|Flatland: A Romance of Many Dimensions|
The cover to Flatland, 6th Edition.
|Author||Edwin A. Abbott|
|Illustrator||Edwin A. Abbott|
|Publisher||Seely & Co.|
|Text||Flatland: A Romance of Many Dimensions at Wikisource|
Flatland: A Romance of Many Dimensions is an 1884 satirical novella by the English schoolmaster Edwin Abbott Abbott. Writing pseudonymously as "A Square", the book used the fictional two-dimensional world of Flatland to offer pointed observations on the social hierarchy of Victorian culture. However, the novella's more enduring contribution is its examination of dimensions.
Several films have been made from the story, including a feature film in 2007 called Flatland. Other efforts have been short or experimental films, including one narrated by Dudley Moore and the short films Flatland: The Movie and Flatland 2: Sphereland starring Martin Sheen and Kristen Bell.
The story is about a two-dimensional world referred to as Flatland which is occupied by geometric figures. Women are simple line-segments, while men are polygons with various numbers of sides. The narrator is a humble square, a member of the social caste of gentlemen and professionals in a society of geometric figures, who guides the readers through some of the implications of life in two dimensions. The Square has a dream about a visit to a one-dimensional world (Lineland) which is inhabited by "lustrous points". He 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.
He is then visited by a three-dimensional sphere, which he cannot comprehend until he sees Spaceland for himself. This Sphere (who remains nameless, like all characters in the novella) 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.
The Square 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):
'You see,' said my Teacher, 'how little your words have done. So far as the Monarch understands them at all, he accepts them as his own – for he cannot conceive of any other except himself – and plumes himself upon the variety of Its Thought as an instance of creative Power. Let us leave this God of Pointland to the ignorant fruition of his omnipresence and omniscience: nothing that you or I can do can rescue him from his self-satisfaction.'— the Sphere
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, higher 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, where he spends the rest of his days attempting to explain the third dimension to his brother.
Men are portrayed as polygons whose social status is determined by their regularity and the number of their sides with a Circle considered to be the "perfect" shape. On the other hand, females consist only of lines and are required by law to sound a "peace-cry" as they walk, because when a line is coming towards an observer in a 2-D world, her body appears merely as a point. The Square evinces accounts of cases where women have accidentally or deliberately stabbed men to death, as evidence of the need for separate doors for women and men in buildings.
In the world of Flatland, classes are distinguished using the "Art of Hearing," the "Art of Feeling" and the "Art of Sight Recognition." Classes can be distinguished by the sound of one's voice, but the lower classes have more developed vocal organs, enabling them to feign the voice of a polygon or even a circle. 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. Colour of any kind was banned in Flatland after Isosceles workers painted themselves to impersonate noble Polygons. The Square describes these events, and the ensuing class war at length.
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) with only two congruent sides. The smallest angle of an isosceles triangle gains thirty arc minutes (half a degree) each generation. Additionally, the rule does not seem to apply to many-sided polygons. For example, the sons of several hundred-sided polygons will often develop fifty or more sides more than their parents. Furthermore, the angle of an isosceles triangle or the number of sides of a (regular) polygon may be altered during life by deeds or surgical adjustments.
An equilateral Triangle is a member of the craftsman class. Squares and Pentagons are the "gentlemen" class, as doctors, lawyers, and other professions. Hexagons are the lowest rank of nobility, all the way up to (near) circles, who make up the priest class. The higher-order polygons have much less of a chance of producing sons, preventing Flatland from being overcrowded with noblemen.
Regular polygons were considered in isolation until chapter seven of the book when the issue of irregularity, or physical deformity, became considered. In a two dimensional world a regular polygon can be identified by a single angle and/or vertex. In order to maintain social cohesion, irregularity is to be abhorred, with moral irregularity and criminality cited, "by some" (in the book), as inevitable additional deformities, a sentiment with which the Square concurs. If the error of deviation is above a stated amount, the irregular polygon faces euthanasia; if below, he becomes the lowest rank of civil servant. An irregular polygon is not destroyed at birth, but allowed to develop to see if the irregularity could be “cured” or reduced. If the deformity could not be corrected then the irregular should be “painlessly and mercifully consumed.”
In Flatland Abbott describes a society rigidly divided into classes. Social ascent is the main aspiration of its inhabitants, apparently granted to everyone but in reality strictly controlled by the few that are already positioned at the top of the hierarchy. Freedom is despised and the laws are cruel. Innovators are either imprisoned or suppressed. Members of lower classes who are intellectually valuable, and potential leaders of riots, are either killed or corrupted by being promoted to the upper classes. The organization and government of 'Flatland' is so self-satisfied and perfect that every attempt for change is considered dangerous and harmful. This world, as ours, is not prepared to receive 'Revelations from another world'.
The satirical part is mainly concentrated in the first part of the book, 'This World', which describes Flatland. The main points of interest are the Victorian concept on women's roles in the society and in the class-based hierarchy of men.
Abbott has been accused of misogyny due to his portrait of women in 'Flatland'. In his Preface to the Second and Revised Edition, 1884, he answers such critics by stating that the Square:
was writing as a Historian, he has identified himself (perhaps too closely) with the views generally adopted by Flatland and (as he has been informed) even by Spaceland, Historians; in whose pages (until very recent times) the destinies of Women and of the masses of mankind have seldom been deemed worthy of mention and never of careful consideration.—the Editor
The book was discovered again after Albert Einstein's general theory of relativity was published, which introduced the concept of a fourth dimension. Flatland was mentioned in a letter entitled "Euclid, Newton and Einstein" published in Nature on February 12, 1920. In this letter Abbott is depicted, in a sense, as a prophet due to his intuition of the importance of time to explain certain phenomena:
Some thirty or more years ago a little jeu d'esprit was written by Dr. Edwin Abbott entitled Flatland. At the time of its publication it did not attract as much attention as it deserved... If there is motion of our three-dimensional space relative to the fourth dimension, all the changes we experience and assign to the flow of time will be due simply to this movement, the whole of the future as well as the past always existing in the fourth dimension. —from a "Letter to the Editor" by William Garnett. in Nature on February 12, 1920.
The Oxford Dictionary of National Biography now contains a reference to Flatland.
Editions in print
- Flatland (5th edition, 1963), 1983 reprint with foreword by Isaac Asimov, HarperCollins, ISBN 0-06-463573-2
- The Annotated Flatland (2002), coauthor Ian Stewart, Perseus Publishing, ISBN 0-7382-0541-9
- 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 1-4404-1778-4
Adaptations and parodies
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 (2001), and Spaceland by Rudy Rucker (2002). Short stories inspired by Flatland include The Incredible Umbrella by Marvin Kaye (1980), Message Found in a Copy of "Flatland" by Rudy Rucker (1983), and The Dot and the Line: A Romance in Lower Mathematics by Norton Juster (1963).
Flatland (1965) was an animated short film based on the novella, directed by Eric Martin and based on an idea by John Hubley. Flatland (2007), a 98-minute animated independent feature film version directed by Ladd Ehlinger Jr, updates the satire from Victorian England to the modern-day United States. Flatland: The Movie (2007), by Dano Johnson & Jeffrey Travis, was a 34-minute animated educational film with the voices of Martin Sheen, Kristen Bell, Michael York, and Tony Hale. Its sequel was Flatland 2: Sphereland (2012), inspired by the novel Sphereland by Dionys Burger and starring Kristen Bell, Danny Pudi, Michael York, Tony Hale, Danica McKellar, and Kate Mulgrew.
Physicists and science popularizers Carl Sagan and Stephen Hawking have both commented on and postulated about the effects of Flatland. Dr. Sagan recreates the thought experiment as a set-up to discussing the possibilities of higher dimensions of the physical universe in both the book and television series Cosmos, whereas Dr. Hawking notes the impossibility of life in two-dimensional space, as any inhabitants would necessarily be unable to digest their own food.
Flatland features prominently in The Big Bang Theory episode "The Psychic Vortex" when Dr. Sheldon Cooper declares it one of his favorite imaginary places to visit. Dr. Cooper (portrayed by American actor Jim Parsons) further comments about the aforementioned appeal of circles in Flatland to Dr. Rajesh Koothrappali (portrayed by Indian-American actor Kunal Nayyar), with whom he attempts to engage in an exercise in imagination during the episode.
It also features in the Futurama episode "2-D Blacktop" when Professor Farnsworth's adventures in drag racing lead to a foray of drifting in and out of inter-dimensional spaces. The characters' experience in Flatland is used as an opportunity to point out the flawed reasoning that something doesn't exist simply because you can't conceive it.
- Animal Farm, novella by George Orwell
- Blind men and an elephant
- Fourth dimension in literature
- Triangle and Robert
- The Dot and the Line
- "—And He Built a Crooked House—"
- Dimension-bending video games:
- Tuck, Donald H. (1974). The Encyclopedia of Science Fiction and Fantasy. Chicago: Advent. p. 1. ISBN 0-911682-20-1.
- Abbott, Edwin A. (1884). Flatland: A romance in Many dimensions. Dover thrift Edition (1992 unabridged). New York, p. ii.
- Stewart, Ian (2008). The Annotated Flatland: A Romance of Many Dimensions. New York: Basic Books. pp. xiii. ISBN 0-465-01123-3.
- Science News Review of Flatland: The Movie and Flatland 2: Sphereland
- Abbott, Edwin A. (1884) Flatland, Part II, § 20.—How the Sphere encouraged me in a Vision, p 92
- Abbott, Edwin A. Flatland: A romance in Many Dimensions. (1992, Page 25). Dover thrift Edition (unabridged). New York.
- Stewart, Ian (2008). The Annotated Flatland: A Romance of Many Dimensions. New York: Basic Books. pp. xvii. ISBN 0-465-01123-3.
- "Flatland Reviews". Retrieved 2011-04-02.
- "Flatland Reviews - Nature, February 1920". Retrieved 2011-04-02.
- Flatland at the Internet Movie Database
- "DER Documentary: Flatland". Retrieved 11 October 2012.
- "Flatland Animation: The project". Retrieved 11 October 2012.
- "Flatland the Film". Retrieved 2007-01-14.
- "Flatland: The Movie". Retrieved 2007-01-14.
- IMDB Flatland: The Movie
- "Flatland 2: Sphereland".
- IMDB Flatland 2: Sphereland
- GeekDad.com Review of Flatland: The Movie and Flatland 2: Sphereland
- Tremlin, Todd (2006). Minds and Gods: The Cognitive Foundations of Religion. USA: Oxford University Press. p. 91. ISBN 978-0199739011.
- Gott, J. Richard (2001-05-21). Time Travel in Einstein's Universe: The Physical Possibilities of Travel through Time. USA: Houghton Mifflin Company. p. 61. ISBN 978-0395955635.
- VanDerWerff, Todd. "The Big Bang Theory: "The Psychic Vortex"". A.V. Club. Retrieved 2014-03-14.
- "Flatland Featured on The Big Bang Theory on CBS Television". Giant Screen Cinema Association. Retrieved 2014-03-14.
- ref needed
- DeNitto, Nick. "Futurama Invades Flatland". Stage Buddy. Retrieved 2014-03-14.
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Online and downloadable versions of the text
- Flatland, a Romance of Many Dimensions (first edition) on Wikisource
- Flatland, a Romance of Many Dimensions (second edition) on Wikisource
- Flatland at Project Gutenberg, text, no illustrations
- Flatland at Project Gutenberg (with ASCII illustrations)
- Flatland, a digitized copy of the first edition from the Internet Archive.
- Flatland, Second Edition, Revised with original illustrations (HTML format, one page)
- Flatland, Fifth Edition, Revised, with original illustrations (HTML format, one chapter per page)
- Flatland, Fifth Edition, Revised, with original illustrations (PDF format, all pages, with LaTeX source on github)
- Flatland audio book (mp3 format from Librivox)
- Flatland on Open Library at the Internet Archive
- "Sci-Fri Bookclub" recording of National Public Radio discussion of Flatland, featuring mathematician Ian Stewart (Sept. 21, 2012)