''Flatland: A Romance of Many Dimensions'' is a
satirical
Satire is a genre of the visual, literary, and performing arts, usually in the form of fiction and less frequently non-fiction, in which vices, follies, abuses, and shortcomings are held up to ridicule, often with the intent of shaming o ...
novella by the English
schoolmaster
The word schoolmaster, or simply master, refers to a male school teacher. This usage survives in British independent schools, both secondary and preparatory, and a few Indian boarding schools (such as The Doon School) that were modelled aft ...
Edwin Abbott Abbott, first published in 1884 by
Seeley & Co. of London. Written pseudonymously by "A Square", the book used the fictional
two-dimensional world of Flatland to comment on the hierarchy of
Victorian
Victorian or Victorians may refer to:
19th century
* Victorian era, British history during Queen Victoria's 19th-century reign
** Victorian architecture
** Victorian house
** Victorian decorative arts
** Victorian fashion
** Victorian literature ...
culture, but the novella's more enduring contribution is its examination of
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coor ...
s.
Several films have been made from the story, including the feature film ''
Flatland'' (2007). Other efforts have been short or experimental films, including one narrated by
Dudley Moore
Dudley Stuart John Moore CBE (19 April 193527 March 2002) was an English actor, comedian, musician and composer. Moore first came to prominence in the UK as a leading figure in the British satire boom of the 1960s. He was one of the four writ ...
and the short films ''
Flatland: The Movie'' (2007) and ''
Flatland 2: Sphereland'' (2012).
Plot
The story describes a
two-dimensional world occupied by
geometric figures
Lists of shapes cover different types of geometric shape and related topics. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools.
Mathematics
* List of mathematical shapes
* List of two-d ...
; women are simple
line segment
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between ...
s, while men are
polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two t ...
s with various numbers of sides. The narrator is a
square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
, a member of the
caste
Caste is a form of social stratification characterised by endogamy, hereditary transmission of a style of life which often includes an occupation, ritual status in a hierarchy, and customary social interaction and exclusion based on cultural ...
of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions. The first half of the story goes through the practicalities of existing in a two-dimensional universe, as well as a history leading up to the year 1999 on the eve of the 3rd Millennium.
On New Year's Eve, the Square dreams about a visit to a
one-dimensional world (Lineland) inhabited by men, consisting of lines, while the women consisted of "lustrous points". These
points
Point or points may refer to:
Places
* Point, Lewis, a peninsula in the Outer Hebrides, Scotland
* Point, Texas, a city in Rains County, Texas, United States
* Point, the NE tip and a ferry terminal of Lismore, Inner Hebrides, Scotland
* Point ...
and lines are unable to see the Square as anything other than a set of points on a line. Thus, the Square attempts to convince the realm's
monarch
A monarch is a head of stateWebster's II New College DictionarMonarch Houghton Mifflin. Boston. 2001. p. 707. Life tenure, for life or until abdication, and therefore the head of state of a monarchy. A monarch may exercise the highest authority ...
of a second dimension but cannot do so. In the end, the monarch of Lineland tries to kill the Square rather than tolerate him any further.
Following this vision, the Square is visited by a
sphere
A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
. Similar to the "points" in Lineland, he is unable to see the three-dimensional object as anything other than a
circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...
(more precisely, a
disk). The Sphere then levitates up and down through Flatland, allowing the Square to see the circle expand and contract between
great circle
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.
Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry ...
and small circles. The Sphere then tries further to convince the Square of the
third dimension
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...
by dimensional analogies (a point becomes a line, a line becomes a square). The Square is still unable to comprehend the third dimension, so the Sphere resorts to deeds: he gives info about the "insides" of the house, moves a cup through the third dimension, and even goes inside the Square for a bit. Still unable to comprehend 3D, the Sphere takes the Square to the third dimension, Spaceland. This Sphere visits Flatland at the turn of each millennium to introduce a new
apostle
An apostle (), in its literal sense, is an emissary, from Ancient Greek ἀπόστολος (''apóstolos''), literally "one who is sent off", from the verb ἀποστέλλειν (''apostéllein''), "to send off". The purpose of such sending ...
to the idea of a third dimension in the hope of eventually educating the population of Flatland. From the safety of Spaceland, they can oversee the leaders of Flatland, acknowledging the Sphere's existence and prescribing the silencing. After this
proclamation
A proclamation (Lat. ''proclamare'', to make public by announcement) is an official declaration issued by a person of authority to make certain announcements known. Proclamations are currently used within the governing framework of some nations ...
is made, many witnesses are massacred or imprisoned (according to caste), including the Square's brother.
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 dimension
Fourth dimension may refer to:
Science
* Time in physics, the continued progress of existence and events
* Four-dimensional space, the concept of a fourth spatial dimension
* Spacetime, the unification of time and space as a four-dimensional con ...
and higher spatial dimensions. Still, the Sphere returns his student to Flatland in disgrace.
The Square then has a dream in which the Sphere revisits him, this time to introduce him to a
zero-dimensional space
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space. A graphical ...
, Pointland, of whom the Point (sole inhabitant, monarch, and universe in one) perceives any communication as a thought originating in his own mind (cf.
Solipsism
Solipsism (; ) is the philosophical idea that only one's mind is sure to exist. As an epistemological position, solipsism holds that knowledge of anything outside one's own mind is unsure; the external world and other minds cannot be known and ...
):
The Square recognises the identity of the ignorance of the monarchs of Pointland and Lineland with his own (and the Sphere's) previous ignorance of the existence of higher dimensions. Once returned to Flatland, the Square cannot convince anyone of Spaceland's existence, especially after official
decree
A decree is a legal proclamation, usually issued by a head of state (such as the president of a republic or a monarch), according to certain procedures (usually established in a constitution). It has the force of law. The particular term used f ...
s are announced that anyone preaching the existence of three dimensions will be imprisoned (or executed, depending on caste). For example, he tries to convince his relative of the third dimension but cannot move a square "upward," as opposed to forward or sideways. Eventually, the Square himself is imprisoned for just this reason, with only occasional contact with his brother, who is imprisoned in the same facility. He cannot convince his brother, even after all they have both seen. Seven years after being imprisoned, A Square writes out the book ''Flatland'' as a
memoir
A memoir (; , ) is any nonfiction narrative writing based in the author's personal memories. The assertions made in the work are thus understood to be factual. While memoir has historically been defined as a subcategory of biography or autobio ...
, hoping to keep it as posterity for a future generation that can see beyond their two-dimensional existence.
Social elements
Men are portrayed as polygons whose
social status
Social status is the level of social value a person is considered to possess. More specifically, it refers to the relative level of respect, honour, assumed competence, and deference accorded to people, groups, and organizations in a society. S ...
is determined by their
regularity and the number of their sides, with a Circle considered the "perfect" shape. On the other hand, women consist only of lines and are required by law to sound a "peace-cry" as they walk, lest they be mistaken face-to-face for a point. The Square gives 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 by 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 its
angles
The Angles ( ang, Ængle, ; la, Angli) were one of the main Germanic peoples who settled in Great Britain in the post-Roman period. They founded several kingdoms of the Heptarchy in Anglo-Saxon England. Their name is the root of the name ...
. 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 more rapidly than polygons with more gradual angles. Colour of any kind is banned in Flatland after
Isosceles workers painted themselves to impersonate
noble Polygons. The Square describes these events, and the ensuing
class war
Class War is an anarchist group and newspaper established by Ian Bone and others in 1983 in the United Kingdom. An incarnation of Class War was briefly registered as a political party for the purposes of fighting the 2015 United Kingdom genera ...
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
In geometry, a pentagon (from the Greek language, Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple polygon, simple pentagon is ...
, the son of a Pentagon, a
Hexagon
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
Regular hexagon
A ''regular hexagon'' h ...
; 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 30
arc minutes
ARC may refer to:
Business
* Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s
* Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services
* ...
(half a
degree
Degree may refer to:
As a unit of measurement
* Degree (angle), a unit of angle measurement
** Degree of geographical latitude
** Degree of geographical longitude
* Degree symbol (°), a notation used in science, engineering, and mathemati ...
) 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 50 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
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each oth ...
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.
Apart from Isosceles Triangles, only regular Polygons are considered until chapter seven of the book when the issue of irregularity, or physical deformity is brought up. In a two-dimensional world, a regular polygon can be identified by a single angle and/or
vertex. To maintain
social cohesion
Group cohesiveness (also called group cohesion and social cohesion) arises when bonds link members of a social group to one another and to the group as a whole. Although cohesion is a multi-faceted process, it can be broken down into four main c ...
, 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
Euthanasia (from el, εὐθανασία 'good death': εὖ, ''eu'' 'well, good' + θάνατος, ''thanatos'' 'death') is the practice of intentionally ending life to eliminate pain and suffering.
Different countries have different eut ...
; if below, he becomes the lowest rank of
civil servant
The civil service is a collective term for a sector of government composed mainly of career civil servants hired on professional merit rather than appointed or elected, whose institutional tenure typically survives transitions of political leaders ...
. An irregular Polygon is not destroyed at birth, but allowed to develop to see if the irregularity can be "cured" or reduced. If the deformity remains, the irregular is "painlessly and mercifully consumed."
As social satire
In ''Flatland'', Abbott describes a society rigidly divided into classes. Social ascent is the main aspiration of its inhabitants, apparently granted to everyone but strictly controlled by the top of the hierarchy. Freedom is despised and the laws are cruel. Innovators are imprisoned or suppressed. Members of lower classes who are intellectually valuable, and potential leaders of
riots
A riot is a form of civil disorder commonly characterized by a group lashing out in a violent public disturbance against authority, property, or people.
Riots typically involve destruction of property, public or private. The property targete ...
, are either killed or promoted to the higher classes. Every attempt for change is considered dangerous and harmful. This world 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 of women's roles in the society and in the class-based hierarchy of men.
Abbott has been accused of
misogyny
Misogyny () is hatred of, contempt for, or prejudice against women. It is a form of sexism that is used to keep women at a lower social status than men, thus maintaining the societal roles of patriarchy. Misogyny has been widely practiced ...
due to his portrait of women in ''Flatland''. In his Preface to the Second and Revised Edition, 1884, he answers such critics by emphasizing that the description of women was satirizing the viewpoints held, stating that the Square:
Critical reception
Although ''Flatland'' was not ignored when it was published,
it did not obtain great success. In the entry on Edwin Abbott in the ''
Dictionary of National Biography
The ''Dictionary of National Biography'' (''DNB'') is a standard work of reference on notable figures from British history, published since 1885. The updated ''Oxford Dictionary of National Biography'' (''ODNB'') was published on 23 September ...
'' for persons who died in the period of 1922 to 1930, ''Flatland'' was not even mentioned.
The book was discovered again after
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...
's
general theory of relativity was published, which brought to prominence the concept of a fourth dimension. ''Flatland'' was mentioned in a letter entitled "Euclid, Newton and Einstein" published in ''
Nature
Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans ar ...
'' on 12 February 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:
The ''
Oxford Dictionary of National Biography
The ''Dictionary of National Biography'' (''DNB'') is a standard work of reference on notable figures from British history, published since 1885. The updated ''Oxford Dictionary of National Biography'' (''ODNB'') was published on 23 September ...
'' subsequently revised his biography, and it states that
bbott"is most remembered as the author of ''Flatland: A Romance of Many Dimensions''.
Adaptations and parodies
Numerous imitations or sequels to ''Flatland'' have been created. Examples include:
; Films and TV
* ''
Flatland'' (1965), an animated short film based on the novella, was directed by Eric Martin and based on an idea by
John Hubley.
* ''
Flatlandia'' (1982), an Italian animated short film, directed by Michele Emmer.
* ''
Flatland'' (2007), a 98-minute animated independent feature film version directed by
Ladd Ehlinger Jr.
Ladd Ehlinger Jr. (born August 21, 1968 in New Orleans, Louisiana) is an American filmmaker. He is the director and animator of the 2007 film '' Flatland'' as well as a creator of numerous political videos promoting a libertarian conservative view ...
, updates the satire from Victorian England to the modern-day United States.
* ''
Flatland: The Movie'' (2007), by Dano Johnson and Jeffrey Travis, is a 34-minute animated educational film. Its sequel was ''
Flatland 2: Sphereland'' (2012), inspired by the novel ''
Sphereland'' by
Dionys Burger.
* In the ''
Star Trek: The Next Generation'' episode "
The Loss
"The Loss" is the 84th episode of the American science fiction television series '' Star Trek: The Next Generation'', and the tenth episode of the fourth season. It originally aired on December 31, 1990.
Set in the 24th century, the series fol ...
", the
USS ''Enterprise''-D becomes trapped within a field of two-dimensional lifeforms.
; Literature
Books and short stories inspired by ''Flatland'' include:
* ''
An Episode on Flatland: Or How a Plain Folk Discovered the Third Dimension'' by
Charles Howard Hinton
Charles Howard Hinton (1853 – 30 April 1907) was a British mathematician and writer of science fiction works titled ''Scientific Romances''. He was interested in higher dimensions, particularly the fourth dimension. He is known for coining t ...
(1907)
* ''
The Dot and the Line: A Romance in Lower Mathematics'' by
Norton Juster (1963)
* ''
Sphereland'' by
Dionys Burger (1965)
* ''
The Incredible Umbrella
''The'' () is a grammatical article in English, denoting persons or things that are already or about to be mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in E ...
'' by
Marvin Kaye (1980)
* "
Message Found in a Copy of ''Flatland''" by
Rudy Rucker (1983)
* ''
The Planiverse'' by
A. K. Dewdney (1984)
* ''
Flatterland'' by
Ian Stewart (2001)
* ''
Spaceland
Spaceland was an alternative rock/indie rock nightclub in the Silver Lake neighborhood of Los Angeles, California, that existed between 1995 and 2011. The club was formerly a popular disco to young locals called Dreams of LA. Spaceland's owner a ...
'' by
Rudy Rucker (2002)
* ''
VAS: An Opera in Flatland'' (2002) by
Steve Tomasula
Steve Tomasula is an American novelist, critic, short story, and essay author known for cross-genre narratives that explore conceptions of the self, especially as shaped by language and technology.
Biography
Steve Tomasula grew up along the ...
, which uses the two-dimensional world to critique contemporary society
In popular culture
* Physicists and science popularizers
Carl Sagan
Carl Edward Sagan (; ; November 9, 1934December 20, 1996) was an American astronomer, planetary scientist, cosmologist, astrophysicist, astrobiologist, author, and science communicator. His best known scientific contribution is research on ...
and
Stephen Hawking have both commented on and postulated about the effects of ''Flatland''. Sagan recreates the
thought experiment
A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences.
History
The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anci ...
as a set-up to discussing the possibilities of higher dimensions of the physical universe in both the
book
A book is a medium for recording information in the form of writing or images, typically composed of many pages (made of papyrus, parchment, vellum, or paper) bound together and protected by a cover. The technical term for this phys ...
and
television series ''Cosmos'',
whereas Hawking notes the peculiarity of life in two-dimensional space, as any inhabitants would necessarily be unable to digest their own food. (This concept is parodied in the below-described episode of ''Futurama''. The protagonists attempt to eat Flatland food but it falls out immediately. The native organisms in Flatland absorb food somewhat like
amoeba
An amoeba (; less commonly spelled ameba or amœba; plural ''am(o)ebas'' or ''am(o)ebae'' ), often called an amoeboid, is a type of cell or unicellular organism with the ability to alter its shape, primarily by extending and retracting pseudo ...
.)
* In the "
2-D Blacktop
"2-D Blacktop" is the fifteenth episode of the seventh season of the animated sitcom ''Futurama''. It originally aired on Comedy Central on June 19, 2013. The episode was written by Michael Rowe and directed by Raymie Muzquiz. Professor Farnswort ...
" episode of the animated science fiction TV comedy series ''
Futurama'' (season 7, episode 15, originally broadcast June 19, 2013), two spaceships moving at
relativistic speeds crash head on and are compressed together into a flat disk. They meet natives of the realm, who chase after them when the concept of a third dimension is brought up.
* In
David Foster Wallace
David Foster Wallace (February 21, 1962 – September 12, 2008) was an American novelist, short story writer, essayist, and university professor of English and creative writing. Wallace is widely known for his 1996 novel '' Infinite Jest'', whi ...
's novel ''
Infinite Jest
''Infinite Jest'' is a 1996 novel by American writer David Foster Wallace. Categorized as an encyclopedic novel, ''Infinite Jest'' is featured in ''TIME'' magazine's list of the 100 best English-language novels published between 1923 and 2005.
...
'' (1996), it is briefly mentioned that students from the Enfield Tennis Academy could be seen studying and highlighting copies of ''Flatland'' on the bus.
* ''Flatland'' features in ''
The Big Bang Theory'' episode "The Psychic Vortex",
when
Sheldon Cooper declares it one of his favourite imaginary places to visit.
* On the series ''
The Orville
''The Orville'' is an American science fiction comedy-drama television series created by Seth MacFarlane, who also stars as series protagonist Ed Mercer, an officer in the Planetary Union's line of exploratory space vessels in the 25th century ...
'', episode "New Dimensions", after entering a region of two-dimensional space Captain Ed Mercer references Flatland and its theme of social hierarchy.
* In the ''
Sons of Anarchy
''Sons of Anarchy'' is an American action crime drama television series created by Kurt Sutter for FX. Originally aired from September 3, 2008 to December 9, 2014, ''Sons of Anarchy'' follows the lives of a close-knit outlaw motorcycle club o ...
'' episode "Straw," Clay Morrow is lounging on a cot in a private cell in county jail when he first meets retired
U.S. Marshal Lee Toric. Morrow half-ignores Toric while keeping his eyes on a copy of ''Flatland''.
* In ''
Gravity Falls'' its implied by the main antagonist
Bill Cipher
The Disney Channel television series ''Gravity Falls'' created by Alex Hirsch features an extensive cast of characters. All of the characters listed have appeared in the first and second seasons.
Overview
Main
* Dipper Pines (voiced by Ja ...
that he originates from a dimension very similar to Flatland.
See also
* ''
The Dot and the Line''
*
Fourth dimension in literature The idea of a fourth dimension has been a factor in the evolution of modern art, but use of concepts relating to higher dimensions has been little discussed by academics in the literary world. From the late 19th century onwards, many writers began t ...
* ''
Gödel, Escher, Bach''
* ''
The Planiverse''
*
Sphere-world
References
External links
"Sci-Fri Bookclub"recording of National Public Radio discussion of ''Flatland'', featuring mathematician Ian Stewart (21 September 2012)
Online and downloadable versions of the text
; eBooks
*
''Flatland, a Romance of Many Dimensions (first edition)'' on Wikisource
*
''Flatland, a Romance of Many Dimensions (second edition)'' on Wikisource
*
*
*
''Flatland'' digitised copy of the first edition from the
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music ...
''Flatland'' (Second Edition), Revised with original illustrations(HTML format, one page)
(
HTML
The HyperText Markup Language or HTML is the standard markup language for documents designed to be displayed in a web browser. It can be assisted by technologies such as Cascading Style Sheets (CSS) and scripting languages such as JavaScri ...
format, one chapter per page)
''Flatland'' (Fifth Edition), Revised, with original illustrations(
PDF format, all pages, with LaTeX source o
github
(illustrated version) on Manybooks
*
; Recording
*
{{Authority control
1884 British novels
1884 science fiction novels
British novels adapted into films
British satirical novels
British science fiction novels
Dimension
Fictional dimensions
Novels about mathematics
Novels about totalitarianism
Works published under a pseudonym