Line #78 Literature/Flatland


1	[[quoteright:350:https://static.tvtropes.org/pmwiki/pub/images/figure-82_5406.gif]]
2	[[caption-width-right:350:A. Square's home]]
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4	''[[http://www.geom.uiuc.edu/~banchoff/Flatland/ Flatland: A Romance Of Many Dimensions]]'' is an 1884 satirical novella by Edwin A. Abbott. The story takes place in a two-dimensional world made up of polygons, and is narrated by a square named [[StevenUlyssesPerhero A. Square]][[note]]Originally "A Square", the indefinite article evolving to a first initial in later printings[[/note]]. It's also a scathing dissection of Victorian class structures, of biological racism and eugenics, and of misogyny.
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6	The square dreams one night about visiting Lineland, where there is only one dimension, and he tries and fails to explain his existence and that of a second dimension to its king. Later, a sphere from Spaceland speaks to him, pokes his insides, and appears before him in his home, then carries him in an incomprehensibly new direction called "up", where he is able to look down and see into houses and the insides of the other polygons. Suddenly understanding, he speculates that there may be dimensions beyond Spaceland, but the sphere is discomfited by this and returns him to Flatland, where he seems to just appear. Later, he is imprisoned for this talk of a third dimension, and he dreams of himself and the sphere visiting Pointland, where the Point -- monarch, sole inhabitant, and universe in one -- is unable to perceive them as anything but his own thoughts. This causes him to connect the uncomprehending ignorance of the Point, the king of Lineland, and the rulers of Flatland together with the sphere's astonishment at the thought of some dimension beyond Up.
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8	It is part sci-fi, part satire, part philosophy, and part mathematics. Creator/IsaacAsimov described Flatland as "The best introduction one can find into the manner of perceiving dimensions".
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10	Adaptations include a 1965 animated short (''Flatland''), a 1982 stop-motion short [[NoExportForYou only available in Italian]] (''Flatlandia''), a 2007 animated feature film (''Flatland'', aka ''Flatland: The Film''), and, confusingly, another 2007 animated film, this one a short (''Flatland: TheMovie''), and its 2012 sequel, ''[[https://archive.org/details/flatland-2-sphereland-hd/Flatland+2+_+Sphereland+HD.mp4 Sphereland]]''. The story is also summarized by Carl Sagan as part of ''Cosmos''.
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12	!!Tropes:
13	[[foldercontrol]]
14	[[folder: Tropes found in the novel ''Flatland'']]
15	* OneDimensionalThinking: Justified in Lineland, in which the second dimension does not exist.
16	%%* TwoDSpace: Flatland.
17	* AlienGeometries: The third dimension is unfathomably alien to the Flatlanders, and so is the second dimension to the Linelanders. [[Main/ParanoiaFuel The fourth dimension is briefly discussed]].
18	* AnotherDimension: One of the few times in fiction that this term was used correctly.
19	* BedTrick: An isoceles triangle (lower class, basically serfs) paints himself up as a polygon (aristocracy) in order to bed a woman that had rejected him.
20	* BizarreAlienBiology: Linelanders have eyes and mouths at both ends. Additionally, males have two voices, baritone from one end and Tenor from the other.
21	* BizarreAlienSexes: The male Flatlanders are polygons of varying angle count (from triangle on up to quasi-circle) in which intelligence is dictated by angle count, while the females are straight lines and nearly mindless.
22	* BlackAndWhiteInsanity: The ruling caste enforce a BlackAndWhiteMorality worldview to the point where they outlaw color, forcing the world to literally be black and white. Their excuse for this draconian law is that it's needed to preserve the sexual purity of their women.
23	* CallASmeerpARabbit: The {{Living Polyhedron}}s that inhabit Flatland are called "human beings".
24	* CassandraTruth: The square eventually is imprisoned for preaching the Gospel of Three Dimensions. No one will believe him, not even his brother, who witnesses the sphere appearing before the Flatland parliament.
25	* DoesThisRemindYouOfAnything: In addition to its frank discussion of Euclidean geometry, many of the book's depictions of different dimensions are thinly-veiled social satire, largely concerned with the evolution of social and political systems.
26	** Flatland is Abbott's own Victorian Britain--a world whose inhabitants revel in their supposed freedom, but are actually stifled by a rigid class system, shunning any ideas that might expose their limited worldview for what it is. Because they can only think in two dimensions, Flatlanders are utterly incapable of understanding "upward mobility", which is the only way to reach Spaceland and the freedom that it offers.
27	** Lineland is a very primitive monarchy, where all power and influence is determined by proximity to to an autocratic king -- who is actually [[SmallNameBigEgo just a humble line on a line]]. Because he only exists in one dimension, the King of Lineland is incapable of even basic movement, since there's no way for anyone to move aside to permit someone else passage, but he's too drunk on his own ego to realize how little his "authority" really matters.
28	* FantasticRacism: More precisely, fantastic classism and fantastic sexism-- polygons with more sides are the higher classes; triangles -- especially isosceles ones -- are servants or soldiers; circles (technically many-many-many-sided polygons) are priests; women of all classes are just lines[[note]]Technically, as explained by A. Square early on, they're actually very narrow rhombuses, but the distinction isn't really important on a practical level.[[/note]]. It is a satire, thinly veiled, of Victorian society.
29	* FantasticCasteSystem: A Flatlander's intellect is dictated by the degrees of their angles (for triangles), or how many angles they have (for polygons). A perfectly equilateral triangle is the equivalent to an IntrepidMerchant in brainpower; a square is smart enough to be a lawyer. People with "irregular" angles (One example given was a parallelogram) are predestined to criminality, similar to how some people thought of XYY-Chromosome Disorder patients back in the 80's. Females, being straight lines and therefore having no angles, are universally dumb as, well, posts. Polygons go up one caste every generation, and triangles have a chance at producing a square son, who in turn have a chance of producing pentagonal or triangular sons.
30	* FlatWorld: Not really the TropeMaker, as various cultures have believed in a flat Earth since prehistoric times. But ''Flatland'' definitely applies a new spin to the notion.
31	* GenderEqualsBreed: As discussed above, a male Flatlander will be of his father's shape or one angle higher, while females are straight lines regardless of parentage.
32	* AGodAmI: The sole inhabitant of Pointland spends all his time making these speeches to himself, since he has no way of being convinced that anything else even exists.
33	* GovernmentConspiracy: The circles that rule Flatland know that a sphere comes every thousand years to preach the Gospel of Three Dimensions, so they execute any lower-class Flatlander heard spreading the sphere's message and imprison higher-class Flatlanders that do so.
34	* IgnorantOfTheirOwnIgnorance: Former TropeNamer. The King of Pointland believes that he is the only being that exists, because he cannot perceive anything outside of Pointland.
35	* InterspeciesRomance: Romance between the polygonal males and the linear females of Flatland can approach this.
36	* InWhichATropeIsDescribed: All the chapter titles. The second chapter, for instance, is titled "Of the Climate and Houses in Flatland", since the book is supposed to be the Square's description of his country and people.
37	* LivingPolyhedron: All inhabitants of Flatland are two-dimensional polygons. There's also a Sphere, which claims to inhabit a Sphereland with other 3D shapes.
38	* MoreThanThreeDimensions: {{Discussed\|Trope}}. A. Square is a regular guy who happens to be a square, living in a two-dimensional universe. He is visited by a sphere who preaches to him the Gospel of Three Dimensions. The square is scornful of the idea initially, but eventually the sphere convinces him. When the square talks excitedly of the possibility of a ''fourth'' dimension, the sphere immediately dismisses the idea as ridiculous.
39	* NewYearHasCome: The square is seeing in the new year with his wife when the sphere appears to him.
40	%%* PaperPeople
41	* PalsWithJesus: The hero is befriended by a helpful higher-dimensional being.
42	* PunnyName: A. Square. Take into account that the author's name is ''Edwin Abbott Abbott''. Abbott squared = A, squared.
43	* SinisterGeometry: Averted; Flatlanders value perfect geometric symmetry as a sign of high breeding and intelligence. From a spectator point of view, however, Flatlander society in the indie film is shown to be rather cruel and sinister.
44	* SkepticismFailure: A. Square and the Linelanders are skeptical of higher dimensions, and the plot proves them wrong.
45	%%* SmallSecludedWorld: Pointland.
46	* StayInTheKitchen: Women are restricted in their social roles because they are dangerously sharp lines (well, super narrow rhombuses). They are restricted because they can kill people by walking into them: it is segregation based on a physical characteristic. {{Lampshade\|Hanging}}d, in that the Square mentions that it probably seems incredibly misogynistic to the reader, but it beats getting stabbed to death.
47	* ThirdPersonPerson: The King of Pointland, who is unable to conceive of anything other than himself.
48	* TheWarOnStraw: The Flatland priests and government officials' view of a world not being flat.
49	* WhenDimensionsCollide: The presence of the more transcendent sphere in Flatland almost embodies this trope.
50	* WomenAreWiser: Averted. Flatland women (lines) have the [[ForgetfulJones memories of goldfish]] and come off as {{Cloudcuckoolander}}s. One anecdote states that a line once murdered her entire family and then wondered what the hell happened to them a minute later.
51	%%* WorldBuilding: Over half the book is this.
52	* YouCannotGraspTheTrueForm: When the hero is taken into the third dimension by a sphere, he literally [[YouCannotGraspTheTrueForm Cannot Grasp Its True Form]] or the other creatures there at first.
53	[[/folder]]
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55	[[folder:Tropes found in various adaptations of ''Flatland'']]
56	* AdaptationalHeroism: Abbot Square in ''Flatland: The Movie'' is far more accepting of the idea of 3D and assists his brother in helping spread the message.
57	* AdaptationInducedPlotHole:
58	** ''Flatland: The Film'' has a setting update from Victorian England to modern day U.S. so why does the "President" still wear a ''crown''?
59	** ''Flatland: The Movie'' has objects that don't make sense in a 2D world, such as pink unicorn dolls, a fishtank, and skateboards.
60	* AdaptationalIntelligence: In both 2007 adaptations, females are not nearly as braindead as they are in the book.
61	* AdaptationNameChange:
62	** ''Flatland: The Film'':
63	*** Pantocyclus to President Circle.
64	*** Lord Sphere to CEO A. Sphere.
65	** ''Flatland: The Movie'':
66	*** A. Square to Arthur Square.
67	*** B. Square to Abbot Square.
68	*** Lord Sphere to Spherius.
69	* AdaptationSpeciesChange:
70	** Chromatistes is changed from a pentagon to an "irregular" in ''Flatland: The Film''. A. Square also only has one hexagonal child, with the other being changed to a pentagon.
71	** In ''Flatland: The Movie'' females are the same shapes as the males.
72	* AdaptationalVillainy:
73	** B. Square in ''Flatland: The Film'' is the one responsible for planning the Chromatist massacre (and thus causing the ensuing riot) and later tries to kill his brother in prison.
74	** Pantocyclus was originally mostly a WellIntentionedExtremist, and had legitimate reasons to fear chromatism and 3D. Even in the DarkerAndEdgier ''Flatland: The Film'' he had the occasional PetTheDog moment. In ''Flatland: The Movie'' on the other hand, he has the purely selfish motivation of [[FantasticRacism keeping the circles on the top of the food chain]] and also has Arthur sentenced to ''death'' as opposed to imprisonment.
75	* AKindOfOne: In ''Sphereland'', the protagonists discover that there are ''dozens'' of Pointlands, with each one having (and ''being'') a self-proclaimed King of Pointland all ignorantly unaware of each other.
76	* AgeLift: Hex is A. Square's son as opposed to Grandson in ''Flatland: The Film''. In this case the extra side is explained as the result of being born with a deformity.
77	* AlternateUniverse: ''Sphereland'' reveals that Flatland is the surface of a sphere, and that many other such spheres exist all in the third dimension.
78	* AlternateSelf: Near the end of ''Sphereland'', Hex sees multiple alternate versions of the ship, including one where her grandfather Arthur Square is still alive. Hex wonders aloud what that version of her did differently that mader her have a happier ending.
79	* AnimatedAdaptation: Oddly, two were released in the same year (2007). ''Flatland: The Film'' was a feature-length indie film. ''Flatland: the Movie'' was a big-budgeted edutainment short with an AllStarCast.
80	* AscendedExtra: In ''Flatland: The Movie,'' the King of Lineland only appears in one scene, but in the sequel ''Sphereland'', he plays amore prominent role in helping uncover the mystery of Flatland's shape.
81	* AutoCannibalism: A. Line (a political prisoner) in the movie does this as a form of suicide before she's [[BetterToDieThanBeKilled executed by the state.]]
82	* BreakingOldTrends: ''Flatland: The Movie'' had a recurring theme of increasingly-higher-dimensional beings ignorant of a higher dimension than themselves, with the King of Pointland unable to percieve anything outside himself, the King of Lineland being unable to understand Arthur Square's talk of two dimensions, Arthur himself unable to percieve Spherius and even Spherius scoffing at the mere idea of a fourth dimension. The Oversphere breaks this pattern entirely: she fully accepts the potential existence of a fifth, and sixth, and maybe more dimensions, even scolding and punishing Spherius for being so closed-minded and calling the potential of higher dimensions "an infinite set of possibilities."
83	* ChekovsGunman: The King of Lineland in ''Sphereland''. While Hex and Puncto travel alongside Lineland they encounter him again, in which case they ask him if he's been following them. Only when he replies he hasn't the two hexagons realize that they went right back from where they started just by following Lineland: leading to their realization that Lineland is a circle, and Flatland is a sphere.
84	* DimensionalTraveler: The Oversphere from ''Sphereland'' moves through the fourth dimension and visits Spherius just as he visited Arthur Square in the first film.
85	* HappyEndingOverride: ''Flatland: The Movie'' ends on a high note, with Arthur Square and his proof of the third dimension seemingly having revolutionized Flatland. ''Sphereland'' reveals however that he was eventually ostracized for his inability to further explain his discoveries, and he later dies of grief.
86	* FanSequel: Given that Abbott's book is now in the public domain, several authors have tried their hand at this:
87	** ''An Episode on Flatland: Or How a Plain Folk Discovered the Third Dimension'' by Charles Howard Hinton. Published way back in 1907, it features a slightly more realistic take on a 2D universe (the Flatlanders in this version exist on the surface of a circular planet rather than just moving through empty space, for instance).
88	** "Sphereland: A Fantasy About Curved Spaces and an Expanding Universe" by Dionys Burger. It features A. Square's grandson and tries to explain [[ExactlyWhatItSaysOnTheTin curved spaces and expanding universes]] in the same way Flatland tried to explain dimensions. It later gets an [[https://archive.org/details/flatland-2-sphereland-hd/Flatland+2+_+Sphereland+HD.mp4 animated adaptation]] as a direct sequel to ''Flatland: The Movie''.
89	** ''Literature/ThePlaniverse: Computer Contact with a Two-Dimensional World'' by A. K. Dewdney. A SpiritualSequel that focuses on [[WorldBuilding creating a believable 2-D world with its own physics, biology and culture]].
90	** ''Flatterland: Like Flatland, Only More So'' by Ian Stewart. Follows another one of A Square's descendents and her ventures with an [[MakesJustAsMuchSenseInContext interdimensional Space Hopper]]. Sacrifices plot and social commentary for higher math theories and {{pun}}s.
91	** "Spaceland: A Novel of the Fourth Dimension" by Creator/RudyRucker. A NonLinearSequel / SpiritualSequel with its focus on the plot of Silicon Valley hotshot [[PunnyName Joe Cube]] and his encounter with Momo, a woman from the fourth dimension.
92	** The [[UsefulNotes/IOSGames iOS game]] ''VideoGame/ANobleCircle'' is based on the novella.
93	* GainaxEnding: ''Flatland: The Film'' starts to go off the rails in its third act: After hallucinating the King of Pointland, escaping prison and bumping into an both an IdenticalStranger and [[UnexplainedRecovery the trapezoid he saw die earlier]], A. Square's pursuers are slain by the North Kingdom army. One of the Northern officers begins to chase him, and then everything suddenly goes black. A. Square speaks a single line pleading to see his family, and is answered by an unknown voice. Roll Credits.
94	* GenderFlip: Hex is female in ''Flatland: The Movie''.
95	* IgnorantOfTheirOwnIgnorance: Aero the isoceles triangle in ''Sphereland'' vehemently denies the existence of the third dimension and is very dismissive of Hex and Puncto's claims.
96	* TheMovie: [[http://www.flatlandthemovie.com/ You gotta]] [[https://www.youtube.com/watch?v=ZFDTcasgHK4 believe them.]]
97	* ReversePolarity: Happens in all three dimensions in ''Sphereland'':
98	** Spherius is punished by the Oversphere for abandoning the Flatlanders by flipping his directions, forcing him to move in the ''opposite'' direction he wants to go.
99	** The ship is accidentally flipped over in the second dimension by Spherius, causing their direction to reverse.
100	** Hex and Puncto accidentally pop the King of Lineland out of his line, and put him back backwards. The Queen of the Left and the Queen of the Right are thus offended and confused when he refers to them by the wrong names.
101	* NiceJobBreakingItHero: Spherius is punished by the Oversphere for abandoning the Flatlanders and being himself closed-minded, with her forcing him to return to Flatland by reversing his directions and making the only remedy to find the center of Flatland where she awaits.
102	* NotHisSled: In ''Flatland: The Movie'', [[spoiler:Spherius rescues Arthur Square from his death sentence and reveals that he intended his granddaughter Hex to be his prophet]].
103	* SuddenSequelDeathSyndrome: ''Sphereland'' takes place 20 years after ''Flatland: The Movie''. By then, Arthur Square has since passed away.
104	* UglyCute: The guard dogs of the ruins site in ''Sphereland.'' Being two-dimensional, we can ''see their innards''. They're still kind of adorable though, as they play chase with Puncto.
105	[[/folder]]

Context Literature / Flatland