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Flatland: A Romance of Many Dimensions, by Edwin A. Abbot

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Flatland: A Romance of Many Dimensions
Edwin A. Abbott (1838-1926. English scholar, theologian, and writer.)

| "O day and night, but this is wondrous strange" |
| ______ |
| / / /| ------ / /| /| / /-. |
| /---- / /__| / / /__| / | / / / |
| / /___ / | / /___ / | / |/ /__.-' |
| |
| No Dimensions One Dimension |
| |
| Two Dimensions Three Dimensions |
| ___ __ |
| | | /__/| |
| |___| |__|/ |
| "Fie, fie, how franticly I square my talk!" |
With Illustrations by the Author, A SQUARE (Edwin A. Abbott)

The Inhabitants of SPACE IN GENERAL
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
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

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
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."




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


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


"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.



(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.



/ \
/ \
/ \
/ \
R/ \F
\_ /
Men's door _ Women's door
_ /

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?



C (1)
|\ - _ D
| \ ||- _
| \ || - _
| <--- >|| -----------+(> Eye-glance
___C' (2) | / A|| _ -
___--- \ - _D' | / ||_ -
__--- \ || - _ |/ _ - E
| \ || - _ B
| \ || - _
| Eye-glance \ || - _
| <----------- A'>|| ------------------------+(>
| / || _ -
| / || _ -
|__ / || _ -
---___ / || _ -
---___/ _ -E'

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.



/\ - _ 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.



/ \ - 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

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