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01 - Flatland- A Romance of Many Dimensions - Edwin Abbott Abbott · Science Fiction Books - Daily

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Part one. Sections one to three flat Land are Romance of Many Dimensions by
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Edwin Abbot. Abbot to the inhabitants of space in general and hc. In
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particular. This work is dedicated by a humble native of Flatland, in the
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hope that, even as he was initiated into the mysteries of three dimensions,
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having been previously conversant with only two, so the citizens of that celestial region
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may aspire yet higher and higher to the secrets of four, five, or
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even six dimensions, thereby contributing to the enlargement of the imagination and the possible
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development of that most rare and excellent gift of modesty among the superior races of
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solid humanity. Part one. This world, be patient, for the world
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is broad and wide. Section one of the nature of Flatland. I call
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our world flatland, not because we call it so, but to make its
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nature clearer to you, my happy readers, who are privileged to live in
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space. Imagine a vast sheet of paper on which straight lines, triangles,
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squares, pentagons, hexagons, and other figures, instead of remaining fixed in
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their places, move freely about on or in the surface, but without the
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power of rising above or sinking below it, very much like shadows, only
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hard and with luminous edges. And you will then have a pretty correct notion
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of my country and countrymen, alas a few years ago I should have said
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my universe. But now my mind has been opened to higher views of things.
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In such a country, you will perceive at once that it is impossible
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that there should be anything of what you call a solid kind. But I
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dare say you will suppose that we could at least distinguish by sight the triangles,
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squares, and other figures moving about as I have described them. On
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the contrary, we could see nothing of the kind, not at least so
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as to distinguish one figure from another. Nothing was visible, nor could be
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visible to us, except straight lines. And the necessity of this I will
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speedily demonstrate. Place a penny on the middle of one of your tables in
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space, and leaning over it, look down upon it. It will appear
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a circle. But now drawing back to the edge of the table, gradually
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lower your eye, thus bringing yourself more and more into the condition of the
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inhabitance of flat land, and you will find the penny becoming more and more
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oval to your view. And at last, when you have placed your eye
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exactly on the edge of the table, so that you are, as it
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were, actually a flatland citizen. The penny will then have ceased to appear
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oval at all, and will have become so far as you can see,
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a straight line. The same thing would happen if you were to treat in
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the same way a triangle or square, or any other figure cut out of
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pasteboard. As soon as you look at it with your eye on the edge
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of the table, you will find that it ceases to appear to you a
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figure, and that it becomes in appearance a straight line. Take, for
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example, an equilateral triangle who represents with us a tradesman of the respectable class.
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Figure one represents the tradesman as you would see him while you were bending
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over him from above. Reader's note. Figure one is a downward pointing triangle
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with all sides equal. End of reader's note. Figures two and three represent
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the tradesman as you would see him if your eye were close to the level
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or all but on the level of the table. Reader's note. Fig.
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Two shares a much flatter downward pointing triangle, with the top edge much longer
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than the other two sides which are of equal length. Fig. Three is
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flatter, still barely identifiable as a triangle at all end of reader's note.
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And if your eye were quite on the level of the table, and that
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is how we see him in flat land, you would see nothing but a
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straight line. When I was in Spaceland, I heard that your sailors have
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very similar experiences while they traverse your seas and discerned some distant island or coast
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lying on the horizon. The far off land may have bays, fallands,
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angles in and out to any number and extent. Yet at a distance you
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see none of these, unless indeed your sun shines bright upon them, revealing
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the projections and retirements. By means of light and shade. Nothing but a
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gray, unbroken line upon the water. Well, that is just what we
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see when one of our triangular or other acquaintances comes towards us in flatland.
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As there is neither sun with us, nor any light of such a kind
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as to make shadows, we have none of the helps to the sight that
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you have in Spaceland. If our friend comes close to us, we see
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his line becomes larger. If he leaves us it becomes smaller, But still
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he looks like a straight line. Be he a triangle, square, pentagon,
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hexagon, circle? What you will a straight line he looks, and
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nothing else. You may perhaps ask, how, under these disadvantageous circumstances we
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are able to distinguish our friends from one another. But the answer to this
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very natural question will be more fitly and easily given when I come to describe
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the inhabitants of flatland. For the present, let me defer this subject and
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say a word or two about the climate and houses in our country. Section
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two of the Climate and houses in Flatland. As with you, so also
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with us. There are four points of the compass north, south, east,
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and west. There being no sun nor other heavenly bodies, it is
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impossible for us to determine the north in the usual way, but we have
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a method of our own, by a law of nature. With us there
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is a constant attraction to the south, and although in temperate climates, this
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is very slight, so that even a woman in reasonable health can journey several
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furlongs northward without much difficulty. Yet the hampering effect of the southward attraction is
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quite sufficient to serve as a compass in most parts of our earth. Moreover,
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the rain which falls at stated intervals, coming always from the north,
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is an additional assistance. And in the towns we have the guidance of the
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houses, which of course have their side walls running for the most part north
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and south, so that the roofs may keep off the rain from the north.
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In the country where there are no houses, the trunks of the trees
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serve as some sort of guide. Altogether, we have not so much difficulty
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as might be expected in determining our bearings in our more temperate regions, in
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which the southward attraction is hardly felt. Walking sometimes in a perfectly desolate plain,
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where there have been no houses nor trees to guide me, I have
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been occasionally compelled to remain stationary for hours together, waiting till the rain came,
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before continuing my journey. On the week and aged, and especially on
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delicate females, the force of attraction tells much more heavily than on the robust
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of the male sex, so that it is a point of breeding. If
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you meet a lady in the street, always to give her the north side
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of the way, by no means an easy thing to do, always at
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short notice, when you are in rude health, and in a climate where
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it is difficult to tell your north from your south windows, there are none
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in our houses. For the light comes to us alike, in our homes
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and out of them, by day and by night, equally at all times
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and in all places. Whence we know not. It was in old days
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with our learned men, an interesting and oft investigated question, what is the
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origin of light? And the solution of it? Has been repeatedly attempted,
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with no other result than to crowd our lunatic asylums with the would be solvers.
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Hence, after fruitless attempts to suppress such investigations indirectly by making them liable
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to a heavy tax, the legislature in comparatively recent times absolutely prohibited them.
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I alas I alone in flatland, know now only too well the true solution
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of this mysterious problem. But my knowledge cannot be made intelligible to a single
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one of my countrymen. And I am mocked at I the sole possessor of
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the truths of space and of the theory of the introduction of light from the
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world of three dimensions, as if I were the maddest of the mad.
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But a truce to these painful digressions. Let me return to our houses.
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The most common form for the construction of a house is five sided or pentagonal,
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as in the next figure. Reader's note. The figure shows a pentagon
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slightly skewed to the right, with two sides marked RO and O F,
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forming a point marked O to the north. The left or western side,
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which has a large opening marked men's door, is marked a R. The
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right or eastern side, which has a small opening marked women's door, is
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marked b F. The base, or southern side is marked a b end
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of Reader's note. The two northern sides R, O, O F constitute
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the roof and for the most part have no doors. On the east is
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a small door for the women, on the west a much larger one for
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the men. The south side or floor is usually dawless. Square and triangular
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houses are not allowed, and for this reason, the angles of a square,
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and still more those of an equilateral triangle, being much more pointed than
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those of a pentagon, and the lines of inanimate objects such as houses being
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dimmer than the lines of men and women. It follows that there is no
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little danger lest the points of a square or triangular house. Residents might do
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serious injury to an inconsiderate or perhaps absent minded traveler suddenly running against them.
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And therefore, as early as the eleventh century of our era, triangular houses
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were universally forbidden by law, the only exceptions being fortifications, powder magazines,
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barracks, and other state buildings which it is is not desirable that the general
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public should approach without circumspection. At this period, square houses were still everywhere
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permitted, though discouraged by a special tax. But about three centuries afterwards,
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the law decided that in all towns containing a population above ten thousand, the
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angle of a pentagon was the smallest house angle that could be allowed consistently with
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the public safety. The good sense of the community has seconded the efforts of
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the legislature, and now even in the country the pentagonal construction has superseded every
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other. It is only now and then in some very remote and backward agricultural
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district that an antiquarian may still discover a square house. Section three. Concerning
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the inhabitants of flatland. The greatest length or breadth of a full grown inhabitant
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of flat land may be estimated at about eleven of your inches. Twelve inches
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may be regarded as a maximum. Our women are straight lines. Our soldiers
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and lowest classes of workmen are triangles, with two equal sides, each about
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eleven inches long, and a base or third side so short, often not
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exceeding half an inch, that they form at their vertices a very sharp and
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formidable angle. Indeed, when their bases are of the most degraded type,
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not more than the eighth part of an inch in size, they can hardly
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be distinguished from straight lines or women, so extremely pointed are their vertices.
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With us, as with you, these triangles are distinguished from others by being
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called isosceles, and by this name I shall refer to them in the following
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pages. Our middle class consists of equilateral or equal sided triangles. Our professional
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men and gentlemen are squares, to which class I myself belong, and five
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sided figures or pentagons. Next above these come the nobility, of whom there
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are several degrees, beginning at six sided figures or hexagons, and from thence
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rising in the number of their sides, till they receive the honorable title of
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polygonal or many sided. Finally, when the number of the sides becomes so
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numerous, and the sides themselves so small that the figure cannot be distinguished from
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a circle. He is included in the circular or priestly order, and this
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is the highest class of all. It is a law of nature with us
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that a male child shall have one more side than his father, that each
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generation shall rise, as a rule, one step in the scale of development
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and nobility. Thus, the son of a square is a pentagon, the
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son of a pentagon a hexagon, and so on. But this rule applies
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not always to the tradesmen, and still less often to the soldiers and to
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the workmen, who indeed can hardly be said to deserve the name of human
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figures, since they have not all their sides equal with them. Therefore the
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law of nature does not hold, and the son of an Isosceles i e.
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A triangle with two sides equal, remains Isosceles. Still, nevertheless,
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all hope is not shut out, even from the Isosceles, that his posterity
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may ultimately rise above his degraded condition. For after a long series of military
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successes or diligent and skillful laby, it is generally found that the more intelligent
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among the artisan and soldier classes manifest the slight increase of their third side or
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base, and a shrinkage of the two other sides. Intermarriages arranged by the
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priests between the sons and daughters of these more intellectual members of the lower classes
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generally result in an offspring approximating still more to the type of the equal sided
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triangle, rarely in proportion to the vast number of Isosceles births. Is a
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genuine and certifiable equal sided triangle produced from Isosceles parents. Footnote what need of
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a certificate, a spaceland critic may ask, is not the procreation of a
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square son a certificate from nature herself proving the equal sidedness of the father?
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I reply that no lady of any position will marry an NAE certified triangle.
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Square offspring has sometimes resulted from a slightly irregular triangle, but in almost every
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such case, the irregularity of the first generation is visited on the third,
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which either fails to attain the pentagonal rank or relapses to the triangular end of
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footnote. Such a birth requires, as its antecedents not only a series of
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carefully arranged into marriages, but also a long continued exercise of frugality and self
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control on the part of the would be ancestors of the coming equilateral, and
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a patient, systematic and continuous development of the Isosceles intellect through many generations.
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The birth of a true equilateral triangle from Isosceles parents is the subject of rejoicing
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in our country for many furlongs round. After a strict examination conducted by the
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Sanitary and Social Board, the infant, if certified as regular, is,
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with solemn ceremonial admitted into the class of equilaterals. He is then immediately taken
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from his proud yet sorrowing parents and adopted by some childless equilateral who is bound
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by oaths never to permit the child henceforth to enter his former home, or
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so much as to look upon his relations again, for fear lest the freshly
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developed organism may, by force of unconscious imitation, fall back again into his
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hereditary level. The occasional emergence of an Isosceles from the ranks of his serf
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born ancestors is welcomed not only by the poor serfs themselves as a gleam of
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light and hope shed upon the monotonous squalor of their existence, but also by
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the aristocracy at large. For all the higher classes are well aware that these
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rare phenomena, while they do little or nothing to vulgarize their own privileges,
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serve as a most useful barrier against revolution from below. Had the acute angled
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rabble been all without exception, absolutely destitute of hope and of ambition, they
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might have found leaders in some of their many seditious outbreaks, so able as
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to render their superior numbers and strength too much even for the wisdom of the
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circles. But a wise ordinance of nature has decreed that in proportion as the
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working classes increase in intelligence, knowledge, and all virtue, in that same
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proportion, their acute angle, which makes them physically terrible, shall increase also,
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and approximate to the harmless angle of the equilateral triangle. Thus, in
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the most brutal and formidable of the soldier class creatures almost on a level with
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women in their lack of intelligence. It is found that as they wax in
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the mental ability necessary to employ their tremendous penetrating power to advantage, so do
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they wane in the power of penetration itself. How admirable is this law of
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compensation and how perfect a proof of the natural fitness, and I may almost
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say the divine origin of the aristocratic constitution of the states in flatland. By
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a judicious use of this law of nature, the polygons and circles are almost
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always able to stifle sedition in its very cradle, taking advantage of the irrepressible
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and boundless hopefulness of the human mind. Art also comes to the aid of
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law and order. It is generally found possible, by a life artificial compression
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or expansion on the part of the state physicians to make some of the more
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intelligent leaders of a rebellion perfectly irregular, and to admit them at once into
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the privileged classes. A much larger number, who are still below the standard,
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allured by the prospect of being ultimately ennobled, are induced to enter the
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state hospitals, where they are kept in honorable confinement for life. One or
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two alone of the more obstinate, foolish, and hopelessly irregular are led to
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execution. Then the wretched rabble of the Isosceles, planless and leaderless are either
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transfixed without resistance by the small body of their brethren, whom the chief circle
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keeps in pay for emergencies of this kind, or else more often by means
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of jealousies and suspicions skillfully fermented among them by the circular party. They are
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stirred to mutual warfare and perish by one another's angles. No less than one
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hundred and twenty rebellions are recorded in our annals, besides minor outbreaks numbered at
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two hundred and thirty five, and they have all ended thus End of Part
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one, Section three