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Title: Flatland: A Romance of Many Dimensions

Author: Edwin Abbott Abbott

Release date: January 1, 1995 [eBook #201]
Most recently updated: June 26, 2022

Language: English

Other information and formats: www.gutenberg.org/ebooks/201

*** START OF THE PROJECT GUTENBERG EBOOK FLATLAND: A
ROMANCE OF MANY DIMENSIONS ***

Flatland: A Romance of Many
Dimensions
Edwin A. Abbott (1838-1926.
English scholar, theologian, and writer.)

With Illustrations by the Author, A SQUARE (Edwin A. Abbott)

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

Preface to the Second and Revised Edition, 1884.
By the Editor

If my poor Flatland friend retained the vigour of mind which he enjoyed
when he began to compose these Memoirs, I should not now need to represent
him in this preface, in which he desires, firstly, to return his thanks to his
readers and critics in Spaceland, whose appreciation has, with unexpected
celerity, required a second edition of his work; secondly, to apologize for
certain errors and misprints (for which, however, he is not entirely responsible);
and, thirdly, to explain one or two misconceptions. But he is not the Square he
once was. Years of imprisonment, and the still heavier burden of general

incredulity and mockery, have combined with the natural decay of old age to
erase from his mind many of the thoughts and notions, and much also of the
terminology, which he acquired during his short stay in Spaceland. He has,
therefore, requested me to reply in his behalf to two special objections, one of
an intellectual, the other of a moral nature.

The first objection is, that a Flatlander, seeing a Line, sees something that
must be THICK to the eye as well as LONG to the eye (otherwise it would not
be visible, if it had not some thickness); and consequently he ought (it is
argued) to acknowledge that his countrymen are not only long and broad, but
also (though doubtless in a very slight degree) THICK or HIGH. This objection
is plausible, and, to Spacelanders, almost irresistible, so that, I confess, when I
first heard it, I knew not what to reply. But my poor old friend's answer appears
to me completely to meet it.

"I admit," said he—when I mentioned to him this objection—"I admit the
truth of your critic's facts, but I deny his conclusions. It is true that we have
really in Flatland a Third unrecognized Dimension called 'height', just as it is
also true that you have really in Spaceland a Fourth unrecognized Dimension,
called by no name at present, but which I will call 'extra-height'. But we can no
more take cognizance of our 'height' than you can of your 'extra-height'. Even I
—who have been in Spaceland, and have had the privilege of understanding for
twenty-four hours the meaning of 'height'—even I cannot now comprehend it,
nor realize it by the sense of sight or by any process of reason; I can but
apprehend it by faith.

"The reason is obvious. Dimension implies direction, implies measurement,
implies the more and the less. Now, all our lines are EQUALLY and
INFINITESIMALLY thick (or high, whichever you like); consequently, there is
nothing in them to lead our minds to the conception of that Dimension. No
'delicate micrometer'—as has been suggested by one too hasty Spaceland critic
—would in the least avail us; for we should not know WHAT TO MEASURE,
NOR IN WHAT DIRECTION. When we see a Line, we see something that is
long and BRIGHT; BRIGHTNESS, as well as length, is necessary to the
existence of a Line; if the brightness vanishes, the Line is extinguished. Hence,
all my Flatland friends—when I talk to them about the unrecognized Dimension
which is somehow visible in a Line—say, 'Ah, you mean BRIGHTNESS': and
when I reply, 'No, I mean a real Dimension', they at once retort, 'Then measure
it, or tell us in what direction it extends'; and this silences me, for I can do

neither. Only yesterday, when the Chief Circle (in other words our High Priest)
came to inspect the State Prison and paid me his seventh annual visit, and when
for the seventh time he put me the question, 'Was I any better?' I tried to prove
to him that he was 'high', as well as long and broad, although he did not know it.
But what was his reply? 'You say I am "high"; measure my "high-ness" and I
will believe you.' What could I do? How could I meet his challenge? I was
crushed; and he left the room triumphant.

"Does this still seem strange to you? Then put yourself in a similar position.
Suppose a person of the Fourth Dimension, condescending to visit you, were to
say, 'Whenever you open your eyes, you see a Plane (which is of Two
Dimensions) and you INFER a Solid (which is of Three); but in reality you also
see (though you do not recognize) a Fourth Dimension, which is not colour nor
brightness nor anything of the kind, but a true Dimension, although I cannot
point out to you its direction, nor can you possibly measure it.' What would you
say to such a visitor? Would not you have him locked up? Well, that is my fate:
and it is as natural for us Flatlanders to lock up a Square for preaching the Third
Dimension, as it is for you Spacelanders to lock up a Cube for preaching the
Fourth. Alas, how strong a family likeness runs through blind and persecuting
humanity in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes—we
are all liable to the same errors, all alike the Slaves of our respective
Dimensional prejudices, as one of your Spaceland poets has said—

'One touch of Nature makes all worlds akin'."

[Note: The Author desires me to add, that the misconception of some of his
critics on this matter has induced him to insert in his dialogue with the Sphere,
certain remarks which have a bearing on the point in question, and which he
had previously omitted as being tedious and unnecessary.]

On this point the defence of the Square seems to me to be impregnable. I
wish I could say that his answer to the second (or moral) objection was equally
clear and cogent. It has been objected that he is a woman-hater; and as this
objection has been vehemently urged by those whom Nature's decree has
constituted the somewhat larger half of the Spaceland race, I should like to
remove it, so far as I can honestly do so. But the Square is so unaccustomed to
the use of the moral terminology of Spaceland that I should be doing him an
injustice if I were literally to transcribe his defence against this charge. Acting,
therefore, as his interpreter and summarizer, I gather that in the course of an
imprisonment of seven years he has himself modified his own personal views,

both as regards Women and as regards the Isosceles or Lower Classes.
Personally, he now inclines to the opinion of the Sphere that the Straight Lines
are in many important respects superior to the Circles. But, writing as a
Historian, he has identified himself (perhaps too closely) with the views
generally adopted by Flatland, and (as he has been informed) even by
Spaceland, Historians; in whose pages (until very recent times) the destinies of
Women and of the masses of mankind have seldom been deemed worthy of
mention and never of careful consideration.

In a still more obscure passage he now desires to disavow the Circular or
aristocratic tendencies with which some critics have naturally credited him.
While doing justice to the intellectual power with which a few Circles have for
many generations maintained their supremacy over immense multitudes of their
countrymen, he believes that the facts of Flatland, speaking for themselves
without comment on his part, declare that Revolutions cannot always be
suppressed by slaughter, and that Nature, in sentencing the Circles to
infecundity, has condemned them to ultimate failure—"and herein," he says, "I
see a fulfilment of the great Law of all worlds, that while the wisdom of Man
thinks it is working one thing, the wisdom of Nature constrains it to work
another, and quite a different and far better thing." For the rest, he begs his
readers not to suppose that every minute detail in the daily life of Flatland must
needs correspond to some other detail in Spaceland; and yet he hopes that,
taken as a whole, his work may prove suggestive as well as amusing, to those
Spacelanders of moderate and modest minds who—speaking of that which is of
the highest importance, but lies beyond experience—decline to say on the one
hand, "This can never be," and on the other hand, "It must needs be precisely
thus, and we know all about it."

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 I vainly tried to explain the nature of Flatland
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 shewed 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."

Section 1. Of the Nature of Flatland

I call our world Flatland, not because we call it so, but to make its nature
clearer to you, my happy readers, who are privileged to live in Space.

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares,
Pentagons, Hexagons, and other figures, instead of remaining fixed in their
places, move freely about, on or in the surface, but without the power of rising
above or sinking below it, very much like shadows—only hard and with
luminous edges—and you will then have a pretty correct notion of my country
and countrymen. Alas, a few years ago, I should have said "my universe": but
now my mind has been opened to higher views of things.

In such a country, you will perceive at once that it is impossible that there
should be anything of what you call a "solid" kind; but I dare say you will
suppose that we could at least distinguish by sight the Triangles, Squares, and
other figures, moving about as I have described them. On the contrary, we could
see nothing of the kind, not at least so as to distinguish one figure from another.

Nothing was visible, nor could be visible, to us, except Straight Lines; and the
necessity of this I will speedily demonstrate.

Place a penny on the middle of one of your tables in Space; and leaning over
it, look down upon it. It will appear a circle.

But now, drawing back to the edge of the table, gradually lower your eye
(thus bringing yourself more and more into the condition of the inhabitants of
Flatland), and you will find the penny becoming more and more oval to your
view, and at last when you have placed your eye exactly on the edge of the table
(so that you are, as it were, actually a Flatlander) the penny will then have
ceased to appear oval at all, and will have become, so far as you can see, a
straight line.

The same thing would happen if you were to treat in the same way a
Triangle, or Square, or any other figure cut out of pasteboard. As soon as you
look at it with your eye on the edge on the table, you will find that it ceases to
appear to you a figure, and that it becomes in appearance a straight line. Take
for example an equilateral Triangle—who represents with us a Tradesman of the
respectable class. Fig. 1 represents the Tradesman as you would see him while
you were bending over him from above; figs. 2 and 3 represent the Tradesman,
as you would see him if your eye were close to the level, or all but on the level
of the table; and if your eye were quite on the level of the table (and that is how
we see him in Flatland) you would see nothing but a straight line.

When I was in Spaceland I heard that your sailors have very similar
experiences while they traverse your seas and discern some distant island or
coast lying on the horizon. The far-off land may have bays, forelands, angles in
and out to any number and extent; yet at a distance you see none of these
(unless indeed your sun shines bright upon them revealing the projections and
retirements by means of light and shade), nothing but a grey unbroken line upon
the water.

Well, that is just what we see when one of our triangular or other
acquaintances comes toward us in Flatland. As there is neither sun with us, nor

any light of such a kind as to make shadows, we have none of the helps to the
sight that you have in Spaceland. If our friend comes closer to us we see his line
becomes larger; if he leaves us it becomes smaller: but still he looks like a
straight line; be he a Triangle, Square, Pentagon, Hexagon, Circle, what you
will—a straight Line he looks and nothing else.

You may perhaps ask how under these disadvantageous circumstances we
are able to distinguish our friends from one another: but the answer to this very
natural question will be more fitly and easily given when I come to describe the
inhabitants of Flatland. For the present let me defer this subject, and say a word
or two about the climate and houses in our country.

Section 2. Of the Climate and Houses in Flatland

As with you, so also with us, there are four points of the compass North,
South, East, and West.

There being no sun nor other heavenly bodies, it is impossible for us to
determine the North in the usual way; but we have a method of our own. By a
Law of Nature with us, there is a constant attraction to the South; and, although
in temperate climates this is very slight—so that even a Woman in reasonable
health can journey several furlongs northward without much difficulty—yet the
hampering effect of the southward attraction is quite sufficient to serve as a
compass in most parts of our earth. Moreover, the rain (which falls at stated
intervals) coming always from the North, is an additional assistance; and in the
towns we have the guidance of the houses, which of course have their side-
walls running for the most part North and South, so that the roofs may keep off
the rain from the North. In the country, where there are no houses, the trunks of
the trees serve as some sort of guide. Altogether, we have not so much difficulty
as might be expected in determining our bearings.

Yet in our more temperate regions, in which the southward attraction is
hardly felt, walking sometimes in a perfectly desolate plain where there have
been no houses nor trees to guide me, I have been occasionally compelled to

remain stationary for hours together, waiting till the rain came before
continuing my journey. On the weak and aged, and especially on delicate
Females, the force of attraction tells much more heavily than on the robust of
the Male Sex, so that it is a point of breeding, if you meet a Lady in the street,
always to give her the North side of the way—by no means an easy thing to do
always at short notice when you are in rude health and in a climate where it is
difficult to tell your North from your South.

Windows there are none in our houses: for the light comes to us alike in our
homes and out of them, by day and by night, equally at all times and in all
places, whence we know not. It was in old days, with our learned men, an
interesting and oft-investigated question, "What is the origin of light?" and the
solution of it has been repeatedly attempted, with no other result than to crowd
our lunatic asylums with the would-be solvers. Hence, after fruitless attempts to
suppress such investigations indirectly by making them liable to a heavy tax,
the Legislature, in comparatively recent times, absolutely prohibited them. I—
alas, I alone in Flatland—know now only too well the true solution of this
mysterious problem; but my knowledge cannot be made intelligible to a single
one of my countrymen; and I am mocked at—I, the sole possessor of the truths
of Space and of the theory of the introduction of Light from the world of three
Dimensions—as if I were the maddest of the mad! But a truce to these painful
digressions: let me return to our houses.

The most common form for the construction of a house is five-sided or
pentagonal, as in the annexed figure. The two Northern sides RO, OF, constitute
the roof, and for the most part have no doors; on the East is a small door for the
Women; on the West a much larger one for the Men; the South side or floor is
usually doorless.

Square and triangular houses are not allowed, and for this reason. The angles
of a Square (and still more those of an equilateral Triangle), being much more
pointed than those of a Pentagon, and the lines of inanimate objects (such as
houses) being dimmer than the lines of Men and Women, it follows that there is
no little danger lest the points of a square or triangular house residence might
do serious injury to an inconsiderate or perhaps absent-minded traveller
suddenly therefore, running against them: and as early as the eleventh century
of our era, triangular houses were universally forbidden by Law, the only
exceptions being fortifications, powder-magazines, barracks, and other state

buildings, which it is not desirable that the general public should approach
without circumspection.

At this period, square houses were still everywhere permitted, though
discouraged by a special tax. But, about three centuries afterwards, the Law
decided that in all towns containing a population above ten thousand, the angle
of a Pentagon was the smallest house-angle that could be allowed consistently
with the public safety. The good sense of the community has seconded the
efforts of the Legislature; and now, even in the country, the pentagonal
construction has superseded every other. It is only now and then in some very
remote and backward agricultural district that an antiquarian may still discover
a square house.

Section 3. Concerning the Inhabitants of Flatland

The greatest length or breadth of a full grown inhabitant of Flatland may be
estimated at about eleven of your inches. Twelve inches may be regarded as a
maximum.

Our Women are Straight Lines.

Our Soldiers and Lowest Classes of Workmen are Triangles with two equal
sides, each about eleven inches long, and a base or third side so short (often not
exceeding half an inch) that they form at their vertices a very sharp and
formidable angle. Indeed when their bases are of the most degraded type (not
more than the eighth part of an inch in size), they can hardly be distinguished
from Straight Lines or Women; so extremely pointed are their vertices. With us,
as with you, these Triangles are distinguished from others by being called
Isosceles; and by this name I shall refer to them in the following pages.

Our Middle Class consists of Equilateral or Equal-Sided Triangles.

Our Professional Men and Gentlemen are Squares (to which class I myself
belong) and Five-Sided Figures or Pentagons.

Next above these come the Nobility, of whom there are several degrees,
beginning at Six-Sided Figures, or Hexagons, and from thence rising in the
number of their sides till they receive the honourable title of Polygonal, or
many-sided. Finally when the number of the sides becomes so numerous, and
the sides themselves so small, that the figure cannot be distinguished from a
circle, he is included in the Circular or Priestly order; and this is the highest
class of all.

It is a Law of Nature with us that a male child shall have one more side than
his father, so that each generation shall rise (as a rule) one step in the scale of
development and nobility. Thus the son of a Square is a Pentagon; the son of a
Pentagon, a Hexagon; and so on.

But this rule applies not always to the Tradesmen, and still less often to the
Soldiers, and to the Workmen; who indeed can hardly be said to deserve the
name of human Figures, since they have not all their sides equal. With them
therefore the Law of Nature does not hold; and the son of an Isosceles (i.e. a
Triangle with two sides equal) remains Isosceles still. Nevertheless, all hope is
not shut out, even from the Isosceles, that his posterity may ultimately rise
above his degraded condition. For, after a long series of military successes, or
diligent and skilful labours, it is generally found that the more intelligent among
the Artisan and Soldier classes manifest a slight increase of their third side or
base, and a shrinkage of the two other sides. Intermarriages (arranged by the
Priests) between the sons and daughters of these more intellectual members of
the lower classes generally result in an offspring approximating still more to the
type of the Equal-Sided Triangle.

Rarely—in proportion to the vast numbers of Isosceles births—is a genuine
and certifiable Equal-Sided Triangle produced from Isosceles parents. [Note:
"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.] Such a birth requires, as its antecedents, not only a series of
carefully arranged intermarriages, but also a long, continued exercise of
frugality and self-control on the part of the would-be ancestors of the coming
Equilateral, and a patient, systematic, and continuous development of the
Isosceles intellect through many generations.

The birth of a True Equilateral Triangle from Isosceles parents is the subject
of rejoicing in our country for many furlongs around. After a strict examination
conducted by the Sanitary and Social Board, the infant, if certified as Regular,
is with solemn ceremonial admitted into the class of Equilaterals. He is then
immediately taken from his proud yet sorrowing parents and adopted by some
childless Equilateral, who is bound by oath never to permit the child henceforth
to enter his former home or so much as to look upon his relations again, for fear
lest the freshly developed organism may, by force of unconscious imitation, fall
back again into his hereditary level.

The occasional emergence of an Equilateral from the ranks of his serf-born
ancestors is welcomed, not only by the poor serfs themselves, as a gleam of
light and hope shed upon the monotonous squalor of their existence, but also by
the Aristocracy at large; for all the higher classes are well aware that these rare
phenomena, while they do little or nothing to vulgarize their own privileges,
serve as a most useful barrier against revolution from below.

Had the acute-angled rabble been all, without exception, absolutely destitute
of hope and of ambition, they might have found leaders in some of their many
seditious outbreaks, so able as to render their superior numbers and strength too
much even for the wisdom of the Circles. But a wise ordinance of Nature has
decreed that, in proportion as the working-classes increase in intelligence,
knowledge, and all virtue, in that same proportion their acute angle (which
makes them physically terrible) shall increase also and approximate to the
comparatively harmless angle of the Equilateral Triangle. Thus, in the most

brutal and formidable of the soldier class—creatures almost on a level with
women in their lack of intelligence—it is found that, as they wax in the mental
ability necessary to employ their tremendous penetrating power to advantage,
so do they wane in the power of penetration itself.

How admirable is this Law of Compensation! And how perfect a proof of
the natural fitness and, I may almost say, the divine origin of the aristocratic
constitution of the States in Flatland! By a judicious use of this Law of Nature,
the Polygons and Circles are almost always able to stifle sedition in its very
cradle, taking advantage of the irrepressible and boundless hopefulness of the
human mind. Art also comes to the aid of Law and Order. It is generally found
possible—by a little artificial compression or expansion on the part of the State
physicians—to make some of the more intelligent leaders of a rebellion
perfectly Regular, and to admit them at once into the privileged classes; a much
larger number, who are still below the standard, allured by the prospect of being
ultimately ennobled, are induced to enter the State Hospitals, where they are
kept in honourable confinement for life; one or two alone of the more obstinate,
foolish, and hopelessly irregular are led to execution.

Then the wretched rabble of the Isosceles, planless and leaderless, are either
transfixed without resistance by the small body of their brethren whom the
Chief Circle keeps in pay for emergencies of this kind; or else more often, by
means of jealousies and suspicions skilfully fomented among them by the
Circular party, they are stirred to mutual warfare, and perish by one another's
angles. No less than one hundred and twenty rebellions are recorded in our
annals, besides minor outbreaks numbered at two hundred and thirty-five; and
they have all ended thus.

Section 4. Concerning the Women

If our highly pointed Triangles of the Soldier class are formidable, it may be
readily inferred that far more formidable are our Women. For if a Soldier is a
wedge, a Woman is a needle; being, so to speak, ALL point, at least at the two
extremities. Add to this the power of making herself practically invisible at will,

and you will perceive that a Female, in Flatland, is a creature by no means to be
trifled with.

But here, perhaps, some of my younger Readers may ask HOW a woman in
Flatland can make herself invisible. This ought, I think, to be apparent without
any explanation. However, a few words will make it clear to the most
unreflecting.

Place a needle on a table. Then, with your eye on the level of the table, look
at it side-ways, and you see the whole length of it; but look at it end-ways, and
you see nothing but a point, it has become practically invisible. Just so is it with
one of our Women. When her side is turned towards us, we see her as a straight
line; when the end containing her eye or mouth—for with us these two organs
are identical—is the part that meets our eye, then we see nothing but a highly
lustrous point; but when the back is presented to our view, then—being only
sub-lustrous, and, indeed, almost as dim as an inanimate object—her hinder
extremity serves her as a kind of Invisible Cap.

The dangers to which we are exposed from our Women must now be
manifest to the meanest capacity in Spaceland. If even the angle of a
respectable Triangle in the middle class is not without its dangers; if to run
against a Working Man involves a gash; if collision with an officer of the
military class necessitates a serious wound; if a mere touch from the vertex of a
Private Soldier brings with it danger of death;—what can it be to run 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" and not by the Men's or Western door. [Note: 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."]

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
civilized States no female is suffered to stand in any public place without
swaying her back from right to left. This practice has been universal among
ladies of any pretensions to breeding in all well-governed States, as far back as
the memory of Figures can reach. It is considered a disgrace to any State that

legislation should have to enforce what ought to be, and is in every respectable
female, a natural instinct. The rhythmical and, if I may so say, well-modulated
undulation of the back in our ladies of Circular rank is envied and imitated by
the wife of a common Equilateral, who can achieve nothing beyond a mere
monotonous swing, like the ticking of a pendulum; and the regular tick of the
Equilateral is no less admired and copied by the wife of the progressive and
aspiring Isosceles, in the females of whose family no "back-motion" of any kind
has become as yet a necessity of life. Hence, in every family of position and
consideration, "back motion" is as prevalent as time itself; and the husbands and
sons in these households enjoy immunity at least from invisible attacks.

Not that it must be for a moment supposed that our Women are destitute of
affection. But unfortunately the passion of the moment predominates, in the
Frail Sex, over every other consideration. This is, of course, a necessity arising
from their unfortunate conformation. For as they have no pretensions to an
angle, being inferior in this respect to the very lowest of the Isosceles, they are
consequently wholly devoid of brain-power, and have neither reflection,
judgment nor forethought, and hardly any memory. Hence, in their fits of fury,
they remember no claims and recognize no distinctions. I have actually known a
case where a Woman has exterminated her whole household, and half an hour
afterwards, when her rage was over and the fragments swept away, has asked
what has become of her husband and 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 simulation, these reckless creatures too
often neglect the prescribed construction of the women's apartments, or irritate
their wives by ill-advised expressions out of doors, which they refuse
immediately to retract. Moreover a blunt and stolid regard for literal truth

indisposes them to make those lavish promises by which the more judicious
Circle can in a moment pacify his consort. The result is massacre; not, however,
without its advantages, as it eliminates the more brutal and troublesome of the
Isosceles; and by many of our Circles the destructiveness of the Thinner Sex is
regarded as one among many providential arrangements for suppressing
redundant population, and nipping Revolution in the bud.

Yet even in our best regulated and most approximately Circular families I
cannot say that the ideal of family life is so high as with you in Spaceland.
There is peace, in so far as the absence of slaughter may be called by that name,
but there is necessarily little harmony of tastes or pursuits; and the cautious
wisdom of the Circles has ensured safety at the cost of domestic comfort. In
every Circular or Polygonal household it has been a habit from time
immemorial—and now has become a kind of instinct among the women of our
higher classes—that the mothers and daughters should constantly keep their
eyes and mouths towards their husband and his male friends; and for a lady in a
family of distinction to turn her back upon her husband would be regarded as a
kind of portent, involving loss of STATUS. But, as I shall soon shew, this
custom, though it has the advantage of safety, is not without 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.

Section 5. Of our Methods of Recognizing one another

You, who are blessed with shade as well as light, you, who are gifted with
two eyes, endowed with a knowledge of perspective, and charmed with the
enjoyment of various colours, you, who can actually SEE an angle, and
contemplate the complete circumference of a circle in the happy region of the
Three Dimensions—how shall I make clear to you the extreme difficulty which
we in Flatland experience in recognizing one another's configuration?

Recall what I told you above. All beings in Flatland, animate 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
Mr. Jones."

Let not my Reader however suppose that "feeling" is with us the tedious
process that it would be with you, or that we find it necessary to feel right round
all the sides of every individual before we determine the class to which he
belongs. Long practice and training, begun in the schools and continued in the
experience of daily life, enable us to discriminate at once by the sense of touch,
between the angles of an equal-sided Triangle, Square, and Pentagon; and I
need not say that the brainless vertex of an acute-angled Isosceles is obvious to
the dullest touch. It is therefore not necessary, as a rule, to do more than feel a
single angle of an individual; and this, once ascertained, tells us the class of the
person whom we are addressing, unless indeed he belongs to the higher sections
of the nobility. There the difficulty is much greater. Even a Master of Arts in our
University of Wentbridge has been known to confuse a ten-sided with a twelve-
sided Polygon; and there is hardly a Doctor of Science in or out of that famous
University who could pretend to decide promptly and unhesitatingly between a
twenty-sided and a twenty-four sided member of the Aristocracy.

Those of my readers who recall the extracts I gave above from the
Legislative code concerning Women, will readily perceive that the process of
introduction by contact requires some care and discretion. Otherwise the angles
might inflict on the unwary 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 occured to his great-great-great-
Grandfather, a respectable Working Man with an angle or brain of 59 degrees
30 minutes. According to his account, my 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
degrees, and not till the lapse of five generations was the lost ground recovered,
the full 60 degrees attained, and the Ascent from the Isosceles finally achieved.
And all this series of calamities from one little accident in the process of
Feeling.

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 degrees is reached, when the condition of serfdom is quitted, and
the freeman enters the class of Regulars.

Consequently, Nature herself supplies us with an ascending scale or
Alphabet of angles for half a degree up to 60 degrees, 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 degrees. 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 Specimen is lost,
partly in the expenditure for food, and partly in the diminished accuracy of the
angles, which are impaired after a few weeks of constant "feeling". Nor must
we forget to add, in enumerating the advantages of the more expensive system,
that it tends, though slightly yet perceptibly, to the diminution of the redundant
Isosceles population—an object which every statesman in Flatland constantly
keeps in view. On the whole therefore—although I am not ignorant that, in
many popularly elected School Boards, there is a reaction in favour of "the
cheap system" as it is called—I am myself disposed to think that this is one of
the many cases in which expense is the truest economy.

But I must not allow questions of School Board politics to divert me from
my subject. Enough has been said, I trust, to shew that Recognition by Feeling

is not so tedious or indecisive a process as might have been supposed; and it is
obviously more trustworthy than Recognition by hearing. Still there remains, as
has been pointed out above, the objection that this method is not without
danger. For this reason many in the Middle and Lower classes, and all without
exception in the Polygonal and Circular orders, prefer a third method, the
description of which shall be reserved for the next section.

Section 6. Of Recognition by Sight

I am about to appear very inconsistent. In 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
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.

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 AB RECEDE RAPIDLY INTO THE FOG and what

appear to me as the Merchant's extremities, viz. D and E, will be VERY DIM
INDEED.

On the other hand in the case of (2) the Physician, though I shall here also
see a line (D'A'E') with a bright centre (A'), yet it will shade away LESS
RAPIDLY 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 not be NOT SO DIM as the extremities of the Merchant.

The Reader will probably understand from these two instances how—after a
very long training supplemented by constant experience—it is possible for the
well-educated classes among us to discriminate with fair accuracy between the
middle and lowest orders, by the sense of sight. If my Spaceland Patrons have
grasped this general conception, so far as to conceive the possibility of it and
not to reject my account as altogether incredible—I shall have attained all I can
reasonably expect. Were I to attempt further details I should only perplex. Yet
for the sake of the young and inexperienced, who may perchance infer—from
the two simple instances I have given above, of the manner in which I should
recognize my Father and my Sons—that Recognition by sight is an easy affair,
it may be needful to point out that in actual life most of the problems of Sight
Recognition are far more subtle and complex.

If for example, when my Father, the Triangle, approaches me, he happens to
present his side to me instead of his angle, then, until I have asked him to rotate,
or until I have edged my eye 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 towards the extremities C and D.

But I must not give way to the temptation of enlarging on these topics. The
meanest mathematician in Spaceland will readily believe me when I assert that
the problems of life, which present themselves to the well-educated—when they
are themselves in motion, rotating, advancing or retreating, and at the same time
attempting to discriminate by the sense of sight between a number of Polygons
of high rank moving in different directions, as for example in a ball-room or
conversazione—must be of a nature to task the angularity of the most
intellectual, and amply justify the rich endowments of the Learned Professors of
Geometry, both Static and Kinetic, in the illustrious University of Wentbridge,
where the Science and Art of Sight Recognition are regularly taught to large
classes of the ELITE of the States.

It is only a few of the scions of our noblest and wealthiest houses, who are
able to give the time and money necessary for the thorough prosecution of this
noble and valuable Art. Even to me, a Mathematician of no mean standing, and
the Grandfather of two most hopeful and perfectly regular Hexagons, to find
myself in the midst of a crowd of rotating Polygons of the higher classes, is
occasionally very perplexing. And of course to a common Tradesman, or Serf,
such a sight is almost as unintelligible as it would be to you, my Reader, were
you suddenly transported 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 lipspeech 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 shews that the offspring of such unfortunate
and ill-endowed parents is generally itself unfortunate, if not positively
Irregular.

It is from these specimens of the refuse of our Nobility that the great
Tumults and Seditions of past ages have generally derived their leaders; and so
great is the mischief thence arising that an increasing minority of our more
progressive Statesmen are of opinion that true mercy would dictate their entire
suppression, by enacting that all who fail to pass the Final Examination of the

University should be either imprisoned for life, or extinguished by a painless
death.

But I find myself digressing into the subject of Irregularities, a matter of
such vital interest that it demands a separate section.

Section 7. Concerning Irregular Figures

Throughout the previous pages I have been assuming—what perhaps should
have been laid down at the beginning as a distinct and fundamental proposition
—that every human being in Flatland is a Regular Figure, that is to say of
regular construction. By this I mean that a Woman must not only be a line, but a
straight line; that an Artisan or Soldier must have two of his sides equal; that
Tradesmen must have three sides equal; Lawyers (of which class I am a humble
member), four sides equal, and generally, that in every Polygon, all the sides
must be equal.

The 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 two feet or a little more. But
the size of our sides is not under consideration. I am speaking of the
EQUALITY of sides, and it does not need much reflection to see that the whole
of the social life in Flatland rests upon the fundamental fact that Nature wills all
Figures to have their sides equal.

If our sides were unequal our angles might be unequal. Instead of its being
sufficient to feel, or estimate by sight, a single angle in order to determine the
form of an individual, it would be necessary to ascertain each angle by the
experiment of Feeling. But life would be too short for such a tedious grouping.
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 everyone knows to an inch or two the area occupied by an adult
Triangle: but imagine that your Tradesman drags behind his regular and
respectable vertex, a parallelogram of twelve or thirteen inches in diagonal:—
what are you to do with such a monster sticking fast in your house door?

But I am insulting the intelligence of my Readers by accumulating details
which must be patent to everyone who enjoys the advantages of a Residence in
Spaceland. Obviously the measurements of a single angle would no longer be
sufficient under such portentous circumstances; one's whole life would be taken
up in feeling or surveying the perimeter of one's acquaintances. Already the
difficulties of avoiding a collision in a crowd are enough to tax the sagacity of
even a well-educated Square; but if no one could calculate the Regularity of a
single figure in the company, all would be chaos and confusion, and the
slightest panic would cause serious injuries, or—if there happened to be any
Women or Soldiers present—perhaps considerable loss of life.

Expediency therefore concurs with Nature in stamping the seal of its
approval upon Regularity of conformation: nor has the Law been backward in
seconding their efforts. "Irregularity of Figure" means with us the same as, or
more than, a combination of moral obliquity and criminality with you, and is
treated accordingly. There are not wanting, it is true, some promulgators of
paradoxes who maintain that there is no necessary connection between
geometrical and moral Irregularity. "The Irregular", they say, "is from his birth
scouted by his own parents, derided by his brothers and sisters, neglected by the
domestics, scorned and suspected by society, and excluded from all posts of
responsibility, trust, and useful activity. His every movement is jealously
watched by the police till he comes of age and presents himself for inspection;
then he is either destroyed, if he is found to exceed the fixed margin of
deviation, 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 by some States, where an infant whose angle deviates by half
a degree from the correct angularity is summarily destroyed at birth. Some of
our highest and ablest men, men of real genius, have during their earliest days
laboured under deviations as great as, or even greater than, forty-five minutes:
and the loss of their precious lives would have been an irreparable injury to the
State. The art of healing also has achieved some of its most glorious triumphs in
the compressions, extensions, trepannings, colligations, and other surgical or
diaetetic operations by which Irregularity has been partly or wholly cured.
Advocating therefore a VIA MEDIA, I would lay down no fixed or absolute
line of demarcation; but at the period when the frame is just beginning to set,
and when the Medical Board has reported that recovery is improbable, I would
suggest that the Irregular offspring be painlessly and mercifully consumed.

Section 8. Of the Ancient Practice of Painting

If my Readers have followed me with any attention up to this point, they
will not be surprised to hear that life is somewhat dull in Flatland. I do not, of
course, mean that there are not battles, conspiracies, tumults, factions, and all
those other phenomena which are supposed to make History interesting; nor
would I deny that the strange mixture of the problems of life and the problems
of Mathematics, continually inducing conjecture and giving the opportunity of
immediate verification, imparts to our existence a zest which you in Spaceland
can hardly comprehend. I speak now from the aesthetic and artistic point of
view when I say that life with us is dull; aesthetically and artistically, very dull
indeed.

How can it be otherwise, when all one's prospect, all one's landscapes,
historical pieces, portraits, flowers, still life, are nothing but a single line, with
no varieties except degrees of brightness and obscurity?

It was not always thus. Colour, if Tradition speaks the truth, once for the
space of half a dozen centuries or more, threw a transient splendour over the
lives of our ancestors in the remotest ages. Some private individual—a
Pentagon whose name is variously reported—having casually discovered the
constituents of the simpler colours and a rudimentary method of painting, is
said to have begun 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 aesthetic point of view, those ancient days of the Colour
Revolt were the glorious childhood of Art in Flatland—a childhood, alas, that
never ripened into manhood, nor even reached the blossom of youth. To live
was then in itself a delight, because living implied seeing. Even at a small party,
the company was a pleasure to behold; the richly varied hues of the assembly in
a church or theatre are said to have more than once proved too distracting for
our greatest teachers and actors; but most ravishing of all is said to have been
the unspeakable magnificence of a military review.

The sight of a line of battle of twenty thousand Isosceles suddenly facing
about, and exchanging the sombre black of their bases for the orange and purple
of the two sides including their acute angle; the militia of the Equilateral

Triangles tricoloured in red, white, and blue; the mauve, ultra-marine, gamboge,
and burnt umber of the Square artillerymen rapidly rotating near their vermilion
guns; the dashing and flashing of the five-coloured and six-coloured Pentagons
and Hexagons careering across the field in their offices of surgeons,
geometricians and aides-de-camp—all these may well have been sufficient to
render credible the famous story how an illustrious Circle, overcome by the
artistic beauty of the forces under his command, threw aside his marshal's baton
and his royal crown, exclaiming that he henceforth exchanged them for the
artist's pencil. How great and glorious the sensuous development of these days
must have been is in part indicated by the very language and vocabulary of the
period. 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.

Section 9. Of the Universal Colour Bill

But meanwhile the intellectual Arts were fast decaying.

The Art of Sight Recognition, being no longer needed, was no longer
practised; and the studies of Geometry, Statics, Kinetics, and other kindred
subjects, came soon to be considered superfluous, and fell into disrespect and
neglect even at our University. The inferior Art of Feeling speedily experienced
the same fate at our Elementary Schools. Then the Isosceles classes, asserting
that the Specimens were no longer used nor needed, and refusing to pay the
customary tribute from the Criminal classes to the service of Education, waxed
daily more numerous and more insolent on the strength of their immunity from
the old burden which had formerly exercised the twofold wholesome effect of
at once taming their brutal nature and thinning their excessive numbers.

Year by year the Soldiers and Artisans began more vehemently to assert—
and with increasing truth—that there was no great difference between them and
the very highest class of Polygons, now that they were raised to an equality with

the latter, and enabled to grapple with all the difficulties and solve all the
problems of life, whether Statical or Kinetical, by the simple process of Colour
Recognition. Not content with the natural neglect into which Sight Recognition
was falling, they began boldly to demand the legal prohibition of all
"monopolizing and aristocratic Arts" and the consequent abolition of all
endowments for the studies of Sight Recognition, Mathematics, and Feeling.
Soon, they began to insist that inasmuch as Colour, which was a second Nature,
had destroyed the need of aristocratic distinctions, the Law should follow in the
same path, and that henceforth all individuals and all classes should be
recognized as absolutely equal and entitled to equal rights.

Finding the higher Orders wavering and undecided, the leaders of the
Revolution advanced still further in their requirements, and at last demanded
that all classes alike, the Priests and the Women not excepted, should do
homage to Colour by submitting to be painted. When it was objected that
Priests and Women had no sides, they retorted that Nature and Expediency
concurred in dictating that the front half of every human being (that is to say,
the half containing his eye and mouth) should be distinguishable from his
hinder half. They therefore brought before a general and extraordinary
Assembly of all the States of Flatland a Bill proposing that in every Woman the
half containing the eye and mouth should be coloured red, and the other half
green. The Priests were to be painted in the same way, red being applied to that
semicircle in which the eye and mouth formed the middle point; while the other
or hinder semicircle was to be coloured green.

There was no little cunning in this proposal, which indeed emanated not
from any Isosceles—for no being so degraded would have 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.

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 of 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 the other classes by
abstinence from the popular fashion.

Now therefore the artful Irregular whom I described above as the real author
of this diabolical Bill, determined at one blow to lower the status of the
Hierarchy by forcing them to submit to the pollution of Colour, and at the same
time to destroy their domestic opportunities of training in the Art of Sight
Recognition, so as to enfeeble their intellects by depriving them of their pure
and colourless homes. Once subjected to the chromatic taint, every parental and
every childish Circle would demoralize each other. Only in discerning between
the Father and the Mother would the Circular infant find problems for the
exercise of 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.

Section 10. Of the Suppression of the Chromatic Sedition

The agitation for the Universal Colour Bill continued for three years; and up
to the last moment of that period it seemed as though Anarchy were destined to
triumph.

A whole army of Polygons, who turned out to fight as private soldiers, was
utterly annihilated by a superior force of Isosceles Triangles—the Squares and
Pentagons meanwhile remaining neutral. Worse than all, some of the ablest
Circles fell a prey to conjugal fury. Infuriated by political animosity, the wives
in many a noble household wearied their lords with prayers to give up their
opposition to the Colour Bill; and some, finding their entreaties fruitless, fell on
and slaughtered their innocent children and husband, perishing themselves in
the act of carnage. It is recorded that during that triennial agitation no less than
twenty-three Circles perished in domestic discord.

Great indeed was the peril. It seemed as though the Priests had no choice
between submission and extermination; when suddenly the course of events
was completely changed by one of those picturesque incidents which Statesmen
ought never to neglect, often to anticipate, and sometimes perhaps to originate,
because of the absurdly disproportionate power with which they appeal to the
sympathies of the populace.

It happened that an Isosceles of a low type, with a brain little if at all above
four degrees—accidentally dabbling in the colours of some Tradesman whose
shop he had plundered—painted himself, or caused himself to be painted (for
the story varies) with the twelve colours of a Dodecagon. Going into the Market
Place he accosted in a feigned voice a maiden, the orphan daughter of a noble
Polygon, whose affection in former days he had sought in vain; and by a series
of deceptions—aided, on the one side, by a string of lucky accidents too long to
relate, and on the other, by an almost inconceivable fatuity and neglect of
ordinary precautions on the part of the relations of the bride—he succeeded in
consummating the marriage. The unhappy girl committed suicide on
discovering the fraud to which she had been subjected.

When the news of this catastrophe spread from State to State the minds of
the Women were violently agitated. Sympathy with the miserable victim and
anticipations of similar deceptions for themselves, their sisters, and their
daughters, made them now regard the Colour Bill in an entirely new aspect. Not

a few openly avowed themselves converted to antagonism; the rest needed only
a slight stimulus to make a similar avowal. Seizing this favourable opportunity,
the Circles hastily convened an extraordinary Assembly of the States; and
besides the usual guard of Convicts, they secured the attendance of a large
number of reactionary Women.

Amidst an unprecedented concourse, the Chief Circle of those days—by
name Pantocyclus—arose to find himself hissed and hooted by a hundred and
twenty thousand Isosceles. But he secured silence by declaring that henceforth
the Circles would enter on a policy of Concession; yielding to the wishes of the
majority, they would accept the Colour Bill. The uproar being at once converted
to applause, he invited Chromatistes, the leader of the Sedition, into the centre
of the hall, to receive in the name of his followers the submission of the
Hierarchy. Then followed a speech, a masterpiece of rhetoric, which occupied
nearly a day in the delivery, and to which no summary can do justice.

With a grave appearance of impartiality he declared that as they were now
finally committing themselves to Reform or Innovation, it was desirable that
they should take one last view of the perimeter of the whole subject, its defects
as well as its advantages. Gradually 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 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 skillful
generalship of the Circles almost every Woman's charge was fatal and very
many extracted their sting uninjured, ready for a second slaughter. But no
second blow was needed; the rabble of the Isosceles did the rest of the business
for themselves. Surprised, leader-less, attacked in front by invisible foes, and
finding egress cut off by the Convicts behind them, they at once—after their
manner—lost all presence of mind, and raised the cry of "treachery". This
sealed their fate. Every Isosceles now saw and felt a foe in every other. In half
an hour not one of that vast multitude was living; and the fragments of seven
score thousand of the Criminal Class slain by one another's angles attested the
triumph of Order.

The Circles delayed not to push their victory to the uttermost. The Working
Men they spared but decimated. The Militia of the Equilaterals was at once
called out; and every Triangle suspected of Irregularity on reasonable grounds,
was destroyed by Court Martial, without the formality of exact measurement by
the Social Board. The homes of the Military and Artisan classes were inspected
in a course of 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.

Section 11. Concerning our Priests

It is high time that I should pass from these brief and discursive notes about
things in Flatland to the central event of this book, my initiation into the
mysteries of Space. THAT is my subject; all that has gone before is merely
preface.

For this reason I must omit many matters of which the explanation would
not, I flatter myself, be without interest for my Readers: as for example, our
method of propelling and stopping ourselves, although destitute of feet; the
means by which we give fixity to structures of wood, stone, or brick, although
of course we have no hands, nor can we lay foundations as you can, nor avail
ourselves of the lateral pressure of the earth; the manner in which the rain
originates in the intervals between our various zones, so that the northern

regions do not intercept the moisture 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 everyone called a Circle is deemed a Circle, yet among
the better educated Classes it is known that no Circle is really a Circle, but only
a Polygon with a very large number of very small sides. As the number of the
sides increases, a Polygon approximates to a Circle; and, when the number is
very great indeed, say for example three or four hundred, it is extremely
difficult for the most delicate touch to feel any polygonal angles. Let me say
rather, it WOULD be difficult: for, as I have shown above, Recognition by
Feeling is unknown among the highest society, and to FEEL a Circle would be
considered a most audacious insult. This habit of abstention from Feeling in the
best society enables a Circle the more easily to sustain the veil of mystery in
which, from his earliest years, he is wont to enwrap the exact nature of his
Perimeter or Circumference. Three feet being the average Perimeter it follows
that, in a Polygon of three hundred sides each side will be no more than the
hundredth part of a foot in length, or little more than the tenth part of an inch;
and in a Polygon of six or seven hundred sides the sides are little larger than the
diameter of a Spaceland pin-head. It is always assumed, by courtesy, that the
Chief Circle for the time being has ten thousand sides.

The ascent of the posterity of the Circles in the social scale is not restricted,
as it is among the lower Regular classes, by the Law of Nature which limits the
increase of sides to one in each generation. If it were so, the number of sides in
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
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.

Section 12. Of the Doctrine of our Priests

As to the doctrine of the Circles it may briefly be summed up in a single
maxim, "Attend to your Configuration." Whether political, ecclesiastical, or
moral, all their teaching has for its object the improvement of individual and
collective Configuration—with special reference of course to the Configuration
of the Circles, to which all other objects are subordinated.

It is the merit of the Circles that they have effectually suppressed those
ancient heresies which led men to waste energy and sympathy in the vain belief
that conduct depends upon will, effort, training, encouragement, praise, or
anything else but Configuration. It was Pantocyclus—the illustrious Circle
mentioned above, as the queller of the Colour Revolt—who first convinced
mankind that Configuration makes the man; that if, for example, you are born
an Isosceles with two uneven sides, you will assuredly go wrong unless you
have them made even—for which purpose you must go to the Isosceles
Hospital; similarly, if you are a Triangle, or Square, or even a Polygon, born
with any Irregularity, you must be taken to one of the Regular Hospitals to have
your disease cured; otherwise you will end your days in the State Prison or by
the angle of the State Executioner.

All faults or defects, from the slightest misconduct to the most flagitious
crime, Pantocyclus attributed to some deviation from perfect Regularity in the
bodily figure, caused perhaps (if not congenital) by some collision in a crowd;
by neglect to take exercise, or by taking too much of it; or even by a sudden
change of temperature, resulting in a shrinkage or expansion in some too
susceptible part of the frame. Therefore, concluded that illustrious Philosopher,
neither good conduct nor bad conduct is a fit subject, in any sober estimation,
for either praise or blame. For why should you praise, for example, the integrity
of a Square who faithfully defends the interests of his client, when you ought in
reality rather to admire the exact precision of his right angles? Or again, why
blame a lying, thievish Isosceles when you ought rather to deplore the incurable
inequality of his sides?

Theoretically, this doctrine is unquestionable; but it has practical drawbacks.
In dealing with an Isosceles, if a rascal pleads that he cannot help stealing

because of his unevenness, you reply that for that very reason, because he
cannot help being a nuisance to his neighbours, you, the Magistrate, cannot help
sentencing him to be consumed—and there's an end of the matter. But in little
domestic difficulties, 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.

Constantly carrying out their policy of making Configuration the leading
idea in every mind, the Circles reverse the nature of that Commandment which
in Spaceland regulates the relations between parents and children. With you,
children are taught to honour their parents; with us—next to the Circles, who
are the chief object of universal homage—a man is taught to honour his
Grandson, if he has one; or, if not, his Son. By "honour", however, is by no
means 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 inquire above the
five-hundredth generation; a Hexagon or Dodecagon is even more careless of
the wife's pedigree; but a Circle has been known deliberately to take a wife who
has had an Irregular Great-Grandfather, and all because of some slight
superiority of lustre, or because of the charms of a low voice—which, with us,
even more than 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 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!"

Section 13. How I had a Vision of Lineland

It was the last day but one of the 1999th year of our era, and the first day of
the Long Vacation. Having amused myself till a late hour with my favourite
recreation of Geometry, I had retired to rest with an unsolved problem in my
mind. In the night I had a dream.

I saw before me a vast multitude of small Straight Lines (which I naturally
assumed to be Women) interspersed with other Beings still smaller and of the
nature of lustrous points—all moving to and fro in one and the same Straight
Line, and, as nearly as I could judge, with the same velocity.

A noise of confused, multitudinous chirping or twittering issued from them
at intervals as long as they were moving; but sometimes they ceased from
motion, and then all was silence.

Approaching one of the largest of what I thought to be Women, I accosted
her, but received no answer. A second and a 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 having herself ordained that every Man should wed two wives—"
"Why two?" asked I. "You carry your affected simplicity too far", he cried.
"How can there be a completely harmonious union without the combination of
the Four in One, viz. the Bass and Tenor of the Man and the Soprano and
Contralto of the two Women?" "But supposing," said I, "that a man should
prefer one wife or three?" "It is impossible," he said; "it is as inconceivable as
that two and one should make five, or that the human eye should see a Straight
Line." I would have interrupted him; but he proceeded as follows:

"Once in the middle of each week a Law of Nature compels us to move to
and fro with a rhythmic motion of more than usual violence, which continues
for the time you would take to count a hundred and one. In the midst of this
choral dance, at the fifty-first pulsation, the inhabitants of the Universe pause in
full career, and each individual sends forth his richest, fullest, sweetest strain. It
is in this decisive moment that all our marriages are made. So exquisite is the
adaptation of Bass to Treble, of Tenor to Contralto, that oftentimes the Loved
Ones, though twenty thousand leagues away, recognize at once the responsive

note of their destined Lover; and, penetrating the paltry obstacles of distance,
Love unites the three. The marriage in that 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 recognize 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 harmonize. In such
cases Nature has provided that every weekly Chorus shall bring the three
Lovers into closer harmony. Each trial of voice, each fresh discovery of discord,
almost imperceptibly induces the less perfect to modify his or her vocal
utterance so as to approximate to the more perfect. And after many trials and
many approximations, the result is at last achieved. There comes a day at last,
when, while the wonted Marriage Chorus goes forth from universal Lineland,
the three far-off Lovers suddenly find themselves in exact harmony, and, before
they are awake, the wedded Triplet is rapt vocally into a duplicate embrace; and
Nature rejoices over one more marriage and over three more births."

Section 14. How I vainly tried to explain the nature of Flatland

Thinking that it was time to bring down the Monarch from his raptures to the
level of common sense, I determined to endeavour to open up to him some
glimpses of the truth, that is to say of the nature of things in Flatland. So I

began thus: "How does your Royal Highness distinguish the shapes and
positions of his subjects? I for my part noticed by the sense of sight, before I
entered your Kingdom, that some of your people are Lines and others Points,
and that some of the Lines are larger—" "You speak of an impossibility,"
interrupted the King; "you must have seen a vision; for to detect the difference
between a Line and a Point by the sense of sight is, as every one knows, in the
nature of things, impossible; but it can be detected by the sense of hearing, and
by the same means my shape can be exactly ascertained. Behold me—I am a
Line, the longest in Lineland, over six inches of Space—" "Of Length", I
ventured to suggest. "Fool," said he, "Space is Length. Interrupt me again, and I
have done."

I apologized; but he continued scornfully, "Since you are impervious to
argument, you shall hear with your ears how by means of my two voices I
reveal my shape to my Wives, who are at this moment six thousand miles
seventy yards two feet eight inches away, the one to the North, the other to the
South. Listen, I call to them."

He chirruped, and then complacently continued: "My wives at this moment
receiving the sound of one of my 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 recognized as the
echo of the Northern? May not such deceptions cause great inconvenience? And
have you no means of checking frauds of this kind by commanding your
neighbouring subjects to feel one another?" This of course was a very stupid
question, for feeling could not have answered the purpose; but I asked with the
view of irritating the Monarch, and I succeeded perfectly.

"What!" cried he in horror, "explain your meaning." "Feel, touch, come into
contact," I replied. "If you mean by FEELING," said the King, "approaching so
close as to leave no space between two individuals, know, Stranger, that this
offence is punishable in my dominions by death. And the reason is obvious. The

frail form of a Woman, being liable to be shattered by such an approximation,
must be preserved by the State; but since Women cannot be distinguished by the
sense of sight from Men, the Law ordains universally that neither Man nor
Woman shall be approached so closely as to destroy the interval between the
approximator and the approximated.

"And indeed what possible purpose would be served by this illegal and
unnatural excess of approximation which you call TOUCHING, when all the
ends of so brutal and 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, corporeal, mental and spiritual, of every living
being in Lineland. Hark, only hark!"

So saying he paused and listened, as if in an ecstasy, to a sound which
seemed to me no better than a tiny chirping from an innumerable multitude of
lilliputian grasshoppers.

"Truly," replied I, "your sense of hearing serves you in good stead, 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 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 your 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 see also the Men and Women on
the North and South of you, whom I will now enumerate, describing their order,
their size, and the interval between each."

When I had done this at great length, I cried triumphantly, "Does that 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.

Section 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 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.

[Note: 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 recognize 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.]

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 a while 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 shew 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 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 this 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 of 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 third
Millennium had begun.

Section 16. How the Stranger vainly endeavoured to reveal to me in
words the mysteries of Spaceland

As soon as the sound of the Peace-cry of my departing Wife 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. (TO HIMSELF.) What must I do? Stay; one more argument
suggests itself to me. When you see a Straight Line—your wife, for example—
how many Dimensions do you attribute to her?

I. Your Lordship would treat me as if I were one of the vulgar who, being
ignorant of Mathematics, suppose that a Woman is really a Straight Line, and
only of One Dimension. No, no, my Lord; we Squares are better advised, and
are as well aware as your Lordship that a Woman, though popularly called a
Straight Line, is, really and scientifically, a very thin Parallelogram, possessing
Two Dimensions, like the rest of us, viz., length and breadth (or thickness).

STRANGER. But the very fact that a Line is visible implies that it possesses
yet another Dimension.

I. My Lord, I have just acknowledged that a Woman is broad as well as long.
We see her length, we infer her breadth; which, though very slight, is capable of
measurement.

STRANGER. You do not understand me. I mean that when you see a
Woman, you ought—besides inferring her breadth—to see her length, and to
SEE what we call her HEIGHT; although that last Dimension is infinitesimal in
your country. If a Line were mere length without "height", it would cease to
occupy Space and would become invisible. Surely you must recognize this?

I. I must indeed confess that I do not in the least understand your Lordship.
When we in Flatland see a Line, we see length and BRIGHTNESS. If the
brightness disappears, the Line is extinguished, and, as you say, ceases to
occupy Space. But am I to suppose that your Lordship gives to brightness the
title of a Dimension, and that what we call "bright" you call "high"?

STRANGER. No, indeed. By "height" I mean a Dimension like your length:
only, with you, "height" is not so easily perceptible, being extremely small.

I. My Lord, your assertion is easily put to the test. You say I have a Third
Dimension, which you call "height". Now, Dimension implies direction and
measurement. Do but measure my "height", or merely indicate to me the
direction in which my "height" extends, and I will become your convert.
Otherwise, your Lordship's own understanding must hold me excused.

STRANGER. (TO HIMSELF.) I can do neither. 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 sections become smaller. See now, I will rise; and
the effect upon your eye will be that my Circle will become smaller and smaller
till it dwindles to a point and finally vanishes.

There was no "rising" that I could see; but he diminished and finally
vanished. I winked once or twice to make sure that I was not dreaming. But it
was no dream. For from the depths of nowhere came forth a hollow voice—
close to my heart it seemed—"Am I quite 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 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? 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 give yourself 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 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.

Section 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; no 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 still I 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!"

Section 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 shew you that which
you have 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.

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
pick-pockets 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 besides 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 shewed 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 guards. "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.

Section 19. How, though the Sphere shewed me other mysteries of
Spaceland, I still desired more; and what came of it

When I saw my poor brother led away to imprisonment, I attempted to leap
down into the Council Chamber, desiring to intercede on his behalf, or at least
bid him farewell. But I found that I had no motion of my own. I absolutely
depended on the volition of my Guide, who said in gloomy tones, "Heed not thy
brother; haply thou shalt have ample time hereafter to condole with him. Follow
me."

Once more we ascended into space. "Hitherto," said the Sphere, "I have
shewn 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
shew 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 shewn 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. Not inconceivable, my Lord, to me, and therefore still less inconceivable
to my Master. Nay, I despair not that, even here, in this region of Three
Dimensions, your Lordship's art may make the Fourth Dimension visible to me;
just as in the Land of Two Dimensions my Teacher's skill would fain have
opened the eyes of his blind servant to the invisible presence of a Third
Dimension, though I saw it not.

Let me recall the past. Was I not taught below that when I saw a Line and
inferred a Plane, I in reality saw a Third unrecognized Dimension, not the same
as brightness, called "height"? And does it not now follow that, in this region,
when I see a Plane and infer a Solid, I really see a Fourth unrecognized

Dimension, not the same as colour, but existent, though infinitesimal and
incapable of measurement?

And besides this, there is the Argument from Analogy of Figures.

SPHERE. Analogy! Nonsense: what analogy?

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 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 command 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.

Section 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 knew 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 bluebottles, 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, shewed 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, shewing 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.

Section 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 exchanged 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 the 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.

Section 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 danger 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 degrees,
ordered them to be relieved before I began my defence, by an inferior class
of 2 or 3 degrees. 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 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.

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