3604 lines
197 KiB
Plaintext
3604 lines
197 KiB
Plaintext
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The Internet Wiretap Electronic Edition of FLATLAND
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A Public Domain Text
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Instantiated by aloysius@west.darkside.com in November 1990
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The Internet Wiretap, of Cupertino, California
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gopher@wiretap.spies.com
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F L A T L A N D
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A Romance of Many Dimensions
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With Illustrations
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by the Author, A SQUARE
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(EDWIN A. ABBOTT)
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"Fie, fie how franticly I square my talk!"
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[Fifth Edition, Revised]
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* * *
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To
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The Inhabitance of SPACE IN GENERAL
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And H.C. IN PARTICULAR
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This Work is Dedicated
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By a Humble Native of Flatland
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In the Hope that
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Even as he was Initiated into the Mysteries
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Of THREE DIMENSIONS
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Having been previously conversant
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With ONLY TWO
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So the Citizens of that Celestial Region
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May aspire yet higher and higher
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To the Secrets of FOUR FIVE or EVEN SIX Dimensions
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Thereby contributing
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To the Enlargment of THE IMAGINATION
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And the possible Development
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Of that most and excellent Gift of MODESTY
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Among the Superior Races
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Of SOLID HUMANITY
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* * *
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PREFACE TO THE
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SECOND AND REVISED
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EDITION, 1884.
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BY THE EDITOR
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If my poor Flatland friend retained the vigour of mind which he
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enjoyed when he began to compose these Memoirs, I should not now need
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to represent him in this preface, in which he desires, fully, to
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return his thanks to his readers and critics in Spaceland, whose
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appreciation has, with unexpected celerity, required a second edition
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of this work; secondly, to apologize for certain errors and misprints
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(for which, however, he is not entirely responsible); and, thirdly, to
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explain on or two misconceptions. But he is not the Square he once
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was. Years of inprisonment, and the still heavier burden of general
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incredulity and mockery, have combined with the thoughts and notions,
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and much also of the terminology, which he acquired during his short
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stay in spaceland. He has, therefore, requested me to reply in his
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behalf to two special objections, one of an intellectual, the other of
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a moral nature.
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The first objection is, that a Flatlander, seeing a Line, sees
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something that must be _thick_ to the eye as well as _long_ to the eye
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(otherwise it would not be visible, if it had not some thickness); and
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consequently he ought (it is argued) to acknowledge that his
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countrymen are not only long and broad, but also (though doubtless to
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a very slight degree) _thick_ or _high._ This objection is plausible,
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and, to Spacelanders, almost irresistible, so that, I confess, when I
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first heard it, I knew not what to reply. But my poor old friend's
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answer appears to me completely to meet it.
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"I admit," said he -- when I mentioned to him this objection -- "I
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admit the truth of your critic's facts, but I deny his conclusions.
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It is true that we have really in Flatland a Third unrecognized
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Dimension called 'height,' just as it also is true that you have
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really in Spaceland a Fourth unrecognized Dimension, called by no name
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at present, but which I will call 'extra-height.' But we can no more
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take cognizance of our 'height' than you can of your 'extra-height.'
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Even I -- who have been in Spaceland, and have had the privilege of
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understanding for twenty-four hours the meaning of 'height' -- even I
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cannot now comprehend it, nor realize it by the sense of sight or by
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any process of reason; I can but apprehend it by faith.
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"The reason is obvious. Dimension implied direction, implies
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measurement, implies the more and the less. Now, all our lines are
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_equally_ and _infinitesimally_ thick (or high, whichever you like);
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consequently, there is nothing in them to lead our minds to the
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conception of that Dimension. No 'delicate micrometer' -- as has been
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suggested by one too hasty Spaceland critic -- would in the least
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avail us; for we should not know _what to measure, nor in what
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direction._ When we see a Line, we see something that is long and
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_bright; brightness,_ as well as length, is necessary to the existence
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of a Line; if the brightness vanishes, the Line is extinguished.
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Hence, all my Flatland friends -- when I talk to them about the
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unrecognized Dimension which is somehow visible in a Line -- say, 'Ah,
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you mean _brightness_': and when I reply, 'No, I mean a real
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Dimension,' they at once retort, 'Then measure it, or tell us in what
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direction it extends'; and this silences me, for I can do neither.
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Only yesterday, when the Chief Circle (in other words our High Priest)
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came to inspect the State Prison and paid me his seventh annual visit,
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and when for the seventh time he put me the question, 'Was I any
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better?' I tried to prove to him that he was 'high,' as well as long
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and broad, although he did not know it. But what was his reply? 'You
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say I am "high"; measure my "high-ness" and I will believe you.' What
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could I do? How could I meet his challenge? I was crushed; and he
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left the room triumphant.
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"Does this still seem strange to you? Then put yourself in a
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similar position. Suppose a person of the Fourth Dimension,
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condescending to visit you, were to say, 'Whenever you open your eyes,
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you see a Plane (which is of Two Dimensions) and you _infer_ a Solid
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(which is of Three); but in reality you also see (though you do not
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recognize) a Fourth Dimension, which is not colour nor brightness nor
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anything of the kind, but a true Dimension, although I cannot point
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out to you its direction, nor can you posssibly measure it.' What
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would you say to such a visitor? Would not you have him locked up?
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Well, that is my fate: and it is as natural for us Flatlanders to
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lock up a Square for preaching the Third Dimension, as it is for you
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Spacelanders to lock up a Cube for preaching the Fourth. Alas, how
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strong a family likeness runs through blind and persecuting humanity
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in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes -- we
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are all liable to the same errors, all alike the Slavers of our
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respective Dimensional prejudices, as one of our Spaceland poets has
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said --
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'One touch of Nature makes all worlds akin.'" (footnote 1)
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On this point the defence of the Square seems to me to be
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impregnable. I wish I could say that his answer to the second (or
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moral) objection was equally clear and cogent. It has been objected
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that he is a woman-hater; and as this objection has been vehemently
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urged by those whom Nature's decree has constituted the somewhat
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larger half of the Spaceland race, I should like to remove it, so far
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as I can honestly do so. But the Square is so unaccustomed to the use
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of the moral terminology of Spaceland that I should be doing him an
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injustice if I were literally to transcribe his defence against this
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charge. Acting, therefore, as his interpreter and summarizer, I
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gather that in the course of an imprisonment of seven years he has
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himself modified his own personal views, both as regards Women and as
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regards the Isosceles or Lower Classes. Personally, he now inclines
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to the opinion of the Sphere (see page 86) that the Straight Lines are
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in many important respects superior to the Circles. But, writing as a
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Historian, he has identified himself (perhaps too closely) with the
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views generally adopted by Flatland, and (as he has been informed)
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even by Spaceland, Historians; in whose pages (until very recent
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times) the destinies of Women and of the masses of mankind have seldom
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been deemed worthy of mention and never of careful consideration.
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In a still more obscure passage he now desires to disavow the
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Circular or aristocratic tendencies with which some critics have
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naturally credited him. While doing justice to the intellectual power
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with which a few Circles have for many generations maintained their
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supremacy over immense multitudes of their countrymen, he believes
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that the facts of Flatland, speaking for themselves without comment on
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his part, declare that Revolutions cannot always be suppressed by
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slaughter, and that Nature, in sentencing the Circles to infecundity,
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has condemned them to ultimate failure -- "and herein," he says, "I
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see a fulfilment of the great Law of all worlds, that while the wisdom
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of Man thinks it is working one thing, the wisdom of Nature constrains
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it to work another, and quite a different and far better thing." For
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the rest, he begs his readers not to suppose that every minute detail
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in the daily life of Flatland must needs correspond to some other
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detail in Spaceland; and yet he hopes that, taken as a whole, his work
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may prove suggestive as well as amusing, to those Spacelanders of
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moderate and modestminds who -- speaking of that which is of the
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highest importance, but lies beyond experience -- decline to say on
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the one hand, "This can never be," and on the other hand, "It must
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needs be precisely thus, and we know all about it."
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----------
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Footnote 1. The Author desires me to add, that the misconceptions of
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some of his critics on this matter has induced him to insert (on pp.
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74 and 92) in his dialogue with the Sphere, certain remarks which have
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a bearing on the point in question and which he had previously omitted
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as being tedious and unnecessary.
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* * *
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FLATLAND
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PART 1
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THIS WORLD
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SECTION 1. -- Of the Nature of Flatland
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I call our world Flatland, not because we cal it so, but to make
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its nature clearer to you, my happy readers, who are privileged to
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live in Space.
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Imagine a vast sheet of paper on which straight Lines, Triangles,
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Squares, Pentagons, Hexagons, and other figures, instead of remaining
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fixed in their places, move freely about, on or in the surface, but
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without the power of rising above or sinking below it, very much like
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shadows -- only hard with luminous edges -- and you will then have a
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pretty correct notion of my country and countrymen. Alas, a few years
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ago, I should have said "my universe": but now my mind has been
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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
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the Triangles, Squares, and other figures, moving about as I have
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described them. On the contrary, we could see nothing of the kind,
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not at least so as to distinguish one figure from another. Nothing
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was visible, nor could be visible, to us, except Straight Lines; and
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the necessity of this I will speedily demonstrate.
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Place a penny on the middle of one of your tables in Space; and
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leaning over it, look down upon it. It will appear a circle.
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But now, drawling back to the edge of the table, gradually lower
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your eye (thus bringing yourself more and more into the condition of
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the inhabitants of Flatland), and you will find the penny becoming
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more and more oval to your view, and at last when you have placed your
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eye exactly on the edge of the table (so that you are, as it were,
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actually a Flatlander) the penny will then have ceased to appear oval
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at all, and will have become, so far as you can see, a straight line.
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The same thing would happen if you were to treat in the same way a
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Triangle, or a Square, or any other figure cut out from pasteboard.
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As soon as you look at it with your eye on the edge of the table, you
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will find that it ceases to appear to you as a figure, and that it
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becomes in appearance a straight line. Take for example an
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equilateral Triangle -- who represents with us a Tradesman of the
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respectable class. Figure 1 represents the Tradesman as you would see
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him while you were bending over him from above; figures 2 and 3
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represent the Tradesman, as you would see him if your eye were close
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to the level, or all but on the level of the table; and if your eye
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were quite on the level of the table (and that is how we see him in
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Flatland) you would see nothing but a straight line.
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When I was in Spaceland I heard that your sailors have very
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similar experiences while they traverse your seas and discern some
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distant island or coast lying on the horizon. The far-off land may
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have bays, forelands, angles in and out to any number and extent; yet
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at a distance you see none of these (unless indeed your sun shines
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bright upon them revealing the projections and retirements by means of
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light and shade), nothing but a grey unbroken line upon the water.
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Well, that is just what we see when one of our triangular or other
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acquaintances comes towards us in Flatland. As there is neither sun
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with us, nor any light of such a kind as to make shadows, we have none
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of the helps to the sight that you have in Spaceland. If our friend
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comes closer to us we see his line becomes larger; if he leaves us it
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becomes smaller; but still he looks like a straight line; be he a
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Triangle, Square, Pentagon, Hexagon, Circle, what you will -- a
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straight Line he looks and nothing else.
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You may perhaps ask how under these disadvantages circumstances we
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are able to distinguish our friends from one another: but the answer
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to this very natural question will be more fitly and easily given when
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I come to describe the inhabitants of Flatland. For the present let
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me defer this subject, and say a word or two about the climate and
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houses in our country.
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* * *
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SECTION 2. -- Of the Climate and Houses in Flatland
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As with you, so also with us, there are four points of the compass
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North, South, East, and West.
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There being no sun nor other heavenly bodies, it is impossible for
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us to determine the North in the usual way; but we have a method of
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our own. By a Law of Nature with us, there is a constant attraction
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to the South; and, although in temperate climates this is very slight
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-- so that even a Woman in reasonable health can journey several
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furlongs northward without much difficulty -- yet the hampering effort
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of the southward attraction is quite sufficient to serve as a compass
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in most parts of our earth. Moreover, the rain (which falls at stated
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intervals) coming always from the North, is an additional assistiance;
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and in the towns we have the guidance of the houses, which of course
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have their side-walls running for the most part North and South, so
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that the roofs may keep off the rain from the North. In the country,
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where there are no houses, the trunks of the trees serve as some sort
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of guide. Altogether, we have not so much difficulty as might be
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expected in determining our bearings.
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Yet in our more temperate regions, in which the southward
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attraction is hardly felt, walking sometimes in a perfectly desolate
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plain 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,
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waiting till the rain came before continuing my journey. On the weak
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and aged, and especially on delicate Females, the force of attraction
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tells much more heavily than on the robust of the Male Sex, so that it
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is a point of breeding, if you meet a Lady ont he street, always to
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give her the North side of the way -- by no means an easy thing to do
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always at short notice when you are in rude health and in a climate
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where it is difficult to tell your North from your South.
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Windows there are none in our houses: for the light comes to us
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alike in our homes and out of them, by day and by night, equally at
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all times 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-investigate question,
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"What is the origin of light?" and the solution of it has been
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repeatedly attempted, with no other result than to crowd our lunatic
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asylums with the would-be solvers. Hence, after fruitless attempts to
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suppress such investigations indirectly by making them liable to a
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heavy tax, the Legislature, in comparatively recent times, absolutely
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prohibited them. I -- alas, I alone in Flatland -- know now only too
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well the true solution of this mysterious problem; but my knowledge
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cannot be made intelligible to a single one of my countrymen; and I am
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mocked at -- I, the sole possessor of the truths of Space and of the
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theory fo the introduction of Light from the world of three Dimensions
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-- as if I were the maddest of the mad! But a truce to these painful
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digressions: let me return to our homes.
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The most common form for the construction of a house is five-sided
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or pentagonal, as in the annexed figure. The two Northern sides RO,
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OF, constitute the roof, and for the most part have no doors; on the
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East is 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 doorless.
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Square and triangular houses are not allowed, and for this reason.
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The angles of a Square (and still more those of an equilateral
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Triangle,) being much more pointed than those of a Pentagon, and the
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lines of inanimate objects (such as houses) being dimmer than the
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lines of Men and Women, it follows that there is no little danger lest
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the points of a square of triangular house residence might do serious
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injury to an inconsiderate or perhaps absentminded traveller suddenly
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running against them: and therefore, as early as the eleventh century
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of our era, triangular houses were universally forbidden by Law, the
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only exceptions being fortifications, powder-magazines, barracks, and
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other state buildings, which is not desirable that the general public
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should approach without circumspection.
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At this period, square houses were still everywhere permitted,
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though discouraged by a special tax. But, about three centuries
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afterwards, the Law decided that in all towns containing a population
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above ten thousand, the angle of a Pentagon was the smallest house-
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angle that could be allowed consistently with the public safety. The
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good sense of the community has seconded the efforts of the
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Legislature; and now, even in the country, the pentagonal construction
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has superseded every other. It is only now and then in some very
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remote and backward agricultural district that an antiquarian may
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still discover a square house.
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* * *
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SECTION 3. -- Concerning the Inhabitants of Flatland
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The greatest length or breadth of a full grown inhabitant of
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Flatland may be estimated at about eleven of your inches. Twelve
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inches may be regarded as a maximum.
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Our Women are Straight Lines.
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Our Soldiers and Lowest Class of Workmen are Triangles with two
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equal sides, each about eleven inches long, and a base or third side
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so short (often not exceeding half an inch) that they form at their
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vertices a very sharp and formidable angle. Indeed when their bases
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are of the most degraded type (not more than the eighth part of an
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inch in size), they can hardly be distinguished from Straight lines or
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Women; so extremely pointed are their vertices. With us, as with you,
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these Triangles are distinguished from others by being called
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Isosceles; and by this name I shall refer to them in the following
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pages.
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Our Middle Class consists of Equilateral or Equal-Sided Triangles.
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Our Professional Men and Gentlemen are Squares (to which class I
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myself belong) and Five-Sided Figures or Pentagons.
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Next above these come the Nobility, of whom there are several
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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 honourable
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title of Polygonal, or many-Sided. Finally when the number of the
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sides becomes so numerous, and the sides themselve so small, that the
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figure cannot be distinguished from a circle, he is included in the
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Circular or Priestly order; and this is the highest class of all.
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It is a Law of Nature with us that a male child shall have one
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more side than his father, so that each generation shall rise (as a
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rule) one step in the scale of development and nobility. Thus the son
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of a Square is a Pentagon; the son of a Pentagon, a Hexagon; and so
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on.
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But this rule applies not always to the Tradesman, and still less
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often to the Soldiers, and to the Workmen; who indeed can hardly be
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said to deserve the name of human Figures, since they have not all
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their sides equal. With them therefore the Law of Nature does not
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hold; and the son of an Isosceles (i.e. a Triangle with two sides
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equal) remains Isosceles still. Nevertheless, all hope is not such
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out, even from the Isosceles, that his posterity may ultimately rise
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above his degraded condition. For, after a long series of military
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successes, or diligent and skillful labours, it is generally found
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that the more intelligent among the Artisan and Soldier classes
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manifest a slight increase of their third side or base, and a
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shrinkage of the two other sides. Intermarriages (arranged by the
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Priests) between the sons and daughters of these more intellectual
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members of the lower classes generally result in an offspring
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approximating still more to the type of the Equal-Sided Triangle.
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Rarely -- in proportion to the vast numbers of Isosceles births --
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is a genuine and certifiable Equal-Sided Triangle produced from
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Isosceles parents (footnote 1). Such a birth requires, as its
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antecedents, not only a series of carefully arranged intermarriages,
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but also a long-continued exercise of frugality and self-control on
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the part of the would-be ancestors of the coming Equilateral, and a
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patient, systematic, and continuous development of the Isosceles
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intellect through many generations.
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The birth of a True Equilateral Triangle from Isosceles parents is
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the subject of rejoicing in our country for many furlongs round.
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After a strict examination conducted by the Sanitary and Social Board,
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the infant, if certified as Regular, is with solemn ceremonial
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admitted into the class of Equilaterals. He is then immediately taken
|
|
from his proud yet sorrowing parents and adopted by some childless
|
|
Equilateral, who is bound by oath never to permit the child henceforth
|
|
to enter his former home or so much as to look upon his relations
|
|
again, for fear lest the freshly developed organism may, by force of
|
|
unconscious imitation, fall back again into his hereditary level.
|
|
|
|
The occasional emergence of an Equilateral from the ranks of his
|
|
serf-born ancestors is welcomed, not only by the poor serfs
|
|
themselves, as a gleam of light and hope shed upon the monotonous
|
|
squalor of their existence, but also by the Aristocracy at large; for
|
|
all the higher classes are well aware that these rare phenomena, while
|
|
they do little or nothing to vulgarize their own privileges, serve as
|
|
amost useful barrier against revolution from below.
|
|
|
|
Had the acute-angled rabble been all, without exception,
|
|
absolutely destitute of hope and of ambition, they might have found
|
|
leaders in some of their many seditious outbreaks, so able as to
|
|
render their superior numbers and strength too much even for the
|
|
wisdom of the Circles. But a wise ordinance of Nature has decreed
|
|
that, in proportion as the working-classes increase in intelligence,
|
|
knowledge, and all virtue, in that same proportion their acute angle
|
|
(which makes them physically terrible) shall increase also and
|
|
approximate to their comparatively harmless angle of the Equilateral
|
|
Triangle. Thus, in the most brutal and formidable off the soldier
|
|
class -- creatures almost on a level with women in their lack of
|
|
intelligence -- it is found that, as they wax in the mental ability
|
|
necessary to employ their tremendous penetrating power to advantage,
|
|
so do they wane in the power of penetration itself.
|
|
|
|
How admirable is the Law of Compensation! And how perfect a proof
|
|
of the natural fitness and, I may almost say, the divine origin of the
|
|
aristocratic constitution of the States of Flatland! By a juidicious
|
|
use of this Law of Nature, the Polygons and Circles are almost always
|
|
able to stifle sedition in its very cradle, taking advantage of the
|
|
irrepressible and boundless hopefulness of the human mind. Art also
|
|
comes to the aid of Law and Order. It is generall found possible --
|
|
by a little artificial compression or expansion on the part of the
|
|
State physicians -- to make some of the more intelligent leaders of a
|
|
rebellion perfectly Regular, and to admit them at once into the
|
|
privileged classes; a much larger number, who are still below the
|
|
standard, allured by the prospect of being ultimately ennobled, are
|
|
induced to enter the State Hospitals, where they are kept in
|
|
honourable confinement for life; one or two alone of the most
|
|
obstinate, foolish, and hopelessly irregular are led to execution.
|
|
|
|
Then the wretched rabble of the Isosceles, planless and
|
|
leaderless, are ether transfixed without resistance by the small body
|
|
of their brethren whom the Chief Circle keeps in pay for emergencies
|
|
of this kind; or else more often, by means of jealousies and
|
|
suspicious skillfully fomented among them by the Circular party, they
|
|
are stirred to mutual warfare, and perish by one another's angles. No
|
|
less than one hundred and twenty rebellions are recorded in our
|
|
annals, besides minor outbreaks numbered at two hundred and thirty-
|
|
five; and they have all ended thus.
|
|
----------
|
|
Footnote 1. "What need of a certificate?" a Spaceland critic may ask:
|
|
"Is not the procreation of a Square Son a certificate from Nature
|
|
herself, proving the Equal-sidedness of the Father?" I reply that no
|
|
Lady of any position will mary an uncertified Triangle. Square
|
|
offspring has somethimes resulted from a slightly Irregular Triangle;
|
|
but in almost every such case the Irregularity of the first generation
|
|
is visited on the third; which either fails to attain the Pentagonal
|
|
rank, or relapses to the Triangular.
|
|
|
|
* * *
|
|
|
|
SECTION 4. -- Concerning the Women
|
|
|
|
If our highly pointed Triangles of the Soldier class are
|
|
formidable, it may be readily inferred that far more formidable are
|
|
our Women. For, if a Soldier is a wedge, a Woman is a needle; being,
|
|
so to speak, _all_ point, at least at the two extremities. Add to
|
|
this the power of making herself practically invisible at will, and
|
|
you will perceive that a Female, in Flatland, is a creature by no
|
|
means to be trifled with.
|
|
|
|
But here, perhaps, some of my younger Readers may ask _how_ a
|
|
woman in Flatland can make herself invisible. This ought, I think, to
|
|
be apparent without any explanation. However, a few words will make
|
|
it clear to the most unreflecting.
|
|
|
|
Place a needle on the table. Then, with your eye on the level of
|
|
the table, look at it side-ways, and you see the whole length of it;
|
|
but look at it end-ways, and you see nothing but a point, it has
|
|
become practically invisible. Just so is it with one of our Women.
|
|
When her side is turned towards us, we see her as a straight line;
|
|
when the end containing her eye or mouth -- for with us these two
|
|
organs are identical -- is the part that meets our eye, then we see
|
|
nothing but a highly lustrous point; but when the back is presented to
|
|
our view, then -- being only sub-lustrous, and, indeed, almost as dim
|
|
as an inanimate object -- her hinder extremity serves her as a kind of
|
|
Invisible Cap.
|
|
|
|
The dangers to which we are exposed from our Women must now be
|
|
manifest to the meanest capacity of Spaceland. If even the angle of a
|
|
respectable Triangle in the middle class is not without its dangers;
|
|
if to run against a Working Man involves a gash; if collision with an
|
|
Officer of the military class necessitates a serious wound; if a mere
|
|
touch from the vertex of a Private Soldier brings with it danger of
|
|
death; -- what can it be to run against a woman, except absolute and
|
|
immediate destruction? And when a Woman is invisible, or visible only
|
|
as a dim sub-lustrous point, how difficult must it be, even for the
|
|
most cautious, always to avoid collision!
|
|
|
|
Many are the enactments made at different times in the different
|
|
States of Flatland, in order to minimize this peril; and in the
|
|
Southern and less temperate climates, where the force of gravitation
|
|
is greater, and human beings more liable to casual and involuntary
|
|
motions, the Laws concerning Women are naturally much more stringent.
|
|
But a general view of the Code may be obtained from the following
|
|
summary: --
|
|
|
|
1. Every house shall have one entrance on the Eastern side, for
|
|
the use of Females only; by which all females shall enter "in a
|
|
becoming and respectful manner" (footnote 1) and not by the Men's or
|
|
Western door.
|
|
|
|
2. No Female shall walk in any public place without continually
|
|
keeping up her Peace-cry, under penalty of death.
|
|
|
|
3. Any Female, duly certified to be suffering from St. Vitus's
|
|
Dance, fits, chronic cold accompanied by violent sneezing, or any
|
|
disease necessitating involuntary motions, shall be instantly
|
|
destroyed.
|
|
|
|
In some of the States there is an additional Law forbidding
|
|
Females, under penalty of death, from walking or standing in any
|
|
public place without moving their backs constantly from right to left
|
|
so as to indicate their presence to those behind them; other oblige a
|
|
Woman, when travelling, to be followed by one of her sons, or
|
|
servants, or by her husband; others confine Women altogether in their
|
|
houses except during the religious festivals. But it has bbeen found
|
|
by the wisest of our Circles or Statesmen that the multiplication of
|
|
restrictions on Females tends not only to the debilitation and
|
|
diminution of the race, but also to the increase of domestic murders
|
|
to such an extent that a State loses more than it gains by a too
|
|
prohibitive Code.
|
|
|
|
For whenever the temper of the Women is thus exasperated by
|
|
confinement at home or hampering regulations abroad, they are apt to
|
|
vent their spleen upon their husbands and children; and in the less
|
|
temperate climates the whole male population of a village has been
|
|
sometimes destroyed in one or two hours of a simultaneous female
|
|
outbreak. Hence the Three Laws, mentioned above, suffice for the
|
|
better regulated States, and may be accepted as a rough
|
|
exemplification of our Female Code.
|
|
|
|
After all, our principal safeguard is found, not in Legislature,
|
|
but in the interests of the Women themselves. For, although they can
|
|
inflict instantaneous death by a retrograde movement, yet unless they
|
|
can at once disengage their stinging extremity from the struggling
|
|
body of their vectim, their own frail bodies are liable to be
|
|
shattered.
|
|
|
|
The power of Fashion is also on our side. I pointed out that in
|
|
some less civilized States no female is suffered to stand in any
|
|
public place without swaying her back from right to left. This
|
|
practice has been universal among ladies of any pretensions to
|
|
breeding in all well-governed States, as far back as the memory of
|
|
Figures can reach. It is considered a disgrace to any state that
|
|
legislation should have to enforce what ought to be, and is in every
|
|
respectable female, a natural instinct. The rhythmical and, if I may
|
|
so say, well-modulated undulation of the back in our ladies of
|
|
Circular rank is envied and imitated by the wife of a common
|
|
Equilateral, who can achieve nothing beyond a mere monotonous swing,
|
|
like the ticking of a pendulum; and the regular tick of the
|
|
Equilateral is no less advmired and copied by the wife of the
|
|
progressive and aspiring Isosceles, in the females of whose famil no
|
|
"back-motion" of any kind has become as yet a necessity of life.
|
|
Hence, in every family of position and consideration, "back motion" is
|
|
as prevalent as time itself; and the husbands and sons in these
|
|
households enjoy immunity at least from invisible attacks.
|
|
|
|
Not that it must be for a moment supposed that our Women are
|
|
destitute of affection. But unfortunately the passion of the moment
|
|
predominates, in the Frail Sex, over every other consideration. This
|
|
is, of course, a necessity arising from their unfortunate
|
|
conformation. For as they have no pretensions to an angle, being
|
|
inferior in this respect to the very lowest of the Isosceles, they are
|
|
consequently wholly devoid of brainpower, and have neither reflection,
|
|
judgment nor forethought, and hardly any memory. Hence, in their fits
|
|
of fury, they remember no claims and recognize no distinctions. I
|
|
have actually known a case where a Woman has exterminated her whole
|
|
household, and half an hour afterwards, when her rage was over and the
|
|
fragments swept away, has asked what has become of her husband and
|
|
children.
|
|
|
|
Obviously then a Woman is not to be irritated as long as she is in
|
|
a position where she can turn round. When you have them in their
|
|
apartments -- which are constructed with a view to denying them that
|
|
power -- you can say and do what you like; for they are then wholly
|
|
impotent for mischief, and will not remember a few minutes hence the
|
|
incident for which they may be at this moment threatening you with
|
|
death, nor the promises which you may have found it necessary to make
|
|
in order to pacify their fury.
|
|
|
|
On the whole we got on pretty smoothly in our domestic relations,
|
|
except in the lower strata of the Military Classes. There the want of
|
|
tact and discretion on the part of the husbands produces at times
|
|
indescribable disasters. Relying too much on the offensive weapons of
|
|
their acute angles instead of the defensive organs of good sense and
|
|
seasonable simulations, these reckless creatures too often neglect the
|
|
prescribed construction of the women's apartments, or irritate their
|
|
wives by ill-advised expressions out of doors, which they refuse
|
|
immediately to retract. Moreover a blunt and stolid regard for
|
|
literal truth indisposes them to make those lavish promises by which
|
|
the more judicious Circle can in a moment pacify his consort. The
|
|
result is massacre; not, however, without its advantages, as it
|
|
eliminates the more brutal and troublesome of the Isosceles; and by
|
|
many of our Circles the destructiveness of the Thinner Sex is regarded
|
|
as one among many providential arrangements for suppressing redundant
|
|
population, and nipping Revolution in the bud.
|
|
|
|
Yet even in our best regulated and most approximately Circular
|
|
families I cannot say that the ideal of family life is so high as with
|
|
you in Spaceland. There is peace, in so far as the absence of
|
|
slaughter may be called by that name, but there is necessarily little
|
|
harmony of tastes or pursuits; and the cautious wisdom of the FCircles
|
|
has ensured safety at the cost of domestic comfort. In every Circular
|
|
or Polygonal household it has been a habit from time immemorial -- and
|
|
now has become a kind of instinct among the women of our higher
|
|
classes -- that the mothers and daughters should constantly keep their
|
|
eyes and mouths towards their husband and his male friends; and for a
|
|
lady in a family of distinction to turn her back upon her husband
|
|
would be regarded as a kind of portent, involving loss of _status._
|
|
But, as I shall soon shew, this custom, though it has the advantage of
|
|
safety, is not without disadvantages.
|
|
|
|
In the house of the Working Man or respectable Tradesman -- where
|
|
the wife is allowed to turn her back upon her husband, while pursuing
|
|
her household avocations -- there are at least intervals of quiet,
|
|
when the wife is neither seen nor heard, except for the humming sound
|
|
of the continuous Peace-cry; but in the homes of the upper classes
|
|
there is too often no peace. There the voluble mouth and bright
|
|
penetrating eye are ever directed toward the Master of the household;
|
|
and light itself is not more persistent than the stream of Feminine
|
|
discourse. The tact and skill which suffice to avert a Woman's sting
|
|
are unequal to the task of stopping a Woman's mouth; and as the wife
|
|
has absolutely nothing to say, and absolutely no constraint of wit,
|
|
sense, or conscience to prevent her from saying it, not a few cynics
|
|
have been found to aver that they prefer the danger of the death-
|
|
dealing but inaudible sting to the safe sonorousness of a Woman's
|
|
other end.
|
|
|
|
To my readers in Spaceland the condition of our Women may seen
|
|
truly deplorable, and so indeed it is. A Male of the lowest type of
|
|
the Isosceles may look forward to some improvement of his angle, and
|
|
to the ultimate elevation of the whole of his degraded caste; but no
|
|
Woman can entertain such opes for her sex. "Once a Woman, always a
|
|
Woman" is a Decree of Nature; and the very Laws of Evolution seem
|
|
suspended in her disfavour. Yet at least we can admire the wise
|
|
Prearrangement which has ordained that, as they have no hopes, so they
|
|
shall have no memory to recall, and no forethought to anticipate, the
|
|
miseries and humiliations which are at once a necessity of their
|
|
existence and the basis of the constitution of Flatland.
|
|
|
|
* * *
|
|
|
|
SECTION 5. -- Of our Methods of Recognizing one another
|
|
|
|
You, who are blessed with shade as well as light, you, who are
|
|
gifted with two eyes, endowed with a knowledge of perspective, and
|
|
charmed with the enjoyment of various colours, you, who can actually
|
|
_see_ an angle, and contemplate the complete circumference of a Circle
|
|
in the happy region of the Three Dimensions -- how shall I make it
|
|
clear to you the extreme difficulty which we in Flatland experience in
|
|
recognizing one another's configuration?
|
|
|
|
Recall what I told you above. All beings in Flatland, animate and
|
|
inanimate, no matter what their form, present _to our view_ the same,
|
|
or nearly the same, appearance, viz. that of a straight Line. How
|
|
then can one be distinguished from another, where all appear the same?
|
|
|
|
The answer is threefold. The first means of recognition is the
|
|
sense of hearing; which with us is far more highly developed than with
|
|
you, and which enables us not only to distinguish by the voice of our
|
|
personal friends, but even to discriminate between different clases,
|
|
at least so far as concerns the three lowest orders, the Equilateral,
|
|
the Square, and the Pentagon -- for the Isosceles I take no account.
|
|
But as we ascend the social scale, the process of discriminating and
|
|
being discriminated by hearing increases in difficulty, partly because
|
|
voices are assimilated, partly because the faculty of voice-
|
|
discrimination is a plebeian virtue not much developed among the
|
|
Aristocracy. And wherever there is any danger of imposture we cannot
|
|
trust to this method. Amongst our lowest orders, the vocal organs are
|
|
developed to a degree more than correspondent with those of hearing,
|
|
so that an Isosceles can easily feign the voice of a Polygon, and,
|
|
with some training, that of a Circle himself. A second method is
|
|
therefore more commonly resorted to.
|
|
|
|
_Feeling_ is, among our Women and lower classes -- about our upper
|
|
classes I shalls peak presently -- the principal test of recognition,
|
|
at all events between strangers, and when the question is, not as to
|
|
the individual, but as to the class. What therefore "introduction" is
|
|
among the higher classes in Spaceland, that the process of "feeling"
|
|
is with us. "Permit me to ask you to feel and be felt by my friend
|
|
Mr. So-and-so" -- is still, among the more old-fashioned of our
|
|
country gentlemen in districts remote from towns, the customary
|
|
formula for a Flatland introduction. But in the towns, and among men
|
|
of business, the words "be felt by" are omitted and the sentence is
|
|
abbreviated to, "Let me ask you to feel Mr. So-and-so"; although it is
|
|
assumed, of course, that the "feeling" is to be reciprocal. Among our
|
|
still more modern and dashing young gentlemen -- who are extremely
|
|
averse to superfluous effort and supremely indifferent to the purity
|
|
of their native language -- the formula is still further curtailed by
|
|
the use of "to feel" in a technical sense, meaning, "to recommend-for-
|
|
the-purposes-of-feeling-and-being-felt"; and at this moment the
|
|
"slang" of polite or fast society in the upper classes sanctions such
|
|
a barbarism as "Mr. Smith, permit me to feel Mr. Jones."
|
|
|
|
Let not my Reader however suppose that "feeling" is with us the
|
|
tedious process that it would be with you, or that we find it
|
|
necessary to feel right round all the sides of every individual before
|
|
we determine the class to which he belongs. Long practice and
|
|
training, begun in the schooles and continued in the experience of
|
|
daily life, enable us to discriminate at once by the sense of touch,
|
|
between the angles of an equal-sided Triangle, Square, and Pentagon;
|
|
and I need not say that the brainless vertex of an acute-angled
|
|
Isosceles is obvious to the dullest touch. It is therefore not
|
|
necessary, as a rule, to do more than feel a single angle of an
|
|
individual; and this, once ascertained, tells us the class of the
|
|
person whom we are addressing, unless indeed he belongs to the higher
|
|
sections of the nobility. There the difficulty is much greater. Even
|
|
a Master of Arts in our University of Wentbridge has been known to
|
|
confuse a ten-sided with a twelve-sided Polygon; and there is hardly a
|
|
Doctor of Science in or out of that famous University who could
|
|
pretend to decide promptly and unhestitatingly between a twenty-sided
|
|
and a twenty-four sided member of the Aristocracy.
|
|
|
|
Those of my readers who recall the extracts I gave above from the
|
|
Legislative code concerning Women, will readily perceive that the
|
|
process of introduction by contact requires some care and discretion.
|
|
Otherwise the angles might inflict on the unwary Feeling irreparable
|
|
injury. It is essential for the safety of the Feeler that the Felt
|
|
should stand perfectly still. A start, a fidgety shifting of the
|
|
position, yes, even a violent sneeze, has been known before now to
|
|
prove fatal to the incautious, and to nip in the bud many a promising
|
|
friendship. Especially is this true among the lower classes of the
|
|
Triangles. With them, the eye is situated so far from their vertex
|
|
that they can scarcely take cognizance of what goes on at that
|
|
extremity of their frame. They are, moreover, of a rough coarse
|
|
nature, not sensitive to the delicate touch of the highly organized
|
|
Polygon. What wonder then if an involuntary toss of the head has ere
|
|
now deprived the State of a valuable life!
|
|
|
|
I have heard that my excellent Grandfather -- one of the least
|
|
irregular of his unhappy Isosceles class, who indeed obtained, shortly
|
|
before his decease, four out of seven botes from the Sanitary and
|
|
Social Board for passing him into the class of the Equal-sided --
|
|
often deplored, with a tear in his venerable eye, a miscarriage of
|
|
this kind, which had occured to his great-great-great-Grandfather, a
|
|
respectable Working Man with an angle or brain of 59 degrees 30
|
|
minutes. According to his account, my unfortunately Ancestor, being
|
|
afflicted with rheumatism, and in the act of being felt by a Polygon,
|
|
by one sudden start accidentally transfixed the Great Man through the
|
|
diagonal and thereby, partly in consequence of his long imprisonment
|
|
and degradation, and partly because of the moral shock which pervaded
|
|
the whole of my Ancestor's relations, threw back our family a degree
|
|
and a half in their ascent towards better things. The result was that
|
|
in the next generation the family brain was registered at only 58
|
|
degrees, and not till the lapse of five generations was the lost
|
|
ground recovered, the full 60 degrees attained, and the Ascent from
|
|
the Isosceles finally achieved. And all this series of calamaties
|
|
from one little accident in the process of Feeling.
|
|
|
|
As this point I think I hear some of my better educated readers
|
|
exclaim, "How could you in Flatland know anything about angles and
|
|
degrees, or minutes? We _see_ an angle, because we, in the region of
|
|
Space, can see two straight lines inclined to one another; but you,
|
|
who can see nothing but on straight line at a time, or at all events
|
|
onlly a number of bits of straight lines all in one straight line, --
|
|
how can you ever discern an angle, and much less register angles of
|
|
different sizes?"
|
|
|
|
I answer that though we cannot _see- angles, we can _infer_ them,
|
|
and this with great precision. Our sense of touch, stimulated by
|
|
necessity, and developed by long training, enables us to distinguish
|
|
angles far more accurately than your sense of sight, when unaided by a
|
|
rule or measure of angles. nor must I omit to explain that we have
|
|
great natural helps. It is with us a Law of Nature that the brain of
|
|
the Isosceles class shall begin at half a degree, or thirty minutes,
|
|
and shall increase (if it increases at all) by half a degree in every
|
|
generation until the goal of 60 degrees is reached, when the condition
|
|
of serfdom is quitted, and the freeman enters the class of Regulars.
|
|
|
|
Consequently, Nature herself supplies us with an ascending scale
|
|
or Alphabet of angles for half a degree up to 60 degrees, Specimen of
|
|
which are placed in every Elementary School throughout the land.
|
|
Owing to occasional retrogressions, to still more frequent moral and
|
|
intellectual stagnation, and to the extraordinary fecundity of the
|
|
Criminal and Vagabond classes, there is always a vast superfluity of
|
|
individuals of the half degree and single degree class, and a fair
|
|
abundance of Specimens up to 10 degrees. These are absolutely
|
|
destitute of civil rights; and a great number of them, not having even
|
|
intelligence enough for the purposes of warfare, are devoted by the
|
|
States to the service of education. Fettered immovably so as to
|
|
remove all possibility of danger, they are placed in the classrooms of
|
|
our Infant Schools, and there they are utilized by the Board of
|
|
Education for the pupose of imparting to the offspring of the Middle
|
|
Classes the tact and intelligence which these wretched creatures
|
|
themselves are utterly devoid.
|
|
|
|
In some States the Specimens are occasionally fed and suffered to
|
|
exist for several years; butin the more temperate and better regulated
|
|
regions, it is found in the long run more advantageous for the
|
|
educational interests of the young, to dispense with food, and to
|
|
renew the Specimens every month -- which is about the average duration
|
|
of the foodless existence of the Criminal class. In the cheaper
|
|
schools, what is gained by the longer existence of the Specimen is
|
|
lost, partly in the expenditure for food, and partly in the diminished
|
|
accuracy of the angles, which are impaired after a few weeks of
|
|
constant "feeling." Nor must we forget to add, in enumerating the
|
|
advantages of the more expensive system, that it tends, though
|
|
slightly yet perceptibly, to the diminution of the redundant Isosceles
|
|
population -- an object which every statesman in Flatland constantly
|
|
keeps in view. On the whole therefore -- although I am not ignorant
|
|
that, in many popularly elected School Boards, there is a reaction in
|
|
favour of "the cheap system" as it is called -- I am myself disposed
|
|
to think that this is one of the many cases in which expense is the
|
|
truest economy.
|
|
|
|
But I must not allow questions of School Board politics to divert
|
|
me from my subject. Enough has been said, I trust, to shew that
|
|
Recognition by FEeling is not so tedious or indecisive a process as
|
|
might have been supposed; and it is obviously more trustworthy than
|
|
Recognition by hearing. Still there remains, as has been pointed out
|
|
above, the objection that this method is not without danger. For this
|
|
reason many in the Middle and Lower classes, and all without exception
|
|
in the Polygonal and Circular orders, prefer a third method, the
|
|
description of which shall be reserved for the next section.
|
|
|
|
* * *
|
|
|
|
SECTION 6. -- Of Recognition by Sight
|
|
|
|
I am about to appear very inconsistent. In the previous sections
|
|
I have said that all figures in Flatland present the appearance of a
|
|
straight line; and it was added or implied, that it is consequently
|
|
impossible to distinguish by the visual organ between individuals of
|
|
different classes: yet now I am about to explain to my Spaceland
|
|
critics how we are able to recognize one another by the sense of
|
|
sight.
|
|
|
|
If however the Reader will take the trouble to refer to the
|
|
passage in which Recognition by Feeling is stated to be universal, he
|
|
will find this qualification -- "among the lower classes." It is only
|
|
among the higher classes and in our more temperate climates that Sight
|
|
Recognition is practised.
|
|
|
|
That this power exists in any regions and for any classes is the
|
|
result of Fog; which prevails during the greater part of the year in
|
|
all parts save the torrid zones. That which is with you in Spaceland
|
|
an unmixed evil, blotting out the landscape, depressing the spirits,
|
|
and enfeebling the health, is by us recognized as a blessing scarcely
|
|
inferior to air itself, and as the Nurse of arts and Parent os
|
|
sciences. But let me explain my meaning, without further eulogies on
|
|
this beneficent Element.
|
|
|
|
If Fog were non-existent, all lines would appear equally and
|
|
indistinguishably clear; and this is actually the case in those
|
|
unhappy countries in which the atmosphere is perfectly dry and
|
|
transparent. But wherever there is a rich supply of Fog, objects that
|
|
are at a distance, say of three feet, are appreciably dimmer than
|
|
those at the distance of two feet eleven inches; and the result is
|
|
that by careful and constant experimental observation of comparative
|
|
dimness and constant experimental observation of comparative dimness
|
|
and clearness, we are enabled to infer with great exactness the
|
|
configuration of the object observed.
|
|
|
|
An instace will do more than a volume of generalities to make my
|
|
meaning clear.
|
|
|
|
Suppose I see two individuals approaching whose rank I wish to
|
|
ascertain. They are, we will suppose, a Merchant and a Physician, or
|
|
in other words, an Equilaterial Triangle and a Pentagon; how am I to
|
|
distinuish them?
|
|
|
|
It will be obvious, to every child in Spaceland who has touched
|
|
the threshold of Geometrical Studies, that, if I can bring my eye so
|
|
that its glance may bisect an angle (A) of the approaching stranger,
|
|
my view will lie as it were evenly between the two sides that are next
|
|
to me (viz. CA and AB), so that I shall contemplate the two
|
|
impartially, and both will appear of the same size.
|
|
|
|
Now inthe case of (1) the Merchant, what shall I see? I shall see
|
|
a straight line DAE, in which the middle point (A) will be very bright
|
|
because it is nearest to me; but on either side the line will shade
|
|
away _rapidly to dimness,_ because the sides AC and AB _recede rapidly
|
|
into the fog_ and what appear to me as the Merchant's extremities,
|
|
viz. D and E, will be _very dim indeed._
|
|
|
|
On the other hand in the case of (2) the Physician, though I shall
|
|
here also see a line (D'A'E') with a bright centre (A'), yet it will
|
|
shade away _less rapidly_ to dimness, because the sides (A'C', A'B')
|
|
_recede less rapidly into the fog:_ and what appear to me the
|
|
Physician's extremities, viz. D' and E', will not be _not so dim_ as
|
|
the extremities of the Merchant.
|
|
|
|
The Reader will probably understand from these two instances how -
|
|
- after a very long training supplemented by constant experience -- it
|
|
is possible for the well-educated classes among us to discriminate
|
|
with fair accuracy between the middle and lowest orders, by the sense
|
|
of sight. If my Spaceland Patrons have grasped this general
|
|
conception, so far as to conceive the possibility of it and not to
|
|
reject my account as altogether incredible -- I shall have attained
|
|
all I can reasonably expect. Were I to attempt further details I
|
|
should only perplex. Yet for the sake of the young and inexperienced,
|
|
who may perchance infer -- from the two simple instances I have given
|
|
above, of the manner in which I should recognize my Father and my Sons
|
|
-- that Recognition by sight is an easy affair, it may be needful to
|
|
point out that in actual life most of the problems of Sight
|
|
Recognition are far more subtle and complex.
|
|
|
|
If for example, when my Father, the Triangle, approaches me, he
|
|
happens to present his side to me instead of his angle, then, until I
|
|
have asked him to rotate, or until I have edged my eye around him, I
|
|
am for the moment doubtful whether he may not be a Straight Line, or,
|
|
in other words, a Woman. Again, when I am in the company of one of my
|
|
two hexagonal Grandsons, contemplating one of his sides (AB) full
|
|
front, it will be evident from the accompanying diagram that I shall
|
|
see one whole line (AB) in comparative brightness (shading off hardly
|
|
at all at the ends) and two smaller lines (CA and BD) dim throughout
|
|
and shading away into greater dimness towards the extremities C and D.
|
|
|
|
But I must not give way to the temptating of enlarging on these
|
|
topics. The meanest mathematician in Spaceland will readily believe
|
|
me when I assert that the problems of life, which present themselves
|
|
to the well-educated -- when they are themselves in motion, rotating,
|
|
advancing or retreating, and at the same time attempting to
|
|
discriminate by the sense of sight between a number of Polygons of
|
|
high rank moving in different directions, as for example in a ball-
|
|
room or conversazione -- must be of a nature to task the angularity of
|
|
the most intellectual, and amply justify the rich endowments of the
|
|
Learned Professors of Geometry, both Static and Kinetic, in the
|
|
illustrious University of Wentbridge, where the Science and Art of
|
|
Sight Recognition are regularly taught to large classes of the _elite_
|
|
of the States.
|
|
|
|
It is only a few of the scions of our noblest and wealthies
|
|
houses, who are able to give the time and money necessary for the
|
|
thorough prosecution of this noble and valuable Art. Even to me, a
|
|
Mathematician of no mean standing, and the Granddfather of two most
|
|
hopeful and perfectly regular Hexagons, to find myself in the midst of
|
|
a crowd of rotating Polygons of the higher classes, is occasionally
|
|
very perplexing. And of course to a common Tradesman, or Serf, such a
|
|
sight is almost as unintelligible as it would be to you, my Reader,
|
|
were you suddenly transported to my country.
|
|
|
|
In such a crowd you could see on all sides of you nothing but a
|
|
Line, apparently straight, but of which the parts would vary
|
|
irregularly and perpetually in brightness or dimness. Even if you had
|
|
completed your third year in the Pentagonal and Hexagonal classes in
|
|
the University, and were perfect in the theory of the subject, you
|
|
would still find there was need of many years of experience, before
|
|
you could move in a fashionable crowd without jostling against your
|
|
betters, whom it is against etiquette to ask to "feel," and who, by
|
|
their superior culture and breeding, know all about your movements,
|
|
while you know very little or nothing about theirs. in a word, to
|
|
comport oneself with perfect propriety in Polygonal society, one ought
|
|
to be a Polygon oneself. Such at least is the painful teaching of my
|
|
experience.
|
|
|
|
It is astonishing how much the Art -- or I may almost call it
|
|
instinct -- of Sight Recognition is developed by the habitual practice
|
|
of it and by the avoidance of the custom of "Feeling." Just as, with
|
|
you, the deaf and dumb, if once allowed to gesticulate and to use the
|
|
hand-alphabet, will never acquire the more difficult but far more
|
|
valuable art of lip-speech and lip-reading, so it is with us as
|
|
regards "Seeing" and "Feeling." None who in early life resort to
|
|
"Feeling" will ever learn "Seeing" in perfection.
|
|
|
|
For this reason, among our Higher Classes, "Feeling" is
|
|
discouraged or absolutely forbidden. From the cradle their children,
|
|
instead of going to the Public Elementary schools (where the art of
|
|
Feeling is taught,) are sent to higher Seminaries of an exclusive
|
|
character; and at our illustrius University, to "feel" is regarded as
|
|
a most serious fault, involving Rustication for the first offence, and
|
|
Expulsion for the second.
|
|
|
|
But among the lower classes the art of Sight Recognition is
|
|
regarded as an unattainable luxury. A common Tradesman cannot afford
|
|
to let his sun spend a third of his life in abstract studies. The
|
|
children of the poor are therefore allowed to "feel" from their
|
|
earliest years, and they gain thereby a precocity and an early
|
|
vivacity which contrast at first most favourably with the inert,
|
|
undeveloped, and listless behaviour of the half-instructed youths of
|
|
the Polygonal class; but when the latter have at last completed their
|
|
University course, and are prepared to put their theory into practice,
|
|
the change that comes over them may almost be described as a new
|
|
birth, and in every art, science, and social pursuit they rapidly
|
|
overtake and distance their Triangular competitors.
|
|
|
|
Only a few of the Polygonal Class fail to pass the Final Test or
|
|
Leaving Examination at the University. The condition of the
|
|
unsuccessful minority is truly pitiable. Rejected from the higher
|
|
class,, they are also despised by the lower. They have neither the
|
|
matured and systematically trained powers of the Polygonal Bachelors
|
|
and Masters of Arts, nor yet the native precocity and mercurial
|
|
versatility of the youthful Tradesman. The professions, the public
|
|
services, are closed against them, and though in most States they are
|
|
not actually debarred from marriage, yet they have the greatest
|
|
difficulty in forming suitable alliances, as experience shews that the
|
|
offspring of such unfortunate and ill-endowed parents is generally
|
|
itself unfortunate, if not positively Irregular.
|
|
|
|
It is from these specimens of the refuse of our Nobility that the
|
|
great Tumults and Seditions of past ages have generally derived their
|
|
leaders; and so great is the mischief thence arising that an
|
|
increasing minotiry of our more progressive Statesmen are of opinion
|
|
that true mercy would dictate their entire suppression, by enacting
|
|
that all who fail to pass the Final Examination of the University
|
|
should be either imprisoned for life, or extinguished by a painless
|
|
death.
|
|
|
|
But I find myself digressing into the subect of Irregularities, a
|
|
matter of such vital interest that it demans a separate section.
|
|
|
|
* * *
|
|
|
|
SECTION 7. -- Concerning Irregular Figures
|
|
|
|
Throughout the previous pages I have been assuming -- what perhaps
|
|
should have been laid down at the beginning as a distinct and
|
|
fundamental proposition -- that every human being in Flatland is a
|
|
Regular Figure, that is to say of regular construction. By this I
|
|
mean that a Woman must not only be a line, but a straight line; that
|
|
an Artisan or Soldier must have two of his sides equal; that Tradesmen
|
|
must have three sides equal; Lawyers (of which class I am a humble
|
|
member), four sides equal, and, generally, that in every Polygon, all
|
|
the sides must be equal.
|
|
|
|
The sizes of the sides would of course depend upon the age of the
|
|
individual. A Female at birth would be about an inch long, while a
|
|
tall adult Woman might extend to a foot. As to the Males of every
|
|
class, it may be roughly said that the length of an adult's size, when
|
|
added together, is two feet or a little more. But the size of our
|
|
sides is not under consideration. I am speaking of the _equality_ of
|
|
sides, and it does not need much reflection to see that the whole of
|
|
the social life in Flatland rests upon the fundamental fact that
|
|
Nature wills all Figures to have their sides equal.
|
|
|
|
If our sides were unequal our angles might be unequal. Instead of
|
|
its being sufficient to feel, or estimate by sight, a single angle in
|
|
order to determine the form of an individual, it would be necessary to
|
|
ascertain each angle by the experiment of Feeling. But life would be
|
|
too short for such a tedious groping. The whole science and art of
|
|
Sight Recognition would at once perish; Feeling, so far as it is an
|
|
art, would not long survive; intercourse would become perilous or
|
|
impossible; there would be an end to all confidence, all forethought;
|
|
no one would be safe in making the most simple social arrangements; in
|
|
a word, civilization might relapse into barbarism.
|
|
|
|
Am I going too fast to carry my Readers with me to these obvious
|
|
conclusions? Surely a moment's reflection, and a single instance from
|
|
common life, must convince every one that our social system is based
|
|
upon Regularity, or Equality of Angles. You meet, for example, two or
|
|
three Tradesmen in the street, whom your recognize at once to be
|
|
Tradesman by a glance at their angles and rapidly bedimmed sides, and
|
|
you ask them to step into your house to lunch. This you do at present
|
|
with perfect confidence, because everyone knows to an inch or two the
|
|
area occupied by an adult Triangle: but imagine that your Tradesman
|
|
drags behind his regular and respectable vertex, a parallelogram of
|
|
twelve or thirteen inches in diagonal: -- what are you to do with such
|
|
a monster sticking fast in your house door?
|
|
|
|
But I am insulting the intelligence of my Readers by accumulating
|
|
details which must be patent to everyone who enjoys the advantages of
|
|
a Residence in Spaceland. Obviously the measurements of a single
|
|
angle would no longer be sufficient under such portentous
|
|
circumstances; one's whole life would be taken up in feeling or
|
|
surveying the perimeter of one's acquaintances. Already the
|
|
difficulties of avoiding a collision in a crowd are enough to tax the
|
|
sagacity of even a well-educated Square; but if no one could calculate
|
|
the Regularity of a signle figure in the company, all would be chaos
|
|
and confusion, and the slightest panic would cause serious injuries,
|
|
or -- if there happened to be any Women or Soldiers present -- perhaps
|
|
considerable loss of life.
|
|
|
|
Expediency therefore concurs with Nature in stamping the seal of
|
|
its approval upon Regularity of conformation: nor has the Law been
|
|
backward in seconding their efforts. "Irregularity of Figure" means
|
|
with us the same as, or more than, a combination of moral obliquity
|
|
and criminality with you, and is treated accordingly. There are not
|
|
wanting, it is true, some promulgators of paradoxes who maintain that
|
|
there is no necessary connection between geometrical and moral
|
|
Irregularity. "The Irregular," they say, "is from his birth scouted
|
|
by his own parents, derided by his brothers and sisters, neglected by
|
|
the domestics, scorned and suspected by society, and excluded from all
|
|
posts of responsibility, trust, and useful activity. His every
|
|
movement is jealously watched by the police till he comes of age and
|
|
presents himself for inspection; then he is either destroyed, if he is
|
|
found to exceed the fixed margin of deviation, at an uninteresting
|
|
occupation for a miserable stipend; obliged to live and board at the
|
|
office, and to take even his vacation under close supervision; what
|
|
wonder that human nature, even in the best and purest, is embittered
|
|
and perverted by such surroundings!"
|
|
|
|
All this very plausible reasoning does not convince me, as it has
|
|
not convinced the wisest of our Statesmen, that our ancestors erred in
|
|
laying it down as an axiom of policy that the toleration of
|
|
Irregularity is incompatible with the safety of the State. Doubtless,
|
|
the life of an Irregular is hard; but the interests of the Greater
|
|
Number require that it shall be hard. If a man with a triangular frnt
|
|
and a polygonal back were allowed to exist and to propagate a still
|
|
more Irregular posterity, what would become of the arts of life? Are
|
|
the houses and doors and churches in Flatland to be altered in order
|
|
to accommodate such monsters? Are our ticket-collectors to be
|
|
required to measure every man's perimeter before they allow him to
|
|
enter a theatre, or to take his place in a lecture room? Is an
|
|
Irregular to be exempted from the militia? And if not, how is he to
|
|
be prevented from carrying desolation into the ranks of his comrades?
|
|
Again, what irresistible temptations to fraudulent impostures must
|
|
needs beset such a creature! How easy for him to enter a shop with
|
|
his polygonal front foremost, and to order goods to any extent from a
|
|
confiding tradesman! Let the advocates of a falsely called
|
|
Philanthropy plead as they may for the abrogation of the Irregular
|
|
Penal Laws, I for my part have never known an Irregular who was not
|
|
also what Nature evidently intended him to be -- a hypocrite, a
|
|
misanthropist, and, up to the limits of his power, a perpetrator of
|
|
all manner of mischief.
|
|
|
|
Not that I should be disposed to recommend (at present) the
|
|
extreme measures adopted by some States, where an infant whose angle
|
|
deviates by half a degree from the correct angularity is summarily
|
|
destroyed at birth. Some of our highest and ablest men, men of real
|
|
genius, have during their earliest days laboured under deviations as
|
|
great as, or even greater than forty-five minutes: and the loss of
|
|
their precious lives would have been an irreparable injury to the
|
|
State. The art of healing also has achieved some of its most glorious
|
|
triumphs in the compressions, extensions, trepannings, colligations,
|
|
and other surgical or diaetetic operations by which Irregularity has
|
|
been partly or wholly cured. Advocating therefore a _Via Media,_ I
|
|
would lay down no fixed or absolute line of demarcation; but at the
|
|
period when the frame is just beginning to set, and when the Medical
|
|
Board has reported that recovery is improbably, I would suggest that
|
|
the Irregular offspring be painlessly and mercifully consumed.
|
|
|
|
* * *
|
|
|
|
SECTION 8. -- Of the Ancient Practice of Painting
|
|
|
|
If my Readers have followed me with any attention up to this
|
|
point, they will not be surprised to hear that life is somewhat dull
|
|
in Flatland. I do not, of course, mean that there are not battles,
|
|
conspiracies, tumults, factions, and all those other phenomena which
|
|
are supposed to make History interesting; nor would I deny that the
|
|
strange mixture of the problems of life and the problems of
|
|
Mathematics, continually inducing conjecture and giving an opportunity
|
|
of immediate verification, imparts to our existence a zest which you
|
|
in Spaceland can hardly comprehend. I speak now from the aesthetic
|
|
and artistic point of view when I say that life with us is dull;
|
|
aesthetically and artistically, very dull indeed.
|
|
|
|
How can it be otherwise, when all one's prospect, all one's
|
|
landscapes, historical pieces, portraits, flowers, still life, are
|
|
nothing but a single line, with no varieties except degrees of
|
|
brightness and obscurity?
|
|
|
|
It was not always thus. Colour, if Tradition speaks the truth,
|
|
once for the space of half a dozen centuries or more, threw a
|
|
transient splendour over the lives of our ancestors in the remotest
|
|
ages. Some private individual -- a Pentagon whose name is variously
|
|
reported -- having casually discovered the constituents of the simpler
|
|
colours and a rudimentary method of painting, is said to have begun by
|
|
decorating first his house, then his slaves, then his Father, his
|
|
Sons, and Grandsons, lastly himself. The convenience as well as the
|
|
beauty of the results commended themselves to all. Wherever
|
|
Chromatistes, -- for by that name the most trustworthy authorities
|
|
concur in calling him, -- turned his variegated frame, there he at
|
|
once excited attention, and attracted respect. No one now needed to
|
|
"feel" him; no one mistook his front for his back; all his movements
|
|
were readily ascertained by his neighbours without the slightest
|
|
strain on their powers of calculation; no one jostled him, or failed
|
|
to make way for him; his voice was saved the labour of that exhausting
|
|
utterance by which we colourless Squares and Pentagons are often
|
|
forced to proclaim our individuality when we move amid a crowd of
|
|
ignorant Isosceles.
|
|
|
|
The fashion spread like wildfire. Before a week was over, every
|
|
Square and Triangle in the district had copied the example of
|
|
Chromatistes, and only a few of the more conservative Pentagons still
|
|
held out. A month or two found even the Dodecagons infected with the
|
|
innovation. A year had not elapsed before the habit had spread to all
|
|
but the very highest of the Nobility. Needless to say, the custom
|
|
soon made its way from the district of Chromatistes to surrounding
|
|
regions; and within two generations no one in all Flatland was
|
|
colourless except the Women and the Priests.
|
|
|
|
Here Nature herself appeared to erect a barrier, and to plead
|
|
against extending the innovations to these two classes. Many-
|
|
sidedness was almost essential as a pretext for the Innovators.
|
|
"Distinction of sides is intended by Nature to imply distinction of
|
|
colours" -- such was the sophism which in those days flew from mouth
|
|
to mouth, converting whole towns at a time to a new culture. But
|
|
manifestly to our Priests and Women this adage did not apply. The
|
|
latter had only one side, and therefore -- plurally and pedanticallly
|
|
speaking -- _no sides._ The former -- if at least they would assert
|
|
their claim to be readily and truly Circles, and not mere high-class
|
|
Polygons, with an infinitely large number of infinitesimally small
|
|
sides -- were in the habit of boasting (what Women confessed and
|
|
deplored) that they also had no sides, being blessed with a perimeter
|
|
of only one line, or, in other words, a Circumference. Hence it came
|
|
to pass that these two Classes could see no force in the so-called
|
|
axiom about "Distinction of Sides implying Distinction of Colour;" and
|
|
when all others had succumbed to the fascinations of corporal
|
|
decoration, the Priests and the Women alone still remained pure from
|
|
the pollution of paint.
|
|
|
|
Immoral, licentious, anarchical, unscientific -- call them by what
|
|
named you will -- yet, from an aesthetic point of view, those ancient
|
|
days of the Colour Revolt were the glorious childhood of Art in
|
|
Flatland -- a childhood, alas, that never ripened into manhood, nor
|
|
even reached the blossom of youth. To live then in itself a delight,
|
|
because living implied seeing. Even at a small party, the company was
|
|
a pleasure to behold; the richly varied hues of the assembly in a
|
|
church or theatre are said to have more than once proved too
|
|
distracting from our greatest teachers and actors; but most ravishing
|
|
of all is said to have been the unspeakable magnificence of a military
|
|
review.
|
|
|
|
The sight of a line of battle of twenty thousand Isosceles
|
|
suddenly facing about, and exchanging the sombre black of their bases
|
|
for the orange of the two sides including their acute angle; the
|
|
militia of the Equilateral Triangles tricoloured in red, white, and
|
|
blue; the mauve, ultra-marine, gamboge, and burnt umber of the Square
|
|
artillerymen rapidly rotating near their vermillion guns; the dashing
|
|
and flashing of the five-coloured and six-coloured Pentagons and
|
|
Hexagons careering across the field in their offices of surgeons,
|
|
geometricians and aides-de-camp -- all these may well have been
|
|
sufficient to render credible the famous story how an illustrious
|
|
Circle, overcome by the artistic beauty of the forces under his
|
|
command, threw aside his marshal's baton and his royal crown,
|
|
exclaiming that he henceforth exchanged them for the artist's pencil.
|
|
How great and glorious the sensuous development of these days must
|
|
have been is in part indicated by the very language and vocabulary of
|
|
the period. The commonest utterances of the commonest citizens in the
|
|
time of the Colour Revolt seem to have been suffused with a richer
|
|
tinge of word or thought; and to that era we are even now indebted for
|
|
our finest poetry and for whatever rhythm still remains in the more
|
|
scientific utterance of those modern days.
|
|
|
|
* * *
|
|
|
|
SECTION 9. -- Of the Universal Colour Bill
|
|
|
|
But meanwhile the intellectual Arts were fast decaying.
|
|
|
|
The Art of Sight Recognition, being no longer needed, was no
|
|
longer practised; and the studies of Geometry, Statics, Kinetics, and
|
|
other kindred subjects, came soon to be considered superfluous, and
|
|
feel into disrespect and neglect even at our University. The inferior
|
|
Art of Feeling speedly experienced the same fate at our Elementary
|
|
Schools. Then the Isosceles classes, asserting that the Specimens
|
|
were no longer used nor needed, and refusing to pay the customary
|
|
tribute from the Criminal classes to the service of Education, waxed
|
|
daily more numerous and more insolent on the strength of their
|
|
immunity from the old burden which had formerly exercised the twofold
|
|
wholesome effect of at once taming their brutal nature and thinning
|
|
their excessive numbers.
|
|
|
|
Year by year the Soldiers and Artisans began more vehemently to
|
|
assert -- and with increasing truth -- that there was no great
|
|
difference between them and the very highest class of Polygons, now
|
|
that they were raised to an equality with the latter, and enabled to
|
|
grapple with all the difficulties and solve all the problems of life,
|
|
whether Statical or Kinetical, by the simple process of Colour
|
|
Recognition. Not content with the natural neglect into which Sight
|
|
Recognition was falling, they began boldly to demand the legal
|
|
prohibition of all "monopolizing and aristocratic Arts" and the
|
|
consequent abolition of all endowments for the studies of Sight
|
|
Recognition, Mathematics, and Feeling. Soon, they began to insist
|
|
that inasmuch as Colour, which was a second Nature, had destroyed the
|
|
need of aristocratic distinctions, the Law should follow in the same
|
|
path, and that henceforth all individuals and all classes should be
|
|
recognized as absolutely equal and entitled to equal rights.
|
|
|
|
Finding the higher Orders wavering and undecided, the leaders of
|
|
the Revolution advanced still further in their requirements, and at
|
|
last demanded that all classes alike, the Priests and the Women not
|
|
excepted, should do homage to Colour by submitting to be painted.
|
|
When it was objected that Priests and Women had no sides, they
|
|
retorted that Nature and Expediency concurred in dictating that the
|
|
front half of every human being (that is to say, the half containing
|
|
his eye and mouth) should be distinguishable from his hinder half.
|
|
They therefore brought before a general and extraordinary Assembly of
|
|
all the States of Flatland a Bill proposing that in every Woman the
|
|
half containing the eye and mouth should be coloured red, and the
|
|
other half green. The Priests were to be painted in the same way, red
|
|
being applied to that semicircle in which the eye and mouth formed the
|
|
mmiddle point; while the other or hinder semicircle was to be coloured
|
|
green.
|
|
|
|
There was no little cunning in this proposal, which indeed
|
|
emanated not from any Isosceles -- for no being so degraded would have
|
|
angularity enough to appreciate, much less to devise, such a model of
|
|
state-craft -- but from an Irregular Circle who, instead of being
|
|
destroyed in his childhood, was reserved by a foolish indulgence to
|
|
bring desolation on his country and destruction on myriads of
|
|
followers.
|
|
|
|
On the one hand the proposition was calculated to bring the Women
|
|
in all classes over to the side of the Chromatic Innovation. For by
|
|
assigning to the Women the same two colours as were assigned to the
|
|
Priests, the Revolutionists thereby ensured that, in certain
|
|
positions, every Woman would appear as a Priest, and be treated with
|
|
corresponding respect and deference -- a prospect that could not fail
|
|
to attract the Female Sex in a mass.
|
|
|
|
But by some of my Readers the possibility of the identical
|
|
appearance of Priests and Women, under a new Legislation, may not be
|
|
recognized; if so, a word or two will make it obvious.
|
|
|
|
Imagine a woman duly decorated, according to the new Code; with
|
|
the front half (i.e., the half containing the eye and mouth) red, and
|
|
with the hinder half green. Look at her from one side. Obviously you
|
|
will see a straight line, _half red, half green._
|
|
|
|
Now imagine a Priest, whose mouth is at M, and whose front
|
|
semicircle (AMB) is consequently coloured red, while his hinder
|
|
semicircle is green; so that the diameter AB divides the green from
|
|
the red. If you contemplate the Great Man so as to have your eye in
|
|
the same straight line as his dividing diameter (AB), what you will
|
|
see will be a straight line (CBD), of which _one half_ (CB) _will be
|
|
red, and the other_ (BD) _green._ The whole line (CD) will be rather
|
|
shorter perhaps than that of a full-sized Woman, and will shade off
|
|
more rapidly towards its extremities; but the identity of the colours
|
|
would give you an immediate impression of identity in Class, making
|
|
you neglectful of other details. Bear in mind the decay of Sight
|
|
Recognition which threatened society at the time of the Colour revolt;
|
|
add too the certainty that Woman would speedily learn to shade off
|
|
their extremities so as to imitate the Circles; it must then be surely
|
|
obvious to you, my dear Reader, that the Colour Bill placed us under a
|
|
great danger of confounding a Priest with a young Woman.
|
|
|
|
How attractive this prospect must have been to the Frail Sex may
|
|
readily be imagined. They anticipated with delight the confusion that
|
|
would ensue. At home they might hear political and ecclesiastical
|
|
secrets intended not for them but for their husbands and brothers, and
|
|
might even issue some commands in the name of a priestly Circle; out
|
|
of doors the striking combination of red and green without adddition
|
|
of any other colours, would be sure to lead the common people into
|
|
endless mistakes, and the Woman would gain whatever the Circles lost,
|
|
in the deference of the passers by. As for the scandal that would
|
|
befall the Circular Class if the frivolous and unseemly conduct of the
|
|
Women were imputed to them, and as to the consequent subversion of the
|
|
Constitution, the Female Sex could not be expected to give a thought
|
|
to these considerations. Even in the households of the Circles, the
|
|
Women were all in favour of the Univsersal Colour Bill.
|
|
|
|
The second object aimed at by the Bill was the gradual
|
|
demoralization of the Circles themselves. In the general intellectual
|
|
decay they still preserved their pristine clearness and strength of
|
|
understanding. From their earliest childhood, familiarized in their
|
|
Circular households with the total absence of Colour, the Nobles alone
|
|
preserved the Sacred Art of Sight Recognition, with all the advantages
|
|
that result from that admirable training of the intellect. Hence, up
|
|
to the date of the introduction of the Universal Colour Bill, the
|
|
Circles had not only held their own, but even increased their lead of
|
|
the other classes by abstinence from the popular fashion.
|
|
|
|
Now therefore the artful Irregular whom I described above as the
|
|
real author of this diabolical Bill, determined at one blow to lower
|
|
the status of the Hierarchy by forcing them to submit to the pollution
|
|
of Colour, and at the same time to destroy their domestic
|
|
opportunities of training in the Art of Sight Recognition, so as to
|
|
enfeeble their intellects by depriving them of their pure and
|
|
colourless homes. Once subjected to the chromatic taint, every
|
|
parental and every childish Circle would demoralize each other. Only
|
|
in discerning between the Father and the Mother would the Circular
|
|
infant find problems for the exercise of his understanding -- problems
|
|
too often likely to be corrupted by maternal impostures with the
|
|
result of shaking the child's faith in all logical conclusions. Thus
|
|
by degrees the intellectual lustre of the Priestly Order would wane,
|
|
and the road would then lie open for a total destruction of all
|
|
Aristocratic Legislature and for the subversion of our Privileged
|
|
Classes.
|
|
|
|
* * *
|
|
|
|
SECTION 10. -- Of the Suppression of the Chromatic Sedition
|
|
|
|
The agitation for the Universal Colour Bill continued for three
|
|
years; and up to the last moment of that period it seemed as though
|
|
Anarchy were destined to triumph.
|
|
|
|
A whole army of Polygons, who turned out to fight as private
|
|
soldiers, was utterly annihilated by a superior force of Isosceles
|
|
Triangles -- the Squares and Pentagons meanwhile remaining neutral.
|
|
Worsez than all, some of the ablest Circles fell a prey to conjugal
|
|
fury. Infuriated by political animosity, the wives in many a noble
|
|
household wearied their lords with prayers to give up their opposition
|
|
to the Colour Billl; and some, finding their entreaties fruitless,
|
|
fell on and slaughtered their innocent children and husband, perishing
|
|
themselves in the act of carnage. It is recorded that during that
|
|
triennial agitation no less than twenty-three Circles perished in
|
|
domestic discord.
|
|
|
|
Great indeed was the peril. It seemed as though the Priests had
|
|
no choice between submission and extermination; when suddenly the
|
|
course of events was completely changed by one of those picturesque
|
|
incidents which Statesmen ought never to neglect, often to anticipate,
|
|
and sometimes perhaps to originate, because of the absurdly
|
|
disproportionate power with which they appearl to the sympathies of
|
|
the populace.
|
|
|
|
It happened that an Isosceles of a low type, with a brain little
|
|
if at all above four degrees -- accidentally dabbling in the colours
|
|
of some Tradesman whose shop he had plundered -- painted himself, or
|
|
caused himself to be painted (for the story varies) with the twelve
|
|
colours of a Dodecagon. Going into the Market Place he accosted in a
|
|
feigned voice a maiden, the orphan daughter of a noble Polygon, whose
|
|
affection in former days he had sought in vain; and by a series of
|
|
deceptions -- aided, on the one side, by a string of lucky accidents
|
|
too long to relate, and, on the other, by an almost inconceivable
|
|
fatuity and neglect of ordinary precautions on the part of the
|
|
relations of the bride -- he succeeded in consummating the marriage.
|
|
The unhappy girl committed suicide on discovering the fraud to which
|
|
she had been subjected.
|
|
|
|
When the news of this catastrophe spread from State to State the
|
|
minds of the Women were violently agitated. Sympathy with the
|
|
miserable victim and anticipations of similar deceptions for
|
|
themselves, their sisters, and their daughters, made them now regard
|
|
the Colour Bill in an entirely new aspect. Not a few openly avowed
|
|
themselves converted to antagonism; the rest needed only a slight
|
|
stimulus to make a similar avowal. Seizing this favourable
|
|
apportunity, the Circles hastily convened an extraordinary Assembly of
|
|
the States; and besides the usual guard of Convicts, they secured the
|
|
attendance of a large number of reactionary Women.
|
|
|
|
Amidst an unprecedented concourse, the Chief Circle of those days
|
|
-- by name Pantocyclus -- arose to find himself hissed and hooted by a
|
|
hundred and twenty thousand Isosceles. But he secured silence by
|
|
declaring that henceforth the Circles would enter on a policy of
|
|
Concession; yielding to the wishes of the majority, they would accept
|
|
the Colour Bill. The uproar being at once converted to applause, he
|
|
invited Chromatistes, the leader of the Sedition, into the centre of
|
|
the hall, to receive in the name of his followers the submission of
|
|
the Hierarchy. Then followed a speech, a masterpiece of rhetoric,
|
|
which occupied nearly a day in the delivery, and to which no summary
|
|
can do justice.
|
|
|
|
With a grave appearance of impartiality he declared that as they
|
|
were now finally committing themselves to Reform or Innovation, it was
|
|
desirable that they should take one last view of the perimeter of the
|
|
whole subject, its defects as well as its advantages. Gradually
|
|
introduction the mention of the dangers to the Tradesmen, the
|
|
Professional Classes and the Gentlemen, he silenced the rising murmurs
|
|
of the Isosceles by reminding them that, in spite of all these
|
|
defects, he was willing to accept the Bill if it was approved by the
|
|
majority. But it was manifest that all, except the Isosceles, were
|
|
moved by his words and were either neutral or averse to the Bill.
|
|
|
|
Turning now to the Workmen he asserted that their interests must
|
|
not be neglected, and that, if they intended to accept the Colour
|
|
Bill, they ought at least to do so with full view of the consequences.
|
|
Many of them, he said, were on the point of being admitted to the
|
|
class of the Regular Triangles; others anticipated for their children
|
|
a distinction they could not hope for themselves. That honourable
|
|
ambition would not have to be sacrificed. With the universal adoption
|
|
of Colour, all distinctions would cease; Regularity would be confused
|
|
with Irregularity; development would give place to retrogression; the
|
|
Workman would in a few generations be degraded to the level of the
|
|
Militar, or even the Convict Class; political power would be in the
|
|
hands of the greatest number, that is to say the Criminal Classes, who
|
|
were already more numerous than the Workmen, and would soon out-number
|
|
all the other Classes put together when the usual Compensative Laws of
|
|
Nature were violated.
|
|
|
|
A subdued murmur of assent ran through the ranks of the Artisans,
|
|
and Chromatistes, in alarm, attempted to step forward and address
|
|
them. But he found himself encompassed with guards and forced to
|
|
remain silent while the Chief Circle in a few impassioned words made a
|
|
final appeal to the Women, exclaiming that, if the Colour Bill passed,
|
|
no marriage would henceforth be safe, no woman's honour secure; fraud,
|
|
deception, hypocrisy would pervade every household; domestic bliss
|
|
would share the fate of the Constitution and pass to speedy perdition.
|
|
"Sooner than this," he cried, "Come death."
|
|
|
|
At these words, which were the preconcerted signal for action, the
|
|
Isosceles Convicts fell on and transfixed the wretched Chromatistes;
|
|
the Regular Classes, opening their ranks, made way for a band of Women
|
|
who, under direction of the Circles, moved back foremost, inivisibly
|
|
and unerringly upon the unconscious soldiers; the Artisans, imitating
|
|
the example of their betters, also opened their ranks. Meantime bands
|
|
of Convicts occupied every entrance with an impenetrable phalanx.
|
|
|
|
The battle, or rather carnage, was of short duration. Under the
|
|
skillful generalship of the Circles almost every Woman's charge was
|
|
fatal and very many extracted their sting uninjured, ready for a
|
|
second slaughter. But no second blow was needed; the rabble of the
|
|
Isosceles did the rest of the business for themselves. Surprised,
|
|
leader-less, attacked in front by invisible foes, and finding egress
|
|
cut off by the Convicts behind them, they at once -- after their
|
|
manner -- lost all presence of mind, and raised the cry of
|
|
"treachery." This sealed their fate. Every Isosceles now saw and
|
|
felt a foe in every other. In half an hour not one of that vast
|
|
multitude was living; and the fragments of seven score thousand of the
|
|
Criminal Class slain by one another's angles attested the triumph of
|
|
Order.
|
|
|
|
The Circles delayed not to push their victory to the uttermost.
|
|
The Working Men they spared but decimated. The Militia of the
|
|
Equilaterals was at once called out, and every Triangle suspected of
|
|
Irregularity on reasonable grounds, was destroyed by Court Martial,
|
|
without the formality of exact measurement by the Social Board. The
|
|
homes of the Military and Artisan classes were inspected in a course
|
|
of visitation extending through upwards of a year; and during that
|
|
period every town, village, and hamlet was systematically purged of
|
|
that excess of the lower orders which had been brought about by the
|
|
neglect to pay the tribute of Criminals to the Schools and University,
|
|
and by the violation of other natural Laws of the Constitution of
|
|
Flatland. Thus the balance of classes was again restored.
|
|
|
|
Needless to say that henceforth the use of Colour was abolished,
|
|
and its possession prohibited. Even the utterance of any word
|
|
denoting Colour, except by the Circles or by qualified scientific
|
|
teachers, was punished by a severe penalty. Only at our University in
|
|
some of the very highest and most esoteric classes -- which I myself
|
|
have never been privileged to attend -- it is understood that the
|
|
sparing use of Colour is still sanctioned for the purpose of
|
|
illustrating some of the deeper problems of mathematics. But of this
|
|
I can only speak from hearsay.
|
|
|
|
Elsewhere in Flatland, Colour is no non-existent. The art of
|
|
making it is known to only one living person, the Chief Circle for the
|
|
time being; and by him it is handed down on his death-bed to none but
|
|
his Successor. One manufactory alone produces it; and, lest the
|
|
secret should be betrayed, the Workmen are annually consumed, and
|
|
fresh ones introduced. So great is the terror with which even now our
|
|
Aristocracy looks back to the far-distant days of the agitation for
|
|
the Universal Colour Bill.
|
|
|
|
* * *
|
|
|
|
SECTION 11. -- Concerning our Priests
|
|
|
|
It is high time that I should pass from these brief and discursive
|
|
notes about things in Flatland to the central event of this book, my
|
|
initiation into the mysteries of Space. _That_ is my subject; all
|
|
that has gone before is merely preface.
|
|
|
|
For this reason I must omit many matters of which the explanation
|
|
would not, I flatter myself, be without interest for my Readers: as
|
|
for example, our method of propelling and stopping ourselves, although
|
|
destitute of feet; the means by which we give fixity to structuers of
|
|
wood, stone, or brick, although of course we have no hands, nor can we
|
|
lay foundations as you can, nor avail ourselves of the lateral
|
|
pressure of the earth; the manner in which the rain originates in the
|
|
intervals between our various zones, so that the northern regions do
|
|
not intercept the moisture falling on the southern; the nature of our
|
|
hills and mines, our trees and vegetables, our seasons and harvests;
|
|
our Alphabet and method of writing, adapted to our linear tablets;
|
|
these and a hundred other details of our physical existence I must
|
|
pass over, nor do I mention them now except to indicate to my readers
|
|
that their omission proceeds not from forgetfulness on the part of the
|
|
author, but from his regard for the time of the Reader.
|
|
|
|
Yet before I proceed to my legitimate subject some few final
|
|
remarks will no doubt be expected by my Readers upon these pillars and
|
|
mainstays of the Constitution of Flatland, the controllers of our
|
|
conduct and shapers of our destiny, the objects of universal homage
|
|
and almost of adoration: need I say that I mean our Circles or
|
|
Priests?
|
|
|
|
When I call them Priests, let me not be understood as meaning no
|
|
more than the term denotes with you. With us, our Priests are
|
|
Administrators of all Business, Art, and Science; Directors of Trade,
|
|
Commerce, Generalship, Architecture, Engineering, Education,
|
|
Statesmanship, Legislature, Morality, Theology; doing nothing
|
|
themselves, they are the Causes of everything worth doing, that is
|
|
done by others.
|
|
|
|
Although popularly everyone called a Circle is deemed a Circle,
|
|
yet among the better educated Classes it is known that no Circle is
|
|
really a Circle, but only a Polygon with a very large number of very
|
|
small sides. As the number of the sides increases, a Polygon
|
|
approximates to a Circle; and, when the number is very great indeed,
|
|
say for example three or four hundred, it is extremely difficult for
|
|
the most delicate touch to feel any polygonal angles. Let me say
|
|
rather it _would_ be difficult: for, as I hav shown above,
|
|
Recognition by Feeling is unknown among the highest society, and to
|
|
_feel_ a Circle would be considered a most audacious insult. This
|
|
habit of abstention from Feeling in the best society enables a Circle
|
|
the more easily to sustain the veil of mystery in which, from his
|
|
earliest years, he is wont to enwrap the exact nature of his Perimeter
|
|
or Circumference. Three feet being the average Perimeter it follows
|
|
that, in a Polygon of three hundred sides each side will be no more
|
|
than the hundredth part of a foot in length, or little more than the
|
|
tenth part of an inch; and in a Polygon of six or seven hundred sides
|
|
the sides are little larger than the diameter of a Spaceland pin-head.
|
|
It is always assumed, by courtesy, that the Chief Circle for the time
|
|
being has ten thousand sides.
|
|
|
|
The ascent of the posterity of the Circles in the social scale is
|
|
not restricted, as it is among the lower Regular classes, by the Law
|
|
of Nature which limits the increase of sides to one in each
|
|
generation. If it were so, the number of sides in the Circle would be
|
|
a mere question of pedigree and arithmetic, and the four hundrd and
|
|
ninety-seventh descendant of an Equilateral Triangle would necessarily
|
|
be a polygon With five hundred sides. But this is not the case.
|
|
Nature's Law prescribes two antagonstic decrees affecting Circular
|
|
propogation; first, that as the race climbs higher in the scale of
|
|
development, so development shall proceed at an accelerated pace;
|
|
second, that in the same proportion, the race shall become less
|
|
fertile. Consequently in the home of a Polygon of four or five
|
|
hundred sides it is rare to find a son; more than one is never seen.
|
|
On the other hand the son of a five-hundred-sided Polygon has been
|
|
known to possess five hundred and fifty, or even six hundred sides.
|
|
|
|
Art also steps in to help the process of higher Evolution. Our
|
|
physicians have discovered that the small and tender sides of an
|
|
infant Polygon of the higher class can be fractured, and his whole
|
|
frame re-set, with such exactness that a Polygon of two or three
|
|
hundred sides sometimes -- by no means always, for the process is
|
|
attended with serious risk -- but sometimes overleaps two or three
|
|
hundred generations, and as it were double at a stroke, the number of
|
|
his progenitors and the nobility of his descent.
|
|
|
|
Many a promising child is sacrificed in this way. Scarcely one
|
|
out of ten survives. Yet so strong is the parental ambition among
|
|
those Polygons who are, as it were, on the fringe of the Circular
|
|
class, that it is very rare to find the Nobleman of that position in
|
|
society, who has neglected to place his first-born in the Circular
|
|
Neo-Therapeutic Gymnasium before he has attained the age of a month.
|
|
|
|
One year determins success or failure. At the end of that time
|
|
the child has, in all probability, added one more to the tombstones
|
|
that crowd the Neo-Therapeutic Cemetery; but on rare occasional a glad
|
|
procession bares back the little one to his exultant parents, no
|
|
longer a Polygon, but a Circle, at least by courtesy: and a single
|
|
instance of so blessed a result induces multitudes of Polygonal
|
|
parents to submit to simialr domestic sacrifice, which have a
|
|
dissimilar issue.
|
|
|
|
* * *
|
|
|
|
SECTION 12. -- Of the Doctrine of our Priests
|
|
|
|
As to the doctrine of the Circles it may briefly be summed up in a
|
|
single maxim, "Attend to your Configuration." Whether political,
|
|
ecclesiastical, or moral, all their teaching has for its object the
|
|
improvement of individual and collective Configuration -- with special
|
|
reference of course to the Configuration of the Circles, to which all
|
|
other objects are subordinated.
|
|
|
|
It is the merit of the Circles that they have effectually
|
|
suppressed those ancient heresies which led men to waste energy and
|
|
sympathy in the vain belief that conduct depends upon will, effort,
|
|
training, encouragement, praise, or anything else but Configuration.
|
|
It was Pantocyclus -- the illustrious Circle mentioned above, as the
|
|
queller of the Colour Revolt -- who first convinced mankind that
|
|
Configuration makes the man; that if, for example, you are born an
|
|
Isosceles with two uneven sides, you will assuredly go wrong unless
|
|
you have them made even -- for which purpose you must go to the
|
|
Isosceles Hospital; similiarly, if you are a Triangle, or Square, or
|
|
even a Polygon, born with any Irregularity, you must be taken to one
|
|
of the Regular Hospitals to have your disease cured; otherwise you
|
|
will end your days in the State Prison or by the angle of the State
|
|
Executioner.
|
|
|
|
All faults or defects, from the slightest misconduct to the most
|
|
flagitious crime, Pantocyclus attributed to some deviation from
|
|
perfect Regularity in the bodily figure, caused perhaps (if not
|
|
congenital) by some collision in a crowd; by neglect to take exercise,
|
|
or by taking too much of it; or even by a sudden change of
|
|
temperature, resulting in a shrinkage or expansion in some too
|
|
susceptible part of the frame. Therefore, concluded that illustrious
|
|
Philosopher, neither good conduct nor bad conduct is a fit subject, in
|
|
any sober estimation, for eithe praise or blame. For why should you
|
|
praise, for example, the integrity of a Square who faithfully defends
|
|
the interests of his client, when you ought in reality rather to
|
|
admire the exact precision of his right angles? Or again, why blame a
|
|
lying, thievish Isosceles, when you ought rather to deplore the
|
|
incurable inequality of his sides?
|
|
|
|
Theoretically, this doctrine is unquestionable; but it has
|
|
practical drawbacks. In dealing with an Isosceles, if a rascal pleads
|
|
that he cannot help stealing because of his unevenness, you reply that
|
|
for that very reason, because he cannot help being a nuisance to his
|
|
neighbours, you, the Magistrate, cannot help sentencing him to be
|
|
consumed -- and tehre's an end of the matter. But in little domestic
|
|
difficulties, when the penalty of consumption, or death, is out of the
|
|
question, this theory of Configuration sometimes comes in awkwardly;
|
|
and I must confess that occasionally when one of my own Hexagonal
|
|
Grandsons pleads as an excuse for his disobedience that a sudden
|
|
change of temperature has been too much for his Perimeter, and that I
|
|
ought to lay the blame not on him but on his Configuration, which can
|
|
only be strengthened by abundance of the choicest sweetmeats, I
|
|
neither see my way logically to reject, nor practically to accept, his
|
|
conclusions.
|
|
|
|
For my own part, I find it best to assume that a good sound
|
|
scolding or castigation has some latent and strengthening influence on
|
|
my Grandson's Configuration; though I own that I have no grounds for
|
|
thinking so. At all events I am not alone in my way of extricating
|
|
myself from this dilemma; for I find that many of the highest Circles,
|
|
sitting as Judges in law courts, use praise and blame towards Regular
|
|
and Irregular Figures; and in their homes I know by experience that,
|
|
when scolding their children, they speak about "right" and "wrong" as
|
|
vehemently and passionately as if they believe that these names
|
|
represented real existence, and that a human Figure is really capable
|
|
of choosing between them.
|
|
|
|
Constantly carrying out their policy of making Configuration the
|
|
leading idea in every mind, the Circles reverse the nature of that
|
|
Commandment which in Spaceland regulates the relations between parents
|
|
and children. With you, children are taught to honour their parents;
|
|
with us -- next to the Circles, who are the chief object of universal
|
|
homage -- a man is taught to honour his Grandson, if he has one; or,
|
|
if not, his Son. By "honour," however, is by no means mean
|
|
"indulgence," but a reverent regard for their highest interests: and
|
|
the Circles teach that the duty of fathers is to subordinate their own
|
|
interests to those of posterity, thereby advancing the welfare of the
|
|
whole State as well as that of their own immediate descendants.
|
|
|
|
The weak point in the system of the Circles -- if a humble Square
|
|
may venture to speak of anything Circular as containing any element of
|
|
weakness -- appears to me to be found in their relations with Women.
|
|
|
|
As it is of the utmost importance for Society that Irregular
|
|
births should be discouraged, it follows that no Woman who has any
|
|
Irregularities in her ancestry is a fit partner for one who desires
|
|
that his posterity should rise by regular degrees in the social scale.
|
|
|
|
Now the Irregularity of a Male is a matter of measurement; but as
|
|
all Women are straight, and therefore visibly Regular so to speak, one
|
|
has to device some other means of ascertaining what I may call their
|
|
invisible Irregularity, that is to say their potential Irregularities
|
|
as regards possible offspring. This is effected by carefully-kept
|
|
pedigrees, which arepreserved and supervised by the State; and without
|
|
a certified pedigree no Woman is allowed to marry.
|
|
|
|
Now it might have been supposed the a Circle -- proud of his
|
|
ancestry and regardful for a posterity which might possibly issue
|
|
hereafter in a Chief Circle -- would be more careful than any other to
|
|
choose a wife who had no blot on her escutcheon. But it is not so.
|
|
The care in choosing a Regular wife appears to diminish as one rises
|
|
in the social scale. Nothing would induce an aspiring Isosceles, who
|
|
has hopes of generating an Equilateral Son, to take a wife who
|
|
reckoned a single Irregularity among her Ancestors; a Square or
|
|
Pentagon, who is confident that his family is steadily on the rise,
|
|
does not inqure above the five-hundredth generation; a Hexagon or
|
|
Dodecagon is even more careless of the wife's pedigree; but a Circle
|
|
has been known deliberately to take a wife who has had an Irregular
|
|
Great-Grandfather, and all because of some slight superiority of
|
|
lustre, or because of the charms of a low voice -- which, with us,
|
|
even more than with you, is thought "an excellent thing in a Woman."
|
|
|
|
Such ill-judged marriages are, as might be expected, barren, if
|
|
they do not result in positive Irregularity or in diminution of sides;
|
|
but none of these evils have hitherto provied sufficiently deterrent.
|
|
The loss of a few sides in a highly-developed Polygon ios not easily
|
|
noticed, and is sometimes compensated by a successful operation in the
|
|
Neo-Therapeutic Gymnasium, as I have described above; and the Circles
|
|
are too much disposed to acquiesce in infecundity as a law of the
|
|
superior development. Yet, if this evil be not arrested, the gradual
|
|
diminution of the Circular class may soon become more rapid, and the
|
|
time may not be far distant when, the race being no longer able to
|
|
produce a Chief Circle, the Constitution of Flatland must fall.
|
|
|
|
One other word of warning suggest itself to me, though I cannot so
|
|
easily mention a remedy; and this also refers to our relations with
|
|
Women. About three hundred years ago, it was decreed by the Chief
|
|
Circle that, since women are deficient in Reason but abundant in
|
|
Emotion, they ought no longer to be treated as rational, nor receive
|
|
any mental education. The consequence was that they were no longer
|
|
taught to read, nor even to master Arithmetic enough to enable them to
|
|
count the angles of their husband or children; and hence they sensibly
|
|
declined during each generation in intellectual power. And this
|
|
system of female non-education or quietism still prevails.
|
|
|
|
My fear is that, with the best intentions, this policy has been
|
|
carried so far as to react injuriously on the Male Sex.
|
|
|
|
For the consequence is that, as things now are, we Males have to
|
|
lead a kind of bi-lingual, and I may almost say bimental, existence.
|
|
With Women, we speak of "love," "duty," "right," "wrong," "pity,"
|
|
"hope," and other irrational and emotional conceptions, which have no
|
|
existence, and the fiction of which has no object except to control
|
|
feminine exuberances; but among ourselves, and in our books, we have
|
|
an entirely different vocabulary and I may also say, idion. "Love"
|
|
them becomes "the anticipation of benefits"; "duty" becomes
|
|
"necessity" or "fitness"; and other words are correspondingly
|
|
transmuted. Moreover, among Women, we use language implying the
|
|
utmost deference for their Sex; and they fully believe that the Chief
|
|
Circle Himself is not more devoutly adored by us than they are: but
|
|
behind their backs they are both regarded and spoken of -- by all but
|
|
the very young -- as being little better than "mindless organisms."
|
|
|
|
Our Theology also in the Women's chambers is entirely different
|
|
from our Theology elsewhere.
|
|
|
|
Now my humble fear is that this double training, in language as
|
|
well as in thought, imposes somewhat too heavy a burden upon the
|
|
young, especially when, at the age of three years old, they are taken
|
|
from the maternal care and taught to unlearn the old language --
|
|
except for the purpose of repeating it in the presence of the Mothers
|
|
and Nurses -- and to learn the vocabulary and idiom of science.
|
|
Already methinks I discern a weakness in the grasp of mathematical
|
|
truth at the present time as compred with the more robust intellect of
|
|
our ancestors three hundred years ago. I say nothing of the possible
|
|
danger if a Woman should ever surrpetitously learn to read and convey
|
|
to her Sex the result of her perusal of a single popular volumne; nor
|
|
of the possibility that the indiscretion or disobedience of some
|
|
infant Male might reveal to a Mother the secrets of the logical
|
|
dialect. On the simple ground of the enfeebling of the male
|
|
intellect, I rest this humble appeal to the highest Authorities to
|
|
reconsides the regulations of Female education.
|
|
|
|
* * *
|
|
|
|
PART II
|
|
|
|
OTHER WORLDS
|
|
|
|
"O brave new worlds,
|
|
|
|
|
|
|
|
That have such people in them!"
|
|
|
|
SECTION 13. -- How I had a Vision of Lineland
|
|
|
|
IT was the last day but one of the 1999th year of our era, and the
|
|
first day of the Long Vacation. Having amused myself till a late hour
|
|
with my favourite recreation of Gemoetry, I had retired to rest with
|
|
an unsolved problem in my mind. In the night I had a dream.
|
|
|
|
I saw before me a vast multitude of small Straight Lines (which I
|
|
naturally assumed to be Women) interspersed with other Beings still
|
|
smaller and of the nature of lustrous points -- all moving to and fro
|
|
in one and the same Straight Line, and, as nearly as I could judge,
|
|
with the same velocity.
|
|
|
|
A noise of confused, multitudinous chirping or twittering issued
|
|
from them at intervals as long as they were moving; but sometimes they
|
|
ceased from motion, and then all was silence.
|
|
|
|
Approaching one of the largest of what I thought to be Women, I
|
|
accosted her, but received no answer. A second and third appeal on my
|
|
part were equally ineffectual. Losing patience at what appeared to me
|
|
intolerable rudeness, I brought my mouth to a position full in front
|
|
of her mouth so as to intercept her motion, and loudly repeated my
|
|
question, "Woman, what signifies this concourse, and this strange and
|
|
confused chirping, and this monotonous motion to and fro in one and
|
|
the same Straight Line?"
|
|
|
|
"I am no Woman," replied the small Line: "I am the Monarch of the
|
|
world. But thou, whence intrudest thou into my realm of Lineland?"
|
|
Receiving this abrupt reply, I begged pardon if I had in any way
|
|
startled or molested his Royal Highness; and describing myself as a
|
|
stranger I besought the King to give me some account of his dominions.
|
|
But I had the greatest possible difficulty in obtaining any
|
|
information on points that really interested me; for the Monarch could
|
|
not refrain from constantly assuming that whatever was familiar to him
|
|
must also be known to me and that I was simulating ignorance in jest.
|
|
However, by preserving questions I elicited the following facts: It
|
|
seemed that this poor ignorant Monarch -- as he called himself -- was
|
|
persuaded that the Straight Line which he called his Kingdom, and in
|
|
which he passed his existence, constituted the whole of the world, and
|
|
indeed the whole of Space. Not being able either to move or to see,
|
|
save in his Straight Line, he had no conception of anything out of it.
|
|
Though he had heard my voice when I first addressed him, the sounds
|
|
had come to him in a manner so contrary to his experience that he had
|
|
made no answer, "seeing no man," as he expressed it, "and hearing a
|
|
voice as it were from my own intestines." Until the moment when I
|
|
placed my mouth in his World, he had neither seen me, nor heard
|
|
anything except confused sounds beating against, what I called his
|
|
side, but what he called his _inside_ or _stomach_; nor had he even
|
|
now the least conception of the region from which I had come. Outside
|
|
his World, or Line, all was a blank to him; nay, not even a blank, for
|
|
a blank implies Space; say, rather, all was non-existent.
|
|
|
|
His subjects -- of whom the small Lines were men and the Points
|
|
Women -- were all alike confined in motion and eyesight to that single
|
|
Straight Line, which was their World. It need scarcely be added that
|
|
the whole of their horizon was limited to a Point; nor could any one
|
|
ever see anything but a Point. Man, woman, child, thing -- each as a
|
|
Point to the eye of a Linelander. Only by the sound of the voice
|
|
could sex or age be distinguished. Moreover, as each individual
|
|
occupied the whole of the narrow path, so to speak, which constituted
|
|
his Universe, and no one could m ove to the right or left to make way
|
|
for passers by, it followed that no Linlander could ever pass another.
|
|
Once neighbours, always neighbours. Neighbourhood with them was like
|
|
marriage with us. Neighbours remained neighbours till death did them
|
|
part.
|
|
|
|
Such a life, with all vision limited to a Point, and all motion to
|
|
a Straight Line, seemed to me inexpressibly dreary; and I was
|
|
surprised to note that vivacity and cheerfulness of the King.
|
|
Wondering whether it was possible, amid circumstances so unfavourable
|
|
to domestic relations, to enjoy the pleasures of conjugal union, I
|
|
hestitated for some time to question his Royal Highness on so delicate
|
|
a subject; but at last I plunged into it by abruptly inquiring as to
|
|
the health of his family. "My wives and children," he replied, "are
|
|
well and happy."
|
|
|
|
Staggered at this answer -- for in the immediate proximity of the
|
|
Manarch (as I had noted in my dream befor I entered Lineland) there
|
|
were none but Men -- I ventured to reply, "Pardon me, but I cannot
|
|
imagine how your Royal Highness can at any time either se or approach
|
|
their Majesties, when there at least half a dozen intervening
|
|
individuals, whom you can neither see through, nor pass by? Is it
|
|
possible that in Lineland proximity is not necessary for marriage and
|
|
for the generation of children?"
|
|
|
|
"How can you ask so absurd a question?" replied the Monarch. "If
|
|
it were indeed as you suggest, the Universe would soon be depopulated.
|
|
No, no; neighbourhood is needless for the union of hearts; and the
|
|
birth of children is too important a matter to have been allowed to
|
|
depend upon such an accident as proximity. You cannot be ignorant of
|
|
this. Yet since you are pleased to affect ignorance, I will instruct
|
|
you as if you were the veriest baby in Lineland. Know, then, that
|
|
marriages are consummated by means of the faculty of sound and the
|
|
sense of hearing.
|
|
|
|
"You are of course aware that every Man has two mouths or voices -
|
|
- as well as two eyes -- a bass at one and a tenor at the other of his
|
|
extremities. I should not mention this, but that I have been unable
|
|
to distinguish your tenor in the course of our conversation." I
|
|
replied that I had but one voice, and that I had not been aware that
|
|
his Royal Highness had two. "That confirms by impression," said the
|
|
King, "that you are not a Man, but a feminine Monstrosity with a bass
|
|
voice, and an utterly uneducated ear. But to continue.
|
|
|
|
"Nature having herself ordained that every Man should wed two
|
|
wives --" "Why two?" asked I. "You carry your affected simplicity
|
|
too far," he cried. "How can there be a completely harmonious union
|
|
without the combination of the Four in One, viz. the Bass and Tenor of
|
|
the Man and the Soprano and Contralto of the two Women?" "But
|
|
supposing," said I, "that a man should prefer one wife or three?" "It
|
|
is impossible," he said; "it is as inconceivable as that two and one
|
|
should make five, or that the human eye should see a Straight Line."
|
|
I would have interrupted him; but he proceeded as follows:
|
|
|
|
"Once in the middle of each week a Law of Nature compels uus to
|
|
move to and fro with a rhythmic motion of more than usual violence,
|
|
which continues for the time you would take to count a hundred and
|
|
one. In the midst of this choral dance, at the fifty-first pulsation,
|
|
the inhabitants of the Universe pause in full career, and each
|
|
individual sends forth his richest, fullest, sweetest strain. It is
|
|
in this decisive moment that all our marriages are made. So exquisite
|
|
is the adaptation of Bass and Treble, of Tenor to Contralto, that
|
|
oftentimes the Loved Ones, though twenty thousand leagues away,
|
|
recognize at once the responsive note of their destined Lover; and,
|
|
penetrating the paltry obstacles of distance, Love unites the three.
|
|
The marriage in that instance consummated results in a threefold Male
|
|
and Female offspring which takes its place in Lineland."
|
|
|
|
"What! Always threefold?" said I. "Must one wife then always
|
|
have twins?"
|
|
|
|
"Bass-voice Monstrosity! yes," replied the King. "How else could
|
|
the balance of the Sexes be maintained, if two girls were not born for
|
|
every boy? Would you ignore the very Alphabet of Nature?" He ceased,
|
|
speechless for fury; and some time elapsed before I could induce him
|
|
to resume his narrative.
|
|
|
|
"You will not, of course, suppose that every bachelor among us
|
|
finds his mates at the first wooing in this universal Marriage Chorus.
|
|
On the congtrary, the process is by most of us many times repeated.
|
|
Few are the hearts whose happy lot is at once to recognize in each
|
|
other's voice the partner intended for them by Providence, and to fly
|
|
into a reciprocal and perfectly harmonious embrace. With most of us
|
|
the courtship is of long duration. The Wooer's voices may perhaps
|
|
accord with one of the future wives, but not with both; or not, at
|
|
first, with either; or the Soprano and Contralto may not quite
|
|
harmonize. In such cases Nature has provided that every weekly Chorus
|
|
shall bring the three Lovers into closer harmony. Each trial of
|
|
voice, each fresh discovery of discord, almost imperceptibly induces
|
|
the less perfect to modify his or her vocal utterance so as to
|
|
approximate to the more perfect. And after many trials and many
|
|
approximations, the result is at last achieved. There comes a day at
|
|
last when, while the wonted Marriage Chorus goes forth from universal
|
|
Lineland, the three far-off Lovers suddenly find themselves in exact
|
|
harmony, and, befor they are aware, the wedded Triplet is rapt vocally
|
|
into a duplicate embrace; and Nature rejoices over one more marriage
|
|
and over three more births."
|
|
|
|
* * *
|
|
|
|
SECTION 14. -- How I vainly tried to explain the nature of Flatland
|
|
|
|
Thinking that it was time to bring down the Monarch from his
|
|
raptures to the level of common sense, I determined to endeavour to
|
|
open up to him some glimpses of the truth, that is to say of the
|
|
nature of things in Flatland. So I began thus: "How does your Royal
|
|
Highness distinguish the shapes and positions of his subjects? I for
|
|
my part noticed by the sense of sight, before I entered your Kingdom,
|
|
that some of your people are lines and others Points; and that some of
|
|
the lines are larger --" "You speak of an impossibility," interrupted
|
|
the King; "you must have seen a vision; for to detect the difference
|
|
between a Line and a Point by the sense of sight is, as every one
|
|
knows, in the nature of things, impossible; but it can be detected by
|
|
the snese of hearing, and by the same means my shape can be exactly
|
|
ascertained. Behold me -- I am a Line, the longest in Lineland, over
|
|
six inches of Space --" "Of Length," I ventured to suggest. "Fool,"
|
|
said he, "Space is Length. Interrupt me again, and I have done."
|
|
|
|
I apologized; but he continued scornfully, "Since you are
|
|
impervious to argument, you shall hear with your ears how by means of
|
|
my two voices I reveal my shape to my Wives, who are at this moment
|
|
six thousand miles seventy yards two feet eight inches away, the one
|
|
to the North, the other to the South. Listen, I call to them."
|
|
|
|
He chirruped, and then complacently continued: "My wives at this
|
|
moment receiving the sound of one of my voice, closely followed by the
|
|
other, and perceiving that the latter reaches them after an interval
|
|
in which sound can traverse 6.457 inches, infer that one of my mouths
|
|
is 6.457 inches further from them than the other, and accordingly know
|
|
my shape to be 6.457 inches. But you will of course understand that
|
|
my wives do not make this calculation every time they hear my two
|
|
voices. They made it, once for all, before we were married. But they
|
|
_could_ make it at any time. And in the same way I can estimate the
|
|
shape of any of my Male subjects by the sense of sound."
|
|
|
|
"But how," said I, "if a Man feigns a Woman's voice with one of
|
|
his two voices, or so disguises his Southern voice that it cannot be
|
|
recognized as the echo of the Northern? May not such deceptions cause
|
|
great inconvenience? And have you no means of checking frauds of this
|
|
kind by commanding your neighbouring subjects to feel one another?"
|
|
This of course was a very stupid question, for feeling could not have
|
|
answered the purpose; but I asked with the view of irritating the
|
|
Monarch, and I succeeded perfectly.
|
|
|
|
"What!" cried he in horror, "explain your meaning." "Feel, touch,
|
|
come into contact," I replied.. "If you mean by _feeling,_" said the
|
|
King, "approaching so close as to leave no space between two
|
|
individuals, know, Stranger, that this offence is punishable in my
|
|
dominions by death. And the reason is obvious. The frail form of a
|
|
Woman, being liable to be shattered by such an approximation, must be
|
|
preserved by the State; but since Women cannot be distinguished by the
|
|
sense of sight from Men, the Law ordains universally that neither Man
|
|
nor Woman shall be approached so closely as to destroy the interval
|
|
between the approximator and the approximated.
|
|
|
|
"And indeed what possible purpose would be served by this illegal
|
|
and unnatural excess of approximation which you call _touching,_ when
|
|
all the ends of so brutal and course a process are attained at once
|
|
more easily and more exactly by the sense of hearing? As to your
|
|
suggested danger of deception, it is non-existent: for the Voice,
|
|
being the essence of one's Being, cannot be thus changed at will. But
|
|
come, suppose that I had the power of passing through solid things, so
|
|
that I could penetrate my subjects, one after another, even to the
|
|
number of a billion, verifying the size and distance of each by the
|
|
sense of _feeling:_ How much time and energy would be wasted in this
|
|
clumsy and inaccurate method! Whereas now, in one moment of audition,
|
|
I take as it were the census and statistics, local, corporeal, mental
|
|
and spiritual, of every living being in Lineland. Hark, only hark!"
|
|
|
|
So saying he paused and listened, as if in an ecstasy, to a sound
|
|
which seemed to me no better than a tiny chirping from an innumerable
|
|
multitude of lilliputian grasshoppers.
|
|
|
|
"Truly," replied I, "your sense of hearing serves you in good
|
|
stead, and fills up many of your deficiencies. But permit me to point
|
|
out that your life in Lineland must be deplorably dull. To see
|
|
nothing but a Point! Not even to be able to contemplate a Straight
|
|
Line! Nay, not even to know what a Straight Line is! To see, yet to
|
|
be cut off from those Linear prospects which are vouchsafed to us in
|
|
Flatland! Better surely to have no sense of sight at all than to see
|
|
so little! I grant you I have not your discriminative faculty of
|
|
hearing; for the concert of all Lineland which gives you such intense
|
|
pleasure, is to me no better than a multitudinous twittering or
|
|
chirping. But at least I can discern, by sight, a Line from a Point.
|
|
And let me prove it. Just before I came into your kingdom, I saw you
|
|
dancing from left to right, and then from right to left, with Seven
|
|
Men and a Woman in your immediate proximity on the left, and eight Men
|
|
and two Women on your right. Is not this correct?"
|
|
|
|
"It is correct," said the King, "so far as the numbers and sexes
|
|
are cocnerned, though I know now what you mean by 'right' and 'left.'
|
|
But I deny that you saw these things. For how could you see the Line,
|
|
that is to say the inside, of any Man? But you must have heard these
|
|
things, and then dreamed that you saw them. And let me ask what you
|
|
mean by those words 'left' and 'right.' I suppose it is your way of
|
|
saying Northward and Southward."
|
|
|
|
"Not so," replied I; "besides your motion of Northward and
|
|
Southward, there is another motion which I call from right to left."
|
|
|
|
King. Exhibit to me, if you please, this motion from left to
|
|
right.
|
|
|
|
I. Nay, that I cannot do, unless you could setp out of your Line
|
|
altogether.
|
|
|
|
King. Out of my Line? Do you mean out of the world? Out of
|
|
Space?
|
|
|
|
I. Well, yes. Out of _your_ world. Out of _your_ Space. For
|
|
your Space is not the true Space. True Space is a Plane; but your
|
|
Space is only a Line.
|
|
|
|
King. If you cannot indicate this motion from left to right by
|
|
yourself moving in it, then I beg you to describe it to me in words.
|
|
|
|
I. If you cannot tell your right side from your left, I fear that
|
|
no words of mine can make my meaning clearer to you. But surely you
|
|
cannot be ignorant of so simple a distinction.
|
|
|
|
King. I do not in the least understand you.
|
|
|
|
I. Alas! How shall I make it clear? When you move straight on,
|
|
does it not sometimes occur to you that you _could_ move in some other
|
|
way, turning your eye round so as to look in the direction towards
|
|
which your side is now fronting? In other words, instead of always
|
|
moving in the direction of one of your extremities, do you never feel
|
|
a desire to move in the direction, so to speak, of your side?
|
|
|
|
King. Never. And what do you mean? How can a man's inside
|
|
"front" in any direction? Or how can a man move in the direction of
|
|
his inside?
|
|
|
|
I. Well then, since words cannot explain the matter, I will try
|
|
deeds, and will move gradually out of Lineland in the direction which
|
|
I desire to indicate to you.
|
|
|
|
At the word I began to move my body out of Lineland. As long as
|
|
any part of me remained in his dominion and in his view, the King kept
|
|
exclaiming, "I see you, I see you still; you are not moving." But
|
|
when I had at last moved myself out of his Line, he cried in his
|
|
shrillest voice, "She is vanished; she is dead." "I am not dead,"
|
|
replied I; "I am simply out of Lineland, that is to say, out of the
|
|
Straight Line which you call Space, and in the true Space, where I can
|
|
see things as they are. And at this moment I can see your Line, or
|
|
side -- or inside as you are pleased to call it; and I can see also
|
|
the Men and Women on the North and South of you, whom I will now
|
|
enumerate, describing their order, their size, and the interval
|
|
between each."
|
|
|
|
When I had done this at great length, I cried triumphantly, "Does
|
|
that at last convince you?" And, with that, I once more entered
|
|
Lineland, taking up the same position as before.
|
|
|
|
But the Monarch replied, "If you were a Man of sense -- though, as
|
|
you appear to have only one voice I have little doubt you are not a
|
|
Man but a Woman -- but, if you had a particle of sense, you would
|
|
listen to reason. You ask me to believe that there is another Line
|
|
besides that which my senses indicate, and another motion besides that
|
|
of which I am daily conscious. I, in return, ask you to describe in
|
|
words or indicate by motion that other Line of which you speak.
|
|
Instead of moving, you merely exercise some magic art of vanishing and
|
|
returning to sight; and instead of any lucid description of your new
|
|
World, you simply tell me the numbers and sizes of some forty of my
|
|
retinue, facts known to any child in my capital. Can anything be more
|
|
irrational or audacious? Acknowledge your folly or depart from my
|
|
dominions."
|
|
|
|
Furious at his perversity, and especially indignant that he
|
|
professed to be ignorant of my sex, I retorted in no measured terms,
|
|
"Besotted Being! You think yourself the perfection of existence,
|
|
while you are in reality the most imperfect and imbecile. You profess
|
|
to see, whereas you see nothing but a Point! You plume yourself on
|
|
inferring the existence of a Straight Line; but I _can see_ Straight
|
|
Lines, and infer the existence of Angles, Triangles, Squares,
|
|
Pentagons, Hexagons, and even Circles. Why waste more words? Suffice
|
|
it that I am the completion of your incomplete self. You are a Line,
|
|
but I am a Line of Lines called in my country a Square: and even I,
|
|
infinitely superior though I am to you, am of little account among the
|
|
great nobles of Flatland, whence I have come to visit you, in the hope
|
|
of enightening your ignorance."
|
|
|
|
Hearing these words the King advanced towards me with a menacing
|
|
cry as if to pierce me through the diagonal; and in that same movement
|
|
there arose from myriads of his subjects a multitudinous war-cry,
|
|
increasing in vehemence till at last methought it rivalled the roar of
|
|
an army of a hundred thousand Isosceles, and the artillery of a
|
|
thousand Pentagons. Spell-bound and motionless, I could neither speak
|
|
nor move to avert the impending destruction; and still the noise grew
|
|
louder, and the King came closer, when I awoke to find the breakfast-
|
|
bell recalling me to the realities of Flatland.
|
|
|
|
* * *
|
|
|
|
SECTION 15. -- Concerning a Stranger from Spaceland
|
|
|
|
From dreams I proceed to facts.
|
|
|
|
It was the last day of our 1999th year of our era. The patterning
|
|
of the rain had long ago announced nightfall; and I was sitting
|
|
(footnote 3) in the company of my wife, musing on the events of the
|
|
past and the prospects of the coming year, the coming century, the
|
|
comming Millennium.
|
|
|
|
My four Sons and two orphan Grandchildren had retired to their
|
|
several apartments; and my wife alone remained with me to see the old
|
|
Millennium out and the new one in.
|
|
|
|
I was rapt in thought, pondering in my mind some words that had
|
|
casually issued from the mouth of my youngest Grandson, a most
|
|
promising young Hexagon of unusual brilliancy and perfect angularity.
|
|
His uncles and I had been giving him his usual practical lesson in
|
|
Sight Recognition, turning ourselves upon our centres, now rapidly,
|
|
now more slowly, and questioning him as to our positions; and his
|
|
answers had been so satisfactory that I had been induced to reward him
|
|
by giving him a few hints on Arithmetic, as applied to Geometry.
|
|
|
|
Taking nine Squares, each an inch every way, I had put them
|
|
together so as to make one large Square, with a side of three inches,
|
|
and I had hence proved to my little Grandson that -- though it was
|
|
impossible for us to _see_ the inside of the Square -- yet we might
|
|
ascertain the number of square inches in a Square by simply squaring
|
|
the number of inches in the side: "and thus," said I, "we know that
|
|
three-to-the-second, or nine, represents the number of square inches
|
|
in a Square whose side is three inches long."
|
|
|
|
The little Hexagon meditated on this a while and then said to me;
|
|
"But you have been teaching me to raise numbers to the third power: I
|
|
suppose three-to-the-third must mean something in Geometry; what does
|
|
it mean?" "Nothing at all," replied I, "not at least in Geometry; for
|
|
Geometry has only Two Dimensions." And then I began to shew the boy
|
|
how a Point by moving through a length of three inches makes a Line of
|
|
three inches, which may be represented by three; and how a Line of
|
|
three inches, moving parallel to itself through a length of three
|
|
inches, makes a Square of three inches every way, which may be
|
|
represented by three-to-the-second.
|
|
|
|
Upon this, my Grandson, again returning to his former suggestion,
|
|
took me up rather suddenly and exclaimed, "Well, then, if a Point by
|
|
moving three inches, makes a Line of three inches represented by
|
|
three; and if a straight Line of three inches, moving parallel to
|
|
itself, makes a Square of three inches every way, represented by
|
|
three-to-the-second; it must be that a Square of three inches every
|
|
way, moving somehow parallel to itself (but I don't see how) must make
|
|
Something else (but I don't see what) of three inches every way -- and
|
|
this must be represented by three-to-the-third."
|
|
|
|
"Go to bed," said I, a little ruffled by this interruption: "if
|
|
you would talk less nonsense, you would remember more sense."
|
|
|
|
So my Grandson had disappeared in disgrace; and there I sat by my
|
|
Wife's side, endeavouring to form a retrospect of the year 1999 and of
|
|
the possibilities of the year 2000; but not quite able to shake of the
|
|
thoughts suggested by the prattle of my bright little Hexagon. Only a
|
|
few sands now remained in the half-hour glass. Rousing myself from my
|
|
reverie I turned the glass Northward for the last time in the old
|
|
Millennium; and in the act, I exclaimed aloud, "The boy is a fool."
|
|
|
|
Straightway I became conscious of a Presence in the room, and a
|
|
chilling breath thrilled through my very being. "He is no such
|
|
thing," cried my Wife, "and you are breaking the Commandments in thus
|
|
dishonouring your own Grandson." But I took no notice of her.
|
|
Looking around in every direction I could see nothing; yet still I
|
|
_felt_ a Presence, and shivered as the cold whisper came again. I
|
|
started up. "What is the matter?" said my Wife, "there is no draught;
|
|
what are you looking for? There is nothing." There was nothing; and
|
|
I resumed my seat, again exclaiming, "The boy is a fool, I say; three-
|
|
to-the-third can have no meaning in Geometry." At once there came a
|
|
distinctly audible reply, "The boy is not a fool; and three-to-the-
|
|
third has an obvious Geometrical meaning."
|
|
|
|
My Wife as well as myself heard the words, although she did not
|
|
understand their meaning, and both of us sprang forward in the
|
|
direction of the sound. What was our horror when we saw before us a
|
|
Figure! At the first glance it appeared to be a Woman, seen sideways;
|
|
but a moment's observation shewed me that the extremities passed into
|
|
dimness too rapidly to represent one of the Female Sex; and I should
|
|
have thought it a Circle, only that it seemed to change its size in a
|
|
manner impossible for a Circle or for any regular Figure of which I
|
|
had had experience.
|
|
|
|
But my Wife had not my experience, nor the coolness necessary to
|
|
note these characteristics. With the usual hastiness and unreasoning
|
|
jealousy of her Sex, she flew at once to the conclusion that a Woman
|
|
had entered the house through some small apeture. "How comes this
|
|
person here?" she exclaimed, "you promised me, my dear, that there
|
|
should be no ventilators in our new house." "Nor are they any," said
|
|
I; "but what makes you think that the stranger is a Woman? I see by
|
|
my power of Sight Recoginition --" "Oh, I have no patience with your
|
|
Sight Recognition," replied she, "'Feeling is believing' and 'A
|
|
Straight Line to the touch is worth a Circle to the sight'" -- two
|
|
Proverbs, very common with the Frailer Sex in Flatland.
|
|
|
|
"Well," said I, for I was afraid of irritating her, "if it must be
|
|
so, demand an introduction." Assuming her most gracious manner, my
|
|
Wife advanced towards the Stranger, "Permit me, Madam to feel and be
|
|
felt by --" then, suddenly recoiling, "Oh! it is not a Woman, and
|
|
there are no angles either, not a trace of one. Can it be that I have
|
|
so misbehaved to a perfect Circle?"
|
|
|
|
"I am indeed, in a certain sense a Circle," replied the Voice,
|
|
"and a more perfect Circle than any in Flatland; but to speak more
|
|
accurately, I am many Circles in one." Then he added more mildly, "I
|
|
have a message, dear Madam, to your husband, which I must not deliver
|
|
in your presence; and, if you would suffer us to retire for a few
|
|
minutes --" But my wife would not listen to the propsal that our
|
|
august Visitor should so incommode himself, and assuring the Circle
|
|
that the hour of her own retirement had long passed, with many
|
|
reiterated apologies for her recent indiscretion, she at last
|
|
retreated to her apartment.
|
|
|
|
I glanced at the half-hour glass. The last sands had fallen. The
|
|
third Millennium had begun.
|
|
----------
|
|
Footnote 3. When I say "sitting," of course I do not mean any change
|
|
of attitude such as you in Spaceland signify by that word; for as we
|
|
have no feet, we can no more "sit" nor "stand" (in your sense of the
|
|
word) than one of your soles or flounders.
|
|
|
|
Nevertheless, we perfectly well recognize the different mental
|
|
states of volition implied by "lying," "sitting," and "standing,"
|
|
which are to some extent indicated to a beholder by a slight increase
|
|
of lustre corresponding to the increase of volition.
|
|
|
|
But on this, and a thousand other kindred subjects, time forbids
|
|
me to dwell.
|
|
|
|
* * *
|
|
|
|
SECTION 16. -- How the Stranger vainly endeavoured to reveal to me
|
|
|
|
in words the mysteries of Spaceland
|
|
|
|
As soon as the sound of the Peace-cry of my departing Wife had
|
|
died away, I began to approach the Stranger with the intention of
|
|
taking a nearer view and of bidding him be seated: but his appearance
|
|
struck me dumb and motionless with astonishment. Without the
|
|
slightest symptoms of angularity hee nevertheless varied every instant
|
|
with graduations of size and brightness scarcely possible for any
|
|
Figure within the scope of my experience. The thought flashed across
|
|
me that I might have before me a burglar or cut-throat, some monstrous
|
|
Irregular Isosceles, who, by feigning the voice of a Circle, had
|
|
obtained admission somehow into the house, and was now preparing to
|
|
stab me with his acute angle.
|
|
|
|
In a sitting-room, the absence of Fog (and the season happened to
|
|
be remarkably dry), made it difficult for me to trust to Sight
|
|
Recognition, especially at the short distance at which I was standing.
|
|
Desperate with fear, I rushed forward with an unceremonious, "You must
|
|
permit me, Sir --" and felt him. My Wife was right. There was not
|
|
the trace of an angle, not the slightest roughness or inequality:
|
|
never in my life had I met with a more perfect Circle. He remained
|
|
motionless while I walked around him, beginning from his eye and
|
|
returning to it again. Circular he was throughout, a perfectly
|
|
satisfactory Circle; there could not be a doube of it. Then followed
|
|
a dialogue, which I will endeavour to set down as near as I can
|
|
recollect it, omitting only some of my profuse apologies -- for I was
|
|
covered with shame and humiliation that I, a Square, should have been
|
|
guilty of the impertinence of feeling a Circle. It was commenced by
|
|
the Stranger with some impatience at the lengthiness of my
|
|
introductory process.
|
|
|
|
Stranger. Have you felt me enough by this time? Are you not
|
|
introduced to me yet?
|
|
|
|
I. Most illustrious Sir, excuse my awkwardness, which arises not
|
|
from ignorance of the usages of polite society, but from a little
|
|
surprise and nervousness, consequent on this somewhat unexpected
|
|
visit. And I beseech you to reveal my indiscretion to no one, and
|
|
especially not to my Wife. But before your Lordship enters into
|
|
further communications, would he deign to satisfy the curiosity of one
|
|
who would gladly know whence his visitor came?
|
|
|
|
Stranger. From Space, from Space, Sir: whence else?
|
|
|
|
I. Pardon me, my Lord, but is not your Lordship already in Space,
|
|
your Lordship and his humble servant, even at this moment?
|
|
|
|
Stranger. Pooh! what do you know of Space? Define Space.
|
|
|
|
I. Space, my Lord, is height and breadth indefinitely prolonged.
|
|
|
|
Stranger. Exactly: you see you do not even know what Space is.
|
|
You think it is of Two Dimensions only; but I have come to announce to
|
|
you a Third -- height, breadth, and length.
|
|
|
|
I. Your Lordship is pleased to be merry. We also speak of length
|
|
and height, or breadth and thickness, thus denoting Two Dimensions by
|
|
four names.
|
|
|
|
Stranger. But I mean not only three names, but Three Dimensions.
|
|
|
|
I. Would your Lordship indicate or explain to me in what
|
|
direction is the Third Dimension, unknown to me?
|
|
|
|
Stranger. I came from it. It is up above and down below.
|
|
|
|
I. My Lord means seemingly that it is Northward and Southward.
|
|
|
|
Stranger. I mean nothing of the kind. I mean a direction in
|
|
which you cannot look, because you have no eye in your side.
|
|
|
|
I. Pardon me, my Lord, a moment's inspection will convince your
|
|
Lordship that I have a perfectly luminary at the juncture of my two
|
|
sides.
|
|
|
|
Stranger: Yes: but in order to see into Space you ought to have
|
|
an eye, not on your Perimeter, but on your side, that is, on what you
|
|
would probably call your inside; but we in Spaceland should call it
|
|
your side.
|
|
|
|
I. An eye in my inside! An eye in my stomach! Your Lordship
|
|
jests.
|
|
|
|
Stranger. I am in no jesting humour. I tell you that I come from
|
|
Space, or, since you will not understand what Space means, from the
|
|
Land of Three Dimensions whence I but lately looked down upon your
|
|
Plane which you call Space forsooth. From that position of advantage
|
|
I discerned all that you speak of as _solid_ (by which you mean
|
|
"enclosed on four sides"), your houses, your churches, your very
|
|
chests and safes, yes even your insides and stomachs, all lying open
|
|
and exposed to my view.
|
|
|
|
I. Such assertions are easily made, my Lord.
|
|
|
|
Stranger. But not easily proved, you mean. But I mean to prove
|
|
mine.
|
|
|
|
When I descended here, I saw your four Sons, the Pentagons, each
|
|
in his apartment, and your two Grandsons the Hexagons; I saw your
|
|
youngest Hexagon remain a while with you and then retire to his room,
|
|
leaving you and your Wife alone. I saw your Isosceles servants, three
|
|
in number, in the kitchen at supper, and the little Page in the
|
|
scullery. Then I came here, and how do you think I came?
|
|
|
|
I. Through the roof, I suppose.
|
|
|
|
Strange. Not so. Your roof, as you know very well, has been
|
|
recently repaired, and has no aperture by which even a Woman could
|
|
penetrate. I tell you I come from Space. Are you not convinced by
|
|
what I have told you of your children and household?
|
|
|
|
I. Your Lordship must be aware that such facts touching the
|
|
belongings of his humble servant might be easily ascertained by any
|
|
one of the neighbourhood possessing your Lordship's ample means of
|
|
information.
|
|
|
|
Stranger. (_To himself._) What must I do? Stay; one more
|
|
argument suggests itself to me. When you see a Straight Line -- your
|
|
wife, for example -- how many Dimensions do you attribute to her?
|
|
|
|
I. Your Lordship would treat me as if I were one of the vulgar
|
|
who, being ignorant of Mathematics, suppose that a Woman is really a
|
|
Straight Line, and only of One Dimension. No, no, my Lord; we Squares
|
|
are better advised, and are as well aware of your Lordship that a
|
|
Woman, though popularly called a Straight Line, is, really and
|
|
scientifically, a very thin Parallelogram, possessing Two Dimensions,
|
|
like the rest of us, viz., length and breadth (or thickness).
|
|
|
|
Stranger. But the very fact that a Line is visible implies that
|
|
it possesses yet another Dimension.
|
|
|
|
I. My Lord, I have just acknowledge that a Woman is broad as well
|
|
as long. We see her length, we infer her breadth; which, though very
|
|
slight, is capable of measurement.
|
|
|
|
Stranger. You do not understand me. I mean that when you see a
|
|
Woman, you ought -- besides inferring her breadth -- to see her
|
|
length, and to _see_ what we call her _height_; although the last
|
|
Dimension is infinitesimal in your country. If a Line were mere
|
|
length without "height," it would cease to occupy Space and would
|
|
become invisible. Surely you must recognize this?
|
|
|
|
I. I must indeed confess that I do not in the least understand
|
|
your Lordship. When we in Flatland see a Line, we see length and
|
|
_brightness._ If the brightness disappears, the Line is extinguished,
|
|
and, as you say, ceases to occupy Space. But am I to suppose that
|
|
your Lordship gives the brightness the title of a Dimension, and that
|
|
what we call "bright" you call "high"?
|
|
|
|
Stranger. No, indeed. By "height" I mean a Dimension like your
|
|
length: only, with you, "height" is not so easily perceptible, being
|
|
extremely small.
|
|
|
|
I. My Lord, your assertion is easily put to the test. You say I
|
|
have a Third Dimension, which you call "height." Now, Dimension
|
|
implies direction and measurement. Do but measure my "height," or
|
|
merely indivate to me the direction in which my "height" extends, and
|
|
I will become your convert. Otherwise, your Lordship's own understand
|
|
must hold me excused.
|
|
|
|
Stranger. (_To himself._) I can do neither. How shall I
|
|
convince him? Surely a plain statement of facts followed by ocular
|
|
demonstration ought to suffice. -- Now, Sir; listen to me.
|
|
|
|
You are living on a Plane. What you style Flatland is the vast
|
|
level surface of what I may call a fluid, or in, the top of which you
|
|
and your countrymen move about, without rising above or falling below
|
|
it.
|
|
|
|
I am not a plane Figure, but a Solid. You call me a Circle; but in
|
|
reality I am not a Circle, but an infinite number of Circles, of size
|
|
varying from a Point to a Circle of thirteen inches in diameter, one
|
|
placed on the top of the other. When I cut through your plane as I am
|
|
now doing, I make in your plane a section which you, very rightly,
|
|
call a Circle. For even a Sphere -- which is my proper name in my own
|
|
country -- if he manifest himself at all to an inhabitant of Flatland
|
|
-- must needs manfest himself as a Circle.
|
|
|
|
Do you not remember -- for I, who see all things, discerned last
|
|
night the phantasmal vision of Lineland written upon your brain -- do
|
|
you not remember, I say, how when you entered the realm of Lineland,
|
|
you were compelled to manifest yourself to the King, not as a Square,
|
|
but as a Line, because that Linear Realm had not Dimensions enough to
|
|
represent the whole of you, but only a slice or section of you? In
|
|
precisely the same way, your country of Two Dimensions is not spacious
|
|
enough to represent me, a being of Three, but can only exhibit a slice
|
|
or section of me, which is what you call a Circle.
|
|
|
|
The diminished brightness of your eye indicates incredulity. But
|
|
now prepare to receive proof positive of the truth of my assertions.
|
|
You cannot indeed see more than one of my sections, or Circles, at a
|
|
time; for you have no power to raise your eye out of the plane of
|
|
Flatland; but you can at least see that, as I rise in Space, so my
|
|
sections become smaller. See now, I will rise; and the effect upon
|
|
your eye will be that my Circle will become smaller and smaller till
|
|
it dwindles to a point and finally vanishes.
|
|
|
|
There was no "rising" that I could see; but he diminished and
|
|
finally vanished. I winked once or twice to make sure that I was not
|
|
dreaming. But it was no dream. For from the depths of nowhere came
|
|
forth a hollow voice -- close to my heart it seemed -- "Am I quite
|
|
gone? Are you convinced now? Well, now I will gradually return to
|
|
Flatland and you shall see my section become larger and larger."
|
|
|
|
Every reader in Spaceland will easily understand that my
|
|
mysterious Guest was speaking the language of truth and even of
|
|
simplicity. But to me, proficient though I was in Flatland
|
|
Mathematics, it was by no means a simple matter. The rough diagram
|
|
given above will make it clear to any Spaceland child that the Sphere,
|
|
ascending in the three positions indicated there, must needs have
|
|
manifested himself to me, or to any Flatlander, as a Circle, at first
|
|
of full size, then small, and at last very small indeed, approaching
|
|
to a Point. But to me, although I saw the facts before me, the causes
|
|
were as dark as ever. All that I could comprehend was, that the
|
|
Circle had made himself smaller and vanished, and that he had now re-
|
|
appeared and was rapidly making himself larger.
|
|
|
|
When he regained his original size, he heaved a deep sigh; for he
|
|
perceived by my silence that I had altogether failed to comprehend
|
|
him. And indeed I was now inclining to the belief that he must be no
|
|
Circle at all, but some extremely clever juggler; or else that the old
|
|
wives' tales were true, and that after all there were such people as
|
|
Enchanters and Magicians.
|
|
|
|
After a long pause he muttered to himself, "One resource alone
|
|
remains, if I am not to resort to action. I must try the method of
|
|
Analogy." Then follwed a still longer silence, after which he
|
|
continued our dialogue.
|
|
|
|
Sphere. Tell me, Mr. Mathematician; if a Point moves Northward,
|
|
and leaves a luminous wake, what name would you give to the wake?
|
|
|
|
I. A straight Line.
|
|
|
|
Sphere. And a straight Line has how many extremities?
|
|
|
|
I. Two.
|
|
|
|
Sphere. Now conceive the Northward straight Line momving parallel
|
|
to itself, East and West, so that every point in it leaves behind it
|
|
the wake of a straight Line. What name will you give to the Figure
|
|
thereby formed? We will suppose that it moves through a distance
|
|
equal to the original straight line. --- What name, I say?
|
|
|
|
I. A square.
|
|
|
|
Sphere. And how many sides has a Square? How many angles?
|
|
|
|
I. Four sides and four angles.
|
|
|
|
Sphere. Now stretch your imagination a little, and conceive a
|
|
Square in Flatland, moving parallel to itself upward.
|
|
|
|
I. What? Northward?
|
|
|
|
Sphere. No, not Northward; upward; out of Flatland altogether.
|
|
|
|
If it moved Northward, the Southern points in the Square would
|
|
have to move through the positions previously occupied by the Northern
|
|
points. But that is not my meaning.
|
|
|
|
I mean that every Point in you -- for you are a Square and will
|
|
serve the purpose of my illustration -- every Point in you, that is to
|
|
say in what you call your inside, is to pass upwards through Space in
|
|
such a way that no Point shall pass through the position previously
|
|
occupied by any other Point; but each Point shall describe a straight
|
|
Line of its own. This is all in accordance with Analogy; surely it
|
|
must be clear to you.
|
|
|
|
Restraining my impatience -- for I was now under a strong
|
|
temptation to rush blindly at my Visitor and to precipitate him into
|
|
Space, or out of Flatland, anywhere, so that I could get rid of him --
|
|
I replied: --
|
|
|
|
"And what may be the nature of the Figure which I am to shape out
|
|
by this motion which you are pleased to denote by the word 'upward'?
|
|
I presume it is describable in the language of Flatland."
|
|
|
|
Sphere. Oh, certainly. It is all plain and simple, and in strict
|
|
accordance with Analogy -- only, by the way, you must not speak of the
|
|
result as being a Figure, but as a Solid. But I will describe it to
|
|
you. Or rather not I, but Analogy.
|
|
|
|
We began with a single Point, which of course -- being itself a
|
|
Poine -- has only _one_ terminal Point.
|
|
|
|
One Point produces a Line with _two_ terminal Points.
|
|
|
|
One Line produces a Square with _four_ terminal Points.
|
|
|
|
Now you can give yourself the answer to your own question: 1, 2,
|
|
4, are evidently in Geometrical Progression. What is the next number?
|
|
|
|
I. Eight.
|
|
|
|
Sphere. Exactly. The one Square produces a _Something-which-you-
|
|
do-not-as-yet-know-a-name-for-but-which-we-call-a-Cube_ with _eight_
|
|
terminal Points. Now are you convinced?
|
|
|
|
I. And has this Creature sides, as well as Angles or what you
|
|
call "terminal Points"?
|
|
|
|
Sphere. Of course; and all according to Analogy. But, by the
|
|
way, not what _you_ call sides, but what _we_ call sides. You would
|
|
call them _solids._
|
|
|
|
I. And how many solids or sides will appertain to this Being whom
|
|
I am to generate by the motion of my inside in an "upward" direction,
|
|
and whom you call a Cube?
|
|
|
|
Sphere. How can you ask? And you a mathematician! The side of
|
|
anything is always, if I may so say, one Dimension behind the thing.
|
|
Consequently, as there is no Dimension behind a Point, a Point has 0
|
|
sides; a Line, if I may so say, has 2 sides (for the points of a Line
|
|
may be called by courtesy, its sides); a Square has 4 sides; 0, 2, 4;
|
|
what Progression do you call that?
|
|
|
|
I. Arithmetical.
|
|
|
|
Sphere. And what is the next number?
|
|
|
|
I. Six.
|
|
|
|
Sphere. Exactly. Then you see you have answered your own
|
|
question. The Cube which you will generate will be bounded by six
|
|
sides, that is to say, six of your insides. You see it all now, eh?
|
|
|
|
"Monster," I shrieked, "be thou juggler, enchanter, dream, or
|
|
devil, no more will I endure thy mockeries. Either thou or I must
|
|
perish." And saying these words I precipitated myself upon him.
|
|
|
|
* * *
|
|
|
|
SECTION 17. -- How the Sphere, having in vain tried words,
|
|
|
|
resorted to deeds
|
|
|
|
It was in vain. I brought my hardest right angle into violent
|
|
collision with the Stranger, pressing on him with a force sufficient
|
|
to have destroyed anyt ordinary Circle: but I could feel him slowly
|
|
and unarrestably slipping from my contact; not edging to the right nor
|
|
to the left, but moving somehow out of the world, and vanishing into
|
|
nothing. Soon there was a blank. But still I heard the Intruder's
|
|
voice.
|
|
|
|
Sphere. Why will you refuse to listen to reason? I had hoped to
|
|
find in you -- as being a man of sense and an accomplished
|
|
mathematician -- a fit apostle for the Gospel of the Three Dimensions,
|
|
which I am allowed to preach once only in a thousand years: but now I
|
|
know not how to convince you. Stay, I have it. Deeds, and not words,
|
|
shall proclaim the truth. Listen, my friend.
|
|
|
|
I have told you I can see from my position in Space the inside of
|
|
all things that you consider closed. For example, I see in yonder
|
|
cupboard near which you are standing, several of what you call boxes
|
|
(but like everything else in Flatland, they have no tops or bottom)
|
|
full of money; I see also two tablets of accounts. I am about to
|
|
descend into that cupboard and to bring you one of those tablets. I
|
|
saw you lock the cupboard half an hour ago, and I know you have the
|
|
key in your possession. But I descend from Space; the doors, you see,
|
|
remain unmoved. Now I am in the cupboard and am taking the tablet.
|
|
Now I have it. Now I ascent with it.
|
|
|
|
I rushed to the closet and dashed the door open. One of the
|
|
tablets was gone. With a mocking laugh, the Stranger appeared in the
|
|
other corner of the room, and at the same time the tablet appeared
|
|
upon the floor. I took it up. There could be no doubt -- it was the
|
|
missing tablet.
|
|
|
|
I groaned with horror, doubting whether I was not out of my sense;
|
|
but the Stranger continued: "Surely you must now see that my
|
|
explanation, and no other, suits the phenomena. What you call Solid
|
|
things are really superficial; what you call Space is really nothing
|
|
but a great Plane. I am in Space, and look down upon the insides of
|
|
the things of which you only see the outsides. You could leave the
|
|
Plane yourself, if you could but summon up the necessary volition. A
|
|
slight upward or downward motion would enable you to see all that I
|
|
can see.
|
|
|
|
"The higher I mount, and the further I go from your Plane, the
|
|
more I can see, though of course I see it on a smaller scale. For
|
|
example, I am ascending; now I can see your neighbour the Hexagon and
|
|
his family in their several apartments; now I see the inside of the
|
|
Theatre, ten doors off, from which the audience is only just
|
|
departing; and on the other side a Circle in his study, sitting at his
|
|
books. Now I shall come back to you. And, as a crowning proof, what
|
|
do you say to my giving you a touch, just the least touch, in your
|
|
stomach? It will not seriously injure you, and the slight pain you
|
|
may suffer cannot be compared with the mental benefit you will
|
|
receive."
|
|
|
|
Before I could utter a word of remonstrance, I felt a shooting
|
|
pain in my inside, and a demoniacal laugh seemed to issue from within
|
|
me. A moment afterwards the sharp agony had ceased, leaving nothing
|
|
but a dull ache behind, and the Stranger began to reappear, saying, as
|
|
he gradually increased in size, "There, I have not hurt you much, have
|
|
I? If you are not convinced now, I don't know what will convince you.
|
|
What say you?"
|
|
|
|
My resolution was taken. It seemed intolerable that I should
|
|
endure existence subject to the arbitrary visitations of a Magician
|
|
who could thus play tricks with one's very stomach. If only I could
|
|
in any way manage to pin him against the wall till help came!
|
|
|
|
Once more I dashed my hardest angle against him, at the same time
|
|
alarming the whole household by my cries for aid. I believe, at the
|
|
moment of my onset, the Stranger had sunk below our Plane, and really
|
|
found difficulty in rising. In any case he remained motionless, while
|
|
I, hearing, as I thought, the sound of some help approaching, pressed
|
|
against him with redoubled vigor, and continued to shout for
|
|
assistance.
|
|
|
|
A convulsive shudder ran through the Sphere. "This must not be,"
|
|
I thought I heard him say: "either he must listen to reason, or I
|
|
must have recourse to the last resource of civilization." Then,
|
|
addressing me in a louder tone, he hurriedly exclaimed, "Listen: no
|
|
stranger must witness what you have witnessed. Send your Wife back at
|
|
once, before she enters the apartment. The Gospel of Three Dimensions
|
|
must not be thus frustrated. Not thus must the fruits of one thousand
|
|
years of waiting be thrown away. I hear her coming. Back! back!
|
|
Away from me, or you must go with me -- wither you know not -- into
|
|
the Land of Three Dimensions!"
|
|
|
|
"Fool! Madman! Irregular!" I exclaimed; "never will I release
|
|
thee; thou shalt pay the penalty of thine impostures."
|
|
|
|
"Ha! Is it come to this?" thundered the Stranger: "then meet
|
|
your fate: out of your Plane you go. Once, twice, thrice! 'Tis
|
|
done!"
|
|
|
|
* * *
|
|
|
|
SECTION 18. -- How I came to Spaceland, and what I saw there
|
|
|
|
An unspeakable horror seized me. There was a darkness; then a
|
|
dizzy, sickening sensation of sight that was not like seeing; I saw a
|
|
Line that was no Line; Space that was not Space: I was myself, and
|
|
not myself. When I could find voice, I shrieked loud in agony,
|
|
"Either this is madness or it is Hell." "It is neither, calmly
|
|
replied the voice of the Sphere, "it is Knowledge; it is Three
|
|
Dimensions: open your eye once again and try to look steadily."
|
|
|
|
I looked, and, behold, a new world! There stood before me,
|
|
visibly incorporate, all that I had before inferred, conjectured,
|
|
dreamed, of perfect Circular beauty. What seemed the centre of the
|
|
Stranger's form lay open to my view: yet I could see no heart, lungs,
|
|
nor arteries, only a beautiful harmonious Something -- for which I had
|
|
no words; but you, my Readers in Spaceland, would call it the surface
|
|
of the Sphere.
|
|
|
|
Prostrating myself mentally before my Guide, I cried, "How it is,,
|
|
O divine ideal of consummate loveliness and wisdom that I see thy
|
|
inside, and yet cannot discern thy heart, thy lungs, thy arteries, thy
|
|
liver?" "What you think you see, you see not," he replied; "it is not
|
|
giving to you, nor to any other Being, to behold my internal parts. I
|
|
am of a different order of Beings from those in Flatland. Where I a
|
|
Circle, you could discern my intestines, but I am a Being, composed as
|
|
I told you before, of many Circles, the Many in the One, called in
|
|
this country a Sphere. And, just as the outside of a Cube is a
|
|
Square, so the outside of a Sphere represents the appearance of a
|
|
Circle."
|
|
|
|
Bewildered though I was by my Teacher's enigmatic utterance, I no
|
|
longer chafed against it, but worshipped him in silent adoration. He
|
|
continued, with more mildness in his voice. "Distress not yourself if
|
|
you cannot at first understand the deeper mysteries of Spaceland. By
|
|
degrees they will dawn upon you. Let us begin by casting back a
|
|
glance at the region whence you came. Return with me a while to the
|
|
plains of Flatland and I will shew you that which you have often
|
|
reasoned and thought about, but never seen with the sense of sight --
|
|
a visible angle." "Impossible!" I cried; but, the Sphere leading the
|
|
way, I followed as if in a dream, till once more his voice arrested
|
|
me: "Look yonder, and behold your own Pentagonal house, and all its
|
|
inmates."
|
|
|
|
I looked below, and saw with my physical eye all that domestic
|
|
individuality which I had hitherto merely inferred with the
|
|
understanding. And how poor and shadowy was the inferred conjecture
|
|
in comparison with the reality which I now behold! My four Sons
|
|
calmly asleep in the North-Western rooms, my two orphan Grandsons to
|
|
the South; the Servants, the Butler, my Daughter,, all in their
|
|
several apartments. Only my affection Wife, alarmed by my continued
|
|
absence, had quitter her room and was roving up and down in the Hall,
|
|
anxiously awaiting my return. Also the Page, aroused by my cries, had
|
|
left his room, and under pretext of ascertaining whether I had fallen
|
|
somewhere in a faint, was prying into the cabinet in my study. All
|
|
this I could now _see,_ not merely infer; and as we came nearer and
|
|
nearer, I could discern even the contents of my cabinet, and the two
|
|
chests of gold, and the tablets of which the Sphere had made mention.
|
|
|
|
Touched by my Wife's distress, I would have sprung downward to
|
|
reassure her, but I found myself incapable of motion. "Trouble not
|
|
yourself about your Wife," said my Guide: "she will not be long left
|
|
in anxiety; meantime, let us take a survey of Flatland."
|
|
|
|
Once more I felt myself rising through space. It was even as the
|
|
Sphere had said. The further we receded from the object we beheld,
|
|
the larger became the field of vision. My native city, with the
|
|
interior of every house and every creature therein, lay open to my
|
|
view in miniature. We mounted higher, and lo, the secrets of the
|
|
earth, the depths of the mines and inmost caverns of the hills, were
|
|
bared before me.
|
|
|
|
Awestruck at the sight of the mysteries of the earth, thus
|
|
unveiled before my unworthy eye, I said to my Companion, "Behold, I am
|
|
become as a God. For the wise men in our country say that to see all
|
|
things, or as they express it, _omnividence,_ is the attribute of God
|
|
alone." There was something of scorn in the voice of my Teacher as he
|
|
made answer: "it is so indeed? Then the very pick-pockets and cut-
|
|
throats of my country are to be worshipped by your wise men as being
|
|
Gods: for there is not one of them that does not see as much as you
|
|
see now. But trust me, your wise men are wrong."
|
|
|
|
I. Then is omnividence the attribute of others besides Gods?
|
|
|
|
Sphere. I do not know. But, if a pick-pocket or a cut-throat of
|
|
our country can see everything that is in your country, surely that is
|
|
no reason why the pick-pocket or cut-throat should be accepted by you
|
|
as a God. This omnividence, as you call it -- it is not a common word
|
|
in Spaceland -- does it make you more just, more merciful, less
|
|
selfish, more loving? Not in the least. Then how does it make you
|
|
more divine?
|
|
|
|
I. "More merciful, more loving!" But these are the qualities of
|
|
women! And we know that a Circle is a higher Being than a Straight
|
|
Line, in so far as knowledge and wisdom are more to be esteemed than
|
|
mere affection.
|
|
|
|
Sphere. It is not for me to classify human faculties according to
|
|
merit. Yet many of the best and wisest in Spaceland think more of the
|
|
affections than of the understand, more of your despised Straight
|
|
Lines than of your belauded Circles. But enough of this. Look
|
|
yonder. Do you know that building?
|
|
|
|
I looked, and afar off I saw an immense Polygonal structure, in
|
|
which I recognized the General Assembly Hall of the States of
|
|
Flatland, surrounded by dense lines of Pentagonal buildings at right
|
|
angles to each other, which I knew to be streets; and I perceived that
|
|
I was approaching the great Metropolis.
|
|
|
|
"Here we descend," said my Guide. It was now morning, the first
|
|
hour of the first day of the two thousandth year of our era. Acting,
|
|
as was their wont, in strict accordance with precedent, the highest
|
|
Circles of the realm were meeting in solemn conclave, as they had met
|
|
on the first hour of the first day of the year 1000, and also on the
|
|
first hour of the first day of the year 0.
|
|
|
|
The minutes of the previous meetings were now read by one whom I
|
|
at once recognized as my brother, a perfectly Symmetrical Square, and
|
|
the Chief Clerk of the High Council. It was found recorded on each
|
|
occasion that: "Whereas the States had been troubled by divers ill-
|
|
intentioned persons pretending to have received revelations from
|
|
another World, and professing to produce demonstrations whereby they
|
|
had instigated to frenzy both themselves and others, it had been for
|
|
this cause unanimously resolved by the Grand Council that on the first
|
|
day of each millenary, special injunctions be sent to the Prefects in
|
|
the several districts of Flatland, to make strict search for such
|
|
misguided persons, and without formality of mathematical exanimation,
|
|
to destroy all such as were Isosceles of anyt degree, to scourge and
|
|
imprison any regular Triangle, to cause any Square or Pentagon to be
|
|
sent to the district Asylum, and to arrest any one of higher rank,
|
|
sending him straightway to the Capital to be examined and judged by
|
|
the Council."
|
|
|
|
"You hear your fate," said the Sphere to me, while the Council was
|
|
passing for the third time the formal resolution. "Death or
|
|
imprisonment awaits the Apostle of the Gospel of Three Dimensions."
|
|
"Not so," replied I, "the matter is now so clear to me, the nature of
|
|
real space so palpable, that methinks I could make a child understand
|
|
it. Permit me but to descend at this moment and enlighten them."
|
|
"Not yet," said my Guide, "the time will come for that. Meantime I
|
|
must perform my mission. Stay thou there in thy place." Saying these
|
|
words, he leaped with great dexterity into the sea (if I may so call
|
|
it) of Flatland, right in the midst of the ring of Counsellors. "I
|
|
come," said he, "to proclaim that there is a land of Three
|
|
Dimensions."
|
|
|
|
I could see many of the younger Counsellors start back in manifest
|
|
horror, as the Sphere's circular section widened before them. But on
|
|
a sign from the presiding Circle -- who shewed not the slightest alarm
|
|
or surprise -- six Isosceles of a low type from six different quarters
|
|
rushed upon the Sphere. "We have him," they cried; "No; yes; we have
|
|
him still! he's going! he's gone!"
|
|
|
|
"My Lords," said the President to the Junior Circles of the
|
|
Council, "there is not the slightest need for surprise; the secret
|
|
archives, to which I alone have access, tell me that a similar
|
|
occurrence happened on the last two millennial commencements. You
|
|
will, of course, say nothing of these trifles outside the Cabinet."
|
|
|
|
Raising his voice, he now summoned the guards. "Arrest the
|
|
policemen; gag them. You know your duty." After he had consigned to
|
|
their fate the wretched policemen -- ill-fated and unwilling witnesses
|
|
of a State-secret which they were not to be permitted to reveal -- he
|
|
again addressed the Counsellors. "My Lords, the business of the
|
|
Council being concluded, I have only to wish you a happy New Year."
|
|
Before departing, he expressed, at some length, to the Clerk, my
|
|
excellent but most unfortunate brother, his sincere regret that, in
|
|
accordance with recedent and for the sake of secrecy, he must condemn
|
|
him to perpetual imprisonment, but added his satisfaction that, unless
|
|
some mention were made by him of that day's incident, his life would
|
|
be spared.
|
|
|
|
* * *
|
|
|
|
SECTION 19. -- How, though the Sphere shewed me other mysteries of
|
|
|
|
Spaceland, I still desire more; and what came of it
|
|
|
|
When I saw my poor brother led away to imprisonment, I attempted
|
|
to leap down into the Council Chamber, desiring to intercede on his
|
|
behalf, or at least bid him farewell. But I found that I had no
|
|
motion of my own. I absolutely depended on the volition of my Guide,
|
|
who said in gloomy tones, "Heed not thy brother; haply thou shalt have
|
|
ample time hereafter to condole with him. Follow me."
|
|
|
|
Once more we ascended into space. "Hitherto," said the Sphere, "I
|
|
have shewn you naught save Plane Figures and their interiors. Now I
|
|
must introduce you to Solids, and reveal to you the plan upon which
|
|
they are constructed. Behlod this multitude of moveable square cards.
|
|
See, I put on on another, not, as you supposed, Northward of the
|
|
other, but _on_ the other. Now a second, now a third. See, I am
|
|
building up a Solid by a multitude of Squares parallel to one another.
|
|
Now the Solid is complete, being as high as it is long and broad, and
|
|
we call it a Cube."
|
|
|
|
"Pardon me, my Lord," replied I; "but to my eye the appearance is
|
|
as of an Irregular Figure whose inside is laid open to view; in other
|
|
words, methinks I see no Solid, but a Plane such as we infer in
|
|
Flatland; only of an Irregularity which betokens some monstrous
|
|
criminal, so that the very sight of it is painful to my eyes."
|
|
|
|
"True," said the Sphere; "it appears to you a Plane, because you
|
|
are not accustomed to light and shade and perspective; just as in
|
|
Flatland a Hexagon would appear a Straight Line to one who has not the
|
|
Art of Sight Recognition. But in reality it is a Solid, as you shall
|
|
learn by the sense of Feeling."
|
|
|
|
He then introduced me to the Cube, and I found that this
|
|
marvellous Being was indeed no Plane, but a Solid; and that he was
|
|
endowed with six plane sides and eight terminal points called solid
|
|
angles; and I remembered the saying of the Sphere that just such a
|
|
Creature as this would be formed by the Square moving, in Space,
|
|
parallel to himself: and I rejoiced to think that so insignificant a
|
|
Creature as I could in some sense be called the Progenitor of so
|
|
illustrious an offspring.
|
|
|
|
But still I could not fully understand the meaning of what my
|
|
Teacher had told me concerning "light" and "shade" and "perspective";
|
|
and I did not hesitate to put my difficulties before him.
|
|
|
|
Were I to give the Sphere's explanation of these matters, succinct
|
|
and clear though it was, it would be tedious to an inhabitant of
|
|
Space, who knows these things already. Suffice it, that by his lucid
|
|
statements, and by changing the position of objects and lights, and by
|
|
allowing me to feel the several objects and even his own sacred
|
|
Person, he atlast made all things clear to me, so that I could now
|
|
readily distinguish between a Circle and a Sphere, a Plane Figure and
|
|
a Solid.
|
|
|
|
This was the Climax, the Paradise, of my strange eventful History.
|
|
Henceforth I have to relate the story of my miserable Fall: -- most
|
|
miserable, yet surely most undeserved! For why should the thirst for
|
|
knowledge be aroused, only to be disappointed and punished? My
|
|
volition shrinks from the painful task of recalling my humiliation;
|
|
yet, like a second Prometheus, I will endure this and worse, if by any
|
|
means I may arouse in the interiors of Plane and Solid Humanity a
|
|
spirit of rebellion against the Conceit which would limit our
|
|
Dimensions to Two or Three or any number short of Infinity. Away then
|
|
with all personal considerations! Let me continue to the end, as I
|
|
began, without further digressions or anticipations, pursuing the
|
|
plain path of dispassionate History. The exact facts, the exact
|
|
words, -- and they are burnt in upon my brain, -- shall be set down
|
|
without alteration of an iota; and let my Readers judge between me and
|
|
Destiny.
|
|
|
|
The Sphere would willingly have continued his lessons by
|
|
indoctrinating me in the conformation of all regular Solids,
|
|
Cylinders, Cones, Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons,
|
|
and Spheres: but I ventured to interrupt him. Not that I was wearied
|
|
of knowledge. On the contrary, I thirsted for yet deeper and fuller
|
|
draughts than he was offering to me.
|
|
|
|
"Pardon me," said I, "O Thou Whom I must no longer address as the
|
|
Perfection of all Beauty; but let me beg thee to vouchsafe thy servant
|
|
a slight of thine interior."
|
|
|
|
Sphere. My what?
|
|
|
|
I. Thine interior: thy stomach, thy intestines.
|
|
|
|
Sphere. Whence this ill-timed impertinent request? And what mean
|
|
you by saying that I am no longer the Perfection of all Beauty?
|
|
|
|
I. My Lord, your own wisdom has taught me to aspire to One even
|
|
more great, more beautiful, and more closely approximate to Perfection
|
|
than yourself. As you yourself, superior to all Flatland forms,
|
|
combine many Circles in One, so doubtless there is One above you who
|
|
combines many Spheres in One Supreme Existence, surpassing even the
|
|
Solids of Spaceland. And even as we, who are now in Space, look down
|
|
on Flatland and see the insides of all things, so of a certainty there
|
|
is yet above us some higher, purer region, whither thou dost surely
|
|
purpose to lead me -- O Thou Whom I shall always call, everywhere and
|
|
in all Dimensions, my Priest, Philosopher, and Friend -- some yet more
|
|
spacious Space, some more dimensionable Dimensionality, from the
|
|
vantage-ground of which we shall look down together upon the revealed
|
|
insides of Solid things, and where thine own intestines, and those of
|
|
thy kindred Spheres, will lie exposed to the view of the poor
|
|
wandering exile from Flatland, to whom so much has already been
|
|
vouchsafed.
|
|
|
|
Sphere. Pooh! Stuff! Enough of this trifling! The time is
|
|
short, and much remains to be done before you are fit to proclaim the
|
|
Gospel of Three Dimensions to your blind benighted countrymen in
|
|
Flatland.
|
|
|
|
I. Nay, gracious Teacher, deny me not what I know it is in thy
|
|
power to reform. Grant me but one glimpse of thine interior, and I am
|
|
satisfied for ever, remaining henceforth thy docile pupil, thy
|
|
unemacipable slave, ready to receive all thy teachings and to feed
|
|
upon the words that fall from thy lips.
|
|
|
|
Sphere. Well, then, to content and silence you, let me say at
|
|
once, I would shew you what you wish if I could; but I cannot. Would
|
|
you have me turn my stomach inside out to oblige you?
|
|
|
|
I. But my Lord has shewn me the intestines of all my countrymen
|
|
in the Land of Two Dimensions by taking me with him into the Land of
|
|
Three. What therefore more easy than now to take his servant on a
|
|
second journey into the blessed region of the Fourth Dimension, where
|
|
I shall look down with him once more upon this land of Three
|
|
Dimensions, and see the inside of every three-dimensioned house, the
|
|
secrets of the solid earth, the treasures of the mines of Spaceland,
|
|
and the intestines of every solid living creature, even the noble and
|
|
adorable Spheres.
|
|
|
|
Sphere. But where is this land of Four Dimensions?
|
|
|
|
I. I know not: but doubtless my Teacher knows.
|
|
|
|
Sphere. Not I. There is no such land. The very idea of it is
|
|
utterly inconceivable.
|
|
|
|
I. Not inconceivable, my Lord, to me, and therefore still less
|
|
inconceivable to my Master. Nay, I despair not that, even here, in
|
|
this region of Three Dimensions, your Lordship's art may make the
|
|
Fourth Dimension visible to me; just as in the Land of Two Dimensions
|
|
my Teacher's skill would fain have opened the eyes of his blind
|
|
servant to the invisible presence of a Third Dimension, though I saw
|
|
it not.
|
|
|
|
Let me recall the past. Was I not taught below that when I saw a
|
|
Line and inferred a Plane, I in reality saw a Third unrecognized
|
|
Dimension, not the same as brightness, called "height"? And does it
|
|
not now follow that, in this region, when I see a Plane and infer a
|
|
Solid, I really see a Fourth unrecognized Dimension, not the same as
|
|
colour, but existent, though infinitesimal and incapable of
|
|
measurement?
|
|
|
|
And besides this, there is the Argument from Analogy of Figures.
|
|
|
|
Sphere. Analogy! Nonsense: what analogy?
|
|
|
|
I. Your Lordship tempts his servant to see whether he remembers
|
|
the revelations imparted to him. Trifle not with me, my Lord; I
|
|
crave, I thirst, for more knowledge. Doubtless we cannot _see_ that
|
|
other higher Spaceland now, becauswe we have no eye in our stomachs.
|
|
But, just as there _was_ the realm of Flatland, though that poor puny
|
|
Lineland Monarch could neither turn to left nor right to discern it,
|
|
and just as there _was_ close at hand, and touching my frame, the land
|
|
of Three Dimensions, though I, blind senseless wretch, had no power to
|
|
touch it, no eye in my interior to discern it, so of a surety there is
|
|
a Fourth Dimension, which my Lord perceivesa with the inner eye of
|
|
thought. And that it must exist my Lord himself has taught me. Or
|
|
can he have forgotten what he himself imparted to his servant?
|
|
|
|
In One Dimension, did not a moving Point produce a Line with _two_
|
|
terinal points?
|
|
|
|
In Two Dimensions, did not a moving Line produce a Square with
|
|
_four_ terminal points?
|
|
|
|
In Three Dimensions, did not a moving Square produce -- did not
|
|
this eye of mine behold it -- that blessed Being, a Cube, with _eight_
|
|
terminal points?
|
|
|
|
And in Four Dimensions shall not a moving Cube -- alas, for
|
|
Analogy, and alas for the Progress of Truth, if it be not so -- shall
|
|
not, I say, the motion of a divine Cube result in a still more divine
|
|
Organization with _sixteen_ terminal points?
|
|
|
|
Behold the infallible confirmation of the Series, 2, 4, 8, 16: is
|
|
not this a Geometrical Progression? Is not this -- if I might quote
|
|
my Lord's own words -- "strictly according to Analogy"?
|
|
|
|
Again, was I not taught by my Lord that as in a Line there are
|
|
_two_ bounding Points, and in a Square there are _four_ bounding
|
|
LInes, so in a Cube there must be _six_ bounding Squares? Behold once
|
|
more the confirming Series, 2, 4, 6: is not this an Arithemtical
|
|
Progression? And consequently does it not of necessity follow that
|
|
the more divine offspring of the divine Cube in the Land of Four
|
|
Dimensions, must have 8 bounding Cubes: and is not this also, as my
|
|
Lord has taught me to believe, "strictly according to Analogy"?
|
|
|
|
O, my Lord, my Lord, behold, I cast myself in faith upon
|
|
conjecture, not knowing the facts; and I appeal to your Lordship to
|
|
confirm or deny my logical anticipations. If I am wrong, I yield, and
|
|
will no longer demand a Fourth Dimension; but, if I am right, my Lord
|
|
will listen to reason.
|
|
|
|
I ask therefore, is it, or is it not, the fact, that ere now your
|
|
countrymen also have witnessed the descent of Beings of a higher order
|
|
than their own, entering closed rooms, even as your Lordship entered
|
|
mine, without the opening of doors or windows, and appearing and
|
|
vanishing at will? On the reply to this question I am reaedy to stake
|
|
everything. Deny it, and I am henceforth silent. Only vouchsafe an
|
|
answer.
|
|
|
|
Sphere (_after a pause_). It is reported so. But men are divided
|
|
in opinion as to the facts. And even granting the facts, they explain
|
|
them in different ways. And in any case, however great may be the
|
|
number of different explanations, no one has adopted or suggested the
|
|
theory of a Fourth Dimension. Therefore, pray have done with this
|
|
trifling, and let us return to business.
|
|
|
|
I. I was certain of it. I was certain that my anticipations
|
|
would be fulfilled. And now have patience with me and answer me yet
|
|
one more question, best of Teachers! Those who have thus appeared --
|
|
no one knows whence -- and have returned -- no one knows whither --
|
|
have they also contracted their sections and vanished somehow into
|
|
that more Spacious Space, whither I now entreat you to conduct me?
|
|
|
|
Sphere (_moodily_). They have vanished, certainly -- if they ever
|
|
appeared. But most people say that these visions arose from the
|
|
thought -- you will not understand me -- from the brain; from the
|
|
perturbed angularity of the Seer.
|
|
|
|
I. Say they so? Oh, believe them not. Or if it indeed be so,
|
|
that this other SPace is really Thoughtland, then take me to that
|
|
blessed Region where I in Thought shall see the insides of all solid
|
|
things. There, before my ravished eye, a Cube moving in some
|
|
altogether new direction, but strictly according to Analogy, so as to
|
|
make every particle of his interior pass through a new kind of Space,
|
|
with a wake of its own -- shall create a still more perfect perfection
|
|
than himself, with sixteen terminal Extra-solid angles, and Eight
|
|
solid Cubes for his Perimeter. And once there, shall we stay our
|
|
upward course? In that blessed region of Four Dimensions, shall we
|
|
linger at the threshold of the Fifth, and not enter therein? Ah, no!
|
|
Let us rather resolve that our ambition shall soar with our corporal
|
|
ascent. Then, yielding to our intellectual onset, the gates of the
|
|
Six Dimension shall fly open; after that a Seventh, and then an Eighth
|
|
--
|
|
|
|
How long I should have continued I know not. In vain did the
|
|
Sphere, in his voice of thunder, reiterate his command of silence, and
|
|
threaten me with the direst penalties if I persisted. Nothing could
|
|
stem the flood of my ecstatic aspirations. Perhaps I was to blame;
|
|
but indeed I was intoxicated with the recent draughts of Truth to
|
|
which he himself had introduced me. However, the end was not long in
|
|
coming. My words were cut short by a crash outside, and a
|
|
simultaneous crash inside me, which impelled me through space with a
|
|
velocity that precluded speech. Down! down! down! I was rapidly
|
|
descending; and I knew that return to Flatland was my doom. One
|
|
glimpse, one last and never-to-be-forgotten glimpse I had of that dull
|
|
level wilderness -- which was now to become my Universe again --
|
|
spread out before my eye. Then a darkness. Then a final, all-
|
|
consummating thunder-peal; and, when I came to myself, I was once more
|
|
a common creeping Square, in my Study at home, listening to the Peace-
|
|
Cry of my approaching Wife.
|
|
|
|
* * *
|
|
|
|
SECTION 20. -- How the Sphere encouraged me in a Vision.
|
|
|
|
Although I had less than a minute for reflection, I felt, by a
|
|
kind of instinct, that I must conceal my experiences from my Wife.
|
|
Not that I apprehended, at the moment, any danger from her divulging
|
|
my secret, but I knew that to any Woman in Flatland the narrative of
|
|
my adventures must needs be unintelligible. So I endeavoured to
|
|
reassure her by some story, invented for the occasion, gthat I had
|
|
accidentally fallen through the trap-door of the cellar, and had there
|
|
lain stunned.
|
|
|
|
The Southward attraction in our country is so slight that even to
|
|
a Woman my tale necessarily appeared extraordinary and well-nigh
|
|
incredible; but my Wife, whose good sense far exceeds that of the
|
|
average of her Sex, and who perceived that I was unusually excited,
|
|
did not argue with me on the subject, but insisted that I was will and
|
|
required repose. I was glad of an excuse for retiring to my chamber
|
|
to think quietly over what had happened. When I was at last by
|
|
myself, a drowsy sensation fell on me; but before my eyes closed I
|
|
endeavoured to reproduce the Third Dimension, and especially the
|
|
process by which a Cube is constructed through the motion of a Square.
|
|
It was not so clear as I could have wished; but I remembered that it
|
|
must be "Upward, and yet not Northward," and I determined steadfastly
|
|
to retain these words as the clue which, if firmly grasped, could not
|
|
fail to guide me to the solution. So mechanically repeating, like a
|
|
charm, the words, "Upwaqrd, yet not Northward," I fell into a sound
|
|
refreshing sleep.
|
|
|
|
During my slumber I had a dream. I thought I was once more by the
|
|
side of the Sphere, whose lustrous hue betokened that he had exchanged
|
|
his wrath against me for perfectly placability. We were moving
|
|
together towards a bright but infinitesimally small Ppoint, to which
|
|
my Master directed my attention. As we approached, methought there
|
|
issued from it a slight humming noise as from one of your Spaceland
|
|
bluebottles, only less resonant by far, so slight indeed that even in
|
|
the perfect stillness of the Vacuum through which we soard, the sound
|
|
reached not our ears till we checked our flight at a distant from it
|
|
of something under twenty human diagonals.
|
|
|
|
"Look yonder," said my Guide, "in Flatland thou hast lived; of
|
|
Lineland thou hast received a vision; thou hast soarred with me to the
|
|
heights of Spaceland; now,, in order to complete the range of thy
|
|
experience, I conduct thee downward to the lowest depth of existence,
|
|
even to the realm of Pointland, the Abyss of No dimensions.
|
|
|
|
"Behold yon miserable creature. That Point is a Being like
|
|
ourselves, but confined to the non-dimensional Gulf. He is himself
|
|
his own World, his own Universe; of any other than himself he can form
|
|
no conception; he knows not Length, nor Breadth, nor Height, for he
|
|
has had no experience of them; he has no cognizance even of the number
|
|
Two; nor has he a thought of Plurality; for he is himself his One and
|
|
All, being really Nothing. Yet mark his perfect self-contentment, and
|
|
hence learn his lesson, that to be self-contented is to be vile and
|
|
ignorant, and that to aspire is better than to be blindly and
|
|
impotently happy. Now listen."
|
|
|
|
He ceased; and there arose from the little buzzing creature a
|
|
tiny, low, monotonous, but distinct tinkling, as from one of your
|
|
Spaceland phonographs, from which I caught these words, "Infinite
|
|
beatitude of existence! It is; and there is nothing else beside It."
|
|
|
|
"What," said I, "does the puny creature mean by 'it'?" "He means
|
|
himself," said the Sphere: "have you not noticed before now, that
|
|
babies and babyish peoplle who cannot distinguish themselves from the
|
|
world, speak of themselves in the Third Person? But hush!"
|
|
|
|
"It fills all Space," continued the little soliloquizing Creature,
|
|
"and what It fills, It is. What It thinks, that It utters; and what
|
|
It utters, that It hears; and It itself is Thinker, Utterer, Hearer,
|
|
THought, Word, Audition; it is the One, and yet the All in All. Ah,
|
|
the happiness, ah, the happiness of Being!"
|
|
|
|
"Can you not startle the little thing out of its complacency?"
|
|
said I. "Tell it what it really is, as you told me; reveal to it the
|
|
narrow limitations of Pointland, and lead it up to something higher."
|
|
"That is no easy task," said my Master; "try you."
|
|
|
|
Hereon, raising by voice to the uttermost, I addressed the Point
|
|
as follows:
|
|
|
|
"Silence, silence, contemptible Creature. You call yourself the
|
|
All in All, but you are the Nothing: your so-called Universe is a
|
|
mere speck in a Line, and a Line is a mere shadow as compared with --"
|
|
"Hush, hush, you have said enough," interrupted the Sphere, "now
|
|
listen, and mark the effect of your harangue on the King of
|
|
Pointland."
|
|
|
|
The lustre of the Monarch, who beamed more brightly than ever upon
|
|
hearing my words, shewed clearly that he retained his complacency; and
|
|
I had hardly ceased when he took up his strain again. "Ah, the joy,
|
|
ah, the joy of Thought1 What can It not achieve by thinking! Its own
|
|
Thought coming to Itself, suggestive of ts disparagement, thereby to
|
|
enhance Its happiness! Sweet rebellion stirred up to result in
|
|
triumph! Ah, the divine creative power of the All in One! Ah, the
|
|
joy, the joy of Being!"
|
|
|
|
"You see," said my Teacher, "how little your words have done. So
|
|
far as the Monarch understand them at all, he accepts them as his own
|
|
-- for he cannot conceive of any other except himself -- and plumes
|
|
himself upon the variety of 'Its Thought' as an instance of creative
|
|
Power. Let us leave this God of Pointland to the ignorant fruition of
|
|
his omnipresence and omniscience: nothing that you or I can do can
|
|
rescue him from his self-satisfaction."
|
|
|
|
After this, as we floated gently back to Flatland, I could hear
|
|
the mild voice of my Companion pointing the moral of my vision, and
|
|
stimulating me to aspire, and to teach others to aspire. He had been
|
|
angered at first -- he confessed -- by my ambition to soar to
|
|
Dimensions above the Third; but, since then, he had received fresh
|
|
insight, and he was not too proud to acknowledge his error to a Pupil.
|
|
Then he proceeded to initiate me into mysteries yethigher than those I
|
|
had witnessed, shewing me how to construct Extra-Solids by the motion
|
|
of Solids, and Double Extra-Solids by the motion of Extra-Solids, and
|
|
all "strictly according to Analogy," all by methods so simple, so
|
|
easy, as to be patent even to the Female Sex.
|
|
|
|
* * *
|
|
|
|
SECTION 21. -- How I tried to teach the Theory of Three Dimensions
|
|
|
|
to my Grandson, and with what success
|
|
|
|
I awoke rejoicing, and began to reflect on the glorious career
|
|
before me. I would go forth, methought, at once, and evangelize the
|
|
whole of Flatland. Even to Women and Soldiers should the Gospel of
|
|
Three Dimensions be proclaimed. I would begin with my Wife.
|
|
|
|
Just as I had decided on the plan of my operations, I heard the
|
|
sound of many voices in the street commanding silence. Then followed
|
|
a louder voice. It was a herald's proclamation. Listening
|
|
attentively, I recognized the words of the Resolution of the Council,
|
|
enjoining the arrest, imprisonment, or execution of any one who should
|
|
pervert the minds of people by delusions, and by professing to have
|
|
received revelations from another World.
|
|
|
|
I reflected. This danger was not to be trifled with. It would be
|
|
better to avoid it by omitting all mention of my Revelation, and by
|
|
proceeding on the path of Demonstration -- which after all, seemed so
|
|
simple and so conclusive that nothing would be lost by discarding the
|
|
former means. "Upward, not Northward" -- was the clue to the whole
|
|
proof. It had seemed to me fairly clear before I fell asleep; and
|
|
when I first awoke, fresh from my dream, it had appeared as patent as
|
|
Arithmetic; but somehow it did not seem to me quite so obvious now.
|
|
Though my Wife entered the room opportunely at just that moment, I
|
|
decided, after we had exchanged a few words of commonplace
|
|
conversation, not to begin with her.
|
|
|
|
My Pentagonal Sons were men of character and standing, and
|
|
physicians of no mean reputation, but not great in mathematics, and,
|
|
in that respect, unfit for my purpose. But it occurred to me that a
|
|
young and docile Hexagon, with a mathematical turn, would be a most
|
|
suitable pupil. Why therefore not make my first experiment with my
|
|
little precocious Grandson, whose casual remarks on the meaning of
|
|
three-to-the-third had met with the approval of the Sphere?
|
|
Discussing the matter with him, a mere boy, I should be in perfect
|
|
safety; for he would know nothing of the Proclamation of the Council;
|
|
whereas I could not feel sure that my Sons -- so greatly did their
|
|
patriotism and reverence for the Circles predominate over mere blind
|
|
affection -- might not feel compelled to hand me over to the Prefect,
|
|
if they found me seriously maintaining the seditious heresy of the
|
|
Third Dimension.
|
|
|
|
But the first thing to be done was to satisfy in some way the
|
|
curiosity of my Wife, who naturally wished to know something of the
|
|
reasons for which the Circle had desired that mysterious interview,
|
|
and of the means by which he had entered the house. Without entering
|
|
into the details of the elaborate account I gave her, -- an account, I
|
|
fear, not quite so consistent with truth as my Readers in Spaceland
|
|
might desire, -- I must be content with saying that I succeeded at
|
|
last in persuading her to return quitely to her household duties
|
|
without eliciting from me any reference to the World of Three
|
|
Dimensions. This done, I immediately sent for my Grandson; for, to
|
|
confess the truth, I felt that all that I had seen and heard was in
|
|
some strange way slipping away from me, like the image of a half-
|
|
grasped, tantalizing dream, and I longed to essay my skill in making a
|
|
first disciple.
|
|
|
|
When my Grandson entered the room I carefully secured the door.
|
|
Then, sitting down by his side and taking our mathematical tablets, --
|
|
or, as you would call them, Lines -- I told him we would resume the
|
|
lesson of yesterday. I taught him once more how a Point by motion in
|
|
One Dimension produces a Line, and how a straight Line in Two
|
|
Dimensions produces a Square. After this, forcing a laugh, I said,
|
|
"And now, you scamp, you wanted to make believe that a Square may in
|
|
the same way by motion 'Upward, not Northward' produce another figure,
|
|
a sort of extra square in Three Dimensions. Say that againn, you
|
|
young rascal."
|
|
|
|
At this moment we heard once more the herald's "O yes! O yes!"
|
|
outside in the street proclaiming the REsolution of the Council.
|
|
Young though he was, my Grandson -- who was unusually intelligent for
|
|
his age, and bred up in perfect reverence for the authority of the
|
|
Circles -- took in the situation with an acuteness for which I was
|
|
quite unprepared. He remained silent till the last words of the
|
|
Proclamation had died away, and then, bursting into tears, "Dear
|
|
Grandpapa," he said, "that was only my fun, and of course I meant
|
|
nothing at all by it; and we did not know anything then about the new
|
|
Law; and I don't think I said anything about the Third Dimension; and
|
|
I am sure I did not say one word about 'Upward, not Northward,' for
|
|
that would be such nonsense, you know. How could a thing move Upward,
|
|
and not Northward? Upward and not Northward! Even if I were a baby,
|
|
I could not be so absurd as that. How silly it is! Ha! ha! ha!"
|
|
|
|
"Not at all silly," said I, losing my temper; "here for example, I
|
|
take this Square," and, at the word, I grasped a moveable Square,
|
|
which was lying at hand -- "and I move it, you see, not Northward but
|
|
-- yes, I move it Upward -- that is to say, Northward but I move it
|
|
somewhere -- not exactly like this, but somehow --" Here I brought my
|
|
sentence to an inane conclusion, shaking the Square about in a
|
|
purposeless manner, much to the amusement of my Grandson, who burst
|
|
out laughing louder than ever, and declared that I was not teaching
|
|
him, but joking with him; and so saying he unlocked the door and ran
|
|
out of the room. Thus ended my first attempt to convert a pupil to
|
|
the Gospel of Three Dimensions.
|
|
|
|
* * *
|
|
|
|
SECTION 22. -- How I then tried to diffuse the Theory of Three
|
|
|
|
Dimensions by other means, and of the result
|
|
|
|
My failure with my Grandson did not encourage me to communicate my
|
|
secret to others of my household; yet neither was I led by it to
|
|
despair of success. Only I saw that I must not wholly rely on the
|
|
catch-phrase, "Upward, not Northward," but must rather endeavour to
|
|
seek a demonstration by setting before the public a clear view of the
|
|
whole subject; and for this purpose it seemed necessary to resort to
|
|
writing.
|
|
|
|
So I devoted several months in privacy to the composition of a
|
|
treatise on the mysteries of Three Dimensions. Only, with the view of
|
|
evading the Law, if possible, I spoke not of a physical Dimension, but
|
|
of a Thoughtland whence, in theory, a Figure could look down upon
|
|
Flatland and see simultaneously the insides of all things, and where
|
|
it was possible that there might be supposed to exist a Figure
|
|
environed, as it were, with six Squares, and containing eight terminal
|
|
Points. But in writing this book I found myself sadly hampered by the
|
|
impossibility of drawing such diagrams as were necessary for my
|
|
purpose: for of course, in our country of Flatland, there are no
|
|
tablets but Lines, and no diagrams but Lines, all in one straight Line
|
|
and only distinguishable by difference of size and brightness; so
|
|
that, when I had finished my treatise (which I entitled, "Through
|
|
Flatland to Thoughtland") I could not feel certain that many would
|
|
understand my meaning.
|
|
|
|
Meanwhile my wife was under a cloud. All pleasures palled upon
|
|
me; all sights tantalized and tempted me to outspoke treason, because
|
|
I could not compare what I saw in Two Dimensions with what it really
|
|
was if seen in Three, and could hardly refrain from making my
|
|
comparisons aloud. I neglected my clients and my own business to give
|
|
myself to the contemplation of the mysteries which I had once beheld,
|
|
yet which I could impart to no one, and found daily more difficult to
|
|
reproduce even before my own mental vision.
|
|
|
|
One day, about eleven months after my return from Spaceland, I
|
|
tried to see a Cube with my eye closed, but failed; and though I
|
|
succeeded afterwards, I was not then quite certain (nor have I been
|
|
ever aftewards) that I had exactly realized the original. This made
|
|
me more melancholy than before, and determined me to take some step;
|
|
yet what, I knew not. I felt that I would have been willing to
|
|
sacrifice my life for the Cause, if thereby I could have produced
|
|
conviction. But if I could not convince my Grandson, how could I
|
|
convince the highest and most developed Circles in the land?
|
|
|
|
And yet at times my spirit was too strong for me, and I gave vent
|
|
to dangerous utterances. Already I was considered heterodox if not
|
|
treasonable, and I was keenly alive to the danger of my position;
|
|
nevertheless I could not at times refrain from bursting out into
|
|
suspicious or half-seditious utterances, even among the highest
|
|
Polygonal or Circular society. When, for example, the question arose
|
|
about the treatment of those lunatics who said that they had received
|
|
the power of seeing the insides of things, I would quote the saying of
|
|
an ancient Circle, who declared that prophets and inspired people are
|
|
always considered by the majority to be mad; and I could not help
|
|
occasionally dropping such expressions as "the eye that discerns the
|
|
interiors of things," and "the all-seeing land"; once or twice I even
|
|
let fall the forbidden terms "the Third and Fourth Dimensions." At
|
|
last, to complete a series of minor indiscretions, at a meeting of our
|
|
Local Speculative Society held at the palace of the Prefect himself, -
|
|
- some extremely silly person having read an elaborate paper
|
|
exhibiting the precise reasons why Providence has limited the number
|
|
of Dimensions to Two, and why the attribute of omnividence is assigned
|
|
to the Supreme alone -- I so far forgot myself as to give an exact
|
|
account of the whole of my voyage with the Sphere into Space, and to
|
|
the Assembly Hall in our Metropolis, and then to Space again, and of
|
|
my return home, and of everything that I had seen and heard in fact or
|
|
vision. At first, indeed, I pretended that I was describing the
|
|
imaginary experiences of a ficitious person; but my enthusiasm soon
|
|
forced me to throw off all disguise, and finally, in a fervent
|
|
peroration, I exhorted all my hearers to divest themselves of
|
|
prejudice and to become believers in the Third Dimesnsion.
|
|
|
|
Need I say that I was at onc arrested and taken before the
|
|
Council?
|
|
|
|
Next morning, standing in the very place where but a very few
|
|
months ago the Sphere had stood in my company, I was allowed to begin
|
|
and to continue my narration unquestioned and uninterrupted. But from
|
|
the first I foresaw my fate; for the President, noting that a guard of
|
|
the better sort of Policemen was in attendance, of angularity little,
|
|
if at all, under 55 degrees, ordered them to be relieved before I
|
|
began my defence, by an inferior class of 2 or 3 degrees. I knew only
|
|
too well what that meant. I was to be executed or imprisoned, and my
|
|
story was to be kept secret from the world by the simultaneous
|
|
destruction of the officials who had heard it; and, this beig the
|
|
case, the Presdient desired to substitute the cheaper for the more
|
|
expensive victims.
|
|
|
|
After I had concluded my defence, the President, perhaps
|
|
perceiving that some of the junior Circles had been moved by evident
|
|
earnestness, asked me two questions: --
|
|
|
|
1. Whether I could indicate the direction which I meant when I
|
|
used the words "Upward, not Northward"?
|
|
|
|
2. Whether I could by any diagrams or descriptions (other than
|
|
the enumeration of imaginary sides and angles) indicate the Figure I
|
|
was pleased to call a Cube?
|
|
|
|
I declared that I could say nothing more, and that I must commit
|
|
myself to the Truth, whose cause would surely prevail in the end.
|
|
|
|
The President replied that he quite concurred in my sentiment, and
|
|
that I could not do better. I must be sentenced to perpetual
|
|
imprisonment; but if the Truth intended that I should emerge from
|
|
prison and evangelize the world, the Truth might be trusted to bring
|
|
that result to pass. Meanwhile I should be subjected to no discomfort
|
|
that was not necessary to preclude escape, and, unless I forfeited the
|
|
privilege by misconduct, I should be occasionally permitted to see my
|
|
brother who had preceded me to my prison.
|
|
|
|
Seven years have elapsed and I am still a prisoner, and -- if I
|
|
except the occasional visits of my brother -- debarred from all
|
|
companionship save that of my jailers. My brother is one of the best
|
|
of Squares, just sensible, cheerful, and not without fraternal
|
|
affection; yet I confess that my weekly interviews, at least in one
|
|
respect, cause me the bitterest pain. He was present when the Sphere
|
|
manifested himself in the Council Chamber; he saw the Sphere's
|
|
changing sections; he heard the explanation of the phenomena then give
|
|
to the Circles. Since that time, scarcely a week has passed during
|
|
seven whole years, without his hearing from me a repitition of the
|
|
part I played in that manifestation, together with ample descriptions
|
|
of all the phenomena in Spaceland, and the arguments for the existence
|
|
of Solid things derivable from Analogy. Yet -- I take shame to be
|
|
forced to confess it -- my brother has not yet grasped the nature of
|
|
Three Dimensions, and frankly avows his disbelief in the existence of
|
|
a Sphere.
|
|
|
|
Hence I am absolutely destitute of converts, and, for aught that I
|
|
can see, the millennial Revelation has been made to me for nothing.
|
|
Prometheus up in Spaceland was bound for bringing down fire for
|
|
mortals, but I -- poor Flatland Prometheus -- lie here in prison for
|
|
bringing down nothing to my countrymen. Yet I existin the hope that
|
|
these memoirs, in some manner, I know not how, may find their way to
|
|
the minds of humanity in Some Dimension, and may stir up a race of
|
|
rebels who shall refuse to be confined to limited Dimensionality.
|
|
|
|
That is the hope of my brighter moments. Alas, it is not always
|
|
so. Heavily weights on me at times the burdensome reflection that I
|
|
cannot honestly say I am confident as to the exact shape of the once-
|
|
seen, oft-regretted Cube; and in my nightly visions the mysterious
|
|
precept, "Upward, not Northward," haunts me like a soul-devouring
|
|
Sphinx. It is part of the martyrdom which I endure for the cause of
|
|
Truth that there are seasons of mental weakness, when Cubes and
|
|
Spheres flit away into the background of scarce-possible existences;
|
|
when the Land of Three Dimensions seems almost as visionary as the
|
|
Land of One or None; nay, when even this hard wall that bars me from
|
|
my freedom, these very tablets on which I am writing, and all the
|
|
substantial realities of Flatland itself, appear no better than the
|
|
offspring of a diseased imagination, or the baseless fabric of a
|
|
dream.
|
|
|
|
THE END
|
|
|
|
of
|
|
|
|
FLATLAND
|
|
|
|
* * *
|
|
|
|
.
|