Part I: This World
"Be patient, for the world is broad and wide."
Section 01. Of the Nature of Flatland
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I don’t call our world Flatland because that’s what we call it, but because I want to make what it’s like 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 geometric shapes are alive, and move freely, instead of being drawn in pencil.
They move on, or maybe you’d call it within, the surface of the paper, but do not and cannot rise above or sink below it. Almost like shadows, but hard and solid, with glowing edges.
If you can imagine this, you’ll have a pretty good idea of what my country looks like.
Just a few years ago, I would have said, “my universe” instead of “my country”, but now I know better.
In such a flat land, you Spacelanders will almost immediately assume that it’s impossible for there to be anything you would consider “solid”. And yet, if you look down, you’ll see the Triangles, Squares, and other Figures, just like I said.
We on the other hand, see no such thing, because the only things we can see are Straight Lines.
If this sounds confusing, let me give you an example, which you can follow along with while you read.
Get a small coin or similar thin object, and place it in the middle of one of your tables in Spaceland.
When you stand above it and look down, you see the coin as a circle.
But, if you move back to the edge of the table, and lower yourself partway towards the ground – more like the way we Flatlanders see the world – you’ll see that the coin now looks less like a circle, and more like an oval.
Then, if your eye is level with the edge of the table, you are closest to what you can get to being “on our level”. You’ll see that the penny, seen from above as a circle, now appears to just be a Straight Line.
The same thing would happen if you did this with a Triangle, or Square, or any other Shape you could cut out of cardboard. As soon as you look at it with your eye on the table, it looks like a straight line.
Take for example an equilateral Triangle—who with us is a Tradesman, or Buisnessman, of the respectable class.
Figure 1 below represents the Tradesman as you would see him while you were bending over him from above, as a Triangle with all three sides of equal length.
Figures 2 and 3 represent the Tradesman as you would see him if you began to move your eye closer to the level of the table.
Figure 4 represents what you would see if your eye were level with the table: nothing but a Straight Line, which is how we see him in Flatland.
[Image description start: Figures 1, 2, 3, and 4. Each is a very simple black and white illustrations of an equal-sided triangle seen from different angles, first from above, where he is plainly seen as a triangle, then slowly moving the view down so that he gets flatter and flatter until he is nothing but a straight line. Image description end.]
When I visited Spaceland, among other things not worth talking about in detail, I was told that your sailors have a similar experience when they’re out on the ocean – distant lands might obviously have bays, cliffs, buildings, and all kind of shapes on them from close by, but until you get close enough, or unless the sun’s bright enough to cast clear shadows, all you can see at a distance is a grey line on the horizon.
That’s like what we see when one of our Triangular or other acquaintances comes towards us in Flatland. We have no shadows like you do, and none of the other advantages your vision has in Spaceland.
If our friend comes closer to us, he becomes larger, if he goes away, he becomes smaller, but he is always a straight Line. It doesn’t matter if he’s a Triangle, Square, Pentagon, Hexagon, Circle, or anything else. He always looks like a Straight Line, and nothing else.
You’ll of course be wondering how we tell eachother apart if this is all we can see, and I’ll be able to make you understand better once I finish describing the people who live in Flatland.
But for the moment, let me pause this subject, and instead tell you about our houses, and the environment of Flatland.
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