Flatland
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Flatland: A Romance of Many Dimensions (1884) is a classic 19th century short story by Edwin Abbott Abbott, still popular among mathematics and computer science students, and considered useful reading for people studying topics such as the concept of other dimensions. As a piece of literature, Flatland is respected for its satire on the social hierarchy of Victorian society.
The story posits a world that exists only in two dimensions, and our narrator, a humble square (named A. Square), guides us through some of the implications of that. He is visited by a three-dimensional sphere, which he cannot comprehend until he sees the third dimension for himself. The role of women is explained, along with a class system, both of which are a satire of Victorian society at the time.
In the book, men are portrayed as polygons whose social class is directly proportional to the number of sides they have; therefore, triangles, having only three sides, are at the bottom of the social ladder, while the Priests are composed of multisided polygons whose shapes approximate a circle, which is considered to be the "perfect" shape. On the other hand, the female population is comprised only of lines, who are required by law to sway back and forth as they walk, due to the fact that when a line is coming towards an observer in a 2-D world, it appears merely as a point. A. Square talks of accounts where men have been killed (both by accident and on purpose) by being stabbed by women. This fact also explains the need for separate doors for women and men in buildings.
In the world of Flatland, people are told apart with the help of "Fog", which allows an observer to determine the depth of an object. With this, sides with sharp angles relative to the observer will fade out more rapidly than sides that have more obtuse angles. The population of Flatland can "evolve" through the Law of Nature, which states:
"a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility. Thus the son of a Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on."
This rule is not the case when dealing with isosceles triangles (Soldiers and Workmen), for their evolution occurs through eventually achieving the status of an equilateral triangle, removing them from serfdom.
It poses several interesting thoughts, including the idea that higher dimensional beings have god-like powers over lesser dimensions. In the book, the three-dimensional Sphere has the ability to stand inches away from a Flatlander and observe them without being perceived, can remove 2-D objects from locked containers and "teleport" them via the third dimension apparently without traversing the space in between, and is capable of seeing and touching the inside and outside of everything in the 2-D universe; at one point, the Sphere gently pokes the narrator's intestines as proof of his powers. The book implies that higher dimensions than our own exist, and that a 4D being could have the same powers over our world as the Sphere had over Flatland.
