Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmasterEdwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by "A Square",[1] the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions.[2]
The story describes a two-dimensional world inhabited by geometric figures (flatlanders[4]); women are line segments, while men are polygons with various numbers of sides. The narrator is a square, a member of the caste 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 of a visit to a one-dimensional world, "Lineland", inhabited by men, consisting of lines, while the women consisted of "lustrous points". These points 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 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. Similar to the "points" in Lineland, he is unable to see the three-dimensional object as anything other than a circle (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 and small circles. The Sphere then tries further to convince the Square of the third dimension 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 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 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 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, 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):
"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."[5]
—the Sphere
The last sketch in the book.
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 decrees 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, 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 is determined by their regularity and the number of their sides, with a Circle considered the "perfect" shape. Women are lines, quite fragile but also dangerous, as they can disappear from view and possibly stab someone. To prevent this, they are required by law to sound a "peace-cry" while moving about and to use separate doors from men.
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 "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 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 30 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 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 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, 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 can be "cured" or reduced. If the deformity remains, the irregular is "painlessly and mercifully consumed."[6]
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, 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.[7] Abbott has been accused[weaselwords][by whom?] of misogyny due to his portrayal 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:
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.
Critical reception
Flatland did not have much success when published, although it was not entirely ignored.[8] In the entry on Edwin Abbott in the Dictionary of National Biography for persons who died in the period of 1922 to 1930, Flatland was not even mentioned.[2]
The book was discovered again after Albert Einstein's general theory of relativity was published, which brought to prominence the concept of a fourth dimension. Flatland was mentioned in a letter by William Garnett entitled "Euclid, Newton and Einstein" published in Nature 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:[9][10]
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.
The Oxford Dictionary of National Biography subsequently revised his biography to state that [Abbott] "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.[11][12][13]
Flatlandia (1982), an Italian animated short film, directed by Michele Emmer.[14]
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.[15]
Physicists and science popularizers Carl Sagan and Stephen Hawking have both commented on and postulated about the effects of Flatland. 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,[23] 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.)[24]
The League of Extraordinary Gentlemen, Volume 2, issue 3, in chapter 3 of the series of writings New Traveller's Almanac, it is mentioned that in an unknown basement of New York, Flatland was discovered by a mathematician.
In the "2-D Blacktop" episode of the animated science fiction TV comedy series Futurama (season 10 episode 1, originally broadcast June 17, 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.[25]
In David Foster Wallace's novel Infinite Jest (1996), it is briefly mentioned that students from the Enfield Tennis Academy could be seen studying and highlighting copies of Flatland on the bus.[26]
On the series The Orville, episode "New Dimensions", after entering a region of two-dimensional space Captain Ed Mercer references Flatland and its theme of social hierarchy.[29]
In the Sons of Anarchy 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, it is implied by the main antagonist Bill Cipher that he originates from a dimension very similar to Flatland.
In the Gravity Falls book titled "The Book of Bill" a picture of Flatland's cover is shown on a TV screen on the chapter titled "My Story".
In the 1964 episode of Outer Limits “Behold Eck!” a 2-dimensional creature accidentally visits earth through a time-hole and causes some damage before it can get back home.
In physics and mathematics, the dimension of a mathematical space 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 coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
Edwin Abbott Abbott was an English schoolmaster, theologian, and Anglican priest, best known as the author of the novella Flatland (1884).
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle. The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex; the shortest segment between the base and apex is the height. The area of a triangle equals one-half the product of height and base length.
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal ; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term "oblong" is used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as ABCD.
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties.
In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from the rest of the class; "degeneracy" is the condition of being a degenerate case.
In four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}. It is also called C24, or the icositetrachoron, octaplex (short for "octahedral complex"), icosatetrahedroid, octacube, hyper-diamond or polyoctahedron, being constructed of octahedral cells.
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.
Charles Howard Hinton 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 the word "tesseract" and for his work on methods of visualising the geometry of higher dimensions.
Flatterland is a 2001 book written by mathematician and science popularizer Ian Stewart about non-Euclidean geometry. It was written as a sequel to Flatland, an 1884 novel that discussed different dimensions.
The Planiverse is a novel by A. K. Dewdney, written in 1984 about a two-dimensional world.
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height. This concept of ordinary space is called Euclidean space because it corresponds to Euclid's geometry, which was originally abstracted from the spatial experiences of everyday life.
Sphereland: A Fantasy About Curved Spaces and an Expanding Universe is a 1965 translation of Bolland : een roman van gekromde ruimten en uitdijend heelal, a 1957 novel by Dionys Burger, and is a sequel to Flatland, a novel by "A Square". The novel expands upon the social and mathematical foundations on which Flatland is based. It is markedly different from the first novel in that it has a more prosaic ending and treatment of society.
Spaceland is a science fiction novel by American mathematician and computer scientist Rudy Rucker, and published in 2002 by Tor Books.
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences.
Flatland is a 2007 American animated science fiction film based on the 1884 novella Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott. The film was directed and animated by Ladd Ehlinger Jr. in Lightwave 3D. The screenplay was written by author Tom Whalen. The music was composed by Mark Slater.
Flatland: The Movie is a short animated film which was released to video in 2007. The cast includes the voices of actors Martin Sheen, Kristen Bell and Tony Hale. The story is based on the 1884 science fiction novella Flatland: A Romance of Many Dimensions written by Edwin A. Abbott.
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 to make use of possibilities opened up by the exploration of such concepts as hypercube geometry. While many writers took the fourth dimension to be one of time, others preferred to think of it in spatial terms, and some associated the new mathematics with wider changes in modern culture.
References
↑ Abbott, Edwin A. (1884). Flatland: A Romance in Many Dimensions. New York: Dover Thrift Edition (1992 unabridged). p.ii.
1 2 Stewart, Ian (2008). The Annotated Flatland: A Romance of Many Dimensions. New York: Basic Books. pp.xiii. ISBN978-0-465-01123-0.
This page is based on this Wikipedia article Text is available under the CC BY-SA 4.0 license; additional terms may apply. Images, videos and audio are available under their respective licenses.
