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

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  Speaker 1: Part one. Sections one to three flat Land are Romance
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  Speaker 1: of Many Dimensions by Edwin Abbot. Abbot to the inhabitants
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  Speaker 1: of space in general and hc. In particular. This work
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  Speaker 1: is dedicated by a humble native of Flatland, in the
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  Speaker 1: hope that, even as he was initiated into the mysteries
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  Speaker 1: of three dimensions, having been previously conversant with only two,
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  Speaker 1: so the citizens of that celestial region may aspire yet
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  Speaker 1: higher and higher to the secrets of four, five, or
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  Speaker 1: even six dimensions, thereby contributing to the enlargement of the
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  Speaker 1: imagination and the possible development of that most rare and
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  Speaker 1: excellent gift of modesty among the superior races of solid humanity.
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  Speaker 1: Part one. This world, be patient, for the world is
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  Speaker 1: broad and wide. Section one of the nature of Flatland.
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  Speaker 1: I call our world flatland, not because we call it so,
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  Speaker 1: but to make its nature clearer to you, my happy readers,
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  Speaker 1: who are privileged to live in space. Imagine a vast
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  Speaker 1: sheet of paper on which straight lines, triangles, squares, pentagons, hexagons,
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  Speaker 1: and other figures, instead of remaining fixed in their places,
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  Speaker 1: move freely about on or in the surface, but without
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  Speaker 1: the power of rising above or sinking below it, very
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  Speaker 1: much like shadows, only hard and with luminous edges. And
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  Speaker 1: you will then have a pretty correct notion of my
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  Speaker 1: country and countrymen, alas a few years ago I should
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  Speaker 1: have said my universe. But now my mind has been
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  Speaker 1: opened to higher views of things. In such a country,
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  Speaker 1: you will perceive at once that it is impossible that
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  Speaker 1: there should be anything of what you call a solid kind.
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  Speaker 1: But I dare say you will suppose that we could
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  Speaker 1: at least distinguish by sight the triangles, squares, and other
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  Speaker 1: figures moving about as I have described them. On the contrary,
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  Speaker 1: we could see nothing of the kind, not at least
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  Speaker 1: so as to distinguish one figure from another. Nothing was visible,
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  Speaker 1: nor could be visible to us, except straight lines. And
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  Speaker 1: the necessity of this I will speedily demonstrate. Place a
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  Speaker 1: penny on the middle of one of your tables in space,
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  Speaker 1: and leaning over it, look down upon it. It will
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  Speaker 1: appear a circle. But now drawing back to the edge
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  Speaker 1: of the table, gradually lower your eye, thus bringing yourself
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  Speaker 1: more and more into the condition of the inhabitance of
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  Speaker 1: flat land, and you will find the penny becoming more
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  Speaker 1: and more oval to your view. And at last, when
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  Speaker 1: you have placed your eye exactly on the edge of
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  Speaker 1: the table, so that you are, as it were, actually
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  Speaker 1: a flatland citizen. The penny will then have ceased to
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  Speaker 1: appear oval at all, and will have become so far
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  Speaker 1: as you can see, a straight line. The same thing
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  Speaker 1: would happen if you were to treat in the same
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  Speaker 1: way a triangle or square, or any other figure cut
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  Speaker 1: out of pasteboard. As soon as you look at it
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  Speaker 1: with your eye on the edge of the table, you
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  Speaker 1: will find that it ceases to appear to you a figure,
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  Speaker 1: and that it becomes in appearance a straight line. Take,
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  Speaker 1: for example, an equilateral triangle who represents with us a
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  Speaker 1: tradesman of the respectable class. Figure one represents the tradesman
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  Speaker 1: as you would see him while you were bending over
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  Speaker 1: him from above. Reader's note. Figure one is a downward
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  Speaker 1: pointing triangle with all sides equal. End of reader's note.
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  Speaker 1: Figures two and three represent the tradesman as you would
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  Speaker 1: see him if your eye were close to the level
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  Speaker 1: or all but on the level of the table. Reader's note. Fig.
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  Speaker 1: Two shares a much flatter downward pointing triangle, with the
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  Speaker 1: top edge much longer than the other two sides which
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  Speaker 1: are of equal length. Fig. Three is flatter, still barely
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  Speaker 1: identifiable as a triangle at all end of reader's note.
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  Speaker 1: And if your eye were quite on the level of
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  Speaker 1: the table, and that is how we see him in
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  Speaker 1: flat land, you would see nothing but a straight line.
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  Speaker 1: When I was in Spaceland, I heard that your sailors
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  Speaker 1: have very similar experiences while they traverse your seas and
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  Speaker 1: discerned some distant island or coast lying on the horizon.
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  Speaker 1: The far off land may have bays, fallands, angles in
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  Speaker 1: and out to any number and extent. Yet at a
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  Speaker 1: distance you see none of these, unless indeed your sun
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  Speaker 1: shines bright upon them, revealing the projections and retirements. By
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  Speaker 1: means of light and shade. Nothing but a gray, unbroken
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  Speaker 1: line upon the water. Well, that is just what we
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  Speaker 1: see when one of our triangular or other acquaintances comes
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  Speaker 1: towards us in flatland. As there is neither sun with us,
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  Speaker 1: nor any light of such a kind as to make shadows,
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  Speaker 1: we have none of the helps to the sight that
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  Speaker 1: you have in Spaceland. If our friend comes close to us,
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  Speaker 1: we see his line becomes larger. If he leaves us
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  Speaker 1: it becomes smaller, But still he looks like a straight line.
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  Speaker 1: Be he a triangle, square, pentagon, hexagon, circle? What you
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  Speaker 1: will a straight line he looks, and nothing else. You
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  Speaker 1: may perhaps ask, how, under these disadvantageous circumstances we are
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  Speaker 1: able to distinguish our friends from one another. But the
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  Speaker 1: answer to this very natural question will be more fitly
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  Speaker 1: and easily given when I come to describe the inhabitants
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  Speaker 1: of flatland. For the present, let me defer this subject
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  Speaker 1: and say a word or two about the climate and
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  Speaker 1: houses in our country. Section two of the Climate and
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  Speaker 1: houses in Flatland. As with you, so also with us.
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  Speaker 1: There are four points of the compass north, south, east,
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  Speaker 1: and west. There being no sun nor other heavenly bodies,
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  Speaker 1: it is impossible for us to determine the north in
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  Speaker 1: the usual way, but we have a method of our own,
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  Speaker 1: by a law of nature. With us there is a
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  Speaker 1: constant attraction to the south, and although in temperate climates,
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  Speaker 1: this is very slight, so that even a woman in
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  Speaker 1: reasonable health can journey several furlongs northward without much difficulty.
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  Speaker 1: Yet the hampering effect of the southward attraction is quite
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  Speaker 1: sufficient to serve as a compass in most parts of
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  Speaker 1: our earth. Moreover, the rain which falls at stated intervals,
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  Speaker 1: coming always from the north, is an additional assistance. And
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  Speaker 1: in the towns we have the guidance of the houses,
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  Speaker 1: which of course have their side walls running for the
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  Speaker 1: most part north and south, so that the roofs may
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  Speaker 1: keep off the rain from the north. In the country
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  Speaker 1: where there are no houses, the trunks of the trees
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  Speaker 1: serve as some sort of guide. Altogether, we have not
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  Speaker 1: so much difficulty as might be expected in determining our
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  Speaker 1: bearings in our more temperate regions, in which the southward
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  Speaker 1: attraction is hardly felt. Walking sometimes in a perfectly desolate plain,
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  Speaker 1: where there have been no houses nor trees to guide me,
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  Speaker 1: I have been occasionally compelled to remain stationary for hours together,
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  Speaker 1: waiting till the rain came, before continuing my journey. On
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  Speaker 1: the week and aged, and especially on delicate females, the
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  Speaker 1: force of attraction tells much more heavily than on the
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  Speaker 1: robust of the male sex, so that it is a
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  Speaker 1: point of breeding. If you meet a lady in the street,
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  Speaker 1: always to give her the north side of the way,
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  Speaker 1: by no means an easy thing to do, always at
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  Speaker 1: short notice, when you are in rude health, and in
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  Speaker 1: a climate where it is difficult to tell your north
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  Speaker 1: from your south windows, there are none in our houses.
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  Speaker 1: For the light comes to us alike, in our homes
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  Speaker 1: and out of them, by day and by night, equally
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  Speaker 1: at all times and in all places. Whence we know not.
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  Speaker 1: It was in old days with our learned men, an
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  Speaker 1: interesting and oft investigated question, what is the origin of light?
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  Speaker 1: And the solution of it? Has been repeatedly attempted, with
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  Speaker 1: no other result than to crowd our lunatic asylums with
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  Speaker 1: the would be solvers. Hence, after fruitless attempts to suppress
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  Speaker 1: such investigations indirectly by making them liable to a heavy tax,
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  Speaker 1: the legislature in comparatively recent times absolutely prohibited them. I
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  Speaker 1: alas I alone in flatland, know now only too well
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  Speaker 1: the true solution of this mysterious problem. But my knowledge
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  Speaker 1: cannot be made intelligible to a single one of my countrymen.
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  Speaker 1: And I am mocked at I the sole possessor of
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  Speaker 1: the truths of space and of the theory of the
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  Speaker 1: introduction of light from the world of three dimensions, as
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  Speaker 1: if I were the maddest of the mad. But a
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  Speaker 1: truce to these painful digressions. Let me return to our houses.
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  Speaker 1: The most common form for the construction of a house
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  Speaker 1: is five sided or pentagonal, as in the next figure.
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  Speaker 1: Reader's note. The figure shows a pentagon slightly skewed to
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  Speaker 1: the right, with two sides marked RO and O F,
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  Speaker 1: forming a point marked O to the north. The left
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  Speaker 1: or western side, which has a large opening marked men's door,
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  Speaker 1: is marked a R. The right or eastern side, which
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  Speaker 1: has a small opening marked women's door, is marked b F.
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  Speaker 1: The base, or southern side is marked a b end
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  Speaker 1: of Reader's note. The two northern sides R, O, O
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  Speaker 1: F constitute the roof and for the most part have
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  Speaker 1: no doors. On the east is a small door for
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  Speaker 1: the women, on the west a much larger one for
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  Speaker 1: the men. The south side or floor is usually dawless.
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  Speaker 1: Square and triangular houses are not allowed, and for this reason,
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  Speaker 1: the angles of a square, and still more those of
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  Speaker 1: an equilateral triangle, being much more pointed than those of
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  Speaker 1: a pentagon, and the lines of inanimate objects such as
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  Speaker 1: houses being dimmer than the lines of men and women.
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  Speaker 1: It follows that there is no little danger lest the
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  Speaker 1: points of a square or triangular house. Residents might do
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  Speaker 1: serious injury to an inconsiderate or perhaps absent minded traveler
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  Speaker 1: suddenly running against them. And therefore, as early as the
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  Speaker 1: eleventh century of our era, triangular houses were universally forbidden
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  Speaker 1: by law, the only exceptions being fortifications, powder magazines, barracks,
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  Speaker 1: and other state buildings which it is is not desirable
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  Speaker 1: that the general public should approach without circumspection. At this period,
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  Speaker 1: square houses were still everywhere permitted, though discouraged by a
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  Speaker 1: special tax. But about three centuries afterwards, the law decided
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  Speaker 1: that in all towns containing a population above ten thousand,
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  Speaker 1: the angle of a pentagon was the smallest house angle
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  Speaker 1: that could be allowed consistently with the public safety. The
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  Speaker 1: good sense of the community has seconded the efforts of
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  Speaker 1: the legislature, and now even in the country the pentagonal
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  Speaker 1: construction has superseded every other. It is only now and
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  Speaker 1: then in some very remote and backward agricultural district that
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  Speaker 1: an antiquarian may still discover a square house. Section three.
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  Speaker 1: Concerning the inhabitants of flatland. The greatest length or breadth
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  Speaker 1: of a full grown inhabitant of flat land may be
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  Speaker 1: estimated at about eleven of your inches. Twelve inches may
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  Speaker 1: be regarded as a maximum. Our women are straight lines.
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  Speaker 1: Our soldiers and lowest classes of workmen are triangles, with
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  Speaker 1: two equal sides, each about eleven inches long, and a
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  Speaker 1: base or third side so short, often not exceeding half
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  Speaker 1: an inch, that they form at their vertices a very
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  Speaker 1: sharp and formidable angle. Indeed, when their bases are of
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  Speaker 1: the most degraded type, not more than the eighth part
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  Speaker 1: of an inch in size, they can hardly be distinguished
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  Speaker 1: from straight lines or women, so extremely pointed are their vertices.
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  Speaker 1: With us, as with you, these triangles are distinguished from
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  Speaker 1: others by being called isosceles, and by this name I
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  Speaker 1: shall refer to them in the following pages. Our middle
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  Speaker 1: class consists of equilateral or equal sided triangles. Our professional
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  Speaker 1: men and gentlemen are squares, to which class I myself belong,
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  Speaker 1: and five sided figures or pentagons. Next above these come
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  Speaker 1: the nobility, of whom there are several degrees, beginning at
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  Speaker 1: six sided figures or hexagons, and from thence rising in
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  Speaker 1: the number of their sides, till they receive the honorable
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  Speaker 1: title of polygonal or many sided. Finally, when the number
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  Speaker 1: of the sides becomes so numerous, and the sides themselves
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  Speaker 1: so small that the figure cannot be distinguished from a circle.
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  Speaker 1: He is included in the circular or priestly order, and
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  Speaker 1: this is the highest class of all. It is a
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  Speaker 1: law of nature with us that a male child shall
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  Speaker 1: have one more side than his father, that each generation
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  Speaker 1: shall rise, as a rule, one step in the scale
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  Speaker 1: of development and nobility. Thus, the son of a square
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  Speaker 1: is a pentagon, the son of a pentagon a hexagon,
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  Speaker 1: and so on. But this rule applies not always to
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  Speaker 1: the tradesmen, and still less often to the soldiers and
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  Speaker 1: to the workmen, who indeed can hardly be said to
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  Speaker 1: deserve the name of human figures, since they have not
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  Speaker 1: all their sides equal with them. Therefore the law of
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  Speaker 1: nature does not hold, and the son of an Isosceles
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  Speaker 1: i e. A triangle with two sides equal, remains Isosceles. Still, nevertheless,
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  Speaker 1: all hope is not shut out, even from the Isosceles,
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  Speaker 1: that his posterity may ultimately rise above his degraded condition.
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  Speaker 1: For after a long series of military successes or diligent
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  Speaker 1: and skillful laby, it is generally found that the more
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  Speaker 1: intelligent among the artisan and soldier classes manifest the slight
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  Speaker 1: increase of their third side or base, and a shrinkage
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  Speaker 1: of the two other sides. Intermarriages arranged by the priests
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  Speaker 1: between the sons and daughters of these more intellectual members
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  Speaker 1: of the lower classes generally result in an offspring approximating
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  Speaker 1: still more to the type of the equal sided triangle,
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  Speaker 1: rarely in proportion to the vast number of Isosceles births.
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  Speaker 1: Is a genuine and certifiable equal sided triangle produced from
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  Speaker 1: Isosceles parents. Footnote what need of a certificate, a spaceland
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  Speaker 1: critic may ask, is not the procreation of a square
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  Speaker 1: son a certificate from nature herself proving the equal sidedness
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  Speaker 1: of the father? I reply that no lady of any
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  Speaker 1: position will marry an NAE certified triangle. Square offspring has
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  Speaker 1: sometimes resulted from a slightly irregular triangle, but in almost
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  Speaker 1: every such case, the irregularity of the first generation is
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  Speaker 1: visited on the third, which either fails to attain the
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  Speaker 1: pentagonal rank or relapses to the triangular end of footnote.
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  Speaker 1: Such a birth requires, as its antecedents not only a
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  Speaker 1: series of carefully arranged into marriages, but also a long
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  Speaker 1: continued exercise of frugality and self control on the part
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  Speaker 1: of the would be ancestors of the coming equilateral, and
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  Speaker 1: a patient, systematic and continuous development of the Isosceles intellect
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  Speaker 1: through many generations. The birth of a true equilateral triangle
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  Speaker 1: from Isosceles parents is the subject of rejoicing in our
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  Speaker 1: country for many furlongs round. After a strict examination conducted
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  Speaker 1: by the Sanitary and Social Board, the infant, if certified
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  Speaker 1: as regular, is, with solemn ceremonial admitted into the class
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  Speaker 1: of equilaterals. He is then immediately taken from his proud
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  Speaker 1: yet sorrowing parents and adopted by some childless equilateral who
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  Speaker 1: is bound by oaths never to permit the child henceforth
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  Speaker 1: to enter his former home, or so much as to
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  Speaker 1: look upon his relations again, for fear lest the freshly
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  Speaker 1: developed organism may, by force of unconscious imitation, fall back
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  Speaker 1: again into his hereditary level. The occasional emergence of an
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  Speaker 1: Isosceles from the ranks of his serf born ancestors is
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  Speaker 1: welcomed not only by the poor serfs themselves as a
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  Speaker 1: gleam of light and hope shed upon the monotonous squalor
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  Speaker 1: of their existence, but also by the aristocracy at large.
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  Speaker 1: For all the higher classes are well aware that these
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  Speaker 1: rare phenomena, while they do little or nothing to vulgarize
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  Speaker 1: their own privileges, serve as a most useful barrier against
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  Speaker 1: revolution from below. Had the acute angled rabble been all
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  Speaker 1: without exception, absolutely destitute of hope and of ambition, they
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  Speaker 1: might have found leaders in some of their many seditious outbreaks,
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  Speaker 1: so able as to render their superior numbers and strength
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  Speaker 1: too much even for the wisdom of the circles. But
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  Speaker 1: a wise ordinance of nature has decreed that in proportion
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  Speaker 1: as the working classes increase in intelligence, knowledge, and all virtue,
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  Speaker 1: in that same proportion, their acute angle, which makes them
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  Speaker 1: physically terrible, shall increase also, and approximate to the harmless
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  Speaker 1: angle of the equilateral triangle. Thus, in the most brutal
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  Speaker 1: and formidable of the soldier class creatures almost on a
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  Speaker 1: level with women in their lack of intelligence. It is
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  Speaker 1: found that as they wax in the mental ability necessary
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  Speaker 1: to employ their tremendous penetrating power to advantage, so do
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  Speaker 1: they wane in the power of penetration itself. How admirable
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  Speaker 1: is this law of compensation and how perfect a proof
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  Speaker 1: of the natural fitness, and I may almost say the
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  Speaker 1: divine origin of the aristocratic constitution of the states in flatland.
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  Speaker 1: By a judicious use of this law of nature, the
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  Speaker 1: polygons and circles are almost always able to stifle sedition
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  Speaker 1: in its very cradle, taking advantage of the irrepressible and
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  Speaker 1: boundless hopefulness of the human mind. Art also comes to
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  Speaker 1: the aid of law and order. It is generally found possible,
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  Speaker 1: by a life artificial compression or expansion on the part
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  Speaker 1: of the state physicians to make some of the more
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  Speaker 1: intelligent leaders of a rebellion perfectly irregular, and to admit
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  Speaker 1: them at once into the privileged classes. A much larger number,
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  Speaker 1: who are still below the standard, allured by the prospect
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  Speaker 1: of being ultimately ennobled, are induced to enter the state hospitals,
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  Speaker 1: where they are kept in honorable confinement for life. One
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  Speaker 1: or two alone of the more obstinate, foolish, and hopelessly
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  Speaker 1: irregular are led to execution. Then the wretched rabble of
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  Speaker 1: the Isosceles, planless and leaderless are either transfixed without resistance
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  Speaker 1: by the small body of their brethren, whom the chief
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  Speaker 1: circle keeps in pay for emergencies of this kind, or
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  Speaker 1: else more often by means of jealousies and suspicions skillfully
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  Speaker 1: fermented among them by the circular party. They are stirred
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  Speaker 1: to mutual warfare and perish by one another's angles. No
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  Speaker 1: less than one hundred and twenty rebellions are recorded in
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  Speaker 1: our annals, besides minor outbreaks numbered at two hundred and
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  Speaker 1: thirty five, and they have all ended thus End of
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  Speaker 1: Part one, Section three