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Title: Flatland: A Romance of Many Dimensions
Author: Edwin Abbott Abbott
Release date: January 1, 1995 [eBook #201]
Most recently updated: June 26, 2022
Language: English
Other information and formats: www.gutenberg.org/ebooks/201
*** START OF THE PROJECT GUTENBERG EBOOK FLATLAND: A ROMANCE OF MANY DIMENSIONS ***
Flatland: A Romance of Many Dimensions
Edwin A. Abbott (1838-1926. English scholar, theologian, and writer.)
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| "O day and night, but this is wondrous strange" |
| ______ |
| / / /| ------ / /| /| / /-. |
| /---- / /__| / / /__| / | / / / |
| / /___ / | / /___ / | / |/ /__.-' |
| |
| No Dimensions One Dimension |
| . A ROMANCE OF MANY DIMENSIONS ----- |
| POINTLAND LINELAND |
| |
| Two Dimensions Three Dimensions |
| ___ __ |
| | | /__/| |
| |___| |__|/ |
| FLATLAND SPACELAND |
| "Fie, fie, how franticly I square my talk!" |
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With Illustrations by the Author, A SQUARE (Edwin A. Abbott)
To
The Inhabitants of SPACE IN GENERAL
And H. C. IN PARTICULAR
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of THREE Dimensions
Having been previously conversant
With ONLY TWO
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE OR EVEN SIX Dimensions
Thereby contributing
To the Enlargement of THE IMAGINATION
And the possible Development
Of that most rare and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY
Preface to the Second and Revised Edition, 1884.
By the Editor
If my poor Flatland friend retained the vigour of mind which he enjoyed
when he began to compose these Memoirs, I should not now need to
represent him in this preface, in which he desires, firstly, to return
his thanks to his readers and critics in Spaceland, whose appreciation
has, with unexpected celerity, required a second edition of his work;
secondly, to apologize for certain errors and misprints (for which,
however, he is not entirely responsible); and, thirdly, to explain one
or two misconceptions. But he is not the Square he once was. Years of
imprisonment, and the still heavier burden of general incredulity and
mockery, have combined with the natural decay of old age to erase from
his mind many of the thoughts and notions, and much also of the
terminology, which he acquired during his short stay in Spaceland. He
has, therefore, requested me to reply in his behalf to two special
objections, one of an intellectual, the other of a moral nature.
The first objection is, that a Flatlander, seeing a Line, sees
something that must be THICK to the eye as well as LONG to the eye
(otherwise it would not be visible, if it had not some thickness); and
consequently he ought (it is argued) to acknowledge that his countrymen
are not only long and broad, but also (though doubtless in a very
slight degree) THICK or HIGH. This objection is plausible, and, to
Spacelanders, almost irresistible, so that, I confess, when I first
heard it, I knew not what to reply. But my poor old friend's answer
appears to me completely to meet it.
"I admit," said he--when I mentioned to him this objection--"I admit
the truth of your critic's facts, but I deny his conclusions. It is
true that we have really in Flatland a Third unrecognized Dimension
called 'height', just as it is also true that you have really in
Spaceland a Fourth unrecognized Dimension, called by no name at
present, but which I will call 'extra-height'. But we can no more take
cognizance of our 'height' than you can of your 'extra-height'. Even
I--who have been in Spaceland, and have had the privilege of
understanding for twenty-four hours the meaning of 'height'--even I
cannot now comprehend it, nor realize it by the sense of sight or by
any process of reason; I can but apprehend it by faith.
"The reason is obvious. Dimension implies direction, implies
measurement, implies the more and the less. Now, all our lines are
EQUALLY and INFINITESIMALLY thick (or high, whichever you like);
consequently, there is nothing in them to lead our minds to the
conception of that Dimension. No 'delicate micrometer'--as has been
suggested by one too hasty Spaceland critic--would in the least avail
us; for we should not know WHAT TO MEASURE, NOR IN WHAT DIRECTION.
When we see a Line, we see something that is long and BRIGHT;
BRIGHTNESS, as well as length, is necessary to the existence of a Line;
if the brightness vanishes, the Line is extinguished. Hence, all my
Flatland friends--when I talk to them about the unrecognized Dimension
which is somehow visible in a Line--say, 'Ah, you mean BRIGHTNESS':
and when I reply, 'No, I mean a real Dimension', they at once retort,
'Then measure it, or tell us in what direction it extends'; and this
silences me, for I can do neither. Only yesterday, when the Chief
Circle (in other words our High Priest) came to inspect the State
Prison and paid me his seventh annual visit, and when for the seventh
time he put me the question, 'Was I any better?' I tried to prove to
him that he was 'high', as well as long and broad, although he did not
know it. But what was his reply? 'You say I am "high"; measure my
"high-ness" and I will believe you.' What could I do? How could I
meet his challenge? I was crushed; and he left the room triumphant.
"Does this still seem strange to you? Then put yourself in a similar
position. Suppose a person of the Fourth Dimension, condescending to
visit you, were to say, 'Whenever you open your eyes, you see a Plane
(which is of Two Dimensions) and you INFER a Solid (which is of Three);
but in reality you also see (though you do not recognize) a Fourth
Dimension, which is not colour nor brightness nor anything of the kind,
but a true Dimension, although I cannot point out to you its direction,
nor can you possibly measure it.' What would you say to such a
visitor? Would not you have him locked up? Well, that is my fate: and
it is as natural for us Flatlanders to lock up a Square for preaching
the Third Dimension, as it is for you Spacelanders to lock up a Cube
for preaching the Fourth. Alas, how strong a family likeness runs
through blind and persecuting humanity in all Dimensions! Points,
Lines, Squares, Cubes, Extra-Cubes--we are all liable to the same
errors, all alike the Slaves of our respective Dimensional prejudices,
as one of your Spaceland poets has said--
'One touch of Nature makes all worlds akin'."
[Note: The Author desires me to add, that the misconception of some of
his critics on this matter has induced him to insert in his dialogue
with the Sphere, certain remarks which have a bearing on the point in
question, and which he had previously omitted as being tedious and
unnecessary.]
On this point the defence of the Square seems to me to be impregnable.
I wish I could say that his answer to the second (or moral) objection
was equally clear and cogent. It has been objected that he is a
woman-hater; and as this objection has been vehemently urged by those
whom Nature's decree has constituted the somewhat larger half of the
Spaceland race, I should like to remove it, so far as I can honestly do
so. But the Square is so unaccustomed to the use of the moral
terminology of Spaceland that I should be doing him an injustice if I
were literally to transcribe his defence against this charge. Acting,
therefore, as his interpreter and summarizer, I gather that in the
course of an imprisonment of seven years he has himself modified his
own personal views, both as regards Women and as regards the Isosceles
or Lower Classes. Personally, he now inclines to the opinion of the
Sphere that the Straight Lines are in many important respects superior
to the Circles. But, writing as a Historian, he has identified himself
(perhaps too closely) with the views generally adopted by Flatland, and
(as he has been informed) even by Spaceland, Historians; in whose pages
(until very recent times) the destinies of Women and of the masses of
mankind have seldom been deemed worthy of mention and never of careful
consideration.
In a still more obscure passage he now desires to disavow the Circular
or aristocratic tendencies with which some critics have naturally
credited him. While doing justice to the intellectual power with which
a few Circles have for many generations maintained their supremacy over
immense multitudes of their countrymen, he believes that the facts of
Flatland, speaking for themselves without comment on his part, declare
that Revolutions cannot always be suppressed by slaughter, and that
Nature, in sentencing the Circles to infecundity, has condemned them to
ultimate failure--"and herein," he says, "I see a fulfilment of the
great Law of all worlds, that while the wisdom of Man thinks it is
working one thing, the wisdom of Nature constrains it to work another,
and quite a different and far better thing." For the rest, he begs his
readers not to suppose that every minute detail in the daily life of
Flatland must needs correspond to some other detail in Spaceland; and
yet he hopes that, taken as a whole, his work may prove suggestive as
well as amusing, to those Spacelanders of moderate and modest minds
who--speaking of that which is of the highest importance, but lies
beyond experience--decline to say on the one hand, "This can never be,"
and on the other hand, "It must needs be precisely thus, and we know
all about it."
CONTENTS:
PART I: THIS WORLD
Section
1. Of the Nature of Flatland
2. Of the Climate and Houses in Flatland
3. Concerning the Inhabitants of Flatland
4. Concerning the Women
5. Of our Methods of Recognizing one another
6. Of Recognition by Sight
7. Concerning Irregular Figures
8. Of the Ancient Practice of Painting
9. Of the Universal Colour Bill
10. Of the Suppression of the Chromatic Sedition
11. Concerning our Priests
12. Of the Doctrine of our Priests
PART II: OTHER WORLDS
13. How I had a Vision of Lineland
14. How I vainly tried to explain the nature of Flatland
15. Concerning a Stranger from Spaceland
16. How the Stranger vainly endeavoured to reveal to me
in words the mysteries of Spaceland
17. How the Sphere, having in vain tried words,
resorted to deeds
18. How I came to Spaceland, and what I saw there
19. How, though the Sphere shewed me other mysteries
of Spaceland, I still desired more; and what came of it
20. How the Sphere encouraged me in a Vision
21. How I tried to teach the Theory of Three Dimensions
to my Grandson, and with what success
22. How I then tried to diffuse the Theory
of Three Dimensions by other means, and of the result
PART I: THIS WORLD
"Be patient, for the world is broad and wide."
Section 1. Of the Nature of Flatland
I call our world Flatland, not because we call it so, but to make its
nature clearer to you, my happy readers, who are privileged to live in
Space.
Imagine a vast sheet of paper on which straight Lines, Triangles,
Squares, Pentagons, Hexagons, and other figures, instead of remaining
fixed in their places, move freely about, on or in the surface, but
without the power of rising above or sinking below it, very much like
shadows--only hard and with luminous edges--and you will then have a
pretty correct notion of my country and countrymen. Alas, a few years
ago, I should have said "my universe": but now my mind has been opened
to higher views of things.
In such a country, you will perceive at once that it is impossible that
there should be anything of what you call a "solid" kind; but I dare
say you will suppose that we could at least distinguish by sight the
Triangles, Squares, and other figures, moving about as I have described
them. On the contrary, we could see nothing of the kind, not at least
so as to distinguish one figure from another. Nothing was visible, nor
could be visible, to us, except Straight Lines; and the necessity of
this I will speedily demonstrate.
Place a penny on the middle of one of your tables in Space; and leaning
over it, look down upon it. It will appear a circle.
But now, drawing back to the edge of the table, gradually lower your
eye (thus bringing yourself more and more into the condition of the
inhabitants of Flatland), and you will find the penny becoming more and
more oval to your view, and at last when you have placed your eye
exactly on the edge of the table (so that you are, as it were, actually
a Flatlander) the penny will then have ceased to appear oval at all,
and will have become, so far as you can see, a straight line.
The same thing would happen if you were to treat in the same way a
Triangle, or Square, or any other figure cut out of pasteboard. As
soon as you look at it with your eye on the edge on the table, you will
find that it ceases to appear to you a figure, and that it becomes in
appearance a straight line. Take for example an equilateral
Triangle--who represents with us a Tradesman of the respectable class.
Fig. 1 represents the Tradesman as you would see him while you were
bending over him from above; figs. 2 and 3 represent the Tradesman, as
you would see him if your eye were close to the level, or all but on
the level of the table; and if your eye were quite on the level of the
table (and that is how we see him in Flatland) you would see nothing
but a straight line.
[Illustration 1]
[ASCII approximation follows]
(1) __________ (2) ___________ (3) _________
/ --__ __-- ---
/ -
/
When I was in Spaceland I heard that your sailors have very similar
experiences while they traverse your seas and discern some distant
island or coast lying on the horizon. The far-off land may have bays,
forelands, angles in and out to any number and extent; yet at a
distance you see none of these (unless indeed your sun shines bright
upon them revealing the projections and retirements by means of light
and shade), nothing but a grey unbroken line upon the water.
Well, that is just what we see when one of our triangular or other
acquaintances comes toward us in Flatland. As there is neither sun
with us, nor any light of such a kind as to make shadows, we have none
of the helps to the sight that you have in Spaceland. If our friend
comes closer to us we see his line becomes larger; if he leaves us it
becomes smaller: but still he looks like a straight line; be he a
Triangle, Square, Pentagon, Hexagon, Circle, what you will--a straight
Line he looks and nothing else.
You may perhaps ask how under these disadvantageous circumstances we
are able to distinguish our friends from one another: but the answer to
this very natural question will be more fitly and easily given when I
come to describe the inhabitants of Flatland. For the present let me
defer this subject, and say a word or two about the climate and houses
in our country.
Section 2. Of the Climate and Houses in Flatland
As with you, so also with us, there are four points of the compass
North, South, East, and West.
There being no sun nor other heavenly bodies, it is impossible for us
to determine the North in the usual way; but we have a method of our
own. By a Law of Nature with us, there is a constant attraction to the
South; and, although in temperate climates this is very slight--so that
even a Woman in reasonable health can journey several furlongs
northward without much difficulty--yet the hampering effect of the
southward attraction is quite sufficient to serve as a compass in most
parts of our earth. Moreover, the rain (which falls at stated
intervals) coming always from the North, is an additional assistance;
and in the towns we have the guidance of the houses, which of course
have their side-walls running for the most part North and South, so
that the roofs may keep off the rain from the North. In the country,
where there are no houses, the trunks of the trees serve as some sort
of guide. Altogether, we have not so much difficulty as might be
expected in determining our bearings.
Yet in our more temperate regions, in which the southward attraction is
hardly felt, walking sometimes in a perfectly desolate plain where
there have been no houses nor trees to guide me, I have been
occasionally compelled to remain stationary for hours together, waiting
till the rain came before continuing my journey. On the weak and aged,
and especially on delicate Females, the force of attraction tells much
more heavily than on the robust of the Male Sex, so that it is a point
of breeding, if you meet a Lady in the street, always to give her the
North side of the way--by no means an easy thing to do always at short
notice when you are in rude health and in a climate where it is
difficult to tell your North from your South.
Windows there are none in our houses: for the light comes to us alike
in our homes and out of them, by day and by night, equally at all times
and in all places, whence we know not. It was in old days, with our
learned men, an interesting and oft-investigated question, "What is the
origin of light?" and the solution of it has been repeatedly attempted,
with no other result than to crowd our lunatic asylums with the
would-be solvers. Hence, after fruitless attempts to suppress such
investigations indirectly by making them liable to a heavy tax, the
Legislature, in comparatively recent times, absolutely prohibited them.
I--alas, I alone in Flatland--know now only too well the true solution
of this mysterious problem; but my knowledge cannot be made
intelligible to a single one of my countrymen; and I am mocked at--I,
the sole possessor of the truths of Space and of the theory of the
introduction of Light from the world of three Dimensions--as if I were
the maddest of the mad! But a truce to these painful digressions: let
me return to our houses.
The most common form for the construction of a house is five-sided or
pentagonal, as in the annexed figure. The two Northern sides RO, OF,
constitute the roof, and for the most part have no doors; on the East
is a small door for the Women; on the West a much larger one for the
Men; the South side or floor is usually doorless.
Square and triangular houses are not allowed, and for this reason. The
angles of a Square (and still more those of an equilateral Triangle),
being much more pointed than those of a Pentagon, and the lines of
inanimate objects (such as houses) being dimmer than the lines of Men
and Women, it follows that there is no little danger lest the points of
a square or triangular house residence might do serious injury to an
inconsiderate or perhaps absent-minded traveller suddenly therefore,
running against them: and as early as the eleventh century of our era,
triangular houses were universally forbidden by Law, the only
exceptions being fortifications, powder-magazines, barracks, and other
state buildings, which it is not desirable that the general public
should approach without circumspection.
[Illustration 2]
[ASCII approximation follows]
O
/
/
/
/
/
R/ F
_ /
_/
Men's door _ Women's door
_ /
____________/
A B
At this period, square houses were still everywhere permitted, though
discouraged by a special tax. But, about three centuries afterwards,
the Law decided that in all towns containing a population above ten
thousand, the angle of a Pentagon was the smallest house-angle that
could be allowed consistently with the public safety. The good sense
of the community has seconded the efforts of the Legislature; and now,
even in the country, the pentagonal construction has superseded every
other. It is only now and then in some very remote and backward
agricultural district that an antiquarian may still discover a square
house.
Section 3. Concerning the Inhabitants of Flatland
The greatest length or breadth of a full grown inhabitant of Flatland
may be estimated at about eleven of your inches. Twelve inches may be
regarded as a maximum.
Our Women are Straight Lines.
Our Soldiers and Lowest Classes of Workmen are Triangles with two equal
sides, each about eleven inches long, and a base or third side so short
(often not exceeding half an inch) that they form at their vertices a
very sharp and formidable angle. Indeed when their bases are of the
most degraded type (not more than the eighth part of an inch in size),
they can hardly be distinguished from Straight Lines or Women; so
extremely pointed are their vertices. With us, as with you, these
Triangles are distinguished from others by being called Isosceles; and
by this name I shall refer to them in the following pages.
Our Middle Class consists of Equilateral or Equal-Sided Triangles.
Our Professional Men and Gentlemen are Squares (to which class I myself
belong) and Five-Sided Figures or Pentagons.
Next above these come the Nobility, of whom there are several degrees,
beginning at Six-Sided Figures, or Hexagons, and from thence rising in
the number of their sides till they receive the honourable title of
Polygonal, or many-sided. Finally when the number of the sides becomes
so numerous, and the sides themselves so small, that the figure cannot
be distinguished from a circle, he is included in the Circular or
Priestly order; and this is the highest class of all.
It is a Law of Nature with us that a male child shall have one more
side than his father, so that each generation shall rise (as a rule)
one step in the scale of development and nobility. Thus the son of a
Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on.
But this rule applies not always to the Tradesmen, and still less often
to the Soldiers, and to the Workmen; who indeed can hardly be said to
deserve the name of human Figures, since they have not all their sides
equal. With them therefore the Law of Nature does not hold; and the
son of an Isosceles (i.e. a Triangle with two sides equal) remains
Isosceles still. Nevertheless, all hope is not shut out, even from the
Isosceles, that his posterity may ultimately rise above his degraded
condition. For, after a long series of military successes, or diligent
and skilful labours, it is generally found that the more intelligent
among the Artisan and Soldier classes manifest a slight increase of
their third side or base, and a shrinkage of the two other sides.
Intermarriages (arranged by the Priests) between the sons and daughters
of these more intellectual members of the lower classes generally
result in an offspring approximating still more to the type of the
Equal-Sided Triangle.
Rarely--in proportion to the vast numbers of Isosceles births--is a
genuine and certifiable Equal-Sided Triangle produced from Isosceles
parents. [Note: "What need of a certificate?" a Spaceland critic may
ask: "Is not the procreation of a Square Son a certificate from Nature
herself, proving the Equal-sidedness of the Father?" I reply that no
Lady of any position will marry an uncertified Triangle. Square
offspring has sometimes resulted from a slightly Irregular Triangle;
but in almost every such case the Irregularity of the first generation
is visited on the third; which either fails to attain the Pentagonal
rank, or relapses to the Triangular.] Such a birth requires, as its
antecedents, not only a series of carefully arranged intermarriages,
but also a long, continued exercise of frugality and self-control on
the part of the would-be ancestors of the coming Equilateral, and a
patient, systematic, and continuous development of the Isosceles
intellect through many generations.
The birth of a True Equilateral Triangle from Isosceles parents is the
subject of rejoicing in our country for many furlongs around. After a
strict examination conducted by the Sanitary and Social Board, the
infant, if certified as Regular, is with solemn ceremonial admitted
into the class of Equilaterals. He is then immediately taken from his
proud yet sorrowing parents and adopted by some childless Equilateral,
who is bound by oath never to permit the child henceforth to enter his
former home or so much as to look upon his relations again, for fear
lest the freshly developed organism may, by force of unconscious
imitation, fall back again into his hereditary level.
The occasional emergence of an Equilateral from the ranks of his
serf-born ancestors is welcomed, not only by the poor serfs themselves,
as a gleam of light and hope shed upon the monotonous squalor of their
existence, but also by the Aristocracy at large; for all the higher
classes are well aware that these rare phenomena, while they do little
or nothing to vulgarize their own privileges, serve as a most useful
barrier against revolution from below.
Had the acute-angled rabble been all, without exception, absolutely
destitute of hope and of ambition, they might have found leaders in
some of their many seditious outbreaks, so able as to render their
superior numbers and strength too much even for the wisdom of the
Circles. But a wise ordinance of Nature has decreed that, in
proportion as the working-classes increase in intelligence, knowledge,
and all virtue, in that same proportion their acute angle (which makes
them physically terrible) shall increase also and approximate to the
comparatively harmless angle of the Equilateral Triangle. Thus, in the
most brutal and formidable of the soldier class--creatures almost on a
level with women in their lack of intelligence--it is found that, as
they wax in the mental ability necessary to employ their tremendous
penetrating power to advantage, so do they wane in the power of
penetration itself.
How admirable is this Law of Compensation! And how perfect a proof of
the natural fitness and, I may almost say, the divine origin of the
aristocratic constitution of the States in Flatland! By a judicious
use of this Law of Nature, the Polygons and Circles are almost always
able to stifle sedition in its very cradle, taking advantage of the
irrepressible and boundless hopefulness of the human mind. Art also
comes to the aid of Law and Order. It is generally found possible--by
a little artificial compression or expansion on the part of the State
physicians--to make some of the more intelligent leaders of a rebellion
perfectly Regular, and to admit them at once into the privileged
classes; a much larger number, who are still below the standard,
allured by the prospect of being ultimately ennobled, are induced to
enter the State Hospitals, where they are kept in honourable
confinement for life; one or two alone of the more obstinate, foolish,
and hopelessly irregular are led to execution.
Then the wretched rabble of the Isosceles, planless and leaderless, are
either transfixed without resistance by the small body of their
brethren whom the Chief Circle keeps in pay for emergencies of this
kind; or else more often, by means of jealousies and suspicions
skilfully fomented among them by the Circular party, they are stirred
to mutual warfare, and perish by one another's angles. No less than
one hundred and twenty rebellions are recorded in our annals, besides
minor outbreaks numbered at two hundred and thirty-five; and they have
all ended thus.
Section 4. Concerning the Women
If our highly pointed Triangles of the Soldier class are formidable, it
may be readily inferred that far more formidable are our Women. For if
a Soldier is a wedge, a Woman is a needle; being, so to speak, ALL
point, at least at the two extremities. Add to this the power of
making herself practically invisible at will, and you will perceive
that a Female, in Flatland, is a creature by no means to be trifled
with.
But here, perhaps, some of my younger Readers may ask HOW a woman in
Flatland can make herself invisible. This ought, I think, to be
apparent without any explanation. However, a few words will make it
clear to the most unreflecting.
Place a needle on a table. Then, with your eye on the level of the
table, look at it side-ways, and you see the whole length of it; but
look at it end-ways, and you see nothing but a point, it has become
practically invisible. Just so is it with one of our Women. When her
side is turned towards us, we see her as a straight line; when the end
containing her eye or mouth--for with us these two organs are
identical--is the part that meets our eye, then we see nothing but a
highly lustrous point; but when the back is presented to our view,
then--being only sub-lustrous, and, indeed, almost as dim as an
inanimate object--her hinder extremity serves her as a kind of
Invisible Cap.
The dangers to which we are exposed from our Women must now be manifest
to the meanest capacity in Spaceland. If even the angle of a
respectable Triangle in the middle class is not without its dangers; if
to run against a Working Man involves a gash; if collision with an
officer of the military class necessitates a serious wound; if a mere
touch from the vertex of a Private Soldier brings with it danger of
death;--what can it be to run against a Woman, except absolute and
immediate destruction? And when a Woman is invisible, or visible only
as a dim sub-lustrous point, how difficult must it be, even for the
most cautious, always to avoid collision!
Many are the enactments made at different times in the different States
of Flatland, in order to minimize this peril; and in the Southern and
less temperate climates where the force of gravitation is greater, and
human beings more liable to casual and involuntary motions, the Laws
concerning Women are naturally much more stringent. But a general view
of the Code may be obtained from the following summary:--
1. Every house shall have one entrance in the Eastern side, for the
use of Females only; by which all females shall enter "in a becoming
and respectful manner" and not by the Men's or Western door. [Note:
When I was in Spaceland I understood that some of your Priestly circles
have in the same way a separate entrance for Villagers, Farmers and
Teachers of Board Schools (`Spectator', Sept. 1884, p. 1255) that they
may "approach in a becoming and respectful manner."]
2. No Female shall walk in any public place without continually
keeping up her Peace-cry, under penalty of death.
3. Any Female, duly certified to be suffering from St. Vitus's Dance,
fits, chronic cold accompanied by violent sneezing, or any disease
necessitating involuntary motions, shall be instantly destroyed.
In some of the States there is an additional Law forbidding Females,
under penalty of death, from walking or standing in any public place
without moving their backs constantly from right to left so as to
indicate their presence to those behind them; others oblige a Woman,
when travelling, to be followed by one of her sons, or servants, or by
her husband; others confine Women altogether to their houses except
during the religious festivals. But it has been found by the wisest of
our Circles or Statesmen that the multiplication of restrictions on
Females tends not only to the debilitation and diminution of the race,
but also to the increase of domestic murders to such an extent that a
State loses more than it gains by a too prohibitive Code.
For whenever the temper of the Women is thus exasperated by confinement
at home or hampering regulations abroad, they are apt to vent their
spleen upon their husbands and children; and in the less temperate
climates the whole male population of a village has been sometimes
destroyed in one or two hours of simultaneous female outbreak. Hence
the Three Laws, mentioned above, suffice for the better regulated
States, and may be accepted as a rough exemplification of our Female
Code.
After all, our principal safeguard is found, not in Legislature, but in
the interests of the Women themselves. For, although they can inflict
instantaneous death by a retrograde movement, yet unless they can at
once disengage their stinging extremity from the struggling body of
their victim, their own frail bodies are liable to be shattered.
The power of Fashion is also on our side. I pointed out that in some
less civilized States no female is suffered to stand in any public
place without swaying her back from right to left. This practice has
been universal among ladies of any pretensions to breeding in all
well-governed States, as far back as the memory of Figures can reach.
It is considered a disgrace to any State that legislation should have
to enforce what ought to be, and is in every respectable female, a
natural instinct. The rhythmical and, if I may so say, well-modulated
undulation of the back in our ladies of Circular rank is envied and
imitated by the wife of a common Equilateral, who can achieve nothing
beyond a mere monotonous swing, like the ticking of a pendulum; and the
regular tick of the Equilateral is no less admired and copied by the
wife of the progressive and aspiring Isosceles, in the females of whose
family no "back-motion" of any kind has become as yet a necessity of
life. Hence, in every family of position and consideration, "back
motion" is as prevalent as time itself; and the husbands and sons in
these households enjoy immunity at least from invisible attacks.
Not that it must be for a moment supposed that our Women are destitute
of affection. But unfortunately the passion of the moment
predominates, in the Frail Sex, over every other consideration. This
is, of course, a necessity arising from their unfortunate conformation.
For as they have no pretensions to an angle, being inferior in this
respect to the very lowest of the Isosceles, they are consequently
wholly devoid of brain-power, and have neither reflection, judgment nor
forethought, and hardly any memory. Hence, in their fits of fury, they
remember no claims and recognize no distinctions. I have actually
known a case where a Woman has exterminated her whole household, and
half an hour afterwards, when her rage was over and the fragments swept
away, has asked what has become of her husband and her children.
Obviously then a Woman is not to be irritated as long as she is in a
position where she can turn round. When you have them in their
apartments--which are constructed with a view to denying them that
power--you can say and do what you like; for they are then wholly
impotent for mischief, and will not remember a few minutes hence the
incident for which they may be at this moment threatening you with
death, nor the promises which you may have found it necessary to make
in order to pacify their fury.
On the whole we get on pretty smoothly in our domestic relations,
except in the lower strata of the Military Classes. There the want of
tact and discretion on the part of the husbands produces at times
indescribable disasters. Relying too much on the offensive weapons of
their acute angles instead of the defensive organs of good sense and
seasonable simulation, these reckless creatures too often neglect the
prescribed construction of the women's apartments, or irritate their
wives by ill-advised expressions out of doors, which they refuse
immediately to retract. Moreover a blunt and stolid regard for literal
truth indisposes them to make those lavish promises by which the more
judicious Circle can in a moment pacify his consort. The result is
massacre; not, however, without its advantages, as it eliminates the
more brutal and troublesome of the Isosceles; and by many of our
Circles the destructiveness of the Thinner Sex is regarded as one among
many providential arrangements for suppressing redundant population,
and nipping Revolution in the bud.
Yet even in our best regulated and most approximately Circular families
I cannot say that the ideal of family life is so high as with you in
Spaceland. There is peace, in so far as the absence of slaughter may
be called by that name, but there is necessarily little harmony of
tastes or pursuits; and the cautious wisdom of the Circles has ensured
safety at the cost of domestic comfort. In every Circular or Polygonal
household it has been a habit from time immemorial--and now has become
a kind of instinct among the women of our higher classes--that the
mothers and daughters should constantly keep their eyes and mouths
towards their husband and his male friends; and for a lady in a family
of distinction to turn her back upon her husband would be regarded as a
kind of portent, involving loss of STATUS. But, as I shall soon shew,
this custom, though it has the advantage of safety, is not without its
disadvantages.
In the house of the Working Man or respectable Tradesman--where the
wife is allowed to turn her back upon her husband, while pursuing her
household avocations--there are at least intervals of quiet, when the
wife is neither seen nor heard, except for the humming sound of the
continuous Peace-cry; but in the homes of the upper classes there is
too often no peace. There the voluble mouth and bright penetrating eye
are ever directed towards the Master of the household; and light itself
is not more persistent than the stream of feminine discourse. The tact
and skill which suffice to avert a Woman's sting are unequal to the
task of stopping a Woman's mouth; and as the wife has absolutely
nothing to say, and absolutely no constraint of wit, sense, or
conscience to prevent her from saying it, not a few cynics have been
found to aver that they prefer the danger of the death-dealing but
inaudible sting to the safe sonorousness of a Woman's other end.
To my readers in Spaceland the condition of our Women may seem truly
deplorable, and so indeed it is. A Male of the lowest type of the
Isosceles may look forward to some improvement of his angle, and to the
ultimate elevation of the whole of his degraded caste; but no Woman can
entertain such hopes for her sex. "Once a Woman, always a Woman" is a
Decree of Nature; and the very Laws of Evolution seem suspended in her
disfavour. Yet at least we can admire the wise Prearrangement which
has ordained that, as they have no hopes, so they shall have no memory
to recall, and no forethought to anticipate, the miseries and
humiliations which are at once a necessity of their existence and the
basis of the constitution of Flatland.
Section 5. Of our Methods of Recognizing one another
You, who are blessed with shade as well as light, you, who are gifted
with two eyes, endowed with a knowledge of perspective, and charmed
with the enjoyment of various colours, you, who can actually SEE an
angle, and contemplate the complete circumference of a circle in the
happy region of the Three Dimensions--how shall I make clear to you the
extreme difficulty which we in Flatland experience in recognizing one
another's configuration?
Recall what I told you above. All beings in Flatland, animate or
inanimate, no matter what their form, present TO OUR VIEW the same, or
nearly the same, appearance, viz. that of a straight Line. How then
can one be distinguished from another, where all appear the same?
The answer is threefold. The first means of recognition is the sense
of hearing; which with us is far more highly developed than with you,
and which enables us not only to distinguish by the voice our personal
friends, but even to discriminate between different classes, at least
so far as concerns the three lowest orders, the Equilateral, the
Square, and the Pentagon--for of the Isosceles I take no account. But
as we ascend in the social scale, the process of discriminating and
being discriminated by hearing increases in difficulty, partly because
voices are assimilated, partly because the faculty of
voice-discrimination is a plebeian virtue not much developed among the
Aristocracy. And wherever there is any danger of imposture we cannot
trust to this method. Amongst our lowest orders, the vocal organs are
developed to a degree more than correspondent with those of hearing, so
that an Isosceles can easily feign the voice of a Polygon, and, with
some training, that of a Circle himself. A second method is therefore
more commonly resorted to.
FEELING is, among our Women and lower classes--about our upper classes
I shall speak presently--the principal test of recognition, at all
events between strangers, and when the question is, not as to the
individual, but as to the class. What therefore "introduction" is
among the higher classes in Spaceland, that the process of "feeling" is
with us. "Permit me to ask you to feel and be felt by my friend Mr.
So-and-so"--is still, among the more old-fashioned of our country
gentlemen in districts remote from towns, the customary formula for a
Flatland introduction. But in the towns, and among men of business,
the words "be felt by" are omitted and the sentence is abbreviated to,
"Let me ask you to feel Mr. So-and-so"; although it is assumed, of
course, that the "feeling" is to be reciprocal. Among our still more
modern and dashing young gentlemen--who are extremely averse to
superfluous effort and supremely indifferent to the purity of their
native language--the formula is still further curtailed by the use of
"to feel" in a technical sense, meaning, "to
recommend-for-the-purposes-of-feeling-and-being-felt"; and at this
moment the "slang" of polite or fast society in the upper classes
sanctions such a barbarism as "Mr. Smith, permit me to feel Mr. Jones."
Let not my Reader however suppose that "feeling" is with us the tedious
process that it would be with you, or that we find it necessary to feel
right round all the sides of every individual before we determine the
class to which he belongs. Long practice and training, begun in the
schools and continued in the experience of daily life, enable us to
discriminate at once by the sense of touch, between the angles of an
equal-sided Triangle, Square, and Pentagon; and I need not say that the
brainless vertex of an acute-angled Isosceles is obvious to the dullest
touch. It is therefore not necessary, as a rule, to do more than feel
a single angle of an individual; and this, once ascertained, tells us
the class of the person whom we are addressing, unless indeed he
belongs to the higher sections of the nobility. There the difficulty
is much greater. Even a Master of Arts in our University of Wentbridge
has been known to confuse a ten-sided with a twelve-sided Polygon; and
there is hardly a Doctor of Science in or out of that famous University
who could pretend to decide promptly and unhesitatingly between a
twenty-sided and a twenty-four sided member of the Aristocracy.
Those of my readers who recall the extracts I gave above from the
Legislative code concerning Women, will readily perceive that the
process of introduction by contact requires some care and discretion.
Otherwise the angles might inflict on the unwary Feeler irreparable
injury. It is essential for the safety of the Feeler that the Felt
should stand perfectly still. A start, a fidgety shifting of the
position, yes, even a violent sneeze, has been known before now to
prove fatal to the incautious, and to nip in the bud many a promising
friendship. Especially is this true among the lower classes of the
Triangles. With them, the eye is situated so far from their vertex
that they can scarcely take cognizance of what goes on at that
extremity of their frame. They are, moreover, of a rough coarse
nature, not sensitive to the delicate touch of the highly organized
Polygon. What wonder then if an involuntary toss of the head has ere
now deprived the State of a valuable life!
I have heard that my excellent Grandfather--one of the least irregular
of his unhappy Isosceles class, who indeed obtained, shortly before his
decease, four out of seven votes from the Sanitary and Social Board for
passing him into the class of the Equal-sided--often deplored, with a
tear in his venerable eye, a miscarriage of this kind, which had
occured to his great-great-great-Grandfather, a respectable Working Man
with an angle or brain of 59 degrees 30 minutes. According to his
account, my unfortunate Ancestor, being afflicted with rheumatism, and
in the act of being felt by a Polygon, by one sudden start accidentally
transfixed the Great Man through the diagonal; and thereby, partly in
consequence of his long imprisonment and degradation, and partly
because of the moral shock which pervaded the whole of my Ancestor's
relations, threw back our family a degree and a half in their ascent
towards better things. The result was that in the next generation the
family brain was registered at only 58 degrees, and not till the lapse
of five generations was the lost ground recovered, the full 60 degrees
attained, and the Ascent from the Isosceles finally achieved. And all
this series of calamities from one little accident in the process of
Feeling.
At this point I think I hear some of my better educated readers
exclaim, "How could you in Flatland know anything about angles and
degrees, or minutes? We can SEE an angle, because we, in the region of
Space, can see two straight lines inclined to one another; but you, who
can see nothing but one straight line at a time, or at all events only
a number of bits of straight lines all in one straight line--how can
you ever discern any angle, and much less register angles of different
sizes?"
I answer that though we cannot SEE angles, we can INFER them, and this
with great precision. Our sense of touch, stimulated by necessity, and
developed by long training, enables us to distinguish angles far more
accurately than your sense of sight, when unaided by a rule or measure
of angles. Nor must I omit to explain that we have great natural
helps. It is with us a Law of Nature that the brain of the Isosceles
class shall begin at half a degree, or thirty minutes, and shall
increase (if it increases at all) by half a degree in every generation;
until the goal of 60 degrees is reached, when the condition of serfdom
is quitted, and the freeman enters the class of Regulars.
Consequently, Nature herself supplies us with an ascending scale or
Alphabet of angles for half a degree up to 60 degrees, Specimens of
which are placed in every Elementary School throughout the land. Owing
to occasional retrogressions, to still more frequent moral and
intellectual stagnation, and to the extraordinary fecundity of the
Criminal and Vagabond Classes, there is always a vast superfluity of
individuals of the half degree and single degree class, and a fair
abundance of Specimens up to 10 degrees. These are absolutely
destitute of civic rights; and a great number of them, not having even
intelligence enough for the purposes of warfare, are devoted by the
States to the service of education. Fettered immovably so as to remove
all possibility of danger, they are placed in the class rooms of our
Infant Schools, and there they are utilized by the Board of Education
for the purpose of imparting to the offspring of the Middle Classes
that tact and intelligence of which these wretched creatures themselves
are utterly devoid.
In some States the Specimens are occasionally fed and suffered to exist
for several years; but in the more temperate and better regulated
regions, it is found in the long run more advantageous for the
educational interests of the young, to dispense with food, and to renew
the Specimens every month--which is about the average duration of the
foodless existence of the Criminal class. In the cheaper schools, what
is gained by the longer existence of the Specimen is lost, partly in
the expenditure for food, and partly in the diminished accuracy of the
angles, which are impaired after a few weeks of constant "feeling".
Nor must we forget to add, in enumerating the advantages of the more
expensive system, that it tends, though slightly yet perceptibly, to
the diminution of the redundant Isosceles population--an object which
every statesman in Flatland constantly keeps in view. On the whole
therefore--although I am not ignorant that, in many popularly elected
School Boards, there is a reaction in favour of "the cheap system" as
it is called--I am myself disposed to think that this is one of the
many cases in which expense is the truest economy.
But I must not allow questions of School Board politics to divert me
from my subject. Enough has been said, I trust, to shew that
Recognition by Feeling is not so tedious or indecisive a process as
might have been supposed; and it is obviously more trustworthy than
Recognition by hearing. Still there remains, as has been pointed out
above, the objection that this method is not without danger. For this
reason many in the Middle and Lower classes, and all without exception
in the Polygonal and Circular orders, prefer a third method, the
description of which shall be reserved for the next section.
Section 6. Of Recognition by Sight
I am about to appear very inconsistent. In previous sections I have
said that all figures in Flatland present the appearance of a straight
line; and it was added or implied, that it is consequently impossible
to distinguish by the visual organ between individuals of different
classes: yet now I am about to explain to my Spaceland critics how we
are able to recognize one another by the sense of sight.
If however the Reader will take the trouble to refer to the passage in
which Recognition by Feeling is stated to be universal, he will find
this qualification--"among the lower classes". It is only among the
higher classes and in our temperate climates that Sight Recognition is
practised.
That this power exists in any regions and for any classes is the result
of Fog; which prevails during the greater part of the year in all parts
save the torrid zones. That which is with you in Spaceland an unmixed
evil, blotting out the landscape, depressing the spirits, and
enfeebling the health, is by us recognized as a blessing scarcely
inferior to air itself, and as the Nurse of arts and Parent of
sciences. But let me explain my meaning, without further eulogies on
this beneficent Element.
If Fog were non-existent, all lines would appear equally and
indistinguishably clear; and this is actually the case in those unhappy
countries in which the atmosphere is perfectly dry and transparent.
But wherever there is a rich supply of Fog objects that are at a
distance, say of three feet, are appreciably dimmer than those at a
distance of two feet eleven inches; and the result is that by careful
and constant experimental observation of comparative dimness and
clearness, we are enabled to infer with great exactness the
configuration of the object observed.
An instance will do more than a volume of generalities to make my
meaning clear.
Suppose I see two individuals approaching whose rank I wish to
ascertain. They are, we will suppose, a Merchant and a Physician, or
in other words, an Equilateral Triangle and a Pentagon: how am I to
distinguish them?
[Illustration 3]
[ASCII approximation follows]
C (1)
| - _ D
| ||- _
| || - _
| || -----------+(> Eye-glance
___C' (2) | / A|| _ -
___--- - _D' | / ||_ -
__--- || - _ |/ _ - E
| || - _ B
| || - _
| Eye-glance || - _
| || ------------------------+(>
| / || _ -
| / || _ -
|__ / || _ -
---___ / || _ -
---___/ _ -E'
B'
It will be obvious, to every child in Spaceland who has touched the
threshold of Geometrical Studies, that, if I can bring my eye so that
its glance may bisect an angle (A) of the approaching stranger, my view
will lie as it were evenly between his two sides that are next to me
(viz. CA and AB), so that I shall contemplate the two impartially, and
both will appear of the same size.
Now in the case of (1) the Merchant, what shall I see? I shall see a
straight line DAE, in which the middle point (A) will be very bright
because it is nearest to me; but on either side the line will shade
away RAPIDLY INTO DIMNESS, because the sides AC and AB RECEDE RAPIDLY
INTO THE FOG and what appear to me as the Merchant's extremities, viz.
D and E, will be VERY DIM INDEED.
On the other hand in the case of (2) the Physician, though I shall here
also see a line (D'A'E') with a bright centre (A'), yet it will shade
away LESS RAPIDLY into dimness, because the sides (A'C', A'B') RECEDE
LESS RAPIDLY INTO THE FOG: and what appear to me the Physician's
extremities, viz. D' and E', will not be NOT SO DIM as the extremities
of the Merchant.
The Reader will probably understand from these two instances how--after
a very long training supplemented by constant experience--it is
possible for the well-educated classes among us to discriminate with
fair accuracy between the middle and lowest orders, by the sense of
sight. If my Spaceland Patrons have grasped this general conception,
so far as to conceive the possibility of it and not to reject my
account as altogether incredible--I shall have attained all I can
reasonably expect. Were I to attempt further details I should only
perplex. Yet for the sake of the young and inexperienced, who may
perchance infer--from the two simple instances I have given above, of
the manner in which I should recognize my Father and my Sons--that
Recognition by sight is an easy affair, it may be needful to point out
that in actual life most of the problems of Sight Recognition are far
more subtle and complex.
If for example, when my Father, the Triangle, approaches me, he happens
to present his side to me instead of his angle, then, until I have
asked him to rotate, or until I have edged my eye round him, I am for
the moment doubtful whether he may not be a Straight Line, or, in other
words, a Woman. Again, when I am in the company of one of my two
hexagonal Grandsons, contemplating one of his sides (AB) full front, it
will be evident from the accompanying diagram that I shall see one
whole line (AB) in comparative brightness (shading off hardly at all at
the ends) and two smaller lines (CA and BD) dim throughout and shading
away into greater dimness towards the extremities C and D.
[Illustration 4]
[ASCII approximation follows]
/ - _ C
/ || _
/ || - _
/ || - _
| A || - _
| || -+(> (Eye)
| B || _ -
/|| _ -
/ || _ -
/ || -
/ _ - D
But I must not give way to the temptation of enlarging on these topics.
The meanest mathematician in Spaceland will readily believe me when I
assert that the problems of life, which present themselves to the
well-educated--when they are themselves in motion, rotating, advancing
or retreating, and at the same time attempting to discriminate by the
sense of sight between a number of Polygons of high rank moving in
different directions, as for example in a ball-room or
conversazione--must be of a nature to task the angularity of the most
intellectual, and amply justify the rich endowments of the Learned
Professors of Geometry, both Static and Kinetic, in the illustrious
University of Wentbridge, where the Science and Art of Sight
Recognition are regularly taught to large classes of the ELITE of the
States.
It is only a few of the scions of our noblest and wealthiest houses,
who are able to give the time and money necessary for the thorough
prosecution of this noble and valuable Art. Even to me, a
Mathematician of no mean standing, and the Grandfather of two most
hopeful and perfectly regular Hexagons, to find myself in the midst of
a crowd of rotating Polygons of the higher classes, is occasionally
very perplexing. And of course to a common Tradesman, or Serf, such a
sight is almost as unintelligible as it would be to you, my Reader,
were you suddenly transported into our country.
In such a crowd you could see on all sides of you nothing but a Line,
apparently straight, but of which the parts would vary irregularly and
perpetually in brightness or dimness. Even if you had completed your
third year in the Pentagonal and Hexagonal classes in the University,
and were perfect in the theory of the subject, you would still find
that there was need of many years of experience, before you could move
in a fashionable crowd without jostling against your betters, whom it
is against etiquette to ask to "feel", and who, by their superior
culture and breeding, know all about your movements, while you know
very little or nothing about theirs. In a word, to comport oneself
with perfect propriety in Polygonal society, one ought to be a Polygon
oneself. Such at least is the painful teaching of my experience.
It is astonishing how much the Art--or I may almost call it
instinct--of Sight Recognition is developed by the habitual practice of
it and by the avoidance of the custom of "Feeling". Just as, with you,
the deaf and dumb, if once allowed to gesticulate and to use the
hand-alphabet, will never acquire the more difficult but far more
valuable art of lipspeech and lip-reading, so it is with us as regards
"Seeing" and "Feeling". None who in early life resort to "Feeling"
will ever learn "Seeing" in perfection.
For this reason, among our Higher Classes, "Feeling" is discouraged or
absolutely forbidden. From the cradle their children, instead of going
to the Public Elementary schools (where the art of Feeling is taught),
are sent to higher Seminaries of an exclusive character; and at our
illustrious University, to "feel" is regarded as a most serious fault,
involving Rustication for the first offence, and Expulsion for the
second.
But among the lower classes the art of Sight Recognition is regarded as
an unattainable luxury. A common Tradesman cannot afford to let his
son spend a third of his life in abstract studies. The children of the
poor are therefore allowed to "feel" from their earliest years, and
they gain thereby a precocity and an early vivacity which contrast at
first most favourably with the inert, undeveloped, and listless
behaviour of the half-instructed youths of the Polygonal class; but
when the latter have at last completed their University course, and are
prepared to put their theory into practice, the change that comes over
them may almost be described as a new birth, and in every art, science,
and social pursuit they rapidly overtake and distance their Triangular
competitors.
Only a few of the Polygonal Class fail to pass the Final Test or
Leaving Examination at the University. The condition of the
unsuccessful minority is truly pitiable. Rejected from the higher
class, they are also despised by the lower. They have neither the
matured and systematically trained powers of the Polygonal Bachelors
and Masters of Arts, nor yet the native precocity and mercurial
versatility of the youthful Tradesman. The professions, the public
services, are closed against them; and though in most States they are
not actually debarred from marriage, yet they have the greatest
difficulty in forming suitable alliances, as experience shews that the
offspring of such unfortunate and ill-endowed parents is generally
itself unfortunate, if not positively Irregular.
It is from these specimens of the refuse of our Nobility that the great
Tumults and Seditions of past ages have generally derived their
leaders; and so great is the mischief thence arising that an increasing
minority of our more progressive Statesmen are of opinion that true
mercy would dictate their entire suppression, by enacting that all who
fail to pass the Final Examination of the University should be either
imprisoned for life, or extinguished by a painless death.
But I find myself digressing into the subject of Irregularities, a
matter of such vital interest that it demands a separate section.
Section 7. Concerning Irregular Figures
Throughout the previous pages I have been assuming--what perhaps should
have been laid down at the beginning as a distinct and fundamental
proposition--that every human being in Flatland is a Regular Figure,
that is to say of regular construction. By this I mean that a Woman
must not only be a line, but a straight line; that an Artisan or
Soldier must have two of his sides equal; that Tradesmen must have
three sides equal; Lawyers (of which class I am a humble member), four
sides equal, and generally, that in every Polygon, all the sides must
be equal.
The size of the sides would of course depend upon the age of the
individual. A Female at birth would be about an inch long, while a
tall adult Woman might extend to a foot. As to the Males of every
class, it may be roughly said that the length of an adult's sides, when
added together, is two feet or a little more. But the size of our
sides is not under consideration. I am speaking of the EQUALITY of
sides, and it does not need much reflection to see that the whole of
the social life in Flatland rests upon the fundamental fact that Nature
wills all Figures to have their sides equal.
If our sides were unequal our angles might be unequal. Instead of its
being sufficient to feel, or estimate by sight, a single angle in order
to determine the form of an individual, it would be necessary to
ascertain each angle by the experiment of Feeling. But life would be
too short for such a tedious grouping. The whole science and art of
Sight Recognition would at once perish; Feeling, so far as it is an
art, would not long survive; intercourse would become perilous or
impossible; there would be an end to all confidence, all forethought;
no one would be safe in making the most simple social arrangements; in
a word, civilization would relapse into barbarism.
Am I going too fast to carry my Readers with me to these obvious
conclusions? Surely a moment's reflection, and a single instance from
common life, must convince every one that our whole social system is
based upon Regularity, or Equality of Angles. You meet, for example,
two or three Tradesmen in the street, whom you recognize at once to be
Tradesmen by a glance at their angles and rapidly bedimmed sides, and
you ask them to step into your house to lunch. This you do at present
with perfect confidence, because everyone knows to an inch or two the
area occupied by an adult Triangle: but imagine that your Tradesman
drags behind his regular and respectable vertex, a parallelogram of
twelve or thirteen inches in diagonal:--what are you to do with such a
monster sticking fast in your house door?
But I am insulting the intelligence of my Readers by accumulating
details which must be patent to everyone who enjoys the advantages of a
Residence in Spaceland. Obviously the measurements of a single angle
would no longer be sufficient under such portentous circumstances;
one's whole life would be taken up in feeling or surveying the
perimeter of one's acquaintances. Already the difficulties of avoiding
a collision in a crowd are enough to tax the sagacity of even a
well-educated Square; but if no one could calculate the Regularity of a
single figure in the company, all would be chaos and confusion, and the
slightest panic would cause serious injuries, or--if there happened to
be any Women or Soldiers present--perhaps considerable loss of life.
Expediency therefore concurs with Nature in stamping the seal of its
approval upon Regularity of conformation: nor has the Law been
backward in seconding their efforts. "Irregularity of Figure" means
with us the same as, or more than, a combination of moral obliquity and
criminality with you, and is treated accordingly. There are not
wanting, it is true, some promulgators of paradoxes who maintain that
there is no necessary connection between geometrical and moral
Irregularity. "The Irregular", they say, "is from his birth scouted by
his own parents, derided by his brothers and sisters, neglected by the
domestics, scorned and suspected by society, and excluded from all
posts of responsibility, trust, and useful activity. His every
movement is jealously watched by the police till he comes of age and
presents himself for inspection; then he is either destroyed, if he is
found to exceed the fixed margin of deviation, or else immured in a
Government Office as a clerk of the seventh class; prevented from
marriage; forced to drudge at an uninteresting occupation for a
miserable stipend; obliged to live and board at the office, and to take
even his vacation under close supervision; what wonder that human
nature, even in the best and purest, is embittered and perverted by
such surroundings!"
All this very plausible reasoning does not convince me, as it has not
convinced the wisest of our Statesmen, that our ancestors erred in
laying it down as an axiom of policy that the toleration of
Irregularity is incompatible with the safety of the State. Doubtless,
the life of an Irregular is hard; but the interests of the Greater
Number require that it shall be hard. If a man with a triangular front
and a polygonal back were allowed to exist and to propagate a still
more Irregular posterity, what would become of the arts of life? Are
the houses and doors and churches in Flatland to be altered in order to
accommodate such monsters? Are our ticket-collectors to be required to
measure every man's perimeter before they allow him to enter a theatre
or to take his place in a lecture room? Is an Irregular to be exempted
from the militia? And if not, how is he to be prevented from carrying
desolation into the ranks of his comrades? Again, what irresistible
temptations to fraudulent impostures must needs beset such a creature!
How easy for him to enter a shop with his polygonal front foremost, and
to order goods to any extent from a confiding tradesman! Let the
advocates of a falsely called Philanthropy plead as they may for the
abrogation of the Irregular Penal Laws, I for my part have never known
an Irregular who was not also what Nature evidently intended him to
be--a hypocrite, a misanthropist, and, up to the limits of his power, a
perpetrator of all manner of mischief.
Not that I should be disposed to recommend (at present) the extreme
measures adopted by some States, where an infant whose angle deviates
by half a degree from the correct angularity is summarily destroyed at
birth. Some of our highest and ablest men, men of real genius, have
during their earliest days laboured under deviations as great as, or
even greater than, forty-five minutes: and the loss of their precious
lives would have been an irreparable injury to the State. The art of
healing also has achieved some of its most glorious triumphs in the
compressions, extensions, trepannings, colligations, and other surgical
or diaetetic operations by which Irregularity has been partly or wholly
cured. Advocating therefore a VIA MEDIA, I would lay down no fixed or
absolute line of demarcation; but at the period when the frame is just
beginning to set, and when the Medical Board has reported that recovery
is improbable, I would suggest that the Irregular offspring be
painlessly and mercifully consumed.
Section 8. Of the Ancient Practice of Painting
If my Readers have followed me with any attention up to this point,
they will not be surprised to hear that life is somewhat dull in
Flatland. I do not, of course, mean that there are not battles,
conspiracies, tumults, factions, and all those other phenomena which
are supposed to make History interesting; nor would I deny that the
strange mixture of the problems of life and the problems of
Mathematics, continually inducing conjecture and giving the opportunity
of immediate verification, imparts to our existence a zest which you in
Spaceland can hardly comprehend. I speak now from the aesthetic and
artistic point of view when I say that life with us is dull;
aesthetically and artistically, very dull indeed.
How can it be otherwise, when all one's prospect, all one's landscapes,
historical pieces, portraits, flowers, still life, are nothing but a
single line, with no varieties except degrees of brightness and
obscurity?
It was not always thus. Colour, if Tradition speaks the truth, once
for the space of half a dozen centuries or more, threw a transient
splendour over the lives of our ancestors in the remotest ages. Some
private individual--a Pentagon whose name is variously reported--having
casually discovered the constituents of the simpler colours and a
rudimentary method of painting, is said to have begun decorating first
his house, then his slaves, then his Father, his Sons, and Grandsons,
lastly himself. The convenience as well as the beauty of the results
commended themselves to all. Wherever Chromatistes,--for by that name
the most trustworthy authorities concur in calling him,--turned his
variegated frame, there he at once excited attention, and attracted
respect. No one now needed to "feel" him; no one mistook his front for
his back; all his movements were readily ascertained by his neighbours
without the slightest strain on their powers of calculation; no one
jostled him, or failed to make way for him; his voice was saved the
labour of that exhausting utterance by which we colourless Squares and
Pentagons are often forced to proclaim our individuality when we move
amid a crowd of ignorant Isosceles.
The fashion spread like wildfire. Before a week was over, every Square
and Triangle in the district had copied the example of Chromatistes,
and only a few of the more conservative Pentagons still held out. A
month or two found even the Dodecagons infected with the innovation. A
year had not elapsed before the habit had spread to all but the very
highest of the Nobility. Needless to say, the custom soon made its way
from the district of Chromatistes to surrounding regions; and within
two generations no one in all Flatland was colourless except the Women
and the Priests.
Here Nature herself appeared to erect a barrier, and to plead against
extending the innovation to these two classes. Many-sidedness was
almost essential as a pretext for the Innovators. "Distinction of
sides is intended by Nature to imply distinction of colours"--such was
the sophism which in those days flew from mouth to mouth, converting
whole towns at a time to the new culture. But manifestly to our
Priests and Women this adage did not apply. The latter had only one
side, and therefore--plurally and pedantically speaking--NO SIDES. The
former--if at least they would assert their claim to be really and
truly Circles, and not mere high-class Polygons with an infinitely
large number of infinitesimally small sides--were in the habit of
boasting (what Women confessed and deplored) that they also had no
sides, being blessed with a perimeter of one line, or, in other words,
a Circumference. Hence it came to pass that these two Classes could
see no force in the so-called axiom about "Distinction of Sides
implying Distinction of Colour"; and when all others had succumbed to
the fascinations of corporal decoration, the Priests and the Women
alone still remained pure from the pollution of paint.
Immoral, licentious, anarchical, unscientific--call them by what names
you will--yet, from an aesthetic point of view, those ancient days of
the Colour Revolt were the glorious childhood of Art in Flatland--a
childhood, alas, that never ripened into manhood, nor even reached the
blossom of youth. To live was then in itself a delight, because living
implied seeing. Even at a small party, the company was a pleasure to
behold; the richly varied hues of the assembly in a church or theatre
are said to have more than once proved too distracting for our greatest
teachers and actors; but most ravishing of all is said to have been the
unspeakable magnificence of a military review.
The sight of a line of battle of twenty thousand Isosceles suddenly
facing about, and exchanging the sombre black of their bases for the
orange and purple of the two sides including their acute angle; the
militia of the Equilateral Triangles tricoloured in red, white, and
blue; the mauve, ultra-marine, gamboge, and burnt umber of the Square
artillerymen rapidly rotating near their vermilion guns; the dashing
and flashing of the five-coloured and six-coloured Pentagons and
Hexagons careering across the field in their offices of surgeons,
geometricians and aides-de-camp--all these may well have been
sufficient to render credible the famous story how an illustrious
Circle, overcome by the artistic beauty of the forces under his
command, threw aside his marshal's baton and his royal crown,
exclaiming that he henceforth exchanged them for the artist's pencil.
How great and glorious the sensuous development of these days must have
been is in part indicated by the very language and vocabulary of the
period. The commonest utterances of the commonest citizens in the time
of the Colour Revolt seem to have been suffused with a richer tinge of
word or thought; and to that era we are even now indebted for our
finest poetry and for whatever rhythm still remains in the more
scientific utterance of these modern days.
Section 9. Of the Universal Colour Bill
But meanwhile the intellectual Arts were fast decaying.
The Art of Sight Recognition, being no longer needed, was no longer
practised; and the studies of Geometry, Statics, Kinetics, and other
kindred subjects, came soon to be considered superfluous, and fell into
disrespect and neglect even at our University. The inferior Art of
Feeling speedily experienced the same fate at our Elementary Schools.
Then the Isosceles classes, asserting that the Specimens were no longer
used nor needed, and refusing to pay the customary tribute from the
Criminal classes to the service of Education, waxed daily more numerous
and more insolent on the strength of their immunity from the old burden
which had formerly exercised the twofold wholesome effect of at once
taming their brutal nature and thinning their excessive numbers.
Year by year the Soldiers and Artisans began more vehemently to
assert--and with increasing truth--that there was no great difference
between them and the very highest class of Polygons, now that they were
raised to an equality with the latter, and enabled to grapple with all
the difficulties and solve all the problems of life, whether Statical
or Kinetical, by the simple process of Colour Recognition. Not content
with the natural neglect into which Sight Recognition was falling, they
began boldly to demand the legal prohibition of all "monopolizing and
aristocratic Arts" and the consequent abolition of all endowments for
the studies of Sight Recognition, Mathematics, and Feeling. Soon, they
began to insist that inasmuch as Colour, which was a second Nature, had
destroyed the need of aristocratic distinctions, the Law should follow
in the same path, and that henceforth all individuals and all classes
should be recognized as absolutely equal and entitled to equal rights.
Finding the higher Orders wavering and undecided, the leaders of the
Revolution advanced still further in their requirements, and at last
demanded that all classes alike, the Priests and the Women not
excepted, should do homage to Colour by submitting to be painted. When
it was objected that Priests and Women had no sides, they retorted that
Nature and Expediency concurred in dictating that the front half of
every human being (that is to say, the half containing his eye and
mouth) should be distinguishable from his hinder half. They therefore
brought before a general and extraordinary Assembly of all the States
of Flatland a Bill proposing that in every Woman the half containing
the eye and mouth should be coloured red, and the other half green.
The Priests were to be painted in the same way, red being applied to
that semicircle in which the eye and mouth formed the middle point;
while the other or hinder semicircle was to be coloured green.
There was no little cunning in this proposal, which indeed emanated not
from any Isosceles--for no being so degraded would have had angularity
enough to appreciate, much less to devise, such a model of
state-craft--but from an Irregular Circle who, instead of being
destroyed in his childhood, was reserved by a foolish indulgence to
bring desolation on his country and destruction on myriads of his
followers.
On the one hand the proposition was calculated to bring the Women in
all classes over to the side of the Chromatic Innovation. For by
assigning to the Women the same two colours as were assigned to the
Priests, the Revolutionists thereby ensured that, in certain positions,
every Woman would appear like a Priest, and be treated with
corresponding respect and deference--a prospect that could not fail to
attract the Female Sex in a mass.
But by some of my Readers the possibility of the identical appearance
of Priests and Women, under the new Legislation, may not be recognized;
if so, a word or two will make it obvious.
Imagine a woman duly decorated, according to the new Code; with the
front half (i.e. the half containing eye and mouth) red, and with the
hinder half green. Look at her from one side. Obviously you will see
a straight line, HALF RED, HALF GREEN.
[Illustration 5]
[ASCII approximation follows]
[for simplicity's sake, the circle is approximated as an octogon]
M
_____
/ - C_
/ || - _
| || - _
A|- - - - - - -||B- - - - - -_-+(> (Eye)
| || _ -
/||_ -
_____ / - D
Now imagine a Priest, whose mouth is at M, and whose front semicircle
(AMB) is consequently coloured red, while his hinder semicircle is
green; so that the diameter AB divides the green from the red. If you
contemplate the Great Man so as to have your eye in the same straight
line as his dividing diameter (AB), what you will see will be a
straight line (CBD), of which ONE HALF (CB) WILL BE RED, AND THE OTHER
(BD) GREEN. The whole line (CD) will be rather shorter perhaps than
that of a full-sized Woman, and will shade off more rapidly towards its
extremities; but the identity of the colours would give you an
immediate impression of identity of Class, making you neglectful of
other details. Bear in mind the decay of Sight Recognition which
threatened society at the time of the Colour Revolt; add too the
certainty that Women would speedily learn to shade off their
extremities so as to imitate the Circles; it must then be surely
obvious to you, my dear Reader, that the Colour Bill placed us under a
great danger of confounding a Priest with a young Woman.
How attractive this prospect must have been to the Frail Sex may
readily be imagined. They anticipated with delight the confusion that
would ensue. At home they might hear political and ecclesiastical
secrets intended not for them but for their husbands and brothers, and
might even issue commands in the name of a priestly Circle; out of
doors the striking combination of red and green, without addition of
any other colours, would be sure to lead the common people into endless
mistakes, and the Women would gain whatever the Circles lost, in the
deference of the passers by. As for the scandal that would befall the
Circular Class if the frivolous and unseemly conduct of the Women were
imputed to them, and as to the consequent subversion of the
Constitution, the Female Sex could not be expected to give a thought to
these considerations. Even in the households of the Circles, the Women
were all in favour of the Universal Colour Bill.
The second object aimed at by the Bill was the gradual demoralization
of the Circles themselves. In the general intellectual decay they
still preserved their pristine clearness and strength of understanding.
From their earliest childhood, familiarized in their Circular
households with the total absence of Colour, the Nobles alone preserved
the Sacred Art of Sight Recognition, with all the advantages that
result from that admirable training of the intellect. Hence, up to the
date of the introduction of the Universal Colour Bill, the Circles had
not only held their own, but even increased their lead of the other
classes by abstinence from the popular fashion.
Now therefore the artful Irregular whom I described above as the real
author of this diabolical Bill, determined at one blow to lower the
status of the Hierarchy by forcing them to submit to the pollution of
Colour, and at the same time to destroy their domestic opportunities of
training in the Art of Sight Recognition, so as to enfeeble their
intellects by depriving them of their pure and colourless homes. Once
subjected to the chromatic taint, every parental and every childish
Circle would demoralize each other. Only in discerning between the
Father and the Mother would the Circular infant find problems for the
exercise of its understanding--problems too often likely to be
corrupted by maternal impostures with the result of shaking the child's
faith in all logical conclusions. Thus by degrees the intellectual
lustre of the Priestly Order would wane, and the road would then lie
open for a total destruction of all Aristocratic Legislature and for
the subversion of our Privileged Classes.
Section 10. Of the Suppression of the Chromatic Sedition
The agitation for the Universal Colour Bill continued for three years;
and up to the last moment of that period it seemed as though Anarchy
were destined to triumph.
A whole army of Polygons, who turned out to fight as private soldiers,
was utterly annihilated by a superior force of Isosceles Triangles--the
Squares and Pentagons meanwhile remaining neutral. Worse than all,
some of the ablest Circles fell a prey to conjugal fury. Infuriated by
political animosity, the wives in many a noble household wearied their
lords with prayers to give up their opposition to the Colour Bill; and
some, finding their entreaties fruitless, fell on and slaughtered their
innocent children and husband, perishing themselves in the act of
carnage. It is recorded that during that triennial agitation no less
than twenty-three Circles perished in domestic discord.
Great indeed was the peril. It seemed as though the Priests had no
choice between submission and extermination; when suddenly the course
of events was completely changed by one of those picturesque incidents
which Statesmen ought never to neglect, often to anticipate, and
sometimes perhaps to originate, because of the absurdly
disproportionate power with which they appeal to the sympathies of the
populace.
It happened that an Isosceles of a low type, with a brain little if at
all above four degrees--accidentally dabbling in the colours of some
Tradesman whose shop he had plundered--painted himself, or caused
himself to be painted (for the story varies) with the twelve colours of
a Dodecagon. Going into the Market Place he accosted in a feigned
voice a maiden, the orphan daughter of a noble Polygon, whose affection
in former days he had sought in vain; and by a series of
deceptions--aided, on the one side, by a string of lucky accidents too
long to relate, and on the other, by an almost inconceivable fatuity
and neglect of ordinary precautions on the part of the relations of the
bride--he succeeded in consummating the marriage. The unhappy girl
committed suicide on discovering the fraud to which she had been
subjected.
When the news of this catastrophe spread from State to State the minds
of the Women were violently agitated. Sympathy with the miserable
victim and anticipations of similar deceptions for themselves, their
sisters, and their daughters, made them now regard the Colour Bill in
an entirely new aspect. Not a few openly avowed themselves converted
to antagonism; the rest needed only a slight stimulus to make a similar
avowal. Seizing this favourable opportunity, the Circles hastily
convened an extraordinary Assembly of the States; and besides the usual
guard of Convicts, they secured the attendance of a large number of
reactionary Women.
Amidst an unprecedented concourse, the Chief Circle of those days--by
name Pantocyclus--arose to find himself hissed and hooted by a hundred
and twenty thousand Isosceles. But he secured silence by declaring
that henceforth the Circles would enter on a policy of Concession;
yielding to the wishes of the majority, they would accept the Colour
Bill. The uproar being at once converted to applause, he invited
Chromatistes, the leader of the Sedition, into the centre of the hall,
to receive in the name of his followers the submission of the
Hierarchy. Then followed a speech, a masterpiece of rhetoric, which
occupied nearly a day in the delivery, and to which no summary can do
justice.
With a grave appearance of impartiality he declared that as they were
now finally committing themselves to Reform or Innovation, it was
desirable that they should take one last view of the perimeter of the
whole subject, its defects as well as its advantages. Gradually
introducing the mention of the dangers to the Tradesmen, the
Professional Classes and the Gentlemen, he silenced the rising murmurs
of the Isosceles by reminding them that, in spite of all these defects,
he was willing to accept the Bill if it was approved by the majority.
But it was manifest that all, except the Isosceles, were moved by his
words and were either neutral or averse to the Bill.
Turning now to the Workmen he asserted that their interests must not be
neglected, and that, if they intended to accept the Colour Bill, they
ought at least to do so with full view of the consequences. Many of
them, he said, were on the point of being admitted to the class of the
Regular Triangles; others anticipated for their children a distinction
they could not hope for themselves. That honourable ambition would now
have to be sacrificed. With the universal adoption of Colour, all
distinctions would cease; Regularity would be confused with
Irregularity; development would give place to retrogression; the
Workman would in a few generations be degraded to the level of the
Military, or even the Convict Class; political power would be in the
hands of the greatest number, that is to say the Criminal Classes, who
were already more numerous than the Workmen, and would soon out-number
all the other Classes put together when the usual Compensative Laws of
Nature were violated.
A subdued murmur of assent ran through the ranks of the Artisans, and
Chromatistes, in alarm, attempted to step forward and address them.
But he found himself encompassed with guards and forced to remain
silent while the Chief Circle in a few impassioned words made a final
appeal to the Women, exclaiming that, if the Colour Bill passed, no
marriage would henceforth be safe, no woman's honour secure; fraud,
deception, hypocrisy would pervade every household; domestic bliss
would share the fate of the Constitution and pass to speedy perdition.
"Sooner than this," he cried, "Come death."
At these words, which were the preconcerted signal for action, the
Isosceles Convicts fell on and transfixed the wretched Chromatistes;
the Regular Classes, opening their ranks, made way for a band of Women
who, under direction of the Circles, moved, back foremost, invisibly
and unerringly upon the unconscious soldiers; the Artisans, imitating
the example of their betters, also opened their ranks. Meantime bands
of Convicts occupied every entrance with an impenetrable phalanx.
The battle, or rather carnage, was of short duration. Under the
skillful generalship of the Circles almost every Woman's charge was
fatal and very many extracted their sting uninjured, ready for a second
slaughter. But no second blow was needed; the rabble of the Isosceles
did the rest of the business for themselves. Surprised, leader-less,
attacked in front by invisible foes, and finding egress cut off by the
Convicts behind them, they at once--after their manner--lost all
presence of mind, and raised the cry of "treachery". This sealed their
fate. Every Isosceles now saw and felt a foe in every other. In half
an hour not one of that vast multitude was living; and the fragments of
seven score thousand of the Criminal Class slain by one another's
angles attested the triumph of Order.
The Circles delayed not to push their victory to the uttermost. The
Working Men they spared but decimated. The Militia of the Equilaterals
was at once called out; and every Triangle suspected of Irregularity on
reasonable grounds, was destroyed by Court Martial, without the
formality of exact measurement by the Social Board. The homes of the
Military and Artisan classes were inspected in a course of visitations
extending through upwards of a year; and during that period every town,
village, and hamlet was systematically purged of that excess of the
lower orders which had been brought about by the neglect to pay the
tribute of Criminals to the Schools and University, and by the
violation of the other natural Laws of the Constitution of Flatland.
Thus the balance of classes was again restored.
Needless to say that henceforth the use of Colour was abolished, and
its possession prohibited. Even the utterance of any word denoting
Colour, except by the Circles or by qualified scientific teachers, was
punished by a severe penalty. Only at our University in some of the
very highest and most esoteric classes--which I myself have never been
privileged to attend--it is understood that the sparing use of Colour
is still sanctioned for the purpose of illustrating some of the deeper
problems of mathematics. But of this I can only speak from hearsay.
Elsewhere in Flatland, Colour is now non-existent. The art of making
it is known to only one living person, the Chief Circle for the time
being; and by him it is handed down on his death-bed to none but his
Successor. One manufactory alone produces it; and, lest the secret
should be betrayed, the Workmen are annually consumed, and fresh ones
introduced. So great is the terror with which even now our Aristocracy
looks back to the far-distant days of the agitation for the Universal
Colour Bill.
Section 11. Concerning our Priests
It is high time that I should pass from these brief and discursive
notes about things in Flatland to the central event of this book, my
initiation into the mysteries of Space. THAT is my subject; all that
has gone before is merely preface.
For this reason I must omit many matters of which the explanation would
not, I flatter myself, be without interest for my Readers: as for
example, our method of propelling and stopping ourselves, although
destitute of feet; the means by which we give fixity to structures of
wood, stone, or brick, although of course we have no hands, nor can we
lay foundations as you can, nor avail ourselves of the lateral pressure
of the earth; the manner in which the rain originates in the intervals
between our various zones, so that the northern regions do not
intercept the moisture from falling on the southern; the nature of our
hills and mines, our trees and vegetables, our seasons and harvests;
our Alphabet and method of writing, adapted to our linear tablets;
these and a hundred other details of our physical existence I must pass
over, nor do I mention them now except to indicate to my readers that
their omission proceeds not from forgetfulness on the part of the
author, but from his regard for the time of the Reader.
Yet before I proceed to my legitimate subject some few final remarks
will no doubt be expected by my Readers upon those pillars and
mainstays of the Constitution of Flatland, the controllers of our
conduct and shapers of our destiny, the objects of universal homage and
almost of adoration: need I say that I mean our Circles or Priests?
When I call them Priests, let me not be understood as meaning no more
than the term denotes with you. With us, our Priests are
Administrators of all Business, Art, and Science; Directors of Trade,
Commerce, Generalship, Architecture, Engineering, Education,
Statesmanship, Legislature, Morality, Theology; doing nothing
themselves, they are the Causes of everything worth doing, that is done
by others.
Although popularly everyone called a Circle is deemed a Circle, yet
among the better educated Classes it is known that no Circle is really
a Circle, but only a Polygon with a very large number of very small
sides. As the number of the sides increases, a Polygon approximates to
a Circle; and, when the number is very great indeed, say for example
three or four hundred, it is extremely difficult for the most delicate
touch to feel any polygonal angles. Let me say rather, it WOULD be
difficult: for, as I have shown above, Recognition by Feeling is
unknown among the highest society, and to FEEL a Circle would be
considered a most audacious insult. This habit of abstention from
Feeling in the best society enables a Circle the more easily to sustain
the veil of mystery in which, from his earliest years, he is wont to
enwrap the exact nature of his Perimeter or Circumference. Three feet
being the average Perimeter it follows that, in a Polygon of three
hundred sides each side will be no more than the hundredth part of a
foot in length, or little more than the tenth part of an inch; and in a
Polygon of six or seven hundred sides the sides are little larger than
the diameter of a Spaceland pin-head. It is always assumed, by
courtesy, that the Chief Circle for the time being has ten thousand
sides.
The ascent of the posterity of the Circles in the social scale is not
restricted, as it is among the lower Regular classes, by the Law of
Nature which limits the increase of sides to one in each generation.
If it were so, the number of sides in a Circle would be a mere question
of pedigree and arithmetic, and the four hundred and ninety-seventh
descendant of an Equilateral Triangle would necessarily be a Polygon
with five hundred sides. But this is not the case. Nature's Law
prescribes two antagonistic decrees affecting Circular propagation;
first, that as the race climbs higher in the scale of development, so
development shall proceed at an accelerated pace; second, that in the
same proportion, the race shall become less fertile. Consequently in
the home of a Polygon of four or five hundred sides it is rare to find
a son; more than one is never seen. On the other hand the son of a
five-hundred-sided Polygon has been known to possess five hundred and
fifty, or even six hundred sides.
Art also steps in to help the process of the higher Evolution. Our
physicians have discovered that the small and tender sides of an infant
Polygon of the higher class can be fractured, and his whole frame
re-set, with such exactness that a Polygon of two or three hundred
sides sometimes--by no means always, for the process is attended with
serious risk--but sometimes overleaps two or three hundred generations,
and as it were doubles at a stroke, the number of his progenitors and
the nobility of his descent.
Many a promising child is sacrificed in this way. Scarcely one out of
ten survives. Yet so strong is the parental ambition among those
Polygons who are, as it were, on the fringe of the Circular class, that
it is very rare to find a Nobleman of that position in society, who has
neglected to place his first-born in the Circular Neo-Therapeutic
Gymnasium before he has attained the age of a month.
One year determines success or failure. At the end of that time the
child has, in all probability, added one more to the tombstones that
crowd the Neo-Therapeutic Cemetery; but on rare occasions a glad
procession bears back the little one to his exultant parents, no longer
a Polygon, but a Circle, at least by courtesy: and a single instance of
so blessed a result induces multitudes of Polygonal parents to submit
to similar domestic sacrifices, which have a dissimilar issue.
Section 12. Of the Doctrine of our Priests
As to the doctrine of the Circles it may briefly be summed up in a
single maxim, "Attend to your Configuration." Whether political,
ecclesiastical, or moral, all their teaching has for its object the
improvement of individual and collective Configuration--with special
reference of course to the Configuration of the Circles, to which all
other objects are subordinated.
It is the merit of the Circles that they have effectually suppressed
those ancient heresies which led men to waste energy and sympathy in
the vain belief that conduct depends upon will, effort, training,
encouragement, praise, or anything else but Configuration. It was
Pantocyclus--the illustrious Circle mentioned above, as the queller of
the Colour Revolt--who first convinced mankind that Configuration makes
the man; that if, for example, you are born an Isosceles with two
uneven sides, you will assuredly go wrong unless you have them made
even--for which purpose you must go to the Isosceles Hospital;
similarly, if you are a Triangle, or Square, or even a Polygon, born
with any Irregularity, you must be taken to one of the Regular
Hospitals to have your disease cured; otherwise you will end your days
in the State Prison or by the angle of the State Executioner.
All faults or defects, from the slightest misconduct to the most
flagitious crime, Pantocyclus attributed to some deviation from perfect
Regularity in the bodily figure, caused perhaps (if not congenital) by
some collision in a crowd; by neglect to take exercise, or by taking
too much of it; or even by a sudden change of temperature, resulting in
a shrinkage or expansion in some too susceptible part of the frame.
Therefore, concluded that illustrious Philosopher, neither good conduct
nor bad conduct is a fit subject, in any sober estimation, for either
praise or blame. For why should you praise, for example, the integrity
of a Square who faithfully defends the interests of his client, when
you ought in reality rather to admire the exact precision of his right
angles? Or again, why blame a lying, thievish Isosceles when you ought
rather to deplore the incurable inequality of his sides?
Theoretically, this doctrine is unquestionable; but it has practical
drawbacks. In dealing with an Isosceles, if a rascal pleads that he
cannot help stealing because of his unevenness, you reply that for that
very reason, because he cannot help being a nuisance to his neighbours,
you, the Magistrate, cannot help sentencing him to be consumed--and
there's an end of the matter. But in little domestic difficulties,
where the penalty of consumption, or death, is out of the question,
this theory of Configuration sometimes comes in awkwardly; and I must
confess that occasionally when one of my own Hexagonal Grandsons pleads
as an excuse for his disobedience that a sudden change of the
temperature has been too much for his Perimeter, and that I ought to
lay the blame not on him but on his Configuration, which can only be
strengthened by abundance of the choicest sweetmeats, I neither see my
way logically to reject, nor practically to accept, his conclusions.
For my own part, I find it best to assume that a good sound scolding or
castigation has some latent and strengthening influence on my
Grandson's Configuration; though I own that I have no grounds for
thinking so. At all events I am not alone in my way of extricating
myself from this dilemma; for I find that many of the highest Circles,
sitting as Judges in law courts, use praise and blame towards Regular
and Irregular Figures; and in their homes I know by experience that,
when scolding their children, they speak about "right" or "wrong" as
vehemently and passionately as if they believed that these names
represented real existences, and that a human Figure is really capable
of choosing between them.
Constantly carrying out their policy of making Configuration the
leading idea in every mind, the Circles reverse the nature of that
Commandment which in Spaceland regulates the relations between parents
and children. With you, children are taught to honour their parents;
with us--next to the Circles, who are the chief object of universal
homage--a man is taught to honour his Grandson, if he has one; or, if
not, his Son. By "honour", however, is by no means meant "indulgence",
but a reverent regard for their highest interests: and the Circles
teach that the duty of fathers is to subordinate their own interests to
those of posterity, thereby advancing the welfare of the whole State as
well as that of their own immediate descendants.
The weak point in the system of the Circles--if a humble Square may
venture to speak of anything Circular as containing any element of
weakness--appears to me to be found in their relations with Women.
As it is of the utmost importance for Society that Irregular births
should be discouraged, it follows that no Woman who has any
Irregularities in her ancestry is a fit partner for one who desires
that his posterity should rise by regular degrees in the social scale.
Now the Irregularity of a Male is a matter of measurement; but as all
Women are straight, and therefore visibly Regular so to speak, one has
to devise some other means of ascertaining what I may call their
invisible Irregularity, that is to say their potential Irregularities
as regards possible offspring. This is effected by carefully-kept
pedigrees, which are preserved and supervised by the State; and without
a certified pedigree no Woman is allowed to marry.
Now it might have been supposed that a Circle--proud of his ancestry
and regardful for a posterity which might possibly issue hereafter in a
Chief Circle--would be more careful than any other to choose a wife who
had no blot on her escutcheon. But it is not so. The care in choosing
a Regular wife appears to diminish as one rises in the social scale.
Nothing would induce an aspiring Isosceles, who had hopes of generating
an Equilateral Son, to take a wife who reckoned a single Irregularity
among her Ancestors; a Square or Pentagon, who is confident that his
family is steadily on the rise, does not inquire above the
five-hundredth generation; a Hexagon or Dodecagon is even more careless
of the wife's pedigree; but a Circle has been known deliberately to
take a wife who has had an Irregular Great-Grandfather, and all because
of some slight superiority of lustre, or because of the charms of a low
voice--which, with us, even more than you, is thought "an excellent
thing in Woman".
Such ill-judged marriages are, as might be expected, barren, if they do
not result in positive Irregularity or in diminution of sides; but none
of these evils have hitherto proved sufficiently deterrent. The loss
of a few sides in a highly-developed Polygon is not easily noticed, and
is sometimes compensated by a successful operation in the
Neo-Therapeutic Gymnasium, as I have described above; and the Circles
are too much disposed to acquiesce in infecundity as a Law of the
superior development. Yet, if this evil be not arrested, the gradual
diminution of the Circular class may soon become more rapid, and the
time may be not far distant when, the race being no longer able to
produce a Chief Circle, the Constitution of Flatland must fall.
One other word of warning suggests itself to me, though I cannot so
easily mention a remedy; and this also refers to our relations with
Women. About three hundred years ago, it was decreed by the Chief
Circle that, since women are deficient in Reason but abundant in
Emotion, they ought no longer to be treated as rational, nor receive
any mental education. The consequence was that they were no longer
taught to read, nor even to master Arithmetic enough to enable them to
count the angles of their husband or children; and hence they sensibly
declined during each generation in intellectual power. And this system
of female non-education or quietism still prevails.
My fear is that, with the best intentions, this policy has been carried
so far as to react injuriously on the Male Sex.
For the consequence is that, as things now are, we Males have to lead a
kind of bi-lingual, and I may almost say bi-mental, existence. With
Women, we speak of "love", "duty", "right", "wrong", "pity", "hope",
and other irrational and emotional conceptions, which have no
existence, and the fiction of which has no object except to control
feminine exuberances; but among ourselves, and in our books, we have an
entirely different vocabulary and I may almost say, idiom. "Love" then
becomes "the anticipation of benefits"; "duty" becomes "necessity" or
"fitness"; and other words are correspondingly transmuted. Moreover,
among Women, we use language implying the utmost deference for their
Sex; and they fully believe that the Chief Circle Himself is not more
devoutly adored by us than they are: but behind their backs they are
both regarded and spoken of--by all except the very young--as being
little better than "mindless organisms".
Our Theology also in the Women's chambers is entirely different from
our Theology elsewhere.
Now my humble fear is that this double training, in language as well as
in thought, imposes somewhat too heavy a burden upon the young,
especially when, at the age of three years old, they are taken from the
maternal care and taught to unlearn the old language--except for the
purpose of repeating it in the presence of their Mothers and
Nurses--and to learn the vocabulary and idiom of science. Already
methinks I discern a weakness in the grasp of mathematical truth at the
present time as compared with the more robust intellect of our
ancestors three hundred years ago. I say nothing of the possible
danger if a Woman should ever surreptitiously learn to read and convey
to her Sex the result of her perusal of a single popular volume; nor of
the possibility that the indiscretion or disobedience of some infant
Male might reveal to a Mother the secrets of the logical dialect. On
the simple ground of the enfeebling of the Male intellect, I rest this
humble appeal to the highest Authorities to reconsider the regulations
of Female education.
PART II: OTHER WORLDS
"O brave new worlds, that have such people in them!"
Section 13. How I had a Vision of Lineland
It was the last day but one of the 1999th year of our era, and the
first day of the Long Vacation. Having amused myself till a late hour
with my favourite recreation of Geometry, I had retired to rest with an
unsolved problem in my mind. In the night I had a dream.
I saw before me a vast multitude of small Straight Lines (which I
naturally assumed to be Women) interspersed with other Beings still
smaller and of the nature of lustrous points--all moving to and fro in
one and the same Straight Line, and, as nearly as I could judge, with
the same velocity.
A noise of confused, multitudinous chirping or twittering issued from
them at intervals as long as they were moving; but sometimes they
ceased from motion, and then all was silence.
Approaching one of the largest of what I thought to be Women, I
accosted her, but received no answer. A second and a third appeal on
my part were equally ineffectual. Losing patience at what appeared to
me intolerable rudeness, I brought my mouth into a position full in
front of her mouth so as to intercept her motion, and loudly repeated
my question, "Woman, what signifies this concourse, and this strange
and confused chirping, and this monotonous motion to and fro in one and
the same Straight Line?"
[Illustration 6]
[ASCII approximation follows]
My view of Lineland
---------
| |
| Myself|
| |
My eye o--------
Women A boy Men The KING Men A boy Women
+ + + + - --- -- -- -- -- (>----<) -- -- -- -- --- - + + + +
^ ^
The KING'S eyes
much larger than the reality
shewing that HIS MAJESTY
could see nothing but a point.
"I am no Woman," replied the small Line. "I am the Monarch of the
world. But thou, whence intrudest thou into my realm of Lineland?"
Receiving this abrupt reply, I begged pardon if I had in any way
startled or molested his Royal Highness; and describing myself as a
stranger I besought the King to give me some account of his dominions.
But I had the greatest possible difficulty in obtaining any information
on points that really interested me; for the Monarch could not refrain
from constantly assuming that whatever was familiar to him must also be
known to me and that I was simulating ignorance in jest. However, by
persevering questions I elicited the following facts:
It seemed that this poor ignorant Monarch--as he called himself--was
persuaded that the Straight Line which he called his Kingdom, and in
which he passed his existence, constituted the whole of the world, and
indeed the whole of Space. Not being able either to move or to see,
save in his Straight Line, he had no conception of anything out of it.
Though he had heard my voice when I first addressed him, the sounds had
come to him in a manner so contrary to his experience that he had made
no answer, "seeing no man", as he expressed it, "and hearing a voice as
it were from my own intestines." Until the moment when I placed my
mouth in his World, he had neither seen me, nor heard anything except
confused sounds beating against--what I called his side, but what he
called his INSIDE or STOMACH; nor had he even now the least conception
of the region from which I had come. Outside his World, or Line, all
was a blank to him; nay, not even a blank, for a blank implies Space;
say, rather, all was non-existent.
His subjects--of whom the small Lines were men and the Points
Women--were all alike confined in motion and eye-sight to that single
Straight Line, which was their World. It need scarcely be added that
the whole of their horizon was limited to a Point; nor could any one
ever see anything but a Point. Man, woman, child, thing--each was a
Point to the eye of a Linelander. Only by the sound of the voice could
sex or age be distinguished. Moreover, as each individual occupied the
whole of the narrow path, so to speak, which constituted his Universe,
and no one could move to the right or left to make way for passers by,
it followed that no Linelander could ever pass another. Once
neighbours, always neighbours. Neighbourhood with them was like
marriage with us. Neighbours remained neighbours till death did them
part.
Such a life, with all vision limited to a Point, and all motion to a
Straight Line, seemed to me inexpressibly dreary; and I was surprised
to note the vivacity and cheerfulness of the King. Wondering whether
it was possible, amid circumstances so unfavourable to domestic
relations, to enjoy the pleasures of conjugal union, I hesitated for
some time to question his Royal Highness on so delicate a subject; but
at last I plunged into it by abruptly inquiring as to the health of his
family. "My wives and children," he replied, "are well and happy."
Staggered at this answer--for in the immediate proximity of the Monarch
(as I had noted in my dream before I entered Lineland) there were none
but Men--I ventured to reply, "Pardon me, but I cannot imagine how your
Royal Highness can at any time either see or approach their Majesties,
when there are at least half a dozen intervening individuals, whom you
can neither see through, nor pass by? Is it possible that in Lineland
proximity is not necessary for marriage and for the generation of
children?"
"How can you ask so absurd a question?" replied the Monarch. "If it
were indeed as you suggest, the Universe would soon be depopulated.
No, no; neighbourhood is needless for the union of hearts; and the
birth of children is too important a matter to have been allowed to
depend upon such an accident as proximity. You cannot be ignorant of
this. Yet since you are pleased to affect ignorance, I will instruct
you as if you were the veriest baby in Lineland. Know, then, that
marriages are consummated by means of the faculty of sound and the
sense of hearing.
"You are of course aware that every Man has two mouths or voices--as
well as two eyes--a bass at one and a tenor at the other of his
extremities. I should not mention this, but that I have been unable to
distinguish your tenor in the course of our conversation." I replied
that I had but one voice, and that I had not been aware that his Royal
Highness had two. "That confirms my impression," said the King, "that
you are not a Man, but a feminine Monstrosity with a bass voice, and an
utterly uneducated ear. But to continue.
"Nature having herself ordained that every Man should wed two wives--"
"Why two?" asked I. "You carry your affected simplicity too far", he
cried. "How can there be a completely harmonious union without the
combination of the Four in One, viz. the Bass and Tenor of the Man and
the Soprano and Contralto of the two Women?" "But supposing," said I,
"that a man should prefer one wife or three?" "It is impossible," he
said; "it is as inconceivable as that two and one should make five, or
that the human eye should see a Straight Line." I would have
interrupted him; but he proceeded as follows:
"Once in the middle of each week a Law of Nature compels us to move to
and fro with a rhythmic motion of more than usual violence, which
continues for the time you would take to count a hundred and one. In
the midst of this choral dance, at the fifty-first pulsation, the
inhabitants of the Universe pause in full career, and each individual
sends forth his richest, fullest, sweetest strain. It is in this
decisive moment that all our marriages are made. So exquisite is the
adaptation of Bass to Treble, of Tenor to Contralto, that oftentimes
the Loved Ones, though twenty thousand leagues away, recognize at once
the responsive note of their destined Lover; and, penetrating the
paltry obstacles of distance, Love unites the three. The marriage in
that instant consummated results in a threefold Male and Female
offspring which takes its place in Lineland."
"What! Always threefold?" said I. "Must one wife then always have
twins?"
"Bass-voiced Monstrosity! yes," replied the King. "How else could the
balance of the Sexes be maintained, if two girls were not born for
every boy? Would you ignore the very Alphabet of Nature?" He ceased,
speechless for fury; and some time elapsed before I could induce him to
resume his narrative.
"You will not, of course, suppose that every bachelor among us finds
his mates at the first wooing in this universal Marriage Chorus. On
the contrary, the process is by most of us many times repeated. Few
are the hearts whose happy lot it is at once to recognize in each
other's voices the partner intended for them by Providence, and to fly
into a reciprocal and perfectly harmonious embrace. With most of us
the courtship is of long duration. The Wooer's voices may perhaps
accord with one of the future wives, but not with both; or not, at
first, with either; or the Soprano and Contralto may not quite
harmonize. In such cases Nature has provided that every weekly Chorus
shall bring the three Lovers into closer harmony. Each trial of voice,
each fresh discovery of discord, almost imperceptibly induces the less
perfect to modify his or her vocal utterance so as to approximate to
the more perfect. And after many trials and many approximations, the
result is at last achieved. There comes a day at last, when, while the
wonted Marriage Chorus goes forth from universal Lineland, the three
far-off Lovers suddenly find themselves in exact harmony, and, before
they are awake, the wedded Triplet is rapt vocally into a duplicate
embrace; and Nature rejoices over one more marriage and over three more
births."
Section 14. How I vainly tried to explain the nature of Flatland
Thinking that it was time to bring down the Monarch from his raptures
to the level of common sense, I determined to endeavour to open up to
him some glimpses of the truth, that is to say of the nature of things
in Flatland. So I began thus: "How does your Royal Highness
distinguish the shapes and positions of his subjects? I for my part
noticed by the sense of sight, before I entered your Kingdom, that some
of your people are Lines and others Points, and that some of the Lines
are larger--" "You speak of an impossibility," interrupted the King;
"you must have seen a vision; for to detect the difference between a
Line and a Point by the sense of sight is, as every one knows, in the
nature of things, impossible; but it can be detected by the sense of
hearing, and by the same means my shape can be exactly ascertained.
Behold me--I am a Line, the longest in Lineland, over six inches of
Space--" "Of Length", I ventured to suggest. "Fool," said he, "Space
is Length. Interrupt me again, and I have done."
I apologized; but he continued scornfully, "Since you are impervious to
argument, you shall hear with your ears how by means of my two voices I
reveal my shape to my Wives, who are at this moment six thousand miles
seventy yards two feet eight i