_FLATLAND_
A Romance of Many Dimensions
_With Illustrations
by the Author_, A SQUARE
“_Fie, fie, how franticly I square my talk!_”
LONDON
SEELEY & Co., 46, 47 & 48, ESSEX STREET, STRAND
(_Late of_ 54 Fleet Street)
1884
LONDON:
R. Clay, Sons, and Taylor,
BREAD STREET HILL.
To
The Inhabitants of Space in General
And H. C. in Particular
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of Three Dimensions
Having been previously conversant
With Only Two
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of Four Five or even Six Dimensions
Thereby contributing
To the Enlargement of the Imagination
And the possible Development
Of that most rare and excellent Gift of Modesty
Among the Superior Races
Of Solid Humanity
_CONTENTS_
_PART I
THIS WORLD_
_Section_
1 _Of the Nature of Flatland_
2 _Of the Climate and Houses in Flatland_
3 _Concerning the Inhabitants of Flatland_
4 _Concerning the Women_
5 _Of our Methods of Recognizing one another_
6 _Of Recognition by Sight_
7 _Concerning Irregular Figures_
8 _Of the Ancient Practice of Painting_
9 _Of the Universal Colour Bill_
10 _Of the Suppression of the Chromatic Sedition_
11 _Concerning our Priests_
12 _Of the Doctrine of our Priests_
_PART II
OTHER WORLDS_
13 _How I had a Vision of Lineland_
14 _How in my Vision I endeavoured to explain the nature of
Flatland, but could not_
15 _Concerning a Stranger from Spaceland_
16 _How the Stranger vainly endeavoured to reveal to me in words
the mysteries of Spaceland_
17 _How the Sphere, having in vain tried words, resorted to deeds_
18 _How I came to Spaceland and what I saw there_
19 _How, though the Sphere showed me other mysteries of Spaceland,
I still desired more; and what came of it_
20 _How the Sphere encouraged me in a Vision_
21 _How I tried to teach the Theory of Three Dimensions to my
Grandson, and with what success_
22 _How I then tried to diffuse the Theory of Three Dimensions by
other means, and of the result_
_PART I
THIS WORLD_
“_Be patient, for the world is broad and wide._”
_FLATLAND_
_PART I_
THIS WORLD
§ 1.—_Of the Nature of Flatland._
I call our world Flatland, not because we call it so, but to make its
nature clearer to you, my happy readers, who are privileged to live in
Space.
Imagine a vast sheet of paper on which straight Lines, Triangles,
Squares, Pentagons, Hexagons, and other figures, instead of remaining
fixed in their places, move freely about, on or in the surface, but
without the power of rising above or sinking below it, very much like
shadows—only hard and with luminous edges—and you will then have a pretty
correct notion of my country and countrymen. Alas, a few years ago, I
should have said “my universe”: but now my mind has been opened to higher
views of things.
In such a country, you will perceive at once that it is impossible that
there should be anything of what you call a “solid” kind; but I dare say
you will suppose that we could at least distinguish by sight the
Triangles, Squares and other figures moving about as I have described
them. On the contrary, we could see nothing of the kind, not at least so
as to distinguish one figure from another. Nothing was visible, nor could
be visible, to us, except straight Lines; and the necessity of this I
will speedily demonstrate.
Place a penny on the middle of one of your tables in Space; and leaning
over it, look down upon it. It will appear a circle.
But now, drawing back to the edge of the table, gradually lower your eye
(thus bringing yourself more and more into the condition of the
inhabitants of Flatland), and you will find the penny becoming more and
more oval to your view; and at last when you have placed your eye exactly
on the edge of the table (so that you are, as it were, actually a
Flatland citizen) the penny will then have ceased to appear oval at all,
and will have become, so far as you can see, a straight line.
The same thing would happen if you were to treat in the same way a
Triangle, or Square, or any other figure cut out of pasteboard. As soon
as you look at it with your eye on the edge of the table, you will find
that it ceases to appear to you a figure, and that it becomes in
appearance a straight line. Take for example an equilateral Triangle—who
represents with us a Tradesman of the respectable class. Fig. 1
represents the Tradesman as you would see him while you were bending over
him from above; figs. 2 and 3 represent the Tradesman, as you would see
him if your eye were close to the level, or all but on the level of the
table; and if your eye were quite on the level of the table (and that is
how we see him in Flatland) you would see nothing but a straight line.
[Illustration: ]
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 close
to us we see his line becomes larger; if he leaves us it becomes smaller:
but still he looks like a straight line; be he a Triangle, Square,
Pentagon, Hexagon, Circle, what you will—a straight Line he looks and
nothing else.
You may perhaps ask how under these disadvantageous circumstances we are
able to distinguish our friends from one another: but the answer to this
very natural question will be more fitly and easily given when I come to
describe the inhabitants of Flatland. For the present let me defer this
subject, and say a word or two about the climate and houses in our
country.
§ 2.—_Of the climate and houses in Flatland._
As with you, so also with us, there are four points of the compass North,
South, East, and West.
There being no sun nor other heavenly bodies, it is impossible for us to
determine the North in the usual way; but we have a method of our own. By
a Law of Nature with us, there is a constant attraction to the South;
and, although in temperate climates this is very slight—so that even a
Woman in reasonable health can journey several furlongs northward without
much difficulty—yet the hampering effect of the southward attraction is
quite sufficient to serve as a compass in most parts of our earth.
Moreover the rain (which falls at stated intervals) coming always from
the North, is an additional assistance; and in the towns we have the
guidance of the houses, which of course have their side-walls running for
the most part North and South, so that the roofs may keep off the rain
from the North. In the country, where there are no houses, the trunks of
the trees serve as some sort of guide. Altogether, we have not so much
difficulty as might be expected in determining our bearings.
Yet in our more temperate regions, in which the southward attraction is
hardly felt, walking sometimes in a perfectly desolate plain where there
have been no houses nor trees to guide me, I have been occasionally
compelled to remain stationary for hours together, waiting till the rain
came before continuing my journey. On the weak and aged, and especially
on delicate Females, the force of attraction tells much more heavily than
on the robust of the Male Sex, so that it is a point of breeding, if you
meet a Lady in the street, always to give her the North side of the
way—by no means an easy thing to do always at short notice when you are
in rude health and in a climate where it is difficult to tell your North
from your South.
Windows there are none in our houses: for the light comes to us alike in
our homes and out of them, by day and by night, equally at all times and
in all places, whence we know not. It was in old days, with our learned
men, an interesting and oft-investigated question, What is the origin of
light; and the solution of it has been repeatedly attempted, with no
other result than to crowd our lunatic asylums with the would-be solvers.
Hence, after fruitless attempts to suppress such investigations
indirectly by making them liable to a heavy tax, the Legislature, in
comparatively recent times, absolutely prohibited them. I, alas I alone
in Flatland—know now only too well the true solution of this mysterious
problem; but my knowledge cannot be made intelligible to a single one of
my countrymen; and I am mocked at—I, the sole possessor of the truths of
Space and of the theory of the introduction of Light from the world of
Three Dimensions—as if I were the maddest of the mad! But a truce to
these painful digressions: let me return to our houses.
The most common form for the construction of a house is five-sided or
pentagonal, as in the annexed figure. The two Northern sides _RO_, _OF_,
constitute the roof, and for the most part have no doors; on the East is
a small door for the Women; on the West a much larger one for the Men;
the South side or floor is usually doorless.
[Illustration: ]
Square and triangular houses are not allowed, and for this reason. The
angles of a Square (and still more those of an equilateral Triangle)
being much more pointed than those of a Pentagon, and the lines of
inanimate objects (such as houses) being dimmer than the lines of Men and
Women, it follows that there is no little danger lest the points of a
square or triangular house residence might do serious injury to an
inconsiderate or perhaps absent-minded traveller suddenly running against
them: and therefore, as early as the eleventh century of our era,
triangular houses were universally forbidden by Law, the only exceptions
being fortifications, powder-magazines, barracks, and other state
buildings, which it is not desirable that the general public should
approach without circumspection.
At this period, square houses were still everywhere permitted, though
discouraged by a special tax. But, about three centuries afterwards, the
Law decided that in all towns containing a population above ten thousand,
the angle of a Pentagon was the smallest house-angle that could be
allowed consistently with the public safety. The good sense of the
community has seconded the efforts of the Legislature; and now, even in
the country, the pentagonal construction has superseded every other. It
is only now and then in some very remote and backward agricultural
district that an antiquarian may still discover a square house.
§ 3.—_Concerning the Inhabitants of Flatland._
The greatest length or breadth of a full-grown inhabitant of Flatland may
be estimated at about eleven of your inches. Twelve inches may be
regarded as a maximum.
Our Women are Straight Lines.
Our Soldiers and Lowest Classes of Workmen are Triangles with two equal
sides, each about eleven inches long, and a base or third side so short
(often not exceeding half an inch) that they form at their vertices a
very sharp and formidable angle. Indeed when their bases are of the most
degraded type (not more than the eighth part of an inch in size), they
can hardly be distinguished from Straight Lines or Women; so extremely
pointed are their vertices. With us, as with you, these Triangles are
distinguished from others by being called Isosceles; and by this name I
shall refer to them in the following pages.
Our Middle Class consists of Equilateral or Equal-sided Triangles.
Our Professional Men and Gentlemen are Squares (to which class I myself
belong) and Five-sided figures or Pentagons.
Next above these come the Nobility, of whom there are several degrees,
beginning at Six-sided Figures, or Hexagons, and from thence rising in
the number of their sides till they receive the honourable title of
Polygonal, or many-sided. Finally when the number of the sides becomes so
numerous, and the sides themselves so small, that the figure cannot be
distinguished from a circle, he is included in the Circular or Priestly
order; and this is the highest class of all.
It is a Law of Nature with us that a male child shall have one more side
than his father, so that each generation shall rise (as a rule) one step
in the scale of development and nobility. Thus the son of a Square is a
Pentagon; the son of a Pentagon, a Hexagon; and so on.
But this rule applies not always to the Tradesmen, and still less often
to the Soldiers, and to the Workmen; who indeed can hardly be said to
deserve the name of human Figures, since they have not all their sides
equal. With them therefore the Law of Nature does not hold; and the son
of an Isosceles (_i.e._ a Triangle with two sides equal) remains
Isosceles still. Nevertheless, all hope is not shut out, even from the
Isosceles, that his posterity may ultimately rise above his degraded
condition. For, after a long series of military successes, or diligent
and skilful labours, it is generally found that the more intelligent
among the Artisan and Soldier classes manifest a slight increase of their
third side or base, and a shrinkage of the two other sides.
Intermarriages (arranged by the Priests) between the sons and daughters
of these more intellectual members of the lower classes generally result
in an offspring approximating still more to the type of the Equal-sided
Triangle.
Rarely—in proportion to the vast number of Isosceles births—is a genuine
and certifiable Equal-sided Triangle produced from Isosceles parents.[1]
Such a birth requires, as its antecedents, not only a series of carefully
arranged intermarriages, but also a long-continued exercise of frugality
and self-control on the part of the would-be ancestors of the coming
Equilateral, and a patient, systematic, and continuous development of the
Isosceles intellect through many generations.
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 Isosceles from the ranks of his serf-born
ancestors, is welcomed not only by the poor serfs themselves, as a gleam
of light and hope shed upon the monotonous squalor of their existence,
but also by the Aristocracy at large; for all the higher classes are well
aware that these rare phenomena, while they do little or nothing to
vulgarise their own privileges, serve as a most useful barrier against
revolution from below.
Had the acute-angled rabble been all, without exception, absolutely
destitute of hope and of ambition, they might have found leaders in some
of their many seditious outbreaks, so able as to render their superior
numbers and strength too much even for the wisdom of the Circles. But a
wise ordinance of Nature has decreed that, in proportion as the
working-classes increase in intelligence, knowledge, and all virtue, in
that same proportion their acute angle (which makes them physically
terrible) shall increase also and approximate to the harmless angle of
the Equilateral Triangle. Thus, in the most brutal and formidable of the
soldier class creatures almost on a level with women in their lack of
intelligence—it is found that, as they wax in the mental ability
necessary to employ their tremendous penetrating power to advantage, so
do they wane in the power of penetration itself.
How admirable is this Law of Compensation! And how perfect a proof of the
natural fitness and, I may almost say, the divine origin of the
aristocratic constitution of the States in Flatland! By a judicious use
of this Law of Nature, the Polygons and Circles are almost always able to
stifle sedition in its very cradle, taking advantage of the irrepressible
and boundless hopefulness of the human mind. Art also comes to the aid of
Law and Order. It is generally found possible—by a little artificial
compression or expansion on the part of the State physicians—to make some
of the more intelligent leaders of a rebellion perfectly Regular, and to
admit them at once into the privileged classes; a much larger number, who
are still below the standard, allured by the prospect of being ultimately
ennobled, are induced to enter the State Hospitals, where they are kept
in honourable confinement for life; one or two alone of the more
obstinate, foolish, and hopelessly irregular are led to execution.
Then the wretched rabble of the Isosceles, planless and leaderless, are
either transfixed without resistance by the small body of their brethren
whom the Chief Circle keeps in pay for emergencies of this kind; or else
more often, by means of jealousies and suspicions skilfully fomented
among them by the Circular party, they are stirred to mutual warfare, and
perish by one another’s angles. No less than one hundred and twenty
rebellions are recorded in our annals, besides minor outbreaks numbered
at two hundred and thirty-five; and they have all ended thus.
§ 4.—_Concerning the Women._
If our highly pointed Triangles of the Soldier class are formidable, it
may be readily inferred that far more formidable are our Women. For, if a
Soldier is a wedge, a Woman is a needle; being, so to speak, _all_ point,
at least at the two extremities. Add to this the power of making herself
practically invisible at will, and you will perceive that a Female, in
Flatland, is a creature by no means to be trifled with.
But here, perhaps, some of my younger Readers may ask _how_ a woman in
Flatland can make herself invisible. This ought, I think, to be apparent
without any explanation. However, a few words will make it clear to the
most unreflecting.
Place a needle on a table. Then, with your eye on the level of the table,
look at it side-ways, and you see the whole length of it; but look at it
end-ways, and you see nothing but a point: it has become practically
invisible. Just so is it with one of our Women. When her side is turned
towards us, we see her as a straight line; when the end containing her
eye or mouth—for with us these two organs are identical—is the part that
meets our eye, then we see nothing but a highly lustrous point; but when
the back is presented to our view, then—being only sub-lustrous, and,
indeed, almost as dim as an inanimate object—her hinder extremity serves
her as a kind of Invisible Cap.
The dangers to which we are exposed from our Women must now be manifest
to the meanest capacity in Spaceland. If even the angle of a respectable
Triangle in the middle class is not without its dangers; if to run
against a Working Man involves a gash; if collision with an Officer of
the military class necessitates a serious wound; if a mere touch from the
vertex of a Private Soldier brings with it danger of death;—what can it
be to run against a Woman, except absolute and immediate destruction? And
when a Woman is invisible, or visible only as a dim sub-lustrous point,
how difficult must it be, even for the most cautious, always to avoid
collision!
Many are the enactments made at different times in the different States
of Flatland, in order to minimize this peril; and in the Southern and
less temperate climates, where the force of gravitation is greater, and
human beings more liable to casual and involuntary motions, the Laws
concerning Women are naturally much more stringent. But a general view of
the Code may be obtained from the following summary:—
1. Every house shall have one entrance in the Eastern side, for the use
of Females only; by which all females shall enter “in a becoming and
respectful manner”[2] and not by the Men’s or Western door.
2. No Female shall walk in any public place without continually keeping
up her Peace-cry, under penalty of death.
3. Any Female, duly certified to be suffering from St. Vitus’s Dance,
fits, chronic cold accompanied by violent sneezing, or any disease
necessitating involuntary motions, shall be instantly destroyed.
In some of the States there is an additional Law forbidding Females,
under penalty of death, from walking or standing in any public place
without moving their backs constantly from right to left so as to
indicate their presence to those behind them; others oblige a Woman, when
travelling, to be followed by one of her sons, or servants, or by her
husband; others confine Women altogether to their houses except during
the religious festivals. But it has been found by the wisest of our
Circles or Statesmen that the multiplication of restrictions on Females
tends not only to the debilitation and diminution of the race, but also
to the increase of domestic murders to such an extent that a State loses
more than it gains by a too prohibitive Code.
For whenever the temper of the Women is thus exasperated by confinement
at home or hampering regulations abroad, they are apt to vent their
spleen upon their husbands and children; and in the less temperate
climates the whole male population of a village has been sometimes
destroyed in one or two hours of simultaneous female outbreak. Hence the
Three Laws, mentioned above, suffice for the better regulated States, and
may be accepted as a rough exemplification of our Female Code.
After all, our principal safeguard is found, not in Legislature, but in
the interests of the Women themselves. For, although they can inflict
instantaneous death by a retrograde movement, yet unless they can at once
disengage their stinging extremity from the struggling body of their
victim, their own frail bodies are liable to be shattered.
The power of Fashion is also on our side. I pointed out that in some less
civilised States no female is suffered to stand in any public place
without swaying her back from right to left. This practice has been
universal among ladies of any pretensions to breeding in all
well-governed States, as far back as the memory of Figures can reach. It
is considered a disgrace to any State that legislation should have to
enforce what ought to be, and is in every respectable female, a natural
instinct. The rhythmical and, if I may so say, well-modulated undulation
of the back in our ladies of Circular rank is envied and imitated by the
wife of a common Equilateral, who can achieve nothing beyond a mere
monotonous swing, like the ticking of a pendulum; and the regular tick of
the Equilateral is no less admired and copied by the wife of the
progressive and aspiring Isosceles, in the females of whose family no
“back-motion” of any kind has become as yet a necessity of life. Hence,
in every family of position and consideration, “back motion” is as
prevalent as time itself; and the husbands and sons in these households
enjoy immunity at least from invisible attacks.
Not that it must be for a moment supposed that our Women are destitute of
affection. But unfortunately the passion of the moment predominates, in
the Frail Sex, over every other consideration. This is, of course, a
necessity arising from their unfortunate conformation. For as they have
no pretensions to an angle, being inferior in this respect to the very
lowest of the Isosceles, they are consequently wholly devoid of
brain-power, and have neither reflection, judgment nor forethought, and
hardly any memory. Hence, in their fits of fury, they remember no claims
and recognise no distinctions. I have actually known a case where a Woman
has exterminated her whole household, and half an hour afterwards, when
her rage was over and the fragments swept away, has asked what has become
of her husband and her children!
Obviously then a Woman is not to be irritated as long as she is in a
position where she can turn round. When you have them in their
apartments—which are constructed with a view to denying them that
power—you can say and do what you like; for they are then wholly impotent
for mischief, and will not remember a few minutes hence the incident for
which they may be at this moment threatening you with death, nor the
promises which you may have found it necessary to make in order to pacify
their fury.
On the whole we get on pretty smoothly in our domestic relations, except
in the lower strata of the Military Classes. There the want of tact and
discretion on the part of the husbands produces at times indescribable
disasters. Relying too much on the offensive weapons of their acute
angles instead of the defensive organs of good sense and seasonable
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 has now become a kind of
instinct among the women of our higher classes—that the mothers and
daughters should constantly keep their eyes and mouths towards their
husband and his male friends; and for a lady in a family of distinction
to turn her back upon her husband would be regarded as a kind of portent,
involving loss of _status_. But, as I shall soon shew, this custom,
though it has the advantage of safety, is not without its disadvantages.
In the house of the Working Man or respectable Tradesman—where the wife
is allowed to turn her back upon her husband, while pursuing her
household avocations—there are at least intervals of quiet, when the wife
is neither seen nor heard, except for the humming sound of the continuous
Peace-cry; but in the homes of the upper classes there is too often no
peace. There the voluble mouth and bright penetrating eye are ever
directed towards the Master of the household; and light itself is not
more persistent than the stream of feminine discourse. The tact and skill
which suffice to avert a Woman’s sting are unequal to the task of
stopping a Woman’s mouth; and as the wife has absolutely nothing to say,
and absolutely no constraint of wit, sense, or conscience to prevent her
from saying it, not a few cynics have been found to aver that they prefer
the danger of the death-dealing but inaudible sting to the safe
sonorousness of a Woman’s other end.
To my readers in Spaceland the condition of our Women may seem truly
deplorable, and so indeed it is. A Male of the lowest type of the
Isosceles may look forward to some improvement of his angle, and to the
ultimate elevation of the whole of his degraded caste; but no Woman can
entertain such hopes for her sex. “Once a Woman, always a Woman” is a
Decree of Nature; and the very Laws of Evolution seem suspended in her
disfavour. Yet at least we can admire the wise Prearrangement which has
ordained that, as they have no hopes, so they shall have no memory to
recall, and no forethought to anticipate, the miseries and humiliations
which are at once a necessity of their existence and the basis of the
constitution of Flatland.
§ 5.—_Of our methods of recognizing one another._
You, who are blessed with shade as well as light, you who are gifted with
two eyes, endowed with a knowledge of perspective, and charmed with the
enjoyment of various colours, you, who can actually _see_ an angle, and
contemplate the complete circumference of a Circle in the happy region of
the Three Dimensions—how shall I make clear to you the extreme difficulty
which we in Flatland experience in recognizing one another’s
configurations?
Recall what I told you above. All beings in Flatland, animate or
inanimate, no matter what their form, present _to our view_ the same, or
nearly the same, appearance, viz. that of a straight Line. How then can
one be distinguished from another, where all appear the same?
The answer is threefold. The first means of recognition is the sense of
hearing; which with us is far more highly developed than with you, and
which enables us not only to distinguish by the voice our personal
friends, but even to discriminate between different classes, at least so
far as concerns the three lowest orders, the Equilateral, the Square, and
the Pentagon—for of the Isosceles I take no account. But as we ascend in
the social scale, the process of discriminating and being discriminated
by hearing increases in difficulty, partly because voices are
assimilated, partly because the faculty of voice-discrimination is a
plebeian virtue not much developed among the Aristocracy. And wherever
there is any danger of imposture we cannot trust to this method. Amongst
our lowest orders, the vocal organs are developed to a degree more than
correspondent with those of hearing, so that an Isosceles can easily
feign the voice of a 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 you Mr. Jones.”
Let not my Reader however suppose that “feeling” is with us the tedious
process that it would be with you, or that we find it necessary to feel
right round all the sides of every individual before we determine the
class to which he belongs. Long practice and training, begun in the
schools and continued in the experience of daily life, enable us to
discriminate at once by the sense of touch, between the angles of an
equal-sided Triangle, Square, and Pentagon; and I need not say that the
brainless vertex of an acute-angled Isosceles is obvious to the dullest
touch. It is therefore not necessary, as a rule, to do more than feel a
single angle of any individual; and this, once ascertained, tells us the
class of the person whom we are addressing, unless indeed he belongs to
the higher sections of the nobility. There the difficulty is much
greater. Even a Master of Arts in our University of Wentbridge has been
known to confuse a ten-sided with a twelve-sided Polygon; and there is
hardly a Doctor of Science in or out of that famous University who could
pretend to decide promptly and unhesitatingly between a twenty-sided and
a twenty-four sided member of the Aristocracy.
Those of my readers who recall the extracts I gave above from the
Legislative code concerning Women, will readily perceive that the process
of introduction by contact requires some care and discretion. Otherwise
the angles might inflict on the unwary Feeler irreparable injury. It is
essential for the safety of the Feeler that the Felt should stand
perfectly still. A start, a fidgety shifting of the position, yes, even a
violent sneeze, has been known before now to prove fatal to the
incautious, and to nip in the bud many a promising friendship. Especially
is this true among the lower classes of the Triangles. With them, the eye
is situated so far from their vertex that they can scarcely take
cognizance of what goes on at that extremity of their frame. They are
moreover of a rough coarse nature, not sensitive to the delicate touch of
the highly organized Polygon. What wonder then if an involuntary toss of
the head has ere now deprived the State of a valuable life!
I have heard that my excellent Grandfather—one of the least irregular of
his unhappy Isosceles class, who indeed obtained, shortly before his
decease, four out of seven votes from the Sanitary and Social Board for
passing him into the class of the Equal-sided—often deplored with a tear
in his venerable eye, a miscarriage of this kind, which had occurred to
his great-great-great-Grandfather, a respectable Working Man with an
angle or brain of 59° 30′. According to his account, my unfortunate
Ancestor, being afflicted with rheumatism, and in the act of being felt
by a Polygon, by one sudden start accidentally transfixed the Great Man
through the diagonal; and thereby, partly in consequence of his long
imprisonment and degradation, and partly because of the moral shock which
pervaded the whole of my Ancestor’s relations, threw back our family a
degree and a half in their ascent towards better things. The result was
that in the next generation the family brain was registered at only 58°,
and not till the lapse of five generations was the lost ground recovered,
the full 60° attained, and the Ascent from the Isosceles finally
achieved. And all this series of calamities from one little accident in
the process of Feeling.
At this point I think I hear some of my better educated readers exclaim,
“How could you in Flatland know anything about angles and degrees, or
minutes? We can _see_ an angle, because we in the region of Space, can
see two straight lines inclined to one another; but you, who can see
nothing but one straight line at a time, or at all events only a number
of bits of straight lines all in one straight line,—how can you ever
discern any angle, and much less register angles of different sizes?”
I answer that though we cannot _see_ angles, we can _infer_ them, and
this with great precision. Our sense of touch, stimulated by necessity,
and developed by long training, enables us to distinguish angles far more
accurately than your sense of sight, when unaided by a rule or measure of
angles. Nor must I omit to explain that we have great natural helps. It
is with us a Law of Nature that the brain of the Isosceles class shall
begin at half a degree, or thirty minutes, and shall increase (if it
increases at all) by half a degree in every generation; until the goal of
60° is reached, when the condition of serfdom is quitted, and the freeman
enters the class of Regulars.
Consequently, Nature herself supplies us with an ascending scale or
Alphabet of angles for half a degree up to 60°, Specimens of which are
placed in every Elementary School throughout the land. Owing to
occasional retrogressions, to still more frequent moral and intellectual
stagnation, and to the extraordinary fecundity of the Criminal and
Vagabond Classes, there is always a vast superfluity of individuals of
the half degree and single degree class, and a fair abundance of
Specimens up to 10°. These are absolutely destitute of civic rights; and
a great number of them, not having even intelligence enough for the
purposes of warfare, are devoted by the States to the service of
education. Fettered immovably so as to remove all possibility of danger,
they are placed in the class rooms of our Infant Schools, and there they
are utilized by the Board of Education for the purpose of imparting to
the offspring of the Middle Classes that tact and intelligence of which
these wretched creatures themselves are utterly devoid.
In some states the Specimens are occasionally fed and suffered to exist
for several years; but in the more temperate and better regulated
regions, it is found in the long run more advantageous for the
educational interests of the young, to dispense with food, and to renew
the Specimens every month,—which is about the average duration of the
foodless existence of the Criminal class. In the cheaper schools, what is
gained by the longer existence of the Specimens is lost, partly in the
expenditure for food, and partly in the diminished accuracy of the
angles, which are impaired after a few weeks of constant “feeling.” Nor
must we forget to add, in enumerating the advantages of the more
expensive system, that it tends, though slightly yet perceptibly, to the
diminution of the redundant Isosceles population—an object which every
statesman in Flatland constantly keeps in view. On the whole
therefore—although I am not ignorant that, in many popularly elected
School Boards, there is a reaction in favour of “the cheap system,” as it
is called—I am myself disposed to think that this is one of the many
cases in which expense is the truest economy.
But I must not allow questions of School Board politics to divert me from
my subject. Enough has been said, I trust, to show that Recognition by
Feeling is not so tedious or indecisive a process as might have been
supposed; and it is obviously more trustworthy than Recognition by
hearing. Still there remain, as has been pointed out above, the objection
that this method is not without danger. For this reason many in the
Middle and Lower classes, and all without exception in the Polygonal and
Circular orders, prefer a third method, the description of which shall be
reserved for the next section.
§ 6.—_Of Recognition by Sight._
I am about to appear very inconsistent. In previous sections I have said
that all figures in Flatland present the appearance of a straight line;
and it was added or implied, that it is consequently impossible to
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 a distance of two
feet eleven inches; and the result is that by careful and constant
experimental observation of comparative dimness and clearness, we are
enabled to infer with great exactness the configuration of the object
observed.
An instance will do more than a volume of generalities to make my meaning
clear.
Suppose I see two individuals approaching whose rank I wish to ascertain.
They are, we will suppose, a Merchant and a Physician, or in other words,
an Equilateral Triangle and a Pentagon: how am I to distinguish them?
It will be obvious, to every child in Spaceland who has touched the
threshold of Geometrical Studies, that, if I can bring my eye so that its
glance may bisect an angle (A) of the approaching stranger, my view will
lie as it were evenly between his two sides that are next to me (viz. CA
and AB), so that I shall contemplate the two impartially, and both will
appear of the same size.
[Illustration: ]
Now in the case of (1) the Merchant, what shall I see? I shall see a
straight line DAE, in which the middle point (A) will be very bright
because it is nearest to me; but on either side the line will shade away
_rapidly into dimness_, because the sides AC and AD _recede rapidly into
the fog_; and what appear to me as the Merchant’s extremities, viz. D and
C, will be _very dim indeed_.
On the other hand in the case of (2) the Physician, though I shall here
also see a line (D′A′E′) with a bright centre (A′), yet it will shade
away _less rapidly_ into dimness, because the sides (A′C′, A′B′) _recede
less rapidly into the fog_; and what appear to me the Physician’s
extremities, viz. D′ and E′, will 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.
[Illustration: ]
If for example, when my Father, the Triangle, approaches me, he happens
to present his side to me instead of his angle, then, until I have asked
him to rotate, or until I have edged my eye round him, I am for the
moment doubtful whether he may not be a Straight Line, or, in other
words, a Woman. Again, when I am in the company of one of my two
hexagonal Grandsons, contemplating one of his sides (AB) full front, it
will be evident from the accompanying diagram that I shall see one whole
line (AB) in comparative brightness (shading off hardly at all at the
ends) and two smaller lines (CA and BD) dim throughout and shading away
into greater dimness toward the extremities C and D.
But I must not give way to the temptation of enlarging on these topics.
The meanest mathematician in Spaceland will readily believe me when I
assert that the problems of life, which present themselves to the
well-educated—when they are themselves in motion, rotating, advancing or
retreating, and at the same time attempting to discriminate by the sense
of sight between a number of Polygons of high rank moving in different
directions, as for example in a ball-room or conversazione—must be of a
nature to task the angularity of the most intellectual, and amply justify
the rich endowments of the Learned Professors of Geometry, both Static
and Kinetic, in the illustrious University of Wentbridge, where the
Science and Art of Sight Recognition are regularly taught to large
classes of the _élite_ of the States.
It is only a few of the scions of our noblest and wealthiest houses, who
are able to give the time and money necessary for the thorough
prosecution of this noble and valuable Art. Even to me, a Mathematician
of no mean standing, and the Grandfather of two most hopeful and
perfectly regular Hexagons, to find myself in the midst of a crowd of
rotating Polygons of the higher classes, is occasionally very perplexing.
And of course to a common Tradesman, or Serf, such a sight is almost as
unintelligible as it would be to you, my Reader, were you suddenly
transported into our country.
In such a crowd you could see on all sides of you nothing but a Line,
apparently straight, but of which the parts would vary irregularly and
perpetually in brightness or dimness. Even if you had completed your
third year in the Pentagonal and Hexagonal classes in the University, and
were perfect in the theory of the subject, you would still find that
there was need of many years of experience, before you could move in a
fashionable crowd without jostling against your betters, whom it is
against etiquette to ask to “feel,” and who, by their superior culture
and breeding, know all about your movements, while you know very little
or nothing about theirs. In a word, to comport oneself with perfect
propriety in Polygonal society, one ought to be a Polygon oneself. Such
at least is the painful teaching of my experience.
It is astonishing how much the Art—or I may almost call it instinct—of
Sight Recognition is developed by the habitual practice of it and by the
avoidance of the custom of “Feeling.” Just as, with you, the deaf and
dumb, if once allowed to gesticulate and to use the hand-alphabet, will
never acquire the more difficult but far more valuable art of lip-speech
and lip-reading, so it is with us as regards “Seeing” and “Feeling.” None
who in early life resort to “Feeling” will ever learn “Seeing” in
perfection.
For this reason, among our Higher Classes, “Feeling” is discouraged or
absolutely forbidden. From the cradle their children, instead of going to
the Public Elementary schools (where the art of Feeling is taught,) are
sent to higher Seminaries of an exclusive character; and at our
illustrious University, to “feel” is regarded as a most serious fault,
involving Rustication for the first offence, and Expulsion for the
second.
But among the lower classes the art of Sight Recognition is regarded as
an unattainable luxury. A common Tradesman cannot afford to let his son
spend a third of his life in abstract studies. The children of the poor
are therefore allowed to “feel” from their earliest years, and they gain
thereby a precocity and an early vivacity which contrast at first most
favourably with the inert, undeveloped, and listless behaviour of the
half-instructed youths of the Polygonal class; but when the latter have
at last completed their University course, and are prepared to put their
theory into practice, the change that comes over them may almost be
described as a new birth, and in every art, science, and social pursuit
they rapidly overtake and distance their Triangular competitors.
Only a few of the Polygonal Class fail to pass the Final Test or Leaving
Examination at the University. The condition of the unsuccessful minority
is truly pitiable. Rejected from the higher class, they are also despised
by the lower. They have neither the matured and systematically trained
powers of the Polygonal Bachelors and Masters of Arts, nor yet the native
precocity and mercurial versatility of the youthful Tradesman. The
professions, the public services are closed against them; and though in
most States they are not actually debarred from marriage, yet they have
the greatest difficulty in forming suitable alliances, as experience
shows that the offspring of such unfortunate and ill-endowed parents is
generally itself unfortunate, if not positively Irregular.