Flatland, by Edwin A. Abbott
Part 1 out of 2
Flatland by Edwin A. Abbott
The Inhabitance 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
To the Enlargment of THE IMAGINATION
And the possible Development
Of that most and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY
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
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 a Square, or any other figure
cut out from 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 as 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. Figure 1 represents
the Tradesman as you would see him while you were bending over
him from above; figures 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.
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 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 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 disadvantagous 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 effort 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 on 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-investigate 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 homes.
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 of triangular house
residence might do serious injury to an inconsiderate
or perhaps absentminded 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 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 Class 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 Tradesman,
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 such 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 skillful 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 (footnote 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.
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 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 almost 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 their
comparatively harmless angle of the Equilateral Triangle.
Thus, in the most brutal and formidable off 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 the 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 of 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 most obstinate, foolish,
and hopelessly irregular are led to execution.
Then the wretched rabble of the Isosceles, planless
and leaderless, are ether 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 suspicious skillfully 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.
"What need of a certificate?" a Spaceland critic may ask:
"Is not the procreation of a Square Son a certificate
from Nature herself, proving the Equal-sidedness of the Father?"
I reply that no Lady of any position will mary 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.
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 the 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 of Spaceland.
If even the angle of a respectable Triangle in the
middle class is not without its dangers;
if to run against a Working Man involves a gash;
if collision with an Officer of the military class
necessitates a serious wound; if a mere touch from
the vertex of a Private Soldier brings with it danger of death;
--what can it be to run against a woman, except absolute
and immediate destruction? And when a Woman is invisible,
or visible only as a dim sub-lustrous point,
how difficult must it be, even for the most cautious,
always to avoid collision!
Many are the enactments made at different times in the different
States of Flatland, in order to minimize this peril;
and in the Southern and less temperate climates,
where the force of gravitation is greater,
and human beings more liable to casual
and involuntary motions, the Laws concerning
Women are naturally much more stringent.
But a general view of the Code may be obtained
from the following summary:--
1. Every house shall have one entrance on the Eastern side,
for the use of Females only; by which all females shall enter
"in a becoming and respectful manner" (footnote 1) 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; other oblige a Woman,
when travelling, to be followed by one of her sons,
or servants, or by her husband; others confine
Women altogether in their houses except during
the religious festivals. But it has been found
by the wisest of our Circles or Statesmen
that the multiplication of restrictions on Females
tends not only to the debilitation and diminution
of the race, but also to the increase of domestic
murders to such an extent that a State loses
more than it gains by a too prohibitive Code.
For whenever the temper of the Women is thus exasperated
by confinement at home or hampering regulations abroad,
they are apt to vent their spleen upon their husbands and children;
and in the less temperate climates the whole male population
of a village has been sometimes destroyed in one or two hours
of a simultaneous female outbreak. Hence the Three Laws,
mentioned above, suffice for the better regulated States,
and may be accepted as a rough exemplification of our Female Code.
After all, our principal safeguard is found, not in Legislature,
but in the interests of the Women themselves. For, although they
can inflict instantaneous death by a retrograde movement,
yet unless they can at once disengage their stinging extremity
from the struggling body of their victim, their own frail bodies
are liable to be shattered.
The power of Fashion is also on our side. I pointed out that
in some less civilized States no female is suffered to stand
in any public place without swaying her back from right to left.
This practice has been universal among ladies of any pretensions
to breeding in all well-governed States, as far back as the memory
of Figures can reach. It is considered a disgrace to any state
that legislation should have to enforce what ought to be,
and is in every respectable female, a natural instinct.
The rhythmical and, if I may so say, well-modulated undulation
of the back in our ladies of Circular rank is envied and imitated
by the wife of a common Equilateral, who can achieve nothing beyond
a mere monotonous swing, like the ticking of a pendulum;
and the regular tick of the Equilateral is no less admired
and copied by the wife of the progressive and aspiring Isosceles,
in the females of whose family no "back-motion" of any kind
has become as yet a necessity of life. Hence, in every family
of position and consideration, "back motion" is as prevalent
as time itself; and the husbands and sons in these households
enjoy immunity at least from invisible attacks.
Not that it must be for a moment supposed that our Women are
destitute of affection. But unfortunately the passion of the
moment predominates, in the Frail Sex, over every other consideration.
This is, of course, a necessity arising from their unfortunate
conformation. For as they have no pretensions to an angle,
being inferior in this respect to the very lowest of the Isosceles,
they are consequently wholly devoid of brainpower, and have
neither reflection, judgment nor forethought, and hardly any memory.
Hence, in their fits of fury, they remember no claims and recognize
no distinctions. I have actually known a case where a Woman
has exterminated her whole household, and half an hour afterwards,
when her rage was over and the fragments swept away,
has asked what has become of her husband and children.
Obviously then a Woman is not to be irritated as long as she
is in a position where she can turn round. When you have them
in their apartments--which are constructed with a view
to denying them that power--you can say and do what you like;
for they are then wholly impotent for mischief, and will
not remember a few minutes hence the incident for which
they may be at this moment threatening you with death,
nor the promises which you may have found it necessary
to make in order to pacify their fury.
On the whole we got 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 comfort.
In every Circular or Polygonal household it has been a habit
from time immemorial--and now has become a kind of instinct
among the women of our higher classes--that the mothers and daughters
should constantly keep their eyes and mouths towards their husband
and his male friends; and for a lady in a family of distinction
to turn her back upon her husband would be regarded as a kind of portent,
involving loss of STATUS. But, as I shall soon shew, this custom,
though it has the advantage of safety, is not without 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 toward 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 seen
truly deplorable, and so indeed it is. A Male of the lowest type
of the Isosceles may look forward to some improvement of his angle,
and to the ultimate elevation of the whole of his degraded caste;
but no Woman can entertain such hopes for her sex. "Once a Woman,
always a Woman" is a Decree of Nature; and the very Laws of Evolution
seem suspended in her disfavour. Yet at least we can admire the wise
Prearrangement which has ordained that, as they have no hopes, so they
shall have no memory to recall, and no forethought to anticipate,
the miseries and humiliations which are at once a necessity of their
existence and the basis of the constitution of Flatland.
SECTION 5 Of our Methods of Recognizing one another
You, who are blessed with shade as well as light, you, who are
gifted with two eyes, endowed with a knowledge of perspective,
and charmed with the enjoyment of various colours, you, who can
actually SEE an angle, and contemplate the complete circumference
of a Circle in the happy region of the Three Dimensions--
how shall I make it clear to you the extreme difficulty which we
in Flatland experience in recognizing one another's configuration?
Recall what I told you above. All beings in Flatland, animate and
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 of 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 the Isosceles I take no account.
But as we ascend the social scale, the process of discriminating
and being discriminated by hearing increases in difficulty, partly because
voices are assimilated, partly because the faculty of voice-discrimination
is a plebeian virtue not much developed among the Aristocracy. And wherever
there is any danger of imposture we cannot trust to this method.
Amongst our lowest orders, the vocal organs are developed to a degree
more than correspondent with those of hearing, so that an Isosceles
can easily feign the voice of a Polygon, and, with some training,
that of a Circle himself. A second method is therefore more
commonly resorted to.
FEELING is, among our Women and lower classes--about our upper
classes I shall speak presently--the principal test of recognition,
at all events between strangers, and when the question is, not as to
the individual, but as to the class. What therefore "introduction"
is among the higher classes in Spaceland, that the process of "feeling"
is with us. "Permit me to ask you to feel and be felt by my friend
Mr. So-and-so"--is still, among the more old-fashioned of our
country gentlemen in districts remote from towns, the customary
formula for a Flatland introduction. But in the towns, and among men
of business, the words "be felt by" are omitted and the sentence is
abbreviated to, "Let me ask you to feel Mr. So-and-so"; although it is
assumed, of course, that the "feeling" is to be reciprocal. Among our
still more modern and dashing young gentlemen--who are extremely
averse to superfluous effort and supremely indifferent to the
purity of their native language--the formula is still further
curtailed by the use of "to feel" in a technical sense, meaning,
"to recommend-for- the-purposes-of-feeling-and-being-felt";
and at this moment the "slang" of polite or fast society
in the upper classes sanctions such a barbarism as "Mr. Smith,
permit me to feel Mr. Jones."
Let not my Reader however suppose that "feeling" is with us
the tedious process that it would be with you, or that we find
it necessary to feel right round all the sides of every individual
before we determine the class to which he belongs. Long practice
and training, begun in the schools and continued in the experience
of daily life, enable us to discriminate at once by the sense of touch,
between the angles of an equal-sided Triangle, Square, and Pentagon;
and I need not say that the brainless vertex of an acute-angled
Isosceles is obvious to the dullest touch. It is therefore
not necessary, as a rule, to do more than feel a single angle
of an individual; and this, once ascertained, tells us the class
of the person whom we are addressing, unless indeed he belongs to the
higher sections of the nobility. There the difficulty is much greater.
Even a Master of Arts in our University of Wentbridge has been known
to confuse a ten-sided with a twelve-sided Polygon; and there is hardly
a Doctor of Science in or out of that famous University who could
pretend to decide promptly and unhesitatingly between a twenty-sided
and a twenty-four sided member of the Aristocracy.
Those of my readers who recall the extracts I gave above from the
Legislative code concerning Women, will readily perceive that the
process of introduction by contact requires some care and discretion.
Otherwise the angles might inflict on the unwary Feeling irreparable
injury. It is essential for the safety of the Feeler that the Felt
should stand perfectly still. A start, a fidgety shifting
of the position, yes, even a violent sneeze, has been known before
now to prove fatal to the incautious, and to nip in the bud many
a promising friendship. Especially is this true among the lower classes
of the Triangles. With them, the eye is situated so far from their vertex
that they can scarcely take cognizance of what goes on at that extremity
of their frame. They are, moreover, of a rough coarse nature, not sensitive
to the delicate touch of the highly organized Polygon. What wonder then
if an involuntary toss of the head has ere now deprived the State
of a valuable life!
I have heard that my excellent Grandfather--one of the least
irregular of his unhappy Isosceles class, who indeed obtained,
shortly before his decease, four out of seven votes from the Sanitary
and Social Board for passing him into the class of the Equal-sided--
often deplored, with a tear in his venerable eye, a miscarriage of
this kind, which had occurred to his great-great-great-Grandfather,
a respectable Working Man with an angle or brain of 59 degrees
30 minutes. According to his account, my unfortunately Ancestor,
being afflicted with rheumatism, and in the act of being felt
by a Polygon, by one sudden start accidentally transfixed
the Great Man through the diagonal and thereby, partly in consequence
of his long imprisonment and degradation, and partly because
of the moral shock which pervaded the whole of my Ancestor's relations,
threw back our family a degree and a half in their ascent towards
better things. The result was that in the next generation
the family brain was registered at only 58 degrees,
and not till the lapse of five generations was the lost
ground recovered, the full 60 degrees attained,
and the Ascent from the Isosceles finally achieved.
And all this series of calamities from one little accident
in the process of Feeling.
As 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 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 on 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 an angle, and much less register angles
of different sizes?"
I answer that though we cannot SEE angles, we can INFER them, and this
with great precision. Our sense of touch, stimulated by necessity,
and developed by long training, enables us to distinguish angles
far more accurately than your sense of sight, when unaided by a rule
or measure of angles. nor must I omit to explain that we have great
natural helps. It is with us a Law of Nature that the brain
of the Isosceles class shall begin at half a degree,
or thirty minutes, and shall increase (if it increases at all)
by half a degree in every generation until the goal of 60 degrees
is reached, when the condition of serfdom is quitted, and the freeman
enters the class of Regulars.
Consequently, Nature herself supplies us with an ascending scale
or Alphabet of angles for half a degree up to 60 degrees, Specimen
of which are placed in every Elementary School throughout the land.
Owing to occasional retrogressions, to still more frequent moral
and intellectual stagnation, and to the extraordinary fecundity
of the Criminal and Vagabond classes, there is always a vast superfluity
of individuals of the half degree and single degree class, and a fair
abundance of Specimens up to 10 degrees. These are absolutely
destitute of civil 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 classrooms 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 the tact and intelligence which these wretched
creatures themselves are utterly devoid.
In some States the Specimens are occasionally fed and suffered
to exist for several years; but in the more temperate and better
regulated regions, it is found in the long run more advantageous
for the educational interests of the young, to dispense with food,
and to renew the Specimens every month--which is about the average
duration of the foodless existence of the Criminal class.
In the cheaper schools, what is gained by the longer existence
of the Specimen is lost, partly in the expenditure for food,
and partly in the diminished accuracy of the angles, which
are impaired after a few weeks of constant "feeling."
Nor must we forget to add, in enumerating the advantages
of the more expensive system, that it tends, though slightly
yet perceptibly, to the diminution of the redundant Isosceles population--
an object which every statesman in Flatland constantly keeps in view.
On the whole therefore--although I am not ignorant that,
in many popularly elected School Boards, there is a reaction
in favour of "the cheap system" as it is called--
I am myself disposed to think that this is one
of the many cases in which expense is the truest economy.
But I must not allow questions of School Board politics to divert
me from my subject. Enough has been said, I trust, to shew that
Recognition by Feeling is not so tedious or indecisive a process
as might have been supposed; and it is obviously more trustworthy
than Recognition by hearing. Still there remains, as has been pointed
out above, the objection that this method is not without danger.
For this reason many in the Middle and Lower classes, and all
without exception in the Polygonal and Circular orders,
prefer a third method, the description of which
shall be reserved for the next section.
SECTION 6 Of Recognition by Sight
I am about to appear very inconsistent. In the previous sections
I have said that all figures in Flatland present the appearance
of a straight line; and it was added or implied, that it is consequently
impossible to distinguish by the visual organ between individuals
of different classes: yet now I am about to explain to my Spaceland
critics how we are able to recognize one another by the sense of sight.
If however the Reader will take the trouble to refer to the passage
in which Recognition by Feeling is stated to be universal,
he will find this qualification--"among the lower classes."
It is only among the higher classes and in our 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 indistinguishably clear; and this is actually the case
in those unhappy countries in which the atmosphere is perfectly
dry and transparent. But wherever there is a rich supply of Fog,
objects that are at a distance, say of three feet, are appreciably
dimmer than those at the distance of two feet eleven inches; and the
result is that by careful and constant experimental observation
of comparative dimness and clearness, we are enabled to infer
with great exactness the configuration of the object observed.
An instance will do more than a volume of generalities to make
my meaning clear.
Suppose I see two individuals approaching whose rank I wish to ascertain.
They are, we will suppose, a Merchant and a Physician, or in other words,
an Equilateral Triangle and a Pentagon; how am I to distinguish them?
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 the two sides that are next
to me (viz. CA and AB), so that I shall contemplate the two impartially,
and both will appear of the same size.
Now in the case of (1) the Merchant, what shall I see? I shall see
a straight line DAE, in which the middle point (A) will be very bright
because it is nearest to me; but on either side the line will shade
away RAPIDLY TO DIMNESS, because the sides AC and AB RECEDE RAPIDLY
INTO THE FOG and what appear to me as the Merchant's extremities,
viz. D and E, will be VERY DIM INDEED.
On the other hand in the case of (2) the Physician, though I shall
here also see a line (D'A'E') with a bright centre (A'), yet it will
shade away LESS RAPIDLY to dimness, because the sides (A'C', A'B')
RECEDE LESS RAPIDLY INTO THE FOG: and what appear to me the Physician's
extremities, viz. D' and E', will not be NOT SO DIM as the extremities
of the Merchant.
The Reader will probably understand from these two instances how
--after a very long training supplemented by constant experience--
it is possible for the well-educated classes among us to discriminate
with fair accuracy between the middle and lowest orders, by the sense
of sight. If my Spaceland Patrons have grasped this general conception,
so far as to conceive the possibility of it and not to reject my account
as altogether incredible--I shall have attained all I can reasonably expect.
Were I to attempt further details I should only perplex. Yet for the sake
of the young and inexperienced, who may perchance infer--from the two simple
instances I have given above, of the manner in which I should recognize
my Father and my Sons--that Recognition by sight is an easy affair,
it may be needful to point out that in actual life most of the problems
of Sight Recognition are far more subtle and complex.
If for example, when my Father, the Triangle, approaches me,
he happens to present his side to me instead of his angle, then,
until I have asked him to rotate, or until I have edged my eye around him,
I am for the moment doubtful whether he may not be a Straight Line, or,
in other words, a Woman. Again, when I am in the company of one of my
two hexagonal Grandsons, contemplating one of his sides (AB) full front,
it will be evident from the accompanying diagram that I shall see one whole
line (AB) in comparative brightness (shading off hardly at all at the ends)
and two smaller lines (CA and BD) dim throughout and shading away into greater
dimness towards the extremities C and D.
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 to my country.
In such a crowd you could see on all sides of you nothing but a Line,
apparently straight, but of which the parts would vary irregularly
and perpetually in brightness or dimness. Even if you had completed
your third year in the Pentagonal and Hexagonal classes in the University,
and were perfect in the theory of the subject, you would still find 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"
For this reason, among our Higher Classes, "Feeling" is discouraged
or absolutely forbidden. From the cradle their children, instead of going
to the Public Elementary schools (where the art of Feeling is taught,)
are sent to higher Seminaries of an exclusive character; and at our
illustrious University, to "feel" is regarded as a most serious fault,
involving Rustication for the first offence, and Expulsion for the second.
But among the lower classes the art of Sight Recognition is regarded
as an unattainable luxury. A common Tradesman cannot afford to let
his sun spend a third of his life in abstract studies. The children
of the poor are therefore allowed to "feel" from their earliest years,
and they gain thereby a precocity and an early vivacity which contrast
at first most favourably with the inert, undeveloped, and listless
behaviour of the half-instructed youths of the Polygonal class;
but when the latter have at last completed their University course,
and are prepared to put their theory into practice, the change
that comes over them may almost be described as a new birth,
and in every art, science, and social pursuit they rapidly
overtake and distance their Triangular competitors.
Only a few of the Polygonal Class fail to pass the Final Test
or Leaving Examination at the University. The condition of the
unsuccessful minority is truly pitiable. Rejected from the higher
class,, they are also despised by the lower. They have neither the
matured and systematically trained powers of the Polygonal Bachelors
and Masters of Arts, nor yet the native precocity and mercurial
versatility of the youthful Tradesman. The professions, the public
services, are closed against them, and though in most States they
are not actually debarred from marriage, yet they have the greatest
difficulty in forming suitable alliances, as experience shews that
the offspring of such unfortunate and ill-endowed parents is generally
itself unfortunate, if not positively Irregular.
It is from these specimens of the refuse of our Nobility that the great
Tumults and Seditions of past ages have generally derived their leaders;
and so great is the mischief thence arising that an increasing minority
of our more progressive Statesmen are of opinion that true mercy would
dictate their entire suppression, by enacting that all who fail to pass
the Final Examination of the University should be either imprisoned
for life, or extinguished by a painless death.
But I find myself digressing into the subject of Irregularities,
a matter of such vital interest that it demands a separate section.
SECTION 7 Concerning Irregular Figures
Throughout the previous pages I have been assuming--what perhaps
should have been laid down at the beginning as a distinct and
fundamental proposition--that every human being in Flatland
is a Regular Figure, that is to say of regular construction.
By this I mean that a Woman must not only be a line, but a straight line;
that an Artisan or Soldier must have two of his sides equal;
that Tradesmen must have three sides equal; Lawyers (of which class
I am a humble member), four sides equal, and, generally,
that in every Polygon, all the sides must be equal.
The sizes 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 size,
when added together, is two feet or a little more. But the size of our sides
is not under consideration. I am speaking of the EQUALITY of sides,
and it does not need much reflection to see that the whole of the
social life in Flatland rests upon the fundamental fact that
Nature wills all Figures to have their sides equal.
If our sides were unequal our angles might be unequal. Instead of
its being sufficient to feel, or estimate by sight, a single angle
in order to determine the form of an individual, it would be necessary
to ascertain each angle by the experiment of Feeling. But life would
be too short for such a tedious 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 might 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 social system is based upon Regularity,
or Equality of Angles. You meet, for example, two or three Tradesmen
in the street, whom your recognize at once to be Tradesman by a glance
at their angles and rapidly bedimmed sides, and you ask them to step into
your house to lunch. This you do at present with perfect confidence,
because everyone knows to an inch or two the area occupied by
an adult Triangle: but imagine that your Tradesman drags behind
his regular and respectable vertex, a parallelogram of twelve
or thirteen inches in diagonal:--what are you to do with such
a monster sticking fast in your house door?
But I am insulting the intelligence of my Readers by accumulating
details which must be patent to everyone who enjoys the advantages
of a Residence in Spaceland. Obviously the measurements of a single
angle would no longer be sufficient under such portentous circumstances;
one's whole life would be taken up in feeling or surveying the perimeter
of one's acquaintances. Already the difficulties of avoiding a collision
in a crowd are enough to tax the sagacity of even a well-educated Square;
but if no one could calculate the Regularity of a single figure in the company,
all would be chaos and confusion, and the slightest panic would cause
serious injuries, or--if there happened to be any Women or Soldiers present--
perhaps considerable loss of life.
Expediency therefore concurs with Nature in stamping the seal
of its approval upon Regularity of conformation: nor has the Law
been backward in seconding their efforts. "Irregularity of Figure"
means with us the same as, or more than, a combination of moral obliquity
and criminality with you, and is treated accordingly. There are not
wanting, it is true, some promulgators of paradoxes who maintain that
there is no necessary connection between geometrical and moral Irregularity.
"The Irregular," they say, "is from his birth scouted by his own parents,
derided by his brothers and sisters, neglected by the domestics,
scorned and suspected by society, and excluded from all posts
of responsibility, trust, and useful activity. His every
movement is jealously watched by the police till he comes
of age and presents himself for inspection; then he is either destroyed,
if he is found to exceed the fixed margin of deviation, at an uninteresting
occupation for a miserable stipend; obliged to live and board at the office,
and to take even his vacation under close supervision; what wonder that
human nature, even in the best and purest, is embittered and perverted
by such surroundings!"
All this very plausible reasoning does not convince me, as it has not
convinced the wisest of our Statesmen, that our ancestors erred in laying
it down as an axiom of policy that the toleration of Irregularity
is incompatible with the safety of the State. Doubtless, the life
of an Irregular is hard; but the interests of the Greater Number
require that it shall be hard. If a man with a triangular front
and a polygonal back were allowed to exist and to propagate a still
more Irregular posterity, what would become of the arts of life?
Are the houses and doors and churches in Flatland to be altered
in order to accommodate such monsters? Are our ticket-collectors
to be required to measure every man's perimeter before they allow
him to enter a theatre, or to take his place in a lecture room?
Is an Irregular to be exempted from the militia? And if not,
how is he to be prevented from carrying desolation into the ranks
of his comrades? Again, what irresistible temptations to fraudulent
impostures must needs beset such a creature! How easy for him to enter
a shop with his polygonal front foremost, and to order goods to any extent
from a confiding tradesman! Let the advocates of a falsely called
Philanthropy plead as they may for the abrogation of the Irregular Penal Laws,
I for my part have never known an Irregular who was not also what Nature
evidently intended him to be--a hypocrite, a misanthropist, and,
up to the limits of his power, a perpetrator of all manner of mischief.
Not that I should be disposed to recommend (at present)
the extreme measures adopted by some States, where an infant
whose angle deviates by half a degree from the correct angularity
is summarily destroyed at birth. Some of our highest and ablest men,
men of real genius, have during their earliest days laboured under
deviations as great as, or even greater than forty-five minutes:
and the loss of their precious lives would have been an irreparable
injury to the State. The art of healing also has achieved some
of its most glorious triumphs in the compressions, extensions,
trepannings, colligations, and other surgical or diaetetic
operations by which Irregularity has been partly or wholly cured.
Advocating therefore a VIA MEDIA, I would lay down no fixed
or absolute line of demarcation; but at the period when the frame
is just beginning to set, and when the Medical Board has reported
that recovery is improbably, I would suggest that the Irregular
offspring be painlessly and mercifully consumed.
SECTION 8 Of the Ancient Practice of Painting
If my Readers have followed me with any attention up to this point,
they will not be surprised to hear that life is somewhat dull in Flatland.
I do not, of course, mean that there are not battles, conspiracies,
tumults, factions, and all those other phenomena which are supposed
to make History interesting; nor would I deny that the strange mixture
of the problems of life and the problems of Mathematics, continually
inducing conjecture and giving an opportunity of immediate verification,
imparts to our existence a zest which you in Spaceland can hardly comprehend.
I speak now from the aesthetic and artistic point of view when I say that life
with us is dull; aesthetically and artistically, very dull indeed.
How can it be otherwise, when all one's prospect, all one's landscapes,
historical pieces, portraits, flowers, still life, are nothing but
a single line, with no varieties except degrees of brightness and obscurity?
It was not always thus. Colour, if Tradition speaks the truth,
once for the space of half a dozen centuries or more, threw a transient
splendour over the lives of our ancestors in the remotest ages.
Some private individual--a Pentagon whose name is variously reported--
having casually discovered the constituents of the simpler colours
and a rudimentary method of painting, is said to have begun by decorating
first his house, then his slaves, then his Father, his Sons, and Grandsons,
lastly himself. The convenience as well as the beauty of the results
commended themselves to all. Wherever Chromatistes,--for by that name
the most trustworthy authorities concur in calling him,--turned his
variegated frame, there he at once excited attention, and attracted respect.
No one now needed to "feel" him; no one mistook his front for his back;
all his movements were readily ascertained by his neighbours without
the slightest strain on their powers of calculation; no one jostled him,
or failed to make way for him; his voice was saved the labour
of that exhausting utterance by which we colourless Squares
and Pentagons are often forced to proclaim our individuality
when we move amid a crowd of ignorant Isosceles.
The fashion spread like wildfire. Before a week was over,
every Square and Triangle in the district had copied the example
of Chromatistes, and only a few of the more conservative Pentagons
still held out. A month or two found even the Dodecagons infected
with the innovation. A year had not elapsed before the habit
had spread to all but the very highest of the Nobility.
Needless to say, the custom soon made its way from the district
of Chromatistes to surrounding regions; and within two generations
no one in all Flatland was colourless except the Women and the Priests.
Here Nature herself appeared to erect a barrier, and to plead
against extending the innovations 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 a 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 readily and truly Circles, and not mere high-class Polygons,
with an infinitely large number of infinitesimally small sides--
were in the habit of boasting (what Women confessed and deplored)
that they also had no sides, being blessed with a perimeter
of only 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 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 from 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 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 vermillion guns;
the dashing and flashing of the five-coloured and six-coloured
Pentagons and Hexagons careering across the field in their
offices of surgeons, geometricians and aides-de-camp--all
these may well have been sufficient to render credible the
famous story how an illustrious Circle, overcome by the artistic
beauty of the forces under his command, threw aside
his marshal's baton and his royal crown, exclaiming
that he henceforth exchanged them for the artist's pencil.
How great and glorious the sensuous development of these days must
have been is in part indicated by the very language and vocabulary
of the period. The commonest utterances of the commonest citizens
in the time of the Colour Revolt seem to have been suffused with a richer
tinge of word or thought; and to that era we are even now indebted
for our finest poetry and for whatever rhythm still remains in the more
scientific utterance of those modern days.
SECTION 9 Of the Universal Colour Bill
But meanwhile the intellectual Arts were fast decaying.
The Art of Sight Recognition, being no longer needed, was
no longer practised; and the studies of Geometry, Statics, Kinetics,
and other kindred subjects, came soon to be considered superfluous,
and feel into disrespect and neglect even at our University.
The inferior Art of Feeling speedily experienced the same fate
at our Elementary Schools. Then the Isosceles classes,
asserting that the Specimens were no longer used nor needed,
and refusing to pay the customary tribute from the Criminal classes
to the service of Education, waxed daily more numerous and more insolent
on the strength of their immunity from the old burden which had formerly
exercised the twofold wholesome effect of at once taming their brutal
nature and thinning their excessive numbers.
Year by year the Soldiers and Artisans began more vehemently
to assert--and with increasing truth--that there was no great
difference between them and the very highest class of Polygons,
now that they were raised to an equality with the latter, and enabled
to grapple with all the difficulties and solve all the problems of life,
whether Statical or Kinetical, by the simple process of Colour Recognition.
Not content with the natural neglect into which Sight Recognition was falling,
they began boldly to demand the legal prohibition of all "monopolizing
and aristocratic Arts" and the consequent abolition of all endowments
for the studies of Sight Recognition, Mathematics, and Feeling.
Soon, they began to insist that inasmuch as Colour, which was
a second Nature, had destroyed the need of aristocratic distinctions,
the Law should follow in the same path, and that henceforth all
individuals and all classes should be recognized as absolutely equal
and entitled to equal rights.
Finding the higher Orders wavering and undecided, the leaders
of the Revolution advanced still further in their requirements,
and at last demanded that all classes alike, the Priests and the Women
not excepted, should do homage to Colour by submitting to be painted.
When it was objected that Priests and Women had no sides, they retorted
that Nature and Expediency concurred in dictating that the front half
of every human being (that is to say, the half containing his eye and mouth)
should be distinguishable from his hinder half. They therefore brought
before a general and extraordinary Assembly of all the States of Flatland
a Bill proposing that in every Woman the half containing the eye and mouth
should be coloured red, and the other half green. The Priests were to be
painted in the same way, red being applied to that semicircle in which
the eye and mouth formed the middle point; while the other or hinder
semicircle was to be coloured green.
There was no little cunning in this proposal, which indeed emanated
not from any Isosceles--for no being so degraded would have 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 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 as a Priest, and be treated with
corresponding respect and deference--a prospect that could not fail
to attract the Female Sex in a mass.
But by some of my Readers the possibility of the identical appearance
of Priests and Women, under a 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 the 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 in 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 Woman would speedily learn to
shade off their extremities so as to imitate the Circles;
it must then be surely obvious to you, my dear Reader,
that the Colour Bill placed us under a great danger
of confounding a Priest with a young Woman.
How attractive this prospect must have been to the Frail Sex may
readily be imagined. They anticipated with delight the confusion that
would ensue. At home they might hear political and ecclesiastical
secrets intended not for them but for their husbands and brothers, and
might even issue some 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 Woman would gain whatever the Circles lost,
in the deference of the passers by. As for the scandal that would
befall the Circular Class if the frivolous and unseemly conduct of the
Women were imputed to them, and as to the consequent subversion of the
Constitution, the Female Sex could not be expected to give a thought
to these considerations. Even in the households of the Circles, the
Women were all in favour of the Universal Colour Bill.
The second object aimed at by the Bill was the gradual
demoralization of the Circles themselves. In the general intellectual
decay they still preserved their pristine clearness and strength of
understanding. From their earliest childhood, familiarized in their
Circular households with the total absence of Colour, the Nobles alone
preserved the Sacred Art of Sight Recognition, with all the advantages
that result from that admirable training of the intellect. Hence, up
to the date of the introduction of the Universal Colour Bill, the
Circles had not only held their own, but even increased their lead of
the other classes by abstinence from the popular fashion.
Now therefore the artful Irregular whom I described above as
the real author of this diabolical Bill, determined at one blow
to lower the status of the Hierarchy by forcing them to submit
to the pollution of Colour, and at the same time to destroy their
domestic opportunities of training in the Art of Sight Recognition,
so as to enfeeble their intellects by depriving them of their pure
and colourless homes. Once subjected to the chromatic taint,
every parental and every childish Circle would demoralize each other.
Only in discerning between the Father and the Mother would the Circular
infant find problems for the exercise of his understanding--problems
too often likely to be corrupted by maternal impostures with the
result of shaking the child's faith in all logical conclusions.
Thus by degrees the intellectual lustre of the Priestly Order would wane,
and the road would then lie open for a total destruction of all Aristocratic
Legislature and for the subversion of our Privileged Classes.
SECTION 10 Of the Suppression of the Chromatic Sedition
The agitation for the Universal Colour Bill continued for three years;
and up to the last moment of that period it seemed as though Anarchy
were destined to triumph.
A whole army of Polygons, who turned out to fight as private soldiers,
was utterly annihilated by a superior force of Isosceles Triangles--
the Squares and Pentagons meanwhile remaining neutral.
Worse than all, some of the ablest Circles fell a prey to conjugal fury.
Infuriated by political animosity, the wives in many a noble household
wearied their lords with prayers to give up their opposition to the
Colour Bill; and some, finding their entreaties fruitless, fell on
and slaughtered their innocent children and husband, perishing
themselves in the act of carnage. It is recorded that during
that triennial agitation no less than twenty-three Circles
perished in domestic discord.
Great indeed was the peril. It seemed as though the Priests
had no choice between submission and extermination; when suddenly
the course of events was completely changed by one of those picturesque
incidents which Statesmen ought never to neglect, often to anticipate,
and sometimes perhaps to originate, because of the absurdly
disproportionate power with which they appeal to the sympathies
of the populace.
It happened that an Isosceles of a low type, with a brain little
if at all above four degrees--accidentally dabbling in the colours
of some Tradesman whose shop he had plundered--painted himself,
or caused himself to be painted (for the story varies) with the twelve
colours of a Dodecagon. Going into the Market Place he accosted
in a feigned voice a maiden, the orphan daughter of a noble Polygon,
whose affection in former days he had sought in vain; and by a series
of deceptions--aided, on the one side, by a string of lucky accidents
too long to relate, and, on the other, by an almost inconceivable
fatuity and neglect of ordinary precautions on the part of the
relations of the bride--he succeeded in consummating the marriage.
The unhappy girl committed suicide on discovering the fraud to which
she had been subjected.
When the news of this catastrophe spread from State to State
the minds of the Women were violently agitated. Sympathy with
the miserable victim and anticipations of similar deceptions
for themselves, their sisters, and their daughters, made them now regard
the Colour Bill in an entirely new aspect. Not a few openly avowed
themselves converted to antagonism; the rest needed only a slight
stimulus to make a similar avowal. Seizing this favourable opportunity,
the Circles hastily convened an extraordinary Assembly of the States;
and besides the usual guard of Convicts, they secured the attendance
of a large number of reactionary Women.
Amidst an unprecedented concourse, the Chief Circle of those days
--by name Pantocyclus--arose to find himself hissed and hooted by a
hundred and twenty thousand Isosceles. But he secured silence
by declaring that henceforth the Circles would enter on a policy
of Concession; yielding to the wishes of the majority,
they would accept the Colour Bill. The uproar being
at once converted to applause, he invited Chromatistes,
the leader of the Sedition, into the centre of the hall,
to receive in the name of his followers the submission
of the Hierarchy. Then followed a speech, a masterpiece
of rhetoric, which occupied nearly a day in the delivery,
and to which no summary can do justice.
With a grave appearance of impartiality he declared that as they
were now finally committing themselves to Reform or Innovation,
it was desirable that they should take one last view of the perimeter
of the whole subject, its defects as well as its advantages.
Gradually introduction the mention of the dangers to the Tradesmen,
the Professional Classes and the Gentlemen, he silenced the rising murmurs
of the Isosceles by reminding them that, in spite of all these defects,
he was willing to accept the Bill if it was approved by the majority.
But it was manifest that all, except the Isosceles, were moved
by his words and were either neutral or averse to the Bill.
Turning now to the Workmen he asserted that their interests must
not be neglected, and that, if they intended to accept the Colour Bill,
they ought at least to do so with full view of the consequences.
Many of them, he said, were on the point of being admitted
to the class of the Regular Triangles; others anticipated
for their children a distinction they could not hope for themselves.
That honourable ambition would not have to be sacrificed. With the
universal adoption of Colour, all distinctions would cease;
Regularity would be confused with Irregularity;
development would give place to retrogression;
the Workman would in a few generations be degraded
to the level of the Military, or even the Convict Class;
political power would be in the hands of the greatest number,
that is to say the Criminal Classes, who were already more
numerous than the Workmen, and would soon out-number all
the other Classes put together when the usual Compensative Laws
of Nature were violated.
A subdued murmur of assent ran through the ranks of the Artisans,
and Chromatistes, in alarm, attempted to step forward and address them.
But he found himself encompassed with guards and forced to remain silent
while the Chief Circle in a few impassioned words made a final appeal
to the Women, exclaiming that, if the Colour Bill passed, no marriage
would henceforth be safe, no woman's honour secure; fraud, deception,
hypocrisy would pervade every household; domestic bliss would share
the fate of the Constitution and pass to speedy perdition.
"Sooner than this," he cried, "Come death."
At these words, which were the preconcerted signal for action,
the Isosceles Convicts fell on and transfixed the wretched Chromatistes;
the Regular Classes, opening their ranks, made way for a band of Women who,
under direction of the Circles, moved back foremost, invisibly and unerringly
upon the unconscious soldiers; the Artisans, imitating the example of their
betters, also opened their ranks. Meantime bands of Convicts occupied
every entrance with an impenetrable phalanx.
The battle, or rather carnage, was of short duration. Under the
skillful generalship of the Circles almost every Woman's charge
was fatal and very many extracted their sting uninjured, ready for
a second slaughter. But no second blow was needed; the rabble
of the Isosceles did the rest of the business for themselves.
Surprised, leader-less, attacked in front by invisible foes,
and finding egress cut off by the Convicts behind them, they at once--
after their manner--lost all presence of mind, and raised the cry
of "treachery." This sealed their fate. Every Isosceles now saw
and felt a foe in every other. In half an hour not one of that vast
multitude was living; and the fragments of seven score thousand
of the Criminal Class slain by one another's angles attested
the triumph of Order.
The Circles delayed not to push their victory to the uttermost.
The Working Men they spared but decimated. The Militia of the
Equilaterals was at once called out, and every Triangle suspected
of Irregularity on reasonable grounds, was destroyed by Court Martial,
without the formality of exact measurement by the Social Board.
The homes of the Military and Artisan classes were inspected in a course
of visitation 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 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 no non-existent. The art of making
it is known to only one living person, the Chief Circle for the time being;
and by him it is handed down on his death-bed to none but his Successor.
One manufactory alone produces it; and, lest the secret should be betrayed,
the Workmen are annually consumed, and fresh ones introduced. So great
is the terror with which even now our Aristocracy looks back to the
far-distant days of the agitation for the Universal Colour Bill.
SECTION 11 Concerning our Priests
It is high time that I should pass from these brief and discursive
notes about things in Flatland to the central event of this book,
my initiation into the mysteries of Space. THAT is my subject;
all that has gone before is merely preface.
For this reason I must omit many matters of which the explanation
would not, I flatter myself, be without interest for my Readers:
as for example, our method of propelling and stopping ourselves,
although destitute of feet; the means by which we give fixity
to structures of wood, stone, or brick, although of course
we have no hands, nor can we lay foundations as you can,
nor avail ourselves of the lateral pressure of the earth;
the manner in which the rain originates in the intervals
between our various zones, so that the northern regions
do not intercept the moisture 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 these pillars and mainstays
of the Constitution of Flatland, the controllers of our conduct
and shapers of our destiny, the objects of universal homage
and almost of adoration: need I say that I mean our Circles or Priests?
When I call them Priests, let me not be understood as meaning
no more than the term denotes with you. With us, our Priests
are Administrators of all Business, Art, and Science; Directors of Trade,
Commerce, Generalship, Architecture, Engineering, Education,
Statesmanship, Legislature, Morality, Theology; doing nothing
themselves, they are the Causes of everything worth doing,
that is done by others.
Although popularly everyone called a Circle is deemed a Circle,
yet among the better educated Classes it is known that no Circle
is really a Circle, but only a Polygon with a very large number
of very small sides. As the number of the sides increases, a Polygon
approximates to a Circle; and, when the number is very great indeed,
say for example three or four hundred, it is extremely difficult
for the most delicate touch to feel any polygonal angles. Let me
say rather it WOULD be difficult: for, as I have shown above,
Recognition by Feeling is unknown among the highest society,
and to FEEL a Circle would be considered a most audacious insult.
This habit of abstention from Feeling in the best society enables
a Circle the more easily to sustain the veil of mystery in which,
from his earliest years, he is wont to enwrap the exact nature of his
Perimeter or Circumference. Three feet being the average Perimeter
it follows that, in a Polygon of three hundred sides each side will
be no more than the hundredth part of a foot in length, or little more
than the tenth part of an inch; and in a Polygon of six or seven hundred
sides the sides are little larger than the diameter of a Spaceland pin-head.
It is always assumed, by courtesy, that the Chief Circle for the time being
has ten thousand sides.
The ascent of the posterity of the Circles in the social scale is
not restricted, as it is among the lower Regular classes, by the Law
of Nature which limits the increase of sides to one in each generation.
If it were so, the number of sides in the 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 higher Evolution.
Our physicians have discovered that the small and tender sides
of an infant Polygon of the higher class can be fractured, and his whole
frame re-set, with such exactness that a Polygon of two or three
hundred sides sometimes--by no means always, for the process
is attended with serious risk--but sometimes overleaps two or three
hundred generations, and as it were double 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 the Nobleman of that position
in society, who has neglected to place his first-born in the Circular
Neo-Therapeutic Gymnasium before he has attained the age of a month.
One year determines success or failure. At the end of that time
the child has, in all probability, added one more to the tombstones
that crowd the Neo-Therapeutic Cemetery; but on rare occasional a glad
procession bares 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 sacrifice, which have a dissimilar issue.
SECTION 12 Of the Doctrine of our Priests
As to the doctrine of the Circles it may briefly be summed up
in a single maxim, "Attend to your Configuration." Whether political,
ecclesiastical, or moral, all their teaching has for its object
the improvement of individual and collective Configuration--with special
reference of course to the Configuration of the Circles, to which all
other objects are subordinated.
It is the merit of the Circles that they have effectually
suppressed those ancient heresies which led men to waste energy
and sympathy in the vain belief that conduct depends upon will, effort,
training, encouragement, praise, or anything else but Configuration.
It was Pantocyclus--the illustrious Circle mentioned above, as the
queller of the Colour Revolt--who first convinced mankind that
Configuration makes the man; that if, for example, you are born
an Isosceles with two uneven sides, you will assuredly go wrong
unless you have them made even--for which purpose you must go
to the Isosceles Hospital; similarly, if you are a Triangle,
or Square, or even a Polygon, born with any Irregularity,
you must be taken to one of the Regular Hospitals to
have your disease cured; otherwise you will end your days
in the State Prison or by the angle of the State Executioner.
All faults or defects, from the slightest misconduct to the
most flagitious crime, Pantocyclus attributed to some deviation
from perfect Regularity in the bodily figure, caused perhaps
(if not congenital) by some collision in a crowd; by neglect
to take exercise, or by taking too much of it; or even by
a sudden change of temperature, resulting in a shrinkage
or expansion in some too susceptible part of the frame.
Therefore, concluded that illustrious Philosopher,
neither good conduct nor bad conduct is a fit subject,
in any sober estimation, for either praise or blame.
For why should you praise, for example, the integrity
of a Square who faithfully defends the interests of his client,
when you ought in reality rather to admire the exact precision
of his right angles? Or again, why blame a lying,
thievish Isosceles, when you ought rather to deplore
the incurable inequality of his sides?
Theoretically, this doctrine is unquestionable; but it
has practical drawbacks. In dealing with an Isosceles,
if a rascal pleads that he cannot help stealing because
of his unevenness, you reply that for that very reason,
because he cannot help being a nuisance to his neighbours,
you, the Magistrate, cannot help sentencing him to be consumed--
and there's an end of the matter. But in little domestic difficulties,
when 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 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,
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" and "wrong"
as vehemently and passionately as if they believe that these names
represented real existence, and that a human Figure is really capable
of choosing between them.
Constantly carrying out their policy of making Configuration
the leading idea in every mind, the Circles reverse the nature
of that Commandment which in Spaceland regulates the relations between
parents and children. With you, children are taught to honour their parents;
with us--next to the Circles, who are the chief object of universal homage--
a man is taught to honour his Grandson, if he has one; or, if not, his Son.
By "honour," however, is by no means mean "indulgence," but a reverent
regard for their highest interests: and the Circles teach that the duty
of fathers is to subordinate their own interests to those of posterity,
thereby advancing the welfare of the whole State as well as that
of their own immediate descendants.
The weak point in the system of the Circles--if a humble Square
may venture to speak of anything Circular as containing any element
of weakness--appears to me to be found in their relations with Women.
As it is of the utmost importance for Society that Irregular
births should be discouraged, it follows that no Woman who has any
Irregularities in her ancestry is a fit partner for one who desires
that his posterity should rise by regular degrees in the social scale.
Now the Irregularity of a Male is a matter of measurement; but as
all Women are straight, and therefore visibly Regular so to speak, one
has to device 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 the 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 has hopes of generating an Equilateral Son, to take a wife
who reckoned a single Irregularity among her Ancestors; a Square
or Pentagon, who is confident that his family is steadily on the rise,
does not inquire above the five-hundredth generation; a Hexagon
or Dodecagon is even more careless of the wife's pedigree;
but a Circle has been known deliberately to take a wife
who has had an Irregular Great-Grandfather, and all because
of some slight superiority of lustre, or because of the charms
of a low voice--which, with us, even more than with you,
is thought "an excellent thing in a 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 provided sufficiently deterrent.
The loss of a few sides in a highly-developed Polygon is not easily
noticed, and is sometimes compensated by a successful operation in
the Neo-Therapeutic Gymnasium, as I have described above; and the Circles
are too much disposed to acquiesce in infecundity as a law of the
superior development. Yet, if this evil be not arrested, the gradual
diminution of the Circular class may soon become more rapid, and the
time may not be 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 suggest 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 bimental, existence.
With Women, we speak of "love," "duty," "right," "wrong," "pity,"
"hope," and other irrational and emotional conceptions, which have
no existence, and the fiction of which has no object except to control
feminine exuberances; but among ourselves, and in our books, we have
an entirely different vocabulary and I may also say, idiom. "Love"
them becomes "the anticipation of benefits"; "duty" becomes "necessity"
or "fitness"; and other words are correspondingly transmuted.
Moreover, among Women, we use language implying the utmost deference
for their Sex; and they fully believe that the Chief Circle Himself
is not more devoutly adored by us than they are: but behind their
backs they are both regarded and spoken of--by all but the very young--
as being little better than "mindless organisms."
Our Theology also in the Women's chambers is entirely different
from our Theology elsewhere.
Now my humble fear is that this double training, in language
as well as in thought, imposes somewhat too heavy a burden upon
the young, especially when, at the age of three years old, they are
taken from the maternal care and taught to unlearn the old language--
except for the purpose of repeating it in the presence of the Mothers
and Nurses--and to learn the vocabulary and idiom of science.
Already methinks I discern a weakness in the grasp of mathematical
truth at the present time as compared with the more robust intellect
of our ancestors three hundred years ago. I say nothing of the possible
danger if a Woman should ever surreptitiously learn to read and convey
to her Sex the result of her perusal of a single popular volume;
nor of the possibility that the indiscretion or disobedience of some
infant Male might reveal to a Mother the secrets of the logical dialect.
On the simple ground of the enfeebling of the male intellect,
I rest this humble appeal to the highest Authorities to reconsider
the regulations of Female education.
"O brave new worlds,
That have such people in them!"
SECTION 13 How I had a Vision of Lineland
It was the last day but one of the 1999th year of our era, and the
first day of the Long Vacation. Having amused myself till a late hour
with my favourite recreation of Geometry, I had retired to rest
with an unsolved problem in my mind. In the night I had a dream.
I saw before me a vast multitude of small Straight Lines
(which I naturally assumed to be Women) interspersed with other Beings
still smaller and of the nature of lustrous points--all moving to and fro
in one and the same Straight Line, and, as nearly as I could judge,
with the same velocity.
A noise of confused, multitudinous chirping or twittering issued
from them at intervals as long as they were moving; but sometimes
they ceased from motion, and then all was silence.
Approaching one of the largest of what I thought to be Women,
I accosted her, but received no answer. A second and third appeal
on my part were equally ineffectual. Losing patience at what appeared
to me intolerable rudeness, I brought my mouth to 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 preserving questions I elicited the following facts:
It seemed that this poor ignorant Monarch--as he called himself--
was persuaded that the Straight Line which he called his Kingdom,
and in which he passed his existence, constituted the whole of the world,
and indeed the whole of Space. Not being able either to move or to see,
save in his Straight Line, he had no conception of anything out of it.
Though he had heard my voice when I first addressed him, the sounds
had come to him in a manner so contrary to his experience that he had
made no answer, "seeing no man," as he expressed it, "and hearing
a voice as it were from my own intestines." Until the moment when
I placed my mouth in his World, he had neither seen me, nor heard
anything except confused sounds beating against, what I called his side,
but what he called his INSIDE or STOMACH; nor had he even now the least
conception of the region from which I had come. Outside his World,
or Line, all was a blank to him; nay, not even a blank, for a blank
implies Space; say, rather, all was non-existent.
His subjects--of whom the small Lines were men and the Points Women--
were all alike confined in motion and eyesight 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 as 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 that 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 se or approach their Majesties,
when there at least half a dozen intervening individuals, whom you can
neither see through, nor pass by? Is it possible that in Lineland
proximity is not necessary for marriage and for the generation of children?"
"How can you ask so absurd a question?" replied the Monarch. "If it were
indeed as you suggest, the Universe would soon be depopulated. No, no;
neighbourhood is needless for the union of hearts; and the birth
of children is too important a matter to have been allowed to depend
upon such an accident as proximity. You cannot be ignorant of this.
Yet since you are pleased to affect ignorance, I will instruct you
as if you were the veriest baby in Lineland. Know, then, that marriages
are consummated by means of the faculty of sound and the sense of hearing.
"You are of course aware that every Man has two mouths or voices--
as well as two eyes--a bass at one and a tenor at the other of his
extremities. I should not mention this, but that I have been
unable to distinguish your tenor in the course of our conversation."
I replied that I had but one voice, and that I had not been aware
that his Royal Highness had two. "That confirms by impression,"
said the King, "that you are not a Man, but a feminine Monstrosity
with a bass voice, and an utterly uneducated ear. But to continue.
"Nature having herself ordained that every Man should wed two wives--"
"Why two?" asked I. "You carry your affected simplicity too far,"
he cried. "How can there be a completely harmonious union without
the combination of the Four in One, viz. the Bass and Tenor of the Man
and the Soprano and Contralto of the two Women?" "But supposing,"
said I, "that a man should prefer one wife or three?" "It is impossible,"
he said; "it is as inconceivable as that two and one should make five,
or that the human eye should see a Straight Line." I would have
interrupted him; but he proceeded as follows:
"Once in the middle of each week a Law of Nature compels us to move
to and fro with a rhythmic motion of more than usual violence,
which continues for the time you would take to count a hundred and one.
In the midst of this choral dance, at the fifty-first pulsation,
the inhabitants of the Universe pause in full career, and each
individual sends forth his richest, fullest, sweetest strain.
It is in this decisive moment that all our marriages are made.
So exquisite is the adaptation of Bass and Treble, of Tenor to Contralto,
that oftentimes the Loved Ones, though twenty thousand leagues away,
recognize at once the responsive note of their destined Lover; and,
penetrating the paltry obstacles of distance, Love unites the three.
The marriage in that instance 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-voice 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 is at once to recognize in each
other's voice the partner intended for them by Providence, and to fly
into a reciprocal and perfectly harmonious embrace. With most of us
the courtship is of long duration. The Wooer's voices may perhaps
accord with one of the future wives, but not with both; or not,
at first, with either; or the Soprano and Contralto may not quite
harmonize. In such cases Nature has provided that every weekly Chorus
shall bring the three Lovers into closer harmony. Each trial of voice,
each fresh discovery of discord, almost imperceptibly induces the less
perfect to modify his or her vocal utterance so as to approximate
to the more perfect. And after many trials and many approximations,
the result is at last achieved. There comes a day at last when,
while the wonted Marriage Chorus goes forth from universal Lineland,
the three far-off Lovers suddenly find themselves in exact harmony,
and, before they are aware, the wedded Triplet is rapt vocally into
a duplicate embrace; and Nature rejoices over one more marriage
and over three more births."
SECTION 14 How I vainly tried to explain the nature of Flatland
Thinking that it was time to bring down the Monarch from his raptures
to the level of common sense, I determined to endeavour to open up
to him some glimpses of the truth, that is to say of the nature
of things in Flatland. So I began thus: "How does your Royal Highness
distinguish the shapes and positions of his subjects? I for my part
noticed by the sense of sight, before I entered your Kingdom,
that some of your people are lines and others Points;
and that some of the lines are larger --" "You speak of an impossibility,"
interrupted the King; "you must have seen a vision; for to detect the difference
between a Line and a Point by the sense of sight is, as every one knows,
in the nature of things, impossible; but it can be detected by the sense
of hearing, and by the same means my shape can be exactly ascertained.
Behold me--I am a Line, the longest in Lineland, over six inches of Space --"
"Of Length," I ventured to suggest. "Fool," said he, "Space is Length.
Interrupt me again, and I have done."
I apologized; but he continued scornfully, "Since you are impervious
to argument, you shall hear with your ears how by means of my two voices
I reveal my shape to my Wives, who are at this moment six thousand miles
seventy yards two feet eight inches away, the one to the North,
the other to the South. Listen, I call to them."
He chirruped, and then complacently continued: "My wives at this
moment receiving the sound of one of my voice, 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 recognized 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 Men,
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 all the ends of so brutal and course 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, corporeal, 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,
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