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A ROMANCE
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I [ABBOT (E.)] Flatland : a Romance of
original parchment wrappers, VERY SCAR<
by A Square, sm. 410.,
1884
FLATLAND
A Romance of Many Dimensions
FLATLAND
A Romance of Many Dimensions
With Illustrations
by the Author, A SQUARE
" Fie, fie, how franticly 1 square my talk!'
LONDON
SEELEY &f Co., 46, 47 &r 48, ESSEX STREET, STRAND
(Late 15/54 FLEET STREET)
1884
LONDON :
R. CLAY, SONS, AND TAYLOR,
BREAD STREET HILL.
To
The Inhabitants of SPACE IN GENERAL
And H. C. IN PARTICULAR
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of THREE Dimensions
Having been previously conversant
With ONLY Two
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE OR EVEN Six Dimensions
Thereby contributing
To the Enlargement of THE IMAGINATION
And the possible Development
Of that most rare and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY
CONTENTS
PART I
THIS WORLD
Section
1 Of the Nature of Flatland
2 Of the Climate and Houses in Flatland
3 Concerning the Inhabitants of Flatland
4 Concerning the Women
5 Of our Methods of Recognizing one another
6 Of Recognition by Sight
7 Concerning Irregular Figures
8 Of the Ancient Practice of Painting
9 Of the Universal Colour Bill
10 Of the Suppression of the Chromatic Sedition
1 1 Concerning our Priests
12 Of the Doctrine of our Priests
viii Contents
Section
13 How 1 had a Vision of Lineland
14 How in my Vision I endeavoured to explain the nature of Flatland, but
could not
15 Concerning a Stranger from Spaceland
1 6 How the Stranger vainly endeavoured to reveal to me in words the mysteries
of Spaceland
1 7 How the Sphere, having in vain tried words ; resorted to deeds
1 8 How I came to Spaceland and what I saw there
19 How, though the Sphere showed me other mysteries of Spaceland, I still
desired more ; and what came of it
20 How the Sphere encouraged me in a Vision
2 1 How I tried to teach the Theory of Three Dimensions to my Grandson, and
with what success
22 How I then tried to diffuse the Theory of Three Dimensions by other means,
and of the result
PART 1
"Be -patient, for the world is broad and wide"
FLATLAND
PART I
THIS WORLD
§ i. — Of the Nature of Flat land.
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
4 Flatland
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 Flatland citizen) 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 of
the table, you will find that it ceases to appear
to you a figure, and that it becomes in appear-
ance a straight line. Take for example an
equilateral Triangle — who represents with us a
Tradesman of the respectable class. Fig. I
represents the Tradesman as you would see him
while you were bending over him from above ;
•(2)
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
(3)
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.
When I was in Spaceland I heard that your sailors have very similar
experiences while they traverse your seas and discern some distant island
Flatland 5
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 towards 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 close 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.
§ 2. — Of the climate ana 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
6 Flatland
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,
Flatland
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 running against them : and therefore, 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.
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
8 Flatland
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.
§ 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 ryour 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 approxi-
mating still more to the type of the Equal-sided Triangle.
Rarely — in proportion to the vast number of Isosceles births— is a
genuine and certifiable Equal-sided Triangle produced from Isosceles
parents.1 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.
1 " What need of a certificate?" a Spaceland critic may ask : " Is not the procreation of a Square
Son a certificate from Nature herself, proving the Equal-sidedness of the Father ? " 1 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.
B
io Flat land
The birth of a True Equilateral Triangle from Isosceles parents is the
subject of rejoicing in our country for many furlongs round. After a
strict eximination 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 Isosceles 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 vulgarise 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 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.
1 1
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 ulti-
mately 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.
§ 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.
B 2
1 2 Flatland
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 : —
Flatland 1 3
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.
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 con-
finement 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
1 When I was in Spaceland I understood that some of your Priestly Circles have in the same
way a separate entrance for Villagers, Fanners, and Teachers of Board Schools (Spectator, Sept.
1884, p. 1255) that they may "approach in a becoming and respectful manner."
14 Flat land
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 civilised States no female is suffered to stand in any public place with-
out 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 recognise no distinctions. I have actually known a case
where a Woman has exterminated her whole household, and half an hour
Flat land 15
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 thtir
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 simulations,
these reckless creatures too often neglect the prescribed construction of the
Women's apartments, or irritate their wives by ill-advised expressions
out of doors, which they refuse immediately to retract. Moreover a blunt
and stolid regard for literal truth indisposes them to make those lavish
promises by which the more judicious Circle can in a moment pacify his
consort. The result is massacre ; not however without its advantages,
as it eliminates the more brutal and troublesome of the Isosceles ; and
by many of our Circles the destructiveness of the Thinner Sex is
regarded as one among many providential arrangements for suppressing
redundant population, and nipping Revolution in the bud.
Yet even in our best regulated and most approximately circular families
I cannot say that the ideal of family life is so high as with you in Spaceland.
There is peace, in so far as the absence of slaughter may be called by that
name, but there is necessarily little harmony of tastes or pursuits ; and the
cautious wisdom of the Circles has ensured safety at the cost of domestic
1 6 Flat land
comfort. In every Circular or Polygonal household it has been a habit
from time immemorial — and has now 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
Flat land 1 7
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.
§ 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 configurations ?
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
i8 Flat land
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 recipro-
cal. 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 you 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 any individual ;
and this, once ascertained, tells us the class of the person whom we are
Flat land 19
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 incau-
tious, 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 occurred
to his great-great-great- Grand father, a respectable Working Man with
an angle or brain of 59° 30'. 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
2O Flatland
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°, and not till the lapse of five generations was the lost
ground recovered, the full 60° 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° 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°, Specimens of which
are placed in every Elementary School throughout the land. Owing
to occasional retrogressions, to still more frequent moral and intellectual
Flat land 2 1
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°. 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 Specimens 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 show that Recognition
22
Flatland
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 remain, 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.
§ 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 distin-
guish by the visual organ between individuals of different classes : yet
now I am about to explain to my Spaceland Critics how we are able
to recognize one another by the sense of sight.
If however the Reader will take the trouble to refer to the passage
in which Recognition by Feeling is stated to be universal, he will find
this qualification — "among the lower classes." It is only among the
higher classes and in our more temperate climates that Sight Recognition
is practised.
That this power exists in any regions and for any classes, is the result
of Fog; which prevails during the greater part of the year in all parts
save the torrid zones. That which is with you in Spaceland an unmixed
evil, blotting out the landscape, depressing the spirits, and enfeebling the
health, is by us recognized as a blessing scarcely inferior to air itself, and
as the Nurse of arts and Parent 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 in-
distinguishably clear ; and this is actually the case in those unhappy
countries in which the atmosphere is perfectly dry and transparent.
Flatland
c
D
E
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 experi-
mental 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 ap-
proaching 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 ?
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 (i) 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 AD recede rapidly into the fog ; and
24 Flat land
what appear to me as the Merchant's extremities, viz. D and C, 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 (A7), yet it will shade away less
rapidly into dimness, because the sides (A'C', A'B7) recede less rapidly into
the fog ; and what appear to me the Physician's extremities, viz. D' and E',
will 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
"-•fit he may not be a Straight Line,
or, in other words, a Woman.
Again, when I am in the com-
pany of one of my two hexa-
gonal Grandsons, contemplating
one of his sides (AB) full front,
Flat land 25
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 through-
out and shading away into greater dimness toward the extremities
C and 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
C
26 Flatland
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 lip-speech
and lip-reading, so it is with us as regards " Seeing " and " Feeling."
None who in early life resort to "Feeling" will ever learn "Seeing" in
perfection.
For this reason, among our Higher Classes, " Feeling" is discouraged
or absolutely forbidden. From the cradle their children, instead of going
to the Public Elementary schools (where the art of Feeling is taught,)
are sent to higher Seminaries of an exclusive character ; and at our illus-
trious 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
Flatland 27
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 Leav-
ing 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
shows 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.
§ 7. — Of 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
C 2
28 Flatland
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 three 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 would be unequal. Instead of
its being sufficient to feel, or estimate by sight, a single angle in order to
determine the form of an individual, it would be necessary to ascertain
each angle by the experiment of Feeling. But life would be too short for
such a tedious groping. The whole science and art of Sight Recognition
would at once perish ; Feeling, so far as it is an art, would not long survive ;
intercourse would become perilous or impossible ; there would be an end
to all confidence, all forethought ; no one would be safe in making the
most simple social arrangements; in a word, civilization 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 every one knows to an inch or two the
Flatland 29
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 every one 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
30 Flatland
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 in 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
Flatland 3 1
<
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. Ad-
vocating 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 im-
probable, I would suggest that the Irregular offspring be painlessly and
mercifully consumed.
§ 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 charm upon
the lives of our ancestors in the remotest ages. Some private individual
— a Pentagon whose name is variously reported — having casually dis-
covered the constituents of the simpler colours and a rudimentary method of
painting, is said to have begun by decorating first his house, then his slaves,
32 Flat I and
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
Flatland 33
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.
34 Flatland
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.
§ 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 disrepute
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 and 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 " monopolising 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
Flatland 35
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 semi-
circle 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.
36 Flatland
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.
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
if not 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
Flatland 37
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 house-
holds 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 demor-
alization 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 intro-
duction of the Universal Colour Bill, the Circles had not only held their
own, but even increased their lead of 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
38 Flatland
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.
§ 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, rinding
their entreaties fruitless, fell on and slaughtered their innocent children and
husbands, 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 some-
times 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
Flatland 39
Dodecahedron. 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 pre-
cautions on the part of the relations of the bride, he succeeded in con-
summating 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
40 Flatland
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 a 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
Flat land 41
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
skilful 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
D
42 Flatland
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.
§ ii. — 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. T/iat 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
Flatland 43
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 Adminis-
trators of all Business, Art, and Science ; Directors of Trade, Commerce,
Generalship, Architecture, Engineering, Education, Statesmanship, Legis-
lature, Morality, Theology ; doing nothing themselves, they are the
Causes of everything, worth doing, that is done by others.
Although popularly every one 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. In proportion to the number of the sides the Polygon approxi-
mates to a Circle ; and, when the number is very great, 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
D 2
44 Flatland
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 eides 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 some-
times— by no means always, for the process is attended with serious risk —
but sometimes overleaps two or three hundred generations, and as it were
Flatland 45
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 son 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.
§ 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 improve-
ment 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, encourage-
ment, 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,
46 Flatland
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, con-
cluded 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 faith-
fully defends the interests of his client, when you ought in reality rather
to admire the exact precision of his Rectangles ? 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
Flatland 47
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.
Consistently carrying out their policy of making Configuration the lead-
ing 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," how-
ever, is by no means meant " indulgence," but a reverent regard for their
highest interests : and the Circles teach that the duty of fathers is to
subordinate their own interests to those of posterity, thereby advancing
the welfare of the whole State as well as that of their own immediate
descendants.
The weak point in the system of the Circles — if a humble Square may
venture to speak of anything Circular as containing any element of weak-
ness— appears to me to be found in their relations with Women.
As it is of the utmost importance for Society that Irregular births should
be discouraged, it follows that no Woman who has any Irregularities in her
48 Flatland
ancestry is a fit partner for one who desires that his posterity should rise
by regular degrees in the social scale.
Now the Irregularity of a Male is a matter of measurement ; but as
all Women are straight, and therefore visibly Regular so to speak, one has
to devise some other means of ascertaining what I may call their invisible
Irregularity, that is to say their potential Irregularities as regards possible
offspring. This is effected by carefully-kept pedigrees, which are preserved
and supervised by the State ; and without a certified pedigree no Woman
is allowed to marry.
Now it might have been supposed that a Circle — proud of his ancestry
and regardful for a posterity which might possibly issue hereafter in a
Chief Circle — would be more careful than any other to choose a wife who
had no blot on her escutcheon. But it is not so. The care in choosing a
Regular wife appears to diminish as one rises in the social scale. Nothing
would induce an aspiring Isosceles, who had hopes of generating an Equi-
lateral Son, to take a wife who reckoned a single Irregularity among her
Ancestors; a Square or Pentagon, who is confident that his family is steadily
on the rise, does not enquire above the five-hundredth generation ; a Hex-
agon or Dodecahedron is even more careless of the wife's pedigree ; but a
Circle has been known deliberately to take a wife who has had an Irregular
Great-Grandfather, and all because of some slight superiority of lustre, or
because of the charms of a low voice — which, with us, even more than with
you, is thought " an excellent thing in Woman."
Such ill-judged marriages are, as might be expected, barren, if they do
not result in positive Irregularity or in diminution of sides ; but none of
these evils have hitherto proved sufficiently deterrent. The loss of a few
sides in a highly-developed Polygon is not easily noticed, and is sometimes
compensated by a successful operation in the Neo-Therapeutic Gymnasium,
as I have described above ; and the Circles are too much disposed to acquiesce
in infecundity as a Law of the superior development. Yet, if this evil be
Flatland 49
not arrested, the gradual diminution of the Circular class may soon become
more rapid, and the time may be not far distant when, the race being no
longer able to produce a Chief Circle, the Constitution of Flatland must
fall.
One other word of warning suggests itself to me, though I cannot so
easily mention a remedy ; and this also refers to our relations .with Women.
About three hundred years ago, it was decreed by the Chief Circle that,
since women are deficient in Reason but abundant in Emotion, they ought
no longer to be treated as rational, nor receive any mental education. .[The
consequence was that they were no longer taught to read, nor even to master
Arithmetic enough to enable them to count the angles of their husband
or children ; and hence they sensibly declined during each generation in
intellectual power. And this system of female non-education or quietism
still prevails.
My fear is that, with the best intentions, this policy has been carried so
far as to react injuriously on the Male Sex.
For the consequence is that, as things now are, we Males have to lead a
kind of bi-lingual, and I may almost say bi-mental existence. With the
Women, we speak of " love," "duty," "right," "wrong," "pity," "hope,"
and other irrational and emotional conceptions, which have no existence,
and the fiction of which has no object except to control feminine exuber-
ances ; but among ourselves, and in our books, we have an entirely different
vocabulary and I may almost say, idiom. " Love " then becomes ' the an-
ticipation of benefits ; " . " duty " becomes " necessity " or " fitness ; " and
other words are correspondingly transmuted. Moreover, among Women,
we use language implying the utmost deference for their Sex ; and they
fully believe that the Chief Circle Himself is not more devoutly adored by
us than they are : but behind their backs they are both regarded and spoken
of — by all except the very young — as being little better than " mindless
organisms."
50 Flatland
Our Theology also in the Women's chambers is entirely different from
our Theology elsewhere.
Now my humble fear is that this double training, in language as well
as in thought, imposes somewhat too heavy a burden upon the young,
especially when, at the age of three years old, they are taken from the
maternal care and taught to unlearn the old language — except for the pur-
pose of repeating it in the presence of their Mothers and Nurses — and to
learn the vocabulary and idiom of science. Already methinks I discern a
weakness in the grasp of mathematical truth at the present time as com-
pared with the more robust intellect of our ancestors three hundred years
ago. I say nothing of the possible danger if a Woman should ever sur-
reptitiously learn to read and convey to her Sex the result of her perusal
of a single popular volume ; nor of the possibility that the indiscretion or
disobedience of some infant Male might reveal to a Mother the secrets of
the logical dialect. On the simple ground of the enfeebling of the Male
intellect, I rest this humble appeal to the highest Authorities to reconsider
the regulations of Female Education.
PART II
OTHER WORLDS
" O brave new worlds,
That have such people in them ! "
§ 13. — How I had a Vision of Lineland.
IT was the last day but one of the 1 999th year of our era, and the first
day of the Long Vacation. Having amused myself till a late hour with
my favourite recreation of Geometry, I had retired to rest with an unsolved
problem in my mind. In the night I had a dream.
I saw before me a vast multitude of small Straight Lines (which I
naturally assumed to be Women) interspersed with other Beings still
smaller and of the nature of lustrous Points — all moving to and fro in one
and the same Straight Line, and, as nearly as I could judge, with the
same velocity.
54 Plat land
A noise of confused, multitudinous chirping or twittering issued from
them at intervals as long as they were moving ; but sometimes they
ceased from motion, and then all was silence.
Approaching one of the largest of what I thought to be Women, I
accosted her, but received no answer. A second and third appeal on my
part were equally ineffectual. Losing patience at what appeared to me
intolerable rudeness, I brought my mouth into a position full in front of
her mouth so as to intercept her motion, and loudly repeated my question,
" Woman, what signifies this concourse, and this strange and confused
chirping, and this monotonous motion to and fro in one and the same
Straight Line?"
" I am no Woman," replied the small Line ; " I am the Monarch of the
world. But thou, whence intrudest thou into my realm of Lineland ? "
Receiving this abrupt reply, I begged pardon if I had in any way startled
or molested his Royal Highness ; and describing myself as a stranger I
besought the King to give me some account of his dominions. But I had
the greatest possible difficulty in obtaining any information on points that
really interested me ; for the Monarch could not refrain from constantly
assuming that whatever was familiar to him must also be known to me and
that I was simulating ignorance in jest. However, by persevering questions
I elicited the following facts:
It seemed that this poor ignorant Monarch — as he called himself — was
persuaded that the Straight Line which he called his Kingdom, and in
which he passed his existence, constituted the whole of the world, and
indeed the whole of Space. Not being able either to move or to see, save
in his Straight Line, he had no conception of anything out of it. Though
he had heard my voice when I first addressed him, the sounds had come to
him in a manner so contrary to his experience that he had made no answer,
" seeing no man," as he expressed it, " and hearing a voice as it were from
my own intestines." Until the moment when I placed my mouth in his
Flatland
55
World, he had neither seen me, nor heard anything except confused sounds
beating against what I called his side, but what he called his inside or
stomach ; nor had he even now the least conception of the region from
which I had come. Outside his World, or Line, all was a blank to him ;
nay, not even a blank, for a blank implies Space ; say, rather, all was
non-existent.
His subjects — of whom the small Lines were Men and the Points
Women — were all alike confined in motion and eye- sight to that single
Straight Line, which was their World. It need scarcely be added that the
whole of their horizon was limited to a Point ; nor could any one ever see
anything but a Point. Man, woman, child, thing — each was a Point to the
eye of a Linelander. Only by the sound of the voice could sex or age be
distinguished. Moreover, as each individual occupied the whole of the
narrow path, so to speak, which constituted his Universe, and no one could
move to the right or left to make way for passers by, it followed that no
Linelander could ever pass another. Once neighbours, always neighbours.
Neighbourhood with them was like marriage with us. Neighbours remained
neighbours till death did them part.
Such a life, with all vision limited to a Point, and all motion to a Straight
Line, seemed to me inexpressibly dreary ; and I was surprised to note the
vivacity and cheerfulness of the King. Wondering whether it was possible,
amid circumstances so unfavourable to domestic relations, to enjoy the
pleasures of conjugal union, I hesitated for some time to question his
Royal Highness on so delicate a subject ; but at last I plunged into it
by abruptly inquiring as to the health of his family. " My wives and
children," he replied, " are well and happy."
Staggered at this answer — for in the immediate proximity of the
Monarch (as I had noted in my dream before I entered Lineland) there
were none but Men — I ventured to reply, " Pardon me, but I cannot
imagine how your Royal Highness can at any time either see or approach
56 Flatland
their: Majesties, when there are at least half a dozen intervening indi-
viduals, whom you can neither see through, nor pass by ? Is it possible
that in Lineland proximity is not necessary for marriage and for the
generation of children ? "
"How can you ask so absurd a question ?" replied the Monarch. "If
it were indeed as you suggest, the Universe would soon be depopulated.
No, no ; neighbourhood is needless for the union of hearts ; and the birth
of children is too important a matter to have been allowed to depend upon
such an accident as proximity. You cannot be ignorant of this. Yet
since you are pleased to affect ignorance, I will instruct you as if you
were the veriest baby in Lineland. Know, then, that marriages are
consummated by means of the faculty of sound and the sense of hearing.
" You are of course aware that every Man has two mouths or voices —
as well as two eyes — a bass at one and a tenor at the other of his ex-
tremities. I should not mention this, but that I have been unable to
distinguish your tenor in the course of our conversation." I replied that
I had but one voice, and that I had not been aware that His Royal
Highness had two. " That confirms my impression," said the King, " that
you are not a Man, but a feminine Monstrosity with a bass voice and an
utterly uneducated ear. But to continue.
" Nature herself having ordained that every Man should wed two
wives " Why two ? " asked I. " You carry your affected simplicity
too far," he cried. " How can there be a completely harmonious union
without the combination of the Four in One, viz. the Bass and Tenor of
the Man and the Soprano and Contralto of the two Women ? " " But
supposing," said I, " that a man should prefer one wife or three ? " " It
is impossible," he said ; " it is as inconceivable as that two and one should
make five, or that the human eye should see a Straight Line." I would
have interrupted him ; but he proceeded as follows :
" Once in the middle of each week a Law of Nature compels us to
Flatland 57
move to and fro with a rhythmic motion of more than usual violence, which
continues for the time you would take to count a hundred and one. In the
midst of this choral dance, at the fifty-first pulsation, the inhabitants of the
Universe pause in full career, and each individual sends forth his richest,
fullest, sweetest strain. It is in this decisive moment that all our marriages
are made. So exquisite is the adaptation of Bass to Treble, of Tenor to
Contralto, that oftentimes the Loved Ones, though twenty thousand
leagues away, recognise at once the responsive note of their destined
Lover ; and, penetrating the paltry obstacles of distance, Love unites the
three. The marriage in that instant consummated results in a threefold
Male and Female offspring which takes its place in Lineland.
" What ! Always threefold ? " said I. " Must one wife then always
have twins ? "
" Bass-voiced Monstrosity ! yes," replied the King. " How else could
the balance of the Sexes be maintained, if two girls were not born for
every boy ? Would you ignore the very Alphabet of Nature ? " He
ceased, speechless for fury ; and some time elapsed before I could induce
him to resume his narrative.
" You will not, of course, suppose that every bachelor among us finds
his mates at the first wooing in this universal Marriage Chorus. On the
contrary, the process is by most of us many times repeated. Few are the
hearts whose happy lot it is at once to recognise in each other's voices the
partner intended for them by Providence, and to fly into a reciprocal and
perfectly harmonious embrace. With most of us the courtship is of long
duration. The Wooer's voices may perhaps accord with one of the future
wives, but not with both ; or not, at first, with either ; or the Soprano and
Contralto may not quite harmonise. In such cases Nature has provided
that every weekly Chorus shall bring the three Lovers into closer harmony.
Each trial of voice, each fresh discovery of discord, almost imperceptibly
induces the less perfect to modify his or her vocal utterance so as to
E
58 Flatland
approximate to the more perfect. And after many trials and many ap-
proximations, the result is at last achieved. There comes a day at last,
when, while the wonted Marriage Chorus goes forth from universal
Lineland, the three far-off Lovers suddenly find themselves in exact
harmony, and, before they are aware, the wedded Triplet is rapt vocally
into a duplicate embrace ; and Nature rejoices over one more marriage and
over three more births. "
§ 14. — How I vainly tried to explain the nature of Flatland.
Thinking that it was time to bring down the Monarch from his raptures
to the level of common sense, I determined to endeavour to open up to
him some glimpses of the truth, that is to say of the nature of things in
Flatland. So I began thus : " How does your Royal Highness distinguish
the shapes and positions of his subjects ? I for my part noticed by the
sense of sight, before I entered your Kingdom, that some of your people
are Lines and others Points, and that some of the Lines are larger "
" You speak of an impossibility," interrupted the King ; " you must have
seen a vision ; for to detect the difference between a Line and a Point by
the sense of sight is, as every one knows, in the nature of things, impossible ;
but it can be detected by the sense of hearing, and by the same means my
shape can be exactly ascertained. Behold me — I am a Line, the longest in
Lineland, over six inches of Space " " Of Length," I ventured to suggest.
" Fool," said he, " Space is Length. Interrupt me again, and I have
done."
I apologised; but he continued scornfully, "Since you are impervious
to argument, you shall hear with your ears how by means of my two
voices I reveal my shape to my Wives, who are at this moment six
thousand miles seventy yards two feet eight inches away, the one to
the North, the other to the South. Listen, I call to them."
Flatland
59
He chirruped, and then complacently continued : " My wives at this
moment receiving the sound of one of my voices, closely followed by the
other, and perceiving that the latter reaches them after an interval in which
sound can traverse 6*457 inches, infer that one of my mouths is 6*457
inches further from them than the other, and accordingly know my shape
to be 6*457 inches. But you will of course understand that my wives
do not make this calculation every time they hear my two voices. They
made it, once for all, before we were married. But they could make
it at any time. And in the same way I can estimate the shape of
any of my Male subjects by the sense of sound,"
" But how," said I, " if a Man feigns a Woman's voice with one
of his two voices, or so disguises his Southern voice that it cannot be
recognised as the echo of the Northern ? May not such deceptions
cause great inconvenience ? And have you no means of checking frauds
of this kind by commanding your neighbouring subjects to feel one
another ? " This of course was a very stupid question, for feeling could
not have answered the purpose ; but I asked with the view of irritating
the Monarch, and I succeeded perfectly.
" What ! " cried he in horror, " explain your meaning." " Feel, touch,
come into contact," I replied. " If you mean by feeling" said the King,
"approaching so close as to leave no space between two individuals,
know, Stranger, that this offence is punishable in my dominions by death.
And the reason is obvious. The frail form of a Woman, being liable to be
shattered by such an approximation, must be preserved by the State ;
but since Women cannot be distinguished by the sense of sight from
Man, the Law ordains universally that neither Man nor Woman shall be
approached so closely as to destroy the interval between the approximator
and the approximated.
"And indeed what possible purpose would be served by this illegal
and unnatural excess of approximation which you call touching, when
E 2
60 Flatland
all the ends of so brutal and coarse a process are attained at once more
easily and more exactly by the sense of hearing. As to your suggested
danger of deception, it is non-existent : for the Voice, being the essence of
one's Being, cannot be thus changed at will. But come, suppose that
I had the power of passing through solid things, so that I could penetrate
my subjects, one after another, even to the number of a billion,
verifying the size and distance of each by the sense of feeling: how
much time and energy would be wasted in this clumsy and inaccurate
method ! Whereas now, in one moment of audition, I take as it were the
census and statistics, local, corporal, mental, and spiritual, of every living
being in Lineland. Hark, only hark ! "
So saying he paused and listened, as if in an ecstasy, to a sound
which seemed to me no better than a tiny chirping from an innumerable
multitude of lilliputian grasshoppers.
" Truly," replied I, " your sense of hearing serves you in good stead,
and fills up many of your deficiencies. But permit me to point out
that your life in Lineland must be deplorably dull. To see nothing but
a Point ! Not even to be able to Contemplate a Straight Line ! Nay, not
even to know what a Straight Line is ! To see, yet to be cut off from
those Linear prospects which are vouchsafed to us in Flatland ! Better
surely to have no sense of sight at all than to see so little ! I
grant you I have not your discriminative faculty of hearing ; for the
concert of all Lineland which gives you such intense pleasure, is to
me no better than a multitudinous twittering or chirping. But at
least I can discern, by sight, a Line from a Point. And let me prove
it. Just before I Came into your kingdom, I saw you dancing from
left to right, and then from right to left, with seven Men and a Woman
in your immediate proximity on the left, and eight Men and two Women
on your right. Is not this correct ? "
"It is correct," said the King, "so far as the numbers and sexes are
Flat land 61
concerned, though I know not what you mean by ' right ' and ' left.'
But I deny that you saw these things. For how could you see the Line,
that is to say the inside, of any Man ? But you must have heard these
things, and then dreamed that you saw them. And let me ask what you
mean by those words ' left ' and ' right.' I suppose it is your way of
saying Northward and Southward."
" Not so," replied I ; " besides your motion of Northward and
Southward, there is another motion which I call from right to left."
King. Exhibit to me, if you please, this motion from left to
right.
/. Nay, that I cannot do, unless you could step out of your Line
altogether.
King. Out of my Line ? Do you mean out of the World ? Out
of Space ?
/. Well, yes. Out of your World. Out of your Space. For your
Space is not the true Space. True Space is a Plane ; but your Space
is only a Line.
King. If you cannot indicate this motion from left to right by
yourself moving in it, then I beg you to describe it to me in words.
/. If you cannot tell your right side from my left, I fear that no words
of mine can make my meaning clear to you. But surely you cannot be
ignorant of so simple a distinction.
King. I do not in the least understand you.
/. Alas ! How shall I make it clear ? When you move straight on,
does it not sometimes occur to you that you could move in some other
way, turning your eye round so as to look in the direction towards
which your side is now fronting ? In other words, instead of always
moving in the direction of one of your extremities, do you never feel a
desire to move in the direction, so to speak, of your side ?
King. Never. And what do you mean ? How can a man's inside
62 Flatland
"front" in any direction? Or how can a man move in the direction
of his inside ?
/. Well then, since words cannot explain the matter, I will try deeds,
and will move gradually out of Lineland in the direction which I
desire to indicate to you.
At the word I began to move my body out of Lineland. As long as
any part of me remained in his dominion and in his view, the King
kept exclaim-
ing, " I see
you, I see you
still ; you are
not moving."
But when I
had at last moved myself out of his Line, he cried in his shrillest voice,
" She is vanished ; she is dead." " I am not dead," replied I ; "I am
simply out of Lineland, that is to say, out of the Straight Line which you
call Space, and in the true Space, where I can see things as they are.
And at this moment I can see your Line, or side — or inside as you are
pleased to call it ; and I can also see the Men and Women on the North
and South of you, whom I will now enumerate, describing their order, their
size, and the interval between each,"
When I had done this at great length, I cried triumphantly, " Does
this at last convince you ? " And, with that, I once more entered
Lineland, taking up the same position as before.
But the Monarch replied, " If you were a Man of sense-^-though, as you
appear to have only one voice I have little doubt you are not a Man but a
Woman — but, if you had a particle of sense, you would listen to reason.
You ask me to believe that there is another Line besides that which my
senses indicate, and another motion besides that of which I am daily
conscious. I, in return, ask you to describe in words or indicate by
Flatland 63
motion that other Line of which you speak. Instead of moving, you
merely exercise some magic art of vanishing and returning to sight ; and
instead of any lucid description of your new World, you simply tell me the
numbers and sizes of some forty of my retinue, facts known to any
child in my capital. Can anything be more irrational or audacious ?
Acknowledge your folly or depart from my dominions."
Furious at his perversity, and especially indignant that he professed to
be ignorant of my Sex, I retorted in no measured terms, " Besotted Being !
You think yourself the perfection of existence, while you are in reality
the most imperfect and' imbecile. You profess to see, whereas you can see
nothing but a Point ! You plume yourself on inferring the existence of a
Straight Line; but I can see Straight Lines and infer the existence of
Angles, Triangles, Squares, Pentagons, Hexagons, and even Circles. Why
waste more words ? suffice it that I am the completion of your incomplete
self. You are a Line, but I am a Line of Lines, called in my country
a Square : and even I, infinitely superior though I am to you, am of little
account among the great Nobles of Flatland, whence I have come to
visit you, in the hope of enlightening your ignorance."
Hearing these words the King advanced towards me with a menacing
cry as if to pierce me through the diagonal ; and in that same moment
there arose from myriads of his subjects a multitudinous war-cry,
increasing in vehemence till at last methpught it rivalled the roar of
an army of a hundred thousand Isosceles, and the artillery of a
thousand] Pentagons. Spell-bound and motionless I could neither
speak nor move to avert the impending destruction ; and still the
noise grew louder, and the King came closer, when I awoke to find
the breakfast-bell recalling me to the realities of Flatland,
64 Flat land
§ 15. — Concerning a Stranger from Spac eland.
From dreams I proceed to facts.
It was the last day of the 1999^1 year of our era. The pattering of
the rain had long ago announced nightfall ; and I was sitting 1 in the
company of my wife, musing on the events of the past and the prospects
of the coming year, the coming century, the coming Millennium.
My four Sons and two orphan Grandchildren had retired to their
several apartments ; and my Wife alone remained with me to see the old
Millennium out and the new one in.
I was rapt in thought, pondering in my mind some words that had
casually issued from the mouth of my youngest Grandson, a most promising
young Hexagon of unusual brilliancy and perfect angularity. His uncles
and I had been giving him his usual practical lesson in Sight Recognition,
turning ourselves upon our centres, now rapidly, now more slowly, and
questioning him as to our positions ; and his answers had been so satis-
factory that I had been induced to reward him by giving him a few hints
on Arithmetic, as applied to Geometry.
Taking nine Squares, each an inch every way, I had put them together
so as to make one large Square, with a side of three inches, and I had
hence proved to my little Grandson that — though it was impossible for us
to see the inside of the Square — yet we might ascertain the number of
square inches in a Square by simply squaring the number of inches
1 When I say " sitting," of course I do not mean any change of attitude such as you in Flatland
signify by that word ; for as we have no feet, we can no more "sit " nor " stand " (in your sense of
the word) than one of your soles or flounders.
Nevertheless, we perfectly well recognise the different mental states of volition implied in
" tying>" "sitting," and " standing," which are to some extent indicated to a beholder by a slight
increase of lustre corresponding to the increase of volition.
But on this, and a thousand other kindred subjects, time forbids me to dwell.
Flatland 65
,
in the side : " and thus," said I, " we know that y, or 9, represents the
number of square inches in a Square whose side is 3 inches long."
The little Hexagon meditated on this awhile and then said jo me: "But
you have been teaching me to raise numbers to the third power ; I suppose
33 must mean something in Geometry ; what does it mean ? " " Nothing
at all," replied I, " not at least in Geometry ; for Geometry has only Two
Dimensions." And then I began to show the boy how a Point by moving
through a length of three inches makes a Line of three inches, which may
be represented by 3 ; and how a Line of three inches, moving parallel to
itself through a length of three inches, makes a Square of three inches
every way, which may be represented by y.
Upon this, my Grandson, again returning to his former suggestion, took
me up rather suddenly and exclaimed, " Well, then, if a Point by moving
three inches, makes a Line of three inches represented by 3 ; and if a straight
Line of three inches, moving parallel to itself, makes a Square of three
inches every way, represented by 32 ; it must be that a Square of three
inches every way, moving somehow parallel to itself (but I don't see how)
must make a Something else (but I don't see what) of three inches every
way — and this must be represented by 33."
" Go to bed," said I, a little ruffled by his interruption ; " if you would
talk less nonsense, you would remember more sense."
So my Grandson had disappeared in disgrace ; and there I sat by my
Wife's side, endeavouring to form a retrospect of the year 1999 and of the
possibilities of the year 2000, but not quite able to shake off the thoughts
suggested by the prattle of my bright little Hexagon. Only a few sands
now remained in the half-hour glass. Rousing myself from my reverie I
turned the glass Northward for the last time in the old Millennium ; and in
the act, I exclaimed aloud, " The boy is a fool."
Straightway I became conscious of a Presence in the room, and a
chilling breath thrilled through my very being. " He is no such thing,"
66 Flatland
cried my Wife, "and you are breaking the Commandments in thus dis-
honouring your own Grandson." But I took no notice of her. Looking
round in every direction I could see nothing ; yet still I felt a Presence,
and shivered as the cold whisper came again. I started up. " What is
the matter ? " said my Wife, " there is no draught ; what are you
looking for ? There is nothing." There was nothing ; and I resumed
my seat, again exclaiming, " The boy is a fool, I say ; 33 can have no
meaning in Geometry." At once there came a distinctly audible reply,
" The boy is not a fool ; and 33 has an obvious Geometrical meaning."
My Wife as well as myself heard the words, although she did not
understand their meaning, and both of us sprang forward in the direction
of the sound. What was our horror when we saw before us a Figure !
At the first glance it appeared to be a Woman, seen sideways ; but a
moment's observation shewed me that the extremities passed into dimness
too rapidly to represent one of the Female Sex; and I should have
thought it a Circle, only that it seemed to change its size in a manner
impossible for a Circle or for any Regular Figure of which I had had
experience.
But my Wife had not my experience, nor the~ coolness necessary to
note these characteristics. With the usual hastiness and unreasoning
jealousy of her Sex, she flew at once to the conclusion that a Woman
had entered the house through some small aperture. " How comes this
person here?" she exclaimed, "you promised me, my dear, that there
should be no ventilators in our new house." " Nor are there any," said I ;
" but what makes you think that the stranger is a Woman ? I see by my
power of Sight Recognition " " Oh, I have no patience with your
Sight Recognition," replied she, " ' Feeling is believing ' and ' A Straight
Line to the touch is worth a Circle to the sight ' " — two Proverbs, very
common with the Frailer Sex in Flatland.
"Well," said I, for I was afraid of irritating her, "if it must be so,
Flatland 67
demand an introduction." Assuming her most gracious manner, my Wife
advanced towards the Stranger, " Permit me, Madam, to feel and be felt
by " then, suddenly recoiling, " Oh ! it is not a Woman, and there
are no angles either, not a trace of one. Can it be that I have so
misbehaved to a perfect Circle ? "
" I am indeed, in a certain sense a Circle," replied the Voice, "and a
more perfect Circle than any in Flatland ; but to speak more accurately,
I am many Circles in one." Then he added more mildly, " I have a
message, dear Madam, to your husband, which I must not deliver in
your presence ; arid, if )rou would suffer us to retire for a few minutes '
But my Wife would not listen to the proposal that our august Visitor should
so incommode himself, and assuring the Circle that the hour for her own
retirement had long passed, with many reiterated apologies for her recent
indiscretion, she at last retreated to her apartment.
I glanced at the half-hour glass. The last sands had fallen. The
second Millennium had begun,
§ 1 6. — How the Stranger vainly endeavoured to reveal to me in
words the mysteries of Sfiaceland.
As soon as the sound of my Wife's retreating footsteps had died away,
I began to approach the Stranger with the intention of taking a nearer
view and of bidding him be seated : but his appearance struck me dumb
and motionless with astonishment. Without the slightest symptoms of
angularity he nevertheless varied every instant with gradations of size
and brightness scarcely possible for any Figure within the scope of my
experience. The thought flashed across me that I might have before me
a burglar or cut-throat, some monstrous Irregular Isosceles, who, by
feigning the voice of a Circle, had obtained admission somehow into the
house, and was now preparing to stab me with his acute angle.
68 Flatland
In a sitting-room, the absence of Fog (and the season happened to be
remarkably dry), made it difficult for me to trust to Sight Recognition,
especially at the short distance at which I was standing. Desperate with
fear, I rushed forward with an unceremonious " You must permit me,
Sir — " and felt him. My Wife was right. There was not the trace of an
angle, not the slightest roughness or inequality : never in my life had
I met with a more perfect Circle. He remained motionless while I
walked round him, beginning from his eye and returning to it again.
Circular he was throughout, a perfectly satisfactory Circle; there could
not be a doubt of it. Then followed a dialogue, which I will endeavour
to set down as near as I can recollect it, omitting only some of my
profuse apologies — for I was covered with shame and humiliation that I,
a Square, should have been guilty of the impertinence of feeling a
Circle. It was commenced by the Stranger with some impatience at
the lengthiness of my introductory process.
Stranger. Have you felt me enough by this time ? Are you not
introduced to me yet ?
/. Most illustrious Sir, excuse my awkwardness, which arises not from
ignorance of the usages of polite society, but from a little surprise and
nervousness, consequent on this somewhat unexpected visit. And I
beseech you to reveal my indiscretion to no one, and especially not to
my Wife. But before your Lordship enters into further communications,
would he deign to satisfy the curiosity of one who would gladly know
whence his Visitor came ?
Stranger. From Space, from Space, Sir : whence else ?
/. Pardon me, my Lord, but is not your Lordship already in Space,
your Lordship and his humble servant, even at this moment ?
Stranger. Pooh ! what do you know of Space ? Define Space.
/. Space, my Lord, is height and breadth indefinitely prolonged.
Stranger. Exactly : you see you do not even know what Space is.
Flatland 69
You think it is of Two Dimensions only ; but I have come to announce
to you a Third — height, breadth, and length.
/. Your Lordship is pleased to be merry. We also speak of length
and height, or breadth and thickness, thus denoting Two Dimensions by
four names.
Stranger. But I mean not only three names, but Three Dimensions.
/. Would your Lordship indicate or explain to me in what direction
is the Third Dimension, unknown to me ?
Stranger. I came from it. It is up above and down below.
/. My Lord means seemingly that it is Northward and Southward.
Stranger. I mean nothing of the kind. I mean a direction in which
you cannot look, because you have no eye in your side.
/. Pardon me, my Lord, a moment's inspection will convince your
Lordship that I have a perfect luminary at the juncture of two of
my sides.
Stranger. Yes : but in order to see into Space you ought to have an
eye, not on your Perimeter, but on your side, that is, on what you would
probably call your inside ; but we in Spaceland should call it your side.
/. An eye in my inside ! An eye in my stomach ! Your Lordship jests.
Stranger. I am in no jesting humour. I tell you that I come
from Space, or, since you will not understand what Space means, from
the Land of Three Dimensions whence I but lately looked down upon
your Plane which you call Space forsooth. From that position of
advantage I discerned all that you speak of as solid (by which you
mean " enclosed on four sides "), your houses, your churches, your very
chests and safes, yes even your insides and stomachs, all lying open and
exposed to my view.
/. Such assertions are easily made, my Lord.
Stranger. But not easily proved, you mean. But I mean to
prove mine.
70 Flatland
When I descended here, I saw your four Sons, the Pentagons, each in
his apartment, and your two Grandsons the Hexagons ; I saw your
youngest Hexagon remain a while with you and then retire to his room,
leaving you and your Wife alone. I saw your Isosceles servants, three
in number, in the kitchen at supper, and the little Page in the scullery.
Then I came here, and how do you think I came ?
/. Through the roof, I suppose.
Stranger. Not so. Your roof, as you know very well, has been
recently repaired, and has no aperture by which even a Woman could
penetrate. I tell you I come from Space. Are you not convinced by
what I have told you of your children and household.
/. Your Lordship must be aware that such facts touching the belong-
ings of his humble servant might be easily ascertained by any one in
the neighbourhood possessing your Lordship's ample means of obtaining
information.
Stranger. How shall I convince him ? Surely a plain statement
of facts followed by ocular demonstration ought to suffice. — Now, Sir ;
listen to me.
You are living on a Plane. What you style Flatland is the vast
level surface of what I may call a fluid, on, or in, the top of which you
and your countrymen move about, without rising above it or falling
below it.
I am not a plane Figure, but a Solid. You call me a Circle ; but in
reality I am not a Circle, but an infinite number of Circles, of size
varying from a Point to a Circle of thirteen inches in diameter, one
placed on the top of the othen When I cut through your plane as I am
now doing, I make in your plane a section which you, very rightly,
call a Circle. For even a Sphere — which is my proper name in my
own country — if he manifest himself at all to an inhabitant of Flatland —
must needs manifest himself as a Circle.
Flatland 7 1
Do you not remember — for I, who see all things, discerned last night
the phantasmal vision of Lineland written upon your brain — do you not
remember, I say, how, when you entered the realm of Lineland, you were
compelled to manifest yourself to the King not as a Square, but as a
Line, because that Linear Realm had not Dimensions enough to represent
the whole of you, but only a slice or section of you ? In precisely the
same way, your country of Two Dimensions is not spacious enough
to represent me, a being of Three, but can only exhibit a slice or section
of me, which is what you call a Circle.
The diminished brightness of your eye indicates incredulity. But now
prepare to receive proof positive of the truth of my assertions. You
cannot indeed see more than one of my sections, or Circles, at a time ;
for you have no power to raise your eye out of the plane of Flatland ;
but you can at least see that, as I rise in Space, so my section becomes
smaller. See now, I will rise; and the effect upon your eye will be
that my Circle will become smaller and smaller till it dwindles to a
point and finally vanishes.
There was no "rising" that I could see; but he diminished and
finally vanished. I winked once or twice to make sure that I was not
dreaming. But it was no dream. For from the depths of nowhere
came forth a hollow voice — close to my heart it seemed — " Am I quite
72 Flat land
gone? Are you convinced now? Well, now I will gradually return
to Flatland, and you shall see my section become larger and larger."
Every reader in Spaceland will easily understand that my mysterious
Guest was speaking the language of truth and even of simplicity.
But to me, proficient though I was in Flatland Mathematics, it was by
no means a simple matter. The rough diagram given above will make
it clear to any Spaceland child that the Sphere, ascending in the three
positions indicated there, must needs have manifested himself to me,
or to any Flatlander, as a Circle, at first of full size, then small, and
at last very small indeed, approaching to a Point. But to me, although
I saw the facts before me, the causes were as dark as ever. All that
I could comprehend was, that the Circle had made himself smaller
and vanished, and that he had now reappeared and was rapidly
making himself larger.
When he had regained his original size, he heaved a deep sigh ; for he
perceived by my silence that I had altogether failed to comprehend him.
And indeed I was now inclining to the belief that he must be no Circle
at all, but some extremely clever juggler ; or else that the old wives'
tales were true, and that after all there were such people as Enchanters
and Magicians.
After a long pause he muttered to himself, "One resource alone
remains, if I am not to resort to action. I must try the method of
Analogy." Then followed a still longer silence, after which he continued
our dialogue.
SpJiere. Tell me, Mr. Mathematician ; if a Point moves Northward,
and leaves a luminous wake, what name would you give to the wake ?
/. A straight Line.
Sphere. And a straight Line has how many extremities ?
/. Two.
SpJiere. Now conceive the Northward straight line moving parallel
Flatland
73
to itself, East and West, so that every point in it leaves behind it the
wake of a straight Line. What name will you give to the Figure
thereby formed ? We will suppose that it moves through a distance
equal to the original straight Line. — What name, I say ?
/. A Square.
SpJiere. And how many sides has a Square ? And how many Angles ?
/. Four sides and four angles.
Sphere. Now stretch your imagination a little, and conceive a
Square in Flatland, moving parallel to itself upward.
/. What? Northward?
Sphere. No, not Northward ; upward ; out of Flatland altogether.
If it moved Northward, the Southern points in the Square would
have to move through the positions previously occupied by the Northern
points. But that is not my meaning.
I mean that every Point in you — for you are a Square and will serve
the purpose of my illustration — every Point in you, that is to say in
what you call your inside, is to pass upwards through Space in such a
way that no Point shall pass through the position previously occupied
by any other Point ; but each Point shall describe a straight Line of its own.
This is all in accordance with Analogy ; surely it must be clear to you.
Restraining my impatience — for I was now under a strong temptation
to rush blindly at my Visitor and to precipitate him into Space, or out
of Flatland, anywhere, so that I could get rid of him — I replied : —
" And what may be the nature of the Figure which I am to shape
out by this motion which you are pleased to denote by the word
' upward ' ? I presume it is describable in the language of Flatland."
Sphere. Oh, certainly. It is all plain and simple, and in strict
accordance with Analogy — only, by the way, you must not speak of
the result as being a Figure, but as a Solid. But I will describe it to
you. Or rather not I, but Analogy.
F
74
Flatland
We began with a single Point, which of course — being itself a Point
— has only one terminal Point.
One Point produces a Line with two terminal Points.
One Line produces a Square with four terminal Points.
Now you can yourself give the answer to your own question : I, 2,
4, are evidently in Geometrical Progression. What is the next number.
/. Eight.
Sphere. Exactly. The one Square produces a Something-which-you-
do-not-as-yet-know-a-name-for-but-which-we-call-a-Cube with eight terminal
Points. Now are you convinced ?
/. And has this Creature sides, as well as angles or what you call
" terminal Points ? "
Sphere. Of course ; and all according to Analogy. But, by the
way, not what you call sides, but what we call sides. You would call
them solids.
I. And how many solids or sides will appertain to this Being whom I
am to generate by the motion of my inside in an " upward " direction, and
whom you call a Cube ?
Sphere. How can you ask ? And you a mathematician ! The side
of anything is always, if I may so say, one Dimension behind the thing.
Consequently, as there is no Dimension behind a Point, a Point has o
sides ; a Line, if I may so say, has 2 sides (for the Points of a Line may
be called by courtesy, its sides) ; a Square has 4 sides ; o, 2, 4 ; what
Progression do you call that ?
/. Arithmetical.
Sphere. And what is the next number ?
/. Six.
Sphere. Exactly. Then you see you have answered your own question.
The Cube which you will generate will be bounded by six sides, that is to
say, six of your insides. You see it all now, eh ?
Flatland
75
"Monster," I shrieked, "be thou juggler, enchanter, dream, or devil, no
more will I endure thy mockeries. Either thou or I must perish." And
saying these words I precipitated myself upon him.
§ 17. — How the Sphere, having in vain tried words, resorted to deeds.
It was in vain. I brought my hardest right angle into violent collision
with the Stranger, pressing on him with a force sufficient to have destroyed
any ordinary Circle : but I could feel him slowly and unarrestably slipping
from my contact ; not edging to the right nor to the left, but moving
somehow out of the world and vanishing to nothing. Soon there was a
blank. But I still heard the Intruder's voice.
Sphere. Why will- you refuse to listen to reason ? I had hoped to find
in you — as being a man of sense and an accomplished mathematician — a
fit apostle for the Gospel of the Three Dimensions, which I am allowed to
preach once only in a thousand years : but now I know not how to con-
vince you. Stay, I have it. Deeds, and not words, shall proclaim the
truth. Listen, my friend.
I have told you I can see from my position in Space the inside of all
things that you consider closed. For example, I see in yonder cupboard
near which you are standing, several of what you call boxes (but like
everything else in Flatland, they have no tops nor bottoms) full of money ;
I see also two tablets of accounts. I am about to descend into that cup-
board and to bring you one of those tablets. I saw you lock the cupboard
half an hour ago, and I know you have the key in your possession. But I
descend from Space ; the doors, you see, remain unmoved. Now I am in
the cupboard and am taking the tablet. Now I have it. Now I ascend
with it.
I rushed to the closet and dashed the door open. One of the tablets
was gone. With a mocking laugh, the Stranger appeared in the other
F 2
j6 Flatland
corner of the room, and at the same time the tablet appeared upon the
floor. I took it up. There could be no doubt — it was the missing
tablet.
I groaned with horror, doubting whether I was not out of my senses ;
but the Stranger continued : " Surely you must now see that my explana-
tion, and no other, suits the phenomena What you call Solid things are
really superficial ; what you call Space is really nothing but a great Plane.
I am in Space, and look down upon the insides of the things of which you
only see the outsides. You could leave this Plane yourself, if you could
but summon up the necessary volition. A slight upward or downward
motion would enable you to see all that I can see.
" The higher I mount, and the further I go from your Plane, the more I
can see, though of course I see it on a smaller scale. For example, I am
ascending ; now I can see your neighbour the Hexagon and his family in
their several apartments ; now I see the inside of the Theatre, ten doors off,
from which the audience is only just departing ; and on the other side a
Circle in his study, sitting at his books. Now I shall come back to you.
And, as a crowning proof, what do you say to my giving you a touch, just
the least touch, in your stomach ? It will not seriously injure you, and the
slight pain you may suffer cannot be compared with the mental benefit
you will receive."
Before I could utter a word of remonstrance, I felt a shooting pain in
my inside, and a demoniacal laugh seemed to issue from within me. A
moment afterwards the sharp agony had ceased, leaving nothing but a dull
ache behind, and the Stranger began to reappear, saying, as he gradually
increased in size, " There, I have not hurt you much, have I ? If you
are not convinced now, I don't know what will convince you. What
say you ? "
My resolution was taken. It seemed intolerable that I should endure
existence subject to the arbitrary visitations of a Magician who could thus
Flat land 77
play tricks with one's very stomach. If only I could in any way manage
to pin him against the wall till help came !
Once more I dashed my hardest angle against him, at the same time
alarming the whole household by my cries for aid. I believe, at the
moment of my onset, the Stranger had sunk below our Plane, and really
found difficulty in rising. In any case he remained motionless, while I,
hearing, as I thought, the sound of some help approaching, pressed against
him with redoubled vigour, and continued to shout for assistance.
A convulsive shudder ran through the Sphere. " This must not be,"
I thought I heard him say ; " either he must listen to reason, or I must
have recourse to the last resource of civilization." Then, addressing me
in a louder tone, he hurriedly exclaimed, " Listen : no stranger must
witness what you have witnessed. Send your Wife back at once, before
she enters the apartment. The Gospel of Three Dimensions must not
be thus frustrated. Not thus must the fruits of one thousand years of
waiting be thrown away. I hear her coming. Back ! back ! Away
from me, or you must go with me — whither you know not — into the
Land of Three Dimensions!"
" Fool ! Madman ! Irregular ! " I exclaimed ; " never will I release
thee ; thou shalt pay the penalty of thine impostures."
" Ha ! Is it come to this ? " thundered the Stranger : " then meet
your fate : out of your Plane you go. Once, twice, thrice ! 'Tis done ! "
§ 1 8. — How I came to Space land, and what I saw there.
An unspeakable horror seized me. There was a darkness ; then a
dizzy, sickening sensation of sight that was not like seeing ; I saw a Line
that was no Line ; Space that was not Space ; I was myself, and not myself.
When I could find voice, I shrieked aloud in agony, " Either this is mad-
ness or it is Hell." " It is neither," calmly replied the voice of the Sphere,
jS Flatland
"it is Knowledge; it is Three Dimensions: open your eye once again
and try to look steadily."
I looked, and, behold, a new world ! There stood before me, visibly
incorporate, all that I had before inferred, conjectured, dreamed, of perfect
Circular beauty. What seemed the centre of the Stranger's form lay
open to my view : yet I could see no heart, nor lungs, nor arteries, only
a beautiful harmonious Something — for which I had no words ; but you,
my Readers in Spaceland, would call it the surface of the Sphere.
Prostrating myself mentally before my Guide, I cried, " How is it, O
divine ideal of consummate loveliness and wisdom, that I see thy inside,
and yet cannot discern thy heart, thy lungs, thy arteries, thy liver?"
" What you think you see, you see not," he replied ; " it is not given to
you, nor to any other Being, to behold my internal parts. I am of a
different order of Beings from those in Flatland. Were I a Circle, you
could discern my intestines, but I am a Being composed, as I told you
before, of many Circles, the Many in the One, called in this country a
Sphere. And, just as the outside of a Cube is a Square, so the outside
of a Sphere presents the appearance of a Circle."
Bewildered though I was by my Teacher's enigmatic utterance, I no
longer chafed against it, but worshipped him in silent adoration. He
continued, with more mildness in his voice : " Distress not yourself if you
cannot at first understand the deeper mysteries of Spaceland. By degrees
they will dawn upon you. Let us begin by casting back a glance at the
region whence you came. Return with me a while to the plains of Flat-
land, and I will show you that which you have so often reasoned and
thought about, but never seen with the sense of sight — a visible angle."
" Impossible ! " I cried ; but, the Sphere leading the way, I followed as if
in a dream, till once more his voice arrested me : " Look yonder, and
behold your own Pentagonal house and all its inmates."
I looked below, and saw with my physical eye all that domestic
Flatland
79
individuality which I had hitherto merely inferred with the understanding.
And how poor and shadowy was the inferred conjecture in comparison
with the reality which I now beheld ! My four Sons calmly asleep in the
North-Western
rooms, my two
orphan Grand-
sons to the
South ; the
Servants, the
Butler, my
Daughter, all
in their several
apartments.
Only my affec-
tionate Wife,
alarmed by my
continued ab-
sence, had quit-
ted her room and was roving up and down in the Hall, anxiously awaiting
my return. Also the Page, aroused by my cries, had left his room, and
under pretext of ascertaining whether, I had fallen somewhere in a faint,
was prying into the cabinet in my study. All this I could now see, not
merely infer ; and as we came nearer and nearer, I could discern even the
contents of my cabinet, and the two chests of gold, and the tablets of
which the Sphere had made mention.
Touched by my Wife's distress, I would have sprung downward to
reassure her, but I found myself incapable of motion. " Trouble not
yourself about your Wife," said my Guide ; " she will not be long left in
anxiety ; meantime, let us take a survey of Flatland."
Once more I felt myself rising through space. It was even as the
8o Flatland
Sphere had said. The further we receded from the object we beheld, the
larger became the field of vision. My native city, with the interior of
every house and every creature therein, lay open to my view in miniature.
We mounted higher, and lo, the secrets of the earth, the depths of mines
and inmost caverns of the hills, were bared before me.
Awestruck at the sight of the mysteries of the earth, thus unveiled
before my unworthy eye, I said to my Companion, " Behold, I am become
as a God. For the wise men in our country say that to see ail things, or
as they express it, omnividence, is the attribute of God alone." There was
something of scorn in the voice of my Teacher as he made answer : " Is it
so indeed ? Then the very pickpockets and cut-throats of my country are
to be worshipped by your wise men as being Gods : for there is not one of
them that does not see as much as you see now. But trust me, your wise
men are wrong."
/. Then is omnividence the attribute of others beside Gods ?
Sphere. I do not know. But, if a pick-pocket or a cut-throat -of our
country can see everything that is m your country, surely that is no reason
why the pick-pocket or cut-throat should be accepted by you as a God.
This omnividence, as you call it — it is not a common word in Space-
land — does it make you more just, more merciful, less selfish, more
loving ? Not in the least. Then how does it make you more divine ?
/. " More merciful, more loving ! " But these are the qualities of
women ! And we know that a Circle is a higher Being than a Straight
Line, in so far as knowledge and wisdom are more to be esteemed than
mere affection.
Sphere. It is not for me to classify human faculties according to
merit. Yet many of the best and wisest in Spaceland think more of the
affections than of the understanding, more of your despised Straight Lines
than of your belauded Circles. But enough of this. Look yonder. Do
you know that building ?
Flat land 81
I looked, and afar off I saw an immense Polygonal structure, in which
I recognized the General Assembly Hall of the States of Flatland, sur-
rounded by dense lines of Pentagonal buildings at right angles to each
other, which I knew to be streets ; and I perceived that I was approaching
the great Metropolis.
" Here we descend," said my Guide. It was now morning, the first hour
of the first day of the two thousandth year of our era. Acting, as was
their wont, in strict accordance with precedent, the highest Circles of the
realm were meeting in solemn conclave, as they had met on the first hour
of the first day of the year 1000, and also on the first hour of the first
day of the year o.
The minutes of the previous meetings were now read by one whom I
at once recognized as my brother, a perfectly Symmetrical Square, and
the Chief Clerk of the High Council. It was found recorded on each
occasion that : " Whereas the States had ^been troubled by divers ill-in-
tentioned persons pretending to hav« received revelations from another
World, and professing to produce demonstrations whereby they had insti-
gated to frenzy both themselves and others, it had been for this cause
unanimously resolved by the Grand Council that on the first day of each
millenary, special injunctions be sent to the Prefects in the several
districts of Flatland, to make strict search for such misguided persons,
and without formality' of mathematical examination, to destroy all such
as were Isosceles of any degree, to scourge and imprison any regular
Triangle, to cause any Square or Pentagon to be sent to the district
Asylum, and to arrest any one of higher rank, sending him straightway to
the Capital to be examined and judged by the Council."
" You hear your fate," said the Sphere to me, while the Council was
passing for the third time the formal resolution. " Death or imprisonment
awaits the Apostle of the Gospel of Three Dimensions." " Not so,"
replied I, "the matter is now so clear to me, the nature of real space so
82 Flatland
palpable, that methinks I could make a child understand it. Permit me
but to descend at this moment and enlighten them." "Not yet," said
my Guide, " the time will come for that. Meantime I must perform my
mission. Stay thou there in thy place." Saying these words, he leaped
with great dexterity into the sea (if I may so call it) of Flatland, right in
the midst of the ring of Counsellors. " I come," cried he, " to proclaim
that there is a land of Three Dimensions."
I could see many of the younger Counsellors start back in manifest
horror, as the Sphere's circular section widened before them. But on a
sign from the presiding Circle, — who showed not the slightest alarm or
surprise — six Isosceles of a low type from six different quarters rushed
upon the Sphere. " We have him," they cried ; " No ; yes ; we have him
still ! he's going ! he's gone ! "
"My Lords," said the President to the Junior Circles of the Council,
" there is not the slightest need for surprise ; the secret archives, to which
I alone have access, tell me that a similar occurrence happened on the
last two millennial commencements. You will, of course, say nothing of
these trifles outside the Cabinet."
Raising his voice, he now summoned the guard. " Arrest the police-
men ; gag them. You know your duty." After he had consigned to
their fate the wretched policemen — ill-fated and unwilling witnesses of a
State-secret which they were not to be permitted to reveal — he again
addressed the Counsellors. " My Lords, the business of the Council being
concluded, I have only to wish you a happy New Year." Before depart-
ing, he expressed, at some length, to the Clerk, my excellent but most
unfortunate brother, his sincere regret that, in accordance with precedent
and for the sake of secrecy, he must condemn him to perpetual imprison-
ment, but added his satisfaction that, unless some mention were made by
him of that day's incident, his life would be spared.
Flatland
§ 19. — How, though the Sphere showed me other mysteries of
Spaceland, I still desired more ; and what came of it.
When I saw my poor brother led away to imprisonment, I attempted to
leap down into the Council Chamber, desiring to intercede on his behalf,
or at least bid him farewell. But I found that I had no motion of my
own. I absolutely depended on the volition of my Guide, who said in
gloomy tones, " Heed not thy brother ; haply thou shalt have ample time
hereafter to condole with him. Follow me."
Once more we ascended into space. " Hitherto,"
said the Sphere, " I have shown you naught save
Plane Figures and their interiors. Now I must
introduce you to Solids, and reveal to you the plan
upon which they are constructed. Behold this
multitude of moveable square cards. See, I put
one on another, not, as you supposed, Northward
of the other, but on the other. Now a second,
now a third. See, I am building up a Solid by
a multitude of Squares parallel to one another.
Now the Solid is complete, being as high as it is
long and broad, and we call it a Cube."
" Pardon me, my Lord," replied I ; " but to my
eye the appearance is as of an Irregular Figure
whose inside is laid open to the view ; in other
words, methinks I see no Solid, but a Plane such
as we infer in Flatland ; only of an Irregularity which betokens some
monstrous criminal, so that the very sight of it is painful to my eyes."
" True," said the Sphere ; " it appears to you a Plane, because you
are not accustomed to light and shade and perspective ; just as in
84 Flat land
Flatland a Hexagon would appear a Straight Line to one who has
not the Art of Sight Recognition. But in reality it is a Solid, as you
shall learn by the sense of Feeling."
He then introduced me to the Cube, and I found that this marvellous
Being was indeed no Plane, but a Solid ; and that he was endowed with
six plane sides and eight terminal points called solid angles ; and I re-
membered the saying of the Sphere that just such a Creature as this
would be formed by a Square moving, in Space, parallel to himself : and
I rejoiced to think that so insignificant a Creature as I could in some
sense be called the Progenitor of so illustrious an offspring.
But still I could not fully understand the meaning of what my
Teacher had told me concerning " light " and " shade " and " perspec-
tive " ; and I did not hesitate to put my difficulties before him.
Were I to give the Sphere's explanation of these matters, succinct
and clear though it was, it would be tedious to an inhabitant of
Space, who knows these things already. Suffice it, that by his lucid
statements, and by changing the position of objects and lights, and by
allowing me to feel the several objects and even his own sacred
Person, he at last made all things clear to me, so that I could now
readily distinguish between a Circle and a Sphere, a Plane Figure
and a Solid.
This was the Climax, the Paradise, of my strange eventful History.
Henceforth I have to relate the story of my miserable Fall: — most
miserable, yet surely most undeserved ! For why should the thirst for
knowledge be aroused, only to be disappointed and punished ! My
volition shrinks from the painful task of recalling my humiliation ; yet,
like a second Prometheus, I will endure this and worse, if by any
means I may arouse in the interiors of Plane and Solid Humanity a
spirit of rebellion against the Conceit which would limit our Dimen-
sions to Two or Three or any number short of Infinity. Away then
Flatland 85
with all personal considerations ! Let me continue to the end, as I
began, without further digressions or anticipations, pursuing the plain
path of dispassionate History. The exact facts, the exact words, —
and they are burnt in upon my brain, — shall be set down without
alteration of an iota ; and let my Readers judge between me and
Destiny.
The Sphere would willingly have continued his lessons by indoc-
trinating me in the conformation of all regular Solids, Cylinders, Cones,
Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons and Spheres :
but I ventured to interrupt him. Not that I was wearied of knowledge.
On the contrary, I thirsted for yet deeper and fuller draughts than
he was offering to me.
" Pardon me," said I, " O Thou Whom I must no longer address as
the Perfection of all Beauty ; but let me beg thee to vouchsafe thy
servant a sight of thine interior."
Sphere. "My what?"
/. " Thine interior : thy stomach, thy intestines."
Sphere. " Whence this ill-timed impertinent request ? And what
mean you by saying that I am no longer the Perfection of all
Beauty ? "
/, My Lord, your own wisdom has taught me to aspire to One
even more great, more beautiful, and more closely approximate to
Perfection than yourself. As you yourself, superior to all Flatland
forms, combine many Circles in One, so doubtless there is One above
you who combines many Spheres in One Supreme Existence, sur-
passing even the Solids of Spaceland. And even as we, who are now
in Space, look down on Flatland and see the insides of all things, so
of a certainty there is yet above us some higher, purer region, whither
thou dost surely purpose to lead me — O Thou Whom I shall always
call, everywhere and in all Dimensions, my Priest, Philosopher, and
86 Flatland
Friend — some yet more spacious Space, some more dimensionable
Dimensionality, from the vantage-ground of which we shall look down
together upon the revealed insides of Solid things, and where thine
own intestines, and those of thy kindred Spheres, will lie exposed to
the view of the poor wandering exile from Flatland, to whom so
much has already been vouchsafed.
Sphere. Pooh! Stuff! Enough of this trifling! The time is short,
and much remains to be done before you are fit to proclaim the Gospel of
Three Dimensions to your blind benighted countrymen in Flatland.
/. Nay, gracious Teacher, deny me not what I know it is in thy power
to perform. Grant me but one glimpse of thine interior, and I am satisfied
for ever, remaining henceforth thy docile pupil, thy unemancipable slave,
ready to receive all thy teachings and to feed upon the words that fall
from thy lips.
Sphere. Well, then, to content and silence you, let me say at once, I
would show you what you wish if I could ; but I cannot. Would you
have me turn my stomach inside out to oblige you ?
7. But my Lord has shown me the intestines of all my countrymen in
the Land of Two Dimensions by taking me with him into the Land of
Three. What therefore more easy than now to take his servant on a
second journey into the blessed region of the Fourth Dimension, where
I shall look down with him once more upon this land of Three Dimen-
sions, and see the inside of every three-dimensioned house, the secrets
of the solid earth, the treasures of the mines in Spaceland, and the
intestines of every solid living creature, even of the noble and adorable
Spheres.
Sphere. But where is this land of Four Dimensions ?
/. I know not : but doubtless my Teacher knows.
Sphere. Not I. There is no such land. The very idea of it is utterly
inconceivable.
Flatland 87
/. Your Lordship tempts his servant to see whether he remembers the
revelations imparted to him. Trifle not with me, my Lord ; I crave, I
thirst, for more knowledge. Doubtless we cannot see that other higher
Spaceland now, because we have no eye in our stomachs. But, just as
there was the realm of Flatland, though that poor puny Lineland
Monarch could neither turn to left nor right to discern it, and just as there
was close at hand, and touching my frame, the land of Three Dimensions,
though I, blind senseless wretch, had no power to touch it, no eye in my
interior to discern it, so of a surety there is a Fourth Dimension, which
my Lord perceives with the inner eye of thought. And that it must exist
my Lord himself has taught me. Or can he have forgotten what he
himself imparted to his servant ?
In One Dimension, did not a moving Point produce a Line with two
terminal points ?
In Two Dimensions, did not a moving Line produce a Square with
four terminal points ?
In Three Dimensions, did not a moving Square produce — did not
this eye of mine behold it — that blessed Being, a Cube, with eight
terminal points ?
And in Four Dimensions shall not a moving Cube — alas, for Analogy,
and alas for the Progress of Truth, if it be not so — shall not, I say, the
motion of a divine Cube result in a still more divine Organization with
sixteen terminal points ?
Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not this
a Geometrical Progression ? Is not this — if I might quote my Lord's own
words — " strictly according to Analogy " ?
Again, was I not taught by my Lord that as in a Line there are two
bounding Points, and in a Square there are four bounding Lines, so in a
Cube there must be six bounding Squares ? Behold once more the con-
firming Series, 2, 4, 6 : is not this an Arithmetical Progression ? And
88 Flatland
consequently does it not of necessity follow that the more divine offspring
of the divine Cube in the Land of Four Dimensions, must have 8 bounding
Cubes : and is not this also, as my Lord has taught me to believe, " strictly
according to Analogy " ?
O, my Lord, my Lord, behold, I cast myself in faith upon conjecture,
not knowing the facts; and I appeal to your Lordship to confirm or deny
my logical anticipations. If I am wrong, I yield, and will no longer demand
a Fourth Dimension ; but, if I am right, my Lord will listen to reason.
I ask therefore, is it, or is it not, the fact, that ere now your country-
men also have witnessed the descent of Beings of a higher order than
their own, entering closed rooms, even as your Lordship entered mine,
without the opening of doors or windows, and appearing and vanish-
ing at will ? On the reply to this question I am ready to stake every-
thing. Deny it, and I am henceforth silent. Only vouchsafe an answer.
Sphere (after a pause}. It is reported so. But men are divided in
opinion as to the facts. And even granting the facts, they explain them
in different ways. And in any case, however great may be the number of
different explanations, no one has adopted or suggested the theory of a
Fourth Dimension. Therefore, pray have done with this trifling, and let
us return to business.
/. I was certain of it. I was certain that my anticipations would be
fulfilled. And now have patience with me and answer me yet one more
question, best of Teachers ! Those who have thus appeared — no one
knows whence — and have returned — no one knows whither — have they
also contracted their sections and vanished somehow into that more
Spacious Space, whither I now entreat you to conduct me ?
Spliere (moodily]. They have vanished, certainly — if they ever ap-
peared. But most people say that these visions arose from the thought —
you will not understand me — from the brain ; from the perturbed angularity
of the Seer.
Flatland 89
7. Say they so ? Oh, believe them not. Or if it indeed be so, that
this other Space is really Thoughtland, then take me to that blessed
Region where I in Thought shall see the insides of all solid things.
There, before my ravished eye, a Cube, moving in some altogether new
direction, but strictly according to Analogy, so as to make every particle
of his interior pass through a new kind of Space with a wake of its own —
shall create a still more perfect perfection than himself, with sixteen terminal
Extra-solid angles, and Eight solid Cubes for his Perimeter. And once
there, shall we stay our upward course ? In that blessed region of Four
Dimensions, shall we linger on the threshold of the Fifth, and not enter
therein ? Ah, no ! Let us rather resolve that our ambition shall soar with
our corporal ascent. Then, yielding to our intellectual onset, the gates of
the Sixth Dimension shall fly open ; after that a Seventh, and then
an Eighth
How long I should have continued I know not. In vain did the
Sphere, in his voice of thunder, reiterate his commands of silence, and
threaten t me with the direst penalties if I persisted. Nothing could
stem the flood of my ecstatic aspirations. Perhaps I was to blame ;
but indeed I was intoxicated with the recent draughts of Truth to
which he himself had introduced me. However, the end was not long
in coming. My words were cut short by a crash outside, and a
simultaneous crash inside me, which impelled me through Space with
a velocity that precluded speech. Down ! down ! down ! I was rapidly
descending; and I knew that return to Flatland was my doom. One
glimpse, one last and never-to-be-forgotten glimpse I had of that dull
level wilderness — which was now to become my Universe again — spread
out before my eye. Then a darkness. Then a final, all-consummating
thunder-peal ; and, when I came to myself, I was once more a common
creeping Square, in my Study at home, listening to the Peace-Cry of
my approaching Wife.
G
90 Flatland
§ 20. — How the Sphere encouraged me in a Vision.
Although I had less than a minute for reflection, I felt, by a kind
of instinct, that I must conceal my experiences from my Wife. Not
that I apprehended, at the moment, any danger from her divulging
my secret, but I know that to^any Woman in Flatland the narrative
of my adventures must needs be unintelligible. So I endeavoured
to reassure her by some story, invented for the occasion, that I had
accidentally fallen through the trap-door of the cellar, and had there
lain stunned.
The Southward attraction in our country is so slight that even to
a Woman my tale necessarily appeared extraordinary and well-nigh
incredible ; but my Wife, whose good sense far exceeds that of
the average of her Sex, and who perceived that I was unusually
excited, did not argue with me on the subject, but insisted that I was
ill and required repose. I was glad of an excuse for retiring to my
chamber to think quietly over what had happened. When I was at
last by myself, a drowsy sensation fell on me ; but before my eyes
closed I endeavoured to reproduce the Third Dimension, and especially
the process by which a Cube is constructed through the motion of a
Square. It was not so clear as I could have wished ; but I remembered
that it must be " Upward, and yet not Northward," and I determined
steadfastly to retain these words as the clue which, if firmly grasped,
could not fail to guide me to the solution. So mechanically repeating,
like a charm, the words, "Upward yet not Northward," I fell into a
sound refreshing sleep.
During my slumber I had a dream. I thought I was once more by
the side of the Sphere, whose lustrous hue betokened that he had
exchanged his wrath against me for perfect placability. We were
moving together towards a bright but infinitesimally small Point, to
Flat land 91
which my Master directed my attention. As we approached, methought
there issued from it a slight humming noise as from one of your
Spaceland blue-bottles, only less resonant by far, so slight indeed that
even in the perfect stillness of the Vacuum through which we soared,
the sound reached not our ears till we checked our flight at a distance
from it of something under twenty human diagonals.
" Look yonder," said my Guide, " in Flatland thou hast lived ;
of Lineland thou hast received a vision ; thou hast soared with me to
the heights of Spaceland; now, in order to complete the range of thy
experience, I conduct thee downward to the lowest depth of existence,
even to the realm of Pointland, the Abyss of No Dimensions.
" Behold yon miserable creature. That Point is a Being like
ourselves, but confined to the non-dimensional Gulf. He is himself
his own World, his own Universe; of any other than himself he can
form no conception ; he knows not Length, nor Breadth, nor Height,
for he has had no experience of them ; he has no cognizance even of
the number Two ; nor has he a thought of Plurality ; for he is himself
his One and All, being really Nothing. Yet mark his perfect self-
contentment, and hence learn this lesson, that to be self-contented is
to be vile and ignorant, and that to aspire is better than to be blindly
and impotently happy. Now listen."
He ceased ; and there arose from the little buzzing creature a tiny,
low, monotonous, but distinct tinkling, as from one of your Spaceland
phonographs, from which I caught these words, " Infinite beatitude of
existence ! It is ; and there is none else beside It."
"What," said I, "does the puny creature mean by 'it'?" "He
means himself," said the Sphere : " have you not noticed before
now, that babies and babyish people who cannot distinguish themselves
from the world, speak of themselves in the Third Person ? But hush ! "
" It fills all Space," continued the little soliloquizing Creature, " and
92 Flatland
what It fills, It is. What It thinks, that It utters ; and what It utters,
that It hears ; and It itself is Thinker, Utterer, Hearer, Thought, Word,
Audition ; it is the One, and yet the All in All. Ah, the happiness,
ah, the happiness of Being ! "
" Can you not startle the little thing out of its complacency ? " said
I. " Tell it what it really is, as you told me ; reveal to it the narrow
limitations of Pointland, and lead it up to something higher." " That is
no easy task," said my Master; "try you."
Hereon, raising my voice to the uttermost, I addressed the Point
as follows :
" Silence, silence, contemptible Creature. You call yourself the All
in All, but you are the Nothing : your so-called Universe is a mere speck
in a Line, and a Line is a mere shadow as compared with — " " Hush,
hush, you have said enough," interrupted the Sphere, " now listen, and
mark the effect of your harangue on the King of Pointland."
The lustre of the Monarch, who beamed more brightly than ever
upon hearing my words, showed clearly that he retained his com-
placency ; and I had hardly ceased when he took up his strain again.
" Ah, the joy, ah, the joy of Thought ! What can It not achieve by
thinking ! Its own Thought coming to Itself, suggestive of Its dis-
paragement, thereby to enhance Its happiness ! Sweet rebellion stirred
up to result in triumph ! Ah, the divine creative power of the All
in One! Ah, the joy, the joy of Being! "
"You see," said my Teacher, "how little your words have done.
So far as the Monarch understands them at all, he accepts them as
his own — for he cannot conceive of any other except himself — and plumes
himself upon the variety of ' Its Thought ' as an instance of creative
Power. Let us leave this God of Pointland to the ignorant fruition of his
omnipresence and omniscience : nothing that you or I can do can rescue
him from his self-satisfaction."
Flatland
93
After this, as we floated gently back to Flatland, I could hear the
mild voice of my Companion pointing the moral of my vision, and
stimulating me to aspire, and to teach others to aspire. He had been
angered at first — he confessed — by my ambition to soar to Dimensions
above the Third ; but, since then, he had received fresh insight, and he was
not too proud to acknowledge his error to a Pupil. Then he proceeded
to initiate me into mysteries yet higher than those I had witnessed,
showing me how to construct Extra-Solids by the motion of Solids, and
Double Extra-Solids by the motion of Extra-Solids, and all "strictly
according to Analogy," all by methods so simple, so easy, as to be
patent even to the Female Sex.
§ 21. — How I tried to teach the theory of Three Dimensions
to my Grandson, and with what success.
I awoke rejoicing, and began to reflect on the glorious career before
me. I would go forth, methought, at once, and evangelize the whole
of Flatland. Even to Women and Soldiers should the Gospel of Three
Dimensions be proclaimed. I would begin with my Wife.
Just as I had decided on the plan of my operations, I heard the
sound of many voices in the street commanding silence. Then followed
a louder voice. It was a herald's proclamation. Listening attentively,
I recognized the words of the Resolution of the Council, enjoining the
arrest, imprisonment, or execution of any one who should pervert the
minds of the people by delusions, and by professing to have received
revelations from another World.
I reflected. This danger was not to be trifled with. It would be
better to avoid it by omitting all mention of my Revelation, and by
proceeding on the path of Demonstration — which after all, seemed so
simple and so conclusive that nothing would be lost by discarding the
94 Flatland
former means. " Upward, not Northward " — was the clue to the whole
proof. It had seemed to me fairly clear before I fell asleep ; and when
I first awoke, fresh from my dream, it had appeared as patent as
Arithmetic ; but somehow it did not seem to me quite so obvious now.
Though my Wife entered the room opportunely just at that moment, I
decided, after we had interchanged a few words of commonplace
conversation, not to begin with her.
My Pentagonal Sons were men of character and standing, and
physicians of no mean reputation, but not great in mathematics, and, in
that respect, unfit for my purpose. But it occurred to me that a young
and docile Hexagon, with a mathematical turn, would be a most suitable
pupil. Why therefore not make my first experiment with my little
precocious Grandson, whose casual remarks on the meaning of 33 had met
with the approval of the Sphere ? Discussing the matter with him, a
mere boy, I should be in perfect safety ; for he would know nothing of
the Proclamation of the Council ; whereas I could not feel sure that my
Sons — so greatly did their patriotism and reverence for the Circles pre-
dominate over mere blind affection — might not feel compelled to hand
me over to the Prefect, if they found me seriously maintaining the
seditious heresy of the Third Dimension.
But the first thing to be done was to satisfy in some way the
curiosity of my Wife, who naturally wished to know something of the
reasons for which the Circle had desired that mysterious interview, and
of the means by which he had entered our house. Without entering
into the details of the elaborate account I gave her, — an account, I fear,
not quite so consistent with truth as my Readers in Spaceland might
desire, — I must be content with saying that I succeeded at last
in persuading her to return quietly to her household duties without
eliciting from me any reference to the World of Three Dimensions.
This done, I immediately sent for my Grandson ; for, to confess the
Flatland 95
truth, I felt that all that I had seen and heard was in some strange way
slipping away from me, like the image of a half-grasped, tantalizing
dream, and I longed to essay my skill in making a first disciple.
When my Grandson entered the room I carefully secured the door.
Then, sitting down by his side and taking our mathematical tablets — or,
as you would call them, Lines — I told him we would resume the lesson
of yesterday. I taught him once more how a Point by motion in One
Dimension produces a Line, and how a straight Line in Two Dimensions
produces a Square. After this, forcing a laugh, I said, " And now, you
scamp, you wanted to make me believe that a Square may in the same way
by motion ' Upward, not Northward,' produce another figure, a sort of
extra Square in Three Dimensions. Say that again, you young rascal."
At this moment we heard once more the herald's " O yes ! O yes ! "
outside in the street proclaiming the Resolution of the Council. Young
though he was, my Grandson — who was unusually intelligent for his age,
and bred up in perfect reverence for the authority of the Circles —
took in the situation with an acuteness for which I was quite unprepared.
He remained silent till the last words of the Proclamation had died away,
and then, bursting into tears, " Dear Grandpapa," he said, " that was
only my fun, and of course I meant nothing at all by it ; and we did
not know anything then about the new Law ; and I don't think I said
anything about the Third Dimension ; and I am sure I did not say one
word about ' Upward, not Northward,' for that would be such nonsense,
you know. How could a thing move Upward, and not Northward ?
Upward, and not Northward ! Even if I were a baby, I could not be
so absurd as that. How silly it is ! Ha ! ha ! ha ! "
" Not at all silly," said I, losing my temper ; " here for example, I
take this Square," — and, at the word, I grasped a moveable Square,
which was lying at hand — " and I move it, you see, not Northward but
— yes, I move it Upward — that is to say, not Northward, but I move it
96 Flatland
somewhere — not exactly like this, but somehow— Here I brought my
sentence to an inane conclusion, shaking the Square about in a purpose-
less manner, much to the amusement of my Grandson, who burst out
laughing louder than ever, and declared that I was not teaching him,
but joking with him ; and so saying he unlocked the door and ran
out of the room. Thus ended my first attempt to convert a pupil to
the Gospel of Three Dimensions.
§ 22. — How I then tried to diffuse the Theory of Three
Dimensions by other means, and of the result.
My failure with my Grandson did not encourage me to communicate
my secret to others of my household ; yet neither was I led by it to
despair of success. Only I saw that I must not wholly rely on the catch-
phrase " Upward, not Northward," but must rather endeavour to seek a
demonstration by setting before the public a clear view of the whole
subject ; and for this purpose it seemed necessary to resort to writing.
So I devoted several months in privacy to the composition of a treatise
on the mysteries of Three Dimensions. Only, with the view of evading
the Law, if possible, I spoke not of a physical Dimension, but of a
Thoughtland whence, in theory, a Figure could look down upon Flatland
and see simultaneously the insides of all things, and where it was
possible that there might be supposed to exist a Figure environed, as it
were, with six Squares, and containing eight terminal Points. But in
writing this book I found myself sadly hampered by the impossibility
of drawing such diagrams as were necessary for my purpose ; for of
course, in our country of Flatland, there are no tablets but Lines, and
no diagrams but Lines, all in one straight Line and only distinguishable
by difference of size and brightness ; so that, when I had finished my
treatise (which I entitled " Through Flatland to Thoughtland ") I could
not feel certain that many would understand my meaning.
Flatland 97
Meanwhile ray life was under a cloud. All pleasures palled upon
me ; all sights tantalized and tempted me to outspoken treason, because
I could not but compare what I saw in Two Dimensions with what it
really was if seen in Three, and could hardly refrain from making my
comparisons aloud. I neglected my clients and my own business to give
myself to the contemplation of the mysteries which I had once beheld,
yet which I could impart to no one, and found daily more difficult to
reproduce even before my own mental vision.
One day, about eleven months after my return from Spaceland, I
tried to see a Cube with my eye closed, but failed ; and though I succeeded
afterwards, I was not then quite certain (nor have I been ever afterwards)
that I had exactly realized the original. This made me more ,melancholy
than before, and determined me to take some step ; yet what, I knew not.
I felt that I would have been willing to sacrifice my life for the Cause,
if thereby I could have produced conviction. But if I could not convince
my Grandson, how could I convince the highest and most developed
Circles in the land ?
And yet at times my spirit was too strong for me, and I gave vent to
dangerous utterances. Already I was considered heterodox if not
treasonable, and I was keenly alive to the dangers of my position ;
nevertheless I could not at times refrain from bursting out into suspicious
or half-seditious utterances, even among the highest Polygonal and
Circular society. When, for example, the question arose about the
treatment of those lunatics who said that they had received the power of
seeing the insides of things, I would quote the saying of an ancient Circle,
who declared that prophets and inspired people are always considered by
the majority to be mad ; and I could not help occasionally dropping such
expressions as " the eye that discerns the interiors of things," and " the
all-seeing land : " once or twice I even let fall the forbidden terms " the
Third and Fourth Dimensions." At last, to complete a series of minor
H
98 Flatland
indiscretions, at a meeting of our Local Speculative Society held at the
palace of the Prefect himself, — some extremely silly person having read an
elaborate paper exhibiting the precise reasons why Providence has limited
the number of Dimensions to Two, and why the attribute of omnividence
is assigned to the Supreme alone^I so far forgot myself as to give an
exact account of the whole of my voyage with the Sphere into Space, and
to the Assembly Hall in our Metropolis, and then to Space again, and of
my return home, and of everything that I had seen and heard in fact or
vision. At first, indeed, I pretended that I was describing the imaginary
experiences of a fictitious person ; but my enthusiasm soon forced me to
throw off all disguise, and finally, in a fervent peroration, I exhorted all
my hearers to divest themselves of prejudice and to become believers in
the Third Dimension.
Need I say that I was at once arrested and taken before the Council ?
Next morning, standing in the very place where but a very few months
ago the Sphere had stood in my company, I was allowed to begin and to
continue my narration unquestioned and uninterrupted. But from the first
I foresaw my fate ; for the President, noting that a guard of the better sort
of Policemen was in attendance, of angularity little, if at all, under 55°,
ordered them to be relieved before I began my defence, by an inferior
class of 2° or 3°. I knew only too well what that meant. I was to be
executed or imprisoned, and my story was to be kept secret from the
world by the simultaneous destruction of the officials who had heard it ;
and, this being the case, the President desired to substitute the cheaper for
the more expensive victims.
After I had concluded my defence, the President, perhaps perceiving
that some of the junior Circles had been moved by my evident earnestness,
asked me two questions : —
i. Whether I could indicate the direction which I meant when I used
the words " Upward, not Northward " ?
Flatland 99
2. Whether I could by any diagrams or descriptions (other than the
enumeration of imaginary sides and angles) indicate the Figure I was
pleased to call a Cube?
I declared that I could say nothing more, and that I must commit
myself to the Truth, whose cause would surely prevail in the end.
The President replied that he quite concurred in my sentiment, and
that I could not do better. I must be sentenced to perpetual imprison-
ment ; but if the Truth intended that I should emerge from prison and
evangelize the world, the Truth might be trusted to bring that result to
pass. Meanwhile I should be subjected to no discomfort that was not
necessary to preclude escape, and, unless I forfeited the privilege by
misconduct, I should be occasionally permitted to see my brother, who
had preceded me to my prison.
Seven years have elapsed and I am still a prisoner, and — if I except
the occasional visits of my brother — debarred from all companionship save
that of my jailers. My brother is one of the best of Squares, just, sensible,
cheerful, and not without fraternal affection ; yet I must confess that my
weekly interviews, at least in one respect, cause me the bitterest pain.
He was present when the Sphere manifested himself in the Council
Chamber ; he saw the Sphere's changing sections ; he heard the ex-
planation of the phenomena then given to the Circles. Since that time,
scarcely a week has passed during seven whole years, without his hearing
from me a repetition of the part I played in that manifestation, together
with ample descriptions of all the phenomena in Spaceland, and the
arguments for the existence of Solid things derivable from Analogy.
Yet — I take shame to be forced to confess it — my brother has not yet
grasped the nature of the Third Dimension, and frankly avows his
disbelief in the existence of a Sphere.
Hence I am absolutely destitute of converts, and, for aught that I
can see, the millennial Revelation has been made to me for nothing.
ioo Flat land
Prometheus up in Spaceland was bound for bringing down fire for
mortals, but I — poor Flatland Prometheus — lie here in prison for bring-
ing down nothing to my countrymen. Yet I exist in the hope that
these memoirs, in some manner, I know not how, may find their way to
the minds of humanity in Some Dimension, and may stir up a race of
rebels who shall refuse to be confined to limited Dimensionality.
That is the hope of my brighter moments. Alas, it is not always so.
Heavily weighs on me at times the burdensome reflection that I cannot
honestly say I am confident as to the exact shape of the once-seen, oft-
regretted Cube ; and in my nightly visions the mysterious precept,
" Upward, not Northward," haunts me like a soul-devouring Sphinx. It
is part of the martyrdom which I endure for the cause of the Truth that
there are seasons of mental weakness, when Cubes and Spheres flit away
into the background of scarce-possible existences ; when the Land of
Three Dimensions seems almost as visionary as the Land of One or
None ; nay, when even this hard wall that bars me from my freedom, these
very tablets on which I am writing, and all the substantial realities of
Flatland itself, appear no better than the offspring of a diseased imagination,
or the baseless fabric of a dream.
LONDON: R. CLAY, SONS, AND TAYLOR, PRINTERS.
J
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