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1The Project Gutenberg EBook of Flatland: A Romance of Many Dimensions
2(Illustrated), by Edwin A. Abbot
3
4This eBook is for the use of anyone anywhere at no cost and with
5almost no restrictions whatsoever. You may copy it, give it away or
6re-use it under the terms of the Project Gutenberg License included
7with this eBook or online at www.gutenberg.net
8
9
10Title: Flatland: A Romance of Many Dimensions (Illustrated)
11
12Author: Edwin A. Abbot
13
14Release Date: March 10, 2008 [EBook #201]
15
16Language: English
17
18Character set encoding: ASCII
19
20*** START OF THIS PROJECT GUTENBERG EBOOK FLATLAND ***
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33Flatland: A Romance of Many Dimensions
34
35Edwin A. Abbott (1838-1926. English scholar, theologian, and writer.)
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37
38
39 -----------------------------------------------------------------
40 | "O day and night, but this is wondrous strange" |
41 | ______ |
42 | / / /| ------ / /| /| / /-. |
43 | /---- / /__| / / /__| / | / / / |
44 | / /___ / | / /___ / | / |/ /__.-' |
45 | |
46 | No Dimensions One Dimension |
47 | . A ROMANCE OF MANY DIMENSIONS ----- |
48 | POINTLAND LINELAND |
49 | |
50 | Two Dimensions Three Dimensions |
51 | ___ __ |
52 | | | /__/| |
53 | |___| |__|/ |
54 | FLATLAND SPACELAND |
55 | "Fie, fie, how franticly I square my talk!" |
56 -----------------------------------------------------------------
57
58With Illustrations by the Author, A SQUARE (Edwin A. Abbott)
59
60
61
62
63
64
65 To
66 The Inhabitants of SPACE IN GENERAL
67 And H. C. IN PARTICULAR
68 This Work is Dedicated
69 By a Humble Native of Flatland
70 In the Hope that
71 Even as he was Initiated into the Mysteries
72 Of THREE Dimensions
73 Having been previously conversant
74 With ONLY TWO
75 So the Citizens of that Celestial Region
76 May aspire yet higher and higher
77 To the Secrets of FOUR FIVE OR EVEN SIX Dimensions
78 Thereby contributing
79 To the Enlargement of THE IMAGINATION
80 And the possible Development
81 Of that most rare and excellent Gift of MODESTY
82 Among the Superior Races
83 Of SOLID HUMANITY
84
85
86
87
88
89
90Preface to the Second and Revised Edition, 1884.
91
92By the Editor
93
94
95
96If my poor Flatland friend retained the vigour of mind which he enjoyed
97when he began to compose these Memoirs, I should not now need to
98represent him in this preface, in which he desires, firstly, to return
99his thanks to his readers and critics in Spaceland, whose appreciation
100has, with unexpected celerity, required a second edition of his work;
101secondly, to apologize for certain errors and misprints (for which,
102however, he is not entirely responsible); and, thirdly, to explain one
103or two misconceptions. But he is not the Square he once was. Years of
104imprisonment, and the still heavier burden of general incredulity and
105mockery, have combined with the natural decay of old age to erase from
106his mind many of the thoughts and notions, and much also of the
107terminology, which he acquired during his short stay in Spaceland. He
108has, therefore, requested me to reply in his behalf to two special
109objections, one of an intellectual, the other of a moral nature.
110
111The first objection is, that a Flatlander, seeing a Line, sees
112something that must be THICK to the eye as well as LONG to the eye
113(otherwise it would not be visible, if it had not some thickness); and
114consequently he ought (it is argued) to acknowledge that his countrymen
115are not only long and broad, but also (though doubtless in a very
116slight degree) THICK or HIGH. This objection is plausible, and, to
117Spacelanders, almost irresistible, so that, I confess, when I first
118heard it, I knew not what to reply. But my poor old friend's answer
119appears to me completely to meet it.
120
121"I admit," said he--when I mentioned to him this objection--"I admit
122the truth of your critic's facts, but I deny his conclusions. It is
123true that we have really in Flatland a Third unrecognized Dimension
124called 'height', just as it is also true that you have really in
125Spaceland a Fourth unrecognized Dimension, called by no name at
126present, but which I will call 'extra-height'. But we can no more take
127cognizance of our 'height' than you can of your 'extra-height'. Even
128I--who have been in Spaceland, and have had the privilege of
129understanding for twenty-four hours the meaning of 'height'--even I
130cannot now comprehend it, nor realize it by the sense of sight or by
131any process of reason; I can but apprehend it by faith.
132
133"The reason is obvious. Dimension implies direction, implies
134measurement, implies the more and the less. Now, all our lines are
135EQUALLY and INFINITESIMALLY thick (or high, whichever you like);
136consequently, there is nothing in them to lead our minds to the
137conception of that Dimension. No 'delicate micrometer'--as has been
138suggested by one too hasty Spaceland critic--would in the least avail
139us; for we should not know WHAT TO MEASURE, NOR IN WHAT DIRECTION.
140When we see a Line, we see something that is long and BRIGHT;
141BRIGHTNESS, as well as length, is necessary to the existence of a Line;
142if the brightness vanishes, the Line is extinguished. Hence, all my
143Flatland friends--when I talk to them about the unrecognized Dimension
144which is somehow visible in a Line--say, 'Ah, you mean BRIGHTNESS':
145and when I reply, 'No, I mean a real Dimension', they at once retort,
146'Then measure it, or tell us in what direction it extends'; and this
147silences me, for I can do neither. Only yesterday, when the Chief
148Circle (in other words our High Priest) came to inspect the State
149Prison and paid me his seventh annual visit, and when for the seventh
150time he put me the question, 'Was I any better?' I tried to prove to
151him that he was 'high', as well as long and broad, although he did not
152know it. But what was his reply? 'You say I am "high"; measure my
153"high-ness" and I will believe you.' What could I do? How could I
154meet his challenge? I was crushed; and he left the room triumphant.
155
156"Does this still seem strange to you? Then put yourself in a similar
157position. Suppose a person of the Fourth Dimension, condescending to
158visit you, were to say, 'Whenever you open your eyes, you see a Plane
159(which is of Two Dimensions) and you INFER a Solid (which is of Three);
160but in reality you also see (though you do not recognize) a Fourth
161Dimension, which is not colour nor brightness nor anything of the kind,
162but a true Dimension, although I cannot point out to you its direction,
163nor can you possibly measure it.' What would you say to such a
164visitor? Would not you have him locked up? Well, that is my fate: and
165it is as natural for us Flatlanders to lock up a Square for preaching
166the Third Dimension, as it is for you Spacelanders to lock up a Cube
167for preaching the Fourth. Alas, how strong a family likeness runs
168through blind and persecuting humanity in all Dimensions! Points,
169Lines, Squares, Cubes, Extra-Cubes--we are all liable to the same
170errors, all alike the Slaves of our respective Dimensional prejudices,
171as one of your Spaceland poets has said--
172
173 'One touch of Nature makes all worlds akin'."
174
175[Note: The Author desires me to add, that the misconception of some of
176his critics on this matter has induced him to insert in his dialogue
177with the Sphere, certain remarks which have a bearing on the point in
178question, and which he had previously omitted as being tedious and
179unnecessary.]
180
181On this point the defence of the Square seems to me to be impregnable.
182I wish I could say that his answer to the second (or moral) objection
183was equally clear and cogent. It has been objected that he is a
184woman-hater; and as this objection has been vehemently urged by those
185whom Nature's decree has constituted the somewhat larger half of the
186Spaceland race, I should like to remove it, so far as I can honestly do
187so. But the Square is so unaccustomed to the use of the moral
188terminology of Spaceland that I should be doing him an injustice if I
189were literally to transcribe his defence against this charge. Acting,
190therefore, as his interpreter and summarizer, I gather that in the
191course of an imprisonment of seven years he has himself modified his
192own personal views, both as regards Women and as regards the Isosceles
193or Lower Classes. Personally, he now inclines to the opinion of the
194Sphere that the Straight Lines are in many important respects superior
195to the Circles. But, writing as a Historian, he has identified himself
196(perhaps too closely) with the views generally adopted by Flatland, and
197(as he has been informed) even by Spaceland, Historians; in whose pages
198(until very recent times) the destinies of Women and of the masses of
199mankind have seldom been deemed worthy of mention and never of careful
200consideration.
201
202In a still more obscure passage he now desires to disavow the Circular
203or aristocratic tendencies with which some critics have naturally
204credited him. While doing justice to the intellectual power with which
205a few Circles have for many generations maintained their supremacy over
206immense multitudes of their countrymen, he believes that the facts of
207Flatland, speaking for themselves without comment on his part, declare
208that Revolutions cannot always be suppressed by slaughter, and that
209Nature, in sentencing the Circles to infecundity, has condemned them to
210ultimate failure--"and herein," he says, "I see a fulfilment of the
211great Law of all worlds, that while the wisdom of Man thinks it is
212working one thing, the wisdom of Nature constrains it to work another,
213and quite a different and far better thing." For the rest, he begs his
214readers not to suppose that every minute detail in the daily life of
215Flatland must needs correspond to some other detail in Spaceland; and
216yet he hopes that, taken as a whole, his work may prove suggestive as
217well as amusing, to those Spacelanders of moderate and modest minds
218who--speaking of that which is of the highest importance, but lies
219beyond experience--decline to say on the one hand, "This can never be,"
220and on the other hand, "It must needs be precisely thus, and we know
221all about it."
222
223
224
225
226
227
228CONTENTS:
229
230
231
232PART I: THIS WORLD
233
234Section
235
236 1. Of the Nature of Flatland
237 2. Of the Climate and Houses in Flatland
238 3. Concerning the Inhabitants of Flatland
239 4. Concerning the Women
240 5. Of our Methods of Recognizing one another
241 6. Of Recognition by Sight
242 7. Concerning Irregular Figures
243 8. Of the Ancient Practice of Painting
244 9. Of the Universal Colour Bill
245 10. Of the Suppression of the Chromatic Sedition
246 11. Concerning our Priests
247 12. Of the Doctrine of our Priests
248
249PART II: OTHER WORLDS
250
251 13. How I had a Vision of Lineland
252 14. How I vainly tried to explain the nature of Flatland
253 15. Concerning a Stranger from Spaceland
254 16. How the Stranger vainly endeavoured to reveal to me
255 in words the mysteries of Spaceland
256 17. How the Sphere, having in vain tried words,
257 resorted to deeds
258 18. How I came to Spaceland, and what I saw there
259 19. How, though the Sphere shewed me other mysteries
260 of Spaceland, I still desired more; and what came of it
261 20. How the Sphere encouraged me in a Vision
262 21. How I tried to teach the Theory of Three Dimensions
263 to my Grandson, and with what success
264 22. How I then tried to diffuse the Theory
265 of Three Dimensions by other means, and of the result
266
267
268
269
270
271
272PART I: THIS WORLD
273
274"Be patient, for the world is broad and wide."
275
276
277
278
279
280
281Section 1. Of the Nature of Flatland
282
283
284
285I call our world Flatland, not because we call it so, but to make its
286nature clearer to you, my happy readers, who are privileged to live in
287Space.
288
289Imagine a vast sheet of paper on which straight Lines, Triangles,
290Squares, Pentagons, Hexagons, and other figures, instead of remaining
291fixed in their places, move freely about, on or in the surface, but
292without the power of rising above or sinking below it, very much like
293shadows--only hard and with luminous edges--and you will then have a
294pretty correct notion of my country and countrymen. Alas, a few years
295ago, I should have said "my universe": but now my mind has been opened
296to higher views of things.
297
298In such a country, you will perceive at once that it is impossible that
299there should be anything of what you call a "solid" kind; but I dare
300say you will suppose that we could at least distinguish by sight the
301Triangles, Squares, and other figures, moving about as I have described
302them. On the contrary, we could see nothing of the kind, not at least
303so as to distinguish one figure from another. Nothing was visible, nor
304could be visible, to us, except Straight Lines; and the necessity of
305this I will speedily demonstrate.
306
307Place a penny on the middle of one of your tables in Space; and leaning
308over it, look down upon it. It will appear a circle.
309
310But now, drawing back to the edge of the table, gradually lower your
311eye (thus bringing yourself more and more into the condition of the
312inhabitants of Flatland), and you will find the penny becoming more and
313more oval to your view, and at last when you have placed your eye
314exactly on the edge of the table (so that you are, as it were, actually
315a Flatlander) the penny will then have ceased to appear oval at all,
316and will have become, so far as you can see, a straight line.
317
318The same thing would happen if you were to treat in the same way a
319Triangle, or Square, or any other figure cut out of pasteboard. As
320soon as you look at it with your eye on the edge on the table, you will
321find that it ceases to appear to you a figure, and that it becomes in
322appearance a straight line. Take for example an equilateral
323Triangle--who represents with us a Tradesman of the respectable class.
324Fig. 1 represents the Tradesman as you would see him while you were
325bending over him from above; figs. 2 and 3 represent the Tradesman, as
326you would see him if your eye were close to the level, or all but on
327the level of the table; and if your eye were quite on the level of the
328table (and that is how we see him in Flatland) you would see nothing
329but a straight line.
330
331
332[Illustration 1]
333
334[ASCII approximation follows]
335
336
337 (1) __________ (2) ___________ (3) _________
338 \ / --__ __-- ---
339 \ / -
340 \/
341
342
343When I was in Spaceland I heard that your sailors have very similar
344experiences while they traverse your seas and discern some distant
345island or coast lying on the horizon. The far-off land may have bays,
346forelands, angles in and out to any number and extent; yet at a
347distance you see none of these (unless indeed your sun shines bright
348upon them revealing the projections and retirements by means of light
349and shade), nothing but a grey unbroken line upon the water.
350
351Well, that is just what we see when one of our triangular or other
352acquaintances comes toward us in Flatland. As there is neither sun
353with us, nor any light of such a kind as to make shadows, we have none
354of the helps to the sight that you have in Spaceland. If our friend
355comes closer to us we see his line becomes larger; if he leaves us it
356becomes smaller: but still he looks like a straight line; be he a
357Triangle, Square, Pentagon, Hexagon, Circle, what you will--a straight
358Line he looks and nothing else.
359
360You may perhaps ask how under these disadvantageous circumstances we
361are able to distinguish our friends from one another: but the answer to
362this very natural question will be more fitly and easily given when I
363come to describe the inhabitants of Flatland. For the present let me
364defer this subject, and say a word or two about the climate and houses
365in our country.
366
367
368
369
370Section 2. Of the Climate and Houses in Flatland
371
372
373
374As with you, so also with us, there are four points of the compass
375North, South, East, and West.
376
377There being no sun nor other heavenly bodies, it is impossible for us
378to determine the North in the usual way; but we have a method of our
379own. By a Law of Nature with us, there is a constant attraction to the
380South; and, although in temperate climates this is very slight--so that
381even a Woman in reasonable health can journey several furlongs
382northward without much difficulty--yet the hampering effect of the
383southward attraction is quite sufficient to serve as a compass in most
384parts of our earth. Moreover, the rain (which falls at stated
385intervals) coming always from the North, is an additional assistance;
386and in the towns we have the guidance of the houses, which of course
387have their side-walls running for the most part North and South, so
388that the roofs may keep off the rain from the North. In the country,
389where there are no houses, the trunks of the trees serve as some sort
390of guide. Altogether, we have not so much difficulty as might be
391expected in determining our bearings.
392
393Yet in our more temperate regions, in which the southward attraction is
394hardly felt, walking sometimes in a perfectly desolate plain where
395there have been no houses nor trees to guide me, I have been
396occasionally compelled to remain stationary for hours together, waiting
397till the rain came before continuing my journey. On the weak and aged,
398and especially on delicate Females, the force of attraction tells much
399more heavily than on the robust of the Male Sex, so that it is a point
400of breeding, if you meet a Lady in the street, always to give her the
401North side of the way--by no means an easy thing to do always at short
402notice when you are in rude health and in a climate where it is
403difficult to tell your North from your South.
404
405Windows there are none in our houses: for the light comes to us alike
406in our homes and out of them, by day and by night, equally at all times
407and in all places, whence we know not. It was in old days, with our
408learned men, an interesting and oft-investigated question, "What is the
409origin of light?" and the solution of it has been repeatedly attempted,
410with no other result than to crowd our lunatic asylums with the
411would-be solvers. Hence, after fruitless attempts to suppress such
412investigations indirectly by making them liable to a heavy tax, the
413Legislature, in comparatively recent times, absolutely prohibited them.
414I--alas, I alone in Flatland--know now only too well the true solution
415of this mysterious problem; but my knowledge cannot be made
416intelligible to a single one of my countrymen; and I am mocked at--I,
417the sole possessor of the truths of Space and of the theory of the
418introduction of Light from the world of three Dimensions--as if I were
419the maddest of the mad! But a truce to these painful digressions: let
420me return to our houses.
421
422The most common form for the construction of a house is five-sided or
423pentagonal, as in the annexed figure. The two Northern sides RO, OF,
424constitute the roof, and for the most part have no doors; on the East
425is a small door for the Women; on the West a much larger one for the
426Men; the South side or floor is usually doorless.
427
428Square and triangular houses are not allowed, and for this reason. The
429angles of a Square (and still more those of an equilateral Triangle),
430being much more pointed than those of a Pentagon, and the lines of
431inanimate objects (such as houses) being dimmer than the lines of Men
432and Women, it follows that there is no little danger lest the points of
433a square or triangular house residence might do serious injury to an
434inconsiderate or perhaps absent-minded traveller suddenly therefore,
435running against them: and as early as the eleventh century of our era,
436triangular houses were universally forbidden by Law, the only
437exceptions being fortifications, powder-magazines, barracks, and other
438state buildings, which it is not desirable that the general public
439should approach without circumspection.
440
441
442[Illustration 2]
443
444[ASCII approximation follows]
445
446
447 O
448 /\
449 / \
450 / \
451 / \
452 / \
453 R/ \F
454 \_ /
455 _/
456 Men's door _ Women's door
457 _ /
458 \____________/
459 A B
460
461
462At this period, square houses were still everywhere permitted, though
463discouraged by a special tax. But, about three centuries afterwards,
464the Law decided that in all towns containing a population above ten
465thousand, the angle of a Pentagon was the smallest house-angle that
466could be allowed consistently with the public safety. The good sense
467of the community has seconded the efforts of the Legislature; and now,
468even in the country, the pentagonal construction has superseded every
469other. It is only now and then in some very remote and backward
470agricultural district that an antiquarian may still discover a square
471house.
472
473
474
475
476Section 3. Concerning the Inhabitants of Flatland
477
478
479
480The greatest length or breadth of a full grown inhabitant of Flatland
481may be estimated at about eleven of your inches. Twelve inches may be
482regarded as a maximum.
483
484Our Women are Straight Lines.
485
486Our Soldiers and Lowest Classes of Workmen are Triangles with two equal
487sides, each about eleven inches long, and a base or third side so short
488(often not exceeding half an inch) that they form at their vertices a
489very sharp and formidable angle. Indeed when their bases are of the
490most degraded type (not more than the eighth part of an inch in size),
491they can hardly be distinguished from Straight Lines or Women; so
492extremely pointed are their vertices. With us, as with you, these
493Triangles are distinguished from others by being called Isosceles; and
494by this name I shall refer to them in the following pages.
495
496Our Middle Class consists of Equilateral or Equal-Sided Triangles.
497
498Our Professional Men and Gentlemen are Squares (to which class I myself
499belong) and Five-Sided Figures or Pentagons.
500
501Next above these come the Nobility, of whom there are several degrees,
502beginning at Six-Sided Figures, or Hexagons, and from thence rising in
503the number of their sides till they receive the honourable title of
504Polygonal, or many-sided. Finally when the number of the sides becomes
505so numerous, and the sides themselves so small, that the figure cannot
506be distinguished from a circle, he is included in the Circular or
507Priestly order; and this is the highest class of all.
508
509It is a Law of Nature with us that a male child shall have one more
510side than his father, so that each generation shall rise (as a rule)
511one step in the scale of development and nobility. Thus the son of a
512Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on.
513
514But this rule applies not always to the Tradesmen, and still less often
515to the Soldiers, and to the Workmen; who indeed can hardly be said to
516deserve the name of human Figures, since they have not all their sides
517equal. With them therefore the Law of Nature does not hold; and the
518son of an Isosceles (i.e. a Triangle with two sides equal) remains
519Isosceles still. Nevertheless, all hope is not shut out, even from the
520Isosceles, that his posterity may ultimately rise above his degraded
521condition. For, after a long series of military successes, or diligent
522and skilful labours, it is generally found that the more intelligent
523among the Artisan and Soldier classes manifest a slight increase of
524their third side or base, and a shrinkage of the two other sides.
525Intermarriages (arranged by the Priests) between the sons and daughters
526of these more intellectual members of the lower classes generally
527result in an offspring approximating still more to the type of the
528Equal-Sided Triangle.
529
530Rarely--in proportion to the vast numbers of Isosceles births--is a
531genuine and certifiable Equal-Sided Triangle produced from Isosceles
532parents. [Note: "What need of a certificate?" a Spaceland critic may
533ask: "Is not the procreation of a Square Son a certificate from Nature
534herself, proving the Equal-sidedness of the Father?" I reply that no
535Lady of any position will marry an uncertified Triangle. Square
536offspring has sometimes resulted from a slightly Irregular Triangle;
537but in almost every such case the Irregularity of the first generation
538is visited on the third; which either fails to attain the Pentagonal
539rank, or relapses to the Triangular.] Such a birth requires, as its
540antecedents, not only a series of carefully arranged intermarriages,
541but also a long, continued exercise of frugality and self-control on
542the part of the would-be ancestors of the coming Equilateral, and a
543patient, systematic, and continuous development of the Isosceles
544intellect through many generations.
545
546The birth of a True Equilateral Triangle from Isosceles parents is the
547subject of rejoicing in our country for many furlongs around. After a
548strict examination conducted by the Sanitary and Social Board, the
549infant, if certified as Regular, is with solemn ceremonial admitted
550into the class of Equilaterals. He is then immediately taken from his
551proud yet sorrowing parents and adopted by some childless Equilateral,
552who is bound by oath never to permit the child henceforth to enter his
553former home or so much as to look upon his relations again, for fear
554lest the freshly developed organism may, by force of unconscious
555imitation, fall back again into his hereditary level.
556
557The occasional emergence of an Equilateral from the ranks of his
558serf-born ancestors is welcomed, not only by the poor serfs themselves,
559as a gleam of light and hope shed upon the monotonous squalor of their
560existence, but also by the Aristocracy at large; for all the higher
561classes are well aware that these rare phenomena, while they do little
562or nothing to vulgarize their own privileges, serve as a most useful
563barrier against revolution from below.
564
565Had the acute-angled rabble been all, without exception, absolutely
566destitute of hope and of ambition, they might have found leaders in
567some of their many seditious outbreaks, so able as to render their
568superior numbers and strength too much even for the wisdom of the
569Circles. But a wise ordinance of Nature has decreed that, in
570proportion as the working-classes increase in intelligence, knowledge,
571and all virtue, in that same proportion their acute angle (which makes
572them physically terrible) shall increase also and approximate to the
573comparatively harmless angle of the Equilateral Triangle. Thus, in the
574most brutal and formidable of the soldier class--creatures almost on a
575level with women in their lack of intelligence--it is found that, as
576they wax in the mental ability necessary to employ their tremendous
577penetrating power to advantage, so do they wane in the power of
578penetration itself.
579
580How admirable is this Law of Compensation! And how perfect a proof of
581the natural fitness and, I may almost say, the divine origin of the
582aristocratic constitution of the States in Flatland! By a judicious
583use of this Law of Nature, the Polygons and Circles are almost always
584able to stifle sedition in its very cradle, taking advantage of the
585irrepressible and boundless hopefulness of the human mind. Art also
586comes to the aid of Law and Order. It is generally found possible--by
587a little artificial compression or expansion on the part of the State
588physicians--to make some of the more intelligent leaders of a rebellion
589perfectly Regular, and to admit them at once into the privileged
590classes; a much larger number, who are still below the standard,
591allured by the prospect of being ultimately ennobled, are induced to
592enter the State Hospitals, where they are kept in honourable
593confinement for life; one or two alone of the more obstinate, foolish,
594and hopelessly irregular are led to execution.
595
596Then the wretched rabble of the Isosceles, planless and leaderless, are
597either transfixed without resistance by the small body of their
598brethren whom the Chief Circle keeps in pay for emergencies of this
599kind; or else more often, by means of jealousies and suspicions
600skilfully fomented among them by the Circular party, they are stirred
601to mutual warfare, and perish by one another's angles. No less than
602one hundred and twenty rebellions are recorded in our annals, besides
603minor outbreaks numbered at two hundred and thirty-five; and they have
604all ended thus.
605
606
607
608
609Section 4. Concerning the Women
610
611
612
613If our highly pointed Triangles of the Soldier class are formidable, it
614may be readily inferred that far more formidable are our Women. For if
615a Soldier is a wedge, a Woman is a needle; being, so to speak, ALL
616point, at least at the two extremities. Add to this the power of
617making herself practically invisible at will, and you will perceive
618that a Female, in Flatland, is a creature by no means to be trifled
619with.
620
621But here, perhaps, some of my younger Readers may ask HOW a woman in
622Flatland can make herself invisible. This ought, I think, to be
623apparent without any explanation. However, a few words will make it
624clear to the most unreflecting.
625
626Place a needle on a table. Then, with your eye on the level of the
627table, look at it side-ways, and you see the whole length of it; but
628look at it end-ways, and you see nothing but a point, it has become
629practically invisible. Just so is it with one of our Women. When her
630side is turned towards us, we see her as a straight line; when the end
631containing her eye or mouth--for with us these two organs are
632identical--is the part that meets our eye, then we see nothing but a
633highly lustrous point; but when the back is presented to our view,
634then--being only sub-lustrous, and, indeed, almost as dim as an
635inanimate object--her hinder extremity serves her as a kind of
636Invisible Cap.
637
638The dangers to which we are exposed from our Women must now be manifest
639to the meanest capacity in Spaceland. If even the angle of a
640respectable Triangle in the middle class is not without its dangers; if
641to run against a Working Man involves a gash; if collision with an
642officer of the military class necessitates a serious wound; if a mere
643touch from the vertex of a Private Soldier brings with it danger of
644death;--what can it be to run against a Woman, except absolute and
645immediate destruction? And when a Woman is invisible, or visible only
646as a dim sub-lustrous point, how difficult must it be, even for the
647most cautious, always to avoid collision!
648
649Many are the enactments made at different times in the different States
650of Flatland, in order to minimize this peril; and in the Southern and
651less temperate climates where the force of gravitation is greater, and
652human beings more liable to casual and involuntary motions, the Laws
653concerning Women are naturally much more stringent. But a general view
654of the Code may be obtained from the following summary:--
655
656
6571. Every house shall have one entrance in the Eastern side, for the
658use of Females only; by which all females shall enter "in a becoming
659and respectful manner" and not by the Men's or Western door. [Note:
660When I was in Spaceland I understood that some of your Priestly circles
661have in the same way a separate entrance for Villagers, Farmers and
662Teachers of Board Schools (`Spectator', Sept. 1884, p. 1255) that they
663may "approach in a becoming and respectful manner."]
664
6652. No Female shall walk in any public place without continually
666keeping up her Peace-cry, under penalty of death.
667
6683. Any Female, duly certified to be suffering from St. Vitus's Dance,
669fits, chronic cold accompanied by violent sneezing, or any disease
670necessitating involuntary motions, shall be instantly destroyed.
671
672
673In some of the States there is an additional Law forbidding Females,
674under penalty of death, from walking or standing in any public place
675without moving their backs constantly from right to left so as to
676indicate their presence to those behind them; others oblige a Woman,
677when travelling, to be followed by one of her sons, or servants, or by
678her husband; others confine Women altogether to their houses except
679during the religious festivals. But it has been found by the wisest of
680our Circles or Statesmen that the multiplication of restrictions on
681Females tends not only to the debilitation and diminution of the race,
682but also to the increase of domestic murders to such an extent that a
683State loses more than it gains by a too prohibitive Code.
684
685For whenever the temper of the Women is thus exasperated by confinement
686at home or hampering regulations abroad, they are apt to vent their
687spleen upon their husbands and children; and in the less temperate
688climates the whole male population of a village has been sometimes
689destroyed in one or two hours of simultaneous female outbreak. Hence
690the Three Laws, mentioned above, suffice for the better regulated
691States, and may be accepted as a rough exemplification of our Female
692Code.
693
694After all, our principal safeguard is found, not in Legislature, but in
695the interests of the Women themselves. For, although they can inflict
696instantaneous death by a retrograde movement, yet unless they can at
697once disengage their stinging extremity from the struggling body of
698their victim, their own frail bodies are liable to be shattered.
699
700The power of Fashion is also on our side. I pointed out that in some
701less civilized States no female is suffered to stand in any public
702place without swaying her back from right to left. This practice has
703been universal among ladies of any pretensions to breeding in all
704well-governed States, as far back as the memory of Figures can reach.
705It is considered a disgrace to any State that legislation should have
706to enforce what ought to be, and is in every respectable female, a
707natural instinct. The rhythmical and, if I may so say, well-modulated
708undulation of the back in our ladies of Circular rank is envied and
709imitated by the wife of a common Equilateral, who can achieve nothing
710beyond a mere monotonous swing, like the ticking of a pendulum; and the
711regular tick of the Equilateral is no less admired and copied by the
712wife of the progressive and aspiring Isosceles, in the females of whose
713family no "back-motion" of any kind has become as yet a necessity of
714life. Hence, in every family of position and consideration, "back
715motion" is as prevalent as time itself; and the husbands and sons in
716these households enjoy immunity at least from invisible attacks.
717
718Not that it must be for a moment supposed that our Women are destitute
719of affection. But unfortunately the passion of the moment
720predominates, in the Frail Sex, over every other consideration. This
721is, of course, a necessity arising from their unfortunate conformation.
722For as they have no pretensions to an angle, being inferior in this
723respect to the very lowest of the Isosceles, they are consequently
724wholly devoid of brain-power, and have neither reflection, judgment nor
725forethought, and hardly any memory. Hence, in their fits of fury, they
726remember no claims and recognize no distinctions. I have actually
727known a case where a Woman has exterminated her whole household, and
728half an hour afterwards, when her rage was over and the fragments swept
729away, has asked what has become of her husband and her children.
730
731Obviously then a Woman is not to be irritated as long as she is in a
732position where she can turn round. When you have them in their
733apartments--which are constructed with a view to denying them that
734power--you can say and do what you like; for they are then wholly
735impotent for mischief, and will not remember a few minutes hence the
736incident for which they may be at this moment threatening you with
737death, nor the promises which you may have found it necessary to make
738in order to pacify their fury.
739
740On the whole we get on pretty smoothly in our domestic relations,
741except in the lower strata of the Military Classes. There the want of
742tact and discretion on the part of the husbands produces at times
743indescribable disasters. Relying too much on the offensive weapons of
744their acute angles instead of the defensive organs of good sense and
745seasonable simulation, these reckless creatures too often neglect the
746prescribed construction of the women's apartments, or irritate their
747wives by ill-advised expressions out of doors, which they refuse
748immediately to retract. Moreover a blunt and stolid regard for literal
749truth indisposes them to make those lavish promises by which the more
750judicious Circle can in a moment pacify his consort. The result is
751massacre; not, however, without its advantages, as it eliminates the
752more brutal and troublesome of the Isosceles; and by many of our
753Circles the destructiveness of the Thinner Sex is regarded as one among
754many providential arrangements for suppressing redundant population,
755and nipping Revolution in the bud.
756
757Yet even in our best regulated and most approximately Circular families
758I cannot say that the ideal of family life is so high as with you in
759Spaceland. There is peace, in so far as the absence of slaughter may
760be called by that name, but there is necessarily little harmony of
761tastes or pursuits; and the cautious wisdom of the Circles has ensured
762safety at the cost of domestic comfort. In every Circular or Polygonal
763household it has been a habit from time immemorial--and now has become
764a kind of instinct among the women of our higher classes--that the
765mothers and daughters should constantly keep their eyes and mouths
766towards their husband and his male friends; and for a lady in a family
767of distinction to turn her back upon her husband would be regarded as a
768kind of portent, involving loss of STATUS. But, as I shall soon shew,
769this custom, though it has the advantage of safety, is not without its
770disadvantages.
771
772In the house of the Working Man or respectable Tradesman--where the
773wife is allowed to turn her back upon her husband, while pursuing her
774household avocations--there are at least intervals of quiet, when the
775wife is neither seen nor heard, except for the humming sound of the
776continuous Peace-cry; but in the homes of the upper classes there is
777too often no peace. There the voluble mouth and bright penetrating eye
778are ever directed towards the Master of the household; and light itself
779is not more persistent than the stream of feminine discourse. The tact
780and skill which suffice to avert a Woman's sting are unequal to the
781task of stopping a Woman's mouth; and as the wife has absolutely
782nothing to say, and absolutely no constraint of wit, sense, or
783conscience to prevent her from saying it, not a few cynics have been
784found to aver that they prefer the danger of the death-dealing but
785inaudible sting to the safe sonorousness of a Woman's other end.
786
787To my readers in Spaceland the condition of our Women may seem truly
788deplorable, and so indeed it is. A Male of the lowest type of the
789Isosceles may look forward to some improvement of his angle, and to the
790ultimate elevation of the whole of his degraded caste; but no Woman can
791entertain such hopes for her sex. "Once a Woman, always a Woman" is a
792Decree of Nature; and the very Laws of Evolution seem suspended in her
793disfavour. Yet at least we can admire the wise Prearrangement which
794has ordained that, as they have no hopes, so they shall have no memory
795to recall, and no forethought to anticipate, the miseries and
796humiliations which are at once a necessity of their existence and the
797basis of the constitution of Flatland.
798
799
800
801
802Section 5. Of our Methods of Recognizing one another
803
804
805
806You, who are blessed with shade as well as light, you, who are gifted
807with two eyes, endowed with a knowledge of perspective, and charmed
808with the enjoyment of various colours, you, who can actually SEE an
809angle, and contemplate the complete circumference of a circle in the
810happy region of the Three Dimensions--how shall I make clear to you the
811extreme difficulty which we in Flatland experience in recognizing one
812another's configuration?
813
814Recall what I told you above. All beings in Flatland, animate or
815inanimate, no matter what their form, present TO OUR VIEW the same, or
816nearly the same, appearance, viz. that of a straight Line. How then
817can one be distinguished from another, where all appear the same?
818
819The answer is threefold. The first means of recognition is the sense
820of hearing; which with us is far more highly developed than with you,
821and which enables us not only to distinguish by the voice our personal
822friends, but even to discriminate between different classes, at least
823so far as concerns the three lowest orders, the Equilateral, the
824Square, and the Pentagon--for of the Isosceles I take no account. But
825as we ascend in the social scale, the process of discriminating and
826being discriminated by hearing increases in difficulty, partly because
827voices are assimilated, partly because the faculty of
828voice-discrimination is a plebeian virtue not much developed among the
829Aristocracy. And wherever there is any danger of imposture we cannot
830trust to this method. Amongst our lowest orders, the vocal organs are
831developed to a degree more than correspondent with those of hearing, so
832that an Isosceles can easily feign the voice of a Polygon, and, with
833some training, that of a Circle himself. A second method is therefore
834more commonly resorted to.
835
836FEELING is, among our Women and lower classes--about our upper classes
837I shall speak presently--the principal test of recognition, at all
838events between strangers, and when the question is, not as to the
839individual, but as to the class. What therefore "introduction" is
840among the higher classes in Spaceland, that the process of "feeling" is
841with us. "Permit me to ask you to feel and be felt by my friend Mr.
842So-and-so"--is still, among the more old-fashioned of our country
843gentlemen in districts remote from towns, the customary formula for a
844Flatland introduction. But in the towns, and among men of business,
845the words "be felt by" are omitted and the sentence is abbreviated to,
846"Let me ask you to feel Mr. So-and-so"; although it is assumed, of
847course, that the "feeling" is to be reciprocal. Among our still more
848modern and dashing young gentlemen--who are extremely averse to
849superfluous effort and supremely indifferent to the purity of their
850native language--the formula is still further curtailed by the use of
851"to feel" in a technical sense, meaning, "to
852recommend-for-the-purposes-of-feeling-and-being-felt"; and at this
853moment the "slang" of polite or fast society in the upper classes
854sanctions such a barbarism as "Mr. Smith, permit me to feel Mr. Jones."
855
856Let not my Reader however suppose that "feeling" is with us the tedious
857process that it would be with you, or that we find it necessary to feel
858right round all the sides of every individual before we determine the
859class to which he belongs. Long practice and training, begun in the
860schools and continued in the experience of daily life, enable us to
861discriminate at once by the sense of touch, between the angles of an
862equal-sided Triangle, Square, and Pentagon; and I need not say that the
863brainless vertex of an acute-angled Isosceles is obvious to the dullest
864touch. It is therefore not necessary, as a rule, to do more than feel
865a single angle of an individual; and this, once ascertained, tells us
866the class of the person whom we are addressing, unless indeed he
867belongs to the higher sections of the nobility. There the difficulty
868is much greater. Even a Master of Arts in our University of Wentbridge
869has been known to confuse a ten-sided with a twelve-sided Polygon; and
870there is hardly a Doctor of Science in or out of that famous University
871who could pretend to decide promptly and unhesitatingly between a
872twenty-sided and a twenty-four sided member of the Aristocracy.
873
874Those of my readers who recall the extracts I gave above from the
875Legislative code concerning Women, will readily perceive that the
876process of introduction by contact requires some care and discretion.
877Otherwise the angles might inflict on the unwary Feeler irreparable
878injury. It is essential for the safety of the Feeler that the Felt
879should stand perfectly still. A start, a fidgety shifting of the
880position, yes, even a violent sneeze, has been known before now to
881prove fatal to the incautious, and to nip in the bud many a promising
882friendship. Especially is this true among the lower classes of the
883Triangles. With them, the eye is situated so far from their vertex
884that they can scarcely take cognizance of what goes on at that
885extremity of their frame. They are, moreover, of a rough coarse
886nature, not sensitive to the delicate touch of the highly organized
887Polygon. What wonder then if an involuntary toss of the head has ere
888now deprived the State of a valuable life!
889
890I have heard that my excellent Grandfather--one of the least irregular
891of his unhappy Isosceles class, who indeed obtained, shortly before his
892decease, four out of seven votes from the Sanitary and Social Board for
893passing him into the class of the Equal-sided--often deplored, with a
894tear in his venerable eye, a miscarriage of this kind, which had
895occured to his great-great-great-Grandfather, a respectable Working Man
896with an angle or brain of 59 degrees 30 minutes. According to his
897account, my unfortunate Ancestor, being afflicted with rheumatism, and
898in the act of being felt by a Polygon, by one sudden start accidentally
899transfixed the Great Man through the diagonal; and thereby, partly in
900consequence of his long imprisonment and degradation, and partly
901because of the moral shock which pervaded the whole of my Ancestor's
902relations, threw back our family a degree and a half in their ascent
903towards better things. The result was that in the next generation the
904family brain was registered at only 58 degrees, and not till the lapse
905of five generations was the lost ground recovered, the full 60 degrees
906attained, and the Ascent from the Isosceles finally achieved. And all
907this series of calamities from one little accident in the process of
908Feeling.
909
910At this point I think I hear some of my better educated readers
911exclaim, "How could you in Flatland know anything about angles and
912degrees, or minutes? We can SEE an angle, because we, in the region of
913Space, can see two straight lines inclined to one another; but you, who
914can see nothing but one straight line at a time, or at all events only
915a number of bits of straight lines all in one straight line--how can
916you ever discern any angle, and much less register angles of different
917sizes?"
918
919I answer that though we cannot SEE angles, we can INFER them, and this
920with great precision. Our sense of touch, stimulated by necessity, and
921developed by long training, enables us to distinguish angles far more
922accurately than your sense of sight, when unaided by a rule or measure
923of angles. Nor must I omit to explain that we have great natural
924helps. It is with us a Law of Nature that the brain of the Isosceles
925class shall begin at half a degree, or thirty minutes, and shall
926increase (if it increases at all) by half a degree in every generation;
927until the goal of 60 degrees is reached, when the condition of serfdom
928is quitted, and the freeman enters the class of Regulars.
929
930Consequently, Nature herself supplies us with an ascending scale or
931Alphabet of angles for half a degree up to 60 degrees, Specimens of
932which are placed in every Elementary School throughout the land. Owing
933to occasional retrogressions, to still more frequent moral and
934intellectual stagnation, and to the extraordinary fecundity of the
935Criminal and Vagabond Classes, there is always a vast superfluity of
936individuals of the half degree and single degree class, and a fair
937abundance of Specimens up to 10 degrees. These are absolutely
938destitute of civic rights; and a great number of them, not having even
939intelligence enough for the purposes of warfare, are devoted by the
940States to the service of education. Fettered immovably so as to remove
941all possibility of danger, they are placed in the class rooms of our
942Infant Schools, and there they are utilized by the Board of Education
943for the purpose of imparting to the offspring of the Middle Classes
944that tact and intelligence of which these wretched creatures themselves
945are utterly devoid.
946
947In some States the Specimens are occasionally fed and suffered to exist
948for several years; but in the more temperate and better regulated
949regions, it is found in the long run more advantageous for the
950educational interests of the young, to dispense with food, and to renew
951the Specimens every month--which is about the average duration of the
952foodless existence of the Criminal class. In the cheaper schools, what
953is gained by the longer existence of the Specimen is lost, partly in
954the expenditure for food, and partly in the diminished accuracy of the
955angles, which are impaired after a few weeks of constant "feeling".
956Nor must we forget to add, in enumerating the advantages of the more
957expensive system, that it tends, though slightly yet perceptibly, to
958the diminution of the redundant Isosceles population--an object which
959every statesman in Flatland constantly keeps in view. On the whole
960therefore--although I am not ignorant that, in many popularly elected
961School Boards, there is a reaction in favour of "the cheap system" as
962it is called--I am myself disposed to think that this is one of the
963many cases in which expense is the truest economy.
964
965But I must not allow questions of School Board politics to divert me
966from my subject. Enough has been said, I trust, to shew that
967Recognition by Feeling is not so tedious or indecisive a process as
968might have been supposed; and it is obviously more trustworthy than
969Recognition by hearing. Still there remains, as has been pointed out
970above, the objection that this method is not without danger. For this
971reason many in the Middle and Lower classes, and all without exception
972in the Polygonal and Circular orders, prefer a third method, the
973description of which shall be reserved for the next section.
974
975
976
977
978Section 6. Of Recognition by Sight
979
980
981
982I am about to appear very inconsistent. In previous sections I have
983said that all figures in Flatland present the appearance of a straight
984line; and it was added or implied, that it is consequently impossible
985to distinguish by the visual organ between individuals of different
986classes: yet now I am about to explain to my Spaceland critics how we
987are able to recognize one another by the sense of sight.
988
989If however the Reader will take the trouble to refer to the passage in
990which Recognition by Feeling is stated to be universal, he will find
991this qualification--"among the lower classes". It is only among the
992higher classes and in our temperate climates that Sight Recognition is
993practised.
994
995That this power exists in any regions and for any classes is the result
996of Fog; which prevails during the greater part of the year in all parts
997save the torrid zones. That which is with you in Spaceland an unmixed
998evil, blotting out the landscape, depressing the spirits, and
999enfeebling the health, is by us recognized as a blessing scarcely
1000inferior to air itself, and as the Nurse of arts and Parent of
1001sciences. But let me explain my meaning, without further eulogies on
1002this beneficent Element.
1003
1004If Fog were non-existent, all lines would appear equally and
1005indistinguishably clear; and this is actually the case in those unhappy
1006countries in which the atmosphere is perfectly dry and transparent.
1007But wherever there is a rich supply of Fog objects that are at a
1008distance, say of three feet, are appreciably dimmer than those at a
1009distance of two feet eleven inches; and the result is that by careful
1010and constant experimental observation of comparative dimness and
1011clearness, we are enabled to infer with great exactness the
1012configuration of the object observed.
1013
1014An instance will do more than a volume of generalities to make my
1015meaning clear.
1016
1017Suppose I see two individuals approaching whose rank I wish to
1018ascertain. They are, we will suppose, a Merchant and a Physician, or
1019in other words, an Equilateral Triangle and a Pentagon: how am I to
1020distinguish them?
1021
1022
1023[Illustration 3]
1024
1025[ASCII approximation follows]
1026
1027
1028 C (1)
1029 |\ - _ D
1030 | \ ||- _
1031 | \ || - _
1032 | <--- >|| -----------+(> Eye-glance
1033 ___C' (2) | / A|| _ -
1034 ___--- \ - _D' | / ||_ -
1035 __--- \ || - _ |/ _ - E
1036 | \ || - _ B
1037 | \ || - _
1038 | Eye-glance \ || - _
1039 | <----------- A'>|| ------------------------+(>
1040 | / || _ -
1041 | / || _ -
1042 |__ / || _ -
1043 ---___ / || _ -
1044 ---___/ _ -E'
1045 B'
1046
1047
1048It will be obvious, to every child in Spaceland who has touched the
1049threshold of Geometrical Studies, that, if I can bring my eye so that
1050its glance may bisect an angle (A) of the approaching stranger, my view
1051will lie as it were evenly between his two sides that are next to me
1052(viz. CA and AB), so that I shall contemplate the two impartially, and
1053both will appear of the same size.
1054
1055Now in the case of (1) the Merchant, what shall I see? I shall see a
1056straight line DAE, in which the middle point (A) will be very bright
1057because it is nearest to me; but on either side the line will shade
1058away RAPIDLY INTO DIMNESS, because the sides AC and AB RECEDE RAPIDLY
1059INTO THE FOG and what appear to me as the Merchant's extremities, viz.
1060D and E, will be VERY DIM INDEED.
1061
1062On the other hand in the case of (2) the Physician, though I shall here
1063also see a line (D'A'E') with a bright centre (A'), yet it will shade
1064away LESS RAPIDLY into dimness, because the sides (A'C', A'B') RECEDE
1065LESS RAPIDLY INTO THE FOG: and what appear to me the Physician's
1066extremities, viz. D' and E', will not be NOT SO DIM as the extremities
1067of the Merchant.
1068
1069The Reader will probably understand from these two instances how--after
1070a very long training supplemented by constant experience--it is
1071possible for the well-educated classes among us to discriminate with
1072fair accuracy between the middle and lowest orders, by the sense of
1073sight. If my Spaceland Patrons have grasped this general conception,
1074so far as to conceive the possibility of it and not to reject my
1075account as altogether incredible--I shall have attained all I can
1076reasonably expect. Were I to attempt further details I should only
1077perplex. Yet for the sake of the young and inexperienced, who may
1078perchance infer--from the two simple instances I have given above, of
1079the manner in which I should recognize my Father and my Sons--that
1080Recognition by sight is an easy affair, it may be needful to point out
1081that in actual life most of the problems of Sight Recognition are far
1082more subtle and complex.
1083
1084If for example, when my Father, the Triangle, approaches me, he happens
1085to present his side to me instead of his angle, then, until I have
1086asked him to rotate, or until I have edged my eye round him, I am for
1087the moment doubtful whether he may not be a Straight Line, or, in other
1088words, a Woman. Again, when I am in the company of one of my two
1089hexagonal Grandsons, contemplating one of his sides (AB) full front, it
1090will be evident from the accompanying diagram that I shall see one
1091whole line (AB) in comparative brightness (shading off hardly at all at
1092the ends) and two smaller lines (CA and BD) dim throughout and shading
1093away into greater dimness towards the extremities C and D.
1094
1095
1096[Illustration 4]
1097
1098[ASCII approximation follows]
1099
1100
1101 /\ - _ C
1102 / \ || _
1103 / \ || - _
1104 / \|| - _
1105 | A || - _
1106 | || -+(> (Eye)
1107 | B || _ -
1108 \ /|| _ -
1109 \ / || _ -
1110 \ / || -
1111 \/ _ - D
1112
1113
1114But I must not give way to the temptation of enlarging on these topics.
1115The meanest mathematician in Spaceland will readily believe me when I
1116assert that the problems of life, which present themselves to the
1117well-educated--when they are themselves in motion, rotating, advancing
1118or retreating, and at the same time attempting to discriminate by the
1119sense of sight between a number of Polygons of high rank moving in
1120different directions, as for example in a ball-room or
1121conversazione--must be of a nature to task the angularity of the most
1122intellectual, and amply justify the rich endowments of the Learned
1123Professors of Geometry, both Static and Kinetic, in the illustrious
1124University of Wentbridge, where the Science and Art of Sight
1125Recognition are regularly taught to large classes of the ELITE of the
1126States.
1127
1128It is only a few of the scions of our noblest and wealthiest houses,
1129who are able to give the time and money necessary for the thorough
1130prosecution of this noble and valuable Art. Even to me, a
1131Mathematician of no mean standing, and the Grandfather of two most
1132hopeful and perfectly regular Hexagons, to find myself in the midst of
1133a crowd of rotating Polygons of the higher classes, is occasionally
1134very perplexing. And of course to a common Tradesman, or Serf, such a
1135sight is almost as unintelligible as it would be to you, my Reader,
1136were you suddenly transported into our country.
1137
1138In such a crowd you could see on all sides of you nothing but a Line,
1139apparently straight, but of which the parts would vary irregularly and
1140perpetually in brightness or dimness. Even if you had completed your
1141third year in the Pentagonal and Hexagonal classes in the University,
1142and were perfect in the theory of the subject, you would still find
1143that there was need of many years of experience, before you could move
1144in a fashionable crowd without jostling against your betters, whom it
1145is against etiquette to ask to "feel", and who, by their superior
1146culture and breeding, know all about your movements, while you know
1147very little or nothing about theirs. In a word, to comport oneself
1148with perfect propriety in Polygonal society, one ought to be a Polygon
1149oneself. Such at least is the painful teaching of my experience.
1150
1151It is astonishing how much the Art--or I may almost call it
1152instinct--of Sight Recognition is developed by the habitual practice of
1153it and by the avoidance of the custom of "Feeling". Just as, with you,
1154the deaf and dumb, if once allowed to gesticulate and to use the
1155hand-alphabet, will never acquire the more difficult but far more
1156valuable art of lipspeech and lip-reading, so it is with us as regards
1157"Seeing" and "Feeling". None who in early life resort to "Feeling"
1158will ever learn "Seeing" in perfection.
1159
1160For this reason, among our Higher Classes, "Feeling" is discouraged or
1161absolutely forbidden. From the cradle their children, instead of going
1162to the Public Elementary schools (where the art of Feeling is taught),
1163are sent to higher Seminaries of an exclusive character; and at our
1164illustrious University, to "feel" is regarded as a most serious fault,
1165involving Rustication for the first offence, and Expulsion for the
1166second.
1167
1168But among the lower classes the art of Sight Recognition is regarded as
1169an unattainable luxury. A common Tradesman cannot afford to let his
1170son spend a third of his life in abstract studies. The children of the
1171poor are therefore allowed to "feel" from their earliest years, and
1172they gain thereby a precocity and an early vivacity which contrast at
1173first most favourably with the inert, undeveloped, and listless
1174behaviour of the half-instructed youths of the Polygonal class; but
1175when the latter have at last completed their University course, and are
1176prepared to put their theory into practice, the change that comes over
1177them may almost be described as a new birth, and in every art, science,
1178and social pursuit they rapidly overtake and distance their Triangular
1179competitors.
1180
1181Only a few of the Polygonal Class fail to pass the Final Test or
1182Leaving Examination at the University. The condition of the
1183unsuccessful minority is truly pitiable. Rejected from the higher
1184class, they are also despised by the lower. They have neither the
1185matured and systematically trained powers of the Polygonal Bachelors
1186and Masters of Arts, nor yet the native precocity and mercurial
1187versatility of the youthful Tradesman. The professions, the public
1188services, are closed against them; and though in most States they are
1189not actually debarred from marriage, yet they have the greatest
1190difficulty in forming suitable alliances, as experience shews that the
1191offspring of such unfortunate and ill-endowed parents is generally
1192itself unfortunate, if not positively Irregular.
1193
1194It is from these specimens of the refuse of our Nobility that the great
1195Tumults and Seditions of past ages have generally derived their
1196leaders; and so great is the mischief thence arising that an increasing
1197minority of our more progressive Statesmen are of opinion that true
1198mercy would dictate their entire suppression, by enacting that all who
1199fail to pass the Final Examination of the University should be either
1200imprisoned for life, or extinguished by a painless death.
1201
1202But I find myself digressing into the subject of Irregularities, a
1203matter of such vital interest that it demands a separate section.
1204
1205
1206
1207
1208Section 7. Concerning Irregular Figures
1209
1210
1211
1212Throughout the previous pages I have been assuming--what perhaps should
1213have been laid down at the beginning as a distinct and fundamental
1214proposition--that every human being in Flatland is a Regular Figure,
1215that is to say of regular construction. By this I mean that a Woman
1216must not only be a line, but a straight line; that an Artisan or
1217Soldier must have two of his sides equal; that Tradesmen must have
1218three sides equal; Lawyers (of which class I am a humble member), four
1219sides equal, and generally, that in every Polygon, all the sides must
1220be equal.
1221
1222The size of the sides would of course depend upon the age of the
1223individual. A Female at birth would be about an inch long, while a
1224tall adult Woman might extend to a foot. As to the Males of every
1225class, it may be roughly said that the length of an adult's sides, when
1226added together, is two feet or a little more. But the size of our
1227sides is not under consideration. I am speaking of the EQUALITY of
1228sides, and it does not need much reflection to see that the whole of
1229the social life in Flatland rests upon the fundamental fact that Nature
1230wills all Figures to have their sides equal.
1231
1232If our sides were unequal our angles might be unequal. Instead of its
1233being sufficient to feel, or estimate by sight, a single angle in order
1234to determine the form of an individual, it would be necessary to
1235ascertain each angle by the experiment of Feeling. But life would be
1236too short for such a tedious grouping. The whole science and art of
1237Sight Recognition would at once perish; Feeling, so far as it is an
1238art, would not long survive; intercourse would become perilous or
1239impossible; there would be an end to all confidence, all forethought;
1240no one would be safe in making the most simple social arrangements; in
1241a word, civilization would relapse into barbarism.
1242
1243Am I going too fast to carry my Readers with me to these obvious
1244conclusions? Surely a moment's reflection, and a single instance from
1245common life, must convince every one that our whole social system is
1246based upon Regularity, or Equality of Angles. You meet, for example,
1247two or three Tradesmen in the street, whom you recognize at once to be
1248Tradesmen by a glance at their angles and rapidly bedimmed sides, and
1249you ask them to step into your house to lunch. This you do at present
1250with perfect confidence, because everyone knows to an inch or two the
1251area occupied by an adult Triangle: but imagine that your Tradesman
1252drags behind his regular and respectable vertex, a parallelogram of
1253twelve or thirteen inches in diagonal:--what are you to do with such a
1254monster sticking fast in your house door?
1255
1256But I am insulting the intelligence of my Readers by accumulating
1257details which must be patent to everyone who enjoys the advantages of a
1258Residence in Spaceland. Obviously the measurements of a single angle
1259would no longer be sufficient under such portentous circumstances;
1260one's whole life would be taken up in feeling or surveying the
1261perimeter of one's acquaintances. Already the difficulties of avoiding
1262a collision in a crowd are enough to tax the sagacity of even a
1263well-educated Square; but if no one could calculate the Regularity of a
1264single figure in the company, all would be chaos and confusion, and the
1265slightest panic would cause serious injuries, or--if there happened to
1266be any Women or Soldiers present--perhaps considerable loss of life.
1267
1268Expediency therefore concurs with Nature in stamping the seal of its
1269approval upon Regularity of conformation: nor has the Law been
1270backward in seconding their efforts. "Irregularity of Figure" means
1271with us the same as, or more than, a combination of moral obliquity and
1272criminality with you, and is treated accordingly. There are not
1273wanting, it is true, some promulgators of paradoxes who maintain that
1274there is no necessary connection between geometrical and moral
1275Irregularity. "The Irregular", they say, "is from his birth scouted by
1276his own parents, derided by his brothers and sisters, neglected by the
1277domestics, scorned and suspected by society, and excluded from all
1278posts of responsibility, trust, and useful activity. His every
1279movement is jealously watched by the police till he comes of age and
1280presents himself for inspection; then he is either destroyed, if he is
1281found to exceed the fixed margin of deviation, or else immured in a
1282Government Office as a clerk of the seventh class; prevented from
1283marriage; forced to drudge at an uninteresting occupation for a
1284miserable stipend; obliged to live and board at the office, and to take
1285even his vacation under close supervision; what wonder that human
1286nature, even in the best and purest, is embittered and perverted by
1287such surroundings!"
1288
1289All this very plausible reasoning does not convince me, as it has not
1290convinced the wisest of our Statesmen, that our ancestors erred in
1291laying it down as an axiom of policy that the toleration of
1292Irregularity is incompatible with the safety of the State. Doubtless,
1293the life of an Irregular is hard; but the interests of the Greater
1294Number require that it shall be hard. If a man with a triangular front
1295and a polygonal back were allowed to exist and to propagate a still
1296more Irregular posterity, what would become of the arts of life? Are
1297the houses and doors and churches in Flatland to be altered in order to
1298accommodate such monsters? Are our ticket-collectors to be required to
1299measure every man's perimeter before they allow him to enter a theatre
1300or to take his place in a lecture room? Is an Irregular to be exempted
1301from the militia? And if not, how is he to be prevented from carrying
1302desolation into the ranks of his comrades? Again, what irresistible
1303temptations to fraudulent impostures must needs beset such a creature!
1304How easy for him to enter a shop with his polygonal front foremost, and
1305to order goods to any extent from a confiding tradesman! Let the
1306advocates of a falsely called Philanthropy plead as they may for the
1307abrogation of the Irregular Penal Laws, I for my part have never known
1308an Irregular who was not also what Nature evidently intended him to
1309be--a hypocrite, a misanthropist, and, up to the limits of his power, a
1310perpetrator of all manner of mischief.
1311
1312Not that I should be disposed to recommend (at present) the extreme
1313measures adopted by some States, where an infant whose angle deviates
1314by half a degree from the correct angularity is summarily destroyed at
1315birth. Some of our highest and ablest men, men of real genius, have
1316during their earliest days laboured under deviations as great as, or
1317even greater than, forty-five minutes: and the loss of their precious
1318lives would have been an irreparable injury to the State. The art of
1319healing also has achieved some of its most glorious triumphs in the
1320compressions, extensions, trepannings, colligations, and other surgical
1321or diaetetic operations by which Irregularity has been partly or wholly
1322cured. Advocating therefore a VIA MEDIA, I would lay down no fixed or
1323absolute line of demarcation; but at the period when the frame is just
1324beginning to set, and when the Medical Board has reported that recovery
1325is improbable, I would suggest that the Irregular offspring be
1326painlessly and mercifully consumed.
1327
1328
1329
1330
1331Section 8. Of the Ancient Practice of Painting
1332
1333
1334
1335If my Readers have followed me with any attention up to this point,
1336they will not be surprised to hear that life is somewhat dull in
1337Flatland. I do not, of course, mean that there are not battles,
1338conspiracies, tumults, factions, and all those other phenomena which
1339are supposed to make History interesting; nor would I deny that the
1340strange mixture of the problems of life and the problems of
1341Mathematics, continually inducing conjecture and giving the opportunity
1342of immediate verification, imparts to our existence a zest which you in
1343Spaceland can hardly comprehend. I speak now from the aesthetic and
1344artistic point of view when I say that life with us is dull;
1345aesthetically and artistically, very dull indeed.
1346
1347How can it be otherwise, when all one's prospect, all one's landscapes,
1348historical pieces, portraits, flowers, still life, are nothing but a
1349single line, with no varieties except degrees of brightness and
1350obscurity?
1351
1352It was not always thus. Colour, if Tradition speaks the truth, once
1353for the space of half a dozen centuries or more, threw a transient
1354splendour over the lives of our ancestors in the remotest ages. Some
1355private individual--a Pentagon whose name is variously reported--having
1356casually discovered the constituents of the simpler colours and a
1357rudimentary method of painting, is said to have begun decorating first
1358his house, then his slaves, then his Father, his Sons, and Grandsons,
1359lastly himself. The convenience as well as the beauty of the results
1360commended themselves to all. Wherever Chromatistes,--for by that name
1361the most trustworthy authorities concur in calling him,--turned his
1362variegated frame, there he at once excited attention, and attracted
1363respect. No one now needed to "feel" him; no one mistook his front for
1364his back; all his movements were readily ascertained by his neighbours
1365without the slightest strain on their powers of calculation; no one
1366jostled him, or failed to make way for him; his voice was saved the
1367labour of that exhausting utterance by which we colourless Squares and
1368Pentagons are often forced to proclaim our individuality when we move
1369amid a crowd of ignorant Isosceles.
1370
1371The fashion spread like wildfire. Before a week was over, every Square
1372and Triangle in the district had copied the example of Chromatistes,
1373and only a few of the more conservative Pentagons still held out. A
1374month or two found even the Dodecagons infected with the innovation. A
1375year had not elapsed before the habit had spread to all but the very
1376highest of the Nobility. Needless to say, the custom soon made its way
1377from the district of Chromatistes to surrounding regions; and within
1378two generations no one in all Flatland was colourless except the Women
1379and the Priests.
1380
1381Here Nature herself appeared to erect a barrier, and to plead against
1382extending the innovation to these two classes. Many-sidedness was
1383almost essential as a pretext for the Innovators. "Distinction of
1384sides is intended by Nature to imply distinction of colours"--such was
1385the sophism which in those days flew from mouth to mouth, converting
1386whole towns at a time to the new culture. But manifestly to our
1387Priests and Women this adage did not apply. The latter had only one
1388side, and therefore--plurally and pedantically speaking--NO SIDES. The
1389former--if at least they would assert their claim to be really and
1390truly Circles, and not mere high-class Polygons with an infinitely
1391large number of infinitesimally small sides--were in the habit of
1392boasting (what Women confessed and deplored) that they also had no
1393sides, being blessed with a perimeter of one line, or, in other words,
1394a Circumference. Hence it came to pass that these two Classes could
1395see no force in the so-called axiom about "Distinction of Sides
1396implying Distinction of Colour"; and when all others had succumbed to
1397the fascinations of corporal decoration, the Priests and the Women
1398alone still remained pure from the pollution of paint.
1399
1400Immoral, licentious, anarchical, unscientific--call them by what names
1401you will--yet, from an aesthetic point of view, those ancient days of
1402the Colour Revolt were the glorious childhood of Art in Flatland--a
1403childhood, alas, that never ripened into manhood, nor even reached the
1404blossom of youth. To live was then in itself a delight, because living
1405implied seeing. Even at a small party, the company was a pleasure to
1406behold; the richly varied hues of the assembly in a church or theatre
1407are said to have more than once proved too distracting for our greatest
1408teachers and actors; but most ravishing of all is said to have been the
1409unspeakable magnificence of a military review.
1410
1411The sight of a line of battle of twenty thousand Isosceles suddenly
1412facing about, and exchanging the sombre black of their bases for the
1413orange and purple of the two sides including their acute angle; the
1414militia of the Equilateral Triangles tricoloured in red, white, and
1415blue; the mauve, ultra-marine, gamboge, and burnt umber of the Square
1416artillerymen rapidly rotating near their vermilion guns; the dashing
1417and flashing of the five-coloured and six-coloured Pentagons and
1418Hexagons careering across the field in their offices of surgeons,
1419geometricians and aides-de-camp--all these may well have been
1420sufficient to render credible the famous story how an illustrious
1421Circle, overcome by the artistic beauty of the forces under his
1422command, threw aside his marshal's baton and his royal crown,
1423exclaiming that he henceforth exchanged them for the artist's pencil.
1424How great and glorious the sensuous development of these days must have
1425been is in part indicated by the very language and vocabulary of the
1426period. The commonest utterances of the commonest citizens in the time
1427of the Colour Revolt seem to have been suffused with a richer tinge of
1428word or thought; and to that era we are even now indebted for our
1429finest poetry and for whatever rhythm still remains in the more
1430scientific utterance of these modern days.
1431
1432
1433
1434
1435Section 9. Of the Universal Colour Bill
1436
1437
1438
1439But meanwhile the intellectual Arts were fast decaying.
1440
1441The Art of Sight Recognition, being no longer needed, was no longer
1442practised; and the studies of Geometry, Statics, Kinetics, and other
1443kindred subjects, came soon to be considered superfluous, and fell into
1444disrespect and neglect even at our University. The inferior Art of
1445Feeling speedily experienced the same fate at our Elementary Schools.
1446Then the Isosceles classes, asserting that the Specimens were no longer
1447used nor needed, and refusing to pay the customary tribute from the
1448Criminal classes to the service of Education, waxed daily more numerous
1449and more insolent on the strength of their immunity from the old burden
1450which had formerly exercised the twofold wholesome effect of at once
1451taming their brutal nature and thinning their excessive numbers.
1452
1453Year by year the Soldiers and Artisans began more vehemently to
1454assert--and with increasing truth--that there was no great difference
1455between them and the very highest class of Polygons, now that they were
1456raised to an equality with the latter, and enabled to grapple with all
1457the difficulties and solve all the problems of life, whether Statical
1458or Kinetical, by the simple process of Colour Recognition. Not content
1459with the natural neglect into which Sight Recognition was falling, they
1460began boldly to demand the legal prohibition of all "monopolizing and
1461aristocratic Arts" and the consequent abolition of all endowments for
1462the studies of Sight Recognition, Mathematics, and Feeling. Soon, they
1463began to insist that inasmuch as Colour, which was a second Nature, had
1464destroyed the need of aristocratic distinctions, the Law should follow
1465in the same path, and that henceforth all individuals and all classes
1466should be recognized as absolutely equal and entitled to equal rights.
1467
1468Finding the higher Orders wavering and undecided, the leaders of the
1469Revolution advanced still further in their requirements, and at last
1470demanded that all classes alike, the Priests and the Women not
1471excepted, should do homage to Colour by submitting to be painted. When
1472it was objected that Priests and Women had no sides, they retorted that
1473Nature and Expediency concurred in dictating that the front half of
1474every human being (that is to say, the half containing his eye and
1475mouth) should be distinguishable from his hinder half. They therefore
1476brought before a general and extraordinary Assembly of all the States
1477of Flatland a Bill proposing that in every Woman the half containing
1478the eye and mouth should be coloured red, and the other half green.
1479The Priests were to be painted in the same way, red being applied to
1480that semicircle in which the eye and mouth formed the middle point;
1481while the other or hinder semicircle was to be coloured green.
1482
1483There was no little cunning in this proposal, which indeed emanated not
1484from any Isosceles--for no being so degraded would have had angularity
1485enough to appreciate, much less to devise, such a model of
1486state-craft--but from an Irregular Circle who, instead of being
1487destroyed in his childhood, was reserved by a foolish indulgence to
1488bring desolation on his country and destruction on myriads of his
1489followers.
1490
1491On the one hand the proposition was calculated to bring the Women in
1492all classes over to the side of the Chromatic Innovation. For by
1493assigning to the Women the same two colours as were assigned to the
1494Priests, the Revolutionists thereby ensured that, in certain positions,
1495every Woman would appear like a Priest, and be treated with
1496corresponding respect and deference--a prospect that could not fail to
1497attract the Female Sex in a mass.
1498
1499But by some of my Readers the possibility of the identical appearance
1500of Priests and Women, under the new Legislation, may not be recognized;
1501if so, a word or two will make it obvious.
1502
1503Imagine a woman duly decorated, according to the new Code; with the
1504front half (i.e. the half containing eye and mouth) red, and with the
1505hinder half green. Look at her from one side. Obviously you will see
1506a straight line, HALF RED, HALF GREEN.
1507
1508
1509[Illustration 5]
1510
1511[ASCII approximation follows]
1512
1513[for simplicity's sake, the circle is approximated as an octogon]
1514
1515
1516 M
1517 _____
1518 / \ - C_
1519 / \|| - _
1520 | || - _
1521 A|- - - - - - -||B- - - - - -_-+(> (Eye)
1522 | || _ -
1523 \ /||_ -
1524 \ _____ / - D
1525
1526
1527Now imagine a Priest, whose mouth is at M, and whose front semicircle
1528(AMB) is consequently coloured red, while his hinder semicircle is
1529green; so that the diameter AB divides the green from the red. If you
1530contemplate the Great Man so as to have your eye in the same straight
1531line as his dividing diameter (AB), what you will see will be a
1532straight line (CBD), of which ONE HALF (CB) WILL BE RED, AND THE OTHER
1533(BD) GREEN. The whole line (CD) will be rather shorter perhaps than
1534that of a full-sized Woman, and will shade off more rapidly towards its
1535extremities; but the identity of the colours would give you an
1536immediate impression of identity of Class, making you neglectful of
1537other details. Bear in mind the decay of Sight Recognition which
1538threatened society at the time of the Colour Revolt; add too the
1539certainty that Women would speedily learn to shade off their
1540extremities so as to imitate the Circles; it must then be surely
1541obvious to you, my dear Reader, that the Colour Bill placed us under a
1542great danger of confounding a Priest with a young Woman.
1543
1544How attractive this prospect must have been to the Frail Sex may
1545readily be imagined. They anticipated with delight the confusion that
1546would ensue. At home they might hear political and ecclesiastical
1547secrets intended not for them but for their husbands and brothers, and
1548might even issue commands in the name of a priestly Circle; out of
1549doors the striking combination of red and green, without addition of
1550any other colours, would be sure to lead the common people into endless
1551mistakes, and the Women would gain whatever the Circles lost, in the
1552deference of the passers by. As for the scandal that would befall the
1553Circular Class if the frivolous and unseemly conduct of the Women were
1554imputed to them, and as to the consequent subversion of the
1555Constitution, the Female Sex could not be expected to give a thought to
1556these considerations. Even in the households of the Circles, the Women
1557were all in favour of the Universal Colour Bill.
1558
1559The second object aimed at by the Bill was the gradual demoralization
1560of the Circles themselves. In the general intellectual decay they
1561still preserved their pristine clearness and strength of understanding.
1562From their earliest childhood, familiarized in their Circular
1563households with the total absence of Colour, the Nobles alone preserved
1564the Sacred Art of Sight Recognition, with all the advantages that
1565result from that admirable training of the intellect. Hence, up to the
1566date of the introduction of the Universal Colour Bill, the Circles had
1567not only held their own, but even increased their lead of the other
1568classes by abstinence from the popular fashion.
1569
1570Now therefore the artful Irregular whom I described above as the real
1571author of this diabolical Bill, determined at one blow to lower the
1572status of the Hierarchy by forcing them to submit to the pollution of
1573Colour, and at the same time to destroy their domestic opportunities of
1574training in the Art of Sight Recognition, so as to enfeeble their
1575intellects by depriving them of their pure and colourless homes. Once
1576subjected to the chromatic taint, every parental and every childish
1577Circle would demoralize each other. Only in discerning between the
1578Father and the Mother would the Circular infant find problems for the
1579exercise of its understanding--problems too often likely to be
1580corrupted by maternal impostures with the result of shaking the child's
1581faith in all logical conclusions. Thus by degrees the intellectual
1582lustre of the Priestly Order would wane, and the road would then lie
1583open for a total destruction of all Aristocratic Legislature and for
1584the subversion of our Privileged Classes.
1585
1586
1587
1588
1589Section 10. Of the Suppression of the Chromatic Sedition
1590
1591
1592
1593The agitation for the Universal Colour Bill continued for three years;
1594and up to the last moment of that period it seemed as though Anarchy
1595were destined to triumph.
1596
1597A whole army of Polygons, who turned out to fight as private soldiers,
1598was utterly annihilated by a superior force of Isosceles Triangles--the
1599Squares and Pentagons meanwhile remaining neutral. Worse than all,
1600some of the ablest Circles fell a prey to conjugal fury. Infuriated by
1601political animosity, the wives in many a noble household wearied their
1602lords with prayers to give up their opposition to the Colour Bill; and
1603some, finding their entreaties fruitless, fell on and slaughtered their
1604innocent children and husband, perishing themselves in the act of
1605carnage. It is recorded that during that triennial agitation no less
1606than twenty-three Circles perished in domestic discord.
1607
1608Great indeed was the peril. It seemed as though the Priests had no
1609choice between submission and extermination; when suddenly the course
1610of events was completely changed by one of those picturesque incidents
1611which Statesmen ought never to neglect, often to anticipate, and
1612sometimes perhaps to originate, because of the absurdly
1613disproportionate power with which they appeal to the sympathies of the
1614populace.
1615
1616It happened that an Isosceles of a low type, with a brain little if at
1617all above four degrees--accidentally dabbling in the colours of some
1618Tradesman whose shop he had plundered--painted himself, or caused
1619himself to be painted (for the story varies) with the twelve colours of
1620a Dodecagon. Going into the Market Place he accosted in a feigned
1621voice a maiden, the orphan daughter of a noble Polygon, whose affection
1622in former days he had sought in vain; and by a series of
1623deceptions--aided, on the one side, by a string of lucky accidents too
1624long to relate, and on the other, by an almost inconceivable fatuity
1625and neglect of ordinary precautions on the part of the relations of the
1626bride--he succeeded in consummating the marriage. The unhappy girl
1627committed suicide on discovering the fraud to which she had been
1628subjected.
1629
1630When the news of this catastrophe spread from State to State the minds
1631of the Women were violently agitated. Sympathy with the miserable
1632victim and anticipations of similar deceptions for themselves, their
1633sisters, and their daughters, made them now regard the Colour Bill in
1634an entirely new aspect. Not a few openly avowed themselves converted
1635to antagonism; the rest needed only a slight stimulus to make a similar
1636avowal. Seizing this favourable opportunity, the Circles hastily
1637convened an extraordinary Assembly of the States; and besides the usual
1638guard of Convicts, they secured the attendance of a large number of
1639reactionary Women.
1640
1641Amidst an unprecedented concourse, the Chief Circle of those days--by
1642name Pantocyclus--arose to find himself hissed and hooted by a hundred
1643and twenty thousand Isosceles. But he secured silence by declaring
1644that henceforth the Circles would enter on a policy of Concession;
1645yielding to the wishes of the majority, they would accept the Colour
1646Bill. The uproar being at once converted to applause, he invited
1647Chromatistes, the leader of the Sedition, into the centre of the hall,
1648to receive in the name of his followers the submission of the
1649Hierarchy. Then followed a speech, a masterpiece of rhetoric, which
1650occupied nearly a day in the delivery, and to which no summary can do
1651justice.
1652
1653With a grave appearance of impartiality he declared that as they were
1654now finally committing themselves to Reform or Innovation, it was
1655desirable that they should take one last view of the perimeter of the
1656whole subject, its defects as well as its advantages. Gradually
1657introducing the mention of the dangers to the Tradesmen, the
1658Professional Classes and the Gentlemen, he silenced the rising murmurs
1659of the Isosceles by reminding them that, in spite of all these defects,
1660he was willing to accept the Bill if it was approved by the majority.
1661But it was manifest that all, except the Isosceles, were moved by his
1662words and were either neutral or averse to the Bill.
1663
1664Turning now to the Workmen he asserted that their interests must not be
1665neglected, and that, if they intended to accept the Colour Bill, they
1666ought at least to do so with full view of the consequences. Many of
1667them, he said, were on the point of being admitted to the class of the
1668Regular Triangles; others anticipated for their children a distinction
1669they could not hope for themselves. That honourable ambition would now
1670have to be sacrificed. With the universal adoption of Colour, all
1671distinctions would cease; Regularity would be confused with
1672Irregularity; development would give place to retrogression; the
1673Workman would in a few generations be degraded to the level of the
1674Military, or even the Convict Class; political power would be in the
1675hands of the greatest number, that is to say the Criminal Classes, who
1676were already more numerous than the Workmen, and would soon out-number
1677all the other Classes put together when the usual Compensative Laws of
1678Nature were violated.
1679
1680A subdued murmur of assent ran through the ranks of the Artisans, and
1681Chromatistes, in alarm, attempted to step forward and address them.
1682But he found himself encompassed with guards and forced to remain
1683silent while the Chief Circle in a few impassioned words made a final
1684appeal to the Women, exclaiming that, if the Colour Bill passed, no
1685marriage would henceforth be safe, no woman's honour secure; fraud,
1686deception, hypocrisy would pervade every household; domestic bliss
1687would share the fate of the Constitution and pass to speedy perdition.
1688"Sooner than this," he cried, "Come death."
1689
1690At these words, which were the preconcerted signal for action, the
1691Isosceles Convicts fell on and transfixed the wretched Chromatistes;
1692the Regular Classes, opening their ranks, made way for a band of Women
1693who, under direction of the Circles, moved, back foremost, invisibly
1694and unerringly upon the unconscious soldiers; the Artisans, imitating
1695the example of their betters, also opened their ranks. Meantime bands
1696of Convicts occupied every entrance with an impenetrable phalanx.
1697
1698The battle, or rather carnage, was of short duration. Under the
1699skillful generalship of the Circles almost every Woman's charge was
1700fatal and very many extracted their sting uninjured, ready for a second
1701slaughter. But no second blow was needed; the rabble of the Isosceles
1702did the rest of the business for themselves. Surprised, leader-less,
1703attacked in front by invisible foes, and finding egress cut off by the
1704Convicts behind them, they at once--after their manner--lost all
1705presence of mind, and raised the cry of "treachery". This sealed their
1706fate. Every Isosceles now saw and felt a foe in every other. In half
1707an hour not one of that vast multitude was living; and the fragments of
1708seven score thousand of the Criminal Class slain by one another's
1709angles attested the triumph of Order.
1710
1711The Circles delayed not to push their victory to the uttermost. The
1712Working Men they spared but decimated. The Militia of the Equilaterals
1713was at once called out; and every Triangle suspected of Irregularity on
1714reasonable grounds, was destroyed by Court Martial, without the
1715formality of exact measurement by the Social Board. The homes of the
1716Military and Artisan classes were inspected in a course of visitations
1717extending through upwards of a year; and during that period every town,
1718village, and hamlet was systematically purged of that excess of the
1719lower orders which had been brought about by the neglect to pay the
1720tribute of Criminals to the Schools and University, and by the
1721violation of the other natural Laws of the Constitution of Flatland.
1722Thus the balance of classes was again restored.
1723
1724Needless to say that henceforth the use of Colour was abolished, and
1725its possession prohibited. Even the utterance of any word denoting
1726Colour, except by the Circles or by qualified scientific teachers, was
1727punished by a severe penalty. Only at our University in some of the
1728very highest and most esoteric classes--which I myself have never been
1729privileged to attend--it is understood that the sparing use of Colour
1730is still sanctioned for the purpose of illustrating some of the deeper
1731problems of mathematics. But of this I can only speak from hearsay.
1732
1733Elsewhere in Flatland, Colour is now non-existent. The art of making
1734it is known to only one living person, the Chief Circle for the time
1735being; and by him it is handed down on his death-bed to none but his
1736Successor. One manufactory alone produces it; and, lest the secret
1737should be betrayed, the Workmen are annually consumed, and fresh ones
1738introduced. So great is the terror with which even now our Aristocracy
1739looks back to the far-distant days of the agitation for the Universal
1740Colour Bill.
1741
1742
1743
1744
1745Section 11. Concerning our Priests
1746
1747
1748
1749It is high time that I should pass from these brief and discursive
1750notes about things in Flatland to the central event of this book, my
1751initiation into the mysteries of Space. THAT is my subject; all that
1752has gone before is merely preface.
1753
1754For this reason I must omit many matters of which the explanation would
1755not, I flatter myself, be without interest for my Readers: as for
1756example, our method of propelling and stopping ourselves, although
1757destitute of feet; the means by which we give fixity to structures of
1758wood, stone, or brick, although of course we have no hands, nor can we
1759lay foundations as you can, nor avail ourselves of the lateral pressure
1760of the earth; the manner in which the rain originates in the intervals
1761between our various zones, so that the northern regions do not
1762intercept the moisture from falling on the southern; the nature of our
1763hills and mines, our trees and vegetables, our seasons and harvests;
1764our Alphabet and method of writing, adapted to our linear tablets;
1765these and a hundred other details of our physical existence I must pass
1766over, nor do I mention them now except to indicate to my readers that
1767their omission proceeds not from forgetfulness on the part of the
1768author, but from his regard for the time of the Reader.
1769
1770Yet before I proceed to my legitimate subject some few final remarks
1771will no doubt be expected by my Readers upon those pillars and
1772mainstays of the Constitution of Flatland, the controllers of our
1773conduct and shapers of our destiny, the objects of universal homage and
1774almost of adoration: need I say that I mean our Circles or Priests?
1775
1776When I call them Priests, let me not be understood as meaning no more
1777than the term denotes with you. With us, our Priests are
1778Administrators of all Business, Art, and Science; Directors of Trade,
1779Commerce, Generalship, Architecture, Engineering, Education,
1780Statesmanship, Legislature, Morality, Theology; doing nothing
1781themselves, they are the Causes of everything worth doing, that is done
1782by others.
1783
1784Although popularly everyone called a Circle is deemed a Circle, yet
1785among the better educated Classes it is known that no Circle is really
1786a Circle, but only a Polygon with a very large number of very small
1787sides. As the number of the sides increases, a Polygon approximates to
1788a Circle; and, when the number is very great indeed, say for example
1789three or four hundred, it is extremely difficult for the most delicate
1790touch to feel any polygonal angles. Let me say rather, it WOULD be
1791difficult: for, as I have shown above, Recognition by Feeling is
1792unknown among the highest society, and to FEEL a Circle would be
1793considered a most audacious insult. This habit of abstention from
1794Feeling in the best society enables a Circle the more easily to sustain
1795the veil of mystery in which, from his earliest years, he is wont to
1796enwrap the exact nature of his Perimeter or Circumference. Three feet
1797being the average Perimeter it follows that, in a Polygon of three
1798hundred sides each side will be no more than the hundredth part of a
1799foot in length, or little more than the tenth part of an inch; and in a
1800Polygon of six or seven hundred sides the sides are little larger than
1801the diameter of a Spaceland pin-head. It is always assumed, by
1802courtesy, that the Chief Circle for the time being has ten thousand
1803sides.
1804
1805The ascent of the posterity of the Circles in the social scale is not
1806restricted, as it is among the lower Regular classes, by the Law of
1807Nature which limits the increase of sides to one in each generation.
1808If it were so, the number of sides in a Circle would be a mere question
1809of pedigree and arithmetic, and the four hundred and ninety-seventh
1810descendant of an Equilateral Triangle would necessarily be a Polygon
1811with five hundred sides. But this is not the case. Nature's Law
1812prescribes two antagonistic decrees affecting Circular propagation;
1813first, that as the race climbs higher in the scale of development, so
1814development shall proceed at an accelerated pace; second, that in the
1815same proportion, the race shall become less fertile. Consequently in
1816the home of a Polygon of four or five hundred sides it is rare to find
1817a son; more than one is never seen. On the other hand the son of a
1818five-hundred-sided Polygon has been known to possess five hundred and
1819fifty, or even six hundred sides.
1820
1821Art also steps in to help the process of the higher Evolution. Our
1822physicians have discovered that the small and tender sides of an infant
1823Polygon of the higher class can be fractured, and his whole frame
1824re-set, with such exactness that a Polygon of two or three hundred
1825sides sometimes--by no means always, for the process is attended with
1826serious risk--but sometimes overleaps two or three hundred generations,
1827and as it were doubles at a stroke, the number of his progenitors and
1828the nobility of his descent.
1829
1830Many a promising child is sacrificed in this way. Scarcely one out of
1831ten survives. Yet so strong is the parental ambition among those
1832Polygons who are, as it were, on the fringe of the Circular class, that
1833it is very rare to find a Nobleman of that position in society, who has
1834neglected to place his first-born in the Circular Neo-Therapeutic
1835Gymnasium before he has attained the age of a month.
1836
1837One year determines success or failure. At the end of that time the
1838child has, in all probability, added one more to the tombstones that
1839crowd the Neo-Therapeutic Cemetery; but on rare occasions a glad
1840procession bears back the little one to his exultant parents, no longer
1841a Polygon, but a Circle, at least by courtesy: and a single instance of
1842so blessed a result induces multitudes of Polygonal parents to submit
1843to similar domestic sacrifices, which have a dissimilar issue.
1844
1845
1846
1847
1848Section 12. Of the Doctrine of our Priests
1849
1850
1851
1852As to the doctrine of the Circles it may briefly be summed up in a
1853single maxim, "Attend to your Configuration." Whether political,
1854ecclesiastical, or moral, all their teaching has for its object the
1855improvement of individual and collective Configuration--with special
1856reference of course to the Configuration of the Circles, to which all
1857other objects are subordinated.
1858
1859It is the merit of the Circles that they have effectually suppressed
1860those ancient heresies which led men to waste energy and sympathy in
1861the vain belief that conduct depends upon will, effort, training,
1862encouragement, praise, or anything else but Configuration. It was
1863Pantocyclus--the illustrious Circle mentioned above, as the queller of
1864the Colour Revolt--who first convinced mankind that Configuration makes
1865the man; that if, for example, you are born an Isosceles with two
1866uneven sides, you will assuredly go wrong unless you have them made
1867even--for which purpose you must go to the Isosceles Hospital;
1868similarly, if you are a Triangle, or Square, or even a Polygon, born
1869with any Irregularity, you must be taken to one of the Regular
1870Hospitals to have your disease cured; otherwise you will end your days
1871in the State Prison or by the angle of the State Executioner.
1872
1873All faults or defects, from the slightest misconduct to the most
1874flagitious crime, Pantocyclus attributed to some deviation from perfect
1875Regularity in the bodily figure, caused perhaps (if not congenital) by
1876some collision in a crowd; by neglect to take exercise, or by taking
1877too much of it; or even by a sudden change of temperature, resulting in
1878a shrinkage or expansion in some too susceptible part of the frame.
1879Therefore, concluded that illustrious Philosopher, neither good conduct
1880nor bad conduct is a fit subject, in any sober estimation, for either
1881praise or blame. For why should you praise, for example, the integrity
1882of a Square who faithfully defends the interests of his client, when
1883you ought in reality rather to admire the exact precision of his right
1884angles? Or again, why blame a lying, thievish Isosceles when you ought
1885rather to deplore the incurable inequality of his sides?
1886
1887Theoretically, this doctrine is unquestionable; but it has practical
1888drawbacks. In dealing with an Isosceles, if a rascal pleads that he
1889cannot help stealing because of his unevenness, you reply that for that
1890very reason, because he cannot help being a nuisance to his neighbours,
1891you, the Magistrate, cannot help sentencing him to be consumed--and
1892there's an end of the matter. But in little domestic difficulties,
1893where the penalty of consumption, or death, is out of the question,
1894this theory of Configuration sometimes comes in awkwardly; and I must
1895confess that occasionally when one of my own Hexagonal Grandsons pleads
1896as an excuse for his disobedience that a sudden change of the
1897temperature has been too much for his Perimeter, and that I ought to
1898lay the blame not on him but on his Configuration, which can only be
1899strengthened by abundance of the choicest sweetmeats, I neither see my
1900way logically to reject, nor practically to accept, his conclusions.
1901
1902For my own part, I find it best to assume that a good sound scolding or
1903castigation has some latent and strengthening influence on my
1904Grandson's Configuration; though I own that I have no grounds for
1905thinking so. At all events I am not alone in my way of extricating
1906myself from this dilemma; for I find that many of the highest Circles,
1907sitting as Judges in law courts, use praise and blame towards Regular
1908and Irregular Figures; and in their homes I know by experience that,
1909when scolding their children, they speak about "right" or "wrong" as
1910vehemently and passionately as if they believed that these names
1911represented real existences, and that a human Figure is really capable
1912of choosing between them.
1913
1914Constantly carrying out their policy of making Configuration the
1915leading idea in every mind, the Circles reverse the nature of that
1916Commandment which in Spaceland regulates the relations between parents
1917and children. With you, children are taught to honour their parents;
1918with us--next to the Circles, who are the chief object of universal
1919homage--a man is taught to honour his Grandson, if he has one; or, if
1920not, his Son. By "honour", however, is by no means meant "indulgence",
1921but a reverent regard for their highest interests: and the Circles
1922teach that the duty of fathers is to subordinate their own interests to
1923those of posterity, thereby advancing the welfare of the whole State as
1924well as that of their own immediate descendants.
1925
1926The weak point in the system of the Circles--if a humble Square may
1927venture to speak of anything Circular as containing any element of
1928weakness--appears to me to be found in their relations with Women.
1929
1930As it is of the utmost importance for Society that Irregular births
1931should be discouraged, it follows that no Woman who has any
1932Irregularities in her ancestry is a fit partner for one who desires
1933that his posterity should rise by regular degrees in the social scale.
1934
1935Now the Irregularity of a Male is a matter of measurement; but as all
1936Women are straight, and therefore visibly Regular so to speak, one has
1937to devise some other means of ascertaining what I may call their
1938invisible Irregularity, that is to say their potential Irregularities
1939as regards possible offspring. This is effected by carefully-kept
1940pedigrees, which are preserved and supervised by the State; and without
1941a certified pedigree no Woman is allowed to marry.
1942
1943Now it might have been supposed that a Circle--proud of his ancestry
1944and regardful for a posterity which might possibly issue hereafter in a
1945Chief Circle--would be more careful than any other to choose a wife who
1946had no blot on her escutcheon. But it is not so. The care in choosing
1947a Regular wife appears to diminish as one rises in the social scale.
1948Nothing would induce an aspiring Isosceles, who had hopes of generating
1949an Equilateral Son, to take a wife who reckoned a single Irregularity
1950among her Ancestors; a Square or Pentagon, who is confident that his
1951family is steadily on the rise, does not inquire above the
1952five-hundredth generation; a Hexagon or Dodecagon is even more careless
1953of the wife's pedigree; but a Circle has been known deliberately to
1954take a wife who has had an Irregular Great-Grandfather, and all because
1955of some slight superiority of lustre, or because of the charms of a low
1956voice--which, with us, even more than you, is thought "an excellent
1957thing in Woman".
1958
1959Such ill-judged marriages are, as might be expected, barren, if they do
1960not result in positive Irregularity or in diminution of sides; but none
1961of these evils have hitherto proved sufficiently deterrent. The loss
1962of a few sides in a highly-developed Polygon is not easily noticed, and
1963is sometimes compensated by a successful operation in the
1964Neo-Therapeutic Gymnasium, as I have described above; and the Circles
1965are too much disposed to acquiesce in infecundity as a Law of the
1966superior development. Yet, if this evil be not arrested, the gradual
1967diminution of the Circular class may soon become more rapid, and the
1968time may be not far distant when, the race being no longer able to
1969produce a Chief Circle, the Constitution of Flatland must fall.
1970
1971One other word of warning suggests itself to me, though I cannot so
1972easily mention a remedy; and this also refers to our relations with
1973Women. About three hundred years ago, it was decreed by the Chief
1974Circle that, since women are deficient in Reason but abundant in
1975Emotion, they ought no longer to be treated as rational, nor receive
1976any mental education. The consequence was that they were no longer
1977taught to read, nor even to master Arithmetic enough to enable them to
1978count the angles of their husband or children; and hence they sensibly
1979declined during each generation in intellectual power. And this system
1980of female non-education or quietism still prevails.
1981
1982My fear is that, with the best intentions, this policy has been carried
1983so far as to react injuriously on the Male Sex.
1984
1985For the consequence is that, as things now are, we Males have to lead a
1986kind of bi-lingual, and I may almost say bi-mental, existence. With
1987Women, we speak of "love", "duty", "right", "wrong", "pity", "hope",
1988and other irrational and emotional conceptions, which have no
1989existence, and the fiction of which has no object except to control
1990feminine exuberances; but among ourselves, and in our books, we have an
1991entirely different vocabulary and I may almost say, idiom. "Love" then
1992becomes "the anticipation of benefits"; "duty" becomes "necessity" or
1993"fitness"; and other words are correspondingly transmuted. Moreover,
1994among Women, we use language implying the utmost deference for their
1995Sex; and they fully believe that the Chief Circle Himself is not more
1996devoutly adored by us than they are: but behind their backs they are
1997both regarded and spoken of--by all except the very young--as being
1998little better than "mindless organisms".
1999
2000Our Theology also in the Women's chambers is entirely different from
2001our Theology elsewhere.
2002
2003Now my humble fear is that this double training, in language as well as
2004in thought, imposes somewhat too heavy a burden upon the young,
2005especially when, at the age of three years old, they are taken from the
2006maternal care and taught to unlearn the old language--except for the
2007purpose of repeating it in the presence of their Mothers and
2008Nurses--and to learn the vocabulary and idiom of science. Already
2009methinks I discern a weakness in the grasp of mathematical truth at the
2010present time as compared with the more robust intellect of our
2011ancestors three hundred years ago. I say nothing of the possible
2012danger if a Woman should ever surreptitiously learn to read and convey
2013to her Sex the result of her perusal of a single popular volume; nor of
2014the possibility that the indiscretion or disobedience of some infant
2015Male might reveal to a Mother the secrets of the logical dialect. On
2016the simple ground of the enfeebling of the Male intellect, I rest this
2017humble appeal to the highest Authorities to reconsider the regulations
2018of Female education.
2019
2020
2021
2022
2023
2024
2025PART II: OTHER WORLDS
2026
2027"O brave new worlds, that have such people in them!"
2028
2029
2030
2031
2032
2033
2034Section 13. How I had a Vision of Lineland
2035
2036
2037
2038It was the last day but one of the 1999th year of our era, and the
2039first day of the Long Vacation. Having amused myself till a late hour
2040with my favourite recreation of Geometry, I had retired to rest with an
2041unsolved problem in my mind. In the night I had a dream.
2042
2043I saw before me a vast multitude of small Straight Lines (which I
2044naturally assumed to be Women) interspersed with other Beings still
2045smaller and of the nature of lustrous points--all moving to and fro in
2046one and the same Straight Line, and, as nearly as I could judge, with
2047the same velocity.
2048
2049A noise of confused, multitudinous chirping or twittering issued from
2050them at intervals as long as they were moving; but sometimes they
2051ceased from motion, and then all was silence.
2052
2053Approaching one of the largest of what I thought to be Women, I
2054accosted her, but received no answer. A second and a third appeal on
2055my part were equally ineffectual. Losing patience at what appeared to
2056me intolerable rudeness, I brought my mouth into a position full in
2057front of her mouth so as to intercept her motion, and loudly repeated
2058my question, "Woman, what signifies this concourse, and this strange
2059and confused chirping, and this monotonous motion to and fro in one and
2060the same Straight Line?"
2061
2062
2063[Illustration 6]
2064
2065[ASCII approximation follows]
2066
2067
2068 My view of Lineland
2069
2070 ---------
2071 | |
2072 | Myself|
2073 | |
2074 My eye o--------
2075
2076
2077 Women A boy Men The KING Men A boy Women
2078 + + + + - --- -- -- -- -- (>----<) -- -- -- -- --- - + + + +
2079 ^ ^
2080 The KING'S eyes
2081 much larger than the reality
2082 shewing that HIS MAJESTY
2083 could see nothing but a point.
2084
2085
2086"I am no Woman," replied the small Line. "I am the Monarch of the
2087world. But thou, whence intrudest thou into my realm of Lineland?"
2088Receiving this abrupt reply, I begged pardon if I had in any way
2089startled or molested his Royal Highness; and describing myself as a
2090stranger I besought the King to give me some account of his dominions.
2091But I had the greatest possible difficulty in obtaining any information
2092on points that really interested me; for the Monarch could not refrain
2093from constantly assuming that whatever was familiar to him must also be
2094known to me and that I was simulating ignorance in jest. However, by
2095persevering questions I elicited the following facts:
2096
2097It seemed that this poor ignorant Monarch--as he called himself--was
2098persuaded that the Straight Line which he called his Kingdom, and in
2099which he passed his existence, constituted the whole of the world, and
2100indeed the whole of Space. Not being able either to move or to see,
2101save in his Straight Line, he had no conception of anything out of it.
2102Though he had heard my voice when I first addressed him, the sounds had
2103come to him in a manner so contrary to his experience that he had made
2104no answer, "seeing no man", as he expressed it, "and hearing a voice as
2105it were from my own intestines." Until the moment when I placed my
2106mouth in his World, he had neither seen me, nor heard anything except
2107confused sounds beating against--what I called his side, but what he
2108called his INSIDE or STOMACH; nor had he even now the least conception
2109of the region from which I had come. Outside his World, or Line, all
2110was a blank to him; nay, not even a blank, for a blank implies Space;
2111say, rather, all was non-existent.
2112
2113His subjects--of whom the small Lines were men and the Points
2114Women--were all alike confined in motion and eye-sight to that single
2115Straight Line, which was their World. It need scarcely be added that
2116the whole of their horizon was limited to a Point; nor could any one
2117ever see anything but a Point. Man, woman, child, thing--each was a
2118Point to the eye of a Linelander. Only by the sound of the voice could
2119sex or age be distinguished. Moreover, as each individual occupied the
2120whole of the narrow path, so to speak, which constituted his Universe,
2121and no one could move to the right or left to make way for passers by,
2122it followed that no Linelander could ever pass another. Once
2123neighbours, always neighbours. Neighbourhood with them was like
2124marriage with us. Neighbours remained neighbours till death did them
2125part.
2126
2127Such a life, with all vision limited to a Point, and all motion to a
2128Straight Line, seemed to me inexpressibly dreary; and I was surprised
2129to note the vivacity and cheerfulness of the King. Wondering whether
2130it was possible, amid circumstances so unfavourable to domestic
2131relations, to enjoy the pleasures of conjugal union, I hesitated for
2132some time to question his Royal Highness on so delicate a subject; but
2133at last I plunged into it by abruptly inquiring as to the health of his
2134family. "My wives and children," he replied, "are well and happy."
2135
2136Staggered at this answer--for in the immediate proximity of the Monarch
2137(as I had noted in my dream before I entered Lineland) there were none
2138but Men--I ventured to reply, "Pardon me, but I cannot imagine how your
2139Royal Highness can at any time either see or approach their Majesties,
2140when there are at least half a dozen intervening individuals, whom you
2141can neither see through, nor pass by? Is it possible that in Lineland
2142proximity is not necessary for marriage and for the generation of
2143children?"
2144
2145"How can you ask so absurd a question?" replied the Monarch. "If it
2146were indeed as you suggest, the Universe would soon be depopulated.
2147No, no; neighbourhood is needless for the union of hearts; and the
2148birth of children is too important a matter to have been allowed to
2149depend upon such an accident as proximity. You cannot be ignorant of
2150this. Yet since you are pleased to affect ignorance, I will instruct
2151you as if you were the veriest baby in Lineland. Know, then, that
2152marriages are consummated by means of the faculty of sound and the
2153sense of hearing.
2154
2155"You are of course aware that every Man has two mouths or voices--as
2156well as two eyes--a bass at one and a tenor at the other of his
2157extremities. I should not mention this, but that I have been unable to
2158distinguish your tenor in the course of our conversation." I replied
2159that I had but one voice, and that I had not been aware that his Royal
2160Highness had two. "That confirms my impression," said the King, "that
2161you are not a Man, but a feminine Monstrosity with a bass voice, and an
2162utterly uneducated ear. But to continue.
2163
2164"Nature having herself ordained that every Man should wed two wives--"
2165"Why two?" asked I. "You carry your affected simplicity too far", he
2166cried. "How can there be a completely harmonious union without the
2167combination of the Four in One, viz. the Bass and Tenor of the Man and
2168the Soprano and Contralto of the two Women?" "But supposing," said I,
2169"that a man should prefer one wife or three?" "It is impossible," he
2170said; "it is as inconceivable as that two and one should make five, or
2171that the human eye should see a Straight Line." I would have
2172interrupted him; but he proceeded as follows:
2173
2174"Once in the middle of each week a Law of Nature compels us to move to
2175and fro with a rhythmic motion of more than usual violence, which
2176continues for the time you would take to count a hundred and one. In
2177the midst of this choral dance, at the fifty-first pulsation, the
2178inhabitants of the Universe pause in full career, and each individual
2179sends forth his richest, fullest, sweetest strain. It is in this
2180decisive moment that all our marriages are made. So exquisite is the
2181adaptation of Bass to Treble, of Tenor to Contralto, that oftentimes
2182the Loved Ones, though twenty thousand leagues away, recognize at once
2183the responsive note of their destined Lover; and, penetrating the
2184paltry obstacles of distance, Love unites the three. The marriage in
2185that instant consummated results in a threefold Male and Female
2186offspring which takes its place in Lineland."
2187
2188"What! Always threefold?" said I. "Must one wife then always have
2189twins?"
2190
2191"Bass-voiced Monstrosity! yes," replied the King. "How else could the
2192balance of the Sexes be maintained, if two girls were not born for
2193every boy? Would you ignore the very Alphabet of Nature?" He ceased,
2194speechless for fury; and some time elapsed before I could induce him to
2195resume his narrative.
2196
2197"You will not, of course, suppose that every bachelor among us finds
2198his mates at the first wooing in this universal Marriage Chorus. On
2199the contrary, the process is by most of us many times repeated. Few
2200are the hearts whose happy lot it is at once to recognize in each
2201other's voices the partner intended for them by Providence, and to fly
2202into a reciprocal and perfectly harmonious embrace. With most of us
2203the courtship is of long duration. The Wooer's voices may perhaps
2204accord with one of the future wives, but not with both; or not, at
2205first, with either; or the Soprano and Contralto may not quite
2206harmonize. In such cases Nature has provided that every weekly Chorus
2207shall bring the three Lovers into closer harmony. Each trial of voice,
2208each fresh discovery of discord, almost imperceptibly induces the less
2209perfect to modify his or her vocal utterance so as to approximate to
2210the more perfect. And after many trials and many approximations, the
2211result is at last achieved. There comes a day at last, when, while the
2212wonted Marriage Chorus goes forth from universal Lineland, the three
2213far-off Lovers suddenly find themselves in exact harmony, and, before
2214they are awake, the wedded Triplet is rapt vocally into a duplicate
2215embrace; and Nature rejoices over one more marriage and over three more
2216births."
2217
2218
2219
2220
2221Section 14. How I vainly tried to explain the nature of Flatland
2222
2223
2224
2225Thinking that it was time to bring down the Monarch from his raptures
2226to the level of common sense, I determined to endeavour to open up to
2227him some glimpses of the truth, that is to say of the nature of things
2228in Flatland. So I began thus: "How does your Royal Highness
2229distinguish the shapes and positions of his subjects? I for my part
2230noticed by the sense of sight, before I entered your Kingdom, that some
2231of your people are Lines and others Points, and that some of the Lines
2232are larger--" "You speak of an impossibility," interrupted the King;
2233"you must have seen a vision; for to detect the difference between a
2234Line and a Point by the sense of sight is, as every one knows, in the
2235nature of things, impossible; but it can be detected by the sense of
2236hearing, and by the same means my shape can be exactly ascertained.
2237Behold me--I am a Line, the longest in Lineland, over six inches of
2238Space--" "Of Length", I ventured to suggest. "Fool," said he, "Space
2239is Length. Interrupt me again, and I have done."
2240
2241I apologized; but he continued scornfully, "Since you are impervious to
2242argument, you shall hear with your ears how by means of my two voices I
2243reveal my shape to my Wives, who are at this moment six thousand miles
2244seventy yards two feet eight inches away, the one to the North, the
2245other to the South. Listen, I call to them."
2246
2247He chirruped, and then complacently continued: "My wives at this
2248moment receiving the sound of one of my voices, closely followed by the
2249other, and perceiving that the latter reaches them after an interval in
2250which sound can traverse 6.457 inches, infer that one of my mouths is
22516.457 inches further from them than the other, and accordingly know my
2252shape to be 6.457 inches. But you will of course understand that my
2253wives do not make this calculation every time they hear my two voices.
2254They made it, once for all, before we were married. But they COULD
2255make it at any time. And in the same way I can estimate the shape of
2256any of my Male subjects by the sense of sound."
2257
2258"But how," said I, "if a Man feigns a Woman's voice with one of his two
2259voices, or so disguises his Southern voice that it cannot be recognized
2260as the echo of the Northern? May not such deceptions cause great
2261inconvenience? And have you no means of checking frauds of this kind
2262by commanding your neighbouring subjects to feel one another?" This of
2263course was a very stupid question, for feeling could not have answered
2264the purpose; but I asked with the view of irritating the Monarch, and I
2265succeeded perfectly.
2266
2267"What!" cried he in horror, "explain your meaning." "Feel, touch, come
2268into contact," I replied. "If you mean by FEELING," said the King,
2269"approaching so close as to leave no space between two individuals,
2270know, Stranger, that this offence is punishable in my dominions by
2271death. And the reason is obvious. The frail form of a Woman, being
2272liable to be shattered by such an approximation, must be preserved by
2273the State; but since Women cannot be distinguished by the sense of
2274sight from Men, the Law ordains universally that neither Man nor Woman
2275shall be approached so closely as to destroy the interval between the
2276approximator and the approximated.
2277
2278"And indeed what possible purpose would be served by this illegal and
2279unnatural excess of approximation which you call TOUCHING, when all the
2280ends of so brutal and coarse a process are attained at once more easily
2281and more exactly by the sense of hearing? As to your suggested danger
2282of deception, it is non-existent: for the Voice, being the essence of
2283one's Being, cannot be thus changed at will. But come, suppose that I
2284had the power of passing through solid things, so that I could
2285penetrate my subjects, one after another, even to the number of a
2286billion, verifying the size and distance of each by the sense of
2287FEELING: how much time and energy would be wasted in this clumsy and
2288inaccurate method! Whereas now, in one moment of audition, I take as
2289it were the census and statistics, local, corporeal, mental and
2290spiritual, of every living being in Lineland. Hark, only hark!"
2291
2292So saying he paused and listened, as if in an ecstasy, to a sound which
2293seemed to me no better than a tiny chirping from an innumerable
2294multitude of lilliputian grasshoppers.
2295
2296"Truly," replied I, "your sense of hearing serves you in good stead,
2297and fills up many of your deficiencies. But permit me to point out
2298that your life in Lineland must be deplorably dull. To see nothing but
2299a Point! Not even to be able to contemplate a Straight Line! Nay, not
2300even to know what a Straight Line is! To see, yet be cut off from
2301those Linear prospects which are vouchsafed to us in Flatland! Better
2302surely to have no sense of sight at all than to see so little! I grant
2303you I have not your discriminative faculty of hearing; for the concert
2304of all Lineland which gives you such intense pleasure, is to me no
2305better than a multitudinous twittering or chirping. But at least I can
2306discern, by sight, a Line from a Point. And let me prove it. Just
2307before I came into your kingdom, I saw you dancing from left to right,
2308and then from right to left, with Seven Men and a Woman in your
2309immediate proximity on the left, and eight Men and two Women on your
2310right. Is not this correct?"
2311
2312"It is correct," said the King, "so far as the numbers and sexes are
2313concerned, though I know not what you mean by 'right' and 'left'. But
2314I deny that you saw these things. For how could you see the Line, that
2315is to say the inside, of any Man? But you must have heard these
2316things, and then dreamed that you saw them. And let me ask what you
2317mean by those words 'left' and 'right'. I suppose it is your way of
2318saying Northward and Southward."
2319
2320"Not so," replied I; "besides your motion of Northward and Southward,
2321there is another motion which I call from right to left."
2322
2323KING. Exhibit to me, if you please, this motion from left to right.
2324
2325I. Nay, that I cannot do, unless you could step out of your Line
2326altogether.
2327
2328KING. Out of my Line? Do you mean out of the world? Out of Space?
2329
2330I. Well, yes. Out of YOUR World. Out of YOUR Space. For your Space
2331is not the true Space. True Space is a Plane; but your Space is only a
2332Line.
2333
2334KING. If you cannot indicate this motion from left to right by
2335yourself moving in it, then I beg you to describe it to me in words.
2336
2337I. If you cannot tell your right side from your left, I fear that no
2338words of mine can make my meaning clear to you. But surely you cannot
2339be ignorant of so simple a distinction.
2340
2341KING. I do not in the least understand you.
2342
2343I. Alas! How shall I make it clear? When you move straight on, does
2344it not sometimes occur to you that you COULD move in some other way,
2345turning your eye round so as to look in the direction towards which
2346your side is now fronting? In other words, instead of always moving in
2347the direction of one of your extremities, do you never feel a desire to
2348move in the direction, so to speak, of your side?
2349
2350KING. Never. And what do you mean? How can a man's inside "front" in
2351any direction? Or how can a man move in the direction of his inside?
2352
2353I. Well then, since words cannot explain the matter, I will try deeds,
2354and will move gradually out of Lineland in the direction which I desire
2355to indicate to you.
2356
2357At the word I began to move my body out of Lineland. As long as any
2358part of me remained in his dominion and in his view, the King kept
2359exclaiming, "I see you, I see you still; you are not moving." But when
2360I had at last moved myself out of his Line, he cried in his shrillest
2361voice, "She is vanished; she is dead." "I am not dead," replied I; "I
2362am simply out of Lineland, that is to say, out of the Straight Line
2363which you call Space, and in the true Space, where I can see things as
2364they are. And at this moment I can see your Line, or side--or inside
2365as you are pleased to call it; and I can see also the Men and Women on
2366the North and South of you, whom I will now enumerate, describing their
2367order, their size, and the interval between each."
2368
2369
2370[Illustration 7]
2371
2372[ASCII approximation follows]
2373
2374
2375 My body just before I disappeared
2376 +---------+
2377 |\ \ \ \ \|
2378 |\ \ \ \ \|
2379 |\ \ \ \ \|
2380 Lineland ----> |\ \ \ \ \| The King
2381 --------------------+---------+--------------========
2382
2383
2384When I had done this at great length, I cried triumphantly, "Does that
2385at last convince you?" And, with that, I once more entered Lineland,
2386taking up the same position as before.
2387
2388But the Monarch replied, "If you were a Man of sense--though, as you
2389appear to have only one voice I have little doubt you are not a Man but
2390a Woman--but, if you had a particle of sense, you would listen to
2391reason. You ask me to believe that there is another Line besides that
2392which my senses indicate, and another motion besides that of which I am
2393daily conscious. I, in return, ask you to describe in words or
2394indicate by motion that other Line of which you speak. Instead of
2395moving, you merely exercise some magic art of vanishing and returning
2396to sight; and instead of any lucid description of your new World, you
2397simply tell me the numbers and sizes of some forty of my retinue, facts
2398known to any child in my capital. Can anything be more irrational or
2399audacious? Acknowledge your folly or depart from my dominions."
2400
2401Furious at his perversity, and especially indignant that he professed
2402to be ignorant of my sex, I retorted in no measured terms, "Besotted
2403Being! You think yourself the perfection of existence, while you are
2404in reality the most imperfect and imbecile. You profess to see,
2405whereas you can see nothing but a Point! You plume yourself on
2406inferring the existence of a Straight Line; but I CAN SEE Straight
2407Lines, and infer the existence of Angles, Triangles, Squares,
2408Pentagons, Hexagons, and even Circles. Why waste more words? Suffice
2409it that I am the completion of your incomplete self. You are a Line,
2410but I am a Line of Lines, called in my country a Square: and even I,
2411infinitely superior though I am to you, am of little account among the
2412great nobles of Flatland, whence I have come to visit you, in the hope
2413of enlightening your ignorance."
2414
2415Hearing these words the King advanced towards me with a menacing cry as
2416if to pierce me through the diagonal; and in that same moment there
2417arose from myriads of his subjects a multitudinous war-cry, increasing
2418in vehemence till at last methought it rivalled the roar of an army of
2419a hundred thousand Isosceles, and the artillery of a thousand
2420Pentagons. Spell-bound and motionless, I could neither speak nor move
2421to avert the impending destruction; and still the noise grew louder,
2422and the King came closer, when I awoke to find the breakfast-bell
2423recalling me to the realities of Flatland.
2424
2425
2426
2427
2428Section 15. Concerning a Stranger from Spaceland
2429
2430
2431
2432From dreams I proceed to facts.
2433
2434It was the last day of the 1999th year of our era. The pattering of
2435the rain had long ago announced nightfall; and I was sitting in the
2436company of my wife, musing on the events of the past and the prospects
2437of the coming year, the coming century, the coming Millennium.
2438
2439[Note: When I say "sitting", of course I do not mean any change of
2440attitude such as you in Spaceland signify by that word; for as we have
2441no feet, we can no more "sit" nor "stand" (in your sense of the word)
2442than one of your soles or flounders.
2443
2444Nevertheless, we perfectly well recognize the different mental states
2445of volition implied in "lying", "sitting", and "standing", which are to
2446some extent indicated to a beholder by a slight increase of lustre
2447corresponding to the increase of volition.
2448
2449But on this, and a thousand other kindred subjects, time forbids me to
2450dwell.]
2451
2452My four Sons and two orphan Grandchildren had retired to their several
2453apartments; and my wife alone remained with me to see the old
2454Millennium out and the new one in.
2455
2456I was rapt in thought, pondering in my mind some words that had
2457casually issued from the mouth of my youngest Grandson, a most
2458promising young Hexagon of unusual brilliancy and perfect angularity.
2459His uncles and I had been giving him his usual practical lesson in
2460Sight Recognition, turning ourselves upon our centres, now rapidly, now
2461more slowly, and questioning him as to our positions; and his answers
2462had been so satisfactory that I had been induced to reward him by
2463giving him a few hints on Arithmetic, as applied to Geometry.
2464
2465Taking nine Squares, each an inch every way, I had put them together so
2466as to make one large Square, with a side of three inches, and I had
2467hence proved to my little Grandson that--though it was impossible for
2468us to SEE the inside of the Square--yet we might ascertain the number
2469of square inches in a Square by simply squaring the number of inches in
2470the side: "and thus," said I, "we know that 3^2, or 9, represents the
2471number of square inches in a Square whose side is 3 inches long."
2472
2473The little Hexagon meditated on this a while and then said to me; "But
2474you have been teaching me to raise numbers to the third power: I
2475suppose 3^3 must mean something in Geometry; what does it mean?"
2476"Nothing at all," replied I, "not at least in Geometry; for Geometry
2477has only Two Dimensions." And then I began to shew the boy how a Point
2478by moving through a length of three inches makes a Line of three
2479inches, which may be represented by 3; and how a Line of three inches,
2480moving parallel to itself through a length of three inches, makes a
2481Square of three inches every way, which may be represented by 3^2.
2482
2483Upon this, my Grandson, again returning to his former suggestion, took
2484me up rather suddenly and exclaimed, "Well, then, if a Point by moving
2485three inches, makes a Line of three inches represented by 3; and if a
2486straight Line of three inches, moving parallel to itself, makes a
2487Square of three inches every way, represented by 3^2; it must be that a
2488Square of three inches every way, moving somehow parallel to itself
2489(but I don't see how) must make Something else (but I don't see what)
2490of three inches every way--and this must be represented by 3^3."
2491
2492"Go to bed," said I, a little ruffled by this interruption: "if you
2493would talk less nonsense, you would remember more sense."
2494
2495So my Grandson had disappeared in disgrace; and there I sat by my
2496Wife's side, endeavouring to form a retrospect of the year 1999 and of
2497the possibilities of the year 2000, but not quite able to shake off the
2498thoughts suggested by the prattle of my bright little Hexagon. Only a
2499few sands now remained in the half-hour glass. Rousing myself from my
2500reverie I turned the glass Northward for the last time in the old
2501Millennium; and in the act, I exclaimed aloud, "The boy is a fool."
2502
2503Straightway I became conscious of a Presence in the room, and a
2504chilling breath thrilled through my very being. "He is no such thing,"
2505cried my Wife, "and you are breaking the Commandments in thus
2506dishonouring your own Grandson." But I took no notice of her. Looking
2507round in every direction I could see nothing; yet still I FELT a
2508Presence, and shivered as the cold whisper came again. I started up.
2509"What is the matter?" said my Wife, "there is no draught; what are you
2510looking for? There is nothing." There was nothing; and I resumed my
2511seat, again exclaiming, "The boy is a fool, I say; 3^3 can have no
2512meaning in Geometry." At once there came a distinctly audible reply,
2513"The boy is not a fool; and 3^3 has an obvious Geometrical meaning."
2514
2515My Wife as well as myself heard the words, although she did not
2516understand their meaning, and both of us sprang forward in the
2517direction of the sound. What was our horror when we saw before us a
2518Figure! At the first glance it appeared to be a Woman, seen sideways;
2519but a moment's observation shewed me that the extremities passed into
2520dimness too rapidly to represent one of the Female Sex; and I should
2521have thought it a Circle, only that it seemed to change its size in a
2522manner impossible for a Circle or for any regular Figure of which I had
2523had experience.
2524
2525But my Wife had not my experience, nor the coolness necessary to note
2526these characteristics. With the usual hastiness and unreasoning
2527jealousy of her Sex, she flew at once to the conclusion that a Woman
2528had entered the house through some small aperture. "How comes this
2529person here?" she exclaimed, "you promised me, my dear, that there
2530should be no ventilators in our new house." "Nor are there any," said
2531I; "but what makes you think that the stranger is a Woman? I see by my
2532power of Sight Recognition----" "Oh, I have no patience with your Sight
2533Recognition," replied she, "'Feeling is believing' and 'A Straight Line
2534to the touch is worth a Circle to the sight'"--two Proverbs, very
2535common with the Frailer Sex in Flatland.
2536
2537"Well," said I, for I was afraid of irritating her, "if it must be so,
2538demand an introduction." Assuming her most gracious manner, my Wife
2539advanced towards the Stranger, "Permit me, Madam, to feel and be felt
2540by----" then, suddenly recoiling, "Oh! it is not a Woman, and there
2541are no angles either, not a trace of one. Can it be that I have so
2542misbehaved to a perfect Circle?"
2543
2544"I am indeed, in a certain sense a Circle," replied the Voice, "and a
2545more perfect Circle than any in Flatland; but to speak more accurately,
2546I am many Circles in one." Then he added more mildly, "I have a
2547message, dear Madam, to your husband, which I must not deliver in your
2548presence; and, if you would suffer us to retire for a few minutes----"
2549But my Wife would not listen to the proposal that our august Visitor
2550should so incommode himself, and assuring the Circle that the hour of
2551her own retirement had long passed, with many reiterated apologies for
2552her recent indiscretion, she at last retreated to her apartment.
2553
2554I glanced at the half-hour glass. The last sands had fallen. The
2555third Millennium had begun.
2556
2557
2558
2559
2560Section 16. How the Stranger vainly endeavoured to reveal to me
2561 in words the mysteries of Spaceland
2562
2563
2564
2565As soon as the sound of the Peace-cry of my departing Wife had died
2566away, I began to approach the Stranger with the intention of taking a
2567nearer view and of bidding him be seated: but his appearance struck me
2568dumb and motionless with astonishment. Without the slightest symptoms
2569of angularity he nevertheless varied every instant with gradations of
2570size and brightness scarcely possible for any Figure within the scope
2571of my experience. The thought flashed across me that I might have
2572before me a burglar or cut-throat, some monstrous Irregular Isosceles,
2573who, by feigning the voice of a Circle, had obtained admission somehow
2574into the house, and was now preparing to stab me with his acute angle.
2575
2576In a sitting-room, the absence of Fog (and the season happened to be
2577remarkably dry), made it difficult for me to trust to Sight
2578Recognition, especially at the short distance at which I was standing.
2579Desperate with fear, I rushed forward with an unceremonious, "You must
2580permit me, Sir--" and felt him. My Wife was right. There was not the
2581trace of an angle, not the slightest roughness or inequality: never in
2582my life had I met with a more perfect Circle. He remained motionless
2583while I walked round him, beginning from his eye and returning to it
2584again. Circular he was throughout, a perfectly satisfactory Circle;
2585there could not be a doubt of it. Then followed a dialogue, which I
2586will endeavour to set down as near as I can recollect it, omitting only
2587some of my profuse apologies--for I was covered with shame and
2588humiliation that I, a Square, should have been guilty of the
2589impertinence of feeling a Circle. It was commenced by the Stranger
2590with some impatience at the lengthiness of my introductory process.
2591
2592STRANGER. Have you felt me enough by this time? Are you not
2593introduced to me yet?
2594
2595I. Most illustrious Sir, excuse my awkwardness, which arises not from
2596ignorance of the usages of polite society, but from a little surprise
2597and nervousness, consequent on this somewhat unexpected visit. And I
2598beseech you to reveal my indiscretion to no one, and especially not to
2599my Wife. But before your Lordship enters into further communications,
2600would he deign to satisfy the curiosity of one who would gladly know
2601whence his Visitor came?
2602
2603STRANGER. From Space, from Space, Sir: whence else?
2604
2605I. Pardon me, my Lord, but is not your Lordship already in Space, your
2606Lordship and his humble servant, even at this moment?
2607
2608STRANGER. Pooh! what do you know of Space? Define Space.
2609
2610I. Space, my Lord, is height and breadth indefinitely prolonged.
2611
2612STRANGER. Exactly: you see you do not even know what Space is. You
2613think it is of Two Dimensions only; but I have come to announce to you
2614a Third--height, breadth, and length.
2615
2616I. Your Lordship is pleased to be merry. We also speak of length and
2617height, or breadth and thickness, thus denoting Two Dimensions by four
2618names.
2619
2620STRANGER. But I mean not only three names, but Three Dimensions.
2621
2622I. Would your Lordship indicate or explain to me in what direction is
2623the Third Dimension, unknown to me?
2624
2625STRANGER. I came from it. It is up above and down below.
2626
2627I. My Lord means seemingly that it is Northward and Southward.
2628
2629STRANGER. I mean nothing of the kind. I mean a direction in which you
2630cannot look, because you have no eye in your side.
2631
2632I. Pardon me, my Lord, a moment's inspection will convince your
2633Lordship that I have a perfect luminary at the juncture of two of my
2634sides.
2635
2636STRANGER. Yes: but in order to see into Space you ought to have an
2637eye, not on your Perimeter, but on your side, that is, on what you
2638would probably call your inside; but we in Spaceland should call it
2639your side.
2640
2641I. An eye in my inside! An eye in my stomach! Your Lordship jests.
2642
2643STRANGER. I am in no jesting humour. I tell you that I come from
2644Space, or, since you will not understand what Space means, from the
2645Land of Three Dimensions whence I but lately looked down upon your
2646Plane which you call Space forsooth. From that position of advantage I
2647discerned all that you speak of as SOLID (by which you mean "enclosed
2648on four sides"), your houses, your churches, your very chests and
2649safes, yes even your insides and stomachs, all lying open and exposed
2650to my view.
2651
2652I. Such assertions are easily made, my Lord.
2653
2654STRANGER. But not easily proved, you mean. But I mean to prove mine.
2655
2656When I descended here, I saw your four Sons, the Pentagons, each in his
2657apartment, and your two Grandsons the Hexagons; I saw your youngest
2658Hexagon remain a while with you and then retire to his room, leaving
2659you and your Wife alone. I saw your Isosceles servants, three in
2660number, in the kitchen at supper, and the little Page in the scullery.
2661Then I came here, and how do you think I came?
2662
2663I. Through the roof, I suppose.
2664
2665STRANGER. Not so. Your roof, as you know very well, has been recently
2666repaired, and has no aperture by which even a Woman could penetrate. I
2667tell you I come from Space. Are you not convinced by what I have told
2668you of your children and household?
2669
2670I. Your Lordship must be aware that such facts touching the belongings
2671of his humble servant might be easily ascertained by any one in the
2672neighbourhood possessing your Lordship's ample means of obtaining
2673information.
2674
2675STRANGER. (TO HIMSELF.) What must I do? Stay; one more argument
2676suggests itself to me. When you see a Straight Line--your wife, for
2677example--how many Dimensions do you attribute to her?
2678
2679I. Your Lordship would treat me as if I were one of the vulgar who,
2680being ignorant of Mathematics, suppose that a Woman is really a
2681Straight Line, and only of One Dimension. No, no, my Lord; we Squares
2682are better advised, and are as well aware as your Lordship that a
2683Woman, though popularly called a Straight Line, is, really and
2684scientifically, a very thin Parallelogram, possessing Two Dimensions,
2685like the rest of us, viz., length and breadth (or thickness).
2686
2687STRANGER. But the very fact that a Line is visible implies that it
2688possesses yet another Dimension.
2689
2690I. My Lord, I have just acknowledged that a Woman is broad as well as
2691long. We see her length, we infer her breadth; which, though very
2692slight, is capable of measurement.
2693
2694STRANGER. You do not understand me. I mean that when you see a Woman,
2695you ought--besides inferring her breadth--to see her length, and to SEE
2696what we call her HEIGHT; although that last Dimension is infinitesimal
2697in your country. If a Line were mere length without "height", it would
2698cease to occupy Space and would become invisible. Surely you must
2699recognize this?
2700
2701I. I must indeed confess that I do not in the least understand your
2702Lordship. When we in Flatland see a Line, we see length and
2703BRIGHTNESS. If the brightness disappears, the Line is extinguished,
2704and, as you say, ceases to occupy Space. But am I to suppose that your
2705Lordship gives to brightness the title of a Dimension, and that what we
2706call "bright" you call "high"?
2707
2708STRANGER. No, indeed. By "height" I mean a Dimension like your
2709length: only, with you, "height" is not so easily perceptible, being
2710extremely small.
2711
2712I. My Lord, your assertion is easily put to the test. You say I have
2713a Third Dimension, which you call "height". Now, Dimension implies
2714direction and measurement. Do but measure my "height", or merely
2715indicate to me the direction in which my "height" extends, and I will
2716become your convert. Otherwise, your Lordship's own understanding must
2717hold me excused.
2718
2719STRANGER. (TO HIMSELF.) I can do neither. How shall I convince him?
2720Surely a plain statement of facts followed by ocular demonstration
2721ought to suffice. --Now, Sir; listen to me.
2722
2723You are living on a Plane. What you style Flatland is the vast level
2724surface of what I may call a fluid, on, or in, the top of which you and
2725your countrymen move about, without rising above it or falling below it.
2726
2727I am not a plane Figure, but a Solid. You call me a Circle; but in
2728reality I am not a Circle, but an infinite number of Circles, of size
2729varying from a Point to a Circle of thirteen inches in diameter, one
2730placed on the top of the other. When I cut through your plane as I am
2731now doing, I make in your plane a section which you, very rightly, call
2732a Circle. For even a Sphere--which is my proper name in my own
2733country--if he manifest himself at all to an inhabitant of
2734Flatland--must needs manifest himself as a Circle.
2735
2736Do you not remember--for I, who see all things, discerned last night
2737the phantasmal vision of Lineland written upon your brain--do you not
2738remember, I say, how, when you entered the realm of Lineland, you were
2739compelled to manifest yourself to the King, not as a Square, but as a
2740Line, because that Linear Realm had not Dimensions enough to represent
2741the whole of you, but only a slice or section of you? In precisely the
2742same way, your country of Two Dimensions is not spacious enough to
2743represent me, a being of Three, but can only exhibit a slice or section
2744of me, which is what you call a Circle.
2745
2746The diminished brightness of your eye indicates incredulity. But now
2747prepare to receive proof positive of the truth of my assertions. You
2748cannot indeed see more than one of my sections, or Circles, at a time;
2749for you have no power to raise your eye out of the plane of Flatland;
2750but you can at least see that, as I rise in Space, so my sections
2751become smaller. See now, I will rise; and the effect upon your eye
2752will be that my Circle will become smaller and smaller till it dwindles
2753to a point and finally vanishes.
2754
2755
2756[Illustration 8]
2757
2758[ASCII approximation follows]
2759
2760
2761 The Sphere on the
2762 point of vanishing
2763 (2) __-----__
2764 The Sphere with The Sphere rising / \ (3)
2765 his section __-----__ / \
2766 at full size / \ | |
2767 __-----__ / \ | |
2768 / \ | | | |
2769 / __ - __ \ | | \ / My
2770 | -- -- | | __ --- __ | \ __ __ / Eye
2771 --|-----------------|----\--__-------__--/------------===----------+(>
2772 | -- __ __ -- | \ __ --- __ /
2773 \ - / -----
2774 \ __ __ /
2775 -----
2776
2777
2778There was no "rising" that I could see; but he diminished and finally
2779vanished. I winked once or twice to make sure that I was not dreaming.
2780But it was no dream. For from the depths of nowhere came forth a
2781hollow voice--close to my heart it seemed--"Am I quite gone? Are you
2782convinced now? Well, now I will gradually return to Flatland and you
2783shall see my section become larger and larger."
2784
2785Every reader in Spaceland will easily understand that my mysterious
2786Guest was speaking the language of truth and even of simplicity. But
2787to me, proficient though I was in Flatland Mathematics, it was by no
2788means a simple matter. The rough diagram given above will make it
2789clear to any Spaceland child that the Sphere, ascending in the three
2790positions indicated there, must needs have manifested himself to me, or
2791to any Flatlander, as a Circle, at first of full size, then small, and
2792at last very small indeed, approaching to a Point. But to me, although
2793I saw the facts before me, the causes were as dark as ever. All that I
2794could comprehend was, that the Circle had made himself smaller and
2795vanished, and that he had now reappeared and was rapidly making himself
2796larger.
2797
2798When he regained his original size, he heaved a deep sigh; for he
2799perceived by my silence that I had altogether failed to comprehend him.
2800And indeed I was now inclining to the belief that he must be no Circle
2801at all, but some extremely clever juggler; or else that the old wives'
2802tales were true, and that after all there were such people as
2803Enchanters and Magicians.
2804
2805After a long pause he muttered to himself, "One resource alone remains,
2806if I am not to resort to action. I must try the method of Analogy."
2807Then followed a still longer silence, after which he continued our
2808dialogue.
2809
2810SPHERE. Tell me, Mr. Mathematician; if a Point moves Northward, and
2811leaves a luminous wake, what name would you give to the wake?
2812
2813I. A straight Line.
2814
2815SPHERE. And a straight Line has how many extremities?
2816
2817I. Two.
2818
2819SPHERE. Now conceive the Northward straight Line moving parallel to
2820itself, East and West, so that every point in it leaves behind it the
2821wake of a straight Line. What name will you give to the Figure thereby
2822formed? We will suppose that it moves through a distance equal to the
2823original straight Line. --What name, I say?
2824
2825I. A Square.
2826
2827SPHERE. And how many sides has a Square? How many angles?
2828
2829I. Four sides and four angles.
2830
2831SPHERE. Now stretch your imagination a little, and conceive a Square
2832in Flatland, moving parallel to itself upward.
2833
2834I. What? Northward?
2835
2836SPHERE. No, not Northward; upward; out of Flatland altogether.
2837
2838If it moved Northward, the Southern points in the Square would have to
2839move through the positions previously occupied by the Northern points.
2840But that is not my meaning.
2841
2842I mean that every Point in you--for you are a Square and will serve the
2843purpose of my illustration--every Point in you, that is to say in what
2844you call your inside, is to pass upwards through Space in such a way
2845that no Point shall pass through the position previously occupied by
2846any other Point; but each Point shall describe a straight Line of its
2847own. This is all in accordance with Analogy; surely it must be clear
2848to you.
2849
2850Restraining my impatience--for I was now under a strong temptation to
2851rush blindly at my Visitor and to precipitate him into Space, or out of
2852Flatland, anywhere, so that I could get rid of him--I replied:--
2853
2854"And what may be the nature of the Figure which I am to shape out by
2855this motion which you are pleased to denote by the word 'upward'? I
2856presume it is describable in the language of Flatland."
2857
2858SPHERE. Oh, certainly. It is all plain and simple, and in strict
2859accordance with Analogy--only, by the way, you must not speak of the
2860result as being a Figure, but as a Solid. But I will describe it to
2861you. Or rather not I, but Analogy.
2862
2863We began with a single Point, which of course--being itself a
2864Point--has only ONE terminal Point.
2865
2866One Point produces a Line with TWO terminal Points.
2867
2868One Line produces a Square with FOUR terminal Points.
2869
2870Now you can give yourself the answer to your own question: 1, 2, 4,
2871are evidently in Geometrical Progression. What is the next number?
2872
2873I. Eight.
2874
2875SPHERE. Exactly. The one Square produces a SOMETHING-WHICH-
2876YOU-DO-NOT-AS-YET-KNOW-A-NAME-FOR-BUT-WHICH-WE-CALL-A-CUBE with EIGHT
2877terminal Points. Now are you convinced?
2878
2879I. And has this Creature sides, as well as angles or what you call
2880"terminal Points"?
2881
2882SPHERE. Of course; and all according to Analogy. But, by the way, not
2883what YOU call sides, but what WE call sides. You would call them
2884SOLIDS.
2885
2886I. And how many solids or sides will appertain to this Being whom I am
2887to generate by the motion of my inside in an "upward" direction, and
2888whom you call a Cube?
2889
2890SPHERE. How can you ask? And you a mathematician! The side of
2891anything is always, if I may so say, one Dimension behind the thing.
2892Consequently, as there is no Dimension behind a Point, a Point has 0
2893sides; a Line, if I may say, has 2 sides (for the Points of a Line may
2894be called by courtesy, its sides); a Square has 4 sides; 0, 2, 4; what
2895Progression do you call that?
2896
2897I. Arithmetical.
2898
2899SPHERE. And what is the next number?
2900
2901I. Six.
2902
2903SPHERE. Exactly. Then you see you have answered your own question.
2904The Cube which you will generate will be bounded by six sides, that is
2905to say, six of your insides. You see it all now, eh?
2906
2907"Monster," I shrieked, "be thou juggler, enchanter, dream, or devil, no
2908more will I endure thy mockeries. Either thou or I must perish." And
2909saying these words I precipitated myself upon him.
2910
2911
2912
2913
2914Section 17. How the Sphere, having in vain tried words,
2915 resorted to deeds
2916
2917
2918
2919It was in vain. I brought my hardest right angle into violent
2920collision with the Stranger, pressing on him with a force sufficient to
2921have destroyed any ordinary Circle: but I could feel him slowly and
2922unarrestably slipping from my contact; no edging to the right nor to
2923the left, but moving somehow out of the world, and vanishing to
2924nothing. Soon there was a blank. But still I heard the Intruder's
2925voice.
2926
2927SPHERE. Why will you refuse to listen to reason? I had hoped to find
2928in you--as being a man of sense and an accomplished mathematician--a
2929fit apostle for the Gospel of the Three Dimensions, which I am allowed
2930to preach once only in a thousand years: but now I know not how to
2931convince you. Stay, I have it. Deeds, and not words, shall proclaim
2932the truth. Listen, my friend.
2933
2934I have told you I can see from my position in Space the inside of all
2935things that you consider closed. For example, I see in yonder cupboard
2936near which you are standing, several of what you call boxes (but like
2937everything else in Flatland, they have no tops nor bottoms) full of
2938money; I see also two tablets of accounts. I am about to descend into
2939that cupboard and to bring you one of those tablets. I saw you lock
2940the cupboard half an hour ago, and I know you have the key in your
2941possession. But I descend from Space; the doors, you see, remain
2942unmoved. Now I am in the cupboard and am taking the tablet. Now I
2943have it. Now I ascend with it.
2944
2945I rushed to the closet and dashed the door open. One of the tablets
2946was gone. With a mocking laugh, the Stranger appeared in the other
2947corner of the room, and at the same time the tablet appeared upon the
2948floor. I took it up. There could be no doubt--it was the missing
2949tablet.
2950
2951I groaned with horror, doubting whether I was not out of my senses; but
2952the Stranger continued: "Surely you must now see that my explanation,
2953and no other, suits the phenomena. What you call Solid things are
2954really superficial; what you call Space is really nothing but a great
2955Plane. I am in Space, and look down upon the insides of the things of
2956which you only see the outsides. You could leave this Plane yourself,
2957if you could but summon up the necessary volition. A slight upward or
2958downward motion would enable you to see all that I can see.
2959
2960"The higher I mount, and the further I go from your Plane, the more I
2961can see, though of course I see it on a smaller scale. For example, I
2962am ascending; now I can see your neighbour the Hexagon and his family
2963in their several apartments; now I see the inside of the Theatre, ten
2964doors off, from which the audience is only just departing; and on the
2965other side a Circle in his study, sitting at his books. Now I shall
2966come back to you. And, as a crowning proof, what do you say to my
2967giving you a touch, just the least touch, in your stomach? It will not
2968seriously injure you, and the slight pain you may suffer cannot be
2969compared with the mental benefit you will receive."
2970
2971Before I could utter a word of remonstrance, I felt a shooting pain in
2972my inside, and a demoniacal laugh seemed to issue from within me. A
2973moment afterwards the sharp agony had ceased, leaving nothing but a
2974dull ache behind, and the Stranger began to reappear, saying, as he
2975gradually increased in size, "There, I have not hurt you much, have I?
2976If you are not convinced now, I don't know what will convince you.
2977What say you?"
2978
2979My resolution was taken. It seemed intolerable that I should endure
2980existence subject to the arbitrary visitations of a Magician who could
2981thus play tricks with one's very stomach. If only I could in any way
2982manage to pin him against the wall till help came!
2983
2984Once more I dashed my hardest angle against him, at the same time
2985alarming the whole household by my cries for aid. I believe, at the
2986moment of my onset, the Stranger had sunk below our Plane, and really
2987found difficulty in rising. In any case he remained motionless, while
2988I, hearing, as I thought, the sound of some help approaching, pressed
2989against him with redoubled vigour, and continued to shout for
2990assistance.
2991
2992A convulsive shudder ran through the Sphere. "This must not be," I
2993thought I heard him say: "either he must listen to reason, or I must
2994have recourse to the last resource of civilization." Then, addressing
2995me in a louder tone, he hurriedly exclaimed, "Listen: no stranger must
2996witness what you have witnessed. Send your Wife back at once, before
2997she enters the apartment. The Gospel of Three Dimensions must not be
2998thus frustrated. Not thus must the fruits of one thousand years of
2999waiting be thrown away. I hear her coming. Back! back! Away from me,
3000or you must go with me--whither you know not--into the Land of Three
3001Dimensions!"
3002
3003"Fool! Madman! Irregular!" I exclaimed; "never will I release thee;
3004thou shalt pay the penalty of thine impostures."
3005
3006"Ha! Is it come to this?" thundered the Stranger: "then meet your
3007fate: out of your Plane you go. Once, twice, thrice! 'Tis done!"
3008
3009
3010
3011
3012Section 18. How I came to Spaceland, and what I saw there
3013
3014
3015
3016An unspeakable horror seized me. There was a darkness; then a dizzy,
3017sickening sensation of sight that was not like seeing; I saw a Line
3018that was no Line; Space that was not Space: I was myself, and not
3019myself. When I could find voice, I shrieked aloud in agony, "Either
3020this is madness or it is Hell." "It is neither," calmly replied the
3021voice of the Sphere, "it is Knowledge; it is Three Dimensions: open
3022your eye once again and try to look steadily."
3023
3024I looked, and, behold, a new world! There stood before me, visibly
3025incorporate, all that I had before inferred, conjectured, dreamed, of
3026perfect Circular beauty. What seemed the centre of the Stranger's form
3027lay open to my view: yet I could see no heart, nor lungs, nor
3028arteries, only a beautiful harmonious Something--for which I had no
3029words; but you, my Readers in Spaceland, would call it the surface of
3030the Sphere.
3031
3032Prostrating myself mentally before my Guide, I cried, "How is it, O
3033divine ideal of consummate loveliness and wisdom that I see thy inside,
3034and yet cannot discern thy heart, thy lungs, thy arteries, thy liver?"
3035"What you think you see, you see not," he replied; "it is not given to
3036you, nor to any other Being to behold my internal parts. I am of a
3037different order of Beings from those in Flatland. Were I a Circle, you
3038could discern my intestines, but I am a Being, composed as I told you
3039before, of many Circles, the Many in the One, called in this country a
3040Sphere. And, just as the outside of a Cube is a Square, so the outside
3041of a Sphere presents the appearance of a Circle."
3042
3043Bewildered though I was by my Teacher's enigmatic utterance, I no
3044longer chafed against it, but worshipped him in silent adoration. He
3045continued, with more mildness in his voice. "Distress not yourself if
3046you cannot at first understand the deeper mysteries of Spaceland. By
3047degrees they will dawn upon you. Let us begin by casting back a glance
3048at the region whence you came. Return with me a while to the plains of
3049Flatland, and I will shew you that which you have often reasoned and
3050thought about, but never seen with the sense of sight--a visible
3051angle." "Impossible!" I cried; but, the Sphere leading the way, I
3052followed as if in a dream, till once more his voice arrested me: "Look
3053yonder, and behold your own Pentagonal house, and all its inmates."
3054
3055I looked below, and saw with my physical eye all that domestic
3056individuality which I had hitherto merely inferred with the
3057understanding. And how poor and shadowy was the inferred conjecture in
3058comparison with the reality which I now beheld! My four Sons calmly
3059asleep in the North-Western rooms, my two orphan Grandsons to the
3060South; the Servants, the Butler, my Daughter, all in their several
3061apartments. Only my affectionate Wife, alarmed by my continued
3062absence, had quitted her room and was roving up and down in the Hall,
3063anxiously awaiting my return. Also the Page, aroused by my cries, had
3064left his room, and under pretext of ascertaining whether I had fallen
3065somewhere in a faint, was prying into the cabinet in my study. All
3066this I could now SEE, not merely infer; and as we came nearer and
3067nearer, I could discern even the contents of my cabinet, and the two
3068chests of gold, and the tablets of which the Sphere had made mention.
3069
3070
3071[Illustration 9]
3072
3073[ASCII approximation follows]
3074
3075
3076 /\
3077 / |My \
3078 / <> |Study \
3079 /______ | ___ \
3080 / <> My Sons\ \|The \
3081 /______/ \ Page / \
3082 N / <> \ / My \
3083 ^ /______/ THE HALL \ Bedroom \
3084 | \ <> My\ /
3085 | \____| /\Wife's /
3086 W--+--E \ My Wife / Apartment/
3087 | ------- /\ --- \ WOMEN'S DOOR
3088 | MEN'S DOOR \My Daughter
3089 | /\ --== \ / The Scullion
3090 S \ My Grandsons \ -==# \/ The Footman
3091 \___ ___ _ _/ \-=#|/ The Butler
3092 \ <> | <> | |THE CELLAR \ /
3093 \____|____|_|____________/
3094
3095 ###===--- ---===###
3096 Policeman Policeman
3097
3098
3099Touched by my Wife's distress, I would have sprung downward to reassure
3100her, but I found myself incapable of motion. "Trouble not yourself
3101about your Wife," said my Guide: "she will not be long left in anxiety;
3102meantime, let us take a survey of Flatland."
3103
3104Once more I felt myself rising through space. It was even as the
3105Sphere had said. The further we receded from the object we beheld, the
3106larger became the field of vision. My native city, with the interior
3107of every house and every creature therein, lay open to my view in
3108miniature. We mounted higher, and lo, the secrets of the earth, the
3109depths of mines and inmost caverns of the hills, were bared before me.
3110
3111Awestruck at the sight of the mysteries of the earth, thus unveiled
3112before my unworthy eye, I said to my Companion, "Behold, I am become as
3113a God. For the wise men in our country say that to see all things, or
3114as they express it, OMNIVIDENCE, is the attribute of God alone." There
3115was something of scorn in the voice of my Teacher as he made answer:
3116"Is it so indeed? Then the very pick-pockets and cut-throats of my
3117country are to be worshipped by your wise men as being Gods: for there
3118is not one of them that does not see as much as you see now. But trust
3119me, your wise men are wrong."
3120
3121I. Then is omnividence the attribute of others besides Gods?
3122
3123SPHERE. I do not know. But, if a pick-pocket or a cut-throat of our
3124country can see everything that is in your country, surely that is no
3125reason why the pick-pocket or cut-throat should be accepted by you as a
3126God. This omnividence, as you call it--it is not a common word in
3127Spaceland--does it make you more just, more merciful, less selfish,
3128more loving? Not in the least. Then how does it make you more divine?
3129
3130I. "More merciful, more loving!" But these are the qualities of
3131women! And we know that a Circle is a higher Being than a Straight
3132Line, in so far as knowledge and wisdom are more to be esteemed than
3133mere affection.
3134
3135SPHERE. It is not for me to classify human faculties according to
3136merit. Yet many of the best and wisest in Spaceland think more of the
3137affections than of the understanding, more of your despised Straight
3138Lines than of your belauded Circles. But enough of this. Look yonder.
3139Do you know that building?
3140
3141I looked, and afar off I saw an immense Polygonal structure, in which I
3142recognized the General Assembly Hall of the States of Flatland,
3143surrounded by dense lines of Pentagonal buildings at right angles to
3144each other, which I knew to be streets; and I perceived that I was
3145approaching the great Metropolis.
3146
3147"Here we descend," said my Guide. It was now morning, the first hour
3148of the first day of the two thousandth year of our era. Acting, as was
3149their wont, in strict accordance with precedent, the highest Circles of
3150the realm were meeting in solemn conclave, as they had met on the first
3151hour of the first day of the year 1000, and also on the first hour of
3152the first day of the year 0.
3153
3154The minutes of the previous meetings were now read by one whom I at
3155once recognized as my brother, a perfectly Symmetrical Square, and the
3156Chief Clerk of the High Council. It was found recorded on each
3157occasion that: "Whereas the States had been troubled by divers
3158ill-intentioned persons pretending to have received revelations from
3159another World, and professing to produce demonstrations whereby they
3160had instigated to frenzy both themselves and others, it had been for
3161this cause unanimously resolved by the Grand Council that on the first
3162day of each millenary, special injunctions be sent to the Prefects in
3163the several districts of Flatland, to make strict search for such
3164misguided persons, and without formality of mathematical examination,
3165to destroy all such as were Isosceles of any degree, to scourge and
3166imprison any regular Triangle, to cause any Square or Pentagon to be
3167sent to the district Asylum, and to arrest any one of higher rank,
3168sending him straightway to the Capital to be examined and judged by the
3169Council."
3170
3171"You hear your fate," said the Sphere to me, while the Council was
3172passing for the third time the formal resolution. "Death or
3173imprisonment awaits the Apostle of the Gospel of Three Dimensions."
3174"Not so," replied I, "the matter is now so clear to me, the nature of
3175real space so palpable, that methinks I could make a child understand
3176it. Permit me but to descend at this moment and enlighten them." "Not
3177yet," said my Guide, "the time will come for that. Meantime I must
3178perform my mission. Stay thou there in thy place." Saying these
3179words, he leaped with great dexterity into the sea (if I may so call
3180it) of Flatland, right in the midst of the ring of Counsellors. "I
3181come," cried he, "to proclaim that there is a land of Three Dimensions."
3182
3183I could see many of the younger Counsellors start back in manifest
3184horror, as the Sphere's circular section widened before them. But on a
3185sign from the presiding Circle--who shewed not the slightest alarm or
3186surprise--six Isosceles of a low type from six different quarters
3187rushed upon the Sphere. "We have him," they cried; "No; yes; we have
3188him still! he's going! he's gone!"
3189
3190"My Lords," said the President to the Junior Circles of the Council,
3191"there is not the slightest need for surprise; the secret archives, to
3192which I alone have access, tell me that a similar occurrence happened
3193on the last two millennial commencements. You will, of course, say
3194nothing of these trifles outside the Cabinet."
3195
3196Raising his voice, he now summoned the guards. "Arrest the policemen;
3197gag them. You know your duty." After he had consigned to their fate
3198the wretched policemen--ill-fated and unwilling witnesses of a
3199State-secret which they were not to be permitted to reveal--he again
3200addressed the Counsellors. "My Lords, the business of the Council
3201being concluded, I have only to wish you a happy New Year." Before
3202departing, he expressed, at some length, to the Clerk, my excellent but
3203most unfortunate brother, his sincere regret that, in accordance with
3204precedent and for the sake of secrecy, he must condemn him to perpetual
3205imprisonment, but added his satisfaction that, unless some mention were
3206made by him of that day's incident, his life would be spared.
3207
3208
3209
3210
3211Section 19. How, though the Sphere shewed me other mysteries
3212 of Spaceland, I still desired more; and what came of it
3213
3214
3215
3216When I saw my poor brother led away to imprisonment, I attempted to
3217leap down into the Council Chamber, desiring to intercede on his
3218behalf, or at least bid him farewell. But I found that I had no motion
3219of my own. I absolutely depended on the volition of my Guide, who said
3220in gloomy tones, "Heed not thy brother; haply thou shalt have ample
3221time hereafter to condole with him. Follow me."
3222
3223
3224[Illustration 10]
3225
3226[ASCII approximation follows]
3227
3228
3229 (1) (2)
3230 __________ __________
3231 |\ |\ | \
3232 | \ | \ | \
3233 | \ ____|____\ | \
3234 | | | | | |
3235 |_____|____| | | |
3236 \ | \ | \ |
3237 \ | \ | \ |
3238 \|_________\| \ __________|
3239
3240
3241Once more we ascended into space. "Hitherto," said the Sphere, "I have
3242shewn you naught save Plane Figures and their interiors. Now I must
3243introduce you to Solids, and reveal to you the plan upon which they are
3244constructed. Behold this multitude of moveable square cards. See, I
3245put one on another, not, as you supposed, Northward of the other, but
3246ON the other. Now a second, now a third. See, I am building up a
3247Solid by a multitude of Squares parallel to one another. Now the Solid
3248is complete, being as high as it is long and broad, and we call it a
3249Cube."
3250
3251"Pardon me, my Lord," replied I; "but to my eye the appearance is as of
3252an Irregular Figure whose inside is laid open to the view; in other
3253words, methinks I see no Solid, but a Plane such as we infer in
3254Flatland; only of an Irregularity which betokens some monstrous
3255criminal, so that the very sight of it is painful to my eyes."
3256
3257"True," said the Sphere, "it appears to you a Plane, because you are
3258not accustomed to light and shade and perspective; just as in Flatland
3259a Hexagon would appear a Straight Line to one who has not the Art of
3260Sight Recognition. But in reality it is a Solid, as you shall learn by
3261the sense of Feeling."
3262
3263He then introduced me to the Cube, and I found that this marvellous
3264Being was indeed no Plane, but a Solid; and that he was endowed with
3265six plane sides and eight terminal points called solid angles; and I
3266remembered the saying of the Sphere that just such a Creature as this
3267would be formed by a Square moving, in Space, parallel to himself: and
3268I rejoiced to think that so insignificant a Creature as I could in some
3269sense be called the Progenitor of so illustrious an offspring.
3270
3271But still I could not fully understand the meaning of what my Teacher
3272had told me concerning "light" and "shade" and "perspective"; and I did
3273not hesitate to put my difficulties before him.
3274
3275Were I to give the Sphere's explanation of these matters, succinct and
3276clear though it was, it would be tedious to an inhabitant of Space, who
3277knows these things already. Suffice it, that by his lucid statements,
3278and by changing the position of objects and lights, and by allowing me
3279to feel the several objects and even his own sacred Person, he at last
3280made all things clear to me, so that I could now readily distinguish
3281between a Circle and a Sphere, a Plane Figure and a Solid.
3282
3283This was the Climax, the Paradise, of my strange eventful History.
3284Henceforth I have to relate the story of my miserable Fall:--most
3285miserable, yet surely most undeserved! For why should the thirst for
3286knowledge be aroused, only to be disappointed and punished? My
3287volition shrinks from the painful task of recalling my humiliation;
3288yet, like a second Prometheus, I will endure this and worse, if by any
3289means I may arouse in the interiors of Plane and Solid Humanity a
3290spirit of rebellion against the Conceit which would limit our
3291Dimensions to Two or Three or any number short of Infinity. Away then
3292with all personal considerations! Let me continue to the end, as I
3293began, without further digressions or anticipations, pursuing the plain
3294path of dispassionate History. The exact facts, the exact words,--and
3295they are burnt in upon my brain,--shall be set down without alteration
3296of an iota; and let my Readers judge between me and Destiny.
3297
3298The Sphere would willingly have continued his lessons by indoctrinating
3299me in the conformation of all regular Solids, Cylinders, Cones,
3300Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons, and Spheres: but I
3301ventured to interrupt him. Not that I was wearied of knowledge. On
3302the contrary, I thirsted for yet deeper and fuller draughts than he was
3303offering to me.
3304
3305"Pardon me," said I, "O Thou Whom I must no longer address as the
3306Perfection of all Beauty; but let me beg thee to vouchsafe thy servant
3307a sight of thine interior."
3308
3309SPHERE. My what?
3310
3311I. Thine interior: thy stomach, thy intestines.
3312
3313SPHERE. Whence this ill-timed impertinent request? And what mean you
3314by saying that I am no longer the Perfection of all Beauty?
3315
3316I. My Lord, your own wisdom has taught me to aspire to One even more
3317great, more beautiful, and more closely approximate to Perfection than
3318yourself. As you yourself, superior to all Flatland forms, combine
3319many Circles in One, so doubtless there is One above you who combines
3320many Spheres in One Supreme Existence, surpassing even the Solids of
3321Spaceland. And even as we, who are now in Space, look down on Flatland
3322and see the insides of all things, so of a certainty there is yet above
3323us some higher, purer region, whither thou dost surely purpose to lead
3324me--O Thou Whom I shall always call, everywhere and in all Dimensions,
3325my Priest, Philosopher, and Friend--some yet more spacious Space, some
3326more dimensionable Dimensionality, from the vantage-ground of which we
3327shall look down together upon the revealed insides of Solid things, and
3328where thine own intestines, and those of thy kindred Spheres, will lie
3329exposed to the view of the poor wandering exile from Flatland, to whom
3330so much has already been vouchsafed.
3331
3332SPHERE. Pooh! Stuff! Enough of this trifling! The time is short,
3333and much remains to be done before you are fit to proclaim the Gospel
3334of Three Dimensions to your blind benighted countrymen in Flatland.
3335
3336I. Nay, gracious Teacher, deny me not what I know it is in thy power
3337to perform. Grant me but one glimpse of thine interior, and I am
3338satisfied for ever, remaining henceforth thy docile pupil, thy
3339unemancipable slave, ready to receive all thy teachings and to feed
3340upon the words that fall from thy lips.
3341
3342SPHERE. Well, then, to content and silence you, let me say at once, I
3343would shew you what you wish if I could; but I cannot. Would you have
3344me turn my stomach inside out to oblige you?
3345
3346I. But my Lord has shewn me the intestines of all my countrymen in the
3347Land of Two Dimensions by taking me with him into the Land of Three.
3348What therefore more easy than now to take his servant on a second
3349journey into the blessed region of the Fourth Dimension, where I shall
3350look down with him once more upon this land of Three Dimensions, and
3351see the inside of every three-dimensioned house, the secrets of the
3352solid earth, the treasures of the mines in Spaceland, and the
3353intestines of every solid living creature, even of the noble and
3354adorable Spheres.
3355
3356SPHERE. But where is this land of Four Dimensions?
3357
3358I. I know not: but doubtless my Teacher knows.
3359
3360SPHERE. Not I. There is no such land. The very idea of it is utterly
3361inconceivable.
3362
3363I. Not inconceivable, my Lord, to me, and therefore still less
3364inconceivable to my Master. Nay, I despair not that, even here, in
3365this region of Three Dimensions, your Lordship's art may make the
3366Fourth Dimension visible to me; just as in the Land of Two Dimensions
3367my Teacher's skill would fain have opened the eyes of his blind servant
3368to the invisible presence of a Third Dimension, though I saw it not.
3369
3370Let me recall the past. Was I not taught below that when I saw a Line
3371and inferred a Plane, I in reality saw a Third unrecognized Dimension,
3372not the same as brightness, called "height"? And does it not now
3373follow that, in this region, when I see a Plane and infer a Solid, I
3374really see a Fourth unrecognized Dimension, not the same as colour, but
3375existent, though infinitesimal and incapable of measurement?
3376
3377And besides this, there is the Argument from Analogy of Figures.
3378
3379SPHERE. Analogy! Nonsense: what analogy?
3380
3381I. Your Lordship tempts his servant to see whether he remembers the
3382revelations imparted to him. Trifle not with me, my Lord; I crave, I
3383thirst, for more knowledge. Doubtless we cannot SEE that other higher
3384Spaceland now, because we we have no eye in our stomachs. But, just as
3385there WAS the realm of Flatland, though that poor puny Lineland Monarch
3386could neither turn to left nor right to discern it, and just as there
3387WAS close at hand, and touching my frame, the land of Three Dimensions,
3388though I, blind senseless wretch, had no power to touch it, no eye in
3389my interior to discern it, so of a surety there is a Fourth Dimension,
3390which my Lord perceives with the inner eye of thought. And that it
3391must exist my Lord himself has taught me. Or can he have forgotten
3392what he himself imparted to his servant?
3393
3394In One Dimension, did not a moving Point produce a Line with TWO
3395terminal points?
3396
3397In Two Dimensions, did not a moving Line produce a Square with FOUR
3398terminal points?
3399
3400In Three Dimensions, did not a moving Square produce--did not this eye
3401of mine behold it--that blessed Being, a Cube, with EIGHT terminal
3402points?
3403
3404And in Four Dimensions shall not a moving Cube--alas, for Analogy, and
3405alas for the Progress of Truth, if it be not so--shall not, I say, the
3406motion of a divine Cube result in a still more divine Organization with
3407SIXTEEN terminal points?
3408
3409Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not
3410this a Geometrical Progression? Is not this--if I might quote my
3411Lord's own words--"strictly according to Analogy"?
3412
3413Again, was I not taught by my Lord that as in a Line there are TWO
3414bounding Points, and in a Square there are FOUR bounding Lines, so in a
3415Cube there must be SIX bounding Squares? Behold once more the
3416confirming Series, 2, 4, 6: is not this an Arithmetical Progression?
3417And consequently does it not of necessity follow that the more divine
3418offspring of the divine Cube in the Land of Four Dimensions, must have
34198 bounding Cubes: and is not this also, as my Lord has taught me to
3420believe, "strictly according to Analogy"?
3421
3422O, my Lord, my Lord, behold, I cast myself in faith upon conjecture,
3423not knowing the facts; and I appeal to your Lordship to confirm or deny
3424my logical anticipations. If I am wrong, I yield, and will no longer
3425demand a fourth Dimension; but, if I am right, my Lord will listen to
3426reason.
3427
3428I ask therefore, is it, or is it not, the fact, that ere now your
3429countrymen also have witnessed the descent of Beings of a higher order
3430than their own, entering closed rooms, even as your Lordship entered
3431mine, without the opening of doors or windows, and appearing and
3432vanishing at will? On the reply to this question I am ready to stake
3433everything. Deny it, and I am henceforth silent. Only vouchsafe an
3434answer.
3435
3436SPHERE. (AFTER A PAUSE). It is reported so. But men are divided in
3437opinion as to the facts. And even granting the facts, they explain
3438them in different ways. And in any case, however great may be the
3439number of different explanations, no one has adopted or suggested the
3440theory of a Fourth Dimension. Therefore, pray have done with this
3441trifling, and let us return to business.
3442
3443I. I was certain of it. I was certain that my anticipations would be
3444fulfilled. And now have patience with me and answer me yet one more
3445question, best of Teachers! Those who have thus appeared--no one knows
3446whence--and have returned--no one knows whither--have they also
3447contracted their sections and vanished somehow into that more Spacious
3448Space, whither I now entreat you to conduct me?
3449
3450SPHERE (MOODILY). They have vanished, certainly--if they ever
3451appeared. But most people say that these visions arose from the
3452thought--you will not understand me--from the brain; from the perturbed
3453angularity of the Seer.
3454
3455I. Say they so? Oh, believe them not. Or if it indeed be so, that
3456this other Space is really Thoughtland, then take me to that blessed
3457Region where I in Thought shall see the insides of all solid things.
3458There, before my ravished eye, a Cube, moving in some altogether new
3459direction, but strictly according to Analogy, so as to make every
3460particle of his interior pass through a new kind of Space, with a wake
3461of its own--shall create a still more perfect perfection than himself,
3462with sixteen terminal Extra-solid angles, and Eight solid Cubes for his
3463Perimeter. And once there, shall we stay our upward course? In that
3464blessed region of Four Dimensions, shall we linger on the threshold of
3465the Fifth, and not enter therein? Ah, no! Let us rather resolve that
3466our ambition shall soar with our corporal ascent. Then, yielding to
3467our intellectual onset, the gates of the Sixth Dimension shall fly
3468open; after that a Seventh, and then an Eighth-- How long I should have
3469continued I know not. In vain did the Sphere, in his voice of thunder,
3470reiterate his command of silence, and threaten me with the direst
3471penalties if I persisted. Nothing could stem the flood of my ecstatic
3472aspirations. Perhaps I was to blame; but indeed I was intoxicated with
3473the recent draughts of Truth to which he himself had introduced me.
3474However, the end was not long in coming. My words were cut short by a
3475crash outside, and a simultaneous crash inside me, which impelled me
3476through space with a velocity that precluded speech. Down! down! down!
3477I was rapidly descending; and I knew that return to Flatland was my
3478doom. One glimpse, one last and never-to-be-forgotten glimpse I had of
3479that dull level wilderness--which was now to become my Universe
3480again--spread out before my eye. Then a darkness. Then a final,
3481all-consummating thunder-peal; and, when I came to myself, I was once
3482more a common creeping Square, in my Study at home, listening to the
3483Peace-Cry of my approaching Wife.
3484
3485
3486
3487
3488Section 20. How the Sphere encouraged me in a Vision
3489
3490
3491
3492Although I had less than a minute for reflection, I felt, by a kind of
3493instinct, that I must conceal my experiences from my Wife. Not that I
3494apprehended, at the moment, any danger from her divulging my secret,
3495but I knew that to any Woman in Flatland the narrative of my adventures
3496must needs be unintelligible. So I endeavoured to reassure her by some
3497story, invented for the occasion, that I had accidentally fallen
3498through the trap-door of the cellar, and had there lain stunned.
3499
3500The Southward attraction in our country is so slight that even to a
3501Woman my tale necessarily appeared extraordinary and well-nigh
3502incredible; but my Wife, whose good sense far exceeds that of the
3503average of her Sex, and who perceived that I was unusually excited, did
3504not argue with me on the subject, but insisted that I was ill and
3505required repose. I was glad of an excuse for retiring to my chamber to
3506think quietly over what had happened. When I was at last by myself, a
3507drowsy sensation fell on me; but before my eyes closed I endeavoured to
3508reproduce the Third Dimension, and especially the process by which a
3509Cube is constructed through the motion of a Square. It was not so
3510clear as I could have wished; but I remembered that it must be "Upward,
3511and yet not Northward", and I determined steadfastly to retain these
3512words as the clue which, if firmly grasped, could not fail to guide me
3513to the solution. So mechanically repeating, like a charm, the words,
3514"Upward, yet not Northward", I fell into a sound refreshing sleep.
3515
3516During my slumber I had a dream. I thought I was once more by the side
3517of the Sphere, whose lustrous hue betokened that he had exchanged his
3518wrath against me for perfect placability. We were moving together
3519towards a bright but infinitesimally small Point, to which my Master
3520directed my attention. As we approached, methought there issued from
3521it a slight humming noise as from one of your Spaceland bluebottles,
3522only less resonant by far, so slight indeed that even in the perfect
3523stillness of the Vacuum through which we soared, the sound reached not
3524our ears till we checked our flight at a distance from it of something
3525under twenty human diagonals.
3526
3527"Look yonder," said my Guide, "in Flatland thou hast lived; of Lineland
3528thou hast received a vision; thou hast soared with me to the heights of
3529Spaceland; now, in order to complete the range of thy experience, I
3530conduct thee downward to the lowest depth of existence, even to the
3531realm of Pointland, the Abyss of No dimensions.
3532
3533"Behold yon miserable creature. That Point is a Being like ourselves,
3534but confined to the non-dimensional Gulf. He is himself his own World,
3535his own Universe; of any other than himself he can form no conception;
3536he knows not Length, nor Breadth, nor Height, for he has had no
3537experience of them; he has no cognizance even of the number Two; nor
3538has he a thought of Plurality; for he is himself his One and All, being
3539really Nothing. Yet mark his perfect self-contentment, and hence learn
3540this lesson, that to be self-contented is to be vile and ignorant, and
3541that to aspire is better than to be blindly and impotently happy. Now
3542listen."
3543
3544He ceased; and there arose from the little buzzing creature a tiny,
3545low, monotonous, but distinct tinkling, as from one of your Spaceland
3546phonographs, from which I caught these words, "Infinite beatitude of
3547existence! It is; and there is none else beside It."
3548
3549"What," said I, "does the puny creature mean by 'it'?" "He means
3550himself," said the Sphere: "have you not noticed before now, that
3551babies and babyish people who cannot distinguish themselves from the
3552world, speak of themselves in the Third Person? But hush!"
3553
3554"It fills all Space," continued the little soliloquizing Creature, "and
3555what It fills, It is. What It thinks, that It utters; and what It
3556utters, that It hears; and It itself is Thinker, Utterer, Hearer,
3557Thought, Word, Audition; it is the One, and yet the All in All. Ah,
3558the happiness ah, the happiness of Being!"
3559
3560"Can you not startle the little thing out of its complacency?" said I.
3561"Tell it what it really is, as you told me; reveal to it the narrow
3562limitations of Pointland, and lead it up to something higher." "That
3563is no easy task," said my Master; "try you."
3564
3565Hereon, raising my voice to the uttermost, I addressed the Point as
3566follows:
3567
3568"Silence, silence, contemptible Creature. You call yourself the All in
3569All, but you are the Nothing: your so-called Universe is a mere speck
3570in a Line, and a Line is a mere shadow as compared with--" "Hush,
3571hush, you have said enough," interrupted the Sphere, "now listen, and
3572mark the effect of your harangue on the King of Pointland."
3573
3574The lustre of the Monarch, who beamed more brightly than ever upon
3575hearing my words, shewed clearly that he retained his complacency; and
3576I had hardly ceased when he took up his strain again. "Ah, the joy,
3577ah, the joy of Thought! What can It not achieve by thinking! Its own
3578Thought coming to Itself, suggestive of Its disparagement, thereby to
3579enhance Its happiness! Sweet rebellion stirred up to result in triumph!
3580Ah, the divine creative power of the All in One! Ah, the joy, the joy
3581of Being!"
3582
3583"You see," said my Teacher, "how little your words have done. So far
3584as the Monarch understands them at all, he accepts them as his own--for
3585he cannot conceive of any other except himself--and plumes himself upon
3586the variety of 'Its Thought' as an instance of creative Power. Let us
3587leave this God of Pointland to the ignorant fruition of his
3588omnipresence and omniscience: nothing that you or I can do can rescue
3589him from his self-satisfaction."
3590
3591After this, as we floated gently back to Flatland, I could hear the
3592mild voice of my Companion pointing the moral of my vision, and
3593stimulating me to aspire, and to teach others to aspire. He had been
3594angered at first--he confessed--by my ambition to soar to Dimensions
3595above the Third; but, since then, he had received fresh insight, and he
3596was not too proud to acknowledge his error to a Pupil. Then he
3597proceeded to initiate me into mysteries yet higher than those I had
3598witnessed, shewing me how to construct Extra-Solids by the motion of
3599Solids, and Double Extra-Solids by the motion of Extra-Solids, and all
3600"strictly according to Analogy", all by methods so simple, so easy, as
3601to be patent even to the Female Sex.
3602
3603
3604
3605
3606Section 21. How I tried to teach the Theory of Three Dimensions
3607 to my Grandson, and with what success
3608
3609
3610
3611I awoke rejoicing, and began to reflect on the glorious career before
3612me. I would go forth, methought, at once, and evangelize the whole of
3613Flatland. Even to Women and Soldiers should the Gospel of Three
3614Dimensions be proclaimed. I would begin with my Wife.
3615
3616Just as I had decided on the plan of my operations, I heard the sound
3617of many voices in the street commanding silence. Then followed a
3618louder voice. It was a herald's proclamation. Listening attentively,
3619I recognized the words of the Resolution of the Council, enjoining the
3620arrest, imprisonment, or execution of any one who should pervert the
3621minds of the people by delusions, and by professing to have received
3622revelations from another World.
3623
3624I reflected. This danger was not to be trifled with. It would be
3625better to avoid it by omitting all mention of my Revelation, and by
3626proceeding on the path of Demonstration--which after all, seemed so
3627simple and so conclusive that nothing would be lost by discarding the
3628former means. "Upward, not Northward"--was the clue to the whole
3629proof. It had seemed to me fairly clear before I fell asleep; and when
3630I first awoke, fresh from my dream, it had appeared as patent as
3631Arithmetic; but somehow it did not seem to me quite so obvious now.
3632Though my Wife entered the room opportunely just at that moment, I
3633decided, after we had exchanged a few words of commonplace
3634conversation, not to begin with her.
3635
3636My Pentagonal Sons were men of character and standing, and physicians
3637of no mean reputation, but not great in mathematics, and, in that
3638respect, unfit for my purpose. But it occurred to me that a young and
3639docile Hexagon, with a mathematical turn, would be a most suitable
3640pupil. Why therefore not make my first experiment with my little
3641precocious Grandson, whose casual remarks on the meaning of 3^3 had met
3642with the approval of the Sphere? Discussing the matter with him, a
3643mere boy, I should be in perfect safety; for he would know nothing of
3644the Proclamation of the Council; whereas I could not feel sure that my
3645Sons--so greatly did their patriotism and reverence for the Circles
3646predominate over mere blind affection--might not feel compelled to hand
3647me over to the Prefect, if they found me seriously maintaining the
3648seditious heresy of the Third Dimension.
3649
3650But the first thing to be done was to satisfy in some way the curiosity
3651of my Wife, who naturally wished to know something of the reasons for
3652which the Circle had desired that mysterious interview, and of the
3653means by which he had entered the house. Without entering into the
3654details of the elaborate account I gave her,--an account, I fear, not
3655quite so consistent with truth as my Readers in Spaceland might
3656desire,--I must be content with saying that I succeeded at last in
3657persuading her to return quietly to her household duties without
3658eliciting from me any reference to the World of Three Dimensions. This
3659done, I immediately sent for my Grandson; for, to confess the truth, I
3660felt that all that I had seen and heard was in some strange way
3661slipping away from me, like the image of a half-grasped, tantalizing
3662dream, and I longed to essay my skill in making a first disciple.
3663
3664When my Grandson entered the room I carefully secured the door. Then,
3665sitting down by his side and taking our mathematical tablets,--or, as
3666you would call them, Lines--I told him we would resume the lesson of
3667yesterday. I taught him once more how a Point by motion in One
3668Dimension produces a Line, and how a straight Line in Two Dimensions
3669produces a Square. After this, forcing a laugh, I said, "And now, you
3670scamp, you wanted to make me believe that a Square may in the same way
3671by motion 'Upward, not Northward' produce another figure, a sort of
3672extra Square in Three Dimensions. Say that again, you young rascal."
3673
3674At this moment we heard once more the herald's "O yes! O yes!" outside
3675in the street proclaiming the Resolution of the Council. Young though
3676he was, my Grandson--who was unusually intelligent for his age, and
3677bred up in perfect reverence for the authority of the Circles--took in
3678the situation with an acuteness for which I was quite unprepared. He
3679remained silent till the last words of the Proclamation had died away,
3680and then, bursting into tears, "Dear Grandpapa," he said, "that was
3681only my fun, and of course I meant nothing at all by it; and we did not
3682know anything then about the new Law; and I don't think I said anything
3683about the Third Dimension; and I am sure I did not say one word about
3684'Upward, not Northward', for that would be such nonsense, you know.
3685How could a thing move Upward, and not Northward? Upward and not
3686Northward! Even if I were a baby, I could not be so absurd as that.
3687How silly it is! Ha! ha! ha!"
3688
3689"Not at all silly," said I, losing my temper; "here for example, I take
3690this Square," and, at the word, I grasped a moveable Square, which was
3691lying at hand--"and I move it, you see, not Northward but--yes, I move
3692it Upward--that is to say, not Northward, but I move it somewhere--not
3693exactly like this, but somehow--" Here I brought my sentence to an
3694inane conclusion, shaking the Square about in a purposeless manner,
3695much to the amusement of my Grandson, who burst out laughing louder
3696than ever, and declared that I was not teaching him, but joking with
3697him; and so saying he unlocked the door and ran out of the room. Thus
3698ended my first attempt to convert a pupil to the Gospel of Three
3699Dimensions.
3700
3701
3702
3703
3704Section 22. How I then tried to diffuse the Theory
3705 of Three Dimensions by other means, and of the result
3706
3707
3708
3709My failure with my Grandson did not encourage me to communicate my
3710secret to others of my household; yet neither was I led by it to
3711despair of success. Only I saw that I must not wholly rely on the
3712catch-phrase, "Upward, not Northward", but must rather endeavour to
3713seek a demonstration by setting before the public a clear view of the
3714whole subject; and for this purpose it seemed necessary to resort to
3715writing.
3716
3717So I devoted several months in privacy to the composition of a treatise
3718on the mysteries of Three Dimensions. Only, with the view of evading
3719the Law, if possible, I spoke not of a physical Dimension, but of a
3720Thoughtland whence, in theory, a Figure could look down upon Flatland
3721and see simultaneously the insides of all things, and where it was
3722possible that there might be supposed to exist a Figure environed, as
3723it were, with six Squares, and containing eight terminal Points. But
3724in writing this book I found myself sadly hampered by the impossibility
3725of drawing such diagrams as were necessary for my purpose; for of
3726course, in our country of Flatland, there are no tablets but Lines, and
3727no diagrams but Lines, all in one straight Line and only
3728distinguishable by difference of size and brightness; so that, when I
3729had finished my treatise (which I entitled, "Through Flatland to
3730Thoughtland") I could not feel certain that many would understand my
3731meaning.
3732
3733Meanwhile my life was under a cloud. All pleasures palled upon me; all
3734sights tantalized and tempted me to outspoken treason, because I could
3735not but compare what I saw in Two Dimensions with what it really was if
3736seen in Three, and could hardly refrain from making my comparisons
3737aloud. I neglected my clients and my own business to give myself to
3738the contemplation of the mysteries which I had once beheld, yet which I
3739could impart to no one, and found daily more difficult to reproduce
3740even before my own mental vision.
3741
3742One day, about eleven months after my return from Spaceland, I tried to
3743see a Cube with my eye closed, but failed; and though I succeeded
3744afterwards, I was not then quite certain (nor have I been ever
3745afterwards) that I had exactly realized the original. This made me
3746more melancholy than before, and determined me to take some step; yet
3747what, I knew not. I felt that I would have been willing to sacrifice
3748my life for the Cause, if thereby I could have produced conviction.
3749But if I could not convince my Grandson, how could I convince the
3750highest and most developed Circles in the land?
3751
3752And yet at times my spirit was too strong for me, and I gave vent to
3753dangerous utterances. Already I was considered heterodox if not
3754treasonable, and I was keenly alive to the danger of my position;
3755nevertheless I could not at times refrain from bursting out into
3756suspicious or half-seditious utterances, even among the highest
3757Polygonal and Circular society. When, for example, the question arose
3758about the treatment of those lunatics who said that they had received
3759the power of seeing the insides of things, I would quote the saying of
3760an ancient Circle, who declared that prophets and inspired people are
3761always considered by the majority to be mad; and I could not help
3762occasionally dropping such expressions as "the eye that discerns the
3763interiors of things", and "the all-seeing land"; once or twice I even
3764let fall the forbidden terms "the Third and Fourth Dimensions". At
3765last, to complete a series of minor indiscretions, at a meeting of our
3766Local Speculative Society held at the palace of the Prefect
3767himself,--some extremely silly person having read an elaborate paper
3768exhibiting the precise reasons why Providence has limited the number of
3769Dimensions to Two, and why the attribute of omnividence is assigned to
3770the Supreme alone--I so far forgot myself as to give an exact account
3771of the whole of my voyage with the Sphere into Space, and to the
3772Assembly Hall in our Metropolis, and then to Space again, and of my
3773return home, and of everything that I had seen and heard in fact or
3774vision. At first, indeed, I pretended that I was describing the
3775imaginary experiences of a fictitious person; but my enthusiasm soon
3776forced me to throw off all disguise, and finally, in a fervent
3777peroration, I exhorted all my hearers to divest themselves of prejudice
3778and to become believers in the Third Dimension.
3779
3780Need I say that I was at once arrested and taken before the Council?
3781
3782Next morning, standing in the very place where but a very few months
3783ago the Sphere had stood in my company, I was allowed to begin and to
3784continue my narration unquestioned and uninterrupted. But from the
3785first I foresaw my fate; for the President, noting that a guard of the
3786better sort of Policemen was in attendance, of angularity little, if at
3787all, under 55 degrees, ordered them to be relieved before I began my
3788defence, by an inferior class of 2 or 3 degrees. I knew only too well
3789what that meant. I was to be executed or imprisoned, and my story was
3790to be kept secret from the world by the simultaneous destruction of the
3791officials who had heard it; and, this being the case, the President
3792desired to substitute the cheaper for the more expensive victims.
3793
3794After I had concluded my defence, the President, perhaps perceiving
3795that some of the junior Circles had been moved by my evident
3796earnestness, asked me two questions:--
3797
37981. Whether I could indicate the direction which I meant when I used
3799the words "Upward, not Northward"?
3800
38012. Whether I could by any diagrams or descriptions (other than the
3802enumeration of imaginary sides and angles) indicate the Figure I was
3803pleased to call a Cube?
3804
3805I declared that I could say nothing more, and that I must commit myself
3806to the Truth, whose cause would surely prevail in the end.
3807
3808The President replied that he quite concurred in my sentiment, and that
3809I could not do better. I must be sentenced to perpetual imprisonment;
3810but if the Truth intended that I should emerge from prison and
3811evangelize the world, the Truth might be trusted to bring that result
3812to pass. Meanwhile I should be subjected to no discomfort that was not
3813necessary to preclude escape, and, unless I forfeited the privilege by
3814misconduct, I should be occasionally permitted to see my brother who
3815had preceded me to my prison.
3816
3817Seven years have elapsed and I am still a prisoner, and--if I except
3818the occasional visits of my brother--debarred from all companionship
3819save that of my jailers. My brother is one of the best of Squares,
3820just, sensible, cheerful, and not without fraternal affection; yet I
3821confess that my weekly interviews, at least in one respect, cause me
3822the bitterest pain. He was present when the Sphere manifested himself
3823in the Council Chamber; he saw the Sphere's changing sections; he heard
3824the explanation of the phenomena then given to the Circles. Since that
3825time, scarcely a week has passed during seven whole years, without his
3826hearing from me a repetition of the part I played in that
3827manifestation, together with ample descriptions of all the phenomena in
3828Spaceland, and the arguments for the existence of Solid things
3829derivable from Analogy. Yet--I take shame to be forced to confess
3830it--my brother has not yet grasped the nature of the Third Dimension,
3831and frankly avows his disbelief in the existence of a Sphere.
3832
3833Hence I am absolutely destitute of converts, and, for aught that I can
3834see, the millennial Revelation has been made to me for nothing.
3835Prometheus up in Spaceland was bound for bringing down fire for
3836mortals, but I--poor Flatland Prometheus--lie here in prison for
3837bringing down nothing to my countrymen. Yet I exist in the hope that
3838these memoirs, in some manner, I know not how, may find their way to
3839the minds of humanity in Some Dimension, and may stir up a race of
3840rebels who shall refuse to be confined to limited Dimensionality.
3841
3842That is the hope of my brighter moments. Alas, it is not always so.
3843Heavily weighs on me at times the burdensome reflection that I cannot
3844honestly say I am confident as to the exact shape of the once-seen,
3845oft-regretted Cube; and in my nightly visions the mysterious precept,
3846"Upward, not Northward", haunts me like a soul-devouring Sphinx. It is
3847part of the martyrdom which I endure for the cause of the Truth that
3848there are seasons of mental weakness, when Cubes and Spheres flit away
3849into the background of scarce-possible existences; when the Land of
3850Three Dimensions seems almost as visionary as the Land of One or None;
3851nay, when even this hard wall that bars me from my freedom, these very
3852tablets on which I am writing, and all the substantial realities of
3853Flatland itself, appear no better than the offspring of a diseased
3854imagination, or the baseless fabric of a dream.
3855
3856
3857
3858
3859 THE END of FLATLAND
3860 -----------------------------------------------------------------
3861 | THE END of |
3862 | ______ |
3863 | / / /| ------ / /| /| / /-. |
3864 | /---- / /__| / / /__| / | / / / |
3865 | / /___ / | / /___ / | / |/ /__.-' |
3866 | |
3867 | The baseless fabric of my vision |
3868 | Melted into air into thin air |
3869 | Such stuff as dreams are made of |
3870 -----------------------------------------------------------------
3871
3872
3873
3874
3875
3876
3877
3878
3879End of the Project Gutenberg EBook of Flatland: A Romance of Many Dimensions
3880(Illustrated), by Edwin A. Abbot
3881
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