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Flatland:''For other uses, see Flatland (disambiguation)''
'''''Flatland: A Romance of Many Dimensions''''' is an 1884 in literature|1884 science fiction novella by the England|English schoolmaster Edwin Abbott Abbott.
As a satire, ''Flatland'' offered pointed observations on the social hierarchy of Victorian era|Victorian culture. However, the novella's more enduring contribution is its examination of dimensions; in a foreword to one of the many publications of the novella, noted science writer Isaac Asimov described ''Flatland'' as "The best introduction one can find into the manner of perceiving dimensions." As such, the novella is still popular amongst mathematics, physics and computer science students.
Several films have been made from the story, including a feature film in 2007 called ''Flatland (film)|Flatland''. Other efforts have been short or experimental films, including one narrated by Dudley Moore and a short film with Martin Sheen titled ''Flatland: The Movie''.
Plot
The story is about a two-dimensional world referred to as Flatland. The unnamed narrator, a humble square (geometry)|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 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.
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 (geometry)|point. The 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 more than their parents.
In the book, the three-dimensional sphere|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 teleportation|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.
Editions in print
- ''Flatland'' (5th edition, 1963), 1983 reprint with foreword by Isaac Asimov, HarperCollins, ISBN 0-06-463573-2
- bound together back-to-back with Dionys Burger's ''Sphereland'' (1994), HarperCollins, ISBN 0-06-273276-5
- ''The Annotated Flatland'' (2002), coauthor Ian Stewart (mathematician)|Ian Stewart, Perseus Publishing, ISBN 0-73820541-9
- Signet Classics edition (2005), ISBN 0-451-52976-6
- Oxford University Press (2006), ISBN 0-19-280598-3
- Dover Publications thrift edition (2007), ISBN 0-486-27263-X
- CreateSpace edition (2008), ISBN 1-440-41778-4
Related works
Literature
Numerous imitations or sequels to ''Flatland'' have been written, 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 (mathematician)|Ian Stewart (2001)
- ''Spaceland (novel)|Spaceland'' by Rudy Rucker (2002)
- '''' 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
- ''The Dot and the Line: A Romance in Lower Mathematics'' by Norton Juster (1963)
- ''Voluntary Committal'' by Joe Hill (writer)|Joe Hill (2005)
Feature Films
- Flatland (film)|''Flatland'' (2007), a 98-minute animated independent feature film version directed by Ladd Ehlinger Jr.Short 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. http://www.mat.uniroma1.it/people/emmer/
- ''Flatland: the Movie'',
- An animated sequence in the film ''What the Bleep Do We Know!?'' shows a human interacting with a Flatlander.
TV
- In an episode of Cosmos: A Personal Voyage|''Cosmos'', Carl Sagan discusses Flatland as an analogy to explain other dimensions other than our three physical dimensions.
- "Behold, Eck!", an episode of the original Outer Limits 60's series, is freely inspired from Flatland; it features a friendly, endearing alien creature named Eck, coming from a two-dimensional reality, trapped into our own three dimensions after a miscalculation during the crossing of a time portal.
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).
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''.
- 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".
- Murray Gell-Mann, a particle physicist, in his book The Quark and the Jaguar: Adventures in the Simple and the Complex, uses the story of Flatland to illustrate the way in which natural laws (in this case, the number of spatial dimensions) dictate the complexity of systems that may inhabit the universe.
See also
- Dimension
- Space
Notes
References
*
External links
Online versions of the text
*
*
- ''Flatland'' audio book (mp3 format from Librivox)
- ''Flatland'' with illustrations (html format, one chapter per page)
- ''Flatland'' with illustrations (html format, one page)
- ''Flatland'' 5th edition 62 pages, no illustrations, pdf format
- ''Flatland'', a digitized copy of the first edition from the Internet Archive.
- Flatland as paperback
Feature films
- Flatland The Movie by Jeffrey Travis and Dano Johnson - 2007
- Flatland The Film by Ladd Ehlinger Jr - 2007
- Flatland (film)|Flatland The Film on Wikipedia
*
- Film Threat Review of Flatland The Film - 2007
- review of Flatland: The Film at Rotten Tomatoes
- SciFi.com Review of Flatland The Film at SciFi.com
Short films
- ''Flatland'' by Eric Martin
- Review of FLATLAND: THE MOVIE
*
- Review of Flatland: The Movie by The American Mathematical Society
- Announcement of Flatland: The Movie by the Mathematical Association of America
Category:1884 novels
Category:Dimension
Category:Fictional dimensions
Category:Mathematics fiction books
Category:Science fiction novels
Related Images- Illustration of a simple house in Flatland.
Sources: StartLearningNow, Wikipedia | Usage license: GNU FDL
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