Flatland

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for the term Flatlander, see Flatlander (disambiguation)

The cover to Flatland, 6th Edition.

Illustration of a simple house in Flatland.

Flatland: A Romance of Many Dimensions (1884) is a classic 19th century novella 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.

1 The story
2 Social elements
3 Works by other writers
4 External links
5 Notes

[edit] The story

The story posits a two dimensional world (Flatland). The narrator, a humble square (named A. Square), guides us through some of the implications of life in two dimensions. A. Square dreams of a visit to a one-dimensional world (Lineland), and attempts to convince the realm's ignorant monarch of a second dimension. The narrator is then visited by a three-dimensional sphere, which he cannot comprehend until he sees the third dimension for himself. He then dreams of visiting Pointland (which comprises a self-aware point that occupies all space and knows nothing but itself) with the Sphere and learns that he cannot "rescue [the point] from his self-satisfaction". He learns to aspire and to teach others to aspire. The role of women is explained, along with a class system, both of which are a satire of Victorian society at the time.

[edit] Social elements

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 and are considered generally unintelligent, 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 and sound a "peace-cry" 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 explains the need for separate doors for women and men in buildings.

In the world of Flatland, classes are distinguished using the "Art of Feeling" and the "Art of Sight Recognition". Feeling, practiced by the lower classes and women, determines the configuration of a person by feeling one of their angles. The "Art of Sight Recognition", practiced by the upper classes, is aided by "Fog", which allows an observer to determine the depth of an object. With this, polygons with sharp angles relative to the observer will fade out more rapidly than polygons with more gradual 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. The smallest angle of an isosceles triangle gains thirty minutes (half a degree) each generation. Additionally, the rule does not seem to apply to many-sided polygons; often the sons of several hundred-sided polygons will often develop fifty or more sides than their parents.

The book 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 seen, can remove Flatland objects from closed 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 two dimensional universe; at one point, the Sphere gently pokes the narrator's intestines and launches him into three dimensions as proof of his powers. The book implies the possibility that higher dimensions than three exist, implies a satirical description of Victorian life, and teaches a lesson about ignorance, closed-mindedness, and self-satisfaction.

[edit] Works by other writers

Numerous companions to Flatland have been written by various authors, including:

An Episode on Flatland: Or How a Plain Folk Discovered the Third Dimension by Charles Howard Hinton (1907)
Sphereland by Dionys Burger (1965)
The Planiverse by A. K. Dewdney (1984)
Flatterland by Ian Stewart (2001)
Spaceland by Rudy Rucker (2002)
VAS: An Opera in Flatland by Steve Tomasula (2002)

Short stories inspired by Flatland include:

The Incredible Umbrella by Marvin Kaye (1980) includes a chapter set in Flatland
Message Found in a Copy of "Flatland" by Rudy Rucker (1983)
Tangents by Greg Bear

Role playing games based on Flatland include:

"The Flatland Role Playing Game" by Marcus Rowland (1998), revised and expanded as "The Original Flatland Role Playing Game" (2006).
"KaSE Edwin A Abbot’s Flatland (Inflated)" by T Craig Drake, Red Anvil Productions (2005)

Films based on Flatland include:

Two movies made from the book, both titled Flatland, which are sometimes confused with each other:
- A 1965 animated film, directed by Eric Martin and narrated by Dudley Moore.
- A 1982 short film was directed by mathematician Michelle Emmer.
A planned, but as of 2006 unreleased, animated film, directed by Jeffrey Travis. ^[1]

Other:

Christian teacher Rob Bell borrowed the "flatland" concept and added it in his everything is spiritual tour.
An animated sequence in the movie What the Bleep Do We Know!? shows a human interacting with a Flatlander.