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03 - Flatland- A Romance of Many Dimensions - Edwin Abbott Abbott · Classic Sci Fi Books - Daily

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Part one, Section six of Recognition by sight, I am about to appear
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very inconsistent. In previous sections. I have said that all figures in flatland
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present the appearance of a straight line, and it was added or implied that
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it is consequently impossible to distinguish by the visual organ between individuals of different classes.
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Yet now I am about to explain to my Spaceland critics how we are
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able to recognize one another by the sense of sight. If, however,
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the reader will take the trouble to refer to the passage in which recognition by
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feeling is stated to be universal, he will find this qualification among the lower
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classes. It is only among the higher classes, and in our more temperate
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climates, that sight recognition is practiced. That this power exists in any regions
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and for any classes, is the result of fog which prevails during the greater
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part of the year in all parts save the torrid zones. That which is
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with you in Spaceland, and unmixed evil, blotting out the landscape, depressing
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the spirits and enfeebling the health, is by us recognized as a blessing scarcely
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inferior to air itself, and as the nurse of arts and parent of sciences.
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But let me explain my meaning without further eulogies on this beneficent element.
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If fog were non existent, all lines would appear equally and indistinguishably clear.
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And this is actually the case in those unhappy countries in which the atmosphere is
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perfectly dry and transparent. But wherever there is a rich supply of fog,
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objects that are at a distant, say, of three feet, are appreciably
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dimmer than those at a distance of two feet eleven inches. And the result
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is that, by careful and constant experimental observation of comparative dimness and clearness,
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we are enabled to infer with great exactness the configuration of the object observed.
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An instance will do more than a volume of generalities to make my meaning clear.
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Suppose I see two individuals approaching whose rank I wish to ascertain they are.
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We will suppose a merchant and a physician, or in other words,
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an equilateral triangle and a pentagon. How am I to distinguish them? Reader's
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note. The following paragraph makes reference to an accompanying diagram. Diagram one is
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a rightward pointing equilateral triangle. The vertical left hand side of which is marked
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B C, the other two sides being marked B A and C A.
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Dotted lines are drawn from B and C to a point further to the right
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to form an Isosceles triangle. The far right hand point of this triangle represents
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the eye of the observer, and a horizontal dotted arrow pointing left from it
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indicates his eye glance. A broad vertical line DAE is drawn to indicate what
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the observer sees. DAE is bright at the center and darkens sharply towards its
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ends. End of reader's note. It will be obvious to every child in
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spaceland who has touched the threshold of geometrical studies, that if I can bring
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my eye so that its glance may bisect an angle A of the approaching stranger,
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my view will lie, as it were, evenly between his two sides
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that are next to me is C A and A B, so that I
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shall contemplate the two impartially, and both will appear of the same size.
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Now, in the case of one the merchant, what shall I see?
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I shall see a straight line DAE, in which the middle point A will
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be very bright, because it is nearest to me, but on either side
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the line will shade away rapidly into dimness, because the sides AC and A
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B recede rapidly into the fog, and what appear to me as the merchant's
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extremities viz. D and E will be very dim Indeed, Reader's note The
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following paragraph makes reference to an accompanying diagram. Diagram two is a regular pentagon
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sitting on a horizontal base, with C one at the apex, A one
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at middle right, and B one at lower right. Longer dotted lines are
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drawn out towards the right, upwards from B one and downwards from C one
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to form an irregular pentagon. The far right hand point of the extended pentagon
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represents the eye of the observer, and a dotted arrow pointing from it towards
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the center of the lower left edge of the pentagon indicates his eye glance.
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Again, a broad line D one A one e one parallel to the lower
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left edge of the pentagon is drawn to indicate what the observer sees. D
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one A one e one is bright at the center and darkens very gradually towards
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its ends. End of Reader's note. On the other hand, in the
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case of two the physician, though I shall here also see a line D
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one, A one, E one with a bright center A one, Yet
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it will shade away less rapidly into dimness, because the sides A one,
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C one, A one, B one recede less rapidly into the fog.
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And what appear to me the physician's extremities is D one and E one will
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be not so dim as the extremities of the merchant. The reader will probably
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understand from these two instances, how after a very long training supplemented by constant
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experience, it is possible for the well educated classes among us to discriminate with
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fair accuracy between the middle and lowest orders by the sense of sight. If
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my spaceland patrons have grasped this general conception so far as to conceive the possibility
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of it, and not to reject my account as altogether incredible, I shall
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have attained all I can reasonably expect. Were I to attempt further details,
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I should only perplex Yet, for the sake of the young and inexperienced,
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who may perchance infer from the two simple instances I have given above of the
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manner in which I should recognize my father and my sons. That recognition by
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sight is an easy affair, it may be needful to point out that,
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in actual life, most of the problems of sight recognition are far more subtle
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and complex. If, for example, when my father the triangle approaches me,
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he happens to present his side to me instead of his angle, then
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until I have asked him to rotate, or until I have edged my eye
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round him, I am for the moment doubtful whether he may not be a
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straight line or in other words, a woman reader's note. The following paragraph
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makes reference to an accompanying diagram. The diagram shows a hexagon with points at
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top and bottom. The vertical right hand side is marked A B. Dotted
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lines are drawn downward from the topmost and upward from the bottomost points of the
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hexagon, and extended to the right until they meet, forming an irregular pentagon.
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The far right hand point of the pentagon represents the eye of the observer.
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The line A B is extended to where it meets the dotted lines to
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form a broad vertical line at C A B D. The middle portion of
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this line A B is bright and the outer portions darken. Towards C and
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D end of reader's note. Again, when I am in the company of
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one of my two hexagonal grandsons, contemplating one of his sides A B full
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front, it will be evident from the accompanying diagram that I shall see one
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whole line A B in comparative brightness, shading off hardly at all at the
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ends, and two smaller lines C, A and B D dim throughout and
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shading away into greater dimness toward the extremities C and D. But I must
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not give way to the temptation of enlarging on these topics. The meanest mathematician
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in Spaceland will readily believe me when I assert that the problems of life which
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present themselves to the well educated when they are themselves in motion, rotating,
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advancing or retreating, and at the same time attempting to discriminate by the sense
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of sight between a number of polygons of high rank moving in different directions,
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as for example, in a ball room or conversazione, must be of a
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nature to task the angularity of the most intellectual and amply justify the rich endowments
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of the learned. Professors of geometry, both static and kinetic in the illustrious
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University of Wentbridge, where the science and art of sight recognition are regularly taught
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to lo large classes of the elite of the States. It is only a
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few of the sciens of our noblest and wealthiest houses who are able to give
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the time and money necessary for the thorough prosecution of this noble and valuable art.
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Even to me, a mathematician of no means standing and the grandfather of
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two most hopeful and perfectly regular hexagons, defined myself in the midst of a
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crowd of rotating polygons of the higher classes is occasionally very perplexing, and of
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course to a common tradesman or surf such a site is almost as unintelligible as
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it would be to you, my reader, were you suddenly transported into our
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country, in such a crowd, you could see on all sides of you
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nothing but a line, apparently straight, but of which the parts would vary
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irregularly and perpetually in brightness or dimness. Even if you had completed your third
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year in the pentagonal and hexagonal classes in the university, and were perfect in
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the theory of the subject, you would still find that there was need of
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many years of experience before you could move in a fashionable crowd without jostling against
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your betters, whom it is against etiquette to ask to feel, and who,
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by their superior culture and breeding, know all about your movements, while
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you know very little or nothing about theirs. In a word, to comport
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oneself with perfect propriety. In polygonal society, one ought to be a polygon
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oneself. Such, at least is the painful teaching of my experience. It
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is astonishing how much the art, or i may almost call it instinct of
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sight recognition is developed by the habitual practice of it and by the avoidance of
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the custom of feeling. Just as with you, the deaf and dumb,
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if once allowed to gesticulate and to use the and alphabet, will never acquire
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the more difficult but far more valuable art of lip speech and lip reading.
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So it is with us as regards seeing and feeling. None who in early
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life resort to feeling will ever learn seeing in perfection. For this reason,
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among our higher classes, feeling is discouraged or absolutely forbidden from the cradle their
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children, instead of going to the public elementary schools, where the art of
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feeling is taught, are sent to higher seminaries of an exclusive character, and
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at our illustrious university, to feel is regarded as a most serious fault,
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involving rustication for the first offense and expulsion for the second. But among the
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lower classes, the art of sight recognition is regarded as an unattainable luxury.
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A common trade cannot afford to let his son spend a third of his life
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in abstract studies. The children of the poor are therefore allowed to feel from
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their earliest years, and they gain thereby a precocity and an early vivacity,
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which contrast, at first most favorably with the inert, undeveloped, and listless
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behavior of the half instructed youths of the polygonal class. But when the latter
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have at last completed their university course and are prepared to put their theory into
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practice, the change that comes over them may almost be described as a new
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birth. And in every art, science, and social pursuit they rapidly overtake
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and distance their triangular competitors. Only a few of the polygonal class fail to
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pass the final test or leaving examination at the university. The condition of the
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unsuccessful minority is truly pitiable. Rejected from the higher class, they are also
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despised by the lower. They have neither the matured and systematically trained powers of
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the polygonal bachelors and masters of arts, nor yet the native precocity and mercurial
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versatility of the useful tradesmen. The professions the public services are closed against them,
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and though in most states they are not actually debarred from marriage, yet
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they have the greatest difficulty in forming suitable alliances, as experience shows that the
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offspring of such unfortunate and ill endowed parents is generally itself unfortunate, if not
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positively irregular. It is from these specimens of the refuse of our nobility that
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the great tumults and seditions of past ages have generally derived their leaders. And
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so great is the miss mischief, thence arising that an increasing minority of our
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more progressive statesmen are of opinion that true mercy would dictate their entire suppression by
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enacting that all who failed to pass the final examination of the university should be
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either imprisoned for life or extinguished by a painless death. But I find myself
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digressing into the subject of irregularities a matter of such vital interest that it demands
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a separate section, Section seven of irregular figures. Throughout the previous pages,
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I have been assuming what perhaps should have been laid down at the beginning as
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a distinct and fundamental proposition, that every human being in flatland is a regular
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figure, that is to say, of regular construction. By this I mean
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that a woman must not only be a line, but a straight line.
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That an artisan or soldier must have two of his sides equal, that tradesmen
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must have three sides equal, lawyers, of which class I am a humble
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member, four sides equal, and generally, that in every polygon all the
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sides must be equal. The size of the sides would, of course,
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depend upon the age of the individual. A female at birth would be about
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an inch long, while a tall adult woman might extend to a foot.
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As to the males of every class, it may be roughly said that the
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lengths of an adult sides, when added together, is three feet or a
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little more. But the size of our sides is not under consideration. I
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am speaking of the equality of sides, and it does not need much reflection
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to see that the whole of the social life in flatland rests upon the fundamental
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fact that nature will all figures to have their sides equal. If our sides
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were unequal, our angles would be unequal. Instead of its being sufficient to
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feel or estimate by sight a single angle in order to determine the form of
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an individual, it would be necessary to ascertain each angle by the experiment of
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feeling. But life would be too short for such a tedious groping. The
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whole science and art of sight recognition would at once perish. Feeling, so
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far as it is an art, would not long survive. Intercourse would become
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perilous or impossible. There would be an end to all confidence all forethought.
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No one would be safe in making the most simple social arrangements. In a
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word, civilization would relapse into barbarism. Am I going too fast to carry
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my readers with me to these obvious cons inclusions. Surely a moment's reflection and
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a single instance from common life must convince everyone that our whole social system is
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based upon regularity or equality of angles. You meet, for example, two
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or three tradesmen in the street whom you recognize at once to be tradesmen by
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a glance at their angles, and rapidly bedimmed sides, and you ask them
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to step into your house to lunch. This you do at present with perfect
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confidence, because everyone knows to an inch or two the area occupied by an
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adult triangle. But imagine that your tradesman drags behind his regular and respectable vertex
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a parallelogram of twelve or thirteen inches in diagonal. What are you to do
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with such a monster sticking fast in your house door? But I am insulting
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the intelligence of my readers by accumulating details which must be patent to everyone who
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enjoys the advantages of a residence in spaceland. Obviously, the measurements of a
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single angle would no longer be sufficient. Under such portentous circumstances. One's whole
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life would be taken up in feeling or surveying the perimeter of one's acquaintances.
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Already, the difficulties of avoiding a collision in a crowd are enough to tax
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the sagacity of even a well educated square. But if no one could calculate
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the regularity of a single figure in the company, all would be chaos and
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confusion, and the slightest panic would cause serious injuries. Or if there happened
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to be any women or soldiers present, perhaps considerable loss of life. Expediency
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therefore concurs with nature in stamping the seal of its approval upon regularity of conformation.
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Nor has the law been backward in seconding their efforts. Irregularity of figure
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means with us the same as or more than a combination of moral obliquity and
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criminality with you, and is treated accordingly. There are not wanting. It
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is true some promulgators of paradoxes who maintain that there is no necessary connection between
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geometrical and moral irregularity. The irregular, they say, is from his birth,
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scouted by his own parents, derided by his brothers and sisters, neglected
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by the domestics, scorned and suspected by society, and excluded from all posts
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of responsibility, trust, and useful activity. His every movement is jealously watched
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by the police till he comes of age and presents himself for inspection. Then
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he is either destroyed if he is found to exceed the fixed margin of deviation,
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or else inured in a government office as a clerk of the seventh class,
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prevented from marriage, forced to drudge at an uninteresting occupation for a miserable
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stipend, obliged to live and board at the office, and to take even
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his vocation under close supervision. What wonder that human nature, even in the
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best and purest, is embittered and perverted by such surroundings. All this very
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plausible reasoning does not convince me, as it has not convinced the wisest of
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our statesmen, that our ancestors erred in laying it down as an axiom of
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policy, that the toleration of irregularity is incompatible with the safety of the state.
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Doubtless, the life of an irregular is hard, But the interests of
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the greater number require that it shall be hard. If a man with a
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triangular front and a polygonal back were allowed to exist and to propagate a still
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more irregular posterity, what would become of the arts of life? Are the
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houses and doors and churches in flatland to be altered in order to accommodate such
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monsters? Are our ticket collectors to be required to measure every man's perimeter before
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they allow him to enter a theater or to take his place in a lecture
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room? Is an irregular to be exempted from the militia. And if not,
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how is he to be prevented from carrying desolation into the ranks of his
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comrades. Again, what irresistible temptations to fraudulent impostures must needs beset such a
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creature? How easy for him to enter a shop with his polygonal front foremost,
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and to order goods to any extent from a confiding tradesman. Let the
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advocates of a falsely called philanthropy pleaders, they may for the abrogation of the
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irregular penal laws. I, for my part, have never known an irregular
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who was not also what nature evidently intended him to be, a hypocrite,
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a misanthropist, and, up to the limits of his power, a perpetrator
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of all manner of mischief. Not that I should be disposed to recommend at
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present the extreme measures adopted in some states where an infant whose angle deviates by
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half a degree from the correct angularity is summarily destroyed at birth. Some of
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our highest and ablest men, men of real genius, have, during their
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earliest days labored under deviations as great as or even greater than forty five minutes,
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and the loss of their precious lives would have been an irreparable injury to
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the state. The art of healing also has achieved some of its most glorious
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triumphs in the compressions, extensions, trepannings, colligations, and other surgical or
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dietetic operations by which irregularity has been partly or wholly cured. Advocating therefore avera
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media, I would lay down no fixed or absolute line of demarcation, but
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at the period when the frame is just beginning to set, and when the
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medical board has reported that recovery is improbable, I would suggest that the irregular
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offspring be painlessly and mercifully consumed. End of Section seven