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.

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(1)     __________     (2)    ___________     (3)     _________
        \        /             --__ __--                 ---
          \    /                   -
            \/

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.

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                             O
                             /\
                           /    \
                         /        \
                       /            \
                     /                \
                  R/                    \F
                   \_                   /
                                      _/
          Men's door                 _   Women's door
                       _             /
                       \____________/
                       A            B