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 of the table, you will find
that it ceases to appear to you a Figure, and that it becomes in
appearance a straight line. Take for example an equilateral
Triangle⁠---who represents with us a tradesman of the respectable class.
Fig. 1 represents the tradesman as you
would see him while you were bending over him from above;
figs. 2 and 3 represent the tradesman, as
you would see him if your eye were close to the level, or all but on the
level of the table; and if your eye were quite on the level of the table
(and that is how we see him in Flatland) you would see nothing but a
straight line.

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.