------------ top of page -------------- FLATLAND. --------- PART I. THIS WORLD. sect 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 that it is impossi-| |ble 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. Noth-| |ing 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 Flatlander) the penny will then have ceased to ap-| |pear 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 on the table,| |you will find that it ceases to appear to you a figure, and that| |it becomes in appearance a straight line. Take for ex- | |ample an equilateral Triangle -- who represents with | |us a Tradesman of the respectable class. Fig. 1 rep- | |resents the Tradesman as you would see him while you | |were bending over him from above; figs. 2 and 3 rep- | |resent the Tradesman, as you would see him if your eye | |were close to the level, or all but on the level of | |the table; and if your eye were quite on the level of | |the table (and that is how we see him in Flatland) you | |would see nothing but a straight line. | | When I was in Spaceland I heard that your sailors | |have very similar experiences while they traverse your | |seas and discern some distant island or coast lying on | |the horizon. The far-off land may have bays, forelands, | |angles in and out to any number and extent; yet at a | |distance you see none of these (unless indeed your sun | |shines bright upon them revealing the projections and | |retirements by means of light and shade), nothing but a grey unbro-| |ken line upon the water. | | Well, that is just what we see when one of our triangular or other| |acquaintances comes toward us in Flatland. As there is neither sun| ------------ bottom of page ----------- ------------ top of page -------------- |with us, nor any light of such a kind as to make shadows, we have| |none of the helps to the sight that you have in Spaceland. If our| |friend comes closer to us we see his line becomes larger; if he leaves| |us it becomes smaller: but still he looks like a straight line; be| |he a Triangle, Square, Pentagon, 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 sub-| |ject, and say a word or two about the climate and houses in our coun-| |try. | sect 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 attrac-| |tion to the South; and, although in temperate climates this is very| |slight -- so that even a Woman in reasonable health can journey sev-| |eral 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. | |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 attrac-| |tion to the South; and, although in temperate climates this is very| |slight -- so that even a Woman in reasonable health can journey sev-| |eral 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. | | Windows there are none in our houses: for the light comes to us| |alike in our homes and out of them, by day and by night, equally| |at all times and in all places, whence we know not. It was in old| |days, with our learned men, an interesting and oft-investigated ques-| |tion, "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| ------------ bottom of page ----------- ------------ top of page -------------- |these painful digressions: let me return to our houses. | | The most common form for the construction of a house is five-sided| |or pentagonal, as in the annexed figure. The two Northern sides RO,| |OF, constitute the roof, and for the most part have no doors; on the| |East is a small door for the Women; on the West a much larger one| |for the Men; the South side or floor is usually doorless. | | Square and triangular houses are not allowed, and for this reason.| |The angles of a Square (and still more those of an equilateral Tri-| |angle,) 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 therefore, running against them: and as early as the eleventh| |century of our era, triangular houses were universally forbidden by| |Law, the only exceptions being fortifications, powder-magazines, bar-| |racks, and other state buildings, which it is not desirable that the| |general public should approach without circumspection. | | At this period, square houses were still ev- | |erywhere permitted, though discouraged by a | |special tax. But, about three centuries after- | |wards, the Law decided that in all towns con- | |taining 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 ev- | |ery other. It is only now and then in some | |very remote and backward agricultural district that an antiquarian may| |still discover a square house. | ------------ bottom of page -----------