Flatland

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For other uses, see Flatlander (disambiguation).
Flatland: A Romance of Many Dimensions
Image:Flatland cover.jpg
The cover to Flatland, 6th Edition.
Author Edwin Abbott Abbott
Illustrator Edwin Abbott Abbott
Country United Kingdom
Language English
Genre(s) Novella
Publisher Seely & Co.
Publication date 1884
Media type Print (Hardback)
Pages viii, 100 pp
ISBN NA

Flatland: A Romance of Many Dimensions is an 1884 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.

Several films have been made from the story, including two from different directors released in 2007.

Contents

[edit] The story

The story posits a two dimensional world (Flatland). The unnamed narrator, a humble square (the social caste of gentlemen and professionals), guides us through some of the implications of life in two dimensions. The Square has a dream about a visit to a one-dimensional world (Lineland), and attempts to convince the realm's ignorant monarch of a second dimension, but finds that it is essentially impossible to make him see outside of his eternally straight line.

The narrator is then visited by a three-dimensional sphere, which he cannot comprehend until he sees the Spaceland for himself. This sphere, who remains nameless, visits Flatland at the turn of each millennium to introduce a new apostle to the idea of a third dimension in the hopes of eventually educating the population of Flatland of the existence of Spaceland. From the safety of Spaceland, they are able to observe the leaders of Flatland secretly acknowledging the existence of the sphere and prescribing the silencing of anyone found preaching the truth of Spaceland and the third dimension. After this proclamation is made, many witnesses are massacred or imprisoned (according to caste).

After the Square's mind is opened to new dimensions, he tries to convince the Sphere of the theoretical possibility of the existence of a fourth (and fifth, and sixth...) spatial dimension. Offended by this presumption and incapable of comprehending other dimensions, the Sphere returns his student to Flatland in disgrace.

He then has a dream in which the Sphere visits him again, this time to introduce him to Pointland. The point (sole inhabitant, monarch, and universe in one) perceives any attempt at communicating with him as simply being a thought originating in his own mind. (cf. Solipsism)

The Square recognizes the connection between the ignorance of the monarchs of Pointland and Lineland with his own (and the Sphere's) previous ignorance of the existence of other dimensions.

Once returned to Flatland, the Square finds it difficult to convince anyone of Spaceland's existence, especially after official decrees are announced - anyone preaching the lies of three dimensions will be imprisoned (or executed, depending on caste). Eventually the Square himself is imprisoned for just this reason.

Image:Flatland house diagram.png
Illustration of a simple house in Flatland.

[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 multi-sided 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, because when a line is coming towards an observer in a 2-D world, it appears merely as a point. 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. Also, colors in Flatland were banned, when lower classes painted themselves to appear to be higher ordered.

In the world of Flatland, classes are distinguished using the "Art of Feeling" and the "Art of Sight Recognition". Feeling, practised by the lower classes and women, determines the configuration of a person by feeling one of their angles. The "Art of Sight Recognition", practised 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; the sons of several hundred-sided polygons will often develop fifty or more sides than their parents.

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 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.

[edit] Editions in print

[edit] Related works

[edit] Literature

Numerous companions to Flatland have been written, including:

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
  • The Dot and the Line: A Romance in Lower Mathematics by Norton Juster (1963)
  • Voluntary Committal by Joe Hill (2005)

[edit] Films

  • Flatland (1965), an animated film directed by Eric Martin and narrated by Dudley Moore.
  • Flatland (1982), a short film directed by mathematician Michele Emmer. [1]
  • Flatland (2007), a 95-minute animated independent feature film version directed by Ladd Ehlinger Jr.[1] Updates satire from Victorian England to modern America (e.g. with a "president" instead of a "king", advanced technology in Spaceland, etc.).[2]
  • Flatland: the Movie,[3] a 30-minute animated educational film with the voices of Martin Sheen, Kristen Bell, Michael York, and Tony Hale
  • An animated sequence in the film What the Bleep Do We Know!? shows a human interacting with a Flatlander.

[edit] TV

  • In an episode of Cosmos, Carl Sagan discusses Flatland as an analogy to explain other dimensions other than our three physical dimensions.

[edit] Games

Role-playing games based on Flatland include:

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

[edit] Other uses

  • Christian teacher Rob Bell borrowed the "flatland" concept in his Everything is Spiritual tour.
  • Christian author David Brandt Berg also used the "flatland" concept in one of his lectures on the existence of the spirit world, published in Dare to be Different.
  • Lisa Randall, a theoretical physicist, gave a brief overview of Flatland in her book Warped Passages.
  • Independent hip-hop musician, proGrammar, penned the following lyrics in his song, "Music": "Flatlanders can't understand the measure of a man from a different planet, with a different plan."
  • Jasper Fforde asserts in his Thursday Next novel The Well of Lost Plots that the writing of Flatland used up the "last [pure] original idea".

[edit] Notes

  1. ^ Flatland the Film. Retrieved on 2007-01-14.
  2. ^ Flatland the Film. Retrieved on 2007-05-18.
  3. ^ Flatland: The Movie. Retrieved on 2007-01-14.

[edit] References

[edit] External links

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Flatland

[edit] Online versions of the text

[edit] Films

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