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 recognize 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 temperate climates that Sight Recognition is practised.

That this power exists in any regions and for any classes, is the result of Fog; which prevails during the greater part of the year in all parts save the torrid zones. That which is with you in Spaceland an unmixed evil, blotting out the landscape, depressing the spirits, and enfeebling the health, is by us recognized as a blessing scarcely inferior to air itself, and as the Nurse of arts and Parent of sciences. But let me explain my meaning, without further eulogies on this beneficent Element.

I awoke rejoicing, and began to reflect on the glorious career before me. I would go forth, me thought, at once, and evangelize 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 recognized the words of the Resolution of the Council, enjoining the arrest, imprisonment, or execution of any one who should pervert the minds of the people by delusions, and by professing to have received 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 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.

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 formy part noticed by the sense of sight, before I entered your Kingdom, that some of your people are Lines and others Points, and that some of the Lines are larger—” “You speak of an impossibility,” interrupted the King; “you must have seen a vision; for to detect the difference between a Line and a Point by the sense of sight is, as every one knows, in the nature of things, impossible; but it can be detected by the sense of hearing, and by the same means my shape can be exactly ascertained. Behold me – I am a Line, the longest in Lineland, over six inches of Space – “Of Length,” I ventured to suggest. “Fool,” said he, “Space 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.”

Edwin Abbott Abbott's Flatland is the story of a two-dimensional universe as told by one of its inhabitants, a square who is introduced to the mysteries of three-dimensional space by a sphere. Since the time of its publication in 1884, Victorian customs have become obscure, the meanings of words have changed, and historical allusions, which were obvious to a contemporary, now require explanation. The present edition is intended to enable a modern-day reader to understand and appreciate the “many dimensions” of this classic satire. The extensive annotations to the text include mathematical notes and illustrations, which enhance the usefulness of Flatland as an elementary introduction to higher-dimensional geometry; historical notes, which show connections to late-Victorian England and to classical Greece; citations from Abbott's other writings and the works of Plato and Aristotle, which serve to interpret the text; commentary on close parallels between Flatland and Plato's “parable of the cave”; notes on the language and literary style of the book, including definitions of obscure words; and an appendix, which gives a comprehensive account of Abbott's life and work.

A Romance of many dimensions.

The word “romance” in Flatland's subtitle means a prose narrative that treats imaginary characters involved in events quite different in time and place from those of ordinary life. The two-dimensional world of Flatland, inhabited by geometric figures, is manifestly different from that of ordinary life; nonetheless, a great majority of its early readers were well acquainted with the “physical space” of Flatland.

Abbott chronology

There is no full-scale biography of the author of Flatland, Edwin Abbott Abbott. The entry for Abbott in the Dictionary of National Biography, written by his student Lewis Farnell and revised by Rosemary Jann, supplies a valuable outline of his life. A. E. Douglas-Smith, who had access to Abbott's weekly letters to Howard Candler as well the autobiographical, “Confessions of a rationalist Christian” (both now lost), gives a good account of Abbott as headmaster in Douglas-Smith (1965). Former students have given compelling testimony to his greatness as a teacher (see Conway (1926); Farnell (1926); Steggall (1926)). Abbott expounds his liberal theology in several popular works, for example, Philochristus, The Kernel and the Husk, and Through Nature to Christ. William Sanday provides an overview of Abbott's prodigious biblical scholarship in his reviews of Abbott's books in The Times Literary Supplement. A biographical sketch of even modest length is beyond our scope; instead we offer this chronology, which provides a framework of Abbott's life and work.

1838. Edwin Abbott Abbott is born in London on December 20. He was the fifth child and oldest son of Edwin Abbott (1808–1882) and Jane Abbott Abbott (1806–1882), who were first cousins. His father was “a most efficient and popular” headmaster of the Philological School, Marylebone, for forty-five years. He was one of the first to advocate a more thorough English training in the schools.

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

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 still I heard the Intruder's voice.

Sphere. Why will you refuse to listen to reason? I had hoped to find in you – as being a man of sense and an accomplished mathematician – a fit apostle for the Gospel of the Three Dimensions, which I am allowed to preach once only in a thousand years: but now I know not how to convince you. Stay, I have it. Deeds, and 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 see also two tablets of accounts. I am about to descend into that cupboard and to bring you one of those tablets. I saw you lock the cupboard half an hour ago, and I know you have the key in your possession.

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 twenty-three 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 Tradesman whose shop he had plundered – painted himself, or caused himself to be painted (for the story varies) with the twelve colours of a Dodecagon.

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

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

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

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