Flatland Reconfigured: An Ode to the Ponderings of Edwin Abbott

1. Ultimate Flatness

"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." - Edwin A. Abbott, Flatland: A Romance of Many Dimensions

While living in three dimensions, it seems trivial to you that there are only three directions to move: back and forth, left and right, up and down.

But imagine that you have been born in two dimensions, with length and width, but with height so infinitesimally small (but still there) that you would assume that you had none?

The fact is that if you could see the world as nothing but a line (which is what you would see if you were two-dimensional), you would automatically assume that since this never changes, as in the world always looks like a line, and that you can only move back and forth, left and right, you'd naturally assume that the world has exactly two, no more and no less, dimensions.

And this is now the point where we begin the story of Flatland, our everyday Flatlanders A. Square and B. Hexagon, and the revelation of the many perceptions on the universe.

To understand the world our characters come from, imagine a flat piece of paper of immense size, perfectly flat and perfectly level. Then imagine all the many kinds of shapes in geometry, triangles, squares, hexagons, octagons, all the way up to circles, all skittering about their daily lives on this paper. Imagine that resources have been scattered and hidden (much like how three-dimensional beings must dig and climb to find materials) in such a way so that these shapes cannot immediately see them, but through inventions can be able to obtain them. Imagine that they have done such things, and have thus over thousands of years built buildings, homes, societies, behaviors, countries, and all of the things that three-dimensional beings have similarly done, except built all these things on a completely flat world, with the buildings and such being flat themselves.

If you understand these things, then you have an understanding of the world of Flatland. The reason we call it Flatland is not because that is what the shapes called it, but rather so that you can better understand the nature of such a place, and what it would feel like to live and grow up on there.

Now that we understand the nature of Flatland, we can now move on to the shapes/people of Flatland, or Flatlanders, as we will now call them. 

All shapes, no matter how many sides, have but one eye to see their world from, which is located on the right side of their bodies, and extends out of the body a bit as to be able to see the world around them. As stated before, Flatlanders can see nothing but a line, and thus to distinguish the shapes of objects, they have but two ways to do this. 

The first, and mainly shunned, way of doing this is known as "feeling", where the Flatlander will approach the object in question, and use the many tiny hairs on itself (which are part of these creature's anatomies) as sensors to "feel" the object, and then work out what the object actually is. The second, and more accepted, way of seeing objects is called "sight recognition", which is the ability to distinguish what an object is by looking at the different amounts of light on the object, and then memorizing what kind of object makes what kind of light patterns based on its shape, its angles, etc.

The problem of sight recognition being much harder for children to learn than feeling objects has caused the creation of two main philosophies of Flatland, which from an outsider may sound disgusting and inhuman. 

Since when a shape is born, it is possible for their sides to be of irregular length, this can confuse young ones greatly, due to the fact that it is harder to remember the light differences of beings with irregular sides. Thus, being irregular in Flatland will generally result in poorer treatment from others, since being of unequal lengths is to be harder for people to recognize your shape. It may also affect what kind of job you can obtain, such as the isosceles triangles being employed for military and the rhombuses usually employed for high security operations.

An encouraged method of practice, commonly employed for the irregular sons of nobles, is to send them to their nearest Hospital of Reconfiguration. This is a hospital specifically designed to treat irregular infants, since their sides are more pliable at their youngest, and "re-correct" their sides to match their perfect configuration. For example, if an infant parallelogram was wished to be corrected to a square by the parents, this could be done. Turning something like an irregular pentagon to a regular hexagon, however, is not possible. It is only possible to correct the pentagon to his regular form. However, reconfiguration is a dangerous process, with only one in five surviving the process, and so mainly higher class families do such things, as to keep up their posterity.

With that out of the way, let us now move on to the men, women, and children of this world.

In almost all cases, when a new child is born, the number of sides it will have will be determined by the number of father's sides plus one. The color (which can be red, orange, yellow, green, blue, indigo, violet, pink, brown, white, or grey) will be decided by the mother's color number (0 for red, 1 for orange, 2 for yellow, etc, etc.) minus the father's color number; if the answer is negative, such as -2, then the color will be the top of the scale (being grey at 10) minus the negative number. The gender of the child is a 50/50 chance, and is not influenced whatsoever by either parent.

An example of this would be the mating of a green female triangle and a white male square. If they happened to have 3 children, all three would be born as blue pentagons, with the genders of each being one of four possibilities: one male two female, one female two male, all male, or all female.

The only exceptions to these rules happens to the first rule, which as mentioned before decides the number of sides of the child. For example, isosceles triangles have a 50/50 chance of having a triangular child, which explains why the triangles, after a few hundred years, did not suddenly vanish off the face of Flatland. Also, a decagon's (a ten-sided shape) offspring will end up being twelve-sided shapes (dodecagons). After the dodecagons mate, the offspring then follow the following pattern: 12 sides have 24-sided offspring, 24 sides have 48-sided ones, 48 sides have 96, 96 have 180, 180 have 270, 270 have 360, and 360 have 540. Once a shape is known to have 48 sides or more, it has earned the honorable title of being a circle, with 48 being the lowest order of circles. Because of the rules of society in Flatland, 540-sided shapes (also called "perfect" circles) are forbidden of marriage and sex, due to their position as the highest order of priests, which we will get to very soon.

It's about time that you should be reminded that this entire society, all of these people, have lived in two dimensions since when they first came to be. They have no concept of three dimensions; they see the world through a line. Their government has been in power for 5,000 years, and all of that time they have forced the idea of  two dimensions, for that would be natural to do, onto the minds of the easily-manipulated children, and they will pass it down too. Is it any wonder, then, that the notion of three dimensions, if mentioned, would be met with misunderstanding and aggression?

Is it no wonder, then, that after thousands of years of tight rule, that this concept is now illegal?