Flatland by Edwin A. Abbott
1884

To
The Inhabitance of SPACE IN GENERAL
And H.C. IN PARTICULAR
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of THREE DIMENSIONS
Having been previously conversant
With ONLY TWO
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE or EVEN SIX Dimensions
Thereby contributing
To the Enlargment of THE IMAGINATION
And the possible Development
Of that most and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY

***

FLATLAND

PART 1

THIS WORLD

SECTION 1  Of the Nature of Flatland

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

Imagine a vast sheet of paper on which straight Lines,
Triangles, Squares, Pentagons, Hexagons, and other figures,
instead of remaining fixed in their places, move freely about,
on or in the surface, but without the power of rising above
or sinking below it, very much like shadows--only hard
with luminous edges--and you will then have a pretty correct
notion of my country and countrymen.  Alas, a few years ago,
I should have said "my universe:"  but now my mind has been
opened to higher views of things.
 
In such a country, you will perceive at once that it is
impossible that there should be anything of what you call
a "solid" kind; but I dare say you will suppose that
we could at least distinguish by sight the Triangles, Squares,
and other figures, moving about as I have described them.
On the contrary, we could see nothing of the kind,
not at least so as to distinguish one figure from another.
Nothing was visible, nor could be visible, to us,
except Straight Lines; and the necessity of this
I will speedily demonstrate.

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

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

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

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

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

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

SECTION 2  Of the Climate and Houses in Flatland

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

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

Yet in our more temperate regions, in which
the southward attraction is hardly felt,
walking sometimes in a perfectly desolate plain
where there have been no houses nor trees to guide me,
I have been occasionally compelled to remain stationary
for hours together, waiting till the rain came
before continuing my journey.  On the weak and aged,
and especially on delicate Females, the force of attraction
tells much more heavily than on the robust of the Male Sex,
so that it is a point of breeding, if you meet a Lady on the street,
always to give her the North side of the way--by no means
an easy thing to do always at short notice when you are
in rude health and in a climate where it is difficult
to tell your North from your South.

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

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

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

At this period, square houses were still everywhere permitted,
though discouraged by a special tax.  But, about three centuries
afterwards, the Law decided that in all towns containing a population