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Title: Flatland - A Romance of Many Dimensions
Author: Abbott, Edwin Abbott
Language: English
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_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.
It is from these specimens of the refuse of our Nobility that the great
Tumults and Seditions of past ages have generally derived their leaders;
and so great is the mischief thence arising that an increasing minority
of our more progressive Statesmen are of opinion that true mercy would
dictate their entire suppression, by enacting that all who fail to pass
the Final Examination of the University should be either imprisoned for
life, or extinguished by a painless death.
But I find myself digressing into the subject of Irregularities, a matter
of such vital interest that it demands a separate section.
§ 7.—_Of Irregular Figures._
Throughout the previous pages I have been assuming—what perhaps should
have been laid down at the beginning as a distinct and fundamental
proposition—that every human being in Flatland is a Regular Figure, that
is to say of regular construction. By this I mean that a Woman must not
only be a line, but a straight line; that an Artisan or Soldier must have
two of his sides equal; that Tradesmen must have three sides equal;
Lawyers (of which class I am a humble member), four sides equal, and,
generally, that in every Polygon, all the sides must be equal.
The size of the sides would of course depend upon the age of the
individual. A Female at birth would be about an inch long, while a tall
adult Woman might extend to a foot. As to the Males of every class, it
may be roughly said that the length of an adult’s sides, when added
together, is three feet or a little more. But the size of our sides is
not under consideration. I am speaking of the _equality_ of sides, and it
does not need much reflection to see that the whole of the social life in
Flatland rests upon the fundamental fact that Nature wills all Figures to
have their sides equal.
If our sides were unequal our angles would be unequal. Instead of its
being sufficient to feel, or estimate by sight, a single angle in order
to determine the form of an individual, it would be necessary to
ascertain each angle by the experiment of Feeling. But life would be too
short for such a tedious groping. The whole science and art of Sight
Recognition would at once perish; Feeling, so far as it is an art, would
not long survive; intercourse would become perilous or impossible; there
would be an end to all confidence, all forethought; no one would be safe
in making the most simple social arrangements; in a word, civilization
would relapse into barbarism.
Am I going too fast to carry my Readers with me to these obvious
conclusions? Surely a moment’s reflection, and a single instance from
common life, must convince every one that our whole social system is
based upon Regularity, or Equality of Angles. You meet, for example, two
or three Tradesmen in the street, whom you recognize at once to be
Tradesmen by a glance at their angles and rapidly bedimmed sides, and you
ask them to step into your house to lunch. This you do at present with
perfect confidence, because every one knows to an inch or two the area
occupied by an adult Triangle: but imagine that your Tradesman drags
behind his regular and respectable vertex, a parallelogram of twelve or
thirteen inches in diagonal:—what are you to do with such a monster
sticking fast in your house door?
But I am insulting the intelligence of my Readers by accumulating details
which must be patent to every one who enjoys the advantages of a
Residence in Spaceland. Obviously the measurements of a single angle
would no longer be sufficient under such portentous circumstances; one’s
whole life would be taken up in feeling or surveying the perimeter of
one’s acquaintances. Already the difficulties of avoiding a collision in
a crowd are enough to tax the sagacity of even a well-educated Square;
but if no one could calculate the Regularity of a single figure in the
company, all would be chaos and confusion, and the slightest panic would
cause serious injuries, or—if there happened to be any Women or Soldiers
present—perhaps considerable loss of life.
Expediency therefore concurs with Nature in stamping the seal of its
approval upon Regularity of conformation: nor has the Law been backward
in seconding their efforts. “Irregularity of Figure” means with us the
same as, or more than, a combination of moral obliquity and criminality
with you, and is treated accordingly. There are not wanting, it is true,
some promulgators of paradoxes who maintain that there is no necessary
connection between geometrical and moral Irregularity. “The Irregular,”
they say, “is from his birth scouted by his own parents, derided by his
brothers and sisters, neglected by the domestics, scorned and suspected
by society, and excluded from all posts of responsibility, trust, and
useful activity. His every movement is jealously watched by the police
till he comes of age and presents himself for inspection; then he is
either destroyed, if he is found to exceed the fixed margin of deviation,
or else immured in a Government Office as a clerk of the seventh class;
prevented from marriage; forced to drudge at an uninteresting occupation
for a miserable stipend; obliged to live and board at the office, and to
take even his vacation under close supervision; what wonder that human
nature, even in the best and purest, is embittered and perverted by such
surroundings!”
All this very plausible reasoning does not convince me, as it has not
convinced the wisest of our Statesmen, that our ancestors erred in laying
it down as an axiom of policy that the toleration of Irregularity is
incompatible with the safety of the State. Doubtless, the life of an
Irregular is hard; but the interests of the Greater Number require that
it shall be hard. If a man with a triangular front and a polygonal back
were allowed to exist and to propagate a still more Irregular posterity,
what would become of the arts of life? Are the houses and doors and
churches in Flatland to be altered in order to accommodate such monsters?
Are our ticket-collectors to be required to measure every man’s perimeter
before they allow him to enter a theatre, or to take his place in a
lecture room? Is an Irregular to be exempted from the militia? And if
not, how is he to be prevented from carrying desolation into the ranks of
his comrades? Again, what irresistible temptations to fraudulent
impostures must needs beset such a creature! How easy for him to enter a
shop with his polygonal front foremost, and to order goods to any extent
from a confiding tradesman! Let the advocates of a falsely called
Philanthropy plead as they may for the abrogation of the Irregular Penal
Laws, I for my part have never known an Irregular who was not also what
Nature evidently intended him to be—a hypocrite, a misanthropist, and, up
to the limits of his power—a perpetrator of all manner of mischief.
Not that I should be disposed to recommend (at present) the extreme
measures adopted in some States, where an infant whose angle deviates by
half a degree from the correct angularity is summarily destroyed at
birth. Some of our highest and ablest men, men of real genius, have
during their earliest days laboured under deviations as great as, or even
greater than, forty-five minutes: and the loss of their precious lives
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 diætetic
operations by which Irregularity has been partly or wholly cured.
Advocating therefore a _Via Media_, I would lay down no fixed or absolute
line of demarcation; but at the period when the frame is just beginning
to set, and when the Medical Board has reported that recovery is
improbable, I would suggest that the Irregular offspring be painlessly
and mercifully consumed.
§ 8.—_Of the Ancient Practice of Painting._
If my Readers have followed me with any attention up to this point, they
will not be surprised to hear that life is somewhat dull in Flatland. I
do not, of course, mean that there are not battles, conspiracies,
tumults, factions, and all those other phenomena which are supposed to
make History interesting; nor would I deny that the strange mixture of
the problems of life and the problems of Mathematics, continually
inducing conjecture and giving the opportunity of immediate verification,
imparts to our existence a zest which you in Spaceland can hardly
comprehend. I speak now from the æsthetic and artistic point of view when
I say that life with us is dull; æsthetically and artistically, very dull
indeed.
How can it be otherwise, when all one’s prospect, all one’s landscapes,
historical pieces, portraits, flowers, still life, are nothing but a
single line, with no varieties except degrees of brightness and
obscurity?
It was not always thus. Colour, if Tradition speaks the truth, once for
the space of half a dozen centuries or more, threw a transient charm upon
the lives of our ancestors in the remotest ages. Some private
individual—a Pentagon whose name is variously reported—having casually
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 innovation to these two classes. Many-sidedness was almost
essential as a pretext for the Innovators. “Distinction of sides is
intended by Nature to imply distinction of colours”—such was the sophism
which in those days flew from mouth to mouth, converting whole towns at a
time to the new culture. But manifestly to our Priests and Women this
adage did not apply. The latter had only one side, and therefore—plurally
and pedantically speaking—_no sides_. The former—if at least they would
assert their claim to be really and truly Circles, and not mere
high-class Polygons with an infinitely large number of infinitesimally
small sides—were in the habit of boasting (what Women confessed and
deplored) that they also had no sides, being blessed with a perimeter of
one line or, in other words, a Circumference. Hence it came to pass that
these two Classes could see no force in the so-called axiom about
“Distinction of Sides implying Distinction of Colour”; and when all
others had succumbed to the fascinations of corporal decoration, the
Priests and the Women alone still remained pure from the pollution of
paint.
Immoral, licentious, anarchical, unscientific—call them by what names you
will—yet, from an æsthetic point of view, those ancient days of the
Colour Revolt were the glorious childhood of Art in Flatland—a childhood,
alas, that never ripened into manhood, nor even reached the blossom of
youth. To live was then in itself a delight, because living implied
seeing. Even at a small party, the company was a pleasure to behold; the
richly varied hues of the assembly in a church or theatre are said to
have more than once proved too distracting for our greatest teachers and
actors; but most ravishing of all is said to have been the unspeakable
magnificence of a military review.
The sight of a line of battle of twenty thousand Isosceles suddenly
facing about, and exchanging the sombre black of their bases for the
orange and purple of the two sides including their acute angle; the
militia of the Equilateral Triangles tricoloured in red, white, and blue;
the mauve, ultramarine, gamboge, and burnt umber of the Square
artillerymen rapidly rotating near their vermilion guns; the dashing and
flashing of the five-coloured and six-coloured Pentagons and Hexagons
careering across the field in their offices of surgeons, geometricians
and aides-de-camp—all these may well have been sufficient to render
credible the famous story how an illustrious Circle, overcome by the
artistic beauty of the forces under his command, threw aside his
marshal’s bâton and his royal crown, exclaiming that he henceforth
exchanged them for the artist’s pencil. How great and glorious the
sensuous development of these days must have been is in part indicated by
the very language and vocabulary of the period. The commonest utterances
of the commonest citizens in the time of the Colour Revolt seem to have
been suffused with a richer tinge of word or thought; and to that era we
are even now indebted for our finest poetry and for whatever rhythm still
remains in the more scientific utterance of these modern days.
§ 9.—_Of the Universal Colour Bill._
But meanwhile the intellectual Arts were fast decaying.
The Art of Sight Recognition, being no longer needed, was no longer
practised; and the studies of Geometry, Statics, Kinetics, and other
kindred subjects, came soon to be considered superfluous, and fell into
disrepute and neglect even at our University. The inferior Art of Feeling
speedily experienced the same fate at our Elementary Schools. Then the
Isosceles classes, asserting that the Specimens were no longer used nor
needed, and refusing to pay the customary tribute from the Criminal
classes to the service of Education, waxed daily more numerous and more
insolent on the strength of their immunity from the old burden which had
formerly exercised the twofold wholesome effect of at once taming their
brutal nature and thinning their excessive numbers.
Year by year the Soldiers and Artisans began more vehemently to
assert—and with increasing truth—that there was no great difference
between them and the very highest class of Polygons, now that they were
raised to an equality with the latter, and enabled to grapple with all
the difficulties and solve all the problems of life, whether Statical and
Kinetical, by the simple process of Colour Recognition. Not content with
the natural neglect into which Sight Recognition was falling, they began
boldly to demand the legal prohibition of all “monopolising and
aristocratic Arts” and the consequent abolition of all endowments for the
studies of Sight Recognition, Mathematics, and Feeling. Soon, they began
to insist that inasmuch as Colour, which was a second Nature, had
destroyed the need of aristocratic distinctions, the Law should follow in
the same path, and that henceforth all individuals and all classes should
be recognized as absolutely equal and entitled to equal rights.
Finding the higher Orders wavering and undecided, the leaders of the
Revolution advanced still further in their requirements, and at last
demanded that all classes alike, the Priests and the Women not excepted,
should do homage to Colour by submitting to be painted. When it was
objected that Priests and Women had no sides, they retorted that Nature
and Expediency concurred in dictating that the front half of every human
being (that is to say, the half containing his eye and mouth) should be
distinguishable from his hinder half. They therefore brought before a
general and extraordinary Assembly of all the States of Flatland a Bill
proposing that in every Woman the half containing the eye and mouth
should be coloured red, and the other half green. The Priests were to be
painted in the same way, red being applied to that semicircle in which
the eye and mouth formed the middle point; while the other or hinder
semicircle was to be coloured green.
There was no little cunning in this proposal, which indeed emanated, not
from any Isosceles—for no being so degraded would have had angularity
enough to appreciate, much less to devise, such a model of
state-craft—but from an Irregular Circle who, instead of being destroyed
in his childhood, was reserved by a foolish indulgence to bring
desolation on his country and destruction on myriads of his followers.
On the one hand the proposition was calculated to bring the Women in all
classes over to the side of the Chromatic Innovation. For by assigning to
the Women the same two colours as were assigned to the Priests, the
Revolutionists thereby ensured that, in certain positions, every Woman
would appear like a Priest, and be treated with corresponding respect and
deference—a prospect that could not fail to attract the Female Sex in a
mass.
But by some of my Readers the possibility of the identical appearance of
Priests and Women, under the new Legislation, may not be recognized; if
so, a word or two will make it obvious.
Imagine a woman duly decorated, according to the new Code; with the front
half (_i.e._ the half containing eye and mouth) red, and with the hinder
half green. Look at her from one side. Obviously you will see a straight
line, _half red_, _half green_.
[Illustration: ]
Now imagine a Priest, whose mouth is at M, and whose front semicircle
(AMB) is consequently coloured red, while his hinder semicircle is green;
so that the diameter AB divides the green from the red. If you
contemplate the Great Man so as to have your eye in the same straight
line as his dividing diameter (AB), what you will see will be a straight
line (CBD), of which _one half_ (CB) _will be red, and the other_ (BD)
_green_. The whole line (CD) will be rather shorter perhaps than that of
a full-sized Woman, and will shade off more rapidly towards its
extremities; but the identity of the colours would give you an immediate
impression of identity if not Class, making you neglectful of other
details. Bear in mind the decay of Sight Recognition which threatened
society at the time of the Colour Revolt; add too the certainty that
Women would speedily learn to shade off their extremities so as to
imitate the Circles; it must then be surely obvious to you, my dear
Reader, that the Colour Bill placed us under a great danger of
confounding a Priest with a young Woman.
How attractive this prospect must have been to the Frail Sex may readily
be imagined. They anticipated with delight the confusion that would
ensue. At home they might hear political and ecclesiastical secrets
intended not for them but for their husbands and brothers, and might even
issue commands in the name of a priestly Circle; out of doors the
striking combination of red and green, without addition of any other
colours, would be sure to lead the common people into endless mistakes,
and the Women would gain whatever the Circles lost, in the deference of
the passers by. As for the scandal that would befall the Circular Class
if the frivolous and unseemly conduct of the Women were imputed to them,
and as to the consequent subversion of the Constitution, the Female Sex
could not be expected to give a thought to these considerations. Even in
the households of the Circles, the Women were all in favour of the
Universal Colour Bill.
The second object aimed at by the Bill was the gradual demoralization of
the Circles themselves. In the general intellectual decay they still
preserved their pristine clearness and strength of understanding. From
their earliest childhood, familiarized in their Circular households with
the total absence of Colour, the Nobles alone preserved the Sacred Art of
Sight Recognition, with all the advantages that result from that
admirable training of the intellect. Hence, up to the date of the
introduction of the Universal Colour Bill, the Circles had not only held
their own, but even increased their lead of other classes by abstinence
from the popular fashion.
Now therefore the artful Irregular whom I described above as the real
author of this diabolical Bill, determined at one blow to lower the
status of the Hierarchy by forcing them to submit to the pollution of
Colour, and at the same time to destroy their domestic opportunities of
training in the Art of Sight Recognition, so as to enfeeble their
intellects by depriving them of their pure and colourless homes. Once
subjected to the chromatic taint, every parental and every childish
Circle would demoralize each other. Only in discerning between the Father
and the Mother would the Circular infant find problems for the exercise
of its understanding—problems too often likely to be corrupted by
maternal impostures with the result of shaking the child’s faith in all
logical conclusions. Thus by degrees the intellectual lustre of the
Priestly Order would wane, and the road would then lie open for a total
destruction of all Aristocratic Legislature and for the subversion of our
Privileged Classes.
§ 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 husbands, perishing themselves in the act of
carnage. It is recorded that during that triennial agitation no less than
twenty-three Circles perished in domestic discord.
Great indeed was the peril. It seemed as though the Priests had no choice
between submission and extermination; when suddenly the course of events
was completely changed by one of those picturesque incidents which
Statesmen ought never to neglect, often to anticipate, and 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
Dodecahedron. Going into the Market Place he accosted in a feigned voice
a maiden, the orphan daughter of a noble Polygon, whose affection in
former days he had sought in vain; and by a series of deceptions, aided
on the one side by a string of lucky accidents too long to relate, and,
on the other, by an almost inconceivable fatuity and neglect of ordinary
precautions on the part of the relations of the bride, he succeeded in
consummating the marriage. The unhappy girl committed suicide on
discovering the fraud to which she had been subjected.
When the news of this catastrophe spread from State to State the minds of
the Women were violently agitated. Sympathy with the miserable victim and
anticipations of similar deceptions for themselves, their sisters, and
their daughters, made them now regard the Colour Bill in an entirely new
aspect. Not a few openly avowed themselves converted to antagonism; the
rest needed only a slight stimulus to make a similar avowal. Seizing this
favourable opportunity the Circles hastily convened an extraordinary
Assembly of the States; and besides the usual guard of Convicts, they
secured the attendance of a large number of reactionary Women.
Amidst an unprecedented concourse, the Chief Circle of those days—by name
Pantocyclus—arose to find himself hissed and hooted by a hundred and
twenty thousand Isosceles. But he secured silence by declaring that
henceforth the Circles would enter on a policy of Concession; yielding to
the wishes of the majority, they would accept the Colour Bill. The uproar
being at once converted to applause, he invited Chromatistes, the leader
of the Sedition, into the centre of the hall, to receive in the name of
his followers the submission of the Hierarchy. Then followed a speech, a
masterpiece of rhetoric, which occupied nearly a day in the delivery, and
to which no summary can do justice.
With a grave appearance of impartiality he declared that as they were now
finally committing themselves to Reform or Innovation, it was desirable
that they should take one last view of the perimeter of the whole
subject, its defects as well as its advantages. Gradually introducing the
mention of the dangers to the Tradesmen, the Professional Classes and the
Gentlemen, he silenced the rising murmurs of the Isosceles by reminding
them that, in spite of all these defects, he was willing to accept the
Bill if it was approved by the majority. But it was manifest that all,
except the Isosceles, were moved by his words and were either neutral or
averse to the Bill.
Turning now to the Workmen he asserted that their interests must not be
neglected, and that, if they intended to accept the Colour Bill, they
ought at least to do so with a full view of the consequences. Many of
them, he said, were on the point of being admitted to the class of the
Regular Triangles; others anticipated for their children a distinction
they could not hope for themselves. That honourable ambition would now
have to be sacrificed. With the universal adoption of Colour, all
distinctions would cease; Regularity would be confused with Irregularity;
development would give place to retrogression; the Workman would in a few
generations be degraded to the level of the Military, or even the Convict
Class; political power would be in the hands of the greatest number, that
is to say the Criminal Classes, who were already more numerous than the
Workmen, and would soon out-number all the other Classes put together
when the usual Compensative Laws of Nature were violated.
A subdued murmur of assent ran through the ranks of the Artisans, and
Chromatistes, in alarm, attempted to step forward and address them. But
he found himself encompassed with guards and forced to remain silent
while the Chief Circle in a few impassioned words made a final appeal to
the Women, exclaiming that, if the Colour Bill passed, no marriage would
henceforth be safe, no woman’s honour secure; fraud, deception, hypocrisy
would pervade every household; domestic bliss would share the fate of the
Constitution and pass to speedy perdition. Sooner than this, he cried
“Come death.”
At these words, which were the preconcerted signal for action, the
Isosceles Convicts fell on and transfixed the wretched Chromatistes; the
Regular Classes opening their ranks, made way for a band of Women who,
under direction of the Circles, moved, back foremost, invisibly and
unerringly upon the unconscious Soldiers; the Artisans, imitating the
example of their betters, also opened their ranks. Meantime bands of
Convicts occupied every entrance with an impenetrable phalanx.
The battle, or rather carnage, was of short duration. Under the skilful
generalship of the Circles almost every Woman’s charge was fatal, and
very many extracted their sting uninjured, ready for a second slaughter.
But no second blow was needed; the rabble of the Isosceles did the rest
of the business for themselves. Surprised, leader-less, attacked in front
by invisible foes, and finding egress cut off by the Convicts behind
them, they at once—after their manner—lost all presence of mind, and
raised the cry of “treachery.” This sealed their fate. Every Isosceles
now saw and felt a foe in every other. In half an hour not one of that
vast multitude was living; and the fragments of seven score thousand of
the Criminal Class slain by one another’s angles attested the triumph of
Order.
The Circles delayed not to push their victory to the uttermost. The
Working Men they spared but decimated. The Militia of the Equilaterals
was at once called out; and every Triangle suspected of Irregularity on
reasonable grounds, was destroyed by Court Martial, without the formality
of exact measurement by the Social Board. The homes of the Military and
Artisan classes were inspected in a course of visitations extending
through upwards of a year; and during that period every town, village,
and hamlet was systematically purged of that excess of the lower orders
which had been brought about by the neglect to pay the Tribute of
Criminals to the Schools and University, and by the violation of the
other natural Laws of the Constitution of Flatland. Thus the balance of
classes was again restored.
Needless to say that henceforth the use of Colour was abolished, and its
possession prohibited. Even the utterance of any word denoting Colour,
except by the Circles or by qualified scientific teachers, was punished
by a severe penalty. Only at our University in some of the very highest
and most esoteric classes—which I myself have never been privileged to
attend—it is understood that the sparing use of Colour is still
sanctioned for the purpose of illustrating some of the deeper problems of
mathematics. But of this I can only speak from hearsay.
Elsewhere in Flatland, Colour is now non-existent. The art of making it
is known to only one living person, the Chief Circle for the time being;
and by him it is handed down on his death-bed to none but his Successor.
One manufactory alone produces it; and, lest the secret should be
betrayed, the Workmen are annually consumed, and fresh ones introduced.
So great is the terror with which even now our Aristocracy looks back to
the far-distant days of the agitation for the Universal Colour Bill.
§ 11.—_Concerning our Priests._
It is high time that I should pass from these brief and discursive notes
about things in Flatland to the central event of this book, my initiation
into the mysteries of Space. _That_ is my subject; all that has gone
before is merely preface.
For this reason I must omit many matters of which the explanation would
not, I flatter myself, be without interest for my Readers: as for
example, our method of propelling and stopping ourselves, although
destitute of feet; the means by which we give fixity to structures of
wood, stone, or brick, although of course we have no hands, nor can we
lay foundations as you can, nor avail ourselves of the lateral pressure
of the earth; the manner in which the rain originates in the intervals
between our various zones, so that the northern regions do not intercept
the moisture from falling on the southern; the nature of our hills and
mines, our trees and vegetables, our seasons and harvests; our Alphabet,
and method of writing, adapted to our linear tablets; these and a hundred
other details of our physical existence I must pass over, nor do I
mention them now except to indicate to my readers that their omission
proceeds not from forgetfulness on the part of the Author, but from his
regard for the time of the Reader.
Yet before I proceed to my legitimate subject some few final remarks will
no doubt be expected by my Readers upon those pillars and mainstays of
the Constitution of Flatland, the controllers of our conduct and shapers
of our destiny, the objects of universal homage and almost of adoration:
need I say that I mean our Circles or Priests?
When I call them Priests, let me not be understood as meaning no more
than the term denotes with you. With us, our Priests are Administrators
of all Business, Art, and Science; Directors of Trade, Commerce,
Generalship, Architecture, Engineering, Education, Statesmanship,
Legislature, Morality, Theology; doing nothing themselves, they are the
Causes of everything, worth doing, that is done by others.
Although popularly every one called a Circle is deemed a Circle, yet
among the better educated Classes it is known that no Circle is really a
Circle, but only a Polygon with a very large number of very small sides.
In proportion to the number of the sides the Polygon approximates to a
Circle; and, when the number is very great, say for example three or four
hundred, it is extremely difficult for the most delicate touch to feel
any polygonal angles. Let me say rather, it _would_ be difficult: for, as
I have shown above, Recognition by Feeling is unknown among the highest
society, and to _feel_ a Circle would be considered a most audacious
insult. This habit of abstention from Feeling in the best society enables
a Circle the more easily to sustain the veil of mystery in which, from
his earliest years, he is wont to enwrap the exact nature of his
Perimeter or Circumference. Three feet being the average Perimeter it
follows that, in a Polygon of three hundred sides, each side will be no
more than the hundredth part of a foot in length, or little more than the
tenth part of an inch; and in a Polygon of six or seven hundred sides the
sides are little larger than the diameter of a Spaceland pin-head. It is
always assumed, by courtesy, that the Chief Circle for the time being has
ten thousand sides.
The ascent of the posterity of the Circles in the social scale is not
restricted, as it is among the lower Regular classes, by the Law of
Nature which limits the increase of sides to one in each generation. If
it were so, the number of sides in a Circle would be a mere question of
pedigree and arithmetic, and the four hundred and ninety-seventh
descendant of an Equilateral Triangle would necessarily be a Polygon with
five hundred sides. But this is not the case. Nature’s Law prescribes two
antagonistic decrees affecting Circular propagation; first, that as the
race climbs higher in the scale of development, so development shall
proceed at an accelerated pace; second, that in the same proportion, the
race shall become less fertile. Consequently in the home of a Polygon of
four or five hundred sides it is rare to find a son; more than one is
never seen. On the other hand the son of a five-hundred-sided Polygon has
been known to possess five hundred and fifty, or even six hundred sides.
Art also steps in to help the process of the higher Evolution. Our
physicians have discovered that the small and tender sides of an infant
Polygon of the higher class can be fractured, and his whole frame re-set,
with such exactness that a Polygon of two or three hundred sides
sometimes—by no means always, for the process is attended with serious
risk—but sometimes overleaps two or three hundred generations, and as it
were doubles at a stroke, the number of his progenitors and the nobility
of his descent.
Many a promising child is sacrificed in this way. Scarcely one out of ten
survives. Yet so strong is the parental ambition among those Polygons who
are, as it were, on the fringe of the Circular class, that it is very
rare to find a Nobleman of that position in society, who has neglected to
place his first-born son in the Circular Neo-Therapeutic Gymnasium before
he has attained the age of a month.
One year determines success or failure. At the end of that time the child
has, in all probability, added one more to the tombstones that crowd the
Neo-Therapeutic Cemetery; but on rare occasions a glad procession bears
back the little one to his exultant parents, no longer a Polygon, but a
Circle, at least by courtesy: and a single instance of so blessed a
result induces multitudes of Polygonal parents to submit to similar
domestic sacrifices, which have a dissimilar issue.
§ 12.—_Of the Doctrine of our Priests._
As to the doctrine of the Circles it may briefly be summed up in a single
maxim, “Attend to your Configuration.” Whether political, ecclesiastical,
or moral, all their teaching has for its object the 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 Rectangles?
Or again, why blame a lying, thievish Isosceles when you ought rather to
deplore the incurable inequality of his sides?
Theoretically, this doctrine is unquestionable; but it has practical
drawbacks. In dealing with an Isosceles, if a rascal pleads that he
cannot help stealing because of his unevenness, you reply that for that
very reason, because he cannot help being a nuisance to his neighbours,
you, the Magistrate, cannot help sentencing him to be consumed—and
there’s an end of the matter. But in little domestic difficulties, where
the penalty of consumption, or death, is out of the question, this theory
of Configuration sometimes comes in awkwardly; and I must confess that
occasionally when one of my own Hexagonal Grandsons pleads as an excuse
for his disobedience that a sudden change of the temperature has been too
much for his Perimeter, and that I ought to lay the blame not on him but
on his Configuration, which can only be strengthened by abundance of the
choicest sweetmeats, I neither see my way logically to reject, nor
practically to accept, his conclusions.
For my own part, I find it best to assume that a good sound scolding or
castigation has some latent and strengthening influence on my Grandson’s
Configuration; though I own that I have no grounds for thinking so. At
all events I am not alone in my way of extricating myself from this
dilemma; for I find that many of the highest Circles, sitting as Judges
in Law courts, use praise and blame towards Regular and Irregular
Figures; and in their homes I know by experience that, when scolding
their children, they speak about “right” or “wrong” as vehemently and
passionately as if they believed that these names represented real
existences, and that a human Figure is really capable of choosing between
them.
Consistently carrying out their policy of making Configuration the
leading idea in every mind, the Circles reverse the nature of that
Commandment which in Spaceland regulates the relations between parents
and children. With you, children are taught to honour their parents; with
us—next to the Circles, who are the chief object of universal homage—a
man is taught to honour his Grandson, if he has one; or, if not, his Son.
By “honour,” however, is by no means meant “indulgence,” but a reverent
regard for their highest interests: and the Circles teach that the duty
of fathers is to subordinate their own interests 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
devise some other means of ascertaining what I may call their invisible
Irregularity, that is to say their potential Irregularities as regards
possible offspring. This is effected by carefully-kept pedigrees, which
are preserved and supervised by the State; and without a certified
pedigree no Woman is allowed to marry.
Now it might have been supposed that a Circle—proud of his ancestry and
regardful for a posterity which might possibly issue hereafter in a Chief
Circle—would be more careful than any other to choose a wife who had no
blot on her escutcheon. But it is not so. The care in choosing a Regular
wife appears to diminish as one rises in the social scale. Nothing would
induce an aspiring Isosceles, who had hopes of generating an 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 enquire above the five-hundredth
generation; a Hexagon or Dodecahedron is even more careless of the wife’s
pedigree; but a Circle has been known deliberately to take a wife who has
had an Irregular Great-Grandfather, and all because of some slight
superiority of lustre, or because of the charms of a low voice—which,
with us, even more than with you, is thought “an excellent thing in
Woman.”
Such ill-judged marriages are, as might be expected, barren, if they do
not result in positive Irregularity or in diminution of sides; but none
of these evils have hitherto proved sufficiently deterrent. The loss of a
few sides in a highly-developed Polygon is not easily noticed, and is
sometimes compensated by a successful operation in the Neo-Therapeutic
Gymnasium, as I have described above; and the Circles are too much
disposed to acquiesce in infecundity as a Law of the superior
development. Yet, if this evil be not arrested, the gradual diminution of
the Circular class may soon become more rapid, and the time may be not
far distant when, the race being no longer able to produce a Chief
Circle, the Constitution of Flatland must fall.
One other word of warning suggests itself to me, though I cannot so
easily mention a remedy; and this also refers to our relations with
Women. About three hundred years ago, it was decreed by the Chief Circle
that, since women are deficient in Reason but abundant in Emotion, they
ought no longer to be treated as rational, nor receive any mental
education. The consequence was that they were no longer taught to read,
nor even to master Arithmetic enough to enable them to count the angles
of their husband or children; and hence they sensibly declined during
each generation in intellectual power. And this system of female
non-education or quietism still prevails.
My fear is that, with the best intentions, this policy has been carried
so far as to react injuriously on the Male Sex.
For the consequence is that, as things now are, we Males have to lead a
kind of bi-lingual, and I may almost say bi-mental existence. With the
Women, we speak of “love,” “duty,” “right,” “wrong,” “pity,” “hope,” and
other irrational and emotional conceptions, which have no existence, and
the fiction of which has no object except to control feminine
exuberances; but among ourselves, and in our books, we have an entirely
different vocabulary and I may almost say, idiom. “Love” then 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 except 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 their Mothers and Nurses—and
to learn the vocabulary and idiom of science. Already methinks I discern
a weakness in the grasp of mathematical truth at the present time as
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.
_PART II
OTHER WORLDS_
“_O brave new worlds,_
_That have such people in them!_”
_PART II_
OTHER LANDS
§ 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.
[Illustration: ]
A noise of confused, multitudinous chirping or twittering issued from
them at intervals as long as they were moving; but sometimes they ceased
from motion, and then all was silence.
Approaching one of the largest of what I thought to be Women, I accosted
her, but received no answer. A second and third appeal on my part were
equally ineffectual. Losing patience at what appeared to me intolerable
rudeness, I brought my mouth into a position full in front of her mouth
so as to intercept her motion, and loudly repeated my question, “Woman,
what signifies this concourse, and this strange and confused chirping,
and this monotonous motion to and fro in one and the same Straight Line?”
“I am no Woman,” replied the small Line; “I am the Monarch of the world.
But thou, whence intrudest thou into my realm of Lineland?” Receiving
this abrupt reply, I begged pardon if I had in any way startled or
molested his Royal Highness; and describing myself as a stranger I
besought the King to give me some account of his dominions. But I had the
greatest possible difficulty in obtaining any information on points that
really interested me; for the Monarch could not refrain from constantly
assuming that whatever was familiar to him must also be known to me and
that I was simulating ignorance in jest. However, by persevering
questions I elicited the following facts:
It seemed that this poor ignorant Monarch—as he called himself—was
persuaded that the Straight Line which he called his Kingdom, and in
which he passed his existence, constituted the whole of the world, and
indeed the whole of Space. Not being able either to move or to see, save
in his Straight Line, he had no conception of anything out of it. Though
he had heard my voice when I first addressed him, the sounds had come to
him in a manner so contrary to his experience that he had made no answer,
“seeing no man,” as he expressed it, “and hearing a voice as it were from
my own intestines.” Until the moment when I placed my mouth in his World,
he had neither seen me, nor heard anything except confused sounds beating
against what I called his side, but what he called his _inside_ or
_stomach_; nor had he even now the least conception of the region from
which I had come. Outside his World, or Line, all was a blank to him;
nay, not even a blank, for a blank implies Space; say, rather, all was
non-existent.
His subjects—of whom the small Lines were Men and the Points Women—were
all alike confined in motion and eye-sight to that single Straight Line,
which was their World. It need scarcely be added that the whole of their
horizon was limited to a Point; nor could any one ever see anything but a
Point. Man, woman, child, thing—each was a Point to the eye of a
Linelander. Only by the sound of the voice could sex or age be
distinguished. Moreover, as each individual occupied the whole of the
narrow path, so to speak, which constituted his Universe, and no one
could move to the right or left to make way for passers by, it followed
that no Linelander could ever pass another. Once neighbours, always
neighbours. Neighbourhood with them was like marriage with us. Neighbours
remained neighbours till death did them part.
Such a life, with all vision limited to a Point, and all motion to a
Straight Line, seemed to me inexpressibly dreary; and I was surprised to
note the vivacity and cheerfulness of the King. Wondering whether it was
possible, amid circumstances so unfavourable to domestic relations, to
enjoy the pleasures of conjugal union, I hesitated for some time to
question his Royal Highness on so delicate a subject; but at last I
plunged into it by abruptly inquiring as to the health of his family. “My
wives and children,” he replied, “are well and happy.”
Staggered at this answer—for in the immediate proximity of the Monarch
(as I had noted in my dream before I entered Lineland) there were none
but Men—I ventured to reply, “Pardon me, but I cannot imagine how your
Royal Highness can at any time either see or approach their Majesties,
when there are 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 my impression,” said the King, “that you are not a Man,
but a feminine Monstrosity with a bass voice and an utterly uneducated
ear. But to continue.
“Nature herself having ordained that every Man should wed two wives——”
“Why two?” asked I. “You carry your affected simplicity too far,” he
cried. “How can there be a completely harmonious union without the
combination of the Four in One, viz. the Bass and Tenor of the Man and
the Soprano and Contralto of the two Women?” “But supposing,” said I,
“that a man should prefer one wife or three?” “It is impossible,” he
said; “it is as inconceivable as that two and one should make five, or
that the human eye should see a Straight Line.” I would have interrupted
him; but he proceeded as follows:
“Once in the middle of each week a Law of Nature compels us to move to
and fro with a rhythmic motion of more than usual violence, which
continues for the time you would take to count a hundred and one. In the
midst of this choral dance, at the fifty-first pulsation, the inhabitants
of the Universe pause in full career, and each individual sends forth his
richest, fullest, sweetest strain. It is in this decisive moment that all
our marriages are made. So exquisite is the adaptation of Bass to Treble,
of Tenor to Contralto, that oftentimes the Loved Ones, though twenty
thousand leagues away, recognise at once the responsive note of their
destined Lover; and, penetrating the paltry obstacles of distance, Love
unites the three. The marriage in that instant consummated results in a
threefold Male and Female offspring which takes its place in Lineland.”
“What! Always threefold?” said I. “Must one wife then always have twins?”
“Bass-voiced Monstrosity! yes,” replied the King. “How else could the
balance of the Sexes be maintained, if two girls were not born for every
boy? Would you ignore the very Alphabet of Nature?” He ceased, speechless
for fury; and some time elapsed before I could induce him to resume his
narrative.
“You will not, of course, suppose that every bachelor among us finds his
mates at the first wooing in this universal Marriage Chorus. On the
contrary, the process is by most of us many times repeated. Few are the
hearts whose happy lot it is at once to recognise in each other’s voices
the partner intended for them by Providence, and to fly into a reciprocal
and perfectly harmonious embrace. With most of us the courtship is of
long duration. The Wooer’s voices may perhaps accord with one of the
future wives, but not with both; or not, at first, with either; or the
Soprano and Contralto may not quite harmonise. In such cases Nature has
provided that every weekly Chorus shall bring the three Lovers into
closer harmony. Each trial of voice, each fresh discovery of discord,
almost imperceptibly induces the less perfect to modify his or her vocal
utterance so as to 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.”
§ 14.—_How I vainly tried to explain the nature of Flatland._
Thinking that it was time to bring down the Monarch from his raptures to
the level of common sense, I determined to endeavour to open up to him
some glimpses of the truth, that is to say of the nature of things in
Flatland. So I began thus: “How does your Royal Highness distinguish the
shapes and positions of his subjects? I for my part noticed by the sense
of sight, before I entered your Kingdom, that some of your people are
Lines and others Points, and that some of the Lines are larger——”
“You speak of an impossibility,” interrupted the King; “you must have
seen a vision; for to detect the difference between a Line and a Point by
the sense of sight is, as every one knows, in the nature of things,
impossible; but it can be detected by the sense of hearing, and by the
same means my shape can be exactly ascertained. Behold me—I am a Line,
the longest in Lineland, over six inches of Space——” “Of Length,” I
ventured to suggest. “Fool,” said he, “Space is Length. Interrupt me
again, and I have done.”
I apologised; but he continued scornfully, “Since you are impervious to
argument, you shall hear with your ears how by means of my two voices I
reveal my shape to my Wives, who are at this moment six thousand miles
seventy yards two feet eight inches away, the one to the North, the other
to the South. Listen, I call to them.”
He chirruped, and then complacently continued: “My wives at this moment
receiving the sound of one of my voices, closely followed by the other,
and perceiving that the latter reaches them after an interval in which
sound can traverse 6.457 inches, infer that one of my mouths is 6.457
inches further from them than the other, and accordingly know my shape to
be 6.457 inches. But you will of course understand that my wives do not
make this calculation every time they hear my two voices. They made it,
once for all, before we were married. But they _could_ make it at any
time. And in the same way I can estimate the shape of any of my Male
subjects by the sense of sound.”
“But how,” said I, “if a Man feigns a Woman’s voice with one of his two
voices, or so disguises his Southern voice that it cannot be recognised
as the echo of the Northern? May not such deceptions cause great
inconvenience? And have you no means of checking frauds of this kind by
commanding your neighbouring subjects to feel one another?” This of
course was a very stupid question, for feeling could not have answered
the purpose; but I asked with the view of irritating the Monarch, and I
succeeded perfectly.
“What!” cried he in horror, “explain your meaning.” “Feel, touch, come
into contact,” I replied. “If you mean by _feeling_,” said the King,
“approaching so close as to leave no space between two individuals, know,
Stranger, that this offence is punishable in my dominions by death. And
the reason is obvious. The frail form of a Woman, being liable to be
shattered by such an approximation, must be preserved by the State; but
since Women cannot be distinguished by the sense of sight from Man, the
Law ordains universally that neither Man nor Woman shall be approached so
closely as to destroy the interval between the approximator and the
approximated.
“And indeed what possible purpose would be served by this illegal and
unnatural excess of approximation which you call _touching_, when all the
ends of so brutal and coarse a process are attained at once more easily
and more exactly by the sense of hearing. As to your suggested danger of
deception, it is non-existent: for the Voice, being the essence of one’s
Being, cannot be thus changed at will. But come, suppose that I had the
power of passing through solid things, so that I could penetrate my
subjects, one after another, even to the number of a billion, verifying
the size and distance of each by the sense of _feeling_: how much time
and energy would be wasted in this clumsy and inaccurate method! Whereas
now, in one moment of audition, I take as it were the census and
statistics, local, corporal, mental, and spiritual, of every living being
in Lineland. Hark, only hark!”
So saying he paused and listened, as if in an ecstasy, to a sound which
seemed to me no better than a tiny chirping from an innumerable multitude
of lilliputian grasshoppers.
“Truly,” replied I, “your sense of hearing serves you in good stead, and
fills up many of your deficiencies. But permit me to point out that your
life in Lineland must be deplorably dull. To see nothing but a Point! Not
even to be able to Contemplate a Straight Line! Nay, not even to know
what a Straight Line is! To see, yet to be cut off from those Linear
prospects which are vouchsafed to us in Flatland! Better surely to have
no sense of sight at all than to see so little! I grant you I have not
your discriminative faculty of hearing; for the concert of all Lineland
which gives you such intense pleasure, is to me no better than a
multitudinous twittering or chirping. But at least I can discern, by
sight, a Line from a Point. And let me prove it. Just before I came into
your kingdom, I saw you dancing from left to right, and then from right
to left, with seven Men and a Woman in your immediate proximity on the
left, and eight Men and two Women on your right. Is not this correct?”
“It is correct,” said the King, “so far as the numbers and sexes are
concerned, though I know not what you mean by ‘right’ and ‘left.’ But I
deny that you saw these things. For how could you see the Line, that is
to say the inside, of any Man? But you must have heard these things, and
then dreamed that you saw them. And let me ask what you mean by those
words ‘left’ and ‘right.’ I suppose it is your way of saying Northward
and Southward.”
“Not so,” replied I; “besides your motion of Northward and Southward,
there is another motion which I call from right to left.”
_King._ Exhibit to me, if you please, this motion from left to right.
_I._ Nay, that I cannot do, unless you could step out of your Line
altogether.
_King._ Out of my Line? Do you mean out of the World? Out of Space?
_I._ Well, yes. Out of _your_ World. Out of _your_ Space. For your Space
is not the true Space. True Space is a Plane; but your Space is only a
Line.
_King._ If you cannot indicate this motion from left to right by yourself
moving in it, then I beg you to describe it to me in words.
_I._ If you cannot tell your right side from my left, I fear that no
words of mine can make my meaning clear to you. But surely you cannot be
ignorant of so simple a distinction.
_King._ I do not in the least understand you.
_I._ Alas! How shall I make it clear? When you move straight on, does it
not sometimes occur to you that you _could_ move in some other way,
turning your eye round so as to look in the direction towards which your
side is now fronting? In other words, instead of always moving in the
direction of one of your extremities, do you never feel a desire to move
in the direction, so to speak, of your side?
_King._ Never. And what do you mean? How can a man’s inside “front” in
any direction? Or how can a man move in the direction of his inside?
_I._ Well then, since words cannot explain the matter, I will try deeds,
and will move gradually out of Lineland in the direction which I desire
to indicate to you.
At the word I began to move my body out of Lineland. As long as any part
of me remained in his dominion and in his view, the King kept exclaiming,
“I see you, I see you still; you are not moving.” But when I had at last
moved myself out of his Line, he cried in his shrillest voice, “She is
vanished; she is dead.” “I am not dead,” replied I; “I am simply out of
Lineland, that is to say, out of the Straight Line which you call Space,
and in the true Space, where I can see things as they are. And at this
moment I can see your Line, or side—or inside as you are pleased to call
it; and I can also see the Men and Women on the North and South of you,
whom I will now enumerate, describing their order, their size, and the
interval between each.”
[Illustration: ]
When I had done this at great length, I cried triumphantly, “Does this at
last convince you?” And, with that, I once more entered Lineland, taking
up the same position as before.
But the Monarch replied, “If you were a Man of sense—though, as you
appear to have only one voice I have little doubt you are not a Man but a
Woman—but, if you had a particle of sense, you would listen to reason.
You ask me to believe that there is another Line besides that which my
senses indicate, and another motion besides that of which I am daily
conscious. I, in return, ask you to describe in words or indicate by
motion that other Line of which you speak. Instead of moving, you merely
exercise some magic art of vanishing and returning to sight; and instead
of any lucid description of your new World, you simply tell me the
numbers and sizes of some forty of my retinue, facts known to any child
in my capital. Can anything be more irrational or audacious? Acknowledge
your folly or depart from my dominions.”
Furious at his perversity, and especially indignant that he professed to
be ignorant of my Sex, I retorted in no measured terms, “Besotted Being!
You think yourself the perfection of existence, while you are in reality
the most imperfect and imbecile. You profess to see, whereas you can see
nothing but a Point! You plume yourself on inferring the existence of a
Straight Line; but I _can see_ Straight Lines and infer the existence of
Angles, Triangles, Squares, Pentagons, Hexagons, and even Circles. Why
waste more words? suffice it that I am the completion of your incomplete
self. You are a Line, but I am a Line of Lines, called in my country a
Square: and even I, infinitely superior though I am to you, am of little
account among the great Nobles of Flatland, whence I have come to visit
you, in the hope of enlightening your ignorance.”
Hearing these words the King advanced towards me with a menacing cry as
if to pierce me through the diagonal; and in that same moment there arose
from myriads of his subjects a multitudinous war-cry, increasing in
vehemence till at last methought it rivalled the roar of an army of a
hundred thousand Isosceles, and the artillery of a thousand Pentagons.
Spell-bound and motionless I could neither speak nor move to avert the
impending destruction; and still the noise grew louder, and the King came
closer, when I awoke to find the breakfast-bell recalling me to the
realities of Flatland.
§ 15.—_Concerning a Stranger from Spaceland._
From dreams I proceed to facts.
It was the last day of the 1999th year of our era. The pattering of the
rain had long ago announced nightfall; and I was sitting[3] in the
company of my wife, musing on the events of the past and the prospects of
the coming year, the coming century, the coming Millennium.
My four Sons and two orphan Grandchildren had retired to their several
apartments; and my Wife alone remained with me to see the old Millennium
out and the new one in.
I was rapt in thought, pondering in my mind some words that had casually
issued from the mouth of my youngest Grandson, a most promising young
Hexagon of unusual brilliancy and perfect angularity. His uncles and I
had been giving him his usual practical lesson in Sight Recognition,
turning ourselves upon our centres, now rapidly, now more slowly, and
questioning him as to our positions; and his answers had been so
satisfactory that I had been induced to reward him by giving him a few
hints on Arithmetic, as applied to Geometry.
Taking nine Squares, each an inch every way, I had put them together so
as to make one large Square, with a side of three inches, and I had hence
proved to my little Grandson that—though it was impossible for us to
_see_ the inside of the Square—yet we might ascertain the number of
square inches in a Square by simply squaring the number of inches in the
side: “and thus,” said I, “we know that 3², or 9, represents the number
of square inches in a Square whose side is 3 inches long.”
The little Hexagon meditated on this awhile and then said to me: “But you
have been teaching me to raise numbers to the third power; I suppose 3³
must mean something in Geometry; what does it mean?” “Nothing at all,”
replied I, “not at least in Geometry; for Geometry has only Two
Dimensions.” And then I began to show the boy how a Point by moving
through a length of three inches makes a Line of three inches, which may
be represented by 3; and how a Line of three inches, moving parallel to
itself through a length of three inches, makes a Square of three inches
every way, which may be represented by 3².
Upon this, my Grandson, again returning to his former suggestion, took me
up rather suddenly and exclaimed, “Well, then, if a Point by moving three
inches, makes a Line of three inches represented by 3; and if a straight
Line of three inches, moving parallel to itself, makes a Square of three
inches every way, represented by 3²; it must be that a Square of three
inches every way, moving somehow parallel to itself (but I don’t see how)
must make a Something else (but I don’t see what) of three inches every
way—and this must be represented by 3³.”
“Go to bed,” said I, a little ruffled by his interruption; “if you would
talk less nonsense, you would remember more sense.”
So my Grandson had disappeared in disgrace; and there I sat by my Wife’s
side, endeavouring to form a retrospect of the year 1999 and of the
possibilities of the year 2000, but not quite able to shake off the
thoughts suggested by the prattle of my bright little Hexagon. Only a few
sands now remained in the half-hour glass. Rousing myself from my reverie
I turned the glass Northward for the last time in the old Millennium; and
in the act, I exclaimed aloud, “The boy is a fool.”
Straightway I became conscious of a Presence in the room, and a chilling
breath thrilled through my very being. “He is no such thing,” cried my
Wife, “and you are breaking the Commandments in thus dishonouring your
own Grandson.” But I took no notice of her. Looking round in every
direction I could see nothing; yet still I _felt_ a Presence, and
shivered as the cold whisper came again. I started up. “What is the
matter?” said my Wife, “there is no draught; what are you looking for?
There is nothing.” There was nothing; and I resumed my seat, again
exclaiming, “The boy is a fool, I say; 3³ can have no meaning in
Geometry.” At once there came a distinctly audible reply, “The boy is not
a fool; and 3³ has an obvious Geometrical meaning.”
My Wife as well as myself heard the words, although she did not
understand their meaning, and both of us sprang forward in the direction
of the sound. What was our horror when we saw before us a Figure! At the
first glance it appeared to be a Woman, seen sideways; but a moment’s
observation shewed me that the extremities passed into dimness too
rapidly to represent one of the Female Sex; and I should have thought it
a Circle, only that it seemed to change its size in a manner impossible
for a Circle or for any Regular Figure of which I had had experience.
But my Wife had not my experience, nor the coolness necessary to note
these characteristics. With the usual hastiness and unreasoning jealousy
of her Sex, she flew at once to the conclusion that a Woman had entered
the house through some small aperture. “How comes this person here?” she
exclaimed, “you promised me, my dear, that there should be no ventilators
in our new house.” “Nor are there any,” said I; “but what makes you think
that the stranger is a Woman? I see by my power of Sight Recognition——”
“Oh, I have no patience with your Sight Recognition,” replied she,
“‘Feeling is believing’ and ‘A Straight Line to the touch is worth a
Circle to the sight’”—two Proverbs, very common with the Frailer Sex in
Flatland.
“Well,” said I, for I was afraid of irritating her, “if it must be so,
demand an introduction.” Assuming her most gracious manner, my Wife
advanced towards the Stranger, “Permit me, Madam, to feel and be felt
by——” then, suddenly recoiling, “Oh! it is not a Woman, and there are no
angles either, not a trace of one. Can it be that I have so misbehaved to
a perfect Circle?”
“I am indeed, in a certain sense a Circle,” replied the Voice, “and a
more perfect Circle than any in Flatland; but to speak more accurately, I
am many Circles in one.” Then he added more mildly, “I have a message,
dear Madam, to your husband, which I must not deliver in your presence;
and, if you would suffer us to retire for a few minutes——” But my Wife
would not listen to the proposal that our august Visitor should so
incommode himself, and assuring the Circle that the hour for her own
retirement had long passed, with many reiterated apologies for her recent
indiscretion, she at last retreated to her apartment.
I glanced at the half-hour glass. The last sands had fallen. The second
Millennium had begun.
§ 16.—_How the Stranger vainly endeavoured to reveal to me in words the
mysteries of Spaceland._
As soon as the sound of my Wife’s retreating footsteps had died away, I
began to approach the Stranger with the intention of taking a nearer view
and of bidding him be seated: but his appearance struck me dumb and
motionless with astonishment. Without the slightest symptoms of
angularity he nevertheless varied every instant with gradations of size
and brightness scarcely possible for any Figure within the scope of my
experience. The thought flashed across me that I might have before me a
burglar or cut-throat, some monstrous Irregular Isosceles, who, by
feigning the voice of a Circle, had obtained admission somehow into the
house, and was now preparing to stab me with his acute angle.
In a sitting-room, the absence of Fog (and the season happened to be
remarkably dry), made it difficult for me to trust to Sight Recognition,
especially at the short distance at which I was standing. Desperate with
fear, I rushed forward with an unceremonious “You must permit me, Sir—”
and felt him. My Wife was right. There was not the trace of an angle, not
the slightest roughness or inequality: never in my life had I met with a
more perfect Circle. He remained motionless while I walked round him,
beginning from his eye and returning to it again. Circular he was
throughout, a perfectly satisfactory Circle; there could not be a doubt
of it. Then followed a dialogue, which I will endeavour to set down as
near as I can recollect it, omitting only some of my profuse
apologies—for I was covered with shame and humiliation that I, a Square,
should have been guilty of the impertinence of feeling a Circle. It was
commenced by the Stranger with some impatience at the lengthiness of my
introductory process.
_Stranger._ Have you felt me enough by this time? Are you not introduced
to me yet?
_I._ Most illustrious Sir, excuse my awkwardness, which arises not from
ignorance of the usages of polite society, but from a little surprise and
nervousness, consequent on this somewhat unexpected visit. And I beseech
you to reveal my indiscretion to no one, and especially not to my Wife.
But before your Lordship enters into further communications, would he
deign to satisfy the curiosity of one who would gladly know whence his
Visitor came?
_Stranger._ From Space, from Space, Sir: whence else?
_I._ Pardon me, my Lord, but is not your Lordship already in Space, your
Lordship and his humble servant, even at this moment?
_Stranger._ Pooh! what do you know of Space? Define Space.
_I._ Space, my Lord, is height and breadth indefinitely prolonged.
_Stranger._ Exactly: you see you do not even know what Space is. You
think it is of Two Dimensions only; but I have come to announce to you a
Third—height, breadth, and length.
_I._ Your Lordship is pleased to be merry. We also speak of length and
height, or breadth and thickness, thus denoting Two Dimensions by four
names.
_Stranger._ But I mean not only three names, but Three Dimensions.
_I._ Would your Lordship indicate or explain to me in what direction is
the Third Dimension, unknown to me?
_Stranger._ I came from it. It is up above and down below.
_I._ My Lord means seemingly that it is Northward and Southward.
_Stranger._ I mean nothing of the kind. I mean a direction in which you
cannot look, because you have no eye in your side.
_I._ Pardon me, my Lord, a moment’s inspection will convince your
Lordship that I have a perfect luminary at the juncture of two of my
sides.
_Stranger._ Yes: but in order to see into Space you ought to have an eye,
not on your Perimeter, but on your side, that is, on what you would
probably call your inside; but we in Spaceland should call it your side.
_I._ An eye in my inside! An eye in my stomach! Your Lordship jests.
_Stranger._ I am in no jesting humour. I tell you that I come from Space,
or, since you will not understand what Space means, from the Land of
Three Dimensions whence I but lately looked down upon your Plane which
you call Space forsooth. From that position of advantage I discerned all
that you speak of as _solid_ (by which you mean “enclosed on four
sides”), your houses, your churches, your very chests and safes, yes even
your insides and stomachs, all lying open and exposed to my view.
_I._ Such assertions are easily made, my Lord.
_Stranger._ But not easily proved, you mean. But I mean to prove mine.
When I descended here, I saw your four Sons, the Pentagons, each in his
apartment, and your two Grandsons the Hexagons; I saw your youngest
Hexagon remain a while with you and then retire to his room, leaving you
and your Wife alone. I saw your Isosceles servants, three in number, in
the kitchen at supper, and the little Page in the scullery. Then I came
here, and how do you think I came?
_I._ Through the roof, I suppose.
_Stranger._ Not so. Your roof, as you know very well, has been recently
repaired, and has no aperture by which even a Woman could penetrate. I
tell you I come from Space. Are you not convinced by what I have told you
of your children and household.
_I._ Your Lordship must be aware that such facts touching the belongings
of his humble servant might be easily ascertained by any one in the
neighbourhood possessing your Lordship’s ample means of obtaining
information.
_Stranger._ How shall I convince him? Surely a plain statement of facts
followed by ocular demonstration ought to suffice.—Now, Sir; listen to
me.
You are living on a Plane. What you style Flatland is the vast level
surface of what I may call a fluid, on, or in, the top of which you and
your countrymen move about, without rising above it or falling below it.
I am not a plane Figure, but a Solid. You call me a Circle; but in
reality I am not a Circle, but an infinite number of Circles, of size
varying from a Point to a Circle of thirteen inches in diameter, one
placed on the top of the other. When I cut through your plane as I am now
doing, I make in your plane a section which you, very rightly, call a
Circle. For even a Sphere—which is my proper name in my own country—if he
manifest himself at all to an inhabitant of Flatland—must needs manifest
himself as a Circle.
Do you not remember—for I, who see all things, discerned last night the
phantasmal vision of Lineland written upon your brain—do you not
remember, I say, how, when you entered the realm of Lineland, you were
compelled to manifest yourself to the King not as a Square, but as a
Line, because that Linear Realm had not Dimensions enough to represent
the whole of you, but only a slice or section of you? In precisely the
same way, your country of Two Dimensions is not spacious enough to
represent me, a being of Three, but can only exhibit a slice or section
of me, which is what you call a Circle.
The diminished brightness of your eye indicates incredulity. But now
prepare to receive proof positive of the truth of my assertions. You
cannot indeed see more than one of my sections, or Circles, at a time;
for you have no power to raise your eye out of the plane of Flatland; but
you can at least see that, as I rise in Space, so my section becomes
smaller. See now, I will rise; and the effect upon your eye will be that
my Circle will become smaller and smaller till it dwindles to a point and
finally vanishes.
[Illustration: ]
There was no “rising” that I could see; but he diminished and finally
vanished. I winked once or twice to make sure that I was not dreaming.
But it was no dream. For from the depths of nowhere came forth a hollow
voice—close to my heart it seemed—“Am I quite gone? Are you convinced
now? Well, now I will gradually return to Flatland, and you shall see my
section become larger and larger.”
Every reader in Spaceland will easily understand that my mysterious Guest
was speaking the language of truth and even of simplicity. But to me,
proficient though I was in Flatland Mathematics, it was by no means a
simple matter. The rough diagram given above will make it clear to any
Spaceland child that the Sphere, ascending in the three positions
indicated there, must needs have manifested himself to me, or to any
Flatlander, as a Circle, at first of full size, then small, and at last
very small indeed, approaching to a Point. But to me, although I saw the
facts before me, the causes were as dark as ever. All that I could
comprehend was, that the Circle had made himself smaller and vanished,
and that he had now reappeared and was rapidly making himself larger.
When he had regained his original size, he heaved a deep sigh; for he
perceived by my silence that I had altogether failed to comprehend him.
And indeed I was now inclining to the belief that he must be no Circle at
all, but some extremely clever juggler; or else that the old wives’ tales
were true, and that after all there were such people as Enchanters and
Magicians.
After a long pause he muttered to himself, “One resource alone remains,
if I am not to resort to action. I must try the method of Analogy.” Then
followed a still longer silence, after which he continued our dialogue.
_Sphere._ Tell me, Mr. Mathematician; if a Point moves Northward, and
leaves a luminous wake, what name would you give to the wake?
_I._ A straight Line.
_Sphere._ And a straight Line has how many extremities?
_I._ Two.
_Sphere._ Now conceive the Northward straight line moving parallel to
itself, East and West, so that every point in it leaves behind it the
wake of a straight Line. What name will you give to the Figure thereby
formed? We will suppose that it moves through a distance equal to the
original straight Line.—What name, I say?
_I._ A Square.
_Sphere._ And how many sides has a Square? And how many Angles?
_I._ Four sides and four angles.
_Sphere._ Now stretch your imagination a little, and conceive a Square in
Flatland, moving parallel to itself upward.
_I._ What? Northward?
_Sphere._ No, not Northward; upward; out of Flatland altogether.
If it moved Northward, the Southern points in the Square would have to
move through the positions previously occupied by the Northern points.
But that is not my meaning.
I mean that every Point in you—for you are a Square and will serve the
purpose of my illustration—every Point in you, that is to say in what you
call your inside, is to pass upwards through Space in such a way that no
Point shall pass through the position previously occupied by any other
Point; but each Point shall describe a straight Line of its own. This is
all in accordance with Analogy; surely it must be clear to you.
Restraining my impatience—for I was now under a strong temptation to rush
blindly at my Visitor and to precipitate him into Space, or out of
Flatland, anywhere, so that I could get rid of him—I replied:—
“And what may be the nature of the Figure which I am to shape out by this
motion which you are pleased to denote by the word ‘upward’? I presume it
is describable in the language of Flatland.”
_Sphere._ Oh, certainly. It is all plain and simple, and in strict
accordance with Analogy—only, by the way, you must not speak of the
result as being a Figure, but as a Solid. But I will describe it to you.
Or rather not I, but Analogy. We began with a single Point, which of
course—being itself a Point—has only _one_ terminal Point.
One Point produces a Line with _two_ terminal Points.
One Line produces a Square with _four_ terminal Points.
Now you can yourself give the answer to your own question: 1, 2, 4, are
evidently in Geometrical Progression. What is the next number.
_I._ Eight.
_Sphere._ Exactly. The one Square produces a
_Something-which-you-do-not-as-yet-know-a-name-for-but-which-we-call-a-Cube_
with _eight_ terminal Points. Now are you convinced?
_I._ And has this Creature sides, as well as angles or what you call
“terminal Points?”
_Sphere._ Of course; and all according to Analogy. But, by the way, not
what _you_ call sides, but what _we_ call sides. You would call them
_solids_.
_I._ And how many solids or sides will appertain to this Being whom I am
to generate by the motion of my inside in an “upward” direction, and whom
you call a Cube?
_Sphere._ How can you ask? And you a mathematician! The side of anything
is always, if I may so say, one Dimension behind the thing. Consequently,
as there is no Dimension behind a Point, a Point has 0 sides; a Line, if
I may so say, has 2 sides (for the Points of a Line may be called by
courtesy, its sides); a Square has 4 sides; 0, 2, 4; what Progression do
you call that?
_I._ Arithmetical.
_Sphere._ And what is the next number?
_I._ Six.
_Sphere._ Exactly. Then you see you have answered your own question. The
Cube which you will generate will be bounded by six sides, that is to
say, six of your insides. You see it all now, eh?
“Monster,” I shrieked, “be thou juggler, enchanter, dream, or devil, no
more will I endure thy mockeries. Either thou or I must perish.” And
saying these words I precipitated myself upon him.
§ 17.—_How the Sphere, having in vain tried words, resorted to deeds._
It was in vain. I brought my hardest right angle into violent collision
with the Stranger, pressing on him with a force sufficient to have
destroyed any ordinary Circle: but I could feel him slowly and
unarrestably slipping from my contact; not edging to the right nor to the
left, but moving somehow out of the world and vanishing to nothing. Soon
there was a blank. But I still heard the Intruder’s voice.
_Sphere._ Why will you refuse to listen to reason? I had hoped to find in
you—as being a man of sense and an accomplished mathematician—a fit
apostle for the Gospel of the Three Dimensions, which I am allowed to
preach once only in a thousand years: but now I know not how to convince
you. Stay, I have it. Deeds, and not words, shall proclaim the truth.
Listen, my friend.
I have told you I can see from my position in Space the inside of all
things that you consider closed. For example, I see in yonder cupboard
near which you are standing, several of what you call boxes (but like
everything else in Flatland, they have no tops nor bottoms) full of
money; I see also two tablets of accounts. I am about to descend into
that cupboard and to bring you one of those tablets. I saw you lock the
cupboard half an hour ago, and I know you have the key in your
possession. But I descend from Space; the doors, you see, remain unmoved.
Now I am in the cupboard and am taking the tablet. Now I have it. Now I
ascend with it.
I rushed to the closet and dashed the door open. One of the tablets was
gone. With a mocking laugh, the Stranger appeared in the other corner of
the room, and at the same time the tablet appeared upon the floor. I took
it up. There could be no doubt—it was the missing tablet.
I groaned with horror, doubting whether I was not out of my senses; but
the Stranger continued: “Surely you must now see that my explanation, and
no other, suits the phenomena. What you call Solid things are really
superficial; what you call Space is really nothing but a great Plane. I
am in Space, and look down upon the insides of the things of which you
only see the outsides. You could leave this Plane yourself, if you could
but summon up the necessary volition. A slight upward or downward motion
would enable you to see all that I can see.
“The higher I mount, and the further I go from your Plane, the more I can
see, though of course I see it on a smaller scale. For example, I am
ascending; now I can see your neighbour the Hexagon and his family in
their several apartments; now I see the inside of the Theatre, ten doors
off, from which the audience is only just departing; and on the other
side a Circle in his study, sitting at his books. Now I shall come back
to you. And, as a crowning proof, what do you say to my giving you a
touch, just the least touch, in your stomach? It will not seriously
injure you, and the slight pain you may suffer cannot be compared with
the mental benefit you will receive.”
Before I could utter a word of remonstrance, I felt a shooting pain in my
inside, and a demoniacal laugh seemed to issue from within me. A moment
afterwards the sharp agony had ceased, leaving nothing but a dull ache
behind, and the Stranger began to reappear, saying, as he gradually
increased in size, “There, I have not hurt you much, have I? If you are
not convinced now, I don’t know what will convince you. What say you?”
My resolution was taken. It seemed intolerable that I should endure
existence subject to the arbitrary visitations of a Magician who could
thus play tricks with one’s very stomach. If only I could in any way
manage to pin him against the wall till help came!
Once more I dashed my hardest angle against him, at the same time
alarming the whole household by my cries for aid. I believe, at the
moment of my onset, the Stranger had sunk below our Plane, and really
found difficulty in rising. In any case he remained motionless, while I,
hearing, as I thought, the sound of some help approaching, pressed
against him with redoubled vigour, and continued to shout for assistance.
A convulsive shudder ran through the Sphere. “This must not be,” I
thought I heard him say; “either he must listen to reason, or I must have
recourse to the last resource of civilization.” Then, addressing me in a
louder tone, he hurriedly exclaimed, “Listen: no stranger must witness
what you have witnessed. Send your Wife back at once, before she enters
the apartment. The Gospel of Three Dimensions must not be thus
frustrated. Not thus must the fruits of one thousand years of waiting be
thrown away. I hear her coming. Back! back! Away from me, or you must go
with me—whither you know not—into the Land of Three Dimensions!”
“Fool! Madman! Irregular!” I exclaimed; “never will I release thee; thou
shalt pay the penalty of thine impostures.”
“Ha! Is it come to this?” thundered the Stranger: “then meet your fate:
out of your Plane you go. Once, twice, thrice! ’Tis done!”
§ 18.—_How I came to Spaceland, and what I saw there._
An unspeakable horror seized me. There was a darkness; then a dizzy,
sickening sensation of sight that was not like seeing; I saw a Line that
was no Line; Space that was not Space; I was myself, and not myself. When
I could find voice, I shrieked aloud in agony, “Either this is madness or
it is Hell.” “It is neither,” calmly replied the voice of the Sphere, “it
is Knowledge; it is Three Dimensions: open your eye once again and try to
look steadily.”
I looked, and, behold, a new world! There stood before me, visibly
incorporate, all that I had before inferred, conjectured, dreamed, of
perfect Circular beauty. What seemed the centre of the Stranger’s form
lay open to my view: yet I could see no heart, nor lungs, nor arteries,
only a beautiful harmonious Something—for which I had no words; but you,
my Readers in Spaceland, would call it the surface of the Sphere.
Prostrating myself mentally before my Guide, I cried, “How is it, O
divine ideal of consummate loveliness and wisdom, that I see thy inside,
and yet cannot discern thy heart, thy lungs, thy arteries, thy liver?”
“What you think you see, you see not,” he replied; “it is not given to
you, nor to any other Being, to behold my internal parts. I am of a
different order of Beings from those in Flatland. Were I a Circle, you
could discern my intestines, but I am a Being composed, as I told you
before, of many Circles, the Many in the One, called in this country a
Sphere. And, just as the outside of a Cube is a Square, so the outside of
a Sphere presents the appearance of a Circle.”
Bewildered though I was by my Teacher’s enigmatic utterance, I no longer
chafed against it, but worshipped him in silent adoration. He continued,
with more mildness in his voice: “Distress not yourself if you cannot at
first understand the deeper mysteries of Spaceland. By degrees they will
dawn upon you. Let us begin by casting back a glance at the region whence
you came. Return with me a while to the plains of Flatland, and I will
show you that which you have so often reasoned and thought about, but
never seen with the sense of sight—a visible angle.” “Impossible!” I
cried; but, the Sphere leading the way, I followed as if in a dream, till
once more his voice arrested me: “Look yonder, and behold your own
Pentagonal house and all its inmates.”
I looked below, and saw with my physical eye all that domestic
individuality which I had hitherto merely inferred with the
understanding. And how poor and shadowy was the inferred conjecture in
comparison with the reality which I now beheld! My four Sons calmly
asleep in the North-Western rooms, my two orphan Grandsons to the South;
the Servants, the Butler, my Daughter, all in their several apartments.
Only my affectionate Wife, alarmed by my continued absence, had quitted
her room and was roving up and down in the Hall, anxiously awaiting my
return. Also the Page, aroused by my cries, had left his room, and under
pretext of ascertaining whether I had fallen somewhere in a faint, was
prying into the cabinet in my study. All this I could now _see_, not
merely infer; and as we came nearer and nearer, I could discern even the
contents of my cabinet, and the two chests of gold, and the tablets of
which the Sphere had made mention.
[Illustration: ]
Touched by my Wife’s distress, I would have sprung downward to reassure
her, but I found myself incapable of motion. “Trouble not yourself about
your Wife,” said my Guide; “she will not be long left in anxiety;
meantime, let us take a survey of Flatland.”
Once more I felt myself rising through space. It was even as the Sphere
had said. The further we receded from the object we beheld, the larger
became the field of vision. My native city, with the interior of every
house and every creature therein, lay open to my view in miniature. We
mounted higher, and lo, the secrets of the earth, the depths of mines and
inmost caverns of the hills, were bared before me.
Awestruck at the sight of the mysteries of the earth, thus unveiled
before my unworthy eye, I said to my Companion, “Behold, I am become as a
God. For the wise men in our country say that to see all things, or as
they express it, _omnividence_, is the attribute of God alone.” There was
something of scorn in the voice of my Teacher as he made answer: “Is it
so indeed? Then the very pickpockets and cut-throats of my country are to
be worshipped by your wise men as being Gods: for there is not one of
them that does not see as much as you see now. But trust me, your wise
men are wrong.”
_I._ Then is omnividence the attribute of others beside Gods?
_Sphere._ I do not know. But, if a pick-pocket or a cut-throat of our
country can see everything that is in your country, surely that is no
reason why the pick-pocket or cut-throat should be accepted by you as a
God. This omnividence, as you call it—it is not a common word in
Spaceland—does it make you more just, more merciful, less selfish, more
loving? Not in the least. Then how does it make you more divine?
_I._ “More merciful, more loving!” But these are the qualities of women!
And we know that a Circle is a higher Being than a Straight Line, in so
far as knowledge and wisdom are more to be esteemed than mere affection.
_Sphere._ It is not for me to classify human faculties according to
merit. Yet many of the best and wisest in Spaceland think more of the
affections than of the understanding, more of your despised Straight
Lines than of your belauded Circles. But enough of this. Look yonder. Do
you know that building?
I looked, and afar off I saw an immense Polygonal structure, in which I
recognized the General Assembly Hall of the States of Flatland,
surrounded by dense lines of Pentagonal buildings at right angles to each
other, which I knew to be streets; and I perceived that I was approaching
the great Metropolis.
“Here we descend,” said my Guide. It was now morning, the first hour of
the first day of the two thousandth year of our era. Acting, as was their
wont, in strict accordance with precedent, the highest Circles of the
realm were meeting in solemn conclave, as they had met on the first hour
of the first day of the year 1000, and also on the first hour of the
first day of the year 0.
The minutes of the previous meetings were now read by one whom I at once
recognized as my brother, a perfectly Symmetrical Square, and the Chief
Clerk of the High Council. It was found recorded on each occasion that:
“Whereas the States had been troubled by divers ill-intentioned persons
pretending to have received revelations from another World, and
professing to produce demonstrations whereby they had instigated to
frenzy both themselves and others, it had been for this cause unanimously
resolved by the Grand Council that on the first day of each millenary,
special injunctions be sent to the Prefects in the several districts of
Flatland, to make strict search for such misguided persons, and without
formality of mathematical examination, to destroy all such as were
Isosceles of any degree, to scourge and imprison any regular Triangle, to
cause any Square or Pentagon to be sent to the district Asylum, and to
arrest any one of higher rank, sending him straightway to the Capital to
be examined and judged by the Council.”
“You hear your fate,” said the Sphere to me, while the Council was
passing for the third time the formal resolution. “Death or imprisonment
awaits the Apostle of the Gospel of Three Dimensions.” “Not so,” replied
I, “the matter is now so clear to me, the nature of real space so
palpable, that methinks I could make a child understand it. Permit me but
to descend at this moment and enlighten them.” “Not yet,” said my Guide,
“the time will come for that. Meantime I must perform my mission. Stay
thou there in thy place.” Saying these words, he leaped with great
dexterity into the sea (if I may so call it) of Flatland, right in the
midst of the ring of Counsellors. “I come,” cried he, “to proclaim that
there is a land of Three Dimensions.”
I could see many of the younger Counsellors start back in manifest
horror, as the Sphere’s circular section widened before them. But on a
sign from the presiding Circle,—who showed not the slightest alarm or
surprise—six Isosceles of a low type from six different quarters rushed
upon the Sphere. “We have him,” they cried; “No; yes; we have him still!
he’s going! he’s gone!”
“My Lords,” said the President to the Junior Circles of the Council,
“there is not the slightest need for surprise; the secret archives, to
which I alone have access, tell me that a similar occurrence happened on
the last two millennial commencements. You will, of course, say nothing
of these trifles outside the Cabinet.”
Raising his voice, he now summoned the guard. “Arrest the policemen; gag
them. You know your duty.” After he had consigned to their fate the
wretched policemen—ill-fated and unwilling witnesses of a State-secret
which they were not to be permitted to reveal—he again addressed the
Counsellors. “My Lords, the business of the Council being concluded, I
have only to wish you a happy New Year.” Before departing, he expressed,
at some length, to the Clerk, my excellent but most unfortunate brother,
his sincere regret that, in accordance with precedent and for the sake of
secrecy, he must condemn him to perpetual imprisonment, but added his
satisfaction that, unless some mention were made by him of that day’s
incident, his life would be spared.
§ 19.—_How, though the Sphere showed me other mysteries of Spaceland, I
still desired more; and what came of it._
When I saw my poor brother led away to imprisonment, I attempted to leap
down into the Council Chamber, desiring to intercede on his behalf, or at
least bid him farewell. But I found that I had no motion of my own. I
absolutely depended on the volition of my Guide, who said in gloomy
tones, “Heed not thy brother; haply thou shalt have ample time hereafter
to condole with him. Follow me.”
[Illustration: ]
Once more we ascended into space. “Hitherto,” said the Sphere, “I have
shown you naught save Plane Figures and their interiors. Now I must
introduce you to Solids, and reveal to you the plan upon which they are
constructed. Behold this multitude of moveable square cards. See, I put
one on another, not, as you supposed, Northward of the other, but _on_
the other. Now a second, now a third. See, I am building up a Solid by a
multitude of Squares parallel to one another. Now the Solid is complete,
being as high as it is long and broad, and we call it a Cube.”
“Pardon me, my Lord,” replied I; “but to my eye the appearance is as of
an Irregular Figure whose inside is laid open to the view; in other
words, methinks I see no Solid, but a Plane such as we infer in Flatland;
only of an Irregularity which betokens some monstrous criminal, so that
the very sight of it is painful to my eyes.”
“True,” said the Sphere; “it appears to you a Plane, because you are not
accustomed to light and shade and perspective; just as in Flatland a
Hexagon would appear a Straight Line to one who has not the Art of Sight
Recognition. But in reality it is a Solid, as you shall learn by the
sense of Feeling.”
He then introduced me to the Cube, and I found that this marvellous Being
was indeed no Plane, but a Solid; and that he was endowed with six plane
sides and eight terminal points called solid angles; and I remembered the
saying of the Sphere that just such a Creature as this would be formed by
a Square moving, in Space, parallel to himself: and I rejoiced to think
that so insignificant a Creature as I could in some sense be called the
Progenitor of so illustrious an offspring.
But still I could not fully understand the meaning of what my Teacher had
told me concerning “light” and “shade” and “perspective”; and I did not
hesitate to put my difficulties before him.
Were I to give the Sphere’s explanation of these matters, succinct and
clear though it was, it would be tedious to an inhabitant of Space, who
knows these things already. Suffice it, that by his lucid statements, and
by changing the position of objects and lights, and by allowing me to
feel the several objects and even his own sacred Person, he at last made
all things clear to me, so that I could now readily distinguish between a
Circle and a Sphere, a Plane Figure and a Solid.
This was the Climax, the Paradise, of my strange eventful History.
Henceforth I have to relate the story of my miserable Fall:—most
miserable, yet surely most undeserved! For why should the thirst for
knowledge be aroused, only to be disappointed and punished! My volition
shrinks from the painful task of recalling my humiliation; yet, like a
second Prometheus, I will endure this and worse, if by any means I may
arouse in the interiors of Plane and Solid Humanity a spirit of rebellion
against the Conceit which would limit our Dimensions to Two or Three or
any number short of Infinity. Away then with all personal considerations!
Let me continue to the end, as I began, without further digressions or
anticipations, pursuing the plain path of dispassionate History. The
exact facts, the exact words,—and they are burnt in upon my brain,—shall
be set down without alteration of an iota; and let my Readers judge
between me and Destiny.
The Sphere would willingly have continued his lessons by indoctrinating
me in the conformation of all regular Solids, Cylinders, Cones, Pyramids,
Pentahedrons, Hexahedrons, Dodecahedrons and Spheres: but I ventured to
interrupt him. Not that I was wearied of knowledge. On the contrary, I
thirsted for yet deeper and fuller draughts than he was offering to me.
“Pardon me,” said I, “O Thou Whom I must no longer address as the
Perfection of all Beauty; but let me beg thee to vouchsafe thy servant a
sight of thine interior.”
_Sphere._ “My what?”
_I._ “Thine interior: thy stomach, thy intestines.”
_Sphere._ “Whence this ill-timed impertinent request? And what mean you
by saying that I am no longer the Perfection of all Beauty?”
_I._ My Lord, your own wisdom has taught me to aspire to One even more
great, more beautiful, and more closely approximate to Perfection than
yourself. As you yourself, superior to all Flatland forms, combine many
Circles in One, so doubtless there is One above you who combines many
Spheres in One Supreme Existence, surpassing even the Solids of
Spaceland. And even as we, who are now in Space, look down on Flatland
and see the insides of all things, so of a certainty there is yet above
us some higher, purer region, whither thou dost surely purpose to lead
me—O Thou Whom I shall always call, everywhere and in all Dimensions, my
Priest, Philosopher, and Friend—some yet more spacious Space, some more
dimensionable Dimensionality, from the vantage-ground of which we shall
look down together upon the revealed insides of Solid things, and where
thine own intestines, and those of thy kindred Spheres, will lie exposed
to the view of the poor wandering exile from Flatland, to whom so much
has already been vouchsafed.
_Sphere._ Pooh! Stuff! Enough of this trifling! The time is short, and
much remains to be done before you are fit to proclaim the Gospel of
Three Dimensions to your blind benighted countrymen in Flatland.
_I._ Nay, gracious Teacher, deny me not what I know it is in thy power to
perform. Grant me but one glimpse of thine interior, and I am satisfied
for ever, remaining henceforth thy docile pupil, thy unemancipable slave,
ready to receive all thy teachings and to feed upon the words that fall
from thy lips.
_Sphere._ Well, then, to content and silence you, let me say at once, I
would show you what you wish if I could; but I cannot. Would you have me
turn my stomach inside out to oblige you?
_I._ But my Lord has shown me the intestines of all my countrymen in the
Land of Two Dimensions by taking me with him into the Land of Three. What
therefore more easy than now to take his servant on a second journey into
the blessed region of the Fourth Dimension, where I shall look down with
him once more upon this land of Three Dimensions, and see the inside of
every three-dimensioned house, the secrets of the solid earth, the
treasures of the mines in Spaceland, and the intestines of every solid
living creature, even of the noble and adorable Spheres.
_Sphere._ But where is this land of Four Dimensions?
_I._ I know not: but doubtless my Teacher knows.
_Sphere._ Not I. There is no such land. The very idea of it is utterly
inconceivable.
_I._ Your Lordship tempts his servant to see whether he remembers the
revelations imparted to him. Trifle not with me, my Lord; I crave, I
thirst, for more knowledge. Doubtless we cannot _see_ that other higher
Spaceland now, because we have no eye in our stomachs. But, just as there
_was_ the realm of Flatland, though that poor puny Lineland Monarch could
neither turn to left nor right to discern it, and just as there _was_
close at hand, and touching my frame, the land of Three Dimensions,
though I, blind senseless wretch, had no power to touch it, no eye in my
interior to discern it, so of a surety there is a Fourth Dimension, which
my Lord perceives with the inner eye of thought. And that it must exist
my Lord himself has taught me. Or can he have forgotten what he himself
imparted to his servant?
In One Dimension, did not a moving Point produce a Line with _two_
terminal points?
In Two Dimensions, did not a moving Line produce a Square with _four_
terminal points?
In Three Dimensions, did not a moving Square produce—did not this eye of
mine behold it—that blessed Being, a Cube, with _eight_ terminal points?
And in Four Dimensions shall not a moving Cube—alas, for Analogy, and
alas for the Progress of Truth, if it be not so—shall not, I say, the
motion of a divine Cube result in a still more divine Organization with
_sixteen_ terminal points?
Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not
this a Geometrical Progression? Is not this—if I might quote my Lord’s
own words—“strictly according to Analogy”?
Again, was I not taught by my Lord that as in a Line there are _two_
bounding Points, and in a Square there are _four_ bounding Lines, so in a
Cube there must be _six_ bounding Squares? Behold once more the
confirming Series, 2, 4, 6: is not this an Arithmetical Progression? And
consequently does it not of necessity follow that the more divine
offspring of the divine Cube in the Land of Four Dimensions, must have 8
bounding Cubes: and is not this also, as my Lord has taught me to
believe, “strictly according to Analogy”?
O, my Lord, my Lord, behold, I cast myself in faith upon conjecture, not
knowing the facts; and I appeal to your Lordship to confirm or deny my
logical anticipations. If I am wrong, I yield, and will no longer demand
a Fourth Dimension; but, if I am right, my Lord will listen to reason.
I ask therefore, is it, or is it not, the fact, that ere now your
countrymen also have witnessed the descent of Beings of a higher order
than their own, entering closed rooms, even as your Lordship entered
mine, without the opening of doors or windows, and appearing and
vanishing at will? On the reply to this question I am ready to stake
everything. Deny it, and I am henceforth silent. Only vouchsafe an
answer.
_Sphere_ (_after a pause_). It is reported so. But men are divided in
opinion as to the facts. And even granting the facts, they explain them
in different ways. And in any case, however great may be the number of
different explanations, no one has adopted or suggested the theory of a
Fourth Dimension. Therefore, pray have done with this trifling, and let
us return to business.
_I._ I was certain of it. I was certain that my anticipations would be
fulfilled. And now have patience with me and answer me yet one more
question, best of Teachers! Those who have thus appeared—no one knows
whence—and have returned—no one knows whither—have they also contracted
their sections and vanished somehow into that more Spacious Space,
whither I now entreat you to conduct me?
_Sphere (moodily)._ They have vanished, certainly—if they ever appeared.
But most people say that these visions arose from the thought—you will
not understand me—from the brain; from the perturbed angularity of the
Seer.
_I._ Say they so? Oh, believe them not. Or if it indeed be so, that this
other Space is really Thoughtland, then take me to that blessed Region
where I in Thought shall see the insides of all solid things. There,
before my ravished eye, a Cube, moving in some altogether new direction,
but strictly according to Analogy, so as to make every particle of his
interior pass through a new kind of Space with a wake of its own—shall
create a still more perfect perfection than himself, with sixteen
terminal Extra-solid angles, and Eight solid Cubes for his Perimeter. And
once there, shall we stay our upward course? In that blessed region of
Four Dimensions, shall we linger on the threshold of the Fifth, and not
enter therein? Ah, no! Let us rather resolve that our ambition shall soar
with our corporal ascent. Then, yielding to our intellectual onset, the
gates of the Sixth Dimension shall fly open; after that a Seventh, and
then an Eighth——
How long I should have continued I know not. In vain did the Sphere, in
his voice of thunder, reiterate his commands of silence, and threaten me
with the direst penalties if I persisted. Nothing could stem the flood of
my ecstatic aspirations. Perhaps I was to blame; but indeed I was
intoxicated with the recent draughts of Truth to which he himself had
introduced me. However, the end was not long in coming. My words were cut
short by a crash outside, and a simultaneous crash inside me, which
impelled me through Space with a velocity that precluded speech. Down!
down! down! I was rapidly descending; and I knew that return to Flatland
was my doom. One glimpse, one last and never-to-be-forgotten glimpse I
had of that dull level wilderness—which was now to become my Universe
again—spread out before my eye. Then a darkness. Then a final,
all-consummating thunder-peal; and, when I came to myself, I was once
more a common creeping Square, in my Study at home, listening to the
Peace-Cry of my approaching Wife.
§ 20.—_How the Sphere encouraged me in a Vision._
Although I had less than a minute for reflection, I felt, by a kind of
instinct, that I must conceal my experiences from my Wife. Not that I
apprehended, at the moment, any danger from her divulging my secret, but
I know that to any Woman in Flatland the narrative of my adventures must
needs be unintelligible. So I endeavoured to reassure her by some story,
invented for the occasion, that I had accidentally fallen through the
trap-door of the cellar, and had there lain stunned.
The Southward attraction in our country is so slight that even to a Woman
my tale necessarily appeared extraordinary and well-nigh incredible; but
my Wife, whose good sense far exceeds that of the average of her Sex, and
who perceived that I was unusually excited, did not argue with me on the
subject, but insisted that I was ill and required repose. I was glad of
an excuse for retiring to my chamber to think quietly over what had
happened. When I was at last by myself, a drowsy sensation fell on me;
but before my eyes closed I endeavoured to reproduce the Third Dimension,
and especially the process by which a Cube is constructed through the
motion of a Square. It was not so clear as I could have wished; but I
remembered that it must be “Upward, and yet not Northward,” and I
determined steadfastly to retain these words as the clue which, if firmly
grasped, could not fail to guide me to the solution. So mechanically
repeating, like a charm, the words, “Upward yet not Northward,” I fell
into a sound refreshing sleep.
During my slumber I had a dream. I thought I was once more by the side of
the Sphere, whose lustrous hue betokened that he had exchanged his wrath
against me for perfect placability. We were moving together towards a
bright but infinitesimally small Point, to which my Master directed my
attention. As we approached, methought there issued from it a slight
humming noise as from one of your Spaceland blue-bottles, only less
resonant by far, so slight indeed that even in the perfect stillness of
the Vacuum through which we soared, the sound reached not our ears till
we checked our flight at a distance from it of something under twenty
human diagonals.
“Look yonder,” said my Guide, “in Flatland thou hast lived; of Lineland
thou hast received a vision; thou hast soared with me to the heights of
Spaceland; now, in order to complete the range of thy experience, I
conduct thee downward to the lowest depth of existence, even to the realm
of Pointland, the Abyss of No Dimensions.
“Behold yon miserable creature. That Point is a Being like ourselves, but
confined to the non-dimensional Gulf. He is himself his own World, his
own Universe; of any other than himself he can form no conception; he
knows not Length, nor Breadth, nor Height, for he has had no experience
of them; he has no cognizance even of the number Two; nor has he a
thought of Plurality; for he is himself his One and All, being really
Nothing. Yet mark his perfect self-contentment, and hence learn this
lesson, that to be self-contented is to be vile and ignorant, and that to
aspire is better than to be blindly and impotently happy. Now listen.”
He ceased; and there arose from the little buzzing creature a tiny, low,
monotonous, but distinct tinkling, as from one of your Spaceland
phonographs, from which I caught these words, “Infinite beatitude of
existence! It is; and there is none else beside It.”
“What,” said I, “does the puny creature mean by ‘it’?” “He means
himself,” said the Sphere: “have you not noticed before now, that babies
and babyish people who cannot distinguish themselves from the world,
speak of themselves in the Third Person? But hush!”
“It fills all Space,” continued the little soliloquizing Creature, “and
what It fills, It is. What It thinks, that It utters; and what It utters,
that It hears; and It itself is Thinker, Utterer, Hearer, Thought, Word,
Audition; it is the One, and yet the All in All. Ah, the happiness, ah,
the happiness of Being!”
“Can you not startle the little thing out of its complacency?” said I.
“Tell it what it really is, as you told me; reveal to it the narrow
limitations of Pointland, and lead it up to something higher.” “That is
no easy task,” said my Master; “try you.”
Hereon, raising my voice to the uttermost, I addressed the Point as
follows:
“Silence, silence, contemptible Creature. You call yourself the All in
All, but you are the Nothing: your so-called Universe is a mere speck in
a Line, and a Line is a mere shadow as compared with—” “Hush, hush, you
have said enough,” interrupted the Sphere, “now listen, and mark the
effect of your harangue on the King of Pointland.”
The lustre of the Monarch, who beamed more brightly than ever upon
hearing my words, showed clearly that he retained his complacency; and I
had hardly ceased when he took up his strain again. “Ah, the joy, ah, the
joy of Thought! What can It not achieve by thinking! Its own Thought
coming to Itself, suggestive of Its disparagement, thereby to enhance Its
happiness! Sweet rebellion stirred up to result in triumph! Ah, the
divine creative power of the All in One! Ah, the joy, the joy of Being!”
“You see,” said my Teacher, “how little your words have done. So far as
the Monarch understands them at all, he accepts them as his own—for he
cannot conceive of any other except himself—and plumes himself upon the
variety of ‘Its Thought’ as an instance of creative Power. Let us leave
this God of Pointland to the ignorant fruition of his omnipresence and
omniscience: nothing that you or I can do can rescue him from his
self-satisfaction.”
After this, as we floated gently back to Flatland, I could hear the mild
voice of my Companion pointing the moral of my vision, and stimulating me
to aspire, and to teach others to aspire. He had been angered at first—he
confessed—by my ambition to soar to Dimensions above the Third; but,
since then, he had received fresh insight, and he was not too proud to
acknowledge his error to a Pupil. Then he proceeded to initiate me into
mysteries yet higher than those I had witnessed, showing me how to
construct Extra-Solids by the motion of Solids, and Double Extra-Solids
by the motion of Extra-Solids, and all “strictly according to Analogy,”
all by methods so simple, so easy, as to be patent even to the Female
Sex.
§ 21.—_How I tried to teach the theory of Three Dimensions to my
Grandson, and with what success._
I awoke rejoicing, and began to reflect on the glorious career before me.
I would go forth, methought, at once, and evangelize the whole of
Flatland. Even to Women and Soldiers should the Gospel of Three
Dimensions be proclaimed. I would begin with my Wife.
Just as I had decided on the plan of my operations, I heard the sound of
many voices in the street commanding silence. Then followed a louder
voice. It was a herald’s proclamation. Listening attentively, I
recognized the words of the Resolution of the Council, enjoining the
arrest, imprisonment, or execution of any one who should pervert the
minds of the people by delusions, and by professing to have received
revelations from another World.
I reflected. This danger was not to be trifled with. It would be better
to avoid it by omitting all mention of my Revelation, and by proceeding
on the path of Demonstration—which after all, seemed so simple and so
conclusive that nothing would be lost by discarding the former means.
“Upward, not Northward”—was the clue to the whole proof. It had seemed to
me fairly clear before I fell asleep; and when I first awoke, fresh from
my dream, it had appeared as patent as Arithmetic; but somehow it did not
seem to me quite so obvious now. Though my Wife entered the room
opportunely just at that moment, I decided, after we had interchanged a
few words of commonplace conversation, not to begin with her.
My Pentagonal Sons were men of character and standing, and physicians of
no mean reputation, but not great in mathematics, and, in that respect,
unfit for my purpose. But it occurred to me that a young and docile
Hexagon, with a mathematical turn, would be a most suitable pupil. Why
therefore not make my first experiment with my little precocious
Grandson, whose casual remarks on the meaning of 3³ had met with the
approval of the Sphere? Discussing the matter with him, a mere boy, I
should be in perfect safety; for he would know nothing of the
Proclamation of the Council; whereas I could not feel sure that my
Sons—so greatly did their patriotism and reverence for the Circles
predominate over mere blind affection—might not feel compelled to hand me
over to the Prefect, if they found me seriously maintaining the seditious
heresy of the Third Dimension.
But the first thing to be done was to satisfy in some way the curiosity
of my Wife, who naturally wished to know something of the reasons for
which the Circle had desired that mysterious interview, and of the means
by which he had entered our house. Without entering into the details of
the elaborate account I gave her,—an account, I fear, not quite so
consistent with truth as my Readers in Spaceland might desire,—I must be
content with saying that I succeeded at last in persuading her to return
quietly to her household duties without eliciting from me any reference
to the World of Three Dimensions. This done, I immediately sent for my
Grandson; for, to confess the truth, I felt that all that I had seen and
heard was in some strange way slipping away from me, like the image of a
half-grasped, tantalizing dream, and I longed to essay my skill in making
a first disciple.
When my Grandson entered the room I carefully secured the door. Then,
sitting down by his side and taking our mathematical tablets—or, as you
would call them, Lines—I told him we would resume the lesson of
yesterday. I taught him once more how a Point by motion in One Dimension
produces a Line, and how a straight Line in Two Dimensions produces a
Square. After this, forcing a laugh, I said, “And now, you scamp, you
wanted to make me believe that a Square may in the same way by motion
‘Upward, not Northward,’ produce another figure, a sort of extra Square
in Three Dimensions. Say that again, you young rascal.”
At this moment we heard once more the herald’s “O yes! O yes!” outside in
the street proclaiming the Resolution of the Council. Young though he
was, my Grandson—who was unusually intelligent for his age, and bred up
in perfect reverence for the authority of the Circles—took in the
situation with an acuteness for which I was quite unprepared. He remained
silent till the last words of the Proclamation had died away, and then,
bursting into tears, “Dear Grandpapa,” he said, “that was only my fun,
and of course I meant nothing at all by it; and we did not know anything
then about the new Law; and I don’t think I said anything about the Third
Dimension; and I am sure I did not say one word about ‘Upward, not
Northward,’ for that would be such nonsense, you know. How could a thing
move Upward, and not Northward? Upward, and not Northward! Even if I were
a baby, I could not be so absurd as that. How silly it is! Ha! ha! ha!”
“Not at all silly,” said I, losing my temper; “here for example, I take
this Square,”—and, at the word, I grasped a moveable Square, which was
lying at hand—“and I move it, you see, not Northward but—yes, I move it
Upward—that is to say, not Northward, but I move it somewhere—not exactly
like this, but somehow—” Here I brought my sentence to an inane
conclusion, shaking the Square about in a purposeless manner, much to the
amusement of my Grandson, who burst out laughing louder than ever, and
declared that I was not teaching him, but joking with him; and so saying
he unlocked the door and ran out of the room. Thus ended my first attempt
to convert a pupil to the Gospel of Three Dimensions.
§ 22.—_How I then tried to diffuse the Theory of Three Dimensions by
other means, and of the result._
My failure with my Grandson did not encourage me to communicate my secret
to others of my household; yet neither was I led by it to despair of
success. Only I saw that I must not wholly rely on the catch-phrase
“Upward, not Northward,” but must rather endeavour to seek a
demonstration by setting before the public a clear view of the whole
subject; and for this purpose it seemed necessary to resort to writing.
So I devoted several months in privacy to the composition of a treatise
on the mysteries of Three Dimensions. Only, with the view of evading the
Law, if possible, I spoke not of a physical Dimension, but of a
Thoughtland whence, in theory, a Figure could look down upon Flatland and
see simultaneously the insides of all things, and where it was possible
that there might be supposed to exist a Figure environed, as it were,
with six Squares, and containing eight terminal Points. But in writing
this book I found myself sadly hampered by the impossibility of drawing
such diagrams as were necessary for my purpose; for of course, in our
country of Flatland, there are no tablets but Lines, and no diagrams but
Lines, all in one straight Line and only distinguishable by difference of
size and brightness; so that, when I had finished my treatise (which I
entitled “Through Flatland to Thoughtland”) I could not feel certain that
many would understand my meaning.
Meanwhile my life was under a cloud. All pleasures palled upon me; all
sights tantalized and tempted me to outspoken treason, because I could
not but compare what I saw in Two Dimensions with what it really was if
seen in Three, and could hardly refrain from making my comparisons aloud.
I neglected my clients and my own business to give myself to the
contemplation of the mysteries which I had once beheld, yet which I could
impart to no one, and found daily more difficult to reproduce even before
my own mental vision.
One day, about eleven months after my return from Spaceland, I tried to
see a Cube with my eye closed, but failed; and though I succeeded
afterwards, I was not then quite certain (nor have I been ever
afterwards) that I had exactly realized the original. This made me more
melancholy than before, and determined me to take some step; yet what, I
knew not. I felt that I would have been willing to sacrifice my life for
the Cause, if thereby I could have produced conviction. But if I could
not convince my Grandson, how could I convince the highest and most
developed Circles in the land?
And yet at times my spirit was too strong for me, and I gave vent to
dangerous utterances. Already I was considered heterodox if not
treasonable, and I was keenly alive to the dangers of my position;
nevertheless I could not at times refrain from bursting out into
suspicious or half-seditious utterances, even among the highest Polygonal
and Circular society. When, for example, the question arose about the
treatment of those lunatics who said that they had received the power of
seeing the insides of things, I would quote the saying of an ancient
Circle, who declared that prophets and inspired people are always
considered by the majority to be mad; and I could not help occasionally
dropping such expressions as “the eye that discerns the interiors of
things,” and “the all-seeing land:” once or twice I even let fall the
forbidden terms “the Third and Fourth Dimensions.” At last, to complete a
series of minor indiscretions, at a meeting of our Local Speculative
Society held at the palace of the Prefect himself,—some extremely silly
person having read an elaborate paper exhibiting the precise reasons why
Providence has limited the number of Dimensions to Two, and why the
attribute of omnividence is assigned to the Supreme alone—I so far forgot
myself as to give an exact account of the whole of my voyage with the
Sphere into Space, and to the Assembly Hall in our Metropolis, and then
to Space again, and of my return home, and of everything that I had seen
and heard in fact or vision. At first, indeed, I pretended that I was
describing the imaginary experiences of a fictitious person; but my
enthusiasm soon forced me to throw off all disguise, and finally, in a
fervent peroration, I exhorted all my hearers to divest themselves of
prejudice and to become believers in the Third Dimension.
Need I say that I was at once arrested and taken before the Council?
Next morning, standing in the very place where but a very few months ago
the Sphere had stood in my company, I was allowed to begin and to
continue my narration unquestioned and uninterrupted. But from the first
I foresaw my fate; for the President, noting that a guard of the better
sort of Policemen was in attendance, of angularity little, if at all,
under 55°, ordered them to be relieved before I began my defence, by an
inferior class of 2° or 3°. I knew only too well what that meant. I was
to be executed or imprisoned, and my story was to be kept secret from the
world by the simultaneous destruction of the officials who had heard it;
and, this being the case, the President desired to substitute the cheaper
for the more expensive victims.
After I had concluded my defence, the President, perhaps perceiving that
some of the junior Circles had been moved by my evident earnestness,
asked me two questions:—
1. Whether I could indicate the direction which I meant when I used the
words “Upward, not Northward”?
2. Whether I could by any diagrams or descriptions (other than the
enumeration of imaginary sides and angles) indicate the Figure I was
pleased to call a Cube?
I declared that I could say nothing more, and that I must commit myself
to the Truth, whose cause would surely prevail in the end.
The President replied that he quite concurred in my sentiment, and that I
could not do better. I must be sentenced to perpetual imprisonment; but
if the Truth intended that I should emerge from prison and evangelize the
world, the Truth might be trusted to bring that result to pass. Meanwhile
I should be subjected to no discomfort that was not necessary to preclude
escape, and, unless I forfeited the privilege by misconduct, I should be
occasionally permitted to see my brother, who had preceded me to my
prison.
Seven years have elapsed and I am still a prisoner, and—if I except the
occasional visits of my brother—debarred from all companionship save that
of my jailers. My brother is one of the best of Squares, just, sensible,
cheerful, and not without fraternal affection; yet I must confess that my
weekly interviews, at least in one respect, cause me the bitterest pain.
He was present when the Sphere manifested himself in the Council Chamber;
he saw the Sphere’s changing sections; he heard the explanation of the
phenomena then given to the Circles. Since that time, scarcely a week has
passed during seven whole years, without his hearing from me a repetition
of the part I played in that manifestation, together with ample
descriptions of all the phenomena in Spaceland, and the arguments for the
existence of Solid things derivable from Analogy. Yet—I take shame to be
forced to confess it—my brother has not yet grasped the nature of the
Third Dimension, and frankly avows his disbelief in the existence of a
Sphere.
Hence I am absolutely destitute of converts, and, for aught that I can
see, the millennial Revelation has been made to me for nothing.
Prometheus up in Spaceland was bound for bringing down fire for mortals,
but I—poor Flatland Prometheus—lie here in prison for bringing down
nothing to my countrymen. Yet I exist in the hope that these memoirs, in
some manner, I know not how, may find their way to the minds of humanity
in Some Dimension, and may stir up a race of rebels who shall refuse to
be confined to limited Dimensionality.
That is the hope of my brighter moments. Alas, it is not always so.
Heavily weighs on me at times the burdensome reflection that I cannot
honestly say I am confident as to the exact shape of the once-seen,
oft-regretted Cube; and in my nightly visions the mysterious precept,
“Upward, not Northward,” haunts me like a soul-devouring Sphinx. It is
part of the martyrdom which I endure for the cause of the Truth that
there are seasons of mental weakness, when Cubes and Spheres flit away
into the background of scarce-possible existences; when the Land of Three
Dimensions seems almost as visionary as the Land of One or None; nay,
when even this hard wall that bars me from my freedom, these very tablets
on which I am writing, and all the substantial realities of Flatland
itself, appear no better than the offspring of a diseased imagination, or
the baseless fabric of a dream.
[Illustration: THE END OF FLATLAND]
Footnotes
[1]“What need of a certificate?” a Spaceland critic may ask: “Is not the
procreation of a Square Son a certificate from Nature herself,
proving the Equal-sidedness of the Father?” I reply that no Lady of
any position will marry an uncertified Triangle. Square offspring has
sometimes resulted from a slightly Irregular Triangle: but in almost
every such case the Irregularity of the first generation is visited
on the third; which either fails to attain the Pentagonal rank, or
relapses to the Triangular.
[2]When I was in Spaceland I understood that some of your Priestly
Circles have in the same way a separate entrance for Villagers,
Farmers, and Teachers of Board Schools (_Spectator_, Sept. 1884, p.
1255) that they may “approach in a becoming and respectful manner.”
[3]When I say “sitting,” of course I do not mean any change of attitude
such as you in Spaceland signify by that word; for as we have no
feet, we can no more “sit” nor “stand” (in your sense of the word)
than one of your soles or flounders.
Nevertheless, we perfectly well recognise the different mental states
of volition implied in “lying,” “sitting,” and “standing,” which are
to some extent indicated to a beholder by a slight increase of lustre
corresponding to the increase of volition.
But on this, and a thousand other kindred subjects, time forbids me
to dwell.
LONDON: R. CLAY, SONS, AND TAYLOR, PRINTERS.
Transcriber’s Notes
--This eBook represents the text of the first printed edition.
--Retained publisher information from the printed copy (the electronic
edition is in the public domain in the country of publication).
--Corrected some palpable typos.
--In the text versions only, text in italics is delimited by
_underscores_; superscripts are preceded by a ^caret.
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