Flatland/main.tex

\title{Flatland} \author{Edwin A. Abbott} 
\date{\today}

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\fancyhead[RE]{\textit{Flatland:}}
\fancyhead[LO]{\textit{A Romance of Many Dimensions}}

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\vspace*{2cm}
\includegraphics[scale=0.45]{flatland_cover}
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\begin{center}
\textit{``Fie, fie, how franticly I square my talk!''}
\end{center}

\clearpage

\thispagestyle{empty}
\noindent{} This work is in the public domain in the United States because it was
published before January 1, 1923.
The author died in 1926, so this work is also in the public domain in
countries and areas where the copyright term is the author's life plus 80
years or less. This work may also be in the public domain in countries and
areas with longer native copyright terms that apply the rule of the shorter
term to foreign works.
\vspace{5mm}

\noindent\emph{Written by} Edwin A. Abbott \\
\emph{Illustrated by} Edwin A. Abbott \\
\emph{Typeset by} Ives van der Flaas\\
\emph{Additional typesetting by} Kenneth John Odle\\ \\
Fifth edition


\chapter*{A Note From The Typesetter}
\thispagestyle{empty}
Although Edwin A. Abbott's essay ``Flatland'' is readily available on the
internet, I failed to find a nicely typeset version. At this time,
the rendering quality of internet browsers doesn't come anywhere near the
quality of a nice book. 

For these reasons, as well as a healthy portion of boredom, I made the version
of ``Flatland'' you are currently reading, in \LaTeX. The \LaTeX\ source can be
found on \url{https://github.com/Ivesvdf/flatland} (feel free to make issues
or send me pull requests when you find bugs or have improvements). It should
also be fairly easy --- a matter of minutes --- to produce a book-sized
version, ready to send to a printer. 

\vspace{1cm}

\hfill Ives van der Flaas <ives.vdf@gmail.com>, 2011-09-20

\vspace{1.5cm}

\noindent{}\textbf{An additional note:}\\

\noindent{}I found this at the location above, where it included an A4 version in pdf. I decided to update this to a letterhalf page size, which is more common in North America.

Where necessary, I also made adjustments such as the scaling of the images, changing to the \texttt{kpfont} font package, reducing the size of the type from 12 points to 9 points, and adjusting the margins and line spacing.

The source can be found on \texttt{\url{https://git.kjodle.net/kjodle/Flatland}}.

\begin{flushright}
\textit{Kenneth John Odle}
\end{flushright}


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\chapter*{Dedication}
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\begin{center}
To\\
The Inhabitants of \textsc{Space in General}\\
And \textsc{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 \textsc{Three Dimensions}\\
Having been previously conversant\\
With \textsc{Only Tow}\\
So the Citizens of that Celestial Region\\
May aspire yet higher and higher\\
To the Secrets of \textsc{Four Five or Even Six} Dimensions\\
Thereby contributing\\
To the Enlargement of \textsc{the Imagination}\\
And the possible Development\\
Of that most rare and excellent Gift of \textsc{Modesty}\\
Among the Superior Races\\
Of \textsc{Solid Humanity}\\
\end{center}

\afterpage{\blankpage}


% \addcontentsline{toc}{chapter}{Preface}
\chapter*{Preface}
\thispagestyle{empty}
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, fully, to return his thanks to his readers
and critics in Spaceland, whose appreciation has, with unexpected celerity,
required a second edition of this work; secondly, to apologize for certain
errors and misprints (for which, however, he is not entirely responsible);
and, thirdly, to explain on 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 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 \textit{thick} to the eye as well as \textit{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 to a very slight degree) \textit{thick} or \textit{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 also is 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 implied direction, implies measurement,
implies the more and the less. Now, all our lines are \textit{equally} and
\textit{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 \textit{what to measure,
nor in what direction}. When we see a Line, we see something that is long and
\textit{bright}; \textit{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 \textit{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 \textit{see} a Plane (which is of Two
Dimensions) and you \textit{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
Slavers of our respective Dimensional prejudices, as one of our Spaceland
poets has said --- `One touch of Nature makes all worlds akin.' '' \footnote{The
Author desires me to add, that the misconceptions 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 fulfillment 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.''



%b\mainmatter

\part{This World}[
\vspace{2cm}
\begin{center}
\begin{normalsize}
	\textit{'Be patient, for the world is broad and wide.'}
\end{normalsize}
\end{center}
]


\chapter{Of the Nature of Flatland} I call our world Flatland, not because we
call it so, but to make its nature clearer to you, my happy readers, who are
privileged to live in Space.

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

In such a country, you will perceive at once that it is impossible that there
should be anything of what you call a ``solid'' kind; but I dare say you will
suppose that we could at least distinguish by sight the Triangles, Squares,
and other figures, moving about as I have described them. On the contrary, we
could see nothing of the kind, not at least so as to distinguish one figure
from another. Nothing was visible, nor could be visible, to us, except
Straight Lines; and the necessity of this I will speedily demonstrate.

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

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

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

\includegraphics[trim=20mm 0mm 0mm 0mm,width=\linewidth]{fig1}

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

Well, that is just what we see when one of our triangular or other
acquaintances comes towards us in Flatland. As there is neither sun with us,
nor any light of such a kind as to make shadows, we have none of the helps to
the sight that you have in Spaceland. If our friend comes closer to us we see
his line becomes larger; if he leaves us it becomes smaller; but still he
looks like a straight line; be he a Triangle, Square, Pentagon, Hexagon,
Circle, what you will --- a straight Line he looks and nothing else.

You may perhaps ask how under these 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.










\chapter{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-investigate question, ``What is the origin of light?'' and
the solution of it has been repeatedly attempted, with no other result than to
crowd our lunatic asylums with the would-be solvers. Hence, after fruitless
attempts to suppress such investigations indirectly by making them liable to a
heavy tax, the Legislature, in comparatively recent times, absolutely
prohibited them. I --- alas, I alone in Flatland --- know now only too well the
true solution of this mysterious problem; but my knowledge cannot be made
intelligible to a single one of my countrymen; and I am mocked at --- I, the
sole possessor of the truths of Space and of the theory of the introduction of
Light from the world of three Dimensions --- as if I were the maddest of the
mad! But a truce to these painful digressions: let me return to our homes.

The most common form for the construction of a house is five-sided or
pentagonal, as in the annexed figure. The two Northern sides \textit{RO}, \textit{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.
\begin{center}
\includegraphics[trim=20mm 0mm 0mm 0mm, scale=0.5]{fig2}
\end{center}


Square and triangular houses are not allowed, and for this reason. The angles
of a Square (and still more those of an equilateral Triangle,) being much more
pointed than those of a Pentagon, and the lines of inanimate objects (such as
houses) being dimmer than the lines of Men and Women, it follows that there is
no little danger lest the points of a square of triangular house residence
might do serious injury to an inconsiderate or perhaps absentminded traveller
suddenly running against them: and therefore, as early as the eleventh century
of our era, triangular houses were universally forbidden by Law, the only
exceptions being fortifications, powder-magazines, barracks, and other state
buildings, which is not desirable that the general public should approach
without circumspection.

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













\chapter{Concerning the Inhabitants of Flatland}
The greatest length or breadth of a full grown inhabitant of Flatland may be
estimated at about eleven of your inches. Twelve inches may be regarded as a
maximum.

Our Women are Straight Lines.

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

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

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

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

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

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

Rarely --- in proportion to the vast numbers of Isosceles births --- is a genuine
and certifiable Equal-Sided Triangle produced from Isosceles parents
\footnote{ ``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 almost useful barrier against revolution from below.

Had the acute-angled rabble been all, without exception, absolutely destitute
of hope and of ambition, they might have found leaders in some of their many
seditious outbreaks, so able as to render their superior numbers and strength
too much even for the wisdom of the Circles. But a wise ordinance of Nature
has decreed that, in proportion as the working-classes increase in
intelligence, knowledge, and all virtue, in that same proportion their acute
angle (which makes them physically terrible) shall increase also and
approximate to their comparatively harmless angle of the Equilateral Triangle.
Thus, in the most brutal and formidable 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 of Flatland! By a judicious use of this Law of
Nature, the Polygons and Circles are almost always able to stifle sedition in
its very cradle, taking advantage of the irrepressible and boundless
hopefulness of the human mind. Art also comes to the aid of Law and Order. It
is generally found possible --- by a little artificial compression or expansion
on the part of the State physicians --- to make some of the more intelligent
leaders of a rebellion perfectly Regular, and to admit them at once into the
privileged classes; a much larger number, who are still below the standard,
allured by the prospect of being ultimately ennobled, are induced to enter the
State Hospitals, where they are kept in honourable confinement for life; one
or two alone of the most obstinate, foolish, and hopelessly irregular are led
to execution.

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














\chapter{Concerning the Women}
If our highly pointed Triangles of the Soldier class are formidable, it may be
readily inferred that far more formidable are our Women. For, if a Soldier is
a wedge, a Woman is a needle; being, so to speak, all point, at least at the
two extremities. Add to this the power of making herself practically invisible
at will, and you will perceive that a Female, in Flatland, is a creature by no
means to be trifled with.

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

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

The dangers to which we are exposed from our Women must now be manifest to the
meanest capacity 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: ---

Every house shall have one entrance on the Eastern side, for the use of
Females only; by which all females shall enter ``in a becoming and respectful
manner'' \footnote{ 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.''} and not by the Men's
or Western door.  No Female shall walk in any public place without continually
keeping up her Peace-cry, under penalty of death.  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 brainpower, and have neither
reflection, judgment nor forethought, and hardly any memory. Hence, in their
fits of fury, they remember no claims and recognize no distinctions. I have
actually known a case where a Woman has exterminated her whole household, and
half an hour afterwards, when her rage was over and the fragments swept away,
has asked what has become of her husband and 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 got on pretty smoothly in our domestic
relations, except in the lower strata of the Military Classes. There the want
of tact and discretion on the part of the husbands produces at times
indescribable disasters. Relying too much on the offensive weapons of their
acute angles instead of the defensive organs of good sense and seasonable
simulations, these reckless creatures too often neglect the prescribed
construction of the women's apartments, or irritate their wives by ill-advised
expressions out of doors, which they refuse immediately to retract. Moreover a
blunt and stolid regard for literal truth indisposes them to make those lavish
promises by which the more judicious Circle can in a moment pacify his
consort. The result is massacre; not, however, without its advantages, as it
eliminates the more brutal and troublesome of the Isosceles; and by many of
our Circles the destructiveness of the Thinner Sex is regarded as one among
many providential arrangements for suppressing redundant population, and
nipping Revolution in the bud.

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

Moving with ease and smoothness in uttering words; of rapid speech;
nimble in speaking; glib; as, a flippant, voluble, tongue.  In the house of
the Working Man or respectable Tradesman --- where the wife is allowed to turn
her back upon her husband, while pursuing her household avocations --- there are
at least intervals of quiet, when the wife is neither seen nor heard, except
for the humming sound of the continuous Peace-cry; but in the homes of the
upper classes there is too often no peace. There the voluble mouth and bright
penetrating eye are ever directed toward the Master of the household; and
light itself is not more persistent than the stream of Feminine discourse. The
tact and skill which suffice to avert a Woman's sting are unequal to the task
of stopping a Woman's mouth; and as the wife has absolutely nothing to say,
and absolutely no constraint of wit, sense, or conscience to prevent her from
saying it, not a few cynics have been found to aver that they prefer the
danger of the death-dealing but inaudible sting to the safe sonorousness of a
Woman's other end.

To my readers in Spaceland the condition of our Women may seen truly
deplorable, and so indeed it is. A Male of the lowest type of the Isosceles
may look forward to some improvement of his angle, and to the ultimate
elevation of the whole of his degraded caste; but no Woman can entertain such
hopes for her sex. ``Once a Woman, always a Woman'' is a Decree of Nature; and
the very Laws of Evolution seem suspended in her disfavour. Yet at least we
can admire the wise Prearrangement which has ordained that, as they have no
hopes, so they shall have no memory to recall, and no forethought to
anticipate, the miseries and humiliations which are at once a necessity of
their existence and the basis of the constitution of Flatland.




\chapter{Of our Methods of Recognizing one another} 

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

Recall what I told you above. All beings in Flatland, animate and inanimate,
no matter what their form, present \textit{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 the
Isosceles I take no account. But as we ascend the social scale, the process of
discriminating and being discriminated by hearing increases in difficulty,
partly because voices are assimilated, partly because the faculty of
voice-discrimination is a plebeian virtue not much developed among the
Aristocracy. And wherever there is any danger of imposture we cannot trust to
this method. Amongst our lowest orders, the vocal organs are developed to a
degree more than correspondent with those of hearing, so that an Isosceles can
easily feign the voice of a Polygon, and, with some training, that of a Circle
himself. A second method is therefore more commonly resorted to.

\textit{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 occurred to his
great-great-great-Grandfather, a respectable Working Man with an angle or
brain of 59$^{\circ}$ 30$'$. According to his account, my unfortunate
Ancestor, being afflicted with rheumatism, and in the act of being felt by a
Polygon, by one sudden start accidentally transfixed the Great Man through the
diagonal and thereby, partly in consequence of his long imprisonment and
degradation, and partly because of the moral shock which pervaded the whole of
my Ancestor's relations, threw back our family a degree and a half in their
ascent towards better things. The result was that in the next generation the
family brain was registered at only 58$^{\circ}$, and not till the lapse of five
generations was the lost ground recovered, the full 60$^{\circ}$ 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
see an angle, because we, in the region of Space, can see two straight lines
inclined to one another; but you, who can see nothing but on straight line at
a time, or at all events only a number of bits of straight lines all in one
straight line, --- how can you ever discern any angle, and much less register
angles of different sizes?''.

I answer that though we cannot \textit{see} angles, we can \textit{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$^{\circ}$ 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$^{\circ}$, 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$^{\circ}$. 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 classrooms of our Infant
Schools, and there they are utilized by the Board of Education for the purpose
of imparting to the offspring of the Middle Classes 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.








\chapter{Of Recognition by Sight} 
I am about to appear very inconsistent. In previous sections I have said that
all figures in Flatland present the appearance of a straight line; and it was
added or implied, that it is consequently impossible to distinguish by the
visual organ between individuals of different classes: yet now I am about to
explain to my Spaceland critics how we are able to recognize one another by
the sense of sight.

If however the Reader will take the trouble to refer to the passage in which
Recognition by Feeling is stated to be universal, he will find this
qualification --- ``among the lower classes''. It is only among the higher classes
and in our more temperate climates that Sight Recognition is practised.

That this power exists in any regions and for any classes is the result of
Fog; which prevails during the greater part of the year in all parts save the
torrid zones. That which is with you in Spaceland an unmixed evil, blotting
out the landscape, depressing the spirits, and enfeebling the health, is by us
recognized as a blessing scarcely inferior to air itself, and as the Nurse of
arts and Parent of sciences. But let me explain my meaning, without further
eulogies on this beneficent Element.

If Fog were non-existent, all lines would appear equally and indistinguishably
clear; and this is actually the case in those unhappy countries in which the
atmosphere is perfectly dry and transparent. But wherever there is a rich
supply of Fog, objects that are at a distance, say of three feet, are
appreciably dimmer than those at the distance of two feet eleven inches; and
the result is that by careful and constant experimental observation of
comparative dimness and clearness, we are enabled to infer with great
exactness the configuration of the object observed.

An instance will do more than a volume of generalities to make my meaning
clear.

Suppose I see two individuals approaching whose rank I wish to ascertain. They
are, we will suppose, a Merchant and a Physician, or in other words, an
Equilateral Triangle and a Pentagon; how am I to distinguish them?

\includegraphics[trim=20mm 0mm 0mm 0mm, width=\linewidth]{fig3}

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 (\textsc{a}) of the approaching stranger, my view will lie as it were
evenly between his two sides that are next to me (viz. \textsc{ca} and \textsc{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 \textsc{dae}, in which the middle point (\textsc{a}) will be very bright because it is
nearest to me; but on either side the line will shade away \textit{rapidly to dimness},
because the sides \textsc{ac} and \textsc{ab} \textit{recede rapidly into the fog} and what appear to me as the Merchant's extremities, viz. \textsc{d} and \textsc{e}, will be \textit{very dim indeed}.

On the other hand in the case of (2) the Physician, though I shall here also
see a line (\textsc{d}$'$\textsc{a}$'$\textsc{e}$'$) with a bright centre (\textsc{a}$'$), yet it will shade away \textit{less rapidly} to dimness, because the sides (\textsc{a}$'$\textsc{c}$'$, \textsc{a}$'$\textsc{b}$'$) \textit{recede less rapidly into
the fog}; and what appear to me the Physician's extremities, viz. \textsc{d}$'$ and \textsc{e}$'$, will not be \textit{not so dim} as the extremities of the Merchant.

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

If for example, when my Father, the Triangle, approaches me, he happens to
present his side to me instead of his angle, then, until I have asked him to
rotate, or until I have edged my eye around him, I am for the moment doubtful
whether he may not be a Straight Line, or, in other words, a Woman. Again,
when I am in the company of one of my two hexagonal Grandsons, contemplating
one of his sides (\textsc{ab}) full front, it will be evident from the accompanying
diagram that I shall see one whole line (\textsc{ab}) in comparative brightness
(shading off hardly at all at the ends) and two smaller lines (\textsc{ca} and \textsc{bd}) dim
throughout and shading away into greater dimness towards the extremities \textsc{c} and
\textsc{d}. 

\begin{center}
\includegraphics[trim=20mm 0mm 0mm 0mm, scale=0.5]{fig4}
\end{center}


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 \textit{élite} of
the States.

It is only a few of the scions of our noblest and wealthiest houses, who are able to give the time and money necessary for the thorough prosecution of this noble and valuable Art. Even to
me, a Mathematician of no mean standing, and the Grandfather of two most
hopeful and perfectly regular Hexagons, to find myself in the midst of a crowd
of rotating Polygons of the higher classes, is occasionally very perplexing.
And of course to a common Tradesman, or Serf, such a sight is almost as
unintelligible as it would be to you, my Reader, were you suddenly transported
to 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 there was need of
many years of experience, before you could move in a fashionable crowd without
jostling against your betters, whom it is against etiquette to ask to ``feel'',
and who, by their superior culture and breeding, know all about your
movements, while you know very little or nothing about theirs. In a word, to
comport oneself with perfect propriety in Polygonal society, one ought to be a
Polygon oneself. Such at least is the painful teaching of my experience.

It is astonishing how much the Art --- or I may almost
call it instinct --- of Sight Recognition is developed by the habitual practice
of it and by the avoidance of the custom of ``Feeling''. Just as, with you, the
deaf and dumb, if once allowed to gesticulate and to use the hand-alphabet,
will never acquire the more difficult but far more valuable art of lip-speech
and lip-reading, so it is with us as regards ``Seeing'' and ``Feeling''. None who
in early life resort to ``Feeling'' will ever learn ``Seeing'' in perfection.

For this reason, among our Higher Classes, ``Feeling'' is discouraged or
absolutely forbidden. From the cradle their children, instead of going to the
Public Elementary schools (where the art of Feeling is taught,) are sent to
higher Seminaries of an exclusive character; and at our illustrious
University, to ``feel'' is regarded as a most serious fault, involving
Rustication for the first offence, and Expulsion for the second.

But among the lower classes the art of Sight Recognition is regarded as an
unattainable luxury. A common Tradesman cannot afford to let his son spend a
third of his life in abstract studies. The children of the poor are therefore
allowed to ``feel'' from their earliest years, and they gain thereby a precocity
and an early vivacity which contrast at first most favourably with the inert,
undeveloped, and listless behaviour of the half-instructed youths of the
Polygonal class; but when the latter have at last completed their University
course, and are prepared to put their theory into practice, the change that
comes over them may almost be described as a new birth, and in every art,
science, and social pursuit they rapidly overtake and distance their
Triangular competitors.

Only a few of the Polygonal Class fail to pass the Final Test or Leaving
Examination at the University. The condition of the unsuccessful minority is
truly pitiable.  Rejected from the higher class, they are also despised by the