Hubbry Logo
FlatlandFlatlandMain
Open search
Flatland
Community hub
Flatland
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Flatland
Flatland
Flatland
View on Wikipedia
from Wikipedia

Flatland: A Romance of Many Dimensions is a satirical novella by the English theologian, Anglican priest and schoolmaster Edwin 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 satirise the class and gender hierarchies of Victorian society, but the novella's more enduring contribution is its examination of dimensions.[2]

Key Information

A sequel, Sphereland, was written by Dionys Burger in 1957. Several films have been based on Flatland, including the feature film Flatland (2007). Other efforts have been short or experimental films, including one narrated by Dudley Moore and the short films Flatland: The Movie (2007) and Flatland 2: Sphereland (2012).[3]

Plot

[edit]
Illustration of a simple house in Flatland.

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, who are lines, while the women are "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 a 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 information about the "insides" of the house, moves a tablet through the third dimension, and even goes inside the Square for a moment. Still unable to comprehend the third dimension, the Square is taken by the Sphere 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. The Sphere at first scoffs at the idea of higher dimensions, just as the Square had done, showing that his comprehension is not as broad as he had thought. 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

[edit]

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 by surgery.

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

[edit]

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[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

[edit]

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".

Wendy Graham reviewed Flatland for Adventurer magazine and stated that "Once again a story with a message – crackpots aren't always crackpots."[11]

Adaptations and parodies

[edit]

Numerous imitations or sequels to Flatland have been created. Examples include:

Films and TV
Literature

Books and short stories inspired by Flatland include:[citation needed]

[edit]
  • 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]
  • In the Star Trek: The Next Generation episode "The Loss", the USS Enterprise-D becomes trapped within a field of two-dimensional lifeforms.[25]
  • 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.[26]
  • 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.[27]
  • Flatland features in The Big Bang Theory episode "The Psychic Vortex",[28] when Sheldon Cooper declares it one of his favourite imaginary places to visit.[29]
  • 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.[30]
  • 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".
  • The novel appears in the film Interstellar.[31]
  • 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.

See also

[edit]

References

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Flatland

View on Grokipedia
from Grokipedia
Flatland: A Romance of Many Dimensions is a satirical on and society authored by English theologian and educator (1838–1926) under the "" and first published in 1884 by Seeley & Co. in . The story depicts a two-dimensional world inhabited by geometric figures whose social status correlates with the number of sides they possess, with lines representing women and polygons denoting men of increasing rank. Through the narrator—a square from this planar realm—the narrative examines perceptual limitations by contrasting encounters with one-dimensional, three-dimensional, and higher realms, thereby illustrating concepts of spatial dimensions and . Abbott employs Flatland's rigid hierarchy—where isosceles triangles occupy the lowest classes, equilateral triangles serve as soldiers, and regular polygons ascend to elite status—as a vehicle for critiquing Victorian England's class prejudices, gender inequalities, and deference to . Women, portrayed as straight lines for visibility and equipped with "" for interaction, highlight era-specific restrictions on female agency, though Abbott himself supported educational reforms for women amid broader societal . The novella's climax involves the square's abduction by a from Spaceland (three dimensions), who reveals the inadequacy of two-dimensional senses, only for the square to face suppression upon preaching dimensional enlightenment, underscoring resistance to paradigm shifts. Since its release, Flatland has endured as a seminal work in popularizing multidimensional geometry, influencing fields from relativity to visualizations, while its layered invites scrutiny of anthropocentric biases in scientific inquiry. Despite occasional critiques of its portrayal of gender dynamics as reflective rather than progressive, the text's enduring appeal lies in its fusion of rigorous geometric reasoning with unflinching social observation, unmarred by later ideological overlays.

Authorship and Publication

Edwin A. Abbott's Background

was born on 20 December 1838 in , , to parents who were first cousins, and he died on 12 October 1926. He received his early education at the , where he later became headmaster, and went on to study at , graduating with honors in classics in 1861. Abbott was ordained as a deacon in the in 1862 and as a priest in 1863, reflecting his commitment to Anglican alongside his educational pursuits. In 1865, at age 26, he assumed the headmastership of the , a position he held until his retirement in 1889, during which he elevated the institution's reputation through innovative teaching methods and emphasis on rigorous scholarship. Abbott authored over thirty books, spanning Shakespearean studies, , and , with notable works including A Shakespearian (1870), which analyzed Elizabethan English differences from modern usage for pedagogical purposes. His theological writings engaged , advocating liberal interpretations that sought to reconcile faith with scientific inquiry, while his educational texts promoted reforms such as expanded curricula and teacher . A vocal proponent of , Abbott supported women's access to and contributed to the Teachers' Training and Registration , an initiative backed by leading educators to professionalize teaching amid Victorian gender restrictions. His interests extended to speculative geometry and higher dimensions, influenced by Victorian debates on non-Euclidean spaces and figures like Charles Dodgson (), whom he knew through educational circles; Abbott viewed multidimensional analogies as tools for theological insight into divine transcendence. In publishing Flatland in 1884 under the ""—a on his initials forming "A²"—Abbott concealed his satirical critique of Victorian social hierarchies, protecting his standing as a conservative-era educator and cleric from potential backlash in a society wary of subversive commentary. This aligned with his broader of embedding reformist ideas within accessible, allegorical forms to challenge rigid class and perceptual norms without direct confrontation.

Publication History and Context

![First edition of Flatland] Flatland: A Romance of Many Dimensions was first published in November 1884 by Seeley & Co. in under the pseudonym "." The work appeared as a mathematical fantasy amid growing Victorian fascination with higher dimensions, influenced by Bernhard Riemann's 1854 hypothesis on multidimensional geometry and subsequent popular speculations about fourth-dimensional spaces. A second and revised edition followed approximately one month later in December 1884, incorporating a new in which the editor— A. Abbott, though authorship remained pseudonymous at the time—defended the book's depictions against early criticisms and expressed gratitude for reader interest from "Spaceland." Initial sales were modest, reflecting the niche appeal of speculative blended with social in a post-Industrial Revolution era marked by rigid class structures and emerging scientific challenges to Euclidean orthodoxy. Abbott's identity as the author became publicly associated with the text in subsequent years, linking Flatland to his broader oeuvre of Shakespearian parodies, such as A Shakespearian Grammar (1870), and theological explorations like Philochristus (1878), which similarly employed narrative innovation to probe philosophical and societal themes. Over time, the book's cult status grew, influencing later works on dimensional theory and mathematics popularization despite its subdued debut.

Plot Summary

Part I: The Social Structure of Flatland

In Flatland: A Romance of Many Dimensions, the narrator introduces the world as a vast plane inhabited by line segments and polygons that exist and move solely within two dimensions, perceiving and interacting with one another primarily through straight-line trajectories. Visibility is limited to edges presented end-on, rendering full shapes discernible only under specific orientations, which necessitates conventions for recognition to prevent collisions and maintain order. Houses and boundaries are formed by straight lines, with interiors accessed via openings that align with the inhabitants' planar form. A constant attraction to the South, governed by a Law of Nature, assists in navigation. Society is stratified by geometric form, reflecting an evolutionary governed by the Universal of , whereby a male offspring typically possesses one more side than his father, facilitating gradual ascent in status. Women, depicted as straight lines without breadth, occupy the lowest tier and are subject to regulations such as mandatory use of separate and a vocal "peace-cry" when approaching others to mitigate their pointed ends, which pose risks in close quarters. The working classes comprise irregular polygons and isosceles triangles with acute apex angles—often around 5.7 degrees for soldiers and laborers—characterized by long equal sides of approximately 11 inches and short bases, rendering them suitable for roles due to their capacity to form acute angles for penetration. The middle classes consist of equilateral triangles, esteemed for their stability and three equal sides, serving as professionals, tradesmen, and gentlemen. Higher strata include quadrilaterals like squares (typically merchants or professionals), pentagons, and progressively more-sided polygons up to near-circles, with social elevation possible through selective intermarriage among isosceles triangles to achieve equilateral progeny over generations. At the apex are circles, the priestly and , appearing as equiangular figures with effectively infinite sides, exempt from certain pedigree restrictions and capable of instantaneous recognition. To preserve this hierarchy, perception of internal structures—known as "goneness"—is suppressed among lower classes, confining recognition to external outlines via touch or aligned sight, while the use of color was historically banned following the Color Revolt, with its subtle gradients deemed disruptive to visual distinctions; only circles and authorized educators retain this sense. Irregular figures, deviating from equal-sided norms, face excision or imprisonment to avert hereditary defects, underscoring the emphasis on geometric regularity as foundational to social stability. Pedigree laws further regulate matrimony to minimize irregular offspring, with penalties escalating for repeated violations across classes.

Part II: Encounters with Higher Dimensions

In Part II of Flatland, titled "Other Worlds," the narrative shifts from the exposition of Flatland's society to A Square's personal encounters with lower and higher dimensions, beginning with a of Lineland on the penultimate day of 1999. In this one-dimensional realm, inhabitants exist solely along a straight line and perceive the world through touch and sound alone, with the Monarch of Lineland dismissing A Square's attempts to describe as incomprehensible madness. A Square's frustrated explanations highlight the perceptual barriers between dimensions, mirroring the limitations he will later confront in his own world. The pivotal encounter occurs on the final day of 1999, when a from Spaceland—a three-dimensional realm—manifests in Flatland, initially appearing as a whose size varies to demonstrate its superior dimensionality. The elevates A Square perpendicularly into Spaceland, granting him a transformative view of , where he observes the interiors of Flatland houses and the true forms of polygons, shattering his prior assumptions about . This revelation extends to glimpses of Spaceland's inhabitants, including vast multitudes of spheres and cubes, underscoring the vastness beyond two dimensions. Emboldened, A Square urges the Sphere to consider a fourth dimension, but the Sphere recoils, refusing to speculate beyond its own perceptual limits. Upon returning to Flatland, preaches the existence of a third dimension as a means of , proclaiming it would resolve social inequalities by allowing into others' natures. His efforts provoke outrage, leading to his arrest for against the state's Circular Party and a sentence of lifelong , with the suppressing his brother to prevent dissemination of the ideas. From confinement, A Square reflects on the futility of his attempts amid societal resistance, yet expresses cautious optimism that his might ignite future enlightenment, warning that "Revolutions cannot always be bloodily suppressed." This resolution emphasizes the narrative's core tension: the insurmountable challenge of transcending ingrained perceptual boundaries.

Mathematical and Geometric Foundations

Geometric Representation of Society

Flatland's is modeled on the , where inhabitants exist as geometric figures defined by their boundaries: women as straight line segments, lowest classes as isosceles triangles with acute bases under half an inch, equilateral triangles for the , squares and pentagons for professionals, higher polygons for , and circles—approximated by polygons with numerous sides—for the priestly . This relies on the regularity and number of sides, with circles representing the limit of infinite sides in Euclidean terms. Perception operates under planar constraints: visually, all figures appear as straight lines when viewed edge-on, differentiated by the rate of luminosity fade in atmospheric "fog," where acute angles cause sharper dimming compared to obtuse ones in higher polygons. Tactile recognition involves tracing the perimeter to count angles, allowing precise identification without visual ambiguity, as a single angle suffices to distinguish between similar-sided figures like squares and pentagons. Mobility adheres to two-dimensional Euclidean motion, confined to the plane without vertical displacement, imposing restrictions on lower shapes due to protruding acute angles that risk penetration upon collision; isosceles triangles and lines thus navigate cautiously to avert accidents. Architectural structures adapt accordingly, employing pentagonal outlines with specialized apertures—eastern slits for line segments and broader western portals for polygons—to facilitate safe entry aligned with shape geometries. The evolution of eyesight from primitive touch-based sensing to fog-mediated visual acuity enabled non-contact shape discernment, geometrically leveraging angle-induced gradients in perceived brightness to infer class without physical proximity, thereby reducing collision risks inherent in planar movement. Edwin A. Abbott, a classicist rather than a specialist , employed these Euclidean simplifications—omitting complexities like inertial paths or boundary effects—for analogical clarity, prioritizing illustrative over rigorous two-dimensional physics.

Concepts of Dimensions and Perception

In Flatland, dimensions are depicted through the perceptual constraints imposed by an entity's spatial , using hierarchical analogies to illustrate the incomprehensibility of higher realms. Inhabitants of Lineland, a one-dimensional realm, experience reality solely along a straight line, perceiving neighbors only as points or segments and possessing no conception of directions; their , for instance, rejects the idea of "left" or "right" as illusory, deeming any deviation from linearity impossible. This limitation extends to Flatland's two-dimensional plane, where beings like the narrator——observe others as mere line segments, inferring shape and size from variations in brightness caused by edge-on views, as is absent. Such observations arise causally from the of sight lines confined to the plane, where rotational orientation determines without volumetric cues. The novel's central thought experiment escalates this analogy when a three-dimensional encounters the Square, demonstrating Spaceland's superiority by lifting him perpendicular to the Flatland plane. This motion reveals the plane's interior as a vast expanse, with the Square experiencing his world anew from an elevated vantage, akin to how a two-dimensional observer might view a one-dimensional line's "interior" by stepping aside. further illustrates perceptual barriers by passing through Flatland objects, manifesting as cross-sections that expand, contract, or vanish—effects indistinguishable from miracles to planar observers, such as a circle appearing to grow and shrink without traceable cause. These visualizations emphasize that higher-dimensional access causally overrides lower-dimensional sensory limits, enabling observations impossible within the native space, yet the Square struggles to retain this comprehension upon return, his two-dimensional senses reverting to planar illusions. Abbott grounds these concepts in intuitive, first-principles reasoning rather than abstract proofs, extrapolating from where each added dimension introduces a mutually axis, progressively expanding perceptual horizons. This approach mirrors 19th-century mathematical developments, including Riemann's work on multi-dimensional manifolds and early topological insights from Möbius in the , which challenged Euclidean intuitions and sparked speculation on spaces beyond three dimensions. Though predating widespread popularization—such as Howard Hinton's 1880s analogies for a fourth dimension—Flatland's depictions align with this era's shift toward visualizing dimensionality as a causal framework for reality, where observation is inextricably tied to the observer's . Empirical validation lies in the analogy's consistency: just as light propagation in lower dimensions yields predictable distortions, higher-dimensional interventions produce verifiable anomalies interpretable only through expanded coordinates.

Satirical and Social Commentary

Critique of Class Hierarchies

In Flatland, is stratified by geometric form, with males classified from acute isosceles triangles at the base—deemed lowest due to their sharp angles and limited capacity—to equilateral triangles and regular polygons of increasing sides, culminating in circles as the priestly elite whose unchanging perfection symbolizes aristocratic immutability. This structure satirizes Victorian Britain's hereditary class system, where birth largely dictated opportunity, as polygons inherit sides from forebears but rarely achieve significant ascent without exceptional training, obscuring true rigidity under nominal meritocratic claims. Abbott, through narrator , exposes hypocrisies such as the elite's prohibition of color and patterns, which could reveal class distinctions and threaten perceptual hierarchies enforced by law. The narrative critiques enforcement mechanisms, particularly the gasification of "irregular" polygons—those deviating from regularity due to hereditary flaws—portrayed as a eugenic measure to avert societal degeneracy and potential rebellion, mirroring fears of inherited inferiority eroding upper strata in 19th-century Britain. Lower classes, with acute angles rendering them physically menacing yet intellectually stunted, are funneled into as expendable "," their numbers swelled for warfare while higher polygons avoid such risks, reflecting the disproportionate conscription of working-class men into the during the era's imperial conflicts. Middle classes, like squares, pursue incremental side gains through education, aspiring to polygonal status amid elite apprehension of "irregular births" diluting bloodlines, thus highlighting how stratification stifles broad talent utilization and fosters over natural variation. Abbott's satire underscores inefficiencies of such hereditary systems, including wasted potential in suppressed who might contribute if reformed, and the causal brittleness of orders reliant on rather than adaptive merit, as evidenced by Flatland's vulnerability to perceptual disruptions like Sphere's interventions. Yet analyses note this portrayal privileges reformist ideals over empirical stabilizers of , such as specialized roles enabling societal coordination, which Victorian data on industrial under class divisions—e.g., division of labor boosting output by up to 300% in factories per Adam Smith's observations—suggest can yield causal efficiencies despite rigidities. The thus effectively unmasks Victorian pretensions to natural order but underemphasizes how enforced stability historically mitigated chaos in pre-modern societies, per historical records of feudal efficiencies in .

Portrayal of Gender Roles

In Flatland, women are portrayed as straight lines, the simplest and most rudimentary inhabitants, possessing no breadth and appearing as mere points when viewed end-on. This form renders them acutely dangerous, capable of inflicting lethal injury through a sudden retrograde motion, prompting stringent protocols such as the mandatory "peace-cry" or "Woman-Warning" emitted upon approach to any or , under penalty of death for non-compliance. Houses feature separate eastern entrances exclusively for women, equipped with peepholes for verification, while some jurisdictions mandate their perpetual backward motion or accompaniment by male escorts to mitigate collision risks. The attributes women's limited to their geometric and a longstanding policy barring them from education for approximately 300 years, decreed by the ruling Circles on grounds of deficient reason and emotional excess, reducing them to beings driven by passion without reflection, judgment, or forethought. Even the narrator, , critiques this suppression, arguing it fosters intellectual decay in women and burdens men with dual linguistic training to accommodate simplistic female speech patterns. In the preface to the second edition of 1884, Abbott addresses accusations of misogyny leveled against the work's authorial stance, asserting respect for women's intelligence and framing the exaggerated depictions as deliberate hyperbole to illuminate societal prejudices rather than endorse them. This aligns with Abbott's broader advocacy for educational reform, including improved opportunities for women amid Victorian constraints, as evidenced by his efforts to highlight injustices in female status through satirical exaggeration. Contemporary scholarly interpretations debate the intent behind these portrayals: some view them as reflective of inherent , perpetuating stereotypes of female inferiority and danger, while others defend them as intentional critiquing Victorian subjugation, supported by the internal narrative's exposure of educational bans and Abbott's progressive reformist writings outside the . from the text's self-critique and favors the satirical reading, as the hyperbolic protocols underscore the irrationality of restrictive norms rather than literal advocacy.

Broader Victorian Social Norms

In Flatland, the educational regimen mandates rigorous training in tactile and visual recognition of geometric forms to enforce social distinctions, reflecting Victorian-era emphasis on rote drills and classical that prioritized over creative inquiry. Abbott, headmaster of the from 1865 to 1889, critiqued such "crammeries" in his educational writings, advocating instead for mathematics as a tool to foster intuitive reasoning and challenge dogmatic instruction prevalent in mid-19th-century British schooling. This mirrors broader Victorian debates, where reformers like Abbott opposed the 1870 Education Act's focus on mechanical proficiency, arguing it stifled intellectual progress amid industrialization's demand for utilitarian skills. The satirizes through the Circles' unchallenged , where priestly elites monopolize perceptual "insight" while quashing , akin to Victorian clerical influence in state affairs and suppression of heterodox ideas under the 1850s-1880s establishments. Historical upheavals, such as the failed Color Revolt around A.D. in Flatland's —which arose from aesthetic innovations blurring class lines and escalated into widespread violence—are depicted as causal failures of enforced uniformity, paralleling Victorian anxieties over Chartist agitations (1838-1857) and resistances (1811-1816) that exposed rigid hierarchies' brittleness without endorsing disorder. Aesthetic suppression underscores utilitarian hypocrisies: the ban on chromatic distinctions, instituted post-revolt to restore order via shape-based , critiques Victorian prioritization of industrial efficiency over arts, as seen in the 1860s Arts and Crafts movement's backlash against soulless . Abbott's portrayal avoids idealizing rebellion, highlighting how such innovations, without structural adaptation, devolve into chaos, thus revealing causal realities of societal in an era claiming moral and technological supremacy yet reliant on outdated perceptual norms.

Philosophical and Theological Dimensions

Analogies to Human Perception and Reality

In Flatland, the inhabitants' perception is confined to length and breadth, rendering them unable to discern the internal contents of shapes or the existence of a third dimension, as their sensory apparatus operates solely within a planar framework. This limitation exemplifies how dimensionality embeds cognitive constraints: a two-dimensional observer encounters a three-dimensional object, such as a , only as a varying circular cross-section, mistaking transient appearances for fundamental reality. Analogously, human perception in three spatial dimensions may analogously obscure higher-dimensional structures, where phenomena like or gravitational effects could represent projections from additional axes inaccessible to direct sensory experience. The demonstrates perceptual , wherein higher-dimensional entities can encompass and manipulate lower-dimensional spaces comprehensively—a lifts out of Flatland's plane effortlessly—while the converse proves impossible without dimensional transcendence. This mirrors empirical observations in and physics, such as shadow projections of three-dimensional objects onto two-dimensional surfaces, which lose volumetric information and appear distorted or illusory to planar viewers. For humans, analogous biases arise in interpreting four-dimensional rotations as sequential three-dimensional slices, as visualized in mathematical models where a hypersphere's with three-space yields expanding and contracting spheres, challenging intuitive grasp but verifiable through coordinate transformations. Epistemologically, Flatland underscores the of equating sensory immediacy with ontological completeness, urging beyond perceptual bounds via logical deduction and empirical patterns rather than dogmatic adherence to observed norms. A Square's initial rejection of spherical claims, grounded in two-dimensional authority, parallels historical resistance to non-Euclidean geometries or relativity, where evidence from anomalous data—such as Mercury's perihelion —necessitated revising perceptual priors. This promotes a causal realism wherein reality's structure precedes and conditions observation: dimensional embedding filters causal interactions, permitting detection of higher influences only through their lower-dimensional traces, as in wave functions collapsing across unobserved variables in . Thus, the work advocates prioritizing verifiable inconsistencies in low-dimensional models over unexamined sensory authority to hypothesize fuller realities.

Religious and Moral Undertones

, an Anglican priest and theologian aligned with the Broad Church movement, embedded Flatland with allegories drawing from Christian to advocate for receptivity to divine truths amid Victorian . The 's visitation to functions as a typological representation of biblical revelations, akin to angelic visitations or theophanies in scripture, where a higher being imparts knowledge inaccessible to lower perceptions, urging recognition of a transcendent order. This descent has been interpreted theologically as paralleling the Incarnation, with the Sphere entering Flatland's plane analogous to God incarnating as Jesus to reveal higher truths and facilitate redemption, illustrating divine transcendence and immanence in sermons and articles. This encounter emphasizes providential intervention, positioning the Sphere not merely as a geometric superior but as a divine emissary whose periodic descents initiate "apostles" into elevated realities, echoing the selective enlightenment in prophetic traditions. The narrative's depiction of A Square's trial and imprisonment for disseminating third-dimensional insights mirrors ecclesiastical persecutions of doctrinal innovators, such as those faced by early Christian reformers or heretics challenging , thereby critiquing institutional suppression of emergent truths within religious hierarchies. Abbott's moral framework promotes as essential for moral and spiritual ascent, portraying denial of higher dimensions as a form of intellectual and ethical that parallels materialist rejections of immaterial realities, a concern rooted in his efforts to harmonize empirical with Christian against agnostic encroachments. His reformist Anglicanism, evident in works advocating for , informs this zeal for perceptual and doctrinal openness. Interpretations diverge on these elements: traditional analyses, informed by Abbott's theological corpus, frame the tale as pro-Christian fostering in unseen verities and providential order, countering reductive naturalism. In contrast, certain secular appropriations repurpose for purely philosophical or scientific ends, attenuating its explicit toward submission to divine-like authority and its warnings against prideful autonomy.

Reception and Interpretations

Initial Victorian-Era Reviews

Upon its anonymous publication in November 1884 as by "," Flatland received modest attention in British literary and scientific periodicals, with reviewers praising its inventive blend of and mathematical while noting its esoteric appeal. The first edition comprised 1,000 copies, followed swiftly by a revised second edition in December 1884, suggesting initial interest sufficient for a small reprint but not widespread commercial success. Contemporary notices highlighted the novella's wit and novelty in depicting a two-dimensional society, though some critiqued its abstract formality as limiting broader readership. Scientific journals such as commended the work's humorous and accurate exploration of dimensional perception, viewing it as a clever tool for illustrating limitations in human understanding of . Similarly, appreciated its consistency and entertainment value for mathematicians, emphasizing the satirical commentary on resistance to higher-dimensional truths. Literary outlets like The Academy and The Literary World lauded the ingenious social satire on class and perception, likening it to a potential against dogmatism in science and religion, though The Athenaeum pointed to minor mathematical inconsistencies in visibility rules. Across these, the dimensional innovation garnered early recognition in mathematical circles, while the social critique—mild compared to contemporaneous works like those of Dickens—was acknowledged but secondary to the geometric fantasy. The book's niche reception reflected its anonymity and specialized themes, with steady but limited circulation through the and no further reprints until the 1920s, indicating it was overlooked by general audiences amid more conventional literature. American coverage, such as in , echoed this by describing it as an amusing yet puzzling geometric romance with constrained appeal.

Modern Scholarly Analyses

In the twentieth century, Flatland experienced a scholarly revival, particularly after the 1920s, as physicists and mathematicians drew analogies between its dimensional thought experiments and emerging theories like general relativity, which challenged Euclidean intuitions about space-time. For instance, the novella's depiction of a sphere appearing as varying 2D shapes to Flatland inhabitants mirrored how higher-dimensional phenomena might manifest in our three-dimensional perception, influencing popular expositions of Einstein's curved spacetime. This renewed attention positioned Flatland as a prescient tool for conceptualizing non-intuitive geometries, though its pre-relativistic publication in 1884 meant such links were retrospective. Mathematician Thomas Banchoff, in his 1980s and 1990s analyses, extended this by integrating Flatland into , demonstrating how digital projections and rotations of four-dimensional objects echo the book's slicing analogies, thereby advancing visualization techniques beyond Abbott's manual descriptions. Banchoff argued that Flatland's narrative framework facilitated empirical exploration of , with over a dozen editions published since the original, reflecting its enduring pedagogical value in for demystifying higher dimensions through iterative 2D-3D analogies. Educators have since adapted it to teach concepts like hypersphere projections, where students model 4D rotations via software, acknowledging the novella's role in bridging intuitive limitations without requiring advanced calculus. Scholars praise Flatland for popularizing dimensional analogies empirically, as its accessible narrative predated formal and enabled about perceptual biases in spatial hierarchies. However, critics note geometric simplifications, such as the idealized frictionless 2D plane ignoring quantum-scale constraints or gravitational anomalies in lower dimensions, which undermine rigor for applications like 2D quantum gravity models. These flaws, while forgivable for satirical purposes, limit its use in precise simulations, where real 2D systems exhibit logarithmic divergences absent in Abbott's Euclidean setup. Interpretations diverge on the social satire: conservative readings, such as those emphasizing inherent shape-based hierarchies, preserve Abbott's bite against egalitarian reforms that flatten natural distinctions, viewing the Universal Recognition Act as a cautionary reductio of imposed uniformity. Progressive analyses, conversely, highlight flaws in rigid class structures, interpreting the dimensional ascent as a of perceptual dogmatism enforcing inequality, though both camps ground claims in Abbott's Victorian context of educational reform debates. Empirical textual evidence, like Sphere's dismissal of lower-order input, supports the former's realism about cognitive variances, while causal chains from priestly suppression underscore the latter's focus on institutional barriers to truth-seeking.

Debates on Misogyny and Satirical Intent

Since the book's publication, interpretations of its gender portrayals have sparked debate, with some post-1970s critics viewing the depiction of women as straight lines—portrayed as intellectually limited, perpetually in motion to avoid collisions, and requiring special protocols like the "cry of 'Woman!'" for safety—as reflective of inherent sexism that normalizes Victorian patriarchal constraints rather than critiques them. Such readings argue the narrative reinforces women's subordination by tying their form to danger and inferiority, potentially embedding biases without sufficient ironic distance to subvert them. Counterarguments emphasize the work's satirical intent, pointing to Abbott's biography as evidence of his advocacy for women's advancement; as a graduate and educator, he actively supported and educational equality from the 1860s onward, co-founding initiatives to expand opportunities for female students. In the 1884 preface to the second edition, Abbott addresses potential misreadings by distinguishing the narrator A Square's biases—rooted in Flatland's fictional norms—from his own views, asserting that emerging real-world educational reforms for women presage greater equity and justify interpreting the exaggerations as hyperbolic critique of societal irrationalities. This defense aligns with of the text's structure: the absurd mechanics of women's visibility and the proposed "Universal Colour Bill" to mitigate their "threat" highlight, through , the self-defeating consequences of undervaluing intellect based on arbitrary traits, mirroring Victorian fears of female agency while urging reform over literal endorsement of hierarchy. Scholarly examinations, less prone to anachronistic projections, substantiate that Abbott's intent targeted the causal chain from rigid norms to stifled potential, as evidenced by his broader oeuvre critiquing and classism alongside gender limits. Interpretations dismissing this as mere cover overlook empirical biographical data favoring intentional over patriarchal affirmation.

Legacy and Influence

Impact on Mathematics and Science

Flatland, published in 1884, popularized the narrative exploration of higher dimensions among lay and scientific audiences, predating Albert Einstein's by two decades and facilitating conceptual bridges to multidimensional . The novella's depiction of perceptual limitations in a two-dimensional provided an intuitive framework for envisioning spaces beyond three dimensions, influencing early literature on non-Euclidean concepts. This analogy extended to the works of , whose Scientific Romances (1896–1898) developed four-dimensional visualizations and mental exercises for perceiving , drawing narrative inspiration from Flatland's stratified society and dimensional visitations. Hinton's models and cube projections built on Abbott's method of analogical storytelling to demystify hypercubes, aiding nascent efforts in geometric intuition for physicists grappling with curvature. In mathematical education, Flatland remains a staple for illustrating topology and dimensional perception, where it demonstrates how embedded observers misinterpret higher-dimensional intrusions as anomalous phenomena. Thomas F. Banchoff, in his analyses and visualizations, integrated Flatland's themes with computer-generated projections of four-dimensional polytopes, enabling students to explore shadows and slices of hypersolids as proxies for abstract manifolds. Though not a rigorous proof text, the work highlights causal disparities in lower-dimensional physics, such as electrostatic forces obeying an inverse-linear law rather than the three-dimensional inverse-square, which parallels derivations in n-dimensional Gauss's theorem. Contemporary applications persist in outreach, where Flatland analogies elucidate compactified in (requiring 10 dimensions) and (11 dimensions), typically curled into tiny microscopic scales such as Calabi-Yau manifolds, rendering them undetectable with current technology. The concept of higher-dimensional beings interacting with lower dimensions—such as perceiving interiors of objects or passing through barriers—is not a formal scientific theory but a popular analogy drawn from Flatland, used by physicists like Michio Kaku to illustrate how entities in higher dimensions could influence lower-dimensional worlds in seemingly miraculous ways. There is no experimental evidence for such beings or macroscopic interactions; extra dimensions remain speculative, with ongoing searches at facilities like CERN for signatures including Kaluza-Klein particles or micro black holes yielding no confirmation. These references underscore its enduring utility for conveying why additional spatial dimensions might manifest as vibrational modes rather than extended volumes. However, such uses emphasize illustrative value over empirical derivation, as Flatland's Euclidean assumptions diverge from curved realities.

Adaptations in Media

In 1965, an animated short film adaptation of Flatland was produced, directed by Eric Martin from an idea by John Hubley, depicting the two-dimensional world and the protagonist's encounter with higher dimensions through simple line animation. This early effort prioritized visualizing the novella's geometric society and perceptual shifts over its social critique, achieving a concise runtime focused on the core dimensional revelation that drives the narrator to madness. Two CGI-animated adaptations followed in 2007. Flatland: The Movie, a 35-minute short directed by Dano Johnson and Jeffrey Travis, expands the original plot by introducing Arthur Square's granddaughter Hex, who challenges societal norms, while emphasizing the conflict between shapes and the intrusion of a three-dimensional ; innovations include dynamic 2D-to-3D transitions via to illustrate perceptual breakthroughs. Similarly, Ladd Ehlinger Jr.'s feature-length Flatland (also known as Flatland: The Film), created single-handedly using Lightwave 3D software with a by Tom Whalen, further innovates by portraying a stratified of geometric figures facing "evil Circles" and higher-dimensional threats, blending adventure elements with the dimensional analogy for broader accessibility. Both films excel in rendering abstract concepts tangible—such as lines representing sight in a flat plane—but have drawn criticism for softening the novella's incisive on Victorian hierarchies into more didactic, family-oriented narratives that prioritize visual spectacle over unvarnished . Stage adaptations have emphasized immersive experiences to evoke the disorienting shift in central to the story. In 2015, Extant Theatre, a company specializing in work for blind and partially sighted performers, staged Flatland in a pitch-black disused church, relying on sound and sensation to simulate the two-dimensional world and its dimensional upheaval, innovating by adapting the narrative for non-visual audiences while retaining themes of perceptual limitation. The 2016 production at Annex Theatre in , adapted and co-directed by Moritz and Isa Leal, incorporated elements extending from zero to ten dimensions, framing through physical movement and projections to heighten the satirical critique of rigid class structures. These theatrical versions innovate by engaging audiences kinesthetically, though they sometimes amplify the moral undertones at the expense of the original's concise, first-person irony. In the 2020s, digital recreations have leveraged VR and AR for interactive dimensionality demonstrations. The Flatland XR project, an embodied geometry game using shared holographic AR, projects 2D and 3D shapes into real space to simulate perceptual expansions, adapting the novella's concepts for educational and experiential fidelity without narrative expansion. Such tools achieve unprecedented visualization of abstract transitions but risk reducing the work to a mere dimensional puzzle, sidelining its causal critique of societal blindness. Audiobook versions, including narrations like those on Audible featuring full-text readings, preserve the original prose fidelity but offer limited innovation beyond vocal interpretation, serving primarily as accessible retellings rather than transformative media. Flatland's dimensional analogy has influenced science fiction authors, with praising the in his foreword to a 1983 edition as providing "the best introduction one can find into the manner of perceiving dimensions," highlighting its role in conceptualizing spatial beyond three dimensions. Similarly, Robert A. Heinlein's (1961) alludes to the protagonist when character references the Flatland narrative to discuss perceptual limitations in unfamiliar realities. Astronomer Carl Sagan employed Flatland's framework in the 1980 PBS series Cosmos: A Personal Voyage, specifically in discussions of the fourth dimension, to illustrate how two-dimensional beings would interpret a three-dimensional sphere's intrusion as a fluctuating circle, thereby analogizing human constraints in grasping higher spatial realities. The novella's motifs of restricted dimensionality recur in video games featuring puzzle mechanics based on planar perception, such as FLATLAND Vol.1 (2020), a Nintendo Switch platformer where players navigate a minimalist two-dimensional world, evoking Abbott's exploration of geometric constraints and perceptual puzzles. In philosophical discourse on the simulation hypothesis, Flatland serves as a recurring analogy for how simulated entities might remain oblivious to enclosing higher-dimensional structures, as noted in analyses critiquing low-dimensional biases in perceiving simulated realities.

References

  1. https://archive.org/details/flatlandromanceo00abbouoft
  2. https://www.geom.uiuc.edu/~banchoff/Flatland/
  3. https://www.math.brown.edu/tbanchof/abbott/Flatland/ISR/
  4. https://personal.colby.edu/personal/s/sataylor/ReadingFlatland.pdf
  5. https://www.open.ac.uk/blogs/MathEd/index.php/2022/09/12/flatland-as-social-satire-womens-status-in-victorian-times-and-the-push-for-educational-reform-by-xiang-fu/
  6. https://maths-from-the-past.org/flatland-a-romance-of-many-dimensions/
  7. https://www.americanscientist.org/article/a-forgivably-flat-classic
  8. https://broadviewpress.com/product/flatland/
  9. https://mathshistory.st-andrews.ac.uk/Biographies/Abbott/
  10. https://archive.org/details/grammarshakesp00abbouoft
  11. https://www.math.brown.edu/tbanchof/MAM2000a/612/people/abbott/satire.html
  12. https://www.math.brown.edu/tbanchof/abbott/Flatland/Publications/intros/dewdney.pdf
  13. https://kasmana.people.charleston.edu/MATHFICT/mfview.php?callnumber=mf1
  14. https://www.manhattanrarebooks.com/pages/books/2844/edwin-abbott-abbott-pseud-a-square/flatland-a-romance-of-many-dimensions
  15. https://historyofinformation.com/detail.php?id=1734
  16. https://blog.uvm.edu/scalexan-vsf/flatland/historical-context-and-non-euclidean-geometry/
  17. https://standardebooks.org/ebooks/edwin-a-abbott/flatland/text/preface
  18. https://www.math.brown.edu/tbanchof/abbott/Flatland/FlatlandAnnotI12.html
  19. https://press.princeton.edu/books/paperback/9780691165554/flatland
  20. https://publicdomainreview.org/essay/aspiring-to-a-higher-plane
  21. https://www.gutenberg.org/files/201/201-h/201-h.htm
  22. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap01
  23. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap02
  24. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap03
  25. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap04
  26. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap11
  27. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap05
  28. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap07
  29. https://www.ibiblio.org/eldritch/eaa/FL.HTM
  30. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap13
  31. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap14
  32. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap15
  33. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap18
  34. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap19
  35. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap20
  36. https://www.gutenberg.org/files/201/201-h/201-h.htm#chap22
  37. https://www.gutenberg.org/files/201/201-h/201-h.htm#Section_13
  38. https://www.gutenberg.org/files/201/201-h/201-h.htm#Section_6
  39. https://www.gutenberg.org/files/201/201-h/201-h.htm#Section_17
  40. https://www.gutenberg.org/files/201/201-h/201-h.htm#Section_16
  41. https://www.gutenberg.org/files/201/201-h/201-h.htm#Section_19
  42. https://www.math.brown.edu/tbanchof/abbott/Flatland/Publications/intros/banchoff.pdf
  43. https://www.gutenberg.org/files/201/201-h/201-h.htm#Section_15
  44. https://ned.ipac.caltech.edu/level5/Abbott/paper.pdf
  45. https://www.litcharts.com/lit/flatland/themes/social-hierarchy-and-oppression
  46. https://www.themontrealreview.com/Articles/From-Flatland-to-the-Holy-Land.php
  47. https://mindlybiz.com/articles/books/edwin-abbott-abbott/flatland-a-romance-of-many-dimensions/
  48. https://mathshistory.st-andrews.ac.uk/Extras/Abbott_Flatland/
  49. http://thediamondsmine.com/files/Ebooks/Flatland.pdf
  50. https://pmc.ncbi.nlm.nih.gov/articles/PMC6519046/
  51. https://www.math.brown.edu/tbanchof/Beyond3d/chapter1/intro.html
  52. https://doi.org/10.1111/tops.12404
  53. http://math.biola.edu/math120/Math120_Chapter_16.pdf
  54. https://www.litcharts.com/lit/flatland/themes/religion-divinity-and-the-unknown
  55. https://pillars.taylor.edu/cgi/viewcontent.cgi?article=1000&context=acmsjournal-2004
  56. https://www.researchgate.net/publication/360156348_Edwin_Abbot%27s_Flatland_and_Religious_Doctrines
  57. https://www.math.brown.edu/tbanchof/abbott/Flatland/Publications/index3.shtml
  58. https://www.math.brown.edu/tbanchof/abbott/Flatland/Reviews/1884litworld.shtml
  59. https://www.math.brown.edu/tbanchof/abbott/PDF/reviews.pdf
  60. https://journal.ilta.ie/index.php/telji/article/view/147/162
  61. https://www.math.brown.edu/tbanchof/abbott/Flatland/ISR/ISR201.html
  62. https://pubs.aip.org/aapt/pte/article/53/1/17/277131/Using-Flatland-2-Sphereland-to-Help-Teach-Motion
  63. https://www.cantorsparadise.com/slicing-through-dimensions-on-gravity-in-edwin-abbotts-flatland-and-the-fabric-of-spacetime-34dea3db452d
  64. https://academic.oup.com/book/6631/chapter/150650888
  65. https://psychologycorner.com/flatland-book-review/
  66. https://prezi.com/f4jqikjjk15k/on-the-females-of-flatland-and-e-abbott-abbotts-apparent-sexism/
  67. https://www.bartleby.com/essay/Feminism-In-Flatland-PJACLFQXZ8T
  68. https://blog.lib.uiowa.edu/speccoll/2021/12/02/the-legacy-of-flatland/
  69. https://publicdomainreview.org/essay/notes-on-the-fourth-dimension
  70. https://mkaku.org/home/articles/hyperspace-a-scientific-odyssey/
  71. https://home.cern/science/physics/extra-dimensions-gravitons-and-tiny-black-holes
  72. https://arxiv.org/abs/2311.16154
  73. https://www.imdb.com/title/tt0823212/
  74. https://www.imdb.com/title/tt0814106/
  75. https://www.imdb.com/title/tt0972374/
  76. http://leepers.us/flatland.htm
  77. https://disabilityarts.online/magazine/reviews/extant-theatre-flatland/
  78. https://www.theatrebloom.com/2016/01/review-flatland-at-annex-theatre/
  79. https://www.researchgate.net/publication/380755347_Flatland_XR_An_Embodied_Geometry_Game_Using_Shared_Holographic_AR
  80. https://www.amazon.com/Flatland-Edwin-A-Abbott-audiobook/dp/B0000632ZN
  81. https://www.shmoop.com/study-guides/stranger-strange-land/allusions.html
  82. https://johnrector.me/2024/06/15/understanding-higher-dimensions-through-flatland-and-carl-sagan/
Add your contribution
Related Hubs
User Avatar
No comments yet.