermost and most acute is labelled the scullion, the next and middle-sized is labelled the footman, and the lowest and least acute is labelled the butler.

At the bottom right point of the pentagon, a large corner room is labelled the cellar and has a door into the hall. Along the left half of the bottom or southern edge, there are two small rooms, each with a door into the hall, and each with a hexagon inside, labeled my grandsons. Continuing clockwise up the left side of the Pentagon, between the men's door and the northern point, there are four small rooms.

Each of these rooms, labelled my sons, has a pentagon inside it, and a door into the hall. In the middle of the central hall is a straight line, labelled my wife. Outside the pentagon, one at each end of the bottom or southern edge, are two very acute isosceles triangles, each labelled policeman. End of reader's note. I looked below and saw with my physical eye all that domestic individuality which I had hitherto merely inferred with the understanding and how poor and shadowy was the inferred conjecture

in comparison with the reality which I now beheld. My four sons calmly asleep in the north-western rooms, my two orphan grandsons to the south, the servants, the butcherns, my daughter, all in their several apartments. Only my affectionate wife, alarmed by my continued absence, had quitted her room, and was roving up and down in the hall anxiously awaiting my return. Also the page, aroused by my cries, had left his room,

and, under pretext of ascertaining whether I had fallen somewhere in a faint, was prying into the cabinet in my study. All this I could now see, not merely infer. And as we came nearer and nearer, I could discern even the contents of my cabinet, and the two chests of gold, and the tablets of which the sphere had made mention. Touched by my wife's distress,

I would have sprung downward to reassure her, but I found myself incapable of motion. Trouble not yourself about your wife. said my guide. She will not be long left in anxiety. Meantime, let us take a survey of flatland. Once more I felt myself rising through space. It was even as the sphere had said.

The further we receded from the object we beheld, the larger became the field of vision. My native city, with the interior of every house and every creature therein, lay open to my view, miniature. We mounted higher, and lo, the secrets of the earth, the depths of mines and and inmost caverns of the hills were bared before me. Orr struck 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 as you see now. But trust me, your wise men are wrong. I. Then is omnividence the attribute of others beside gods?

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? Aye, 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,

insofar 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 space-lands think more of the affections than of the understanding, more of your despised straight lines than of your belawed 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 recognised the General Assembly Hall of the states of Flatland, surrounded by dense lines of pentagonal buildings at right-angled 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 mourning the first hour of the first day of the 2000th year of our era. Acting, as was there won't, in strict accordance with Precedent, the highest circles of the realm were meeting in solemn conclave, as they had met on the first hour of the first day of the year 1000, and also on the first hour of the first day of the year nought. The minutes of the previous meetings were now read by one whom I at at once recognised as my brother, a perfectly symmetrical square, and the chief clerk of the High Council. It was found recorded on each occasion that, whereas the states had been troubled by divers ill-intentioned persons pretending to have received revelations from another world,

and professing to produce demonstrations whereby they had instigated to frenzy both themselves and others, it had been for this cause unanimously resolved by the Grand Council that on the first day of each millennary, 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 anyone 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 me thinks 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 leapt with great dexterity into the sea, if I may say call it, of flatland right in the midst of the ring of councillors. I come, cried he, to proclaim that there is a land of three dimensions. I could see many of the younger councillors start back in manifest horror as the sphere's circular section widened before them. But on a sign from the presiding circle, who showed not the slightest alarm or surprise,

six isosceles of a lone type from six different, quarters rushed upon the sphere. We have him, they cried. No, yes, we have him still. He's going. He's gone. My lords, said the president to the junior circles of the council,

there is not the slightest need for surprise. The secret archives to which I alone have access tell me that a similar occurrence happened on the last two millennial commencements. You will, of course, say nothing of these trifles outside the cabinet. Raising his voice, he now summoned the guard. Arrest the policeman, gag them, you know your duty. After he had consigned to their fate, the wretched policeman,

ill-fated and unwilling witnesses of a state secret which they were not to be permitted to reveal, he again addressed the counsellors. "'My lords, the business of the council being concluded, "'I have only to wish you a happy new year.' "'Before departing, he expressed at some length to the clerk, "'my excellent but most unfortunate brother, "'his sincere regret that, in accordance with precedent, "'and for the sake of secrecy,

"'he must condemn him to perpetual imprisonment, "'but added his satisfaction that, "'unless some mention were made by him of that day, incident, his life would be spared. Section 19. How, though the sphere, showed me other mysteries of spaceland, I still desired more, and what came of it. When I saw my poor brother led away to imprisonment, I attempted to leap down into the council chamber, desiring to intercede on his behalf, or at least bid him farewell. But I found that I had no motion of my own. I absolutely depended on the volition of my guide, who said in gloomy tones,

heed not thy brother. Happily thou shalt have ample time hereafter to condole with him. Follow me. Reader's note, the following paragraph makes reference to a diagram. Diagram 1 shows a three-dimensional cube, with visible edges drawn and hidden edges dotted, giving it a three-dimensional appearance. Horizontal shading makes it appear that the cube is made up of many layers. Diagram 2 shows the same figure, but all lines indicating perspective are missing, with the effect that it no longer appears to be solid, but looks like a two-dimensional irregular hexagonal figure.

End of reader's note. Once more, we are saying, send it into space. Hitherto, said the sphere, I have shown you naught save plain 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 movable square cards. See, I put one on another, not as you supposed northward of the other, but on the other. Now a second, now a third.

see i am building up a solid by a multitude of squares parallel to one another now the solid is complete being as high as it is long and broad and we call it a cube "'Pardon me, my lord,' replied I. "'But to my eye the appearance is as of an irregular figure "'whose inside is laid open to the view. "'In other words, methinks I see no solid, "'but a plane such as we infer in flatland, "'only of an irregularity which betokens some monstrous criminal "'so that the very sight of it is painful to my eyes.'

"'True,' said the sphere, "'it appears to you. a plane, because you are not accustomed to light and shade and perspective. Just as in flatland, a hexagon would appear a straight line to one who has not the art of sight recognition. But in reality it is a solid, as you shall learn by the sense of feeling. He then introduced me to the cube, and I found that this marvellous being was indeed no plane but a solid, and that he was endowed with six plain 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 rejoice to think that so insignificant a creature as I could in some sense be called the progenitor of so illustrious an offspring. but still i could not fully understand the meaning of what my teacher had told me concerning light and shade and perspective and i did not hesitate to put my difficulties before him were i to give the sphere's explanation of these matters succinct and clear though it was it would be tedious to an inhabitant of space who knows these things already Suffice it that by his lucid statements, and by changing the position of objects and lights, and by allowing me to feel the several objects, and even his own sacred person, he at last made all things clear to me, so that I could now readily distinguish between a circle and a sphere,

a plain figure, and a solid. This was the climax, the paradise of my soul. 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 plain 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 confirmation of all regular solids cylinders cones pyramids pentahedrons hexahedrons dodecahedrons and spheres, but I ventured to interrupt him. Not that I was wearied of knowledge, on the contrary, I thirsted for yet deeper and fuller drafts than he was offering to me.

Pardon me, said I, O thou whom I must no longer address as the perfection of all beauty, but let me beg thee to vouchsafe thy servant a sight of thine interior. Sphere. My what? I. Thine interior, thy stomach, thy intestines. Sphere, whence this ill-timed, impertinent request! And what mean you by saying that I am no longer the perfection of all beauty? I, my lord, your own wisdom has taught me to aspire to one even more great, more beautiful,

and more closely approximate to perfection than yourself. As you yourself, superior to all flatland forms, combine many circles in one, so doubtless there is one above you who combines many spheres in one supreme existence, surpassing even the solids of spaceland. And even as we, who are now in space, look down on flatland and see the inside,

of all things, so of a certainty there is yet above us some higher, purer region, whither thou dost surely purpose to lead me, O thou whom I shall always call everywhere and in all dimensions, my priest, philosopher, and friend, some yet more spacious space, some more dimensionable dimensionality, from the vantage ground of which we shall look down together upon the revealed insides of solid things, and where thine own intestines and those of thy kindred spheres will lie exposed to the view of the poor wandering exile from flatland, to whom so much has already been vouchsafed. Sphere.

Foof! 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 countryman 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 unimensible 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 show you what you wish if I could, but I cannot.

Would you have me turn my stomach inside out to oblige you? Aye, but my lord has shown me the intestines of all my countrymen in the land of two dimensions by taking me with him into the land of three. What's therefore more easy than now to take his servant on a second journey, into the blessed region of the fourth dimension, where I shall look down with him once more upon this land of three dimensions and see the inside of every three-dimensioned house, the secrets of the solid earth,

the treasures of the mines in spaceland, and the intestines of every solid living creature, even of the noble and adorable spheres. Sphere. But where is this land of four dimensions? I, I know not, but doubtless my teacher knows. Sphere, not I, there is no such land, the very idea of it is utterly inconceivable. I, 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 have no eye in our stomachs. But just as there was the realm of Flapland, 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.

touch it, no eye in my interior to discern it, so of a surety there is a fourth dimension, which my lord perceives with the inner eye of thought. And that it must exist, my lord himself has taught me, or can he have forgotten what he himself imparted to his servant. In one dimension did not a moving point produce a line with two terminal points? In two dimensions did not a moving line produce a square with four terminal points? In three dimensions did not a moving square produce? Did not this eye of mine behold it? that blessed being a cube with eight terminal points. And in four dimensions shall not a moving cube,

alas for analogy and alas for the progress of truth if it be not so, shall not, I say, the motion of a divine cube result in a still more divine organisation, with sixteen terminal points? behold the infallible confirmation of the series two four eight sixteen is not this a geometrical progression is not this if i might quote my lord's own words strictly according to analogy again was i not taught by my lord that as in a line there are two bounding points and in a square there are four bounding lines so in a cube there must be six bounding squares behold once more the confirming series two four six 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 eight

bounding cubes. And is not this also, as my lord has taught me to believe strictly according to analogy? Oh, 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 the fourth dimension, but if I am right, my lord will listen to reason. I ask, therefore, is it, or is it not the fact, that ere now, your countrymen also have witnessed the descent of beings of a higher order than their own, entering closed rooms, even as your lordship entered mine, without the opening of doors or windows, and appearing and vanishing at will.

On the reply to this question, I am ready to stake everything. Deny it, and I am henceforth silent. Only that safe an answer! Sphere, after a pause, it is reported so. but men are divided in opinion as to the facts, and even granting the facts they explain them in different ways, and in any case, however great may be the number of different explanations, no one has adopted or suggested the theory of a fourth dimension.

Therefore pray have done with this trifling, and let us return to business. I, I was certain of it! I was certain that my anticipations would be fulfilled, and now have patience with me, and answer me yet one more question, best of teachers. Those who have thus appeared, no one knows whence, and have returned, no one knows whither, have they also contracted their sections, and vanished somehow into that more spacious space, whether I now entreat you to conduct me? Moodily. They have vanished, certainly, if they ever appeared. But most people say that these visions arose from the thought. You will not understand me. From the brain, from the perturbed angularity of the seer. I say they so? Oh, believe them not, or if it indeed be so that this other space is really thought land, then take me to. to that blessed region, where I in thought shall see the insides of all solid things. There, before my ravished eye, a cube, moving in some altogether new direction, but strictly according to analogy, so as to make every particle of his interior pass through a new kind

of space with a wake of its own, shall create a still more perfect perfection than himself, with sixteen terminal extra solid angles and eight solid cubes for his perimeter. And once there shall we stay our upward course? In that blessed region of four dimensions, shall we linger on the threshold of the fifth and not enter therein? Ah, no! Let us rather resolve that our ambition shall soar with our corporal assent. Then, yielding to our intellectual onset, the gates of the sixth dimension shall fly open. After that a seventh, and then an eighth!

How long I should have continued, I know not. In vain did the sphere in his voice of thunder reiterate his commands of silence, and threaten me with the direst penalties if I persisted. Nothing could stem the flood of my ecstatic aspirational. Perhaps I was to blame, but indeed I was intoxicated with the recent drafts 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 returned to Flatland was my doom. One glimpse, one last, and never to be forgotten glimpse I had of that dull level wilderness, which was now to become my universe again, spread out before my eye. Then a darkness.

Then a final, all-consumating thunder-peel, and when i came to myself i was once more a common creeping square in my study at home listening to the peace-cry of my approaching wife section twenty how the sphere encouraged me in a vision although i had less than a minute for reflection i felt by a kind of instinct that i must conceal my experiences from my wife not that i apprehended at the moment any danger from her divulging my secret but i knew that to any woman in flatland the narrative of my adventures must needs be unintelligible so I endeavoured to reassure her by some story, invented for the occasion, that I had accidentally fallen through the trap-door of the cellar, and had there lain stunned. The southward attraction in our country is so slight

that even to a woman my tale necessarily appeared extraordinary and well-nigh incredible. But my wife, whose good sense far exceeds that of the average of her sex, and who perceived that I was unusually excited, did not argue with me on the subject, but insisted that I was ill and required repose. I was glad of an excuse for retiring to my chamber to think quietly over what had happened. When I was at last by myself, a drowsy sensation fell on me. But before my eyes closed, I endeavoured to reproduce the third dimension, and especially the process by which a cube is constructed through the motion of a square.

It was not so clear as I could have wished, but I remembered that it must be upward and yet not northward, and I determined steadfastly to retain these words as the clue, which, if firmly grasped, could not fail to guide me to the solution. So, mechanically repeating like a charm, the words, Upward, yet not northward, I fell into a sound, refreshing sleep. During my slumber I had a dream. I thought I was once more by the side of the sphere,

whose lustrous hue betokened that he had exchanged his wrath against me for perfect placability. We were moving together towards a bright but infinitesimally small point, to which my master directed my attention. As we approached, me sought there issued from it a slight humming noise, as from one of your spaceland blue bottles, only less resonant by far, so slight indeed that even in the perfect stillness of the vacuum through which we sawed, the sound reached not our ears till we checked our flight at a distance from it of something under twenty human diagonals.

look yonder said my guide in flat land 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 depths of existence even to the realm of point land the abyss of no dimensions behold yon miserable creature that point is a being like ourselves but confined to the non-dimensional gulf he is himself his own world his own universe of any other than himself he can form no conception he knows not length nor breadth nor height for he has had no experience of them he has no cognizance even though cognizance even though he has no cognizance even of the number two, nor has he a thought of plurality, for he is himself his one and all, being really nothing. Yet mark his perfect self-contentment, and hence learn this lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy. Now listen.

He ceased, and there arose from the little buzzing creature, a tiny, low, monotonous, but distinct tinkling, as from one of your space-land phonographs, from which I caught these words. Infinite beatitude of existence. It is, and there is none else beside it. What, said I, does the puny creature mean by it? he means himself said the sphere have you not noticed before now that babies and babyish people who cannot distinguish themselves from the world speak of themselves in the third person but hush

it fills all space continued the little soliloquising creature and what it feels it is what it thinks that it utters and what it utters that it hears and it itself is thinker utterer hearer thought word audition it is the one and yet the all in all ah the happiness are the happiness of being can you not startle the little thing out of its complacency said i tell it what it really is as you told me reveal to it the narrow limitations of pointland, and lead it up to something higher. That is no easy task, said my master, try you. Hereon, raising my voice to the uttermost, I addressed the point as follows. Silence, silence, contemptible creature. You call yourself the all in all, but you are the nothing.

Your so-called universe is a mere. a mere speck in a line, and a line is a mere shadow as compared with, hush, hush, you have said enough, interrupted the sphere. Now listen, and mark the effect of your harangue on the king of Pointland. The lustre of the monarch, who beamed more brightly than ever upon hearing my words, showed clearly that he retained his complacency, and I had hardly ceased when he took up his strain again. Are the joy, are the joy of thought. What can it not achieve by thinking? Its own thought coming to itself, suggestive of its disparagement thereby to enhance its happiness. Sweet rebellion stirred up to result in triumph. Ah, the divine creative power of the all in one.

Ah, the joy, the joy of being. You see, said my teacher, how little your words have done? So far as the monarch understands them at all, he accepts them as his own, for he cannot conceive of any other except himself, and plumes himself upon the variety of its thought as an instance of creative power. Let us leave this God of Pointland

to the ignorant fruition of his omnipresence and omniscience. Nothing that you or I can do can rescue him from his self-satisfaction. After this, as we floated gently back to Flatland, I could hear the mild voice of my companion pointing the moral of my vision, and stimulating me to aspire, and to teach others to aspire. He had been angered at first he confessed by my ambition to sort

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, showing me how to construct extra solids by the motion of solids and double extra solids by the motion of extra solids and all strictly according to analogy. All by methods so simple, so easy, as to be patent even to the female sex.

End of Section 20, recording by Ruth Golding. Part 2, Sections 20. 21 and 22 of Flatland. This Librivox recording is in the public domain, recording by Ruth Golding. Flatland, a romance of many dimensions by Edwin Abbott, Abbott. Section 21, how I tried to teach the theory of three dimensions to my grandson,

and with what success. I awoke rejoicing and began to reflect on the glorious career before me. I would go forth, me thought, at once, and evangelise the whole of Flatland. Even to women and soldiers should the gospel of three dimensions be proclaimed, I would begin with my wife. Just as I had decided on the plan of my operations, I heard the sound of many voices in the street, commanding silence. Then followed a louder voice. It was a herald's proclamation. Listening attentively, I recognised the words of the resolution of the Council,

enjoining the arrest, imprisonment or execution of anyone who should pervert the minds of the people by delusions and by professing to have received revelations from another world. I reflected, This danger was not to be trifled with. It would be better to avoid it by omitting all mention of my revelation and by proceeding on the path of demonstration, which, after all, seemed so simple and so conclusive that nothing would be lost by discarding the former means. Upward, not northward, was the clue to the whole proof. It had seemed to me fairly clear before I fell asleep, and when I first awoke, fresh from my first awoke, fresh from my first, 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 interchanged a few words of commonplace conversation, not to begin with her. My pentagonal sons were men of character and standing and physicians of no mean reputation, but not great in mathematics, and in that respect unfit for my purpose. But it occurred to me that a young and docile hexagon with a mathematical turn would be a most suitable pupil. Why, therefore, not make my first experiment with my little pretext. cautious grandson, whose casual remarks on the meaning of three-cubed had met with the approval of the sphere.

Discussing the matter with him, a mere boy, I should be in perfect safety, for he would know nothing of the proclamation of the council, whereas I could not feel sure that my sons, so greatly did their patriotism and reverence for the circles predominate over mere blind affection, might not feel compelled to hand me over to the prefect if they found me seriously maintaining the seditious heresy of the third dimension. But the first thing to be done was to satisfy in some way the curiosity of my wife, who naturally wished to know something of the reasons for which the circle had desired that mysterious interview, and of the means by which he had entered our 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 space-land 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 I had seen and heard was, in some strange way, slipping away from me, like the image of a half-grasped, tantalizing dream, and I longed to essay my skill in making a first disciple. When my grandson entered the room, I carefully secured the door, then, sitting down by his side and taking our mathematical tablets, or as you would call them, lines, I told him

we would resume the lesson of yesterday. I taught him once more how a point by motion in one dimension produces a line, and how a straight line in two dimensions produces a square. After this, forcing a laugh, I said, and now you scamp, you wanted to make me believe that you 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 heralds, Oh yes, oh 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 Northwood, "'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! Not at all silly, said I, losing my temper. Here, for example, I take this square, and at the word I grasped a movable square

which was lying at hand. And I move it, you see, not northward, but, yes, I move it upward. That is to say, not northward, but I move it somewhere, not exactly like this, but somehow, Here I brought my sentence to an inane conclusion, shaking the square about in a purposeless manner, much to the amusement of my grandson, who burst out laughing louder than ever, and declared that I was not teaching him, but joking with him.

And so saying, he unlocked the door and ran out of the room. Thus ended my first attempt to convert a pupil to the gospel of three-dimension. Section 22 How I then tried to diffuse the theory of three dimensions by other means and of the result. My failure with my grandson did not encourage me to communicate my secret to others of my household. Yet neither was I led by it to despair of success. Only I saw that I must not wholly rely on the 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 how much, hampered by the impossibility of drawing such diagrams as were necessary for my purpose.

For, of course, in our country of Flatland, there are no tablets but lines, and no diagrams but lines, all in one straight line, and only distinguishable by difference of size and brightness. So that when I had finished my treatise, which I entitled, Through Flatland to Thoughtland, I could not feel certain that many would understand my meaning. Meanwhile my life was under a cloud. All pleasures palled upon me. All sights tantalised 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 realised 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 have could not convince my grandson, how could I convince the highest and most developed circles in the land? And yet, at times, my spirit was too strong for me, and I gave vent to dangerous utterances. Already I was considered heterodox, if not treasonable, and I was keenly alive to the dangers of my position. Nevertheless, I could not at times refrain from bursting out into suspicious or half-seditious utterances, even among the highest polygonal and circular society. When, for example, the question arose about the treatment of those lunatics

who said that they had received the power of seeing the insides of things, I would quote the saying of an ancient circle, who declared that prophets and inspired people are always considered by the majority to be mad, and I could not help occasionally dropping such expressions as the eye that discerns the interiors of things, and the all-seeing land. Once or twice, I even let fall the forbidden terms, the third and fourth dimensions.

At last, to complete a series of minor indiscretions, at a meeting of our local speculative society, held at the palace of the prefect himself some extremely silly person having read an elaborate paper exhibiting the precise reasons why providence has limited the number of dimensions to two and why the attribute of omnividence is assigned to the supreme alone i so far forgot myself as to give an exact account of the whole of my voyage with the sphere into space and to the assembly hall in our metropolis and then to space again and of my return home, and of everything that I had seen and heard in fact or vision. At first, indeed, I pretended that I was describing the imaginary experiences of a fictitious person, but my enthusiasm soon forced me to throw off all disguise, and finally, in a fervent peroration, I exhorted all my heroes to divest themselves of prejudice, and to become

believers in the third dimension. Need I say that I was at once arrested and taken before the council? Next morning, standing in the very place where but a very few months ago the sphere had stood in my company, I was allowed to begin and to continue my narration unquestioned and uninterrupted. But from the first I foresaw my fate. For the President, noting that a guard of the better sort of, 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 two or three degrees. I knew only too well what that meant. I was to be executed or imprisoned, and my story was to be kept secret from the world by the simultaneous destruction of the officials who had heard it. And this being the case, the President desired to substitute the cheaper for the more expensive victims. After I had concluded my defence, the President, perhaps perceiving that some of the junior circles had been moved by my evident earnestness, asked me two questions. One, whether I could indicate the direction which I meant when I used the words upward, not northward.

2. Whether I could, by any diagrams or descriptions, other than the enumeration of imaginary sides and angles, indicate the figure I was pleased to call a cube. I declared that I could say nothing more, and that I must commit myself to the truth, whose cause would surely prevail in the end. The President replied that he quite concurred in my sense, 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 evangelise 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 accept 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 must confess that my weekly interviews, at least in one respect, cause me the bitterest pain. He was present when the sphere manifested himself in the council chamber. He saw the sphere's changing sections. He heard the explanation of the phenomena then given to the circles. Since that time, scarcely a week has passed during seven whole years, without his hearing from me a repetition. of the part I played in that manifestation, together with ample descriptions of all the phenomena in spaceland, and the arguments for the existence of solid things, derivable from analogy.

Yet, I take shame to be forced to confess it. My brother has not yet grasped the nature of the third dimension, and frankly avows his disbelief in the existence of a sphere. Hence I am absolutely destitute of converts, and, for aught that I can see, the millennial revelation has been made to me for nothing. Prometheus up in space-land was bound for bringing down fire for mortals, but I, poor flatland Prometheus, lie here in prison for bringing down nothing to my countrymen. Yet I exist in the hope that these memoirs in some manner, I know not how, may find their way to the minds of humanity in some dimension, and may stir up a race of rebels who shall refuse to be confined to limited dimensionality. That is the hope of my brighter moments.

Alas, it is not always so. Heverly weighs on me. at times the burdensome reflection that I cannot honestly say I am confident as to the exact shape of the once seen oft-regreted cube. And in my nightly visions the mysterious precept, Upward, not northward, haunts me, like a soul-devouring sphinx. It is part of the martyrdom which I endure for the cause of the truth that there are seasons of mental weakness, when cubes and spheres flit away into the background of scarce possible existences, when the land of three dimensions seems almost as visionary as the land of one or none. Nay, when even this hard wall that bars me from my freedom, these very tablets on which I am writing,

and all the substantial realities of flatland itself, appear nobody. better than the offspring of a diseased imagination, or the baseless fabric of a dream. The End of Flatland, a Romance of Many Dimensions, by Edwin Abbott Abbott.