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 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.

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.

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 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 sub-lustrous, and, indeed, almost as dim as an inanimate object⁠—her hinder extremity serves her as a kind of Invisible Cap.

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.

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.

So my grandson had disappeared in disgrace; and there I sat by my wife’s side, endeavouring to form a retrospect of the year 1999 and of the possibilities of the year 2000, but not quite able to shake off the thoughts suggested by the prattle of my bright little Hexagon. Only a few sands now remained in the 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; 3³ can have no meaning in geometry.” At once there came a distinctly audible reply, “The boy is not a fool; and 3³ has an obvious Geometrical meaning.”