PART I: THIS WORLD
"Be patient, for the world is broad and wide."
Section 1.
Of the Nature of Flatland
I call our world Flatland, not because we call it so, but to
make its nature clearer to you, my happy readers, who are
privileged to live in Space.
Imagine a vast sheet of paper on which straight Lines,
Triangles, Squares, Pentagons, Hexagons, and other figures, instead
of remaining fixed in their places, move freely about, on or in the
surface, but without the power of rising above or sinking below it,
very much like shadows—only hard and with luminous edges—and you
will then have a pretty correct notion of my country and
countrymen. Alas, a few years ago, I should have said "my
universe": but now my mind has been opened to higher views of
things.
In such a country, you will perceive at once that it is
impossible that there should be anything of what you call a "solid"
kind; but I dare say you will suppose that we could at least
distinguish by sight the Triangles, Squares, and other figures,
moving about as I have described them. On the contrary, we could
see nothing of the kind, not at least so as to distinguish one
figure from another. Nothing was visible, nor could be visible, to
us, except Straight Lines; and the necessity of this I will
speedily demonstrate.
Place a penny on the middle of one of your tables in Space; and
leaning over it, look down upon it. It will appear a circle.
But now, drawing back to the edge of the table, gradually lower
your eye (thus bringing yourself more and more into the condition
of the inhabitants of Flatland), and you will find the penny
becoming more and more oval to your view, and at last when you have
placed your eye exactly on the edge of the table (so that you are,
as it were, actually a Flatlander) the penny will then have ceased
to appear oval at all, and will have become, so far as you can see,
a straight line.
The same thing would happen if you were to treat in the same way
a Triangle, or Square, or any other figure cut out of pasteboard.
As soon as you look at it with your eye on the edge on the table,
you will find that it ceases to appear to you a figure, and that it
becomes in appearance a straight line. Take for example an
equilateral Triangle—who represents with us a Tradesman of the
respectable class. Fig. 1 represents the Tradesman as you would see
him while you were bending over him from above; figs. 2 and 3
represent the Tradesman, as you would see him if your eye were
close to the level, or all but on the level of the table; and if
your eye were quite on the level of the table (and that is how we
see him in Flatland) you would see nothing but a straight line.
Fig. 1, 2 and 3.
When I was in Spaceland I heard that your sailors have very
similar experiences while they traverse your seas and discern some
distant island or coast lying on the horizon. The far–off land may
have bays, forelands, angles in and out to any number and extent;
yet at a distance you see none of these (unless indeed your sun
shines bright upon them revealing the projections and retirements
by means of light and shade), nothing but a grey unbroken line upon
the water.
Well, that is just what we see when one of our triangular or
other acquaintances comes toward us in Flatland. As there is
neither sun with us, nor any light of such a kind as to make
shadows, we have none of the helps to the sight that you have in
Spaceland. If our friend comes closer to us we see his line becomes
larger; if he leaves us it becomes smaller: but still he looks like
a straight line; be he a Triangle, Square, Pentagon, Hexagon,
Circle, what you will—a straight Line he looks and nothing
else.
You may perhaps ask how under these disadvantageous
circumstances we are able to distinguish our friends from one
another: but the answer to this very natural question will be more
fitly and easily given when I come to describe the inhabitants of
Flatland. For the present let me defer this subject, and say a word
or two about the climate and houses in our country.
Section 2.
Of the Climate and Houses in Flatland
As with you, so also with us, there are four points of the
compass North, South, East, and West.
There being no sun nor other heavenly bodies, it is impossible
for us to determine the North in the usual way; but we have a
method of our own. By a Law of Nature with us, there is a constant
attraction to the South; and, although in temperate climates this
is very slight—so that even a Woman in reasonable health can
journey several furlongs northward without much difficulty—yet the
hampering effect of the southward attraction is quite sufficient to
serve as a compass in most parts of our earth. Moreover, the rain
(which falls at stated intervals) coming always from the North, is
an additional assistance; and in the towns we have the guidance of
the houses, which of course have their side–walls running for the
most part North and South, so that the roofs may keep off the rain
from the North. In the country, where there are no houses, the
trunks of the trees serve as some sort of guide. Altogether, we
have not so much difficulty as might be expected in determining our
bearings.
Yet in our more temperate regions, in which the southward
attraction is hardly felt, walking sometimes in a perfectly
desolate plain where there have been no houses nor trees to guide
me, I have been occasionally compelled to remain stationary for
hours together, waiting till the rain came before continuing my
journey. On the weak and aged, and especially on delicate Females,
the force of attraction tells much more heavily than on the robust
of the Male Sex, so that it is a point of breeding, if you meet a
Lady in the street, always to give her the North side of the way—by
no means an easy thing to do always at short notice when you are in
rude health and in a climate where it is difficult to tell your
North from your South.
Windows there are none in our houses: for the light comes to us
alike in our homes and out of them, by day and by night, equally at
all times and in all places, whence we know not. It was in old
days, with our learned men, an interesting and oft–investigated
question, "What is the origin of light?" and the solution of it has
been repeatedly attempted, with no other result than to crowd our
lunatic asylums with the would–be solvers. Hence, after fruitless
attempts to suppress such investigations indirectly by making them
liable to a heavy tax, the Legislature, in comparatively recent
times, absolutely prohibited them. I—alas, I alone in Flatland—know
now only too well the true solution of this mysterious problem; but
my knowledge cannot be made intelligible to a single one of my
countrymen; and I am mocked at—I, the sole possessor of the truths
of Space and of the theory of the introduction of Light from the
world of three Dimensions—as if I were the maddest of the mad! But
a truce to these painful digressions: let me return to our
houses.
The most common form for the construction of a house is
five–sided or pentagonal, as in the annexed figure. The two
Northern sides RO, OF, constitute the roof, and for the most part
have no doors; on the East is a small door for the Women; on the
West a much larger one for the Men; the South side or floor is
usually doorless.
Square and triangular houses are not allowed, and for this
reason. The angles of a Square (and still more those of an
equilateral Triangle), being much more pointed than those of a
Pentagon, and the lines of inanimate objects (such as houses) being
dimmer than the lines of Men and Women, it follows that there is no
little danger lest the points of a square or triangular house
residence might do serious injury to an inconsiderate or perhaps
absent–minded traveller suddenly therefore, running against them:
and as early as the eleventh century of our era, triangular houses
were universally forbidden by Law, the only exceptions being
fortifications, powder–magazines, barracks, and other state
buildings, which it is not desirable that the general public should
approach without circumspection.
At this period, square houses were still everywhere permitted,
though discouraged by a special tax. But, about three centuries
afterwards, the Law decided that in all towns containing a
population above ten thousand, the angle of a Pentagon was the
smallest house–angle that could be allowed consistently with the
public safety. The good sense of the community has seconded the
efforts of the Legislature; and now, even in the country, the
pentagonal construction has superseded every other. It is only now
and then in some very remote and backward agricultural district
that an antiquarian may still discover a square house.
Section 3.
Concerning the Inhabitants of Flatland
The greatest length or breadth of a full grown inhabitant of
Flatland may be estimated at about eleven of your inches. Twelve
inches may be regarded as a maximum.
Our Women are Straight Lines.
Our Soldiers and Lowest Classes of Workmen are Triangles with
two equal sides, each about eleven inches long, and a base or third
side so short (often not exceeding half an inch) that they form at
their vertices a very sharp and formidable angle. Indeed when their
bases are of the most degraded type (not more than the eighth part
of an inch in size), they can hardly be distinguished from Straight
Lines or Women; so extremely pointed are their vertices. With us,
as with you, these Triangles are distinguished from others by being
called Isosceles; and by this name I shall refer to them in the
following pages.
Our Middle Class consists of Equilateral or Equal–Sided
Triangles.
Our Professional Men and Gentlemen are Squares (to which class I
myself belong) and Five–Sided Figures or Pentagons.
Next above these come the Nobility, of whom there are several
degrees, beginning at Six–Sided Figures, or Hexagons, and from
thence rising in the number of their sides till they receive the
honourable title of Polygonal, or many–sided. Finally when the
number of the sides becomes so numerous, and the sides themselves
so small, that the figure cannot be distinguished from a circle, he
is included in the Circular or Priestly order; and this is the
highest class of all.
It is a Law of Nature with us that a male child shall have one
more side than his father, so that each generation shall rise (as a
rule) one step in the scale of development and nobility. Thus the
son of a Square is a Pentagon; the son of a Pentagon, a Hexagon;
and so on.
But this rule applies not always to the Tradesmen, and still
less often to the Soldiers, and to the Workmen; who indeed can
hardly be said to deserve the name of human Figures, since they
have not all their sides equal. With them therefore the Law of
Nature does not hold; and the son of an Isosceles (i.e. a Triangle
with two sides equal) remains Isosceles still. Nevertheless, all
hope is not shut out, even from the Isosceles, that his posterity
may ultimately rise above his degraded condition. For, after a long
series of military successes, or diligent and skilful labours, it
is generally found that the more intelligent among the Artisan and
Soldier classes manifest a slight increase of their third side or
base, and a shrinkage of the two other sides. Intermarriages
(arranged by the Priests) between the sons and daughters of these
more intellectual members of the lower classes generally result in
an offspring approximating still more to the type of the
Equal–Sided Triangle.
Rarely—in proportion to the vast numbers of Isosceles births—is
a genuine and certifiable Equal–Sided Triangle
produced from Isosceles parents. Such a birth requires, as its
antecedents, not only a series of carefully arranged
intermarriages, but also a long, continued exercise of frugality
and self–control on the part of the would–be ancestors of the
coming Equilateral, and a patient, systematic, and continuous
development of the Isosceles intellect through many
generations.
The birth of a True Equilateral Triangle from Isosceles parents
is the subject of rejoicing in our country for many furlongs
around. After a strict examination conducted by the Sanitary and
Social Board, the infant, if certified as Regular, is with solemn
ceremonial admitted into the class of Equilaterals. He is then
immediately taken from his proud yet sorrowing parents and adopted
by some childless Equilateral, who is bound by oath never to permit
the child henceforth to enter his former home or so much as to look
upon his relations again, for fear lest the freshly developed
organism may, by force of unconscious imitation, fall back again
into his hereditary level.
The occasional emergence of an Equilateral from the ranks of his
serf–born ancestors is welcomed, not only by the poor serfs
themselves, as a gleam of light and hope shed upon the monotonous
squalor of their existence, but also by the Aristocracy at large;
for all the higher classes are well aware that these rare
phenomena, while they do little or nothing to vulgarize their own
privileges, serve as a most useful barrier against revolution from
below.
Had the acute–angled rabble been all, without exception,
absolutely destitute of hope and of ambition, they might have found
leaders in some of their many seditious outbreaks, so able as to
render their superior numbers and strength too much even for the
wisdom of the Circles. But a wise ordinance of Nature has decreed
that, in proportion as the working–classes increase in
intelligence, knowledge, and all virtue, in that same proportion
their acute angle (which makes them physically terrible) shall
increase also and approximate to the comparatively harmless angle
of the Equilateral Triangle. Thus, in the most brutal and
formidable of the soldier class—creatures almost on a level with
women in their lack of intelligence—it is found that, as they wax
in the mental ability necessary to employ their tremendous
penetrating power to advantage, so do they wane in the power of
penetration itself.
How admirable is this Law of Compensation! And how perfect a
proof of the natural fitness and, I may almost say, the divine
origin of the aristocratic constitution of the States in Flatland!
By a judicious use of this Law of Nature, the Polygons and Circles
are almost always able to stifle sedition in its very cradle,
taking advantage of the irrepressible and boundless hopefulness of
the human mind. Art also comes to the aid of Law and Order. It is
generally found possible—by a little artificial compression or
expansion on the part of the State physicians—to make some of the
more intelligent leaders of a rebellion perfectly Regular, and to
admit them at once into the privileged classes; a much larger
number, who are still below the standard, allured by the prospect
of being ultimately ennobled, are induced to enter the State
Hospitals, where they are kept in honourable confinement for life;
one or two alone of the more obstinate, foolish, and hopelessly
irregular are led to execution.
Then the wretched rabble of the Isosceles, planless and
leaderless, are either transfixed without resistance by the small
body of their brethren whom the Chief Circle keeps in pay for
emergencies of this kind; or else more often, by means of
jealousies and suspicions skilfully fomented among them by the
Circular party, they are stirred to mutual warfare, and perish by
one another's angles. No less than one hundred and twenty
rebellions are recorded in our annals, besides minor outbreaks
numbered at two hundred and thirty–five; and they have all ended
thus.
Section 4.
Concerning the Women
If our highly pointed Triangles of the Soldier class are formidable, it may be readily inferred that far more formidable are our Women. For if a Soldier is a wedge, a Woman is a needle; being, so to speak, all point, at least at the two extremities. Add to this the power of making herself practically invisible at will, and you will perceive that a Female, in Flatland, is a creature by no means to be trifled with.
But here, perhaps, some of my younger Readers may ask how a woman in Flatland can make herself invisible. This ought, I think, to be apparent without any explanation. However, a few words will make it clear to the most unreflecting.
Place a needle on a table. Then, with your eye on the level of the table, look at it side–ways, and you see the whole length of it; but look at it end–ways, and you see nothing but a point, it has become practically invisible. Just so is it with one of our Women. When her side is turned towards us, we see her as a straight line; when the end containing her eye or mouth—for with us these two organs are identical—is the part that meets our eye, then we see nothing but a highly lustrous point; but when the back is presented to our view, then—being only sub–lustrous, and, indeed, almost as dim as an inanimate object—her hinder extremity serves her as a kind of Invisible Cap.
The dangers to which we are exposed from our Women must now be manifest to the meanest capacity in Spaceland. If even the angle of a respectable Triangle in the middle class is not without its dangers; if to run against a Working Man involves a gash; if collision with an officer of the military class necessitates a serious wound; if a mere touch from the vertex of a Private Soldier brings with it danger of death;—what can it be to run ag...