Month: February 2005

Flatland, by Edwin A. Abbott

Flatland: 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.