--- title: "Flatland Literary Lexicon" subtitle: "Words Geometry Perception and Power in Edwin A Abbott" author: [] lang: en-GB date: "October 2026" --- # Contents {#contents} - [Introduction and narrative map](#introduction) (p. 5) - [Full articles](#lexicon) (p. 11) - [Defined vocabulary register](#defined-register) (p. 130) - [Expressions and motifs](#contextual-glosses) (p. 186) - [Lexical index](#lexical-index) (p. 201) - [Passage index](#passage-index) (p. 219) - [Thematic index](#thematic-index) (p. 230) - [Source guide and edition notes](#source-guide) (p. 235) ## Full article contents {#article-contents} - [A Square and the voice of the memoir](#entry-a-square) (p. 11) - [Analogy](#entry-analogy) (p. 12) - [Angle](#entry-angle) (p. 14) - [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15) - [Artisan and soldier](#entry-artisan-soldier) (p. 16) - [Attraction and climate](#entry-attraction-climate) (p. 18) - [Birth and ascent](#entry-birth-ascent) (p. 19) - [Chief Circle](#entry-chief-circle) (p. 20) - [Chromatic Sedition](#entry-chromatic-sedition) (p. 21) - [Chromatistes](#entry-chromatistes) (p. 23) - [Circles and Priests](#entry-circle-priest) (p. 24) - [Circular doctrine](#entry-circular-doctrine) (p. 25) - [Class and caste](#entry-class-caste) (p. 27) - [Colour](#entry-colour) (p. 28) - [Compensation](#entry-compensation) (p. 29) - [Configuration](#entry-configuration) (p. 31) - [Conformity and obedience](#entry-conformity-obedience) (p. 32) - [Cube](#entry-cube) (p. 33) - [Cunning and policy](#entry-cunning-policy) (p. 35) - [Dedication and the reader being addressed](#entry-dedication) (p. 36) - [Diagrams and the position of the reader](#entry-diagrams) (p. 38) - [Dimension](#entry-dimension) (p. 39) - [Dodecagon](#entry-dodecagon) (p. 40) - [Doors and houses](#entry-doors-houses) (p. 42) - [Dream and vision](#entry-dream-vision) (p. 43) - [The Editor and the revised Preface](#entry-editor-preface) (p. 45) - [Education and schools](#entry-education-schools) (p. 46) - [Equilateral](#entry-equilateral) (p. 47) - [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) - [Eye and the visible line](#entry-eye-retina) (p. 50) - [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) - [Feeling and touch](#entry-feeling-touch) (p. 53) - [Fertility and extinction](#entry-fertility-extinction) (p. 54) - [Fog](#entry-fog) (p. 55) - [Fourth Dimension](#entry-fourth-dimension) (p. 57) - [Grandson](#entry-grandson) (p. 58) - [History and revolution](#entry-history-revolution) (p. 60) - [Imagination and modesty](#entry-imagination-modesty) (p. 61) - [Initiation and mysteries](#entry-initiation-mysteries) (p. 62) - [Interior and exterior](#entry-interior-exterior) (p. 64) - [Irregularity](#entry-irregularity) (p. 65) - [Isosceles](#entry-isosceles) (p. 67) - [Isosceles rebels](#entry-isosceles-rebel) (p. 68) - [King of Lineland](#entry-king-lineland) (p. 69) - [Language and gender](#entry-language-gender) (p. 71) - [Law and sanction](#entry-law-sanction) (p. 72) - [Lineland](#entry-lineland) (p. 74) - [Marriage and selection](#entry-marriage-selection) (p. 75) - [Memory and forgetting](#entry-memory-forgetting) (p. 76) - [Millennial visit](#entry-millennial-visit) (p. 78) - [Movement and section](#entry-movement-section) (p. 79) - [Nature and law](#entry-nature-law) (p. 81) - [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) - [Painting](#entry-painting) (p. 84) - [Philosophical comparisons and their limits](#entry-philosophical-comparisons) (p. 85) - [Pointland](#entry-pointland) (p. 87) - [Polygon](#entry-polygon) (p. 88) - [Prison and silence](#entry-prison-silence) (p. 90) - [Prometheus Paradise and the cost of knowledge](#entry-prometheus-paradise) (p. 91) - [Providence and the language of necessity](#entry-providence) (p. 93) - [Recognition by sight](#entry-recognition-sight) (p. 94) - [Reform and equality](#entry-reform-equality) (p. 95) - [Regularity](#entry-regularity) (p. 97) - [Revelation and teaching](#entry-revelation-teaching) (p. 98) - [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99) - [Science and institutions](#entry-science-institution) (p. 101) - [Scripture gospel and prophetic speech](#entry-scriptural-language) (p. 102) - [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103) - [Solid humanity and superior races](#entry-solid-superior-races) (p. 105) - [Space and Spaceland](#entry-space-spaceland) (p. 106) - [Sphere](#entry-sphere) (p. 107) - [Straight line](#entry-line-straight) (p. 109) - [Suppression and massacre](#entry-suppression-massacre) (p. 110) - [Surgery and extermination](#entry-surgery-extermination) (p. 112) - [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113) - [Thoughtland and the changing use of an imagined place](#entry-thoughtland) (p. 115) - [Time and the millennium](#entry-time-millennium) (p. 116) - [Touch and bodily proof](#entry-touch-belly) (p. 118) - [Universal Colour Bill](#entry-universal-colour-bill) (p. 119) - [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120) - [Upward and Northward](#entry-direction-upward) (p. 122) - [Voice and hearing](#entry-voice-hearing) (p. 123) - [Voice and selfhood](#entry-voice-selfhood) (p. 125) - [Wives and household](#entry-wives-household) (p. 126) - [Women](#entry-women) (p. 128) # Introduction and narrative map {#introduction} Flatland makes ordinary words change their meaning when a speaker changes position. A side can be a body's boundary, a person's social attribute or the part of a figure visible to an observer. Feeling is touch before it is sympathy; regularity is a geometrical property made into a moral judgement; height is a direction that one society cannot indicate and a status its rulers are unwilling to relinquish. This lexicon follows those changes through the entire work. Its central question is how a limited view becomes a claim about everything that exists, and how that claim can turn into power over other people. The companion follows the supplied Diotimos Editions annotated Flatland of 2026. That edition prints the revised second-edition text of 1884, including the Dedication, the fictional Editor's Preface, both parts and all twenty-two sections. The source also contains extensive modern front and back matter and 228 note records. Its modern commentary is used as commentary, not silently merged into Abbott's words. The four notes explicitly marked Author's note belong to the primary work; the remaining notes are editorial explanations.[^layers] This is a literary lexicon of an English text. It therefore gives English words and exact local forms rather than importing a Greek lemma apparatus. The method is the same close-reading architecture used in the earlier literary companion: substantial articles, a defined vocabulary register, subsidiary expressions and motifs, and three complementary indexes. Its scope includes geometry because the geometry makes the fiction work, and social language because the figures are inhabitants of a society rather than neutral shapes. ## How to use the articles The word defines the term and distinguishes its relevant senses. In the work follows its narrative, rhetorical or philosophical function. The places offers short exact snippets with stable section references and local explanations. In this edition identifies relevant editorial decisions or interpretive commentary. See also connects the article to related discussions. A thematic heading is explicitly identified when the heading names a critical question rather than a phrase used in the primary text. The register is a set of contextual definitions, not a concordance of every token. Its headwords include unusual English, ordinary words whose local meaning changes, geometrical terms, institutional names, characters and significant expressions. The cited form is an actual form printed in the primary text; a normalised headword is a finding aid, not a claim that every inflection or spelling occurs. Multiple local senses can share one headword. The subsidiary glosses explain idioms, euphemisms and concentrated images that need more than a dictionary equivalent. The lexical index provides access by wording; the passage index visits the frame and every numbered section; the thematic index gathers questions that cross sections and article boundaries. Internal links work in the digital formats. Where a page locator accompanies a link, it refers to the matching PDF of this companion, never to an 1884 page or to a page in the supplied edition. Section references such as § 19 remain stable across all formats. ## Voices and kinds of evidence At least four voices must be kept distinct: Edwin A. Abbott, the historical author; A Square, the narrator and ostensible author; the fictional Spaceland Editor of the second-edition Preface; and the modern Diotimos editor. The Sphere, King of Lineland, Circles and other characters introduce further reported positions. A claim that women lack reason, or that killing irregular infants is merciful, belongs first to the character and institution making it. Repeating it without attribution would conceal the satire's object. The narrator's prejudices do not make every description worthless. He can describe a cruel arrangement accurately while praising it wrongly. His later experience can enlarge his knowledge while leaving some of his social habits intact. The Preface reports revisions of opinion but qualifies the moral defence; it is not a certificate that every sentence in Part I has been purified of prejudice. The book also distinguishes kinds of experience. Lineland and Pointland are presented in dreams. The encounter with the Sphere and the excursion into Spaceland are narrated as facts, though later doubt threatens the narrator's ability to sustain his account. The fourth and higher dimensions are objects of analogy and conjecture; no fourth-dimensional world is visited. The Sphere's repentance appears in the dream of § 20, not in a confirmed waking return. These distinctions matter more than forcing the entire narrative into either an unquestioned revelation or an all-a-dream explanation. ## What completeness means here The governing scope is the full literary and intellectual work done by the supplied text: its major word-families, voices, scenes, institutions, images, demonstrations, conflicts and ending. The lexicon is not limited to a fixed list of celebrated geometrical ideas. It includes forms of recognition, school specimens, the economics of killing, female and male dialects, household concealment, colour's artistic attractions, the narrator's hearsay, the difficulties of diagramming and the changing status of memory. An article count is not a measure of exhaustiveness by itself. Closely related forms are grouped when their relation is the subject; a repeated index entry is not a new explanation. Conversely, a minor-sounding expression can deserve a separate gloss when it exposes a policy or a turn of thought. The defined register, articles and indexes intentionally overlap, offering different ways to find the same evidence. This companion does not claim to be a fresh collation of the 1884 printings. The supplied edition's Note on the Text describes its own collation and corrections; this lexicon follows that source and preserves its stated readings. Nor does it establish every historical parallel anew. Contextual identifications from the edition are attributed as such, with particular care over putative philosophical influences. Plato, Aristotle and Emerson are important comparisons in the modern apparatus, not named doctrinal authorities in Abbott's narrative.[^comparisons] ## The narrative in order ### The title dedication and Preface The title page gives the book to A Square and makes a Shakespearean pun on shaping one's talk. The Dedication addresses the superior inhabitants of Space while asking them to acquire imagination and modesty. The revised Preface then reports the Square's imprisonment and answers an objection about thickness and another about misogyny. It lets a fictional Editor mediate the narrator's defence and warns against insisting on an exact earthly counterpart for every detail. ### Part One This World 1. **§ 1 Nature of Flatland.** The Square asks the reader to imagine a populated plane. A lowered view of a coin or cut-out figure shows why different bodies all appear as lines. The distinction between a thing and its appearance is established before any higher visitor arrives 2. **§ 2 Climate and houses.** Southward attraction, northern rain and pentagonal houses explain orientation and building. The apparently practical survey includes separate entrances for women and men and a ban on investigating the origin of light 3. **§ 3 Inhabitants.** Shapes become social classes. The law of increasing sides promises ascent but exempts or restricts the lowest groups. Rare promotion, compulsory adoption and official medical intervention also serve to prevent revolution 4. **§ 4 Women.** The Female Code regulates sound, entry and movement. Practical danger is used to rationalise confinement, and the narrator equates household peace with the absence of slaughter. His language makes his prejudice evidence for the reader 5. **§ 5 Recognition by hearing and touch.** Voice can identify or deceive. Feeling measures angles, requires training and exposes the social body to injury. Schooling relies on living specimens; family history reveals how recently a respectable Square's ancestors were near the lower ranks 6. **§ 6 Recognition by sight.** Fog enables inference from gradients of brightness. Expensive training gives the elite a recognisable skill, while examinations and failures reveal the coercive underside of educational distinction 7. **§ 7 Irregular figures.** Geometrical regularity becomes a criterion of moral worth and civic admission. Reformers propose that exclusion helps cause crime; the narrator rejects their account and approves selective killing as a moderate remedy 8. **§ 8 Painting.** The lost practice of colour transformed perception and created an artistic culture the narrator can still admire. The account gives an inventor named Chromatistes a Pentagon's shape and reports uncertainty about his name 9. **§ 9 Universal Colour Bill.** Colour undermines learned methods of recognizing rank and encourages a demand for equal rights. A proposed red-and-green scheme threatens to make priests and women resemble one another from a specified viewpoint 10. **§ 10 Chromatic Sedition.** Pantocyclus turns apparent concession into a staged massacre. The revolutionary Chromatistes is here an Irregular Circle, not straightforwardly the earlier Pentagon inventor. Suppression extends from painting to colour words and knowledge of its manufacture 11. **§ 11 Priests.** The Circles are revealed as socially certified many-sided polygons. Their power, reproductive difficulty and lethal attempts at bodily improvement expose the institutional manufacture of supposed natural perfection 12. **§ 12 Priestly doctrine.** Configuration is made to explain character and justify constraint, though everyday blame contradicts the doctrine. Suppression of women's education creates a divided language and damages the male intellect that it was intended to protect ### Part Two Other Worlds 13. **§ 13 Lineland.** A dream places the Square before a one-dimensional kingdom whose inhabitants perceive points and use voices to infer what sight cannot disclose. Its immovable neighbourhood and distant courtship make familiar arrangements strange 14. **§ 14 The failed explanation.** The King cannot understand a direction outside his Line, and the Square cannot make him do so. The Square's own impatience anticipates the way a higher teacher will treat him 15. **§ 15 The Stranger.** The Grandson speculates about a third power of length and is rebuked. On the millennial night a Stranger appears inside the closed house; the household’s normal categories of sight and touch cannot identify more than a Circle 16. **§ 16 Words and dimensions.** The Sphere explains sections, height and numerical analogies. The Square assimilates unfamiliar terms to his existing directions, while the revised thickness discussion complicates any easy account of a strictly thicknessless plane 17. **§ 17 Demonstrations and force.** Knowledge of an enclosed cupboard does not convince the Square. The Sphere inflicts a small internal pain and finally removes him from his plane. Pedagogy becomes a struggle over agency and bodily control 18. **§ 18 Spaceland.** The Square sees his world and house from above and confuses interior sight with divinity. The Sphere challenges that inference. Their visit to the Council reveals that authorities preserve records of recurring revelations while suppressing witnesses 19. **§ 19 Desire for more.** Feeling helps the Square learn the Cube. He extends the Sphere's analogy toward a fourth dimension, whereupon the teacher repeats the refusal it had condemned. The pupil's widening speculation ends in a forced return 20. **§ 20 Pointland.** In a dream a self-enclosed Point treats every voice as its own thought. The dream Sphere admits its earlier error and encourages ascent, but even this encouraging dream ends with a patronising comparison to the Female Sex 21. **§ 21 The Grandson.** A proclamation turns inquiry into dangerous heresy. The frightened boy recants, and the Square finds that a remembered formula cannot supply a direction he can no longer show 22. **§ 22 Writing and prison.** An evasively titled treatise fails to overcome the limits of linear diagrams. Public testimony leads to perpetual imprisonment; even a brother who witnessed the manifestation remains unconvinced. The memoir ends between hope for future readers and episodes of doubt reaching down to Flatland itself ## A guide to the ten figures The supplied edition's illustrations can be found at the following sections. They remain part of the primary work; this companion explains their reading rather than silently replacing them with new diagrams. - **§ 1, figure 1:** the Triangle from above and from lower viewpoints; appearance changes while shape remains fixed - **§ 2, figure 2:** a pentagonal house; RO and OF are the northern roof sides, with sex-specific entrances on opposite sides - **§ 6, figures 3 and 4:** triangle, pentagon and hexagon recognition; near and receding portions produce different brightness patterns - **§ 9, figure 5:** the Circle's red and green halves seen along the dividing diameter; an apparent resemblance has a specified viewing condition - **§ 13, figure 6:** Lineland viewed from outside; the diagram grants a perspective unavailable to its inhabitants - **§ 14, figure 7:** the Square withdrawing from Lineland; intersection persists and then disappears - **§ 16, figure 8:** successive positions of a Sphere through the plane; changing sections belong to one unchanged Sphere - **§ 18, figure 9:** the household seen from above, including Wife, Daughter, Sons, Grandsons and Page; spatial access makes private interiors visible - **§ 19, figure 10:** the Cube learned through stacked cards and a shaded solid; this is not an image of a four-dimensional cube [^layers]: The source Markdown's continuous note identifiers are 1–228. The authorial notes are 15, 40, 47 and 142. Local section references are preferable when consulting the PDF or EPUB, whose presentation can make note numbering less convenient. Authorial status is established by the source's explicit label, not inferred because a note happens to concern Abbott. [^comparisons]: A parallel can be illuminating without being a proved influence. The source itself often makes this distinction, for example when discussing nineteenth-century dimensional speculation or identifying possible intellectual resonances. This companion retains that caution and does not claim independent archival evidence. # Full articles {#lexicon} The 85 full articles are arranged alphabetically. The defined register contains 424 consolidated headwords or expressions with 433 contextual records; 43 subsidiary glosses follow it. The three indexes provide routes by wording, passage and theme. These counts describe different kinds of explanation and navigation, not separate totals to add together. ## A Square and the voice of the memoir {#entry-a-square} *A Square; Square; Memoirs; my happy readers* **The word.** A Square is simultaneously a geometrical description, a social identity and the name offered as the book's author. Within Flatland, being a Square places the speaker among Professional Men and Gentlemen, below the nobility and priesthood but above the classes he habitually disparages. The indefinite article in the name makes him an example of a class even when his experience becomes exceptional. **In the work.** The opening voice knows more than its audience about Flatland and less than that audience about Space. This unstable distribution of knowledge is essential to its humour. He instructs privileged three-dimensional readers through elementary demonstrations, calls them happy, and describes institutions whose cruelty he often expects them to admire. The reader's superiority in one respect is offered as a temptation to complacency in another. His social position matters to the prose. A lawyer's orderly classification and respect for established distinctions give authority to the survey of Part I. Phrases such as Law of Nature and public safety can make historically imposed arrangements sound beyond dispute. His professional identity returns in §22 when private business and clients lose their hold on him. Conversion has an economic and domestic cost, not only an intellectual one. The memoir is retrospective. The narrator who says that he once mistook his country for his universe already knows that his earlier certainty was false. Yet retrospective knowledge does not automatically cleanse his descriptions of rank and sex. His encounter with the Sphere enlarges perception faster than sympathy; after it he still withholds instruction from his Wife. The fictional Editor's account of changed opinions in the Preface must therefore be read beside, rather than substituted for, the memoir's stubborn habits. There are also several senses of authorship. Abbott wrote the fiction; the title page attributes the illustrations to A Square; the fictional Editor reports the imprisoned narrator's explanations. These voices are related literary devices, not interchangeable witnesses. A Square's prejudices can make the satire possible precisely because Abbott does not interrupt every sentence to condemn them. Conversely, describing the speaker as unreliable does not make everything he reports false. The book needs his demonstrations, social observations, selective blindness and suffering to remain in contact. **The places.** - **Title Page.** “With Illustrations by the Author, A Square” makes the narrator an ostensible maker of the book and its figures - **§ 1.** “my happy readers” establishes an address to privileged outsiders - **§ 1.** “I should have said ‘my universe’” is the narrator's explicit revision of an earlier limit - **§ 3.** “to which class I myself belong” places him within the hierarchy he describes - **§ 22.** “I neglected my clients and my own business” gives his vocation a cost **In this edition.** The title-page note connects the pseudonym with Edwin Abbott Abbott's repeated initial. This is the edition's biographical explanation, not a fact announced by the fictional narrator. Its introduction also discusses Abbott's teaching and theology; neither supplies permission to assign every statement of the Square directly to Abbott. **See also.** [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120) · [Class and caste](#entry-class-caste) (p. 27) · [The Editor and the revised Preface](#entry-editor-preface) (p. 45) · [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99) ## Analogy {#entry-analogy} *Analogy; the method of Analogy; the Argument from Analogy of Figures* **The word.** Analogy is reasoning from a known relation to a corresponding relation in a less familiar case. The Sphere does not merely liken a Square to a Cube. He invites the Square to carry a rule of construction, and the relations between a figure and its boundaries, from dimensions he knows into one he cannot yet perceive. The word names a disciplined imaginative operation, although the narrative also asks how far its conclusions reach. **In the work.** The method arrives late in the Sphere's first lesson. Statements, household information and the visible shrinking of his section have failed to secure understanding. Analogy is his remaining verbal resource before coercion. His questions deliberately use the Square's competence: a moving Point leaves a Line, a moving Line produces a Square, and numerical sequences supply the expected properties of the next figure. The pupil can calculate the answers without conceiving the unfamiliar movement. Correct mathematical responses and imaginative comprehension are therefore separated within the same conversation. The scene also follows an earlier, less successful experiment in teaching. The grandson has already extended a numerical and spatial pattern to the third power, admitting that he cannot see how the further construction works. His grandfather's command to go to bed suppresses the very reasoning the Sphere now requires. Analogy is not the visitor's exclusive possession. It is available to a child and frustrated by an adult's authority before the visitor formally names it. In §19 the Square turns the method upon its master. If moving a Square generates a Cube, why should moving a Cube in a new direction not generate a figure with sixteen terminal points and eight cubic boundaries? The Sphere's impatient rejection dramatizes a failure of consistency: he wants analogy to license one enlargement and to stop at the world where he already feels at home. The pupil has learned the generative procedure more thoroughly than the teacher's intended curriculum permits. Nevertheless, a correct continuation of a mathematical pattern is not an eyewitness report of another physical world. The Square requests confirmation, asks about alleged visitations, and admits that he does not know the facts. His subsequent rush towards indefinitely many dimensions carries conviction and exhilaration beyond the evidence actually supplied. The novel preserves both the method's intellectual force and this difference of status. Analogy generates an intelligible possibility and a reason to investigate; the journey verifies three dimensions for this traveller, not four or infinity. **The places.** - **§16:** “I must try the method of Analogy” — A last verbal strategy before action - **§16:** “Or rather not I, but Analogy” — The teacher presents the method as speaking independently of him - **§19:** “Analogy! Nonsense: what analogy?” — The higher-world instructor resists his own procedure - **§19:** “not knowing the facts” — The pupil explicitly marks the distance between anticipation and verification - **§22:** “arguments for the existence of Solid things derivable from Analogy” — Repetition still cannot convert his brother **In this edition.** The notes distinguish geometrical from arithmetical progression and explain the correctness of the four-dimensional counts. They do not supply a fourth-dimensional journey missing from Abbott's narrative. The edition's philosophical comparisons belong to its apparatus, whereas *Analogy* is repeatedly and explicitly Abbott's word. **See also.** [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15) · [Grandson](#entry-grandson) (p. 58) · [Fourth Dimension](#entry-fourth-dimension) (p. 57) · [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) ## Angle {#entry-angle} *angle; acute angle; angle or brain; angularity* **The word.** An angle measures the opening between two meeting lines. In Flatland it also supplies a measure of intelligence, a weapon, a hereditary qualification and a social address. A larger interior angle is less pointed: the geometrical relation makes mental advancement coincide with the loss of bodily sharpness. The ordinary compliment *acute*, meaning intellectually penetrating, therefore becomes unstable. **In the work.** The opening taxonomy makes a reader learn two scales together. The Isosceles soldier's narrow angle makes him dangerous, whereas a many-sided nobleman's broad angles advertise refinement. These are not independent attributes accidentally bundled together. The narrator presents their connection as an arrangement that prevents intelligent popular leaders from possessing the physical power necessary to overthrow their rulers. The measured angle becomes a political explanation pretending to be an innocent description of anatomy. The consequences reach into language. In §5, the near-equilateral ancestor has an “angle or brain” of 59° 30′. The conjunction makes measurement and mentality interchangeable without argument. A degree and a half lost after his disastrous collision can describe bodily inheritance, diminished family honour and the consequences of punishment at once. Numbers lend precision to a history whose causal assumptions remain fantastic. They do not eliminate prejudice; they furnish it with a register. Angles also make people readable. If the citizen is regular, one corner can disclose the whole figure and therefore the rank appropriate to him. The single inspected part stands for the person, replacing any enquiry into character. The danger of touching that corner gives this social shorthand its apparent urgency. Courtesy, caution and hierarchy consequently share an instrument. Yet the use of angles is not simply exposed as nonsense. The mathematical difference between a Triangle and a Pentagon genuinely supports the optical demonstration in §6. Abbott lets sound geometrical inference and unsound moral inference use the same confident explanatory manner. A reader must distinguish what the angle establishes from what the society wishes it to establish. The distinction matters throughout the romance: being able to calculate a shape is not being entitled to calculate a person's worth. **The places.** - “a very sharp and formidable angle” (§3) - “their acute angle (which makes them physically terrible)” (§3) - “an angle or brain of 59° 30′” (§5) - “the family brain was registered at only 58°” (§5) - “task the angularity of the most intellectual” (§6) **In this edition.** The Diotimos notes supply numerical checks for the geometry at notes 34, 57 and 59, and discuss phrenological measurement at note 59. Those historical explanations are modern annotation, not terms Abbott inserts into the narrative. The “angle or brain” identification itself belongs to the main text and needs no editorial paraphrase to reveal its violence. **See also.** [Isosceles](#entry-isosceles) (p. 67); [Regularity](#entry-regularity) (p. 97); [Recognition by sight](#entry-recognition-sight) (p. 94); [Birth and ascent](#entry-birth-ascent) (p. 19). ## Arithmetic and geometrical progression {#entry-arithmetic-geometric-series} *Arithmetic; Geometrical Progression; Arithmetical; Series* **The word.** An arithmetical progression increases by a constant difference; a geometrical progression increases by a constant ratio. Abbott uses the familiar schoolroom distinction to organize unfamiliar dimensional constructions. The number of terminal points doubles from Point to Line to Square to Cube, while the number of boundaries of one dimension lower increases by two. The two counts answer different questions and must not be merged. **In the work.** Arithmetic first opens an unintended door in §15. Nine unit Squares form a Square three inches on each side, and the grandfather uses the arrangement to explain the second power. The child asks what the third power means geometrically. Since calculating a third power is already part of his instruction, the denial that it can signify a figure exposes an awkward division in the curriculum: arithmetic is allowed an operation whose possible spatial meaning geometry forbids him to investigate. The Sphere then reconstructs the same ladder in dialogue. His initial terminal-point series begins with one, the Point itself, and proceeds through two and four to eight. His boundary series begins with zero, since a Point has no lower-dimensional side, and proceeds through two and four to six. Abbott makes the Square name the progressions and give their next terms. Nothing in the difficulty is due to inability to calculate. The pupil knows that the next numbers are eight and six, but cannot yet turn those counts into a coherent perceptual object. When the Square subsequently reasons towards four dimensions, he omits the opening terms and restates the operative sequences as two, four, eight, sixteen and two, four, six, eight. The projected object has sixteen corners and eight cubic boundary cells. The eight are not its square faces or its edges. Here ordinary *side* has already been stretched to mean a boundary of the immediately lower dimension, and keeping the vocabulary straight prevents an apparent numerical contradiction. The serial pattern also changes the relation of speaker and listener. What had looked like a closed examination, with the visitor holding the answer, becomes a procedure capable of producing an answer he refuses to hear. The Square quotes his master's own formula against him. Mathematics gives the pupil a resource that does not depend on rank or permission, although calculation alone cannot make the object visible or establish that a corresponding inhabited world exists. The later failed lessons retain this distinction. The Council excludes the enumeration of imaginary sides and angles from the kind of demonstration it will accept. That restriction is politically interested, but the reader has already seen the genuine gap between a count and an image. Abbott therefore makes arithmetic powerful without presenting it as an automatic substitute for every other kind of evidence. **The places.** - **§15:** “raise numbers to the third power” — An authorized operation provokes an unauthorized question - **§16:** “1, 2, 4” — Terminal points form the opening geometrical series - **§16:** “0, 2, 4” — Lower-dimensional boundaries form the arithmetical series - **§19:** “sixteen terminal points” — The anticipated fourth-dimensional count - **§22:** “other than the enumeration of imaginary sides and angles” — The Council narrows acceptable proof **In this edition.** The mathematical notes identify the object now generally called a tesseract, but Abbott does not use that later term in the romance. The lexicon retains his language and explains the counts without silently replacing it with modern terminology. **See also.** [Analogy](#entry-analogy) (p. 12) · [Cube](#entry-cube) (p. 33) · [Dimension](#entry-dimension) (p. 39) · [Grandson](#entry-grandson) (p. 58) ## Artisan and soldier {#entry-artisan-soldier} *Artisan; Soldier; Workmen; Working Man; serf* **The word.** An *artisan* is a skilled worker; a *soldier* belongs to the military. Flatland places both occupations within its Isosceles population, although it distinguishes their grades and uses. *Serf* names their subordinated condition rather than a separately described system of agricultural tenure. Occupational names continually slide into anatomical classifications. **In the work.** The military and labouring classes enter §3 together, through the lengths of their sides. Their work has scarcely been mentioned before the narrator describes their bodies as degraded and their humanity as doubtful. This order of exposition is important: the person is made intelligible first as a dangerous shape, then as a useful worker. The activity that supports the society does not entitle him to equal consideration within it. Work and military success can nevertheless change a family's future. Sustained skill, intelligence and disciplined living are said to widen the narrow base through successive generations. This promise gives labour a moral interpretation, but admission to the next class requires priestly marriage arrangements, official inspection and the removal of the successful child from his parents. The worker can improve the hereditary material from which a future citizen is made; he cannot determine the terms on which that citizen will belong. The state also turns the soldiers' shared bodily power against solidarity. At the end of §3, the Chief Circle keeps some Isosceles in his pay to destroy others, while the remaining population may be induced to kill one another. The description of an inferior class is thus also an account of how superiority maintains itself. The narrator's admiration for the arrangement exposes his distance from those who suffer it. Domestic language sharpens the distinction. In §4 the lower military husband's commitment to literal truth is blamed for his inability to placate his wife through false promises. A conventionally commendable quality becomes a defect when judged by the governing class's expediency. Conversely, the Circle's ability to deceive becomes tact. Neither anatomy nor occupation explains this reversal; the evaluation follows the interests of the speaker. The classes are not entirely voiceless. Isosceles can reproduce prestigious voices with remarkable facility, and the Square's own family emerges from their ranks. These details prevent the taxonomy from remaining safely external to the narrator. His educated account depends upon suppressing capacities and kinships which his story nonetheless records. **The places.** - “Our Soldiers and Lowest Classes of Workmen” (§3) - “diligent and skilful labours” (§3) - “the Artisan and Soldier classes” (§3) - “their brethren whom the Chief Circle keeps in pay” (§3) - “a blunt and stolid regard for literal truth” (§4) **In this edition.** Notes 35 and 39 connect the classification with Victorian social disdain and managed heredity. Note 58 reconstructs the narrator's Isosceles ancestry. These are useful editorial contexts; the text itself supplies the occupational hierarchy and the revealing distinction between celebrated skill and withheld rights. **See also.** [Isosceles](#entry-isosceles) (p. 67); [Class and caste](#entry-class-caste) (p. 27); [Birth and ascent](#entry-birth-ascent) (p. 19); [Voice and hearing](#entry-voice-hearing) (p. 123). ## Attraction and climate {#entry-attraction-climate} *attraction; gravitation; temperate; bearings* **The word.** *Attraction* is Flatland's persistent pull towards the South. It provides an analogue of gravity within the plane, so that direction can be experienced without a sun or stars. *Temperate* denotes milder regions but repeatedly attracts the additional suggestion of social moderation. Climate becomes both a physical setting and a vocabulary of judgement. **In the work.** The compass is a useful early lesson in imaginative reconstruction. A reader accustomed to finding North by heavenly bodies must accept a different set of clues: resistance when moving northward, rain from the North, the orientation of houses and the trunks of trees. The narrator's occasional helplessness on an empty plain makes this reconstruction experiential rather than merely diagrammatic. Knowing directions depends on available contrasts; remove them and even an informed traveller may have to wait. The same passage quietly imports social assumptions. The claimed weakness of women turns a physical tendency into an etiquette of protection: a gentleman gives a lady the northern side. The comedy lies partly in the difficulty of performing the courtesy when the gentleman cannot readily establish where North is. A convention of breeding presents itself as an obvious response to nature, although its performance depends on unstable information. Later, stronger attraction in southern regions helps explain stricter restrictions on women. Involuntary motion can cause injury, but the passage proceeds from that hazard to laws which punish the body liable to move. The geographical account lends necessity to choices about confinement and punishment. Conversely, “better regulated” and “temperate” regions are not consistently humane: §5 assigns the starvation and frequent replacement of classroom specimens to just such places. The reassuring vocabulary cannot be accepted as an independent moral judgement. Climate has another role in the distribution of knowledge. Fog supplies the variable brightness required for sight recognition, and this resource is unavailable in the torrid zones. The cultivation claimed by privileged observers therefore rests partly on an environmental condition rather than on their intrinsic superiority. The text does not reduce culture to weather, but it gives weather a place inside what the society calls culture. These usages make physical world-building inseparable from social explanation. The reader should neither discard the stipulated mechanics nor accept every political conclusion hung upon them. Attraction can genuinely explain a difficulty of movement without justifying the legal treatment of the person who encounters it. **The places.** - “a constant attraction to the South” (§2) - “waiting till the rain came” (§2) - “a point of breeding” (§2) - “the force of gravitation is greater” (§4) - “the more temperate and better regulated regions” (§5) **In this edition.** Note 27 explains the Victorian street courtesy behind giving a lady the North side. Note 31 relates the roof and floor to rain and attraction. The edition offers these as contextual helps; the fiction does not supply a complete physical theory of its climate, and the lexicon should not invent one. **See also.** [Doors and houses](#entry-doors-houses) (p. 42); [Fog](#entry-fog) (p. 55); [Nature and law](#entry-nature-law) (p. 81); [Women](#entry-women) (p. 128). ## Birth and ascent {#entry-birth-ascent} *birth; offspring; posterity; Ascent; hereditary level* **The word.** *Ascent* names hereditary advancement in social rank, measured by sides or, below the equilateral threshold, by the size of an angle. It does not mean bodily motion out of the plane. *Posterity* shifts attention from a living person's condition to the prospects of descendants, making deferred benefit a central social promise. **In the work.** The celebrated law that a son has one more side than his father sounds like universal progress. Its immediate qualifications reveal how unevenly that progress is distributed. The son of a Square rises routinely; the Isosceles lineage may remain where it is. Advancement among the lowest classes requires a prolonged combination of labour, disciplined conduct, arranged marriage and accumulated bodily change. A shared word, development, conceals radically different relations to time. The successful equilateral birth is at once a public festival and a family bereavement. Certification gives the child a class, while adoption prevents him from seeing his parents again. The fear that imitation might undo his new form exposes the uncertainty within an apparently biological system. If inherited rank can be damaged by ordinary association, the barrier is being maintained socially as well as described naturally. The parents' mixed pride and grief momentarily restore an emotional cost which the official ceremony threatens to obscure. Hope is explicitly useful to the rulers. Rare promotions are welcome because they do not substantially diminish privilege but discourage revolution. The passage is unusually direct about this function: the possibility of escape keeps the class in place. Improvement for particular descendants and preservation of the system are not opposite outcomes; here they reinforce one another. The Square's family history makes the promise concrete and precarious. One involuntary movement during an introduction causes legal punishment, disgrace and a hereditary setback. Several generations are required to recover a degree and a half. The numerical account gives genealogy the appearance of an audited balance sheet, but it also reveals how vulnerable the future is to institutions that assign permanent meaning to an accident. Ascent consequently offers a diminished version of enlargement. It supplies more standing within the established order without questioning that order's measure of value. The romance's eventual movement into another dimension will be different in kind, not merely a quicker promotion along this scale. Keeping those senses separate helps a reader hear how persistently the book tests the word *higher*. **The places.** - “one step in the scale of development and nobility” (§3) - “his proud yet sorrowing parents” (§3) - “a most useful barrier against revolution from below” (§3) - “fall back again into his hereditary level” (§3) - “the Ascent from the Isosceles finally achieved” (§5) **In this edition.** Note 41 preserves the 1884 wording “emergence of an Isosceles,” while explaining that the immediate sense calls for an Equilateral born to Isosceles parents. This is an important textual distinction, not a new category of promotion. Abbott's own note 40 discusses certification and irregular inheritance; the historical breeding context in note 39 is Diotimos annotation. **See also.** [Equilateral](#entry-equilateral) (p. 47); [Class and caste](#entry-class-caste) (p. 27); [Angle](#entry-angle) (p. 14); [Nature and law](#entry-nature-law) (p. 81). ## Chief Circle {#entry-chief-circle} *Chief Circle; President; presiding Circle.* **The word.** *Chief* marks the head of the ruling order, not a different geometrical species. The *Chief Circle* is an office held successively. Pantocyclus is its named incumbent during the Colour Revolt; the later narrative has a presiding Circle or President of the Council. The text does not establish that these figures, separated by the history of colour and its remote aftermath, are one person. **In the work.** The office concentrates Flatland's three principal technologies of rule: classification, organized force, and restricted knowledge. In §3 the Chief Circle keeps paid Isosceles to kill other Isosceles when popular leaders have been removed. Their service exposes the weakness of any simple equation between bodily class and political interest. The sharp bodies despised by the governing class become instruments of government when paid and directed by it. The office's own bodily magnificence rests on a conspicuously weaker kind of evidence. In §11 its ten thousand sides are assumed *by courtesy*. They are neither counted nor experimentally verified. The prohibition on feeling members of the highest society protects this claim from ordinary tests. A social convention supplies the numerical precision with which a science-minded civilization adorns its ruler. The discrepancy is not that ten thousand sides would make a mathematically perfect circle: no finite polygon does. It is that even the specified finite number is ceremonially conceded. Secrecy becomes an attribute transmitted with the office. At the end of §10 only the current Chief Circle knows how to make colour, and he passes the knowledge to his successor on his deathbed. The yearly killing of the manufactory's workmen prevents practical knowledge from competing with the ruler's monopoly. The office survives while the people who enable its survival are made replaceable. In §18 the President alone can consult the secret archives recording previous dimensional visitations. His composure before the Sphere differs from the younger Councillors' alarm because he possesses historical knowledge withheld from them. Although this presiding office belongs to the same ruling system, it is safer to retain the narrative's actual titles than to equate every *President* mechanically with the *Chief Circle*. What matters is the repeated architecture of authority: an initiated head, partially informed subordinates, disposable witnesses. The ruler does not simply believe Flatland's limits; he manages evidence that might disturb them. **The places.** - §3: “the Chief Circle keeps in pay” - §10: “by name Pantocyclus” - §10: “handed down on his death-bed” - §11: “assumed, by courtesy” - §18: “the secret archives, to which I alone have access” **In this edition.** The modern note 108 explains the geometrical approximation and the courtesy claim; it does not certify the ruler's side count. Note 99 glosses Pantocyclus's Greek-derived name. The distinction between the named historical ruler and later office-holders must be preserved even when discussing their common methods. **See also.** [Circles and Priests](#entry-circle-priest) (p. 24); [Chromatistes](#entry-chromatistes) (p. 23); [Cunning and policy](#entry-cunning-policy) (p. 35); [Suppression and massacre](#entry-suppression-massacre) (p. 110). ## Chromatic Sedition {#entry-chromatic-sedition} *Chromatic Sedition; Colour Revolt; Revolution; Chromatic Innovation.* **The word.** *Chromatic* means pertaining to colour. *Sedition* names resistance as an offence against established authority; *revolt* and *revolution* can describe the same political movement without exactly the same legal emphasis. The variety of names matters. The section heading announces a suppression from the victor's point of view, while the body of the history allows colour to signify art, convenience, emancipation, imitation, and danger. **In the work.** The change begins without a revolutionary programme. Painting spreads because it is attractive and reduces the difficulty of recognition. Its political force appears when a technique previously associated with intellectual training becomes unnecessary for common purposes. Colour recognition allows the labouring classes to negotiate practical problems without possessing the higher orders' distinctive schooling. Their assertion of diminished difference between classes is granted “increasing truth” even by the hostile narrator. The movement then advances from practical equality to political claims: abolition of exclusive educational endowments, equal rights, and compulsory painting of the privileged as well as the unprivileged. The stages cannot be reduced to an irrational outbreak of the supposedly unintelligent. Nor does recognizing legitimate grievances require treating every revolutionary demand as harmless. Making all bodies submit to a single scheme introduces compulsion, and suppressing older arts would destroy knowledge. Abbott's account makes the relation between intellectual emancipation and political coercion a problem on both sides. The narrator persistently renames these developments in a morally charged vocabulary. *Innovation* may sound merely new, but *pollution*, *taint*, and *diabolical* turn paint into contamination. *Sedition* makes political difference criminal in advance of a particular act. Once the insurgents can be described collectively as criminals, their deaths become the restoration of a natural balance. The heading therefore participates in the history's violence; it is not a neutral label above it. The movement's alliance is unstable. Women hope for respect and access to information, artisans for improved status, soldiers for participation, and the Irregular Circle for an overturning of aristocratic rule. Pantocyclus defeats them by addressing these interests separately. He does not refute a single common argument; he breaks the coalition through fears about marriage, family advancement, and domination by those even lower in rank. The Chromatic Sedition is consequently the book's fullest model of how a popular movement can be reclassified, divided, and destroyed while the victors call themselves guardians of order. **The places.** - §8: “the glorious childhood of Art” - §9: “and with increasing truth” - §9: “absolutely equal and entitled to equal rights” - §10, heading: “Suppression of the Chromatic Sedition” - §10: “the triumph of Order” **In this edition.** Modern notes 93 and 100 relate the agitation and the ruler's fears to nineteenth-century franchise reform. These historical comparisons are editorial interpretation, not dates or institutions named by Flatland's chronicler. The alternation among *Revolt*, *Innovation*, and *Sedition* is Abbott's own language. **See also.** [History and revolution](#entry-history-revolution) (p. 60); [Reform and equality](#entry-reform-equality) (p. 95); [Universal Colour Bill](#entry-universal-colour-bill) (p. 119); [Suppression and massacre](#entry-suppression-massacre) (p. 110). ## Chromatistes {#entry-chromatistes} *Chromatistes.* **The word.** The personal name connects its bearers with colour. The edition's modern note 86 explains it through Greek *chrōma*, colour, and the agent-ending *-istēs*: a colourer or colourist. Abbott gives the name to the Pentagon credited with inventing painting in §8, and then to the revolutionary leader killed in §10. The latter is identified, through §9's account, as an Irregular Circle. The different forms, functions, and historical positions prevent an unqualified composite biography. **In the work.** The first Chromatistes enters under several signs of historical uncertainty. His name is variously reported; his discovery is casual; the narrator invokes the authorities who concur in calling him Chromatistes. The vocabulary mimics an antiquarian reconstruction of cultural origins. What is certain within the story is the pattern of his experiment: house, slaves, father, descendants, self. Painting moves from property and dependants towards the inventor's own body. Its success is at once beautiful and practical. He becomes easier to recognize and safer to encounter. The later Chromatistes is not introduced through private invention. An unnamed Irregular Circle has devised the Universal Colour Bill, and §10 names Chromatistes as the leader of the Sedition who is summoned forward by Pantocyclus. The conjunction identifies the political leader with the Bill's author without erasing the earlier inventor's separate description. The narrated age of colour has already lasted centuries. Neither an explanation of the repeated name nor a genealogy connecting its bearers is supplied. Naming changes register with the second bearer. *Colourist* becomes a political position. Pantocyclus calls him into the centre of the assembly under the promise of receiving the hierarchy's submission. The invitation briefly seems to acknowledge representative authority: he will receive it in his followers' name. It actually isolates him. When he tries to answer the ruler's rhetoric, guards prevent speech; the apparent recognition of a rival ends in his transfixion. The two appearances consequently frame an entire cultural passage. A name first associated with making bodies legible is attached at the end to a man whose public voice is forcibly extinguished. The first bearer produces an accessible visual language; the second is destroyed as that language is withdrawn from general use. This structural parallel is firmer than any claim that Abbott meant the two men to be identical, or that one occurrence is a printer's error. A lexicon should make the unresolved naming visible instead of repairing it silently. **The places.** - §8: “a Pentagon whose name is variously reported” - §8: “Wherever Chromatistes” - §9: “an Irregular Circle” - §10: “Chromatistes, the leader of the Sedition” - §10: “transfixed the wretched Chromatistes” **In this edition.** Note 86 treats the inventor's name and the uncertainty surrounding origins; note 94 concerns the Irregular author of the Bill. The main text supplies no resolution of the two bearers. Their distinction is a reading safeguard, not a claim of a documented textual variant. **See also.** [Painting](#entry-painting) (p. 84); [Colour](#entry-colour) (p. 28); [Universal Colour Bill](#entry-universal-colour-bill) (p. 119); [Chief Circle](#entry-chief-circle) (p. 20). ## Circles and Priests {#entry-circle-priest} *Circle; Circles; Priests; Circular or Priestly order.* **The word.** A geometrical circle has a continuous circumference. Flatland's persons styled *Circles* are, the narrator explicitly admits, polygons with very many small sides. *Priest* names this highest social order, but its functions extend far beyond worship. The two designations join a claim of bodily perfection to a monopoly of institutional authority. **In the work.** §11 corrects a misleading analogy with Spaceland priesthood. Flatland's Priests administer business, art, and science, and direct everything from commerce to theology. Their apparent universality is summarized in a splendidly equivocal compliment: they do nothing themselves but cause everything worth doing that others do. The statement can be heard as a doctrine of supreme direction; it also describes a class appropriating credit for other people's work. The generalization invites readers to separate intellectual leadership from an institution's claim to indispensable causation. The Circle's body explains how this claim is sustained. Its tiny sides make close discrimination difficult, but class etiquette prevents the decisive test: feeling a Circle would be an insult. Deference thus obstructs the very procedure by which the society ordinarily establishes identity. A “veil of mystery” protects the perimeter. The secret is less a miraculous shape than the practical refusal to let inferior observers examine a prestigious one. The name acquires its certainty socially where geometry denies it literally. The class is not closed in a simple hereditary sense. A sufficiently many-sided Polygon may ascend into it, and risky operations promise a sudden increase in sides. This possibility converts deference into aspiration. Parents sacrifice children at the Neo-Therapeutic Gymnasium because one surviving success seems to justify many deaths. The cemetery is the material underside of the courtesy title. The narrative makes rank appear at once inherited, medically manufactured, and ceremonially bestowed. The Circles also cultivate contradictory relations to knowledge. They preserve sight recognition when colour makes it unnecessary; they reportedly reserve colour itself for secret advanced instruction after prohibiting it elsewhere, though the Square marks this university practice as hearsay. Later they maintain archives of dimensional visitations while punishing public testimony about other worlds. These are not simply enemies of science. They make inquiry an unequal possession and remove observations whose circulation would threaten their authority. Their priestliness is therefore most legible in the management of initiation, orthodoxy, and access, rather than in a fully described creed or ritual life. **The places.** - §3: “the Circular or Priestly order” - §11: “doing nothing themselves” - §11: “no Circle is really a Circle” - §11: “the veil of mystery” - §11: “a Circle, at least by courtesy” **In this edition.** Note 107 offers the philosophical First Cause as a comparison for the claim to cause others' work. Note 108 explains the limit approached by regular polygons and the social force of courtesy. These are the modern editor's explanatory frames; the narrator's admission that no Circle is literally a circle is in Abbott's main text. **See also.** [Chief Circle](#entry-chief-circle) (p. 20); [Circular doctrine](#entry-circular-doctrine) (p. 25); [Science and institutions](#entry-science-institution) (p. 101); [Fertility and extinction](#entry-fertility-extinction) (p. 54). ## Circular doctrine {#entry-circular-doctrine} *doctrine of the Circles; heresies; teaching; Theology.* **The word.** *Doctrine* is an authoritative body of teaching. *Heresy* marks a rejected belief from inside an institution's claim to orthodoxy. In §12 the old belief that effort, training, or encouragement influences conduct is demoted to heresy, while bodily Configuration becomes the ruling explanatory principle. *Circular* here belongs primarily to the class of Circles; any suggestion of reasoning that returns to its own premise is an interpretive resonance rather than an explicit definition. **In the work.** The creed has an institutional objective before it has a philosophical proof. The improvement of all Configuration is expressly subordinated to the Configuration of the Circles. The common good is thus organized around the perpetuation of the highest order. Its teachers may speak universally about human bodies, but the paragraph tells readers which bodies finally govern the meaning of improvement. Pantocyclus's doctrine abolishes moral responsibility in theory. If shape causes action, good conduct earns no praise and bad conduct deserves no blame. This proposition might conceivably loosen punitive moral judgment. Flatland instead combines it with ruthless elimination: an offender who cannot help stealing meets a magistrate who claims he cannot help sentencing him to death. Necessity protects the sentence rather than the sentenced. The asymmetry exposes how a doctrine that dissolves individual blame can leave institutional violence untouched. Domestic practice provides a second test. The narrator's grandson invokes temperature-induced deformation and asks for sweetmeats as treatment. The reasoning follows the doctrine so well that the Square cannot refute it logically. He resorts to scolding or punishment and imagines that these strengthen Configuration, while admitting that he has no grounds for this view. The highest Circles themselves employ praise, blame, right, and wrong. Their actual speech recognizes the moral agency their official theory denies. The doctrine is not merely false according to an outsider; its adherents repeatedly suspend it to conduct ordinary relationships. The command to honour descendants extends the creed into time. Since male descendants acquire more sides, moral obligation points forward towards supposedly superior bodies. Parents must sacrifice their own interests, but *honour* does not mean indulgence. This is a severe regimen of improvement, not simple affection for children. The tragic surgeries of §11 provide its material context. That official doctrine can coexist with a different theology in women's rooms adds a final fracture: the system organizes audiences as well as propositions. It teaches some claims as truth and others as instruments for governing those denied education. **The places.** - §12: “with special reference of course” - §12: “those ancient heresies” - §12: “Theoretically, this doctrine is unquestionable” - §12: “I have no grounds for thinking so” - §12: “honour his Grandson” **In this edition.** Modern notes 110–114 supply philosophical and scriptural comparisons, including physiological determinism and the reversal of the Fifth Commandment. They assist interpretation but should not turn the narrator's fictional creed into a documented statement of Abbott's own theology. Its contradictions are demonstrated directly by the main text. **See also.** [Configuration](#entry-configuration) (p. 31); [Conformity and obedience](#entry-conformity-obedience) (p. 32); [Circles and Priests](#entry-circle-priest) (p. 24); [Language and gender](#entry-language-gender) (p. 71). ## Class and caste {#entry-class-caste} *class; caste; order; rank; status* **The word.** Flatland's *classes* are ranked bodily types, reinforced by education, occupations, marriage and law. *Caste* emphasises inherited degradation and the difficulty of escape; *order* gives the privileged groups a corporate dignity. These are overlapping social words, not names for interchangeable geometrical properties. **In the work.** The taxonomy of §3 advances from Women and soldiers through tradesmen and professionals to nobility and priests. Its short declarative sentences mimic the certainty of a handbook. To learn a shape is to learn whom it authorises to command, practise a profession or be treated as human. The phrase naming the narrator's own class places the act of description within the scheme: classification is performed by a beneficiary, not from nowhere. Yet side-count alone cannot explain every boundary. Women belong to no ascending series, even when their husbands are Circles. Isosceles are essential to work and warfare but excluded from the ordinary rule of hereditary promotion. A Polygon who fails his examinations may possess a noble body without the practical standing expected of it. The social machine must continually supplement its anatomical rule with credentials, training and exceptions. Rank is also a problem of knowledge. People who look like lines need methods of distinguishing their betters; the expensive method of sight recognition makes distinction easier for those who already possess privilege. In the fashionable crowd, the superior figure understands the Square's movements while the Square struggles to understand his. Class is therefore enacted through unequal access to information, not merely announced by a title. The narrator's language repeatedly protects this arrangement by shrinking the moral scale. A dangerous encounter costs the state a “valuable life” when the injured figure is a Polygon; the poorest may be converted into disposable educational specimens. The contrast is not between two different degrees of human suffering described with equal care. It is between persons whose lives acquire a public value and bodies whose treatment is discussed as expenditure. The word *caste* does not make Flatland a coded account of one non-European society. Within the book it intensifies an account assembled from familiar British occupations, university distinctions, hereditary aristocracy and exclusionary customs. The satire's power comes from the ease with which those familiar institutions accept a mathematical exterior. The reader is invited to question the taxonomy's moral authority, not merely to admire its inventiveness. **The places.** - “Our Middle Class consists of Equilateral or Equal-sided Triangles” (§3) - “the highest class of all” (§3) - “his degraded caste” (§4) - “loss of *status*” (§4) - “jostling against your betters” (§6) **In this edition.** Notes 35–39 connect the scheme with labour, professions, peerage and hereditary improvement. Those comparisons are editorial interpretation. The social terms in the article are all Abbott's, and their capitalisation frequently makes a group appear an established institution before its claims have been examined. **See also.** [Artisan and soldier](#entry-artisan-soldier) (p. 16); [Polygon](#entry-polygon) (p. 88); [Education and schools](#entry-education-schools) (p. 46); [Women](#entry-women) (p. 128). ## Colour {#entry-colour} *Colour; colours; Colour Recognition; chromatic taint.* **The word.** *Colour* means visible hue, distinguished in Flatland from the degrees of brightness through which shapes are ordinarily recognized. It also becomes a system of signs and a political principle. The capital gives the sensory property the force of a public institution. The phrase *second Nature* names an acquired practice powerful enough to reorganize what people experience as necessary. **In the work.** Colour does not give Flatlanders a second visual dimension. Painted bodies still appear as lines. What changes is the information carried along those lines: a hue identifies a side, distinguishes front from back, and reduces reliance on fine gradations of brightness. This is why the invention can transform perception without changing anatomy. It turns difficult reading of form into an easier code. The consequences reveal that a mode of recognition is never merely technical. Sight recognition has required education, leisure, and difficult exercises; colour enables people excluded from that training to accomplish practical tasks. The narrator admits that the labouring classes thereby approach equality with higher Polygons. *Second Nature* challenges the argument that inherited nature itself demands permanent inequality. An artificial convention can undo part of what rulers describe as the natural order. Yet a code can be imitated. The fraudulent Dodecagon story depends on colour being detachable from the body whose rank it signifies. Twelve colours do not produce twelve sides. The Universal Colour Bill would similarly permit a Woman and a Priest to look alike from particular positions. The possibility does not mean that every viewer must always confuse them: size and fading at the ends remain distinguishable. The narrator's fear depends on people no longer attending to those differences. The crisis concerns habits of interpretation as much as deception. Colour also preserves an artistic promise that the Square's politics cannot extinguish. He describes the lost period with sensuous pleasure and credits it with the finest poetry. After suppression, however, even its vocabulary is forbidden to most inhabitants. The state controls not only possession but the names through which absence might be remembered or desired. The apparent abolition is selective: the Circles and qualified teachers may name it, its advanced instructional use is reported only from hearsay, and the ruler monopolizes production. “Non-existent” is therefore a social verdict with institutional exceptions. Colour is removed from public life precisely because its power remains understood. **The places.** - §8: “degrees of brightness and obscurity” - §8: “To live was then in itself a delight” - §9: “Colour, which was a second Nature” - §9: “the chromatic taint” - §10: “any word denoting Colour” **In this edition.** Note 90 proposes Plato's suspicion of deceptive colour as a comparison; note 95 clarifies the painted Woman–Priest resemblance. The modern editor's comparison does not require treating all appearances as false. Abbott's story keeps colour's convenience, beauty, vulnerability to imitation, and political restriction in tension. **See also.** [Painting](#entry-painting) (p. 84); [Universal Colour Bill](#entry-universal-colour-bill) (p. 119); [Dodecagon](#entry-dodecagon) (p. 40); [Science and institutions](#entry-science-institution) (p. 101). ## Compensation {#entry-compensation} *Law of Compensation; Compensative Laws of Nature; balance of classes.* **The word.** *Compensation* is a balancing or offsetting of one condition by another. In Flatland's political vocabulary, intellectual improvement supposedly offsets the poor's physical dangerousness. The word later expands into *Compensative Laws of Nature*, whose violation allegedly produces an excessive lower-class population. Its consoling suggestion of equilibrium must be tested against the actions performed in its name. **In the work.** §3 offers a geometrical mechanism. As an Isosceles's sharp vertex widens towards the angle of an Equilateral, his capacity to penetrate another body diminishes. Intelligence and moral improvement are asserted to accompany that widening. Clever potential rebels consequently become less dangerous fighters. The narrator celebrates the arrangement as proof of aristocracy's natural, almost divine fitness. A descriptive relationship within the fiction is converted into a justification of political ownership. But the story immediately supplements nature with intervention. Physicians reshape selected leaders; successful candidates enter privileged classes; others are confined in hospitals; a few are executed. The remainder are killed by paid men or induced to attack one another. If nature by itself guaranteed social equilibrium, such elaborate policy would be unnecessary. *Compensation* makes a managed outcome look spontaneous and turns the administrators of violence into interpreters of a prior law. Pantocyclus reuses this logic during the Colour Bill debate. Artisans are told that democratic equality would end the prospect of advancement and empower the more numerous Criminal Classes. Their desire for eventual privilege is made to outweigh solidarity with people beneath them. Compensation here distributes hope as well as danger: selected mobility prevents a common challenge to the hierarchy. Those who have not yet risen can be recruited to protect the unequal system because it promises that they or their children might rise later. After the massacre, the regime's inspections and killings are called the restoration of the “balance of classes.” This is the decisive exposure of the metaphor. The balance has no ethically neutral weight; the ruling class chooses which population counts as excessive and removes it. The school tribute, itself a lethal exploitation of low Isosceles, reappears as one of the allegedly natural regulating mechanisms. The language of compensation does not undo those deaths or confer fairness on them. It teaches beneficiaries to perceive extermination as adjustment and the survivors to regard a violently manufactured order as nature recovered. **The places.** - §3: “How admirable is this Law of Compensation!” - §3: “Art also comes to the aid of Law and Order” - §10: “the usual Compensative Laws of Nature” - §10: “that excess of the lower orders” - §10: “the balance of classes was again restored” **In this edition.** Modern note 42 relates the phrase to nineteenth-century language of universal balance; note 91 exposes the killing implicit in the educational tribute. Those contexts supplement, rather than replace, the internal evidence: the narrator himself describes the operations, confinement, and organized deaths that supposedly natural compensation requires. **See also.** [Isosceles rebels](#entry-isosceles-rebel) (p. 68); [Cunning and policy](#entry-cunning-policy) (p. 35); [Fertility and extinction](#entry-fertility-extinction) (p. 54); [Suppression and massacre](#entry-suppression-massacre) (p. 110). ## Configuration {#entry-configuration} *Configuration; Regularity; bodily figure; Perimeter.* **The word.** *Configuration* is arrangement or shape. In §12 it becomes the total bodily condition said to determine conduct. The capitalized abstraction draws together visible outline, inherited rank, susceptibility to physical change, and moral judgment. It is more expansive than a simple synonym for geometrical form: it claims that the form supplies a sufficient account of the person. **In the work.** The priestly maxim “Attend to your Configuration” resembles practical advice about care of the body. Its next sentence reveals the ideological scale. Political, ecclesiastical, and moral teaching all aim at its improvement, especially that of the ruling Circles. The body becomes the place where society explains both individual behaviour and its collective future. Questions about justice can be redirected into questions about measurable shape. Pantocyclus's examples deliberately move from grave crime to ordinary honesty. A Square's faithful legal work is attributed to the precision of his right angles. A thievish Isosceles deserves pity for unequal sides rather than blame. The parallel sounds impartial, but the institutions attached to it are not. Bodily correction, prison, and execution remain available, while any theory of education or social encouragement is dismissed as heretical. The range of explanation contracts even as the vocabulary of scientific certainty expands. Configuration also has a strangely unstable material basis. A person can apparently become malformed through a crowd collision, too much or too little exercise, or a temperature change. The doctrine is therefore not simply a theory of fixed inheritance. It combines congenital condition with accidental alteration, leaving room for a bodily explanation of virtually any act. This elasticity helps explain its political usefulness: an event that challenges a person's supposed regularity can be absorbed by postulating a change in the frame. The grandson's argument makes that usefulness comic. If temperature explains disobedience, delicacies may be prescribed as strengthening treatment. The child borrows the authoritative explanatory language and redirects it towards his own interests. His grandfather responds with punishment and a hypothetical physical rationale. The resulting circle of argument exposes a doctrine that can justify contrary practices without being experimentally tested. The Square's concession that he has no grounds for his assumption is a small but significant opening in the otherwise confident system. Configuration should consequently be read at three levels at once: a real geometrical property in Flatland; an authorized causal theory; and a vocabulary through which people negotiate power. Abbott's satire does not depend on denying that bodies matter. It exposes the conversion of bodily measurement into an exhaustive account of worth and an excuse for institutional harm. **The places.** - §12: “Attend to your Configuration” - §12: “Configuration makes the man” - §12: “the exact precision of his right angles” - §12: “a sudden change of temperature” - §12: “the choicest sweetmeats” **In this edition.** Note 110 distinguishes the word's ordinary sense from its doctrinal force and discusses physiological determinism. Note 111 reads the maxim about making the man against “Manners makyth man.” Those explanatory allusions belong to the modern annotation; the explanatory reversals and the domestic counterexample are Abbott's. **See also.** [Circular doctrine](#entry-circular-doctrine) (p. 25); [Conformity and obedience](#entry-conformity-obedience) (p. 32); [Marriage and selection](#entry-marriage-selection) (p. 75); [Science and institutions](#entry-science-institution) (p. 101). ## Conformity and obedience {#entry-conformity-obedience} *Thematic heading.* Attested vocabulary: *disobedience; scolding; castigation; homage; training; honour*. **The word.** *Conformity* here is a critical heading for making behaviour and bodies correspond to an accepted form; it is not presented as a distinctive quoted term from these sections. *Obedience* supplies the practical problem behind §12's example of a disobedient grandson. *Castigation* means chastisement or punishment. The surrounding vocabulary moves between moral discipline and physical treatment. **In the work.** Flatland's ruling theory apparently makes obedience a property of correct shape rather than a choice. If Configuration determines conduct, commands cannot be obeyed or resisted through independent will. Yet family life and government continue to require precisely those responses. The resulting inconsistency is enacted rather than merely announced. The narrator's grandson pleads his Perimeter; the grandfather wants him to behave. The grandfather solves the problem by inventing an unproved bridge between punishment and bodily improvement. Scolding or castigation may have some hidden strengthening effect on Configuration. This conjecture preserves his authority at the cost of his scientific standards. It also shows how an ostensibly material explanation can incorporate conventional moral discipline whenever convenient. The doctrine does not abolish the adult's power to punish; it gives him an additional vocabulary for doing so. The Circles make the same compromise on a larger scale. In courts they praise and blame; at home they speak passionately of right and wrong. Their practice treats human Figures as capable of choosing, although their teaching rejects that idea. Ordinary moral language persists because relationships require distinctions that the official system cannot supply. Its persistence is especially significant beside the regime's segregation of male and female vocabularies. Words dismissed as emotional fiction in one context return with practical urgency in another. The command to honour descendants might seem to reverse this hierarchy. A grandfather must honour his grandson because the latter belongs to the ascending chain of bodily development. But the narrator immediately distinguishes honour from indulgence. Adults retain the right to discipline children in the name of their highest interests. Familial submission points in both directions: the older generation must sacrifice for posterity, while the younger must submit to the regimen intended to improve it. The high mortality of surgical promotion gives that regimen its darkest expression. Political homage operates similarly. Circles are universally honoured as embodiments of superior development, and other classes are asked to subordinate present interests to a promised future. Conformity therefore extends beyond passive acquiescence. It recruits aspiration, self-denial, parental affection, and the language of duty into the maintenance of hierarchy. The book's comic scolding scene reveals the friction between this grand system and a child's ordinary refusal. **The places.** - §12: “his disobedience” - §12: “a good sound scolding or castigation” - §12: “as if they believed” - §12: “a reverent regard for their highest interests” - §12: “subordinate their own interests” **In this edition.** The modern note 114 explains the reversal of the biblical injunction to honour parents. The connection between this reversed command and the disciplinary example is an interpretation of their placement in Abbott's chapter, not an additional law supplied by the editor. **See also.** [Configuration](#entry-configuration) (p. 31); [Circular doctrine](#entry-circular-doctrine) (p. 25); [Language and gender](#entry-language-gender) (p. 71); [Fertility and extinction](#entry-fertility-extinction) (p. 54). ## Cube {#entry-cube} *Cube; six plane sides; eight terminal points; solid angles* **The word.** A Cube is a three-dimensional solid bounded by six equal square faces and meeting in eight corners. Abbott calls those corners terminal points or solid angles. In the romance the Cube is successively a predicted construction, an encountered object, a possible progenitor of a higher figure, an imperfect mental image and an object the authorities require the narrator to demonstrate. **In the work.** Before the name is learned, the grandson anticipates a *Something else* that a moving Square might produce. The Sphere subsequently names it through a comically prolonged compound, whose cumbersome form enacts the difficulty of attaching a familiar noun to an unfamiliar conception. A count of eight terminal points and six sides does not make it imaginable to the Square. The word arrives before the knowledge it is supposed to convey. Actual acquaintance occurs in §19. The Sphere stacks square cards, then supplies the practical instruction that the first lesson lacked. The Square initially sees an irregular plane figure and associates its outline with criminality. His mistake is neither pure stupidity nor a mathematical error: he lacks the learned interpretation of light, shade and perspective required to recognize depth. The reassuringly regular Cube looks socially disreputable when read through Flatland's classificatory habits. Touch is decisive. Feeling verifies that the object is a Solid, after which changing the positions of objects and lights teaches the pupil to recognize it visually. A sense associated in Part I with women and lower-status figures becomes indispensable to the accomplished male geometer. The Cube is therefore an experiment in retraining perception, not simply an emblem whose meaning can be delivered in a sentence. Its construction also excites a genealogical pleasure. The Square imagines himself as the progenitor of a being far more illustrious than himself because his motion could generate it. The analogy both resembles and exceeds Flatland's social inheritance, in which a son gains a side. Here generation adds a dimension. That imaginative pleasure soon prompts the more dangerous question of what a Cube might itself produce. After the return, the Cube becomes the measure of memory's failure. About eleven months later the narrator cannot call it up with his eye closed. Later success never entirely restores his confidence that his mental picture matches the original. At the trial he cannot provide a diagram or description satisfactory to the President. In prison he still names it precisely while doubting his grasp of its shape. The familiar object of the reader's world thus becomes the romance's most painful example of knowledge that cannot be securely kept or transmitted. **The places.** - **§15:** “Something else” — The child predicts an unnamed spatial result - **§19:** “a multitude of Squares parallel to one another” — The Cube is constructed by stacking - **§19:** “as you shall learn by the sense of Feeling” — Touch corrects a misleading appearance - **§22:** “I tried to see a Cube with my eye closed, but failed” — Recollection breaks down - **§22:** “the once-seen, oft-regretted Cube” — An ordinary solid becomes the object of loss **In this edition.** The note to §19 distinguishes the six square faces from the eight solid angles, and explains why a perspective image could look like an Irregular to the visitor. Its account of the diagram complements the narrative without making the Square's recovered mental image more certain than he says it is. **See also.** [Movement and section](#entry-movement-section) (p. 79) · [Touch and bodily proof](#entry-touch-belly) (p. 118) · [Memory and forgetting](#entry-memory-forgetting) (p. 76) · [Fourth Dimension](#entry-fourth-dimension) (p. 57) ## Cunning and policy {#entry-cunning-policy} *cunning; policy; state-craft; picturesque incidents; Concession.* **The word.** *Cunning* is strategic cleverness, here often given a morally suspicious colouring. *Policy* denotes a calculated course of government. *State-craft* stresses skilled political management. These words make intellect active: they describe not simply knowing the world but arranging the conditions under which other people judge and act. **In the work.** The narrator grudgingly recognizes cunning in the Universal Colour Bill. Its author understands that the same red-and-green scheme will align the interests of Women with those of the lower classes and weaken the distinctiveness of the priesthood. Yet the Square refuses to credit an Isosceles with inventing it. Strategic intelligence must originate in a high-born body, even a defective one. His account thus preserves the class theory at the very moment it admits effective opposition to class government. Pantocyclus's counter-policy is more elaborate. He announces concession, invites the opposing leader into the centre of the hall, and conducts a supposedly balanced review. His willingness to accept the majority's decision is repeated while he systematically alters that majority. Different groups hear different threatened losses: public rank, family advancement, marital security. The speech creates its audience by partitioning what had seemed a common movement. The apparent impartiality is inseparable from physical preparation. The opposition leader is surrounded and silenced; reactionary Women have been assembled; guards occupy the exits; a final sentence serves as a preconcerted signal. Rhetoric does not simply persuade where violence later intervenes. It buys time, redistributes allegiance, and positions bodies for the attack. The reader should therefore resist calling the event merely a triumph of eloquence. The speech's last meaning is specified by the concealed plan. The opening maxim about “picturesque incidents” makes the historical story itself uncertain. Statesmen should exploit sensational events, foresee them, and perhaps originate them. Immediately thereafter comes the marriage fraud that reverses women's support. The narrator acknowledges variation in its telling and improbably extensive coincidences. This arrangement permits suspicion that a useful story has been manipulated; it does not prove that the Circles staged the fraud. The distinction matters. Abbott gives us a reason to examine the narrative's political use, not sufficient evidence to identify an undisclosed perpetrator. Across these episodes, policy is the practice of governing through the information people receive and the comparisons they are encouraged to make. Colour, hereditary hope, and household fear become instruments. The narrator admires the artistry while revealing its costs, allowing the reader to recognize manipulation inside the language of prudent administration. **The places.** - §9: “such a model of state-craft” - §10: “sometimes perhaps to originate” - §10: “a policy of Concession” - §10: “a grave appearance of impartiality” - §10: “the preconcerted signal for action” **In this edition.** Modern note 97 explicitly draws attention to the cynical maxim and the uncertainty of the following anecdote. That annotation supports suspicion, not a factual assertion that the marriage episode was fabricated. Note 100 connects concession with contemporary Reform politics, as a historical comparison. **See also.** [Chief Circle](#entry-chief-circle) (p. 20); [Dodecagon](#entry-dodecagon) (p. 40); [Reform and equality](#entry-reform-equality) (p. 95); [Suppression and massacre](#entry-suppression-massacre) (p. 110). ## Dedication and the reader being addressed {#entry-dedication} *Space in General; H. C.; a Humble Native of Flatland* **The word.** A dedication offers a work to someone. Here its apparently private particular, H. C., sits within the extraordinarily broad audience of the inhabitants of Space. The inscription makes every three-dimensional reader both an honoured recipient and a subject of the book's experiment. **In the work.** The dedication does more than announce a theme. It distributes positions. The writer calls himself humble, presents his initiation into three dimensions as an ascent, and addresses the readers' world as celestial. From the readers' position, however, three-dimensional life is ordinary. What looks like heaven from below may be merely another locality whose residents have their own limitations. The syntax makes this relation repeatable. Even as the writer passed from two dimensions to three, readers may aspire to four, five or six. This is an invitation to extend an analogy, not an announcement that all those worlds have been visited. The hoped-for change in the reader is an enlarged imagination and a possible development of modesty. The adjective possible matters: neither reading the book nor inhabiting an additional dimension guarantees the virtue. The final compliment to Superior Races of Solid Humanity can be heard as conventional flattery, racial and social self-congratulation, and a geometrical joke at once. The reader is solid because three-dimensional. Nothing in that fact proves greater kindness or a right to dominate others. When the Sphere later insults the Square and refuses to imagine a dimension beyond its own, the dedication's courteous experiment becomes a test the teacher also fails. The dedicatory voice should not be simplified into a decoded political slogan. It works through irony whose object includes the speaker, the addressee and the posture of paying homage. A humble native can still flatter power; an honoured reader can still learn humility. The dedication establishes a standard against which the events of both parts can be read, while declining to certify that any character consistently meets it. **The places.** - **Dedication.** “Space in General” gives the nominal audience an immense extension - **Dedication.** “a Humble Native of Flatland” locates the offering below its recipients - **Dedication.** “Four Five or even Six” extends the dimensional sequence as a hope - **Dedication.** “possible Development” withholds a guarantee of moral progress - **§ 19.** “There is no such land” shows the Sphere refusing the next application of that sequence **In this edition.** The note identifies H. C. as generally understood to mean Howard Candler, while acknowledging that the book does not name him. The lexicon preserves that qualification. The edition's comparisons with mystery rites and the Prayer Book explain resonances in the dedication; they do not turn its geometrical hopes into a completed theology. **See also.** [Imagination and modesty](#entry-imagination-modesty) (p. 61) · [Initiation and mysteries](#entry-initiation-mysteries) (p. 62) · [Solid humanity and superior races](#entry-solid-superior-races) (p. 105) · [Fourth Dimension](#entry-fourth-dimension) (p. 57) ## Diagrams and the position of the reader {#entry-diagrams} *figs.; diagram; diagrams; tablets* **The word.** A diagram gives a visible arrangement through which relations can be grasped. Flatland's figures are also bodies and social persons, so representing one in a diagram can mean offering an otherwise impossible view of another inhabitant. Tablets, by contrast, name the narrator's constrained means of writing: what the Spacelander would call Lines. **In the work.** The first illustration juxtaposes the triangular Tradesman seen from above with progressively lowered views. It does not depict a Triangle changing into a Line. It trains the reader to separate an object's shape from the appearance available at a particular position. That distinction supports nearly every later demonstration. The house plan in §2 makes a second kind of knowledge visible. A reader looking down can inspect the separate entrances for Men and Women and the north-facing roof at once. An ordinary inhabitant cannot occupy this survey position. The picture is therefore both a convenient explanation and an early grant of the access the Sphere later exercises. The reader possesses a view before confronting the moral question of what such access entitles anyone to do. The recognition figures in §6, developing §5’s account, show how rank is inferred from ends, angles, proximity and fading brightness. They combine geometry with trained social reading. Later figures help distinguish a whole Sphere from the changing circular sections intersecting a plane. The pedagogical lesson is not that images replace argument: without a rule connecting the image to the observer's situation, the diagram can be misread as evidence that the object itself grows and shrinks. In §22 the material basis of diagramming returns as a barrier. The Square cannot provide his Flatland readers with the diagrams he needs, because their tablets and figures are all seen along one line. This gives the title page's promise of illustrations a productive fictional strain. The book in our hands successfully offers a kind of display unavailable to the audience within the story. The memoir does not explain every step by which its manuscript and images reach us; that unexplained passage is part of the romance's address across dimensions. The figures accordingly belong to the argument, not merely to decoration. Their usefulness depends on the very asymmetry that the dedication asks readers to recognize. Seeing a plan is an advantage; recognizing the limited conditions of that advantage is the harder achievement. **The places.** - **§ 1.** “Fig. 1 represents the Tradesman” assigns an observer's position to a diagram - **§ 2.** “in the annexed figure” makes household arrangements simultaneously available - **§ 6.** “Recognition by Sight” depends on interpreting appearance rather than seeing a whole outline - **§ 21.** “mathematical tablets” are glossed by the narrator as Lines - **§ 22.** “no diagrams but Lines” names the communicative obstacle **In this edition.** The supplied edition states that it includes ten modern redrawings of Abbott's original figures. This lexicon discusses their functions and supplies section locators rather than reproducing a second set that could blur source and commentary. The initial perspective figure, house plan, recognition diagrams and dimensional demonstrations can be consulted in the supplied PDF or EPUB. **See also.** [Recognition by sight](#entry-recognition-sight) (p. 94) · [Movement and section](#entry-movement-section) (p. 79) · [Interior and exterior](#entry-interior-exterior) (p. 64) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) ## Dimension {#entry-dimension} *Dimension; Dimensions; Dimensionality* **The word.** A dimension is an independent extent or direction in which something may be measured. Abbott repeatedly distinguishes an additional dimension from an additional name for an already familiar extent. The Square has several words for the two dimensions he knows; the Sphere is trying to disclose a third direction, not increase their vocabulary by a synonym. **In the work.** Dimensionality controls what each world's inhabitants can move through, perceive and express. Lineland's King takes length for the entirety of Space. The Square takes his plane for true Space. The Sphere initially treats the three-dimensional world as the final conceivable enlargement. Each locally adequate description becomes false when converted into a declaration about the whole of possible existence. The debate in §16 brings a real conceptual difficulty into the comedy. The Square observes that a dimension implies direction and measurement, and offers to accept the Sphere's assertion if he can measure the alleged height or indicate its direction. The request is not answered by adding *length* to *height and breadth*, because Flatland already distributes these names among two extents. Nor does calling brightness height establish a measurable third axis. The visitor admits that he cannot supply the demanded indication on the pupil's present terms. The revised text adds a further complication: Flatlanders possess an infinitesimal height although they cannot apprehend it as a dimension. Their visible existence requires more than a purely abstract mathematical plane. This physical qualification does not give them free three-dimensional movement, and it should not erase the story's governing restriction. The narrative is investigating an inhabited model, with bodies and sight, rather than supplying a perfectly self-contained set of axioms. Once transported, the Square learns enough to extend the question. A fourth dimension would stand to Spaceland as Spaceland stands to Flatland. The analogy challenges the Sphere's claim that the concept is inconceivable, but no fourth-dimensional realm becomes an object of waking observation. Higher dimensionality remains a possibility reasoned about and, in the later dream, illustrated. The distinction between conceivable, mathematically describable and physically verified remains crucial. The word also acquires ethical and political force without ceasing to be spatial. *Limited Dimensionality* becomes what the imprisoned narrator wants a future race of rebels to refuse. That phrase concerns a restriction upon thought enforced by inherited assumptions and by law. Yet an additional dimension is not itself additional goodness. The Sphere's moral correction of omnividence prevents the book's ladder of spatial powers from becoming a simple ladder of spiritual worth. **The places.** - **§16:** “Two Dimensions by four names” — Verbal plurality does not create spatial independence - **§16:** “Dimension implies direction and measurement” — The Square states a test - **§19:** “a Fourth unrecognized Dimension” — The revised argument extrapolates the earlier difficulty - **§20:** “the Abyss of No Dimensions” — The lower limit is embodied in Pointland - **§22:** “limited Dimensionality” — A geometrical restriction becomes an intellectual challenge **In this edition.** The notes identify additions to §§16 and 19 made for the revised edition of 1884. These respond to objections about visibility and dimensional thickness. They are Abbott's revisions; the modern annotations explaining them should remain distinct from the narrated argument. **See also.** [Space and Spaceland](#entry-space-spaceland) (p. 106) · [Upward and Northward](#entry-direction-upward) (p. 122) · [Fourth Dimension](#entry-fourth-dimension) (p. 57) · [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) ## Dodecagon {#entry-dodecagon} *Dodecagon; Dodecagons.* **The word.** A *dodecagon* is a plane polygon with twelve sides. In Flatland the form is also a degree of nobility. It must not be confused with a *dodecahedron*, a three-dimensional solid with twelve faces. The distinction is unusually important here because the revised edition corrected the wrong solid-name in two passages. **In the work.** The Dodecagons first appear among those reached by the spreading fashion for paint. Their adoption marks the invention's ascent through the social scale: conservative Pentagons hesitate, Dodecagons follow, and finally almost all the nobility participate. The name provides a precise rung in a hierarchy otherwise described through broad classes. Fashion can cross those rungs faster than hereditary development can. In §10 the Dodecagon becomes an identity that can be counterfeited. A low Isosceles paints himself with twelve colours and imitates the voice of a higher-class man. The scheme substitutes a counted visual sign for a counted bodily fact. Because people have grown accustomed to reading colour, the impostor can exploit their trust in the sign while leaving his underlying geometry unchanged. The episode reveals a general vulnerability in any social system whose rank is recognized through an external code. The narration must nevertheless be read with caution. It describes the victim as an orphan daughter of a noble Polygon, gives the deception many fortunate accidents, and reproaches her relatives for failing to take precautions. The young woman's suicide becomes the emotional pivot in a campaign against the Colour Bill. She is scarcely permitted an independent voice; her suffering is turned into an argument about the security of all marriages. The ruler's subsequent appeal enlarges one catastrophe into the prospect of universal domestic ruin. Abbott places the story immediately after a recommendation that statesmen sometimes originate sensational incidents. That placement undermines the innocence of its political circulation without establishing its factual falsity. A lexicon should preserve both levels: within the reported event the Dodecagon is a false identity, and within the larger history the event's evidentiary status is qualified by uncertainty and political usefulness. The word's later appearance in §12 is quieter. A Dodecagon, like a Hexagon, is less rigorous about a wife's remote pedigree than an aspiring lower-class man. The real twelve-sided noble can take liberties with inherited status that the impostor seeks through paint. Together the passages show rank operating as visible form, fashionable sign, matrimonial advantage, and narratively manufactured fear. **The places.** - §8: “even the Dodecagons infected” - §10: “the twelve colours of a Dodecagon” - §10: “for the story varies” - §10: “a string of lucky accidents” - §12: “a Hexagon or Dodecagon” **In this edition.** The Note on the Text states that Abbott's revised second edition corrected *Dodecahedron* to *Dodecagon* in §§10 and 12. Modern note 98 explains the colour-count imposture. The correction belongs to Abbott's revision; the explanation belongs to the present editor. **See also.** [Colour](#entry-colour) (p. 28); [Cunning and policy](#entry-cunning-policy) (p. 35); [Marriage and selection](#entry-marriage-selection) (p. 75); [Universal Colour Bill](#entry-universal-colour-bill) (p. 119). ## Doors and houses {#entry-doors-houses} *door; roof; floor; apartments; pentagonal* **The word.** A Flatland house encloses an area in the plane. Its northern sides are the roof and its southern side the floor; these names describe orientation and function rather than vertical height. A door is an opening in that enclosing boundary, but access through it carries social qualifications. **In the work.** The house is one of Abbott's most efficient devices for teaching a changed spatial situation. Rain arrives from the North, so a pentagonal enclosure can possess a roof without possessing an upper storey. Windows are unnecessary because illumination is everywhere alike. These explanations ask the reader to separate a familiar word from the three-dimensional picture habitually attached to it. Naming can survive the alteration of the world, provided function is understood. Geometry also provides a credible public-safety argument. Sharper corners on dimly luminous buildings threaten passers-by, and regulations replace triangular or square houses with blunter pentagons. The retained exceptions are revealing: dangerous corners remain permissible around state buildings which the public is not meant to approach casually. A material feature becomes an instrument of deterrence. Regulation does not simply abolish danger; it decides whose purposes danger may serve. The two entrances translate gender hierarchy into routine movement. The small eastern door is reserved for Women, the larger western entrance for Men. In §4 the arrangement becomes an explicit law requiring a respectful manner. Abbott's authorial footnote then places the fictional separation beside an English clergyman's insistence that villagers and a teacher use an inferior entrance. The house is not only a diagram. It is a daily lesson in who must acknowledge whom. Women's apartments take the logic further. They are designed to prevent a woman from turning, allowing her husband to speak and act without fear of her point. Domestic architecture thus secures one person's freedom by restricting another's bodily capacity. The narrator presents this as practical wisdom, and his candour makes the violence harder to evade than a melodramatic denunciation would. Finally, the refusal to alter doors for Irregulars becomes an argument against their existence. A supposed impossibility of accommodation is assembled from choices already built into the environment. The obstructed doorway makes difference visible as inconvenience, while the narrator refuses to ask whether the structure, rather than the visitor, might change. Across these scenes, architecture gives the social order a durable external body. **The places.** - “on the East is a small door for the Women” (§2) - “Square and triangular houses are not allowed” (§2) - “a becoming and respectful manner” (§4) - “apartments—which are constructed with a view to denying them that power” (§4) - “Are the houses and doors and churches in Flatland to be altered” (§7) **In this edition.** Note 31 explains the diagram's RO–OF lettering and orientation. Abbott's own note 47 supplies the *Spectator* comparison; Diotimos note 46 clarifies that its English precedent concerns a parsonage entrance. These layers should not be merged into an assertion that the historical incident involved a church door. **See also.** [Attraction and climate](#entry-attraction-climate) (p. 18); [Women](#entry-women) (p. 128); [Irregularity](#entry-irregularity) (p. 65); [Regularity](#entry-regularity) (p. 97). ## Dream and vision {#entry-dream-vision} *dream; Vision; phantasmal vision; nightly visions* **The word.** A dream is an experience during sleep; *vision* can name such an experience, a revelatory sight or a powerful mental image. Abbott exploits that range but also supplies explicit narrative boundaries. Lineland is encountered in a dream, Pointland in another dream, while the intervening visit from the Sphere and journey into Spaceland are initially presented as waking facts. **In the work.** The first dream follows late-night geometry and an unresolved problem. Its world is elaborately social: the King explains marriage, perception and law before the disagreement turns violent. The breakfast-bell ends the apparent attack and restores ordinary Flatland. The dream thus performs anticipatory work. It puts the Square in the position of a superior-dimensional teacher before he has to occupy that of an uncomprehending pupil. At the beginning of §15 the narrator expressly moves from dreams to facts. During the Sphere's first disappearance he checks that he is awake and insists that the event is no dream. Later, his movement through Spaceland is described *as if* in a dream, a comparison of feeling that does not undo the earlier distinction. Extraordinary experience can resemble dreaming without the narrator classifying it as a dream at that point in his account. The second dream follows the expulsion from Spaceland. It supplies an encounter with Pointland and a reconciled Sphere who acknowledges his previous anger as an error. The location of this repentance matters. The waking Sphere has silenced and cast out his pupil; only the dreamed instructor subsequently admits that higher dimensions should be pursued. The dream may educate and encourage the Square, but it cannot serve as independent evidence that the actual Sphere has changed his mind or that Extra-Solids have been witnessed outside sleep. Dream also becomes a comparison for the loss of experience. The traveller feels his knowledge slipping away like a half-grasped dream, and prison fills his nights with the baffling precept about upward movement. At the close, episodes of doubt make Spaceland seem almost as visionary as the worlds of one or no dimensions. The uncertainty even reaches the prison wall and the tablets on which he writes. That final extension prevents a simple retrospective solution in which everything unusual is declared a dream while Flatland remains securely real. The narrator reports periods of weakness, not a final discovery invalidating his journey. His account moves between confident testimony and radical doubt. The reader should preserve the oscillation rather than settle it by treating every use of *vision* as a technical statement that an event never occurred. **The places.** - **§13:** “In the night I had a dream” — Lineland's narrative status is explicit - **§15:** “From dreams I proceed to facts” — A deliberate boundary introduces the visitation - **§16:** “But it was no dream” — The narrator checks and reasserts waking experience - **§20:** “During my slumber I had a dream” — Pointland and the reconciled teacher occur during sleep - **§22:** “there are seasons of mental weakness” — The final doubt is recurrent, not a settled revelation **In this edition.** Its chapter outline and notes distinguish the two dreams from the central journey. Comparative discussions of prophetic visions or philosophical dreams illuminate the pattern but do not authorize changing the narrative status Abbott assigns to individual scenes. **See also.** [Lineland](#entry-lineland) (p. 74) · [Pointland](#entry-pointland) (p. 87) · [Memory and forgetting](#entry-memory-forgetting) (p. 76) · [Sphere](#entry-sphere) (p. 107) ## The Editor and the revised Preface {#entry-editor-preface} *By the Editor; interpreter and summarizer; misconceptions* **The word.** The Editor is the fictional Spacelander who speaks for an imprisoned and ageing Square in the Preface. This voice is distinct from the modern editor of the supplied Diotimos edition. Misconceptions are the two objections the Preface addresses: an intellectual objection concerning thickness and a moral objection concerning the treatment of women. **In the work.** A preface normally stands outside a story to explain its making. Here it continues the story by reporting imprisonment, decline and conversations with the protagonist. Its position before the memoir gives later suffering an anticipatory presence. A reader knows from the outset that revelation will not simply produce triumph or acceptance. The two defences are deliberately unequal. The Editor calls the Square's dimensional answer impregnable, but cannot give the same assurance about his moral defence. The latter is mediated through interpretation and summary because the Square is said to lack Spaceland's moral terminology. The phrase admits a problem larger than mistranslating a single word: the speaker's inherited concepts do not reliably express the values to which the defence appeals. The account of changed opinions is consequential but qualified. The Square now inclines to a more favourable view of Women and the Isosceles; his historical descriptions have identified him, perhaps too closely, with customary historiography. The qualification preserves the evidence of bias in Part I rather than cancelling it. The Preface makes a distinction between reporting a society and endorsing it, while allowing that the narrator has not maintained that distinction securely. The final refusal of a one-to-one correspondence between Flatland and Spaceland is also a rule for interpretation. The Circles can satirize aristocratic and clerical authority without every minor custom corresponding to a particular English institution. The hoped-for reader rejects both absolute impossibility and exhaustive certainty about what lies beyond experience. The Preface therefore corrects readers who would either dismiss the dimensional fiction as incoherent or reduce it to a fully decoded system. **The places.** - **Preface.** “By the Editor” installs an additional fictional speaker - **Preface.** “one of an intellectual, the other of a moral nature” organizes two different defences - **Preface.** “interpreter and summarizer” marks the second defence as mediated - **Preface.** “perhaps too closely” qualifies the Square's identification with established historians - **Preface.** “every minute detail” occurs in the warning against compulsory exact correspondence **In this edition.** The Preface belongs to the revised second edition of 1884 and is absent from the first. Its references to pages 70, 81 and 88 are original-edition references, explained by the modern notes as passages in §§16, 18 and 19. They are not page references to this lexicon or to the supplied modern PDF. **See also.** [A Square and the voice of the memoir](#entry-a-square) (p. 11) · [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113) · [Women](#entry-women) (p. 128) · [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99) ## Education and schools {#entry-education-schools} *Elementary School; Infant Schools; Seminaries; University; Leaving Examination* **The word.** Flatland's educational vocabulary runs from elementary instruction through exclusive seminaries to the University of Wentbridge. *Education* means training perceptual powers as well as transmitting propositions. *Examination* tests competence, but also governs admission to occupations, marriage prospects and continued social belonging. **In the work.** The schools teach children how to recognise class before the adult world requires them to move safely within it. This is practical geometry: the differences between angles must become available to touch or sight. Yet the distribution of methods is itself a class system. Poor children learn Feeling early; wealthy children spend years acquiring the more demanding skill of sight recognition, which the society values more highly. What later appears natural refinement has required protected time and substantial resources. The most disturbing lesson is also the most elementary. Living Isosceles, chained and deprived of rights, constitute an “Alphabet of angles.” Their bodies are made into the material through which middle-class children acquire intelligence. The school does not merely reproduce an existing prejudice; it trains perception through an encounter in which a subordinated person counts as an object. The teaching of recognition is founded on a failure to recognise humanity. The discussion of feeding these specimens adopts the language of economy. A system which replaces them monthly is praised for accuracy and incidental population reduction. Abbott gives the narrator neither a change of voice nor an explicit admission that the topic has become atrocious. The institutional calm is part of the argument: orderly explanation can make exploitation sound like a technical choice between budgets. University training presents a different danger. A graduate's transformation is described as a new birth, while a noble failure becomes a person with no viable position above or below. The proposed answer is lifelong imprisonment or painless death. The contrast exposes a system that invests enormously in selected pupils but cannot tolerate outcomes that fail its categories. Education and hereditary rank reinforce each other until a failed credential becomes grounds for eliminating the candidate. One analogy needs particular care. The narrator compares the suppression of Feeling with discouraging deaf children from signing in order to impose speech and lip-reading. The analogy records a coercive educational judgement; it is not evidence that signed language prevents intellectual or linguistic development. It belongs to the same question raised by the schools generally: who decides which human capacities count as education, and what is lost when one method becomes compulsory? **The places.** - “an ascending scale or Alphabet of angles” (§5) - “Fettered immovably” (§5) - “expense is the truest economy” (§5) - “higher Seminaries of an exclusive character” (§6) - “a new birth” (§6) - “extinguished by a painless death” (§6) **In this edition.** Notes 61–63 explain object teaching and school-board politics; notes 69–74 distinguish Wentbridge's Cambridge features, the oralist controversy and the examination's continental terminology. These annotations contextualise the satire and, at note 70, expressly distinguish modern recognition of sign languages from the narrator's assumptions. **See also.** [Feeling and touch](#entry-feeling-touch) (p. 53); [Recognition by sight](#entry-recognition-sight) (p. 94); [Surgery and extermination](#entry-surgery-extermination) (p. 112); [Language and gender](#entry-language-gender) (p. 71). ## Equilateral {#entry-equilateral} *Equilateral; Equal-sided; True Equilateral Triangle; certifiable* **The word.** An equilateral triangle has three equal sides and three angles of sixty degrees. In Flatland, *Equilateral* also names the respectable middle class: the tradesman or merchant, and the threshold at which a male lineage leaves Isosceles serfdom. Geometrical equality produces a particular rank, not social equality among all persons. **In the work.** The Equilateral first appears in the optical demonstration of §1. A respectable tradesman becomes an object imagined from above and then from the plane. The reader learns something his fellow citizens cannot directly see: his whole shape. But the narrator immediately attaches an occupation and a moral-social adjective to that shape. Even the apparently neutral lesson introduces the way anatomy arrives already interpreted. In §3 this figure becomes the object of prolonged hereditary effort. Families below the threshold may spend generations approaching the required angle. When the condition is attained, the infant undergoes inspection and a public admission ceremony. That passage separates geometrical fact from socially accepted fact. An equal-sided body must be certified before it can function as an Equilateral in marriage and inheritance. Abbott's own note makes the distinction especially clear. The possible birth of a Square son cannot replace certification of the father: no lady of standing will marry the uncertified Triangle, and later generations may expose a concealed irregularity. The social institution refuses to rest its trust on a single apparent outcome. It demands a sanctioned history of the body as well as the body itself. The boundary also divides families. Promotion requires adoption by a childless Equilateral and an oath preventing renewed contact with the child's Isosceles relations. Equality of sides is supposed to mark a stable new condition, yet the fear of imitative relapse demands a permanent social separation. The geometric precision of the threshold coexists with anxiety about its security. The Square's father belongs to this class, while his grandfather came from below it. The Equilateral is therefore the hinge in his own genealogy, not simply one of the lower orders he describes. His family's recent passage across the boundary makes the narrator's complacency more revealing: the vocabulary of respectable humanity can be acquired rapidly, and then directed against those from whom one's own standing has just emerged. Finally, the Equilateral has a genuine function in the optics of §6. Its sides retreat more steeply from a frontal vertex than a Pentagon's, producing a quicker fall in brightness. This demonstrable difference explains identification. It cannot by itself establish respectability, merit or the right to exclude. **The places.** - “a Tradesman of the respectable class” (§1) - “a genuine and certifiable Equal-sided Triangle” (§3) - “The birth of a True Equilateral Triangle” (§3) - “the full 60° attained” (§5) - “my Father, the Triangle” (§6) **In this edition.** Authorial note 40 belongs to Abbott's fiction and explicitly argues for certification. Editorial notes 41 and 58 address, respectively, the retained 1884 reading “Isosceles” in the promotion passage and the narrator's family history. Keeping these sources distinct prevents a modern clarification from being quoted as the narrator's explanation. **See also.** [Birth and ascent](#entry-birth-ascent) (p. 19); [Isosceles](#entry-isosceles) (p. 67); [Class and caste](#entry-class-caste) (p. 27); [Regularity](#entry-regularity) (p. 97). ## Evidence and demonstration {#entry-evidence-demonstration} *proof positive; ocular demonstration; phenomena; Demonstration* **The word.** Evidence is what may support a claim; demonstration is a showing or reasoned proof intended to establish it. The romance repeatedly separates the occurrence of a phenomenon from assent to its explanation. Its speakers use the language of proof confidently, but the narration shows that what one person considers decisive may remain unintelligible, explainable otherwise or politically inadmissible to another. **In the work.** The Square's report of the King's neighbours fails in Lineland because the information is obtainable by hearing. Disappearance proves only disappearance to someone unable to conceive movement beyond his world. The King calls it magic. When the Sphere later inventories the Square's household, the Square likewise notes that a well-connected visitor could have acquired this knowledge by ordinary means. In each case the higher-dimensional teacher mistakes a correct statement about concealed particulars for an unavoidable proof of the means by which he knows them. The changing circular section appears a stronger experiment. Yet the Square perceives expansion and contraction without understanding their cause. The Sphere has not altered his actual size; the plane intersects different parts of him as he moves. The fact seen and the explanation inferred remain separate. The narrator's comment that the causes were dark even with the facts before him states one of the book's central epistemic difficulties. Taking a tablet from a locked cupboard excludes some familiar explanations, and touching the Square's interior provides bodily evidence of access beyond his outline. Both acts nevertheless increase terror rather than understanding. The Sphere declares that his explanation alone fits the phenomena, while the pupil imagines a magician. Coercive transportation finally supplies a new standpoint, but even there learning takes time: light, shade, perspective and touch must be coordinated before a Cube becomes recognizable. After his return, the Square tries to replace testimony about revelation with demonstration, partly to evade a law directed against alleged visitors from another world. His hope is both intellectual and tactical. An argument that anyone can follow seems safer than an exceptional personal story. The failure with his grandson and the limitations of Flatland diagrams show why the substitution is not straightforward. The trial sharpens the ambiguity. The President demands direction or depiction and rules out mere enumeration. Those demands resemble the Square's own earlier requests, but now operate inside a regime already committed to suppression. Neither the legitimacy of asking for evidence nor the truth of the narrator's experience exonerates the Council's procedure. The novel asks the reader to distinguish the difficulty of persuasion from the institutional decision to punish inquiry. **The places.** - **§14:** “facts known to any child in my capital” — Accurate information does not establish an extraordinary source - **§16:** “although I saw the facts before me, the causes were as dark as ever” — Observation and understanding divide - **§17:** “my explanation, and no other, suits the phenomena” — The Sphere claims exclusivity - **§21:** “proceeding on the path of Demonstration” — The narrator seeks a transferable argument - **§22:** “without his hearing from me a repetition” — Seven years of testimony still fail with his brother **In this edition.** The notes explain geometrical causes without erasing the pupils' experience of uncertainty. References to empirical tests and revelation are interpretive descriptions of Abbott's dialogue, not claims that the book provides a formal proof of all the worlds it imagines. **See also.** [Analogy](#entry-analogy) (p. 12) · [Touch and bodily proof](#entry-touch-belly) (p. 118) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) · [Prison and silence](#entry-prison-silence) (p. 90) ## Eye and the visible line {#entry-eye-retina} *eye; sight; visual organ; brightness* **The word.** The *eye* provides a situated field of vision, not an unrestricted view of a geometrical object. For a Flatlander the visible field presents lines; their brightness and changing extent supply evidence from which a shape may be inferred. **In the work.** The first demonstration requires the reader to move an eye. Looking down at a penny permits a circular appearance; bringing the eye exactly to table level produces a line. Nothing has happened to the object, but its appearance has changed with the observer's position. The lesson trains readers to distinguish a limitation of access from a deficiency in the thing observed. The coin is not becoming a line in itself. Flatland's inhabitants cannot repeat the movement which gives the Spaceland reader this advantage. Their perceptual restriction is therefore a condition of existence rather than an error a little greater attentiveness can cure. The narrator's later expertise in interpreting brightness works within that condition. It does not amount to seeing from above. This difference between inference and direct disclosure remains essential to the romance's experiments with other dimensions. The body also makes looking a social act. A Woman's eye and mouth occupy the same end; presented frontally, she becomes a bright point, while the less luminous rear can be almost invisible. Domestic custom requires women of rank to keep the bright, speaking end towards husbands and their male friends. The same orientation that secures men's safety also subjects them to continuous speech and observation, provoking the narrator's complaint. The attempt to control one danger creates a different intimacy he cannot wholly master. The position of the eye can likewise explain a lower-class triangle's inability to monitor its own dangerous vertex. Here the narrative turns a bodily limitation into evidence of coarseness, although it has already required readers to understand their own seeing as position-dependent. The implicit comparison is pointed: a sympathetic account of perception for “us” becomes a judgement of nature when applied to “them.” The Preface complicates visibility further by discussing unrecognised thickness and the tendency to name it brightness. It does not supply a complete anatomy of the organ. The important issue is conceptual: evidence can be present without an observer possessing the category needed to interpret it. The eye supplies evidence; an interpretation makes that evidence a world. **The places.** - “gradually lower your eye” (§1) - “nothing but a straight line” (§1) - “these two organs are identical” (§4) - “the eye is situated so far from their vertex” (§5) - “by the visual organ” (§6) **In this edition.** Notes 22, 25 and 67 explain the plane, the coin experiment and the geometry of sight recognition. The Preface's thickness argument is Abbott's second-edition material; the Diotimos discussion at notes 9–12 is modern apparatus. The distinction between perceptual evidence and dimensional interpretation belongs to the fiction’s argument. **See also.** [Straight line](#entry-line-straight) (p. 109); [Recognition by sight](#entry-recognition-sight) (p. 94); [Women](#entry-women) (p. 128); [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113). ## Faith reason and the reach of experience {#entry-faith-reason} *faith; reason; apprehend; comprehend; beyond experience* **The word.** In the Preface, comprehend denotes a grasp the Square can no longer achieve, while apprehend names his remaining hold upon what he experienced. Faith describes that precarious hold. The terms are not arranged into a general command to abandon reasoning: the memoir repeatedly argues, calculates, tests and compares. **In the work.** The Square's claim to have experienced Spaceland creates a difficult relation between present ability and past knowledge. He once understood height, yet cannot now display its direction or measure it. A present demand for demonstration is reasonable in one sense and unavailable in another. The Preface exposes the limitation of treating what an observer can currently measure as the whole of what could be real. It does not follow that any unsupported assertion becomes true. The analogy works on a reader who already understands three dimensions and can assess the Square's difficulty from a broader position. When it is extended toward a fourth dimension, the evidential situation changes: that further world is proposed by analogy rather than witnessed in the narrative. The book preserves the difference between an experienced disclosure, a geometrical construction and an extrapolated possibility. The Square himself hopes to escape the risks of revelation by using demonstration in §21. His plan is defeated both by political fear and by the difficulty of indicating a direction outside his plane. These are different obstacles. The Grandson's response cannot be explained solely by poor mathematics, and the narrator's failed gestures cannot be explained solely by persecution. A lexicon must allow institutional coercion and genuine conceptual difficulty to coexist. At the end, faith is neither serenely unshakable nor simply exposed as delusion. Memory falters, images fade, and doubt spreads even to the familiar plane and prison wall. The book gives the witness a truthful account of uncertainty instead of making confidence the only measure of fidelity. Its strongest epistemic discipline lies in the Preface's double refusal: neither rule out the unfamiliar in advance nor claim to know exactly what it must be. **The places.** - **Preface.** “I can but apprehend it by faith” names the narrator's reduced present grasp - **Preface.** “by any process of reason” occurs in a statement of what he cannot now recover - **Preface.** “lies beyond experience” sets the scope of the closing caution - **§ 21.** “the path of Demonstration” is the Square's proposed alternative to reporting revelation - **§ 22.** “I cannot honestly say I am confident” makes doubt part of the testimony **In this edition.** The modern notes compare faith with Hebrews 11:1 and report Abbott's later explanation that the Preface's phrase beyond experience concerns the ultimate cause of things. That report is useful contextual evidence supplied by the edition; the lexicon does not treat it as a reason to collapse every geometrical episode into a theological proposition. **See also.** [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) · [Analogy](#entry-analogy) (p. 12) · [Memory and forgetting](#entry-memory-forgetting) (p. 76) · [Providence and the language of necessity](#entry-providence) (p. 93) ## Feeling and touch {#entry-feeling-touch} *Feeling; Feeler; Felt; introduction; tact* **The word.** Capitalised *Feeling* is the practical inspection of another person's angles by touch. It principally establishes class rather than individual identity. The word retains its ordinary associations with sensation, sympathy and sensitivity, allowing the society's highly trained tactile competence to expose its failures of moral feeling. **In the work.** An introduction in §5 becomes a literal mutual examination. The old formula requires a person both to feel and to be felt; the abbreviated urban form assumes reciprocity without saying it. The fashionable construction then makes *feel* mean arranging the whole encounter. This miniature linguistic history is more than a joke about slang. It shows a social procedure becoming so habitual that its terms can be compressed, while the narrator remains more alert to damaged grammar than to the procedure's class assumptions. Feeling answers a genuine epistemic problem. A line-shaped appearance cannot simply disclose how many sides a person possesses, whereas one angle, if regularity can be assumed, provides sufficient evidence. Touch is consequently a rational technique in the fictional world. It is not refuted by the prestige of sight recognition. The higher method is safer at a distance and allows subtler distinctions, but it also costs time and money, and its possessors forbid inferiors to verify their rank by contact. The technique's danger makes hierarchy painfully physical. The Felt must remain motionless, and an involuntary movement can kill the Feeler. The Square's ancestor is punished after a rheumatic start transfixes a Polygon. The account allows distress for the family while treating the nobleman's greater public value as obvious. The intimate contact does not produce equal vulnerability in the social consequences that follow it. The classroom passage takes the contradiction to its limit. Children practise Feeling on immobilised living specimens whose nourishment is discussed as a cost. A word associated with responsiveness now names an activity made possible by refusing the touched body's claims. The young acquire “tact and intelligence” through an arrangement from which compassion has been excluded. Abbott does not need to insert the abstract charge of insensitivity; the double meaning is working throughout the description. The prohibition of Feeling among the educated thus has two readings. It develops a difficult faculty by withholding an easier one, but it also converts refusal of contact into an emblem of superiority. Those who can avoid the bodies of others appear cultivated. Those who must touch are classified as lower, even when their method is more reliable than hearing and capable of remarkable precision. **The places.** - “feel and be felt” (§5) - “the principal test of recognition” (§5) - “the brainless vertex of an acute-angled Isosceles” (§5) - “one little accident in the process of Feeling” (§5) - “that tact and intelligence” (§5) - “discouraged or absolutely forbidden” (§6) **In this edition.** Notes 54–55 discuss introduction etiquette and Abbott's interest in English usage; notes 59–61 address measurement and classroom specimens. The spelling and capitalisation in the narrative distinguish a named method without cancelling the ordinary moral resonances of *feeling*. **See also.** [Angle](#entry-angle) (p. 14); [Education and schools](#entry-education-schools) (p. 46); [Recognition by sight](#entry-recognition-sight) (p. 94); [Voice and hearing](#entry-voice-hearing) (p. 123). ## Fertility and extinction {#entry-fertility-extinction} *fertile; propagation; barren; infecundity; posterity.* **The word.** *Fertile* means capable of producing offspring; *infecundity* and *barrenness* name the failure or absence of such reproduction. *Posterity* means descendants considered collectively and prospectively. In these sections reproduction is a political resource: the state's future depends on the continuation of bodies assigned different ranks. **In the work.** §11 describes two antagonistic laws of Circular propagation. As rank increases, additional sides can appear at an accelerated rate, but fertility declines. A son may surpass his father by many sides; a son may also fail to appear at all. Progress thus accelerates towards a limit that threatens its own continuation. The highest class cannot simply extend the lower classes' rule of one added side per generation indefinitely. The asymmetry of social valuation is sharp. The numerous children of low Isosceles are repeatedly treated as a dangerous excess, while the rarity of Circular sons is a constitutional concern. Population is never merely counted. Its meaning depends on whose children exist. The same regime can call one group's survival a burden and another's reproductive failure a public emergency. Medical ambition compounds the problem. Young high Polygons are fractured and reset in the hope of acquiring many additional sides. Fewer than one in ten survive, according to the narrator's “scarcely” formulation. The occasional triumph returns a child ceremonially promoted to Circular status and encourages other parents to repeat the experiment. The scene resembles a lottery of advancement whose winning procession obscures the cemetery's accumulation. It is not evidence that the procedure is generally effective; the text insists on its lethal failure rate. §12 shifts from surgery to marriage. The Square alleges that prestigious men choose women for lustre or voice despite supposed defects in ancestry, then attributes barrenness or regression to such matches. These causal judgments belong to the narrator's inherited theory of bodies. They should not be repeated as a medical truth. His social observation is more securely available: the higher the male's rank, the less scrupulously he follows the pedigree rules promoted as essential for everyone. The threatened end is constitutional rather than merely familial. If the class can no longer produce a Chief Circle, the whole political order may fall. A system claiming nature as its guarantee proves dependent on precarious reproduction, risky manufacture, and inconsistent marital behaviour. Extinction is the possibility contained inside its own ideal of superior development. The institution's anxiety reveals how narrow its definition of improvement has become: it can increase sides while destroying the children and families meant to carry that increase forward. **The places.** - §11: “two antagonistic decrees” - §11: “the race shall become less fertile” - §11: “Scarcely one out of ten survives” - §12: “acquiesce in infecundity” - §12: “the Constitution of Flatland must fall” **In this edition.** Note 116 glosses *infecundity* and connects the passage to Galton's discussion of aristocratic inheritance. Note 109 describes the surgical institution's mock-learned name. These comparisons do not validate the Square's claims about women, heredity, or ideal human breeding. **See also.** [Circles and Priests](#entry-circle-priest) (p. 24); [Compensation](#entry-compensation) (p. 29); [Marriage and selection](#entry-marriage-selection) (p. 75); [Configuration](#entry-configuration) (p. 31). ## Fog {#entry-fog} *Fog; dimness; clearness; beneficent Element* **The word.** *Fog* is the medium that makes differences of distance visible through differences of brightness. It does not reveal a second visible dimension; it enables the interpretation of a line. The capital letter and ceremonial praise elevate a meteorological condition into a supposed patron of civilisation. **In the work.** The explanation reverses an expectation Abbott can assume of many Spaceland readers. Fog ordinarily obscures an object, yet in Flatland a perfectly clear atmosphere would erase the brightness differences needed to distinguish its receding sides. The medium supplies information precisely because it reduces visibility unequally. The point is not that obscurity is inherently wise, but that knowledge depends on contrasts rather than undifferentiated clarity. The measured example, comparing an object three feet away with one two feet eleven inches away, gives this principle an ordinary scale. From small gradations an experienced observer infers a configuration. The subtle information is available to a trained eye, not to sight in the abstract. Hence the phrase “Nurse of arts” is both comic extravagance and a compressed account of the conditions under which an art can develop. The demonstration with Merchant and Physician makes the contrast useful to rank. The Triangle's sides recede sharply from the nearest vertex and lose brightness rapidly; the Pentagon's decline is gentler. Fog permits the observer to recover depth within the plane from a one-dimensional appearance. That inference remains dependent on orientation and regularity. A side presented frontally can mislead, and a moving crowd requires experience well beyond the elementary diagram. The resource is also unevenly distributed. Fog prevails outside the torrid zones, and mastery of its evidence requires education inaccessible to many. What the narrator praises as refinement therefore has environmental and economic supports. His social hierarchy turns a cultivated response to local conditions into evidence for the superiority of the people best placed to cultivate it. Fog accordingly offers a restrained model for reading the book. A reader needs to notice differences inside apparently uniform assertions, especially where exposition grows most confident. The analogy should not be overextended into a claim that all moral truth is deliberately veiled. Its value is more exact: something that impedes immediate visibility may furnish the very distinctions through which a careful interpreter learns to see. **The places.** - “the result of Fog” (§6) - “Nurse of arts” (§6) - “Parent of sciences” (§6) - “an unmixed evil” (§6) - “experimental observation of comparative dimness and clearness” (§6) - “the atmosphere is perfectly dry and transparent” (§6) **In this edition.** Notes 65–67 identify the London-fog reversal, the elevated phrase's literary resonance and the optical construction. The modern note connects “Nurse of arts” with Shakespearean praise of peace; Abbott's text bestows the phrase on Fog without identifying its source. The argument remains a fictional optical model, not a claim about the health effects of actual polluted air. **See also.** [Recognition by sight](#entry-recognition-sight) (p. 94); [Eye and the visible line](#entry-eye-retina) (p. 50); [Attraction and climate](#entry-attraction-climate) (p. 18); [Education and schools](#entry-education-schools) (p. 46). ## Fourth Dimension {#entry-fourth-dimension} *Fourth Dimension; Four Dimensions; Extra-Solids; Thoughtland* **The word.** The Fourth Dimension is an additional independent extent beyond the three familiar to Spaceland. Abbott presents it as the next term in a dimensional analogy and a possible region of existence. *Extra-Solids* name the figures that would result from moving Solids in such a new direction. An intelligible mathematical construction is not, by itself, evidence of an inhabited physical realm. **In the work.** The Fourth Dimension becomes urgent when the Square asks to see the Sphere's interior. Having learned that a higher viewpoint exposes the interiors of lower-dimensional beings, he assumes another ascent should expose the Sphere's organs. This question turns gratitude into pressure: the instructor who has opened one world now seems culpable if he refuses to open another. The request also reveals the pupil's lingering confusion between increased access and increased perfection. The Sphere first responds with ridicule and then declares that no such land exists and that its very idea is inconceivable. His earlier treatment of the Square makes this response conspicuously inadequate. The teacher has supplied the history of mistaken limits that the pupil now uses against him. The Square's counterargument is not merely rebellious enthusiasm; it carries forward the same constructions and boundary counts that have already led to the Cube. His proposed figure has sixteen terminal points and eight bounding Cubes. These are coherent mathematical properties. He also extends the revised argument about an unrecognized dimension implicit in visibility. Yet he does not claim to have completed a waking journey into four dimensions. He asks his guide to confirm or deny his anticipations, and tests them against reports of beings appearing in closed rooms. The Sphere admits that such phenomena are reported while disputing both their occurrence and their explanation. The exchange leaves the empirical question open. The Square's imagination then accelerates through a fifth, sixth, seventh and eighth dimension. His expanding rhetoric expresses a refusal to let any inhabited standpoint declare itself final. It does not provide separate evidence for each world named. The Sphere ends the discussion by violence, returning the pupil to Flatland rather than answering the argument. Only the dream in §20 offers a reconciled instructor and the easy construction of Extra-Solids and Double Extra-Solids. That sequel changes the Square's confidence but cannot establish a waking retraction by the Sphere. Later, *Thoughtland* serves as a cautious name for a theoretical three-dimensional vantage over Flatland in his treatise, intended to avoid the law. That later use should not be mistaken for the hoped-for fourth-dimensional region of §19. The Fourth Dimension thus remains simultaneously a rigorous possibility, a disputed hypothesis and a focus of aspiration. Its force depends on the reader retaining these differences rather than treating dimensional increase as automatically proved metaphysical ascent. **The places.** - **§19:** “But where is this land of Four Dimensions?” — The guide demands a location he cannot supply - **§19:** “There is no such land” — Ignorance becomes categorical denial - **§19:** “sixteen terminal points” — The anticipated figure has a precise structure - **§19:** “It is reported so” — Alleged visitations remain disputed reports - **§20:** “Extra-Solids by the motion of Solids” — The construction is supplied within a dream **In this edition.** The annotation gives the modern name *tesseract* as later terminology and describes the 1884 context of higher-dimensional speculation. Those historical explanations do not turn the alleged apparitions into confirmed events or identify the Fourth Dimension with divine goodness. **See also.** [Analogy](#entry-analogy) (p. 12) · [Dimension](#entry-dimension) (p. 39) · [Dream and vision](#entry-dream-vision) (p. 43) · [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) ## Grandson {#entry-grandson} *Grandson; little Hexagon; precocious Grandson* **The word.** The grandson is the younger of the narrator's two orphan grandchildren, a Hexagon praised for intelligence and regularity. His higher number of sides gives him a prospective place above his Square grandfather within Flatland's social arithmetic. His brief appearances expose two different relations between education and authority: a child's discovery can outrun the lesson, and the same child's trained obedience can make him retreat from it. **In the work.** In §15 the boy earns an extension of his ordinary instruction by performing well at Sight Recognition. His grandfather teaches the relation between squaring a number and constructing a Square. The boy asks why the already familiar third power should not also possess geometrical meaning. He then carries the construction forward himself, carefully admitting that he cannot see how the required movement works or what it would make. That uncertainty is part of his intelligence, not a defect the narrator needs to correct. The grandfather answers with irritation and sends him to bed. The domestic encounter establishes that Flatland's intellectual limits are reproduced through ordinary affection and instruction, not solely by the police. An educated adult can protect the established account of reality by treating an excellent question as nonsense. When the Sphere arrives, his first correction vindicates the absent child. The Wife has independently defended the boy, though by appealing to the inverted Commandments rather than to his mathematics. After the narrator's return, this same child seems the safest first disciple. His mathematical turn promises comprehension, while his youth supposedly shields him from knowledge of the Council's prohibition. Both calculations prove insecure. The public proclamation reaches him during the lesson, and he immediately understands enough of its danger to deny the seriousness of his former conjecture. He insists that he was only joking, disclaims the Third Dimension and mocks the phrase about upward movement. The episode does not reveal exactly how far inward belief has changed. Tears, legal disclaimers and nervous laughter make fear an essential part of the recantation. It would be too simple to say that the grandson never really meant his earlier argument, or that his new objections represent independent mathematical refutation. Equally, the narrative does not show him secretly retaining a complete conception of the Cube. He withdraws under pressure from a possibility he had once been willing to entertain. The grandfather's demonstration then collapses into purposeless shaking. The pupil's escape closes a circuit of failure: first the adult cannot hear the child's new thought; later the frightened child cannot accept the adult's transformed account. Pedagogy is embedded in family rank, civic obedience, language and risk. Brilliance alone cannot protect the exchange. **The places.** - **§15:** “a most promising young Hexagon” — Social and intellectual promise are presented together - **§15:** “but I don’t see how” — The boy distinguishes inference from visualization - **§15:** “Go to bed” — Authority stops the inquiry - **§21:** “that was only my fun” — The child recants after hearing the law - **§21:** “he unlocked the door and ran out of the room” — The failed lesson ends in withdrawal **In this edition.** The notes compare the lesson with philosophical examples of eliciting knowledge from a pupil, but Abbott does not name those sources in the scene. The local contrast between the boy's original reasoning and his later recantation is directly present in the narrative and requires no external identification. **See also.** [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) · [Wives and household](#entry-wives-household) (p. 126) · [Upward and Northward](#entry-direction-upward) (p. 122) ## History and revolution {#entry-history-revolution} *History; Tradition; annals; Revolution; authorities.* **The word.** *History* can mean past events or the narrative that makes them intelligible. *Tradition* and *authorities* identify channels of transmission; *annals* suggest formal records of successive occurrences. The Square uses all these resources, but his history repeatedly exposes the gap between recorded detail and justified certainty. **In the work.** §8 opens by distinguishing aesthetic dullness from the battles, conspiracies, tumults, and factions conventionally supposed to make History interesting. The remark introduces political drama as a familiar narrative commodity. What follows nevertheless becomes the most colourful stretch of historical writing in Part I: invention, diffusion, cultural brilliance, revolution, sensational crime, parliamentary rhetoric, massacre. The Square reproduces the attractions of the history he has lightly dismissed. His sources are uneven. The origins of paint depend on Tradition; the inventor's name varies; authorities concur on one version. The marriage deception has competing accounts and unexplained coincidences. By contrast, the suppression is rendered with impressive-looking statistics, tactical details, and ceremonial speeches. Precision does not automatically supply reliability. The count of the dead exceeds the earlier count of the hissers, a difference the narration does not explain, and the rhetorically complete catastrophe serves the regime's preferred conclusion. This history also supplies precedents. §3 has already summarized hundreds of failed rebellions in which leaders are absorbed or removed and followers destroy one another. The Colour Revolt expands that habitual pattern into a singular memorable case. It allows readers to see the machinery hidden in the earlier summary: carefully differentiated audiences, blocked exits, a silenced representative, and a prearranged trigger. What the regime calls the recurrence of popular incapacity is inseparable from organized intervention. The distance between the historical Square and his later imprisonment complicates the voice. A man who reports former suppression as a triumph ultimately becomes a punished transmitter of unwelcome knowledge. That later experience does not erase the earlier account's contempt. Instead, the memoir preserves incompatible positions within one speaker: beneficiary of the established history and victim of its continuing methods. The reader must hold the chronology of events together with the failure of moral understanding to progress uniformly. History in Flatland is therefore an institution as well as a sequence. Restricted archives, official anniversaries, and inherited stories decide what may count as collective memory. Colour is banned, but its threatening history is retained by the rulers and reluctantly admired by the narrator. Repression needs remembrance within the governing class even when it enforces forgetting elsewhere. **The places.** - §3: “recorded in our annals” - §8: “supposed to make History interesting” - §8: “if Tradition speaks the truth” - §10: “the story varies” - §18: “The minutes of the previous meetings” **In this edition.** Modern note 101 identifies the unreconciled numerical difference in §10 without calling it a proven contradiction. Note 97 emphasizes the political use of sensational stories. The section's ancient chronology is fictional; editorial comparisons with Victorian revolutions and Reform do not date Flatland's events in European history. **See also.** [Chromatistes](#entry-chromatistes) (p. 23); [Chromatic Sedition](#entry-chromatic-sedition) (p. 21); [Cunning and policy](#entry-cunning-policy) (p. 35); [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120). ## Imagination and modesty {#entry-imagination-modesty} *Imagination; Modesty; moderate and modest minds* **The word.** Imagination here includes the ability to form or entertain what ordinary perception does not provide. Modesty is intellectual and moral restraint concerning one's own apparent superiority. It is not mere timidity or an instruction to obey authority. **In the work.** The dedication joins these capacities because either can fail without the other. An imagination that projects its own certainty onto every unknown world simply enlarges prejudice. A modesty that refuses to inquire because it distrusts itself would leave every dimensional boundary intact. The romance seeks an active willingness to think further while recognizing the limits of the resulting thought. The reader first exercises imagination through manageable instructions: imagine a sheet of paper, lower an eye toward a coin, follow the implications of an intersecting Sphere. These exercises enlist known experience to approach an unfamiliar standpoint. Their success depends on the reader's willingness to suspend an effortless overhead view and inhabit the constraints of a lower-dimensional observer. The Sphere demonstrates the difference between advanced perception and modesty. It can explain the Square's error, yet reacts angrily when the same argument threatens its own limit. The Square, in turn, can become a forceful speculative pupil without ceasing to be a patronizing teacher to those below him. The narrative's reversals show why additional knowledge is not automatically self-criticism. The last image complicates imagination further. Under imprisonment, the narrator fears that the substantial world itself is an offspring of diseased imagination. The faculty named as a hope in the dedication becomes vulnerable to the vocabulary of pathology. This is not a simple reversal from good imagination to bad fantasy. The institutional attack on the witness and his declining ability to picture a Cube make it difficult for him to distinguish failure of representation from failure of reality. The desired reader therefore holds together two responsibilities: to resist official closures of possibility, and to resist turning an attractive possibility into unwarranted certainty. The Preface states this balance; the fate of the narrator makes clear how costly it can be to maintain. **The places.** - **Dedication.** “Enlargement of the Imagination” names one hoped-for effect of reading - **Dedication.** “Gift of Modesty” identifies a virtue rather than an extra dimension - **§ 1.** “Imagine a vast sheet of paper” begins the practical work of changing standpoint - **Preface.** “moderate and modest minds” describes the readers the work seeks - **§ 22.** “a diseased imagination” is the narrator's feared explanation in periods of weakness **In this edition.** The edition notes the Prayer Book resonance of the dedication and compares Abbott's later reflections on modesty. Those connections illuminate the chosen word without proving that every character's ascent is a religious conversion in the same sense. **See also.** [Dedication and the reader being addressed](#entry-dedication) (p. 36) · [Sphere](#entry-sphere) (p. 107) · [Dream and vision](#entry-dream-vision) (p. 43) · [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) ## Initiation and mysteries {#entry-initiation-mysteries} *Initiated; Mysteries; mysteries; secrets* **The word.** Initiation admits a person to knowledge or experience previously unavailable. Mysteries can mean religious secrets, difficult truths, or the marvels of a higher-dimensional world. Their capitalisation and context help disclose how a mathematical lesson borrows the dignity and risk of sacred disclosure. **In the work.** The dedication's initiatory movement is progressive: a creature acquainted only with two dimensions is admitted to three and hopes that its readers may aspire further. The secrets are not simply puzzles answered once and for all. Each disclosed world can become a new enclosure if the initiate treats it as the limit of possibility. Part I gives privileged access a more troubling institutional form. Knowledge, examination and the authority to classify are unequally distributed. The mystery of a Circle's status is protected by social distance and conventions of inspection. The narrator's language of learning is already entangled with the organization of rank before the Sphere appears. The Sphere's teaching combines discourse, demonstration, bodily force and an overwhelming change of position. It does not resemble a freely chosen classroom lesson at every stage. The Square's terror and the teacher's impatience prevent the ceremonial vocabulary from guaranteeing a gentle or ethically impeccable revelation. The resulting knowledge can be genuine within the narrative while its delivery remains coercive. A further difficulty appears after initiation. Seeing is not the same as retaining, describing or communicating. The Square cannot carry a stable three-dimensional representation back into the resources of his ordinary world. His desire to make disciples may repeat the teacher's impatience. His failure to do so turns the familiar prestige of initiation into isolation rather than assured membership in an enlightened community. The word mysteries thus crosses at least three registers: protected institutional knowledge, transformative experience and what remains difficult to articulate after that experience. Keeping those senses distinct prevents the book from becoming a simple story in which a secret elite automatically possesses moral or metaphysical authority. **The places.** - **Dedication.** “Initiated into the Mysteries” makes dimensional learning a graded admission - **§ 11.** “my initiation into the mysteries of Space” announces the central event while the account is still describing priests - **§ 16.** “the mysteries of Spaceland” names what verbal instruction struggles to reveal - **§ 22.** “the mysteries of Three Dimensions” becomes the subject of the narrator's treatise **In this edition.** The dedication note compares Greek mystery cults and Plato's use of initiation in the Symposium. That is a comparative lens supplied by the annotation. The main narrative does not name Diotima, prescribe her sequence of ascent, or identify the Sphere with a Platonic teacher. **See also.** [Circular doctrine](#entry-circular-doctrine) (p. 25) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) · [Philosophical comparisons and their limits](#entry-philosophical-comparisons) (p. 85) · [Imagination and modesty](#entry-imagination-modesty) (p. 61) ## Interior and exterior {#entry-interior-exterior} *inside; interior; stomach; side; outsides* **The word.** An interior is what lies within a boundary; an exterior is what lies outside it or faces outward. In *Flatland* these apparently elementary terms depend on the dimensional position of the observer. A surface or side exposed to a higher-dimensional viewer can be what the lower-dimensional creature calls its inaccessible inside. The vocabulary is relational without becoming arbitrary: the geometry explains each disagreement. **In the work.** The first encounter in Lineland turns the Square's ordinary speech into something apparently arising from the King's intestines. A direction beside the Line does not exist within the King's spatial language. What the Square calls a side the King calls a stomach. The odd bodily terms are not merely grotesque decoration. They make a conceptual limit audible: an outside for one speaker is assigned to the inside by another. The Sphere reproduces this disturbance in Flatland. He explains that an eye on the Square's side, meaning the flat face the Square regards as his interior, would permit a different kind of vision. The Square hears the proposal as an absurd eye in his stomach. Similarly, a house or cupboard enclosed within the plane lies open from above. The Sphere can remove an account tablet without passing through its locked boundary because the enclosure has no power against the direction from which he approaches. That access unsettles the distinction between private and public. Household arrangements, money, written accounts and organs become visible together. The panorama is not an abstract diagram; it abolishes familiar kinds of secrecy. The Square first experiences the new access as vulnerability when the visitor touches his interior, and only later as exhilaration when he can inspect his own country from above. Yet the higher vantage has a boundary of its own. When he sees the Sphere in Spaceland, the Square mistakes the visible surface for an opened interior and wonders why no organs are apparent. The guide corrects him: the outside of a three-dimensional body still conceals what is inside from a three-dimensional observer. The discovery that everything below lies open does not entail that everything whatsoever does. The request to see the Sphere's intestines therefore drives the argument for a fourth dimension. The pupil treats the newly encountered boundary as another invitation to enlarge the viewpoint; the teacher treats it as final. This is why the recurring stomach matters to the book's intellectual structure. It is at once the site of comic embarrassment, intimate violation and a rigorously repeated question: what appears closed only because the observer cannot approach it from another direction? **The places.** - **§13:** “his inside or stomach” — Lineland gives no ordinary name to an external side - **§16:** “not on your Perimeter, but on your side” — The Sphere distinguishes two positions for an eye - **§17:** “the doors, you see, remain unmoved” — The locked enclosure is bypassed dimensionally - **§18:** “What you think you see, you see not” — A surface is mistaken for an interior - **§19:** “a sight of thine interior” — The anatomical request initiates the next dimensional argument **In this edition.** The notes carefully explain the two different uses of *side* and the fact that the Sphere's visible surface does not disclose his organs. This protects the recurrent image from a misleading claim that ordinary Spaceland vision is literally unlimited. **See also.** [Touch and bodily proof](#entry-touch-belly) (p. 118) · [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) · [Fourth Dimension](#entry-fourth-dimension) (p. 57) · [Space and Spaceland](#entry-space-spaceland) (p. 106) ## Irregularity {#entry-irregularity} *Irregular; Irregularity of Figure; moral obliquity; deviation* **The word.** An *Irregular* is a person whose figure departs from the standard prescribed for the class. The capitalised noun turns a relation to a norm into a complete identity. *Deviation* sounds measurable and limited; *moral obliquity* changes the same bodily difference into an accusation of crooked character. **In the work.** Section 7 initially offers a problem of inference. When an observed angle cannot be trusted to represent the rest of a body, recognition becomes less convenient and movement more hazardous. These difficulties matter in the fictional world. The narrator's leap is to treat their existence as proof that the person who presents them is morally defective and should be excluded or killed. The feared Irregular often combines different class-signs: a triangular front with a polygonal back, or the reverse. Such a body disrupts not only spatial planning but the agreement between visible appearance and social credit. The shopkeeper who sees a prestigious front might extend goods on false assumptions. The nightmare is therefore partly that privilege could cease to be securely legible. The Irregular reveals how much supposed trust in persons is actually trust in a classification. Abbott allows the opposing view an unusually sustained speech. It moves through the household, employment, surveillance, marriage and enforced residence, asking whether mistreatment may produce the resentment later cited as evidence of innate perversity. Its sequence gives a life-history where official taxonomy supplies only a shape. The narrator reports the argument accurately enough for readers to find it persuasive, then dismisses it by invoking the state's safety and the majority's convenience. The result is a conflict between explanations. One treats behaviour as the effect of bodily deviation; the other asks what institutions do to a person whose body has already occasioned rejection. The narrator's assertion that he has never met a morally sound Irregular cannot decide between them, since the society he describes systematically creates the conditions the reformers identify. His closing moderation intensifies the exposure. He does not favour immediate destruction in every case, because genius might be lost and treatment might succeed. The potential victim's value is measured by possible service to the state. When recovery seems improbable, the recommended killing is called merciful. Irregularity thus tests the difference between reducing suffering and removing the person who suffers, a distinction the official vocabulary tries to close. **The places.** - “a combination of moral obliquity and criminality” (§7) - “no necessary connection between geometrical and moral Irregularity” (§7) - “the interests of the Greater Number” (§7) - “a clerk of the seventh class” (§7) - “a hypocrite, a misanthropist” (§7) - “painlessly and mercifully consumed” (§7) **In this edition.** Notes 77–83 discuss moralised bodily difference, humanitarian argument, majority-interest reasoning and the final euphemism. These are Diotimos interpretations of the 1884 text. The vocabulary of disability can illuminate the exclusion described, but *Irregular* should not be reduced to a single modern diagnostic or social category. **See also.** [Regularity](#entry-regularity) (p. 97); [Doors and houses](#entry-doors-houses) (p. 42); [Surgery and extermination](#entry-surgery-extermination) (p. 112); [Nature and law](#entry-nature-law) (p. 81). ## Isosceles {#entry-isosceles} *Isosceles; acute-angled; base; vertex* **The word.** *Isosceles* names a triangle with two equal sides; in the fiction it designates the soldiers and labouring population whose third side is shorter. The very narrow base produces a sharp opposite vertex. The word can function as adjective, singular class-name or collective social designation, making a mathematical property into an inherited identity. **In the work.** The category is introduced through exact-looking dimensions, but the description immediately becomes evaluative. A small base belongs to a “degraded type,” and the sharpest bodies approach the appearance of Women. Geometry establishes a continuum of shapes; the narrator turns the continuum into a descent towards reduced humanity. The technical name helps this judgement pass as classification rather than hostility. The Isosceles also exposes an inconsistency in the account of natural equality. In §3, inequality of all three sides is a reason to doubt whether the worker deserves to be called a human Figure. In §7, having two equal sides satisfies the class-specific standard of regularity. The standard is therefore not a single geometrical requirement applied impartially. It varies to preserve the recognised categories, while the language of universal nature disguises that variation. The sharp body contains a political dilemma for the rulers. Soldiers can penetrate and destroy the blunter figures who govern them. The supposed law of compensation resolves this dilemma by making increased intelligence widen the angle and reduce its offensive power. The Isosceles may become cleverer only by becoming less dangerous. Where this natural management fails, the state recruits some members, purchases the allegiance of leaders and sets the rest against one another. The gap between the lowest and near-equilateral members is enormous. Some possess an angle of half a degree and become disposable school apparatus; the Square's ancestor has nearly reached sixty degrees and a recognised claim to respectability. A single class-name collapses these differences when convenient, then subdivides them when labour, warfare, discipline or instruction requires it. Classification serves administration as much as description. Kinship unsettles the narrator's distance from the group. His grandfather belonged to it, and the story of earlier family misfortune invites sympathy for a worker caught in an accident. He can recognise a full human history within his own ancestry while dismissing the class collectively. The inconsistency makes *Isosceles* a key term for reading how prejudice survives knowledge rather than merely resulting from its absence. **The places.** - “Triangles with two equal sides” (§3) - “they can hardly be distinguished from Straight Lines or Women” (§3) - “the wretched rabble of the Isosceles” (§3) - “one of the least irregular of his unhappy Isosceles class” (§5) - “half a degree, or thirty minutes” (§5) - “an Artisan or Soldier must have two of his sides equal” (§7) **In this edition.** Note 35 supplies the Greek derivation; notes 34 and 60 check the narrow-angle geometry. Note 75 explicitly identifies the shifting meaning of regularity. These explanations help separate a mathematical triangle from the particular body-type and social category for which Abbott uses its name. **See also.** [Artisan and soldier](#entry-artisan-soldier) (p. 16); [Angle](#entry-angle) (p. 14); [Equilateral](#entry-equilateral) (p. 47); [Regularity](#entry-regularity) (p. 97). ## Isosceles rebels {#entry-isosceles-rebel} *Thematic heading.* Attested vocabulary: *Isosceles; Workmen; Soldiers; Artisans; Convicts; Criminal Classes*. **The word.** *Isosceles* names triangles with two equal sides, but in the political chapters it gathers several unequal social positions. Artisans, soldiers, and convicts are not interchangeable groups merely because the narrator places them within an acute-angled lower order. *Rebel* describes a relation to authority, not a geometrical species. Some Isosceles oppose the Circles; others enforce their commands. **In the work.** The first history of rebellion in §3 is a theory of leadership removal. More intelligent or reformable figures can be promoted, confined, or executed; their followers are left without plans. Paid members of their own class then attack them, or the rulers foment mutual distrust. The narrator presents the repeated outcome as evidence of the poor's defects. The account simultaneously provides evidence of an institution deliberately producing the conditions in which the poor fail. Colour alters this pattern by making practical competence less dependent on elite education. The Isosceles classes can challenge the need to surrender educational specimens and question aristocratic intellectual monopolies. Their equality claims are not wholly dismissed even by their adversary. This admission matters because it prevents the political history from resting solely on the narrator's bodily insults. He describes a change in capacities that his rigid class language cannot entirely contain. Pantocyclus's decisive manoeuvre separates artisans from those below them. Men expecting admission to the Regular class, or hoping for it for their children, are asked to fear universal equality as a loss of future distinction. The prospect of mobility becomes an inducement to abandon fellow insurgents. The artisans open their ranks, following the Regular classes, and permit the attack upon the soldiers. Hierarchy survives by making its aspirants act as its auxiliaries. The guards at the exits sharpen the contradiction. These Convicts are drawn from the very population whose numerical predominance Pantocyclus has made alarming. Their bodies are useful when they seal the hall, while similar bodies inside it become a “rabble” blamed for fatal panic. Function changes moral description. The tale exposes less a uniform character of the Isosceles than the ruler's capacity to assign the same stigmatized class several incompatible roles. Finally, the artisans' cooperation does not purchase safety. They are subsequently “spared but decimated.” Conditional solidarity with the rulers earns a reduced form of collective killing, not secure recognition. The event makes bodily classification politically powerful without making it an adequate explanation of motive, allegiance, or desert. **The places.** - §3: “planless and leaderless” - §9: “monopolising and aristocratic Arts” - §10: “their children a distinction” - §10: “the Artisans, imitating the example of their betters” - §10: “spared but decimated” **In this edition.** Notes 91 and 102 explain the educational tribute and the strict punitive sense of *decimated*. The modern commentary criticizes the narrator's population language; the article likewise treats *Criminal Classes* as the regime's classification, not a demonstrated moral identity of everyone so labelled. **See also.** [Compensation](#entry-compensation) (p. 29); [Reform and equality](#entry-reform-equality) (p. 95); [Cunning and policy](#entry-cunning-policy) (p. 35); [Suppression and massacre](#entry-suppression-massacre) (p. 110). ## King of Lineland {#entry-king-lineland} *Monarch; King; his Royal Highness* **The word.** The King is the ruler of the one-dimensional world encountered in the Square's first dream. He is a Line, longer than his subjects, with a voice and an eye at each extremity. His title makes spatial limitation politically articulate: this is not simply a creature unable to perceive another direction, but a ruler prepared to define what is rational and punish what is physically permitted. **In the work.** His entrance reverses the Square's confidence before either begins to teach. The visitor assumes a Straight Line must be a Woman and addresses it accordingly. The reply announces sovereign masculinity. Flatland's normal classification fails immediately outside Flatland, although its representative does not draw the lesson about his own assumptions. He continues to regard the ruler as poor and ignorant while requesting information about the realm. The King's pride has a material basis. His hearing performs tasks that the Square cannot perform: it distinguishes sex, measures lengths and discloses a vast social field. His exact account of the delay between his two voices sounds extravagant, but within the imagined conditions it supplies a method of inference. The caricature does not make him incompetent at life in his own world. His error is to turn local expertise into a rule for all possible perception. His language shifts readily from explanation to rebuke. He calls the Square a fool for distinguishing Space from Length, a monstrosity for having one voice, and irrational for claiming movement he cannot exhibit within the Line. These judgments make anatomy, sex, reason and citizenship mutually reinforcing. The visitor's strange evidence is discounted because it cannot be rendered in the sovereign's accepted vocabulary. The Square answers with condescension rather than patient recognition of the difficulty. He calls his own world true Space, presents himself as the completion of the King, and insists on his infinite superiority while invoking nobles greater still. The supposed corrective reproduces hierarchy rather than escaping it. When the King finally advances to attack, the violence follows an exchange in which both speakers have converted a disagreement about perception into wounded rank and injured masculinity. His dream status matters. The King is not an independently verified monarch encountered during the bodily Spaceland journey. He is the figure through whom the narrative rehearses the Square's coming failure as a pupil. That rehearsal makes the later reversals legible without reducing him to a disposable illustration. His marriage system, legal prohibitions and perceptual accomplishments give the line its own lived density. **The places.** - **§13:** “I am the Monarch of the world” — Misgendering is answered with sovereign self-definition - **§13:** “a feminine Monstrosity with a bass voice” — Difference is classified as defective femininity - **§14:** “Space is Length” — A local definition becomes an absolute decree - **§14:** “the census and statistics” — The ruler claims exhaustive social knowledge through hearing - **§14:** “Acknowledge your folly or depart from my dominions” — Argument concludes in an ultimatum **In this edition.** The apparatus points out the Square's unstable forms of royal address and explains the auditory measurement rather than dismissing it as arbitrary fantasy. Literary and biblical comparisons in those notes are offered with their proper degrees of certainty; the King's directly narrated acts remain the entry's basis. **See also.** [Lineland](#entry-lineland) (p. 74) · [Voice and selfhood](#entry-voice-selfhood) (p. 125) · [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) · [Sphere](#entry-sphere) (p. 107) ## Language and gender {#entry-language-gender} *bi-lingual; bi-mental; idiom; logical dialect; quietism* **The word.** Flatland's *bi-lingual* existence is not ordinary bilingualism between national languages. It is a division between a domestic vocabulary of moral sentiments and an authorised male vocabulary that translates those sentiments into utility or necessity. *Bi-mental* extends the division from speech to trained habits of thought. **In the work.** Section 4 repeatedly treats women's supposed lack of reason as a consequence of their shape. Section 12 supplies a history that destabilises that explanation: a decree removed their instruction in reading and arithmetic, and intellectual decline followed. The social order has helped produce the condition it offers as justification for exclusion. The reader is not required to accept the narrator's account of an original female deficiency in order to see this causal sequence. The resulting double language operates through systematic translation. “Love” becomes “the anticipation of benefits”; “duty” becomes “necessity” or “fitness.” The alterations are not merely synonyms chosen for precision. They remove disinterested obligation and affection from the explanation of conduct. The supposedly rational idiom defines away values which the male speakers nevertheless invoke when governing children or managing domestic life. The domestic language is also a managed fiction. Men express supreme deference to women in their presence and deny their rational standing behind their backs. The practice continues the tactical false promises praised in §4. What appears as courtesy can therefore be an instrument of control, and what the narrator calls scientific candour depends on keeping its terms unavailable to those it describes. Children pass between the idioms. At three, boys must unlearn the maternal language while preserving the ability to repeat it before mothers and nurses. Their education is an apprenticeship in selective sincerity. The danger that a child might disclose the male vocabulary shows that the system relies on secrecy, not only on intellectual differences. A woman's surreptitious reading of an ordinary book could likewise expose the contradiction. The narrator finally urges reconsideration, but his stated reason is the damage to male mathematical powers. This is a limited, interested argument, and it should not be made into an uncomplicated declaration of equality. At the same time, the account gives readers grounds for a wider judgement than the speaker is prepared to draw. His preferred vocabulary cannot quite suppress the loss disclosed by words such as love, pity and hope, nor can his fear of female reading sustain his claim that women have no capacity for consequential understanding. **The places.** - “female non-education or quietism” (§12) - “bi-lingual, and I may almost say bi-mental” (§12) - “the anticipation of benefits” (§12) - “mindless organisms” (§12) - “taught to unlearn the old language” (§12) - “the secrets of the logical dialect” (§12) **In this edition.** Notes 117–119 distinguish quietism's religious history, the political and philosophical implications of the double vocabulary, and Abbott's work for women's education. That biographical evidence belongs to the annotation. It should inform, without erasing, the difference between Abbott's concerns and the self-interested reform proposed by his fictional speaker. **See also.** [Women](#entry-women) (p. 128); [Education and schools](#entry-education-schools) (p. 46); [Voice and hearing](#entry-voice-hearing) (p. 123); [Class and caste](#entry-class-caste) (p. 27). ## Law and sanction {#entry-law-sanction} *Law; penalty; sanctioned; Court Martial; Constitution.* **The word.** *Law* oscillates between a description of nature and an enforceable command. *Sanctioned* means officially permitted, as in the reportedly exceptional university use of colour; *penalty* names the punishment attending its unauthorized use. Keeping these senses apart reveals how a system can forbid an act generally while reserving it to privileged practitioners. **In the work.** Flatland's institutions repeatedly align positive law with what the narrator calls natural necessity. In §7 Nature and Expediency endorse regular bodies, and the Law seconds their efforts. In §9 the reformers reverse the same argument: because colour has practically removed distinctions, the Law should follow. Both sides claim that legislation ought to recognize an order already established outside legislation. The dispute is partly over which kind of fact gets to instruct the law. The Colour Bill makes legislative procedure central. Its proponents address an extraordinary Assembly of all the States, proposing a specified bodily code. The Circles answer through a public performance of concession and majority approval. But the apparent parliamentary setting ends in a planned killing. Institutional form does not guarantee deliberation when one side controls guards, speech, and exits. The ruler can invoke the majority while arranging that its composition, voice, and survival depend on him. Afterward, ordinary classificatory procedures are suspended. Suspected Irregular Triangles are destroyed by Court Martial without exact measurement by the Social Board. A society that normally insists on measurement permits suspicion to replace it when repression requires speed. This is more than harsh enforcement of a stable standard: the emergency dissolves the standard's evidentiary safeguards. The narrator calls the outcome a restored balance, letting constitutional vocabulary conceal the change in procedure. The prohibition on colour shows another flexibility. Possession is prohibited; uttering colour words is punishable, with an explicit exception for Circles and qualified scientific teachers. Separately, the Square reports only from hearsay that colour itself is used in advanced university instruction. The certain exception concerns speech, not a general right to paint. Even this narrower permission makes access part of the hierarchy: institutional standing determines who may name what others must not name. Similarly, women's marriage requires a state-certified pedigree, turning intimate choice into a legal mechanism of bodily governance. Part II extends these practices to testimony. The Council prescribes different penalties by rank for claims about another world, and later judges the Square in a procedure whose lethal treatment of witnesses he can infer before speaking. Law here allocates both credibility and vulnerability. It does not merely punish belief after an impartial inquiry; it helps determine whose account may circulate at all. **The places.** - §7: “the Law been backward in seconding” - §9: “the Law should follow in the same path” - §10: “without the formality of exact measurement” - §10: “still sanctioned” - §12: “without a certified pedigree” - §18: “without formality of mathematical examination” **In this edition.** Notes 80, 93, and 102 offer historical comparisons for penal disabilities, franchise reform, and counter-revolutionary punishment. They are modern contextual annotations. The close verbal parallel between waived measurement in §10 and waived mathematical examination in §18 belongs to Abbott's narrative and connects bodily to intellectual policing. **See also.** [Universal Colour Bill](#entry-universal-colour-bill) (p. 119); [Marriage and selection](#entry-marriage-selection) (p. 75); [Science and institutions](#entry-science-institution) (p. 101); [Suppression and massacre](#entry-suppression-massacre) (p. 110). ## Lineland {#entry-lineland} *Lineland; Linear Realm; Straight Line* **The word.** Lineland is Abbott's name for a world confined to a single straight line. Its male inhabitants are Lines and its female inhabitants Points. Their visible horizon is a Point, whatever kind of being stands before them. The name describes a dimensional restriction, but the episode gives that restriction consequences for movement, perception, marriage, law and the language of reality. **In the work.** Encountered in a dream, Lineland is not merely a smaller Flatland. No inhabitant can pass another. Neighbourhood is permanent, and the order of persons along the Line becomes an unalterable social relation. The narrator compares this confinement with marriage, then discovers that marriage itself has been reorganized so that it does not require proximity. The world is developed from its geometrical premise rather than supplied with ordinary institutions unchanged. Sound compensates for restricted vision and immobility. Men's two voices reveal their length through the interval between their arrival at a listener. Courtship and reproduction proceed through coordinated vocal harmony across immense distances. Such inventions are comic, but they resist the Square's immediate assumption that life must be unbearably dull. The King's cheerful absorption in his world is part of what the visitor has to understand and initially cannot. The legal system makes contact a capital offence, ostensibly to protect fragile Women. Feeling, a legitimate method of recognition in Flatland, becomes both dangerous and indecent here. This reversal demonstrates that a practice called natural in one world can be forbidden in another because its bodily conditions differ. It also repeats the combination of paternal protection and severe control already familiar from Flatland's laws. The central conversation concerns whether there can be a direction outside the Line. The King hears the Square's first voice as internal noise, cannot see lateral movement while an intersecting portion remains before him, and interprets disappearance as death or magic. His denials arise from the limits of his access, but his insistence that those limits exhaust Space is an additional act of judgment. The Square's superiority is correspondingly qualified. He correctly understands the King's world from outside, yet claims that a Plane is true Space and that the Line is only an imperfect version of himself. The reader, knowing three-dimensional space, can recognize the same closure one level higher. Lineland therefore creates a reversible experiment: it instructs readers to notice both the blindness of the inhabitant and the arrogance of the visitor. The later Sphere-Square dialogue repeats the arrangement with the roles shifted. **The places.** - **§13:** “all moving to and fro in one and the same Straight Line” — The spatial premise appears as collective movement - **§13:** “Once neighbours, always neighbours” — Geometry fixes social position - **§13:** “neighbourhood is needless for the union of hearts” — Marriage adapts to immobility - **§14:** “this offence is punishable in my dominions by death” — Contact becomes a legal transgression - **§14:** “True Space is a Plane” — The visitor reveals his own unexamined limit **In this edition.** The notes identify *Lineland* as Abbott's coinage, explain the mechanics of auditory measurement and distinguish historical parallels from demonstrated sources. The dream frame is retained throughout; Lineland is a narrated thought-world, not a destination independently verified by the later voyage. **See also.** [King of Lineland](#entry-king-lineland) (p. 69) · [Voice and selfhood](#entry-voice-selfhood) (p. 125) · [Dream and vision](#entry-dream-vision) (p. 43) · [Wives and household](#entry-wives-household) (p. 126) ## Marriage and selection {#entry-marriage-selection} *Thematic heading.* Attested vocabulary: *intermarriages; pedigrees; certified pedigree; ancestry; posterity*. **The word.** *Pedigree* is a recorded line of descent. *Intermarriages* in §3 are deliberately arranged unions among selected families. The heading *selection* describes this institutional activity; it is not an invitation to treat the narrator's hereditary beliefs as established biology. In Flatland, marriage coordinates lineage, legal recognition, bodily rank, and hopes for advancement. **In the work.** The Priests arrange lower-class marriages intended to produce offspring closer to the Equilateral form. The future child's possible promotion retrospectively organizes generations of parental restraint and labour. When the rare certified Equilateral is born, removal from his birth family protects the new rank against supposed relapse. Marriage policy thus makes families instruments of ascent while successful ascent requires the rupture of family relations. The special problem of women in §12 exposes an instability in this classification. All are visibly straight, so male observers cannot read their supposed reproductive irregularity from their bodies. The state substitutes documentary descent for immediate measurement. What the Square calls “invisible Irregularity” is a prediction about possible offspring, made administratively legible through records. Certification grants or withholds the permission to marry. The rule therefore extends bodily government beyond what geometry can actually show. The distribution of caution is inverse to rank. An ambitious Isosceles examines ancestry rigorously; a confident Square or Pentagon stops at an extravagantly remote generation; higher nobles take greater liberties. Circles may prefer brilliance or a low voice to pedigree. The narrator treats their choice as irresponsible, but it also reveals that the law's celebrated natural principle is practiced most anxiously by those seeking entry. People already secure can enjoy exceptions or disregard warnings that aspirants cannot afford to ignore. The Colour Bill threatens another matrimonial mechanism: recognizable class identity. The report of an Isosceles posing as a Dodecagon converts a woman's tragedy into a public warning against reform. Pantocyclus invokes the safety of every marriage to mobilize women against the Bill. The state that excludes them from education and public knowledge now claims to protect them from deception. Its own organized deception, including the false concession to the reformers, is excluded from the moral indictment. Marriage consequently joins the novel's bodily and informational politics. Pedigrees, colours, voices, and certificates are rival ways of identifying a prospective spouse. None is simply nature speaking for itself. Institutions decide which evidence counts, whose preferences are reasonable, and whose lineage must be scrutinized. The woman's own judgment remains largely mediated by the men who tell the history and maintain the records. **The places.** - §3: “Intermarriages (arranged by the Priests)” - §3: “never to permit the child” - §12: “their invisible Irregularity” - §12: “preserved and supervised by the State” - §12: “no blot on her escutcheon” **In this edition.** Modern note 39 places managed breeding beside Galton's work and Plato's imagined state. Note 115 identifies the Shakespearean quotation about a low voice. These annotations explain historical and literary resonances without endorsing the narrator's account of desirable reproduction or women's supposedly defective ancestry. **See also.** [Fertility and extinction](#entry-fertility-extinction) (p. 54); [Dodecagon](#entry-dodecagon) (p. 40); [Configuration](#entry-configuration) (p. 31); [Law and sanction](#entry-law-sanction) (p. 72). ## Memory and forgetting {#entry-memory-forgetting} *recollect; mental vision; slipping away; once-seen, oft-regretted* **The word.** Memory is the retained capacity to recall an experience; forgetting can involve the loss of its particulars without the loss of conviction that it happened. *Flatland* makes that distinction painful. The narrator continues to name a Cube, repeat its properties and defend his journey while becoming less certain that he can reproduce the shape he once saw. **In the work.** The memoir first makes strong claims for retention. The account of the Sphere's dialogue is offered as nearly as the narrator can recollect it, with apologies omitted. In §19 he promises exact words and facts burnt into his brain. Such declarations belong to the rhetoric of testimony, but the closing narrative places them under pressure. The voice preserving the encounter is also a voice confessing that preservation is incomplete. The trouble starts almost immediately after the return. Before sleep the construction of a Cube is less clear than the Square wishes, so he grasps the formula about upward movement as a clue. The dream refreshes his confidence, but the clarity already weakens again as he considers teaching his household. His urgency to gain a disciple is therefore partly an urgency to stabilize knowledge outside his own mind. The failed lesson with the grandson deprives him of that support. Several months of private writing follow, but Flatland's representational tools cannot supply the needed diagrams. Rehearsal, argument and inscription preserve propositions more readily than perceptual acquaintance. They do not simply duplicate the experience of moving through Space and handling a Solid. The specific crisis arrives about eleven months after the return: he closes his eye and cannot see the Cube mentally. Later he succeeds, but never regains certainty that the image is exact. The distinction is subtle. Abbott does not say that all knowledge vanishes at once, nor that failure to visualize disproves the object's existence. He describes the erosion of a traveller's ability to compare a present mental representation with an unavailable original. Imprisonment intensifies the loss by removing ordinary companionship and any possibility of renewed travel. The brother's disbelief deprives testimony of the confirmation the narrator longs to obtain. The memorable catch-phrase now haunts rather than helps him, and moments of doubt spread beyond Spaceland to Flatland's own walls and writing tablets. The final movement is not a clean erasure of knowledge but an alternation between hope and uncertainty. Memory sustains the book even while the book records memory's failure. **The places.** - **§16:** “as near as I can recollect it” — Reconstructed dialogue acknowledges a limit - **§19:** “they are burnt in upon my brain” — The narrator asserts indelible testimony - **§21:** “slipping away from me” — The urgency to teach is also fear of loss - **§22:** “about eleven months after my return” — A particular lapse marks the long decline - **§22:** “confident as to the exact shape” — Uncertainty concerns fidelity as well as existence **In this edition.** The notes link the fading image to comparative accounts of knowledge that cannot be securely held, but the temporal sequence is Abbott's own. The ending is not annotated as an authoritative announcement that the entire adventure was unreal; the narrator explicitly distinguishes brighter moments from periods of mental weakness. **See also.** [Cube](#entry-cube) (p. 33) · [Upward and Northward](#entry-direction-upward) (p. 122) · [Dream and vision](#entry-dream-vision) (p. 43) · [Prison and silence](#entry-prison-silence) (p. 90) ## Millennial visit {#entry-millennial-visit} *once only in a thousand years; millennial Revelation; mission* **The word.** A millennial occurrence recurs at an interval of a thousand years. The Sphere's visit is specifically described as a permitted act of preaching once in that period. The source of the permission is not identified. The schedule supplies the encounter with historical gravity, but it also exposes revelation to administrative anticipation: Flatland's rulers possess records of previous visits and prepare to suppress the next. **In the work.** The domestic scene initially presents the new millennium as an occasion for looking backward and forward. The narrator and his Wife remain awake while the family sleeps; the last sand falls just after the visitor has secured privacy. A large division of historical time coincides with a small, intimate interruption. The scale of the event grows only when the Sphere explains the rarity of his commission. His language of a gospel and an apostle makes the Square more than a curious observer. He is being prepared to transmit what he learns. The long interval also contributes to the visitor's urgency and impatience. When the Wife approaches during their struggle, the Sphere fears that the fruits of a thousand years of waiting will be lost. The mission's supposed importance helps him justify secrecy, pain and ultimately forced removal of the pupil from his plane. The official meeting in §18 discloses a competing use of the same calendar. On the first hour of the first day, the highest Circles read the minutes of earlier meetings and renew orders against claims of revelation. The authorities are not innocently surprised by every anomaly. The President knows from the secret archives that similar manifestations occurred at the two previous millennial commencements. Repetition has generated a machinery of containment rather than a public tradition of inquiry. The Sphere's appearance before the Council might seem designed to leave incontestable collective evidence. Instead it produces frightened junior councillors, endangered guards and the imprisonment of the narrator's brother. Social differences determine who can retain the secret and who must be silenced. A spectacular manifestation does not equal successful communication when its witnesses are subject to coercive institutions. The final phrase *millennial Revelation* therefore carries disappointment. After seven years of imprisonment, the chosen apostle has no converts. The immense waiting time contrasts with the apparent absence of a transmissible result. Yet the memoir remains an attempt to exceed that failure by reaching readers in some other dimension. The visit is neither a comfortably fulfilled providential plan nor an empty event; its consequences remain contested in the act of writing that reports them. **The places.** - **§17:** “once only in a thousand years” — The visitor states the restriction on his preaching - **§17:** “the fruits of one thousand years of waiting” — Urgency enters the confrontation - **§18:** “the last two millennial commencements” — The authorities possess a suppressed history - **§18:** “the secret archives, to which I alone have access” — Knowledge is monopolized institutionally - **§22:** “the millennial Revelation has been made to me for nothing” — The narrator measures the mission by its apparent failure **In this edition.** The notes identify possible resonances of biblical thousand-year periods while stopping short of naming an authority the narrative leaves unnamed. The local calendar and the retained 1884 *second Millennium* reading are treated separately from any claim about Christian dates. **See also.** [Time and the millennium](#entry-time-millennium) (p. 116) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) · [Prison and silence](#entry-prison-silence) (p. 90) · [Scripture gospel and prophetic speech](#entry-scriptural-language) (p. 102) ## Movement and section {#entry-movement-section} *motion; section; slice or section; moving parallel to itself* **The word.** A section is the figure formed where a plane or other lower-dimensional region intersects a body. It is not necessarily the whole body viewed from far away. Abbott pairs sections with movement: motion through a world can alter the intersecting figure even when the moving object's actual size and shape remain unchanged. A second kind of movement generates figures by tracing new paths in an additional direction. **In the work.** The Square's dream visit to Lineland offers the first experiment. The Line can display only the portion of his body lying within it, so the intersecting portion is a Line rather than a Square, though the King’s eye sees only its end as a Point. As he moves laterally out of the realm, the King does not perceive the unfamiliar direction. He perceives continued presence followed by disappearance. The higher figure cannot bring its entire form into a space that has too few dimensions to contain it. The Sphere explains his own appearance by referring to that encounter. His circular manifestation is a section where he intersects Flatland. As he rises, this circular section shrinks towards a Point and disappears; on returning it grows again. The Square sees the section edgewise as a changing line, not as the full circular outline available in the reader’s diagram. The Square's report that the visitor made himself smaller preserves his initial interpretation, not the actual mechanics. The Sphere does not physically contract and expand. Different sections of the same body enter the plane. Movement supplies the generative lesson as well. A Point moving leaves a Line, a Line moving in a new independent direction makes a Square, and a Square moving out of its plane makes a Cube. The crucial condition is that each point trace a path not already traversed by another point of the figure. Simply moving a Square northward within Flatland cannot do the required work, however great the distance. These two uses of motion complement one another without being identical. A section explains the partial manifestation of a body that already exists; generation explains how the extent of a higher-dimensional figure may be conceived from lower-dimensional elements. The Sphere moves his own body through Flatland in the first case and describes or demonstrates a construction in the second. Confusing the two makes the visit resemble shape-changing magic and obscures the mathematical lesson. Finally, movement is not distributed equally between teacher and pupil. Once lifted out of Flatland, the Square cannot move independently. He can see his distressed Wife and imprisoned brother but cannot reach them. Dimensional access enlarges perception while creating dependence upon the guide's volition. Abbott thus makes movement a problem of agency as well as a means of geometrical explanation. **The places.** - **§14:** “I see you still; you are not moving” — An unfamiliar motion remains perceptually unavailable - **§16:** “only a slice or section of you” — The Sphere explains partial manifestation - **§16:** “as I rise in Space, so my section becomes smaller” — Sectional change is not bodily shrinkage - **§16:** “each Point shall describe a straight Line of its own” — Generation requires independent paths - **§19:** “I absolutely depended on the volition of my Guide” — New sight does not bring autonomous movement **In this edition.** The diagrams and notes distinguish changing sections from changing bodily size and explain construction by parallel movement. They also retain the narrator's limited descriptions, allowing readers to see the difference between his first explanation and the geometrical account he later learns. **See also.** [Cube](#entry-cube) (p. 33) · [Dimension](#entry-dimension) (p. 39) · [Upward and Northward](#entry-direction-upward) (p. 122) · [Sphere](#entry-sphere) (p. 107) ## Nature and law {#entry-nature-law} *Law of Nature; ordinance; Decree; Nature wills; Expediency* **The word.** *Nature* can designate a physical condition, an inherited tendency or a personified authority. *Law* likewise names both a general regularity and a statute enforced by a state. The phrase *Law of Nature* connects these registers, often allowing a social arrangement to borrow the apparent necessity of a mathematical or physical relation. **In the work.** The southward attraction is an early, comparatively straightforward example: the narrator stipulates a persistent force and explains how travellers use it. The hereditary law in §3 is more complicated. It promises one additional side to each male generation, then immediately excludes or qualifies much of the population. The confident universal phrase survives exceptions that determine who receives its benefit. The “Law of Compensation” goes further, explaining how increasing intelligence deprives workers of dangerous sharpness. A relation between shapes is celebrated because it preserves an aristocratic constitution. The narrator moves from what the world is said to do to the conclusion that the rulers deserve their position. Calling the arrangement divine converts successful domination into evidence of rightful domination. Yet human intervention is everywhere. Priests arrange marriages, boards certify births, physicians reshape bodies, statutes divide entrances, and schools develop one perceptual faculty while forbidding another. These interventions do not simply apply a completed natural design. They continually produce the social facts subsequently offered as proof of that design. In §7, Expediency joins Nature in approving Regularity, and legislation supplies the enforcement. The personifications stage a consensus among authorities which the narrator has himself made to agree. Women reveal the uneven distribution of necessity. Their inability to rise is named a decree, while men in favoured classes enjoy an almost automatic future improvement. Later, the admission that withholding education has reduced women's powers places historical policy alongside supposed bodily destiny. The account does not explicitly reconcile these explanations, leaving readers to examine the gap. Abbott's satire should not be flattened into a denial of natural laws. The geometry of angles and optical inference is essential to the narrative and often sound on its stated assumptions. The critical distinction is between such relations and the additional claim that a social order is therefore inevitable or just. The same prose can demonstrate an angle accurately and smuggle a moral conclusion through the demonstration. Reading requires attention to the point where *is* turns into *must be* or *ought to remain*. **The places.** - “By a Law of Nature with us” (§2) - “a male child shall have one more side than his father” (§3) - “How admirable is this Law of Compensation!” (§3) - “a Decree of Nature” (§4) - “Nature wills all Figures to have their sides equal” (§7) - “Expediency therefore concurs with Nature” (§7) **In this edition.** Notes 38–43 offer Platonic, hereditary and providential contexts; notes 75 and 79 clarify the regularity assumption and majority-interest argument. These comparisons are modern explanatory apparatus. The capitalised authorities and their argumentative work belong to Abbott's text, whether or not a particular external parallel is pursued. **See also.** [Birth and ascent](#entry-birth-ascent) (p. 19); [Regularity](#entry-regularity) (p. 97); [Irregularity](#entry-irregularity) (p. 65); [Attraction and climate](#entry-attraction-climate) (p. 18). ## Omnividence and the limits of godlike sight {#entry-omniscience} *omnividence; omnipresence and omniscience; all-seeing* **The word.** *Omnividence* means all-seeing; *omniscience* means all-knowing. The distinction matters here. In §18 the Square calls his new view of Flatland omnividence and assumes it makes him godlike. In §20 the dreamed Sphere ironically grants the self-enclosed Point omnipresence and omniscience. Neither episode establishes that increased dimensional access confers complete knowledge or moral divinity. **In the work.** Rising above Flatland makes the interiors of houses, bodies, mines and caverns visible to the Square. The experience overturns his earlier dependence on inference and gives him an intoxicating sense of privilege. His declaration that he has become as a God rests on a doctrine attributed to his country's wise men: seeing all things belongs to God alone. The new geometry therefore appears to justify a religious conclusion. The Sphere breaks the inference by introducing pickpockets and cut-throats. Any such inhabitant of Spaceland could see as much of Flatland as the Square now sees. The capacity belongs to a spatial situation, not to moral excellence. The guide's questions about justice, mercy, selfishness and love supply the needed test. More extensive perception has not by itself improved any of those qualities. The Square's answer exposes the social cost of his inherited theology. He assigns mercy and love to women and takes superior understanding to be the ground on which Circles outrank Straight Lines. The Sphere reports that many of the best in Spaceland value the affections more highly. Geometry here unsettles a moral hierarchy only because the teacher explicitly refuses to identify perceptual advantage with goodness. Dimensional superiority cannot do that ethical work automatically. The visible limits of the Sphere reinforce the warning. His own interior remains concealed from ordinary sight in Spaceland; his understanding falters at the Fourth Dimension; his treatment of his pupil includes anger and force. The book gives him extraordinary access without making him an omniscient, infallible or perfectly charitable being. Pointland provides the inverted joke. A creature whose whole world consists of itself can imagine itself all-present and all-knowing because it recognizes nothing beyond itself. Those grand attributes become trivial or empty when their supposed totality has been obtained by refusing the existence of others. The final prison narrative returns to the public doctrine of omnividence, now used in a paper proving that Providence has limited the dimensions. The reader has learned to ask what is being concealed by the claim that a local account exhausts the whole. **The places.** - **§18:** “omnividence” — The Square names the attribute his new vantage seems to confer - **§18:** “pick-pockets and cut-throats” — The guide separates visual power from goodness - **§18:** “does it make you more just” — A moral question interrupts geometrical exaltation - **§20:** “his omnipresence and omniscience” — Totality becomes a satire on self-enclosure - **§22:** “the attribute of omnividence is assigned to the Supreme alone” — Official speculation repeats the challenged doctrine **In this edition.** The notes explain the rare noun *omnividence* and distinguish it from omniscience. Their discussion of Abbott's theology supports a moral comparison, but the immediate argument already resides in the Sphere's explicit questions. **See also.** [Interior and exterior](#entry-interior-exterior) (p. 64) · [Sphere](#entry-sphere) (p. 107) · [Pointland](#entry-pointland) (p. 87) · [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) ## Painting {#entry-painting} *Painting; Art; painter's vocabulary: mauve, ultra-marine, gamboge, burnt umber, vermilion.* **The word.** *Painting* means applying colour to Flatland's objects and living bodies. The chapter's *Art* can denote both aesthetic creation and a learned practical skill, so its pleasures exist beside the intellectual arts threatened by its success. The *artist's pencil* is a painter's fine brush in the older sense, not necessarily the graphite implement a modern reader imagines. **In the work.** The narrator begins with an inventory of absent pictorial variety: prospects, landscapes, historical pieces, portraits, flowers, still life. These genres collapse into the line along which a Flatlander sees. His dissatisfaction establishes a specifically aesthetic deficiency after chapters devoted to how much information skilled observers can extract from that line. Scientific adequacy has not made existence beautiful. Chromatistes's invention answers the lack through decoration rather than dimensional escape. His painted house and household make ordinary social encounters more legible and attractive. Fashion spreads faster than conservative objections can resist it. The sequence takes art from an individual's practice to a shared environment: domestic meetings, churches, theatres, and military reviews. Painting is not confined to separate objects contemplated in repose; it enters the moving body and the collective arrangement of society. The military scene intensifies the double effect. Each class has a characteristic palette, and motion transforms the visible sequence. Rotating artillerymen, turning Isosceles, and mobile professional attendants produce rhythm as well as hue. The narrator's prose becomes correspondingly animated. *Dashing*, *flashing*, and *careering* make linguistic movement imitate the lost spectacle. His response shows that the pleasure of the period survives even in the supposedly more scientific language that succeeded it. The ruler who exchanges baton and crown for a brush crystallizes the possibility that beauty can redirect authority. The story is offered as something the spectacle renders credible, not as independently verified biography. Its force is emblematic: artistic attention can make command and rank seem relinquishable. That possibility sits awkwardly beside the Square's willingness to call the age immoral or anarchical. The account closes by connecting sensuous richness with poetry. Colour's period is a childhood that never becomes youth or maturity because it is forcibly ended. The developmental metaphor is therefore not a simple inevitable progression from primitive beauty to superior science. The art has been arrested. Aesthetic loss persists after political order is restored, and the narrator's elegiac language makes that cost audible even when his formal judgment favours suppression. Painting preserves the book's strongest evidence that the established system impoverishes its beneficiaries as well as its victims. **The places.** - §8: “æsthetically and artistically, very dull indeed” - §8: “first his house, then his slaves” - §8: “the glorious childhood of Art” - §8: “the artist’s pencil” - §8: “our finest poetry” **In this edition.** Notes 84 and 87 relate the language to the Aesthetic Movement and a historically mixed painter's palette, including contemporary mauve. Note 88 glosses *pencil*. Note 89 offers a period comparison for poetry as cultural youth. These are editorial contexts, not claims that Flatland's ancient chronology is Victorian chronology. **See also.** [Colour](#entry-colour) (p. 28); [Chromatistes](#entry-chromatistes) (p. 23); [History and revolution](#entry-history-revolution) (p. 60); [Science and institutions](#entry-science-institution) (p. 101). ## Philosophical comparisons and their limits {#entry-philosophical-comparisons} *Thematic heading: shadows; higher views; Thoughtland; Analogy* **The word.** This heading is an interpretive category, not an expression used by Abbott's narrator. It gathers places where the edition invites comparison with philosophical texts, especially Plato. A comparison asks how a passage becomes clearer beside another work; it does not by itself identify a source, a doctrine or a concealed code. **In the work.** Flatland's inhabitants are compared with shadows in §1, and the Square retrospectively describes his mind as opened to higher views. A reader of the cave passage in Plato's Republic can usefully ask what happens when a familiar field of appearances is mistaken for the whole of reality. The bodily difficulty of ascent and the returned witness's trouble with his community strengthen that question. But Flatland's figures are living hard bodies with luminous edges; the fiction does not simply reproduce the cave's chain of images and originals. The education scenes offer another productive comparison. The Grandson's numerical speculation outruns what the adults can picture, while the Square later cannot make his knowledge stay available. The edition places these episodes beside Platonic discussions of learning and unstable true opinion. The comparison sharpens the distinction between uttering a correct relation, understanding its grounds and retaining a conception. It does not establish that the Grandson possesses recollection of eternal Forms or that the Sphere supplies a theory of recollection. Thoughtland is particularly tempting. It might sound like a separate realm of pure intelligible objects. In the story, however, the word appears in an argument about dimensional extension and then as the Square's protective name for a treatise intended to evade the law. Its local rhetorical function cannot be replaced by a ready-made doctrine of a world of Forms. The supplied Afterword develops a further comparison with the Symposium. It sets Diotima’s graded initiation, culminating in a final object of contemplation, beside the Square’s wish to resist any dimensional boundary short of Infinity. The fruitful point is the difference: the desire to rise is shared as a pattern, while Flatland refuses to show a final summit. The edition reads that opening of the ladder as a lesson in modesty. This is a comparative interpretation, not an explicit claim made by the Square about Plato. The Afterword also reads Pointland beside Aristotle’s account of self-thinking thought. The Point identifies thinker, speaker and hearer with itself, interpreting an external voice as its own invention. The edition finds a comic inversion in placing such self-satisfaction at the lowest dimensional level rather than at a metaphysical summit. That proposed parody illuminates the episode’s refusal of otherness, but its deliberate dependence on Aristotle cannot be proved from a text that does not name him. Nor should a resemblance in philosophical language turn the Point into a complete account of Aristotle’s theology. The best use of a philosophical comparison is therefore interrogative. What makes an analogy persuasive? Why can a knowledgeable teacher fail to recognize the same reasoning in a pupil's extension? What links a change in standpoint with an ethical change, and what prevents that link from being automatic? These questions belong to Flatland's actual narrative even when the language in which a reader explores them comes from another philosophical tradition. **The places.** - **§ 1.** “very much like shadows” supplies an explicit image, not a named citation of Plato - **§ 1.** “higher views of things” joins changed position with changed understanding - **§ 19.** “Thoughtland” enters speculation about a further dimensional world - **§ 21.** “slipping away from me” names unstable possession of what was learned - **§ 22.** “Through Flatland to Thoughtland” is a strategic title within the narrative **In this edition.** The modern notes propose connections with the Republic, Symposium, Meno, Phaedrus and other works. The introduction and afterword also compare Emerson. This lexicon treats those as editorial comparisons unless the wording itself establishes an explicit allusion; it does not claim that Abbott adopts an entire Platonic or Emersonian system. **See also.** [Analogy](#entry-analogy) (p. 12) · [Initiation and mysteries](#entry-initiation-mysteries) (p. 62) · [Grandson](#entry-grandson) (p. 58) · [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) ## Pointland {#entry-pointland} *Pointland; the Abyss of No Dimensions; non-dimensional Gulf* **The word.** Pointland is the zero-dimensional world of a single Point. It has no length, breadth or height, and its inhabitant has no experience of plurality. The apparent contradiction between the names *Abyss* or *Gulf* and a realm without extension is expressive: the lowest condition in the dimensional sequence is represented as a depth, though it has no internal depth at all. **In the work.** Pointland appears within the Square's second dream. The dreamed Sphere takes him there after their waking quarrel and his return home. Its place in the narrative must be kept clear: the encounter belongs to a consoling and instructive vision, not to a further independently narrated bodily journey. It completes the range of the Square's imagined experience downwards while preparing renewed aspiration upwards. The Point is both inhabitant and universe. Because it can form no conception of another being, whatever occurs must be its own act. Its speech joins thinker, speaker, hearer, thought, word and hearing into an ecstatic self-description. The third-person pronoun *It* gives the performance an impersonal, absolute grandeur while, in the Sphere's explanation, betraying an infantile inability to distinguish self from world. The Square proposes rescue by revelation and immediately chooses insult as his instrument. He calls the being contemptible and tells it that its universe is a speck. The attempted correction fails in a distinctive way. The Point does not deny having heard; it absorbs the hostile address as one of its own thoughts and congratulates itself on the creativity that can generate an apparent objection. Contradiction becomes fresh confirmation of its completeness. This makes Pointland an unusually exact model of self-sealing conviction. The difficulty is not simply that the right evidence has yet to arrive. Any evidence of an other is reclassified as self-generated before it can count against the Point's account. The dreamed guide concludes that neither teacher can rescue it from self-satisfaction. The episode dramatizes a limit of address itself: communication requires at least the possibility that a voice might come from someone else. The lesson against complacency also reaches the dream's teachers. The waking Sphere had rejected a world beyond his own, and in this dream he now confesses that refusal as an error. The Square accepts the call to aspire, but his final claim that the higher constructions are intelligible even to women preserves an old hierarchy inside his new openness. Pointland is therefore not simply a contemptible creature securely beneath enlightened observers. Its total self-satisfaction magnifies a temptation repeatedly shown in figures who possess more dimensions and considerably more knowledge. **The places.** - **§20:** “He is himself his own World, his own Universe” — Existence and self are made coextensive - **§20:** “no cognizance even of the number Two” — Plurality is unavailable to thought - **§20:** “Thinker, Utterer, Hearer, Thought, Word, Audition” — The Point's vocabulary closes every communicative position upon itself - **§20:** “he accepts them as his own” — The attempted rebuttal is absorbed - **§20:** “nothing that you or I can do” — The dreamed guide states a limit to rescue **In this edition.** The notes offer scriptural and philosophical comparisons for the Point's formulas, carefully distinguishing resemblance from an explicit reference by Abbott. They do not identify Pointland with the Neoplatonic One, nor convert this dream encounter into waking evidence of a zero-dimensional population. **See also.** [Voice and selfhood](#entry-voice-selfhood) (p. 125) · [Dream and vision](#entry-dream-vision) (p. 43) · [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) · [Imagination and modesty](#entry-imagination-modesty) (p. 61) ## Polygon {#entry-polygon} *Polygon; Polygonal; many-sided; Nobility* **The word.** A polygon is a closed plane figure bounded by straight sides. Mathematically, triangles and squares are polygons too; socially, Flatland uses *Polygon* and *Polygonal* especially for the many-sided nobility. The restricted honorific sense should not be confused with the general geometrical definition. **In the work.** Section 3 makes the multiplication of sides into a ladder of titles. Nobility begins with the Hexagon and rises towards a figure that can pass as circular. The nearer a body comes to an outline without conspicuous corners, the higher its station. Refinement becomes a literal reduction in the prominence of angles, though the society continues to count and rank those angles minutely. This progression creates an epistemic irony. The more prestigious the figure, the harder it is to distinguish by touch from a slightly different neighbour. A Master of Arts may confuse ten and twelve sides; a Doctor of Science cannot confidently settle the difference between twenty and twenty-four. Rank multiplies distinctions beyond the powers of ordinary observation. Their social importance increases just as their physical visibility diminishes. Sight recognition gives the wealthy a way of inhabiting this complexity. A gathering of moving Polygons demands time, money and long practice. The Square can explain its theory but cannot always comport himself comfortably in the crowd. His embarrassment shows that numerical knowledge alone is not social fluency. The ability to move correctly among one's betters has become a form of cultivated knowledge possessed most securely by those born among them. The word *many-sided* ordinarily permits a metaphor of versatility or breadth. Flatland literalises the phrase, but does not guarantee that additional sides produce a generous understanding of other lives. Polygonal cultivation is closely attached to the protection of rank, and the education that perfects it can leave a failed pupil without a tolerable place in society. Complexity of figure is not equivalent to complexity of sympathy. The class also occupies an unstable position between professional respectability and sacred prestige. A Square looks upward to it; the highest Polygons seek the courtesy of circularity. This relative standing helps explain the restlessness of the hierarchy. Each stage can regard itself as superior while remaining anxious about a boundary above it. The lexicon's geometrical definition provides an essential check on that anxiety: the impressive title never ceases to name a figure made of straight sides. **The places.** - “the honourable title of Polygonal, or many-sided” (§3) - “a ten-sided with a twelve-sided Polygon” (§5) - “the delicate touch of the highly organized Polygon” (§5) - “a crowd of rotating Polygons of the higher classes” (§6) - “to comport oneself with perfect propriety in Polygonal society” (§6) **In this edition.** Note 37 relates the titles to aristocratic grades and the approach towards circularity; note 57 supplies the relevant angle values. Those editorial calculations explain why tactile discrimination becomes difficult. The political restriction of *Polygonal* to noble bodies is a feature of the narrative's usage rather than a rule of mathematics. **See also.** [Class and caste](#entry-class-caste) (p. 27); [Angle](#entry-angle) (p. 14); [Recognition by sight](#entry-recognition-sight) (p. 94); [Education and schools](#entry-education-schools) (p. 46). ## Prison and silence {#entry-prison-silence} *perpetual imprisonment; secret; destitute of converts; jailers* **The word.** Imprisonment is confinement by authority; silence in this narrative is both the imposed prevention of disclosure and the absence of an answering believer. The narrator's prison is therefore more than a conventional penalty for heresy. It is the place where institutional suppression and an already difficult failure of communication combine to erode his confidence. **In the work.** The brother, the Chief Clerk, is imprisoned before the narrator. Present at the Sphere's manifestation before the Council, the clerk is condemned under precedent so that the event will remain secret. The President couples regret with satisfaction that the man's life can be spared if he keeps silent. Courtesy does not mitigate the injustice; it makes administrative violence sound like a scrupulous accommodation. The narrator initially hopes to avoid this danger through a theoretical treatise, then through an account disguised as the adventures of a fictitious person. Both strategies recognize that ideas are judged by their political classification as well as their truth. His enthusiasm finally breaks the disguise at the Local Speculative Society, and arrest follows his explicit appeal for belief in the Third Dimension. The trial is orderly in form. He is allowed to narrate uninterrupted, and the President asks two precise questions about direction and representation. Yet the substitution of low-angle guards for more valuable policemen reveals that secrecy has been arranged in advance. The narrator interprets it as preparation to destroy the officials who hear him. The text reports his inference, not a separately witnessed execution after the trial, and the distinction should be maintained. The sentence appropriates the prisoner's own trust in Truth. If Truth intends him to teach the world, the President argues, it can arrange his release; the Council meanwhile keeps him confined. The reasoning converts a profession of faith into permission for officials to do nothing just. The promised absence of unnecessary discomfort similarly reduces injustice to the regulation of conditions inside a sentence never justified on its merits. Seven years later the brother's visits are the narrator's only companionship beyond his jailers, yet they provide no intellectual company. The brother has seen the circular manifestation and repeatedly hears the account, but does not believe in a Sphere. That failure cannot be explained solely by censorship: shared exposure to phenomena has not produced shared understanding. The memoir addresses an unknown future reader because the immediate human circle remains unconverted. Prison's final victory is incomplete, however, since the text that describes isolation also performs an effort to communicate beyond it. **The places.** - **§18:** “in accordance with precedent and for the sake of secrecy” — Imprisonment is normalized as administrative continuity - **§22:** “the cheaper for the more expensive victims” — The narrator reads the changing guard as a calculation in disposable lives - **§22:** “the Truth might be trusted” — The President turns the prisoner's principle against him - **§22:** “Seven years have elapsed” — The ending speaks from prolonged confinement - **§22:** “absolutely destitute of converts” — Punishment includes the absence of shared conviction **In this edition.** The apparatus notes tensions between the earlier class-specific decree and the narrator's eventual trial before the Council, rather than harmonizing them away. It also distinguishes what is said about the policemen from what the narrator infers. The prison memoir remains distinct from his earlier theoretical treatise. **See also.** [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) · [Memory and forgetting](#entry-memory-forgetting) (p. 76) · [Millennial visit](#entry-millennial-visit) (p. 78) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) ## Prometheus Paradise and the cost of knowledge {#entry-prometheus-paradise} *Prometheus; Paradise; Fall; Sphinx* **The word.** Prometheus is the explicitly named mythic bringer of fire, invoked as a model for carrying higher knowledge to others. Paradise and Fall place the Square's ejection from Space in a vocabulary of lost blessedness. The Sphinx names a riddle whose failure to be understood becomes destructive. These figures form a sequence of aspiration, punishment and threatened intelligibility rather than one seamless allegory. **In the work.** In §19 the Square introduces the analogy himself: like a second Prometheus, he will endure suffering if it helps arouse rebellion against limits imposed on dimensionality. He has just learned enough to question his teacher's limits. His desire therefore combines generosity, pride, intellectual consistency and exhilaration. The wish to become a benefactor cannot be separated from the possibility of conceit, but the Sphere's anger does not by itself establish that the wish is wrong. The narrator's retrospective Paradise and Fall language makes the return to Flatland sound like expulsion. Its cause remains disputed within his telling. He asks whether curiosity and ambition produced the catastrophe, yet calls it undeserved and judges the Sphere's refusal to be narrow. A reader should preserve this hesitation. The higher teacher's displeasure is a fact of the narrative; a just divine judgement is not thereby established. The later Prometheus comparison is more painful. Imprisonment makes the Square resemble the bound benefactor, but no countryman has received the benefit. He says that he brings down nothing. This does not necessarily deny that he saw something real. It measures the failure of communication: a revelation unavailable to another mind has not become the liberating gift its bearer intended. The memoir's hope for readers in Some Dimension tries to reach beyond that failure without reporting that it has already succeeded. The Sphinx then makes the problem internal. The formula Upward, not Northward has survived as words, but it no longer reliably opens the lost conception. The clue becomes a tormenting riddle. This final mythical image is less a public monument to heroism than an account of mental vulnerability: the witness may suffer from his inability to sustain the very knowledge for which he is punished. The sequence prevents a comfortable division between heroic rebels and ignorant persecutors. The regime's cruelty remains explicit, and the Square's ambition remains ethically mixed. Myth lets him tell both kinds of truth. His self-comparison can be grandiose while his isolation is real; his gift can fail socially without being proved empty; his return can resemble a Fall without ratifying the Sphere as an infallible god. **The places.** - **§ 19.** “a second Prometheus” names the narrator's wished-for role as benefactor - **§ 19.** “the Paradise” gives the higher world a retrospectively blessed character - **§ 19.** “my miserable Fall” names an ejection he immediately describes as undeserved - **§ 22.** “poor Flatland Prometheus” revisits the myth after the failure to gain converts - **§ 22.** “a soul-devouring Sphinx” turns a remembered clue into a riddle he cannot master **In this edition.** The notes explain the classical myths and compare the Paradise and Fall language with Genesis. Prometheus and Sphinx are explicit names in Abbott's narrative; the Genesis comparison is an explanatory identification of the surrounding religious imagery. None establishes that the Sphere is God or that the Square's punishment is deserved. **See also.** [Revelation and teaching](#entry-revelation-teaching) (p. 98) · [Fourth Dimension](#entry-fourth-dimension) (p. 57) · [Prison and silence](#entry-prison-silence) (p. 90) · [Memory and forgetting](#entry-memory-forgetting) (p. 76) · [Imagination and modesty](#entry-imagination-modesty) (p. 61) ## Providence and the language of necessity {#entry-providence} *Providence; Nature; Truth; must needs* **The word.** Providence names ordering purpose beyond individual designs. Nature and Truth sometimes take on similarly authoritative grammatical roles. Must needs is an emphatic expression of necessity; its archaic force can make a claim sound settled before its grounds have been examined. **In the work.** The Preface distinguishes the wisdom of human rulers from the larger working of Nature. The Circles' arrangements may pursue one end while producing a different and better outcome through their declining fertility. The claim belongs to the Square's reported interpretation of Flatland's history. It does not make every policy of natural selection or social elimination a beneficial act of Providence. Inside the memoir, necessity is often claimed by the powerful. The treatment of irregular bodies and the doctrine of configuration allow institutional decisions to be described as consequences of physical fact. The distance between an observed shape and a justified punishment is concealed when ought, must and nature are allowed to exchange places without argument. At the Local Speculative Society the language becomes overtly theological. A paper purports to demonstrate why Providence has limited dimensions to two. Its confidence is precisely what the Square's experience challenges. The problem is not simply the use of a religious noun: the speaker claims to know in advance the bounds of reality and the reason those bounds exist. The President's final response is more evasive. He agrees to trust the Truth to free the Square if freedom is required, while imposing the imprisonment that makes such vindication necessary. The form of piety converts an agent's responsibility into passive confidence in a higher agent. That maneuver resembles the narrator's earlier tendency to call humanly administered arrangements natural. The Preface's final ideal avoids both absolute negation and exact speculative certainty. Providence in the lexicon must consequently remain a word with contested uses: a reported hope about history, a premise of complacent closure, and a rhetorical means of declining responsibility. The novel does not provide one authoritative speech that settles all three. **The places.** - **Preface.** “the wisdom of Nature” is said to redirect human purposes - **Preface.** “It must needs be precisely thus” is one of the dogmatic positions rejected - **§ 22.** “Providence has limited the number of Dimensions to Two” summarizes a complacent society paper - **§ 22.** “the Truth might be trusted” lets the President turn trust into a defence of imprisonment **In this edition.** The notes compare the Preface with biblical providence and the President with an inversion of Gamaliel's counsel in Acts. They clarify rhetorical analogies. They do not authorize identifying the Circles' state with a single historical church or treating Abbott's fiction as a proof of a determinate providential scheme. **See also.** [Nature and law](#entry-nature-law) (p. 81) · [Configuration](#entry-configuration) (p. 31) · [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) · [Prison and silence](#entry-prison-silence) (p. 90) ## Recognition by sight {#entry-recognition-sight} *Sight Recognition; infer; discriminate; configuration; experimental observation* **The word.** *Sight Recognition* is the art of inferring a figure's configuration from changes of brightness along its visible line. To *recognise* here commonly means to identify rank or class, rather than to name an individual acquaintance. *Infer* marks the difference between evidence presented to the eye and the shape reconstructed from it. **In the work.** The technique initially seems to contradict §1, where every figure appears as a straight line. Section 6 resolves most of the difficulty by distinguishing outline from variations within it. Fog makes more distant portions dimmer. When the observer faces a vertex symmetrically, the rates at which its two sides fade disclose how sharply they recede. A Triangle and a Pentagon can therefore be distinguished without either becoming visible from above. The explanation is a lesson in mediated knowledge. Observers do not need direct access to a complete object in order to reason reliably about it. They do, however, require conditions, practice and assumptions. Regularity allows one angle to stand for the rest; a suitable orientation makes the elementary construction possible; experience handles cases where neither object nor observer stays still. The method is powerful because these conditions can often be met, not because sight has become omniscient. Social life makes the skill harder and more consequential than the diagram. A crowd contains figures rotating, advancing and retreating together. The observer must calculate while also avoiding collisions and showing due deference. Etiquette forbids the Square to touch his betters, so the easier method cannot settle his uncertainty. Those betters possess a practical understanding of his movements that he cannot reciprocate. The art distributes safety and embarrassment unequally. Training then turns this inequality into apparent character. Wealthy children take years to acquire the privileged faculty; poor children cannot defer useful work for so long. When the trained noble later surpasses the precocious tradesman, the narrator describes a nearly regenerative transformation. The educational investment recedes behind the spectacle of superiority it has produced. There is a further limitation in the very aim of recognition. Identifying a person's number of sides tells the observer how to behave towards his rank. It does not disclose intentions, generosity or truthfulness. The society continually treats success in the first kind of reading as authority in the second. Abbott's lucid optical account makes it possible to admire the faculty while questioning the excessive social and moral claims attached to it. **The places.** - “recognize one another by the sense of sight” (§6) - “infer with great exactness the configuration of the object observed” (§6) - “my view will lie as it were evenly between his two sides” (§6) - “after a very long training supplemented by constant experience” (§6) - “know all about your movements” (§6) - “an unattainable luxury” (§6) **In this edition.** Note 64 records a genuine fault in the narrator's retrospective quotation: §5 does not state the earlier qualification exactly as §6 claims. Note 67 explains the bisected-angle diagram. It is important to preserve both observations: a sound illustrative construction does not make the surrounding narrator infallible. **See also.** [Fog](#entry-fog) (p. 55); [Feeling and touch](#entry-feeling-touch) (p. 53); [Education and schools](#entry-education-schools) (p. 46); [Regularity](#entry-regularity) (p. 97). ## Reform and equality {#entry-reform-equality} *Reform; Innovation; equality; equal rights; majority.* **The word.** *Reform* promises beneficial alteration of an existing order; *Innovation* stresses novelty, which may be praised or feared. *Equality* has distinct uses in Flatland: equality of sides, equality of practical competence, and equality of political rights. The passage from one sense to another drives the Colour Bill debate and its counterargument. **In the work.** The lower classes first claim that colour recognition has made the traditional hierarchy less functionally relevant. They can solve practical problems without the aristocratic arts. The narrator grants increasing truth to this claim. The demand for equal rights therefore develops from altered conditions rather than appearing as a bare slogan. If a privilege's practical justification has diminished, law might be asked to change with it. Yet the reformers' programme contains several distinguishable measures: ending educational tribute, removing endowments, prohibiting exclusive arts, establishing equality, and requiring everyone to be painted. These should not be compressed into a single innocuous or sinister act. A programme can challenge oppression while also proposing coercive restrictions. Abbott gives readers enough detail to assess measures separately, even though the narrator's language encourages collective condemnation. The central political conflict is between equality and advancement. Artisans hope for admission to the Regular classes, either personally or through descendants. Pantocyclus argues that abolishing distinctions would deprive them of this expected honour. An unequal institution recruits support by making individual escape seem more valuable than collective change. The future possibility of being above someone else defeats a present alliance with those below. Majority rule receives a similarly interested description. The Chief Circle professes readiness to accept the Bill if the majority approves, while warning that the greatest number consists of the Criminal Classes. He makes numerical legitimacy and numerical menace alternately available according to the audience he addresses. The phrase *greatest number* does not guarantee the welfare of that number; it becomes a reason to fear their power and later to kill them. Women's support broadens the movement beyond male rank. The proposed colour code promises respect and access to knowledge otherwise reserved for Priests. The narrator caricatures those hopes as vanity and intrusion, but the very content of his fears reveals how much exclusion is being defended. Their eventual mobilization against the Bill does not erase the initial grievance. Reform in these chapters is consequently a field of competing interests, partial emancipations, and diverted expectations. Its defeat demonstrates how a hierarchy can preserve itself without answering every claim made against it. **The places.** - §9: “raised to an equality” - §9: “entitled to equal rights” - §10: “Reform or Innovation” - §10: “if it was approved by the majority” - §10: “That honourable ambition would now have to be sacrificed” **In this edition.** Modern note 93 supplies the 1884 British Reform context and observes women's exclusion from the franchise settlement. Note 100 discusses fears of government by the poorest majority. These comparisons illuminate the fictional debate without making its Bill a one-to-one transcription of a British statute. **See also.** [Universal Colour Bill](#entry-universal-colour-bill) (p. 119); [Isosceles rebels](#entry-isosceles-rebel) (p. 68); [Compensation](#entry-compensation) (p. 29); [Cunning and policy](#entry-cunning-policy) (p. 35). ## Regularity {#entry-regularity} *Regular; Regularity; Equality of Angles; regular construction* **The word.** In geometry a regular polygon has equal sides and equal angles. Flatland's social use is broader and more variable: a Woman must be straight, an Artisan or Soldier must have two equal sides, and other male classes must satisfy their prescribed equal-sided construction. *Regularity* names conformity to these norms and then acquires moral authority. **In the work.** Section 7 belatedly announces the assumption underlying the earlier descriptions. One can recognise a person from a single angle only if that part reliably represents the whole. The reader has already accepted demonstrations built upon this expectation. Disclosing it late mimics the way a society can treat its own classificatory premises as obvious until an excluded case forces them into view. Regularity provides convenience. Bodies can be anticipated, doorways used, crowds negotiated and gatherings planned. Abbott gives those needs enough plausibility that the argument cannot be dismissed as pure absurdity. The satire begins when convenience becomes a sufficient account of a person's right to exist, and when a standard useful for recognition is made a verdict on conduct. The word *equality* produces a particular irony. Equality within one figure sustains inequality between figures. The narrator can praise equal sides as the foundation of civilisation while accepting hereditary subordination and the starvation of the lowest classes. The geometry has no democratic implication unless an interpreter supplies one; the society instead uses internal sameness to stabilise external rank. Certification reveals that the norm is institutional as well as bodily. The newborn Equilateral is examined by a board, the ambitious lineage requires approved marriages, and deviations receive medical intervention. At several points regularity can be produced or acknowledged through official action. It is not simply a self-announcing essence. The state has a continuing role in deciding which apparent exceptions can be repaired, incorporated or removed. The different standard for Isosceles makes the universal language especially suspect. They fail the all-sides-equal test used to diminish their humanity in §3, yet satisfy a two-sides-equal rule in §7. This is not an argument that every geometrical regularity is arbitrary. It is evidence that the narrator's application of the prestigious term responds to the needs of an existing taxonomy. A reader should therefore distinguish three propositions: regular figures support efficient inference; a society may reasonably manage collision risks; and bodily nonconformity proves moral guilt. The first is the narrative's mathematical premise, the second concerns practical arrangements, and the third is the unjustified transformation on which persecution depends. The text's repeated *therefore* cannot make them equivalent. **The places.** - “every human being in Flatland is a Regular Figure” (§7) - “of regular construction” (§7) - “Regularity, or Equality of Angles” (§7) - “the whole of the social life in Flatland” (§7) - “Regularity of conformation” (§7) - “the fixed margin of deviation” (§7) **In this edition.** Notes 75–76 distinguish the mathematical definition and the narrative's use of a single angle as evidence. The claim that equal sides alone guarantee every angle is not adopted here as a general theorem about arbitrary polygons. The article follows the fiction's stipulated regular classes while preserving the mathematical qualification supplied by the edition. **See also.** [Irregularity](#entry-irregularity) (p. 65); [Angle](#entry-angle) (p. 14); [Equilateral](#entry-equilateral) (p. 47); [Nature and law](#entry-nature-law) (p. 81). ## Revelation and teaching {#entry-revelation-teaching} *reveal; Teacher; Pupil; Revelation; Gospel of Three Dimensions* **The word.** Revelation discloses what was hidden; teaching seeks to make knowledge intelligible and usable by another. The romance repeatedly brings them together without treating them as identical. A person may undergo a startling disclosure and still lack a way to understand it, retain it, demonstrate it or transmit it. The Sphere's mission and the Square's later teaching expose those separate difficulties. **In the work.** The Sphere initially relies on a familiar sequence of instructional means: assertion, questions, analogy and demonstration. His pupil's mathematical competence lets him answer numerical questions while failing to conceive the result. His class habits make a perfectly regular unfamiliar figure seem criminal. His fear turns evidence into apparent sorcery. Effective instruction must address the pupil's categories and learned perception, not merely supply more information. The visitor nevertheless resorts to force. He removes a tablet from a locked cupboard, touches the Square's interior without allowing time for objection, and finally lifts him out of the plane. The newly exposed world is called Knowledge, but first feels like madness or Hell. Disclosure is painful before it is clarifying. Only subsequent demonstrations with cards, touch, light and shadow make the Cube comprehensible. Authority itself then obstructs the lesson. The pupil follows the method beyond the teacher's accepted limit and asks about four dimensions. Instead of sustaining inquiry, the Sphere silences him and casts him down. The later admission of error belongs to the Square's dream. Abbott thereby denies readers an uncomplicated narrative of a wise instructor gradually producing a perfected disciple. The returned traveller repeats some of the same problems. He briefly resolves to teach women and soldiers, then seeks the safe and promising grandson. The child has already been trained to revere the Circles, and the public law interrupts the private lesson. The teacher loses patience, cannot indicate the new direction and is abandoned by his laughing pupil. His earlier rebuke of the boy now returns as a failure to recover the inquiry he once suppressed. Writing offers another route, but Flatland's line-like tablets frustrate diagrams. The theoretical treatise *Through Flatland to Thoughtland* is an attempt to teach while evading the prohibition; the prison memoir later attempts testimony across dimensions. These are different works with different immediate strategies. Neither achieves a narrated conversion within Flatland. The romance nevertheless reaches its own Spaceland reader through the failure it recounts. Teaching is placed between the necessity of imagining beyond present experience and the duty to recognize how little a formula, an authority or an overwhelming spectacle guarantees understanding. **The places.** - **§17:** “a fit apostle” — The pupil is selected as a future transmitter - **§18:** “open your eye once again and try to look steadily” — Disclosure requires perceptual adjustment - **§19:** “light and shade and perspective” — Seeing a new world must be learned - **§21:** “my first attempt to convert a pupil” — The grandson's failure tests the new teacher - **§22:** “no diagrams but Lines” — The medium limits what an explanation can show **In this edition.** The notes describe both religious vocabulary and practical geometrical instruction. Their parallels with classical teaching scenes should not collapse the Sphere into an infallible philosopher or the Square into a wholly emancipated disciple. The distinct treatise and memoir remain essential to the narrative's account of transmission. **See also.** [Grandson](#entry-grandson) (p. 58) · [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) · [Sphere](#entry-sphere) (p. 107) · [Diagrams and the position of the reader](#entry-diagrams) (p. 38) ## Romance satire and the refusal of a complete code {#entry-romance-satire} *Romance; Historians; suggestive; amusing* **The word.** Romance announces an imaginative narrative involving marvels rather than a modern romantic love story. Satire is the critical literary operation by which apparently sober description makes prejudice, cruelty and complacency visible. The latter is this lexicon's genre term, not a claim that the narrator openly confesses to mocking his own institutions. **In the work.** Part I borrows the manners of a descriptive treatise: climate, buildings, population, recognition, history and governing doctrine arrive in orderly sequence. This organization produces an air of neutral expertise. Yet the physical rules repeatedly embody distinctions familiar from the reader's society. What can sound like the practical problem of sharp angles becomes the justification for exclusion; what can sound like improving a class becomes the removal of its capable members. The most incisive passages let the narrator's approval disclose what is wrong. A report of prudent policy can reveal the deliberate use of hope to prevent collective resistance. The language of being consumed can convert the death of school specimens into an administrative expense. Satire works in the gap between the description offered and the judgement a reader can form from it. Part II tests the descriptive authority established in Part I. The observer who classified others confidently becomes a provincial pupil unable to understand a teacher. The teacher then reveals the same limitation at the next boundary. Neither narratorial rank nor dimensional rank secures a final vantage immune to irony. The Preface expressly resists a demand that every detail correspond to a Spaceland detail. This prevents two opposite reductions. Flatland is not merely an elementary geometry exercise with an incidental social setting. Nor must each side, door and colour encode a single Victorian event or person. Its structures can gather several analogies, some stronger than others, while retaining their literal role in the fictional world. The romance also admits suffering that a joke cannot dissolve. The ending offers no successful public conversion, restored family happiness or official recognition. Its appeal to readers beyond the narrator's own dimension is the possibility left open by the book's existence. Amusement and suggestion are not incompatible with that severe result; the repeated joke about limited knowledge becomes painful when the cost of enforcing the limit is imprisonment. **The places.** - **Title Page.** “A Romance of Many Dimensions” joins imaginative narrative and mathematical plurality - **Preface.** “writing as a Historian” explains and partly questions the narrator's posture - **Preface.** “suggestive, as well as amusing” describes the work's hoped-for effect - **Preface.** “every minute detail” marks the warning against a total correspondence key - **§ 22.** “imaginary experiences of a fictitious person” makes fiction a temporary protective disguise **In this edition.** The modern apparatus offers specific Victorian contexts for institutions, phrases and reforms. Such contexts are helpful when properly attributed. The lexicon does not turn every proposed resemblance into a documented intention or flatten the fiction into the historical information supplied by its editor. **See also.** [A Square and the voice of the memoir](#entry-a-square) (p. 11) · [Reform and equality](#entry-reform-equality) (p. 95) · [Suppression and massacre](#entry-suppression-massacre) (p. 110) · [The Editor and the revised Preface](#entry-editor-preface) (p. 45) ## Science and institutions {#entry-science-institution} *Thematic heading.* Attested vocabulary: *Science; intellectual Arts; University; endowments; esoteric classes*. **The word.** *Science* here denotes organized knowledge and intellectual method; the *Arts* include learned practices such as recognition, not only fine art. *Endowments* are supporting funds or property assigned to institutions and studies. *Esoteric* describes teaching reserved for an inner group. Together these words locate knowledge in schools, offices, resources, and controlled access. **In the work.** The narrator attributes intellectual decline during the age of colour to disuse. Sight recognition, geometry, statics, and kinetics lose practical urgency; feeling declines in elementary schools. The causal argument deserves attention independently of its politics: a convenient technology can make demanding skills less frequently practised. But the claim of decline is voiced by someone whose rank has depended on those very skills. What counts as intellectual loss may also be the erosion of a professional distinction. The school system's bodies complicate any innocent account of its preservation. Instruction has relied on low Isosceles supplied as specimens, confined for handling and exhausted by the practice. The abolition of their tribute is described as an immunity that permits excessive numbers. Institutional continuity is being valued above the lives consumed in maintaining it. A defence of learning becomes a defence of an exploitative arrangement, though those need not logically be the same defence. The Circles preserve sight recognition in their colourless homes while others abandon it. Their private environment reproduces intellectual advantage across generations. The Colour Bill would disrupt this domestic training, which is one reason the narrator calls it a threat to the hierarchy. Expertise here is neither wholly fraudulent nor neutrally distributed. A real skill is cultivated through selective conditions and used to support a larger claim of inherent superiority. After suppression the relationship reverses. Colour, condemned as corrupting for the public, is reportedly permitted in the highest university classes to illustrate advanced mathematics. The Square has never attended and marks his account as hearsay. This qualification is important: the reader learns of a probable restricted curriculum, not a directly observed lesson. The irony does not require certainty about its contents. The regime's explicit exemptions already show that authorized access determines whether the same material is knowledge or offence. Part II extends the problem from unequal training to blocked discovery. The Council can dispense with mathematical examination when suppressing dimensional claims, and the narrator's final hearing demands demonstrations he cannot supply in the permitted medium. Scientific forms remain in use while the institutional conditions for a fair test have disappeared. The danger is not inquiry itself but the ownership of its instruments, standards, and audience. **The places.** - §9: “the intellectual Arts were fast decaying” - §9: “abolition of all endowments” - §9: “their pure and colourless homes” - §10: “the very highest and most esoteric classes” - §10: “I can only speak from hearsay” **In this edition.** Note 92 explains the Victorian institutional force of endowments; note 103 glosses *esoteric*. The modern note's contextual comparisons should not erase the narrator's evidentiary limitation. The university's exact secret practice remains unobserved by him. **See also.** [Circles and Priests](#entry-circle-priest) (p. 24); [Colour](#entry-colour) (p. 28); [Law and sanction](#entry-law-sanction) (p. 72); [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120). ## Scripture gospel and prophetic speech {#entry-scriptural-language} *Gospel; Revelation; evangelize; prophets; inspired* **The word.** Gospel is good news proclaimed to others, with an unmistakable Christian resonance. Revelation is a disclosure that exceeds the recipient's previous means of knowing. Evangelize describes spreading that news. The capitalised Gospel of Three Dimensions makes religious language carry a geometrical content without making the two vocabularies identical. **In the work.** The Square's transformed mission borrows the scope and urgency of apostolic proclamation. In §21 he wants to include those whom his society excludes, Women and Soldiers. The aspiration matters because the narrator has helped reproduce their exclusion. It also remains a claim tested by conduct: he initially conceals the truth from his Wife and selects a male mathematical pupil. A universal gospel must pass through a speaker whose educational habits are still selective. The institutions against him borrow the same elevated register. The new teaching is treated as both sedition and heresy; disputed knowledge becomes a danger to state and sacred order together. At the end the President appropriates the Square's trust in Truth to justify a sentence. Religious language is not reserved for the imprisoned witness and cannot itself settle who speaks rightly. The analogy with prophetic rejection is also unstable. The Square invokes an ancient Circle's saying about inspired persons being taken for mad. His brother has seen the extraordinary manifestation yet remains unconvinced. An external sign does not mechanically produce understanding, and merely repeating testimony does not overcome the conceptual limit. These uses make the narrative available as a parable of belief, resistance and the limits of miraculous evidence. But it would exceed the text to identify every character with a biblical person or assign the Sphere uncomplicated divine authority. The Sphere's own arrogance and anger interrupt that model. The book's spiritual register is strongest where it questions what a revelation enables a person to understand or become, rather than where it offers a code for matching figures to sacred originals. **The places.** - **§ 21.** “the Gospel of Three Dimensions” names the proposed message - **§ 21.** “seditious heresy” combines offences against political and religious order - **§ 22.** “prophets and inspired people” appear in the narrator's defence of suspect visionaries - **§ 22.** “evangelize the world” is repeated within the President's conditional permission - **§ 22.** “absolutely destitute of converts” measures the mission's failure in communal terms **In this edition.** The notes identify or compare language from the Gospels, Acts and Pauline letters. The primary text sometimes provides clear religious terms without an exact biblical quotation; the lexicon preserves the distinction between a quoted phrase, a strong echo and an editor's thematic comparison. **See also.** [Revelation and teaching](#entry-revelation-teaching) (p. 98) · [Women](#entry-women) (p. 128) · [Providence and the language of necessity](#entry-providence) (p. 93) · [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) ## Shakespeare epigraphs and the changing world {#entry-shakespeare-epigraphs} *square my talk; broad and wide; brave new worlds; baseless fabric* **The word.** An epigraph places borrowed words at a threshold to direct expectation. The Shakespearean phrases in Flatland carry ordinary and dimensional meanings at once: square can mean shape one's speech, broad and wide can name extent or possibility, and world can mean a whole reality that later proves only a locality. **In the work.** The title-page line about squaring one's talk makes language answer to the narrator's body. Its adverb franticly also introduces the possibility that extraordinary speech will be treated as madness. The phrase does not merely label a geometrical character with a convenient pun; it asks what kind of speech can be framed by a figure missing a dimension. Part I's counsel to be patient because the world is broad and wide fits a plane literally. As an epigraph it also asks a confined mind to imagine more than its present enclosure. The borrowed line's consolatory force becomes ironic when Flatland's rulers demand that the world remain exactly as their doctrine describes it. Part II's brave new worlds opens a narrative of wonder. By its ending, the same larger field has become difficult to hold in memory and dangerous to proclaim. The closing reference to the baseless fabric of a dream returns Shakespearean language to the question of whether appearances and remembered visions have secure substance. The allusions frame a passage from astonishing enlargement to threatened confidence without simply cancelling the enlargement. The Preface makes another kind of alteration. One touch of Nature makes all worlds akin extends a familiar Shakespearean saying across dimensions. What unites the worlds is their liability to prejudice and persecution, not just cheerful human fellow-feeling. The altered plural punctures the reader's claim to exemption. Borrowed authority therefore cuts both ways. Shakespeare lends recognisable language to a strange world, while the dimensional setting changes what the familiar words can mean. The reader is asked to hear a phrase again rather than assume that recognition of its source has completed interpretation. **The places.** - **Title Page.** “how franticly I square my talk” joins speech, shape and apparent derangement - **Part I epigraph.** “the world is broad and wide” describes planar extent while inviting patience - **Part II epigraph.** “brave new worlds” supplies a language of wonder - **Preface.** “all worlds akin” alters a familiar line to include shared dimensional prejudice - **§ 22.** “the baseless fabric of a dream” gives the ending a Shakespearean dissolution **In this edition.** The notes identify the relevant passages in Titus Andronicus, Romeo and Juliet, The Tempest and Troilus and Cressida. They also report the Hamlet motto on the first edition's wrapper. That wrapper motto is edition history, not an additional epigraph printed in the supplied primary-text sequence. **See also.** [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99) · [A Square and the voice of the memoir](#entry-a-square) (p. 11) · [Dream and vision](#entry-dream-vision) (p. 43) · [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120) ## Solid humanity and superior races {#entry-solid-superior-races} *Solid Humanity; Superior Races; inferior; superior* **The word.** Solid has a geometrical sense, possessing three dimensions, and ordinary associations of substantiality, firmness and respectability. Superior can describe relative position, rank or alleged excellence. The book repeatedly makes a reader ask which of these senses has been smuggled into another. **In the work.** The dedication flatters the superior inhabitants of Space while asking them to develop modesty. The apparent contradiction is purposeful. A greater number of dimensions provides capabilities; it does not by itself provide a superior moral character. The Sphere's ability to inspect enclosed bodies is an especially sharp test because the Square initially associates such vision with divinity. Flatland's internal hierarchy repeats the slippage in another form. A greater number of sides is treated as evidence of higher intelligence, nobility and entitlement. Even where the fiction stipulates relations between bodily form and ability, the institutions interpret those relations to justify privileges, coercion and the disposal of less valued lives. A geometrical scale does not remove the need to judge how it is used. The Sphere reverses the Square's familiar position. The gentleman who regards lower classes from above becomes a supposedly ignorant creature to be instructed, insulted or moved without consent. This reversal is not a simple argument that all differences are unreal. The Sphere really can do things the Square cannot. It shows instead how a real difference in capacity can encourage an unjustified claim to total superiority. The comparison extends to readers. We effortlessly understand some matters that puzzle the Square and may enjoy his bewilderment. The dedication asks whether that enjoyment reproduces the conduct we condemn in Flatland. The possibility of a still higher-dimensional observer makes our apparent summit provisional. The racial phrase in the dedication belongs to a historical rhetoric of ranking human populations, which the modern edition discusses. A responsible reading can identify that rhetoric without inventing a fixed code in which every geometrical class equals one earthly population. The satire exposes the ease with which material difference becomes a story about who deserves power. **The places.** - **Dedication.** “Superior Races” flatters the addressees in the language of collective rank - **Dedication.** “Solid Humanity” turns a physical property into a social-sounding compliment - **§ 3.** “development and nobility” are placed together on a single rising scale - **§ 18.** “omnividence” becomes the disputed basis for a claim to divinity - **§ 19.** “There is no such land” reveals the higher being's own boundary **In this edition.** The introduction reads the dedication beside Victorian imperial and racial hierarchies. That is useful historical framing. The lexicon attributes the hierarchy-making language to its particular speaker and context rather than naturalising the book's ranks or presenting them as an endorsed classification of people. **See also.** [Class and caste](#entry-class-caste) (p. 27) · [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) · [Sphere](#entry-sphere) (p. 107) · [Imagination and modesty](#entry-imagination-modesty) (p. 61) ## Space and Spaceland {#entry-space-spaceland} *Space; true Space; Spaceland; Land of Three Dimensions* **The word.** *Space* can name extension generally or the particular dimensional world a speaker inhabits. *Spaceland* specifies the three-dimensional region familiar to the book's addressed readers and revealed to its two-dimensional narrator. Much of the dialogue depends on speakers failing to distinguish their own accessible Space from all the Space that might exist. **In the work.** The King of Lineland equates Space with Length. Asked to leave his Line, he hears a proposal to leave the world and Space itself. The Square answers that true Space is a Plane. His correction is accurate only as a correction of the King's exclusion of a second dimension; as an exhaustive account it repeats the King's error. The reader's position makes that limitation visible before the Square recognizes it. When the Sphere announces that he comes from Space, the Square reasonably observes that both speakers seem already to be there. The resulting quarrel over definition cannot be settled by renaming the dimensions, since Flatland has four terms for two extents. The visitor eventually offers the more explicit Land of Three Dimensions. What must be learned is a new spatial relation, not merely deference to the speaker's preferred noun. Spaceland initially looks less like a stable place than a disturbance of identity and perception. The Square sees Space that is not Space and himself as both himself and not himself. Familiar predicates fail at the moment of arrival. After adjustment, the world becomes the place from which Flatland's interiors are visible and where Solids can be encountered by sight and touch. That enlargement does not give the traveller independent movement or exhaustive access. He is dependent on the Sphere, cannot reach his distressed Wife or imprisoned brother, and cannot see the guide's organs. Nor does he explore a complete Spaceland society. The guide mentions ordinary criminals and differences of opinion, but the narrated itinerary primarily serves the dimensional lesson. Claims about the region's universal moral or political superiority would exceed what is shown. The subsequent request for a more spacious Space deliberately destabilizes the new apparent totality. The Square now applies the earlier correction to his guide's home. The Sphere refuses, and the once-opened world becomes another possible enclosure. At the end the memoir seeks humanity in Some Dimension rather than specifying a single guaranteed destination. *Space* has been transformed from a settled possession into a word that demands awareness of the speaker's standpoint and the unknown beyond it. **The places.** - **§14:** “out of the World? Out of Space?” — The King treats his accessible region as exhaustive - **§14:** “True Space is a Plane” — The Square repeats the form of the error - **§16:** “From Space, from Space, Sir: whence else?” — The guide's first announcement assumes what must be taught - **§18:** “Space that was not Space” — Arrival disrupts the traveller's categories - **§19:** “some yet more spacious Space” — The pupil reopens the question beyond three dimensions **In this edition.** The notes explain the changing dimensional senses of *Space* and compare the historical mathematical thought-experiments surrounding the romance. They do not treat *Spaceland* as a synonym for a Christian heaven or a proof that every higher region is morally superior. **See also.** [Dimension](#entry-dimension) (p. 39) · [Lineland](#entry-lineland) (p. 74) · [Fourth Dimension](#entry-fourth-dimension) (p. 57) · [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) ## Sphere {#entry-sphere} *Stranger; Visitor; Sphere; Guide; Teacher* **The word.** A Sphere is the three-dimensional body whose plane sections are circles. Abbott's visitor is a speaking, moving inhabitant of Spaceland who initially manifests to Flatland as such a circular section. His changing designations mark the Square's changing relation to him: an intruder becomes a supposed Circle, then an instructor, guide and object of reverence, and finally an angry authority. **In the work.** The entrance mobilizes both social and supernatural expectations. The Wife thinks a Woman has entered through a narrow aperture; touch then makes her defer to what appears a perfect Circle. The Square fears an impostor able to imitate a Circle's voice. The actual explanation escapes both readings: the visitor is neither a Flatland Woman nor one of its priests, though his section allows him to be mistaken for the latter. He possesses genuine knowledge unavailable to the household. From above the plane he can inspect its contents, remove an account tablet without opening the cupboard and touch the Square's interior. Those powers are dimensional, not evidence of complete knowledge or sanctity. His own rebuke of the narrator's claim to godhood makes this explicit: criminals in his country possess the same ordinary visual access to Flatland. As a teacher he is inventive but impatient. He tries definition, remembered analogy, sectional demonstration and numerical patterns, then treats the failure to understand as a refusal to listen to reason. His increasingly invasive proofs culminate in forced transportation. Once in Spaceland he teaches more patiently, using construction, touch and changing light. The portrait allows both real instruction and ethically troubling coercion to belong to the same figure. His limit emerges when the Square asks about a fourth dimension. The guide calls the idea inconceivable and resists the analogy he himself has taught. The contradiction does not cancel his true account of three-dimensional space, but it prevents his higher position from functioning as universal authority. He knows more than the Square in one domain and still reproduces the habit of treating his own experience as final. The ensuing punishment also tests the disciple's reverence. The Sphere's anger and the Square's inability to move independently expose the asymmetry beneath their apparent companionship. The teacher controls the route, the pace and the return. His later placability and confession of error occur only within the narrator's dream; no verified waking return supplies a reconciliation. The Sphere therefore remains an unresolved teacher: indispensable to an enlargement of knowledge, capable of moral insight, and implicated in the same closure and domination the enlargement ought to challenge. **The places.** - **§15:** “many Circles in one” — The visitor states his identity in terms Flatland can partially grasp - **§16:** “a Circle of thirteen inches in diameter” — The largest section gives a concrete scale - **§17:** “the last resource of civilization” — The instructor names his turn towards force - **§18:** “Then how does it make you more divine?” — He rejects the identification of visual power with goodness - **§19:** “The very idea of it is utterly inconceivable” — His own dimensional boundary becomes absolute - **§20:** “he was not too proud to acknowledge his error” — Reconciliation is narrated within a dream **In this edition.** Its notes distinguish a Sphere's surface from his concealed organs and changing sections from physical shrinkage. They also locate the later repentance in the dream frame. Religious language belongs to the relation staged between characters and does not warrant declaring the Sphere God or an infallible spokesman for Abbott. **See also.** [Movement and section](#entry-movement-section) (p. 79) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) · [Fourth Dimension](#entry-fourth-dimension) (p. 57) · [Touch and bodily proof](#entry-touch-belly) (p. 118) ## Straight line {#entry-line-straight} *straight Line; Straight Lines; line; needle* **The word.** A *straight line* is both what every Flatland figure looks like from within the plane and what a Woman is said to be. These senses must be separated: an appearance shared by all shapes is not proof that all shapes have the same constitution. Capitalisation often marks the social class, but context remains decisive. **In the work.** Section 1 gives the straight line a levelling function. A Triangle, Square, Pentagon or Circle presents the same basic kind of visible object. The inhabitants cannot inspect one another as the reader inspects the diagrams. Their elaborate hierarchy consequently requires indirect techniques to recover distinctions that immediate appearance does not disclose. Section 3 then interrupts the account with the short declaration that Women are Straight Lines. Its bare syntax offers a total definition. Men receive differentiated bodies, professions and prospects; women receive one unchanging geometrical identity. The shared appearance which initially made all figures epistemically comparable now names a sex placed outside the ascending series of male development. The needle experiment in §4 makes orientation crucial. A line viewed from the side shows length; viewed end-on it approaches a point. The woman can become nearly invisible without leaving the plane or acquiring supernatural power. The nickname of an invisible cap imports the language of marvels into an elementary optical fact. It also presents a woman's ordinary body as a source of alarming strategic advantage. The consequences are political and domestic. A point can pierce; a line cannot bend around or turn within every enclosure. Law requires audible warnings and visible movement, while apartments are designed to prevent rotation. What begins as a definition becomes a programme for organising another person's behaviour. The body supplies genuine constraints, but the narrator's chosen remedies distribute freedom unequally. A revealing uncertainty occurs when the Square sees his triangular father side-on and cannot immediately tell whether he is looking at a Woman. The moment does not dissolve bodily difference. It does show that the apparently self-evident sex-classification must be recovered through positioning and inference. The father's recognisable masculinity is not simply present in the visible line. Section 16 subsequently corrects the popular nomenclature: Women are scientifically thin Parallelograms, with measurable breadth within the plane. This second dimension must not be confused with the unrecognised height which the revised Preface attributes to all Flatlanders. The educated Square knows that a familiar social name is not a complete anatomical description, yet continues to reason through it. Thus the straight line carries the romance's larger caution about appearances in miniature. One visible form can belong to different underlying figures; one named figure can be burdened with many social meanings. A reader must distinguish geometry, perception and judgement even when the prose confidently moves from one to another. **The places.** - “Nothing was visible, nor could be visible, to us, except straight Lines” (§1) - “Our Women are Straight Lines” (§3) - “a Woman is a needle” (§4) - “nothing but a highly lustrous point” (§4) - “a Straight Line, or, in other words, a Woman” (§6) - “a very thin Parallelogram” (§16) **In this edition.** Notes 25 and 33 explain the optical and social senses; notes 44–45 discuss the needle and invisibility imagery. Note 159 explains the later Parallelogram correction. These are editorial guides to distinctions in the main text. Capitalisation is useful evidence but not a perfectly consistent logical notation. **See also.** [Eye and the visible line](#entry-eye-retina) (p. 50); [Women](#entry-women) (p. 128); [Recognition by sight](#entry-recognition-sight) (p. 94); [Regularity](#entry-regularity) (p. 97). ## Suppression and massacre {#entry-suppression-massacre} *Suppression; carnage; decimated; consumed; purged; Order.* **The word.** *Suppression* presents force as the putting down of a disturbance. *Carnage* names slaughter more directly. *Decimated* here carries the punitive sense of killing one in ten, according to the edition's annotation; *consumed* serves as Flatland's recurring euphemism for killing. *Purged* transfers a vocabulary of cleansing to the removal of people. **In the work.** §10 offers a sequence of operations rather than a spontaneous riot. Pantocyclus's apparent concession brings the opposition leader into a guarded position. His speech changes or divides the audience's commitments. A preconcerted signal then launches the attack: convicts transfix Chromatistes, women move invisibly backwards into the soldiers, and guards seal every exit. The subsequent panic occurs inside a trap prepared by the ruling class. The narrator partially acknowledges what the event is when he corrects “battle” to “carnage.” A battle would suggest two armed forces meeting with some possibility of mutual action. Here surprise, invisibility, confinement, and leaderlessness remove that possibility. The final deaths by the victims' own angles do not absolve the planners. The account's effort to attribute the catastrophe to habitual lower-class panic sits beside an unusually clear description of how the fatal conditions were created. The number of dead makes the abstraction of order measurable but not humane. “Seven score thousand” means 140,000. Earlier 120,000 Isosceles had hissed the ruler. These counts need not refer to identical populations, but the text does not explain the difference. A responsible reading records the discrepancy rather than inventing either an error or a solution. The more important certainty is the narratorial verdict: human fragments become evidence of a political triumph. The killing continues after the hall is silent. Artisans suffer decimation; suspects are condemned without exact measurement; homes undergo a year of inspections; towns and villages are purged of an alleged excess. The aftermath turns one tactical victory into systematic population control. The supposed restoration of balance depends on selecting whose continued existence is dispensable. The final manufactory returns this extraordinary violence to routine. Workmen who make colour are killed annually to preserve the secret. This coda prevents readers from imagining that exceptional revolutionary danger alone explains the regime's cruelty. Once monopoly has been restored, scheduled killing maintains it. The narrator's calm presentation is a moral fact of the satire: familiar administration can make repeated murder seem less noticeable than a spectacular crowd death. Reading the euphemisms literally is necessary to recover the persons concealed by the language of governance. **The places.** - §10: “the preconcerted signal for action” - §10: “The battle, or rather carnage” - §10: “seven score thousand” - §10: “spared but decimated” - §10: “systematically purged” - §10: “the Workmen are annually consumed” **In this edition.** Notes 101, 102, and 104 explain the numeral, decimation, and the manufactory euphemism. Note 102 compares the language with nineteenth-century counter-revolution. The comparison is the modern editor's; the organized killings and the narrator's approval are in Abbott's text. **See also.** [Chromatic Sedition](#entry-chromatic-sedition) (p. 21); [Cunning and policy](#entry-cunning-policy) (p. 35); [Compensation](#entry-compensation) (p. 29); [Law and sanction](#entry-law-sanction) (p. 72). ## Surgery and extermination {#entry-surgery-extermination} *compression; expansion; trepannings; colligations; consumed; extinguished* **The word.** The heading joins bodily correction to the killing that follows when correction is refused or judged impossible. *Trepanning* means drilling an opening in the skull; *colligation* is binding together. *Consumed* and *extinguished* are euphemistic terms for putting people to death. Their apparent softness does not change the acts they describe. **In the work.** Medical intervention first assists the suppression of rebellion. Selected leaders can be compressed or expanded into Regularity and admitted to privileged classes. Others enter State Hospitals in the hope of eventual promotion, only to remain confined for life. Healing, reward and political neutralisation occupy the same institutional space. The medical vocabulary hides no entirely separate purpose: reshaping a person changes the collective danger he represents. The school specimens undergo another conversion of bodies into public utility. They are kept immobilised, used to train children and in the preferred system allowed to starve. The narrator considers the reduction of the Isosceles population an additional benefit. Here no cure is offered, but the same administrative grammar prevails: the state's desired outcome organises the account, while the victim's experience scarcely enters it. In §6, extermination reaches beyond the poor. Failed noble students may be imprisoned or painlessly killed because they cannot fill their expected place and may produce Irregular offspring. The proposed measure exposes the conditional character of privilege. A person protected by high birth can become “refuse” when the educational and hereditary programme ceases to work through him. Section 7 gathers these practices into the language of moderation. The narrator declines immediate destruction of every deviant infant because some may become useful and medicine may repair them. He lists procedures with professional confidence, then recommends death once the body begins to set and recovery seems improbable. The medical board supplies a prognosis; the narrator turns it into authority for eliminating the patient. The crucial words are *painlessly* and *mercifully*. They shift attention from whether killing is justified to how agreeably it can be carried out. A claim to reduce pain does not answer the question of whose interests the decision serves. Likewise, the proposed “middle way” lies between immediate killing and delayed killing after attempted correction, not necessarily between cruelty and justice. Abbott's method is cumulative. Public safety, schooling, social mobility and compassion each arrive with familiar benevolent associations. Repetition shows them becoming reasons to confine, instrumentalise or destroy. The reader's task is to restore the concrete human consequence whenever the institutional vocabulary threatens to make it disappear. **The places.** - “a little artificial compression or expansion” (§3) - “honourable confinement for life” (§3) - “to dispense with food” (§5) - “the refuse of our Nobility” (§6) - “trepannings, colligations” (§7) - “painlessly and mercifully consumed” (§7) **In this edition.** Notes 43, 61, 74 and 81–83 explain the practices and euphemisms. Note 81 also glosses Abbott's spelling *diaetetic*, treatment through regimen and diet. The article does not treat these fictional procedures as coherent modern medicine: their literary function is to reveal what happens when correction of a social norm becomes the governing purpose of care. **See also.** [Irregularity](#entry-irregularity) (p. 65); [Education and schools](#entry-education-schools) (p. 46); [Birth and ascent](#entry-birth-ascent) (p. 19); [Nature and law](#entry-nature-law) (p. 81). ## Thickness brightness and an unrecognised dimension {#entry-thickness-brightness} *thick; high; brightness; extra-height; infinitesimally* **The word.** In the Preface, thickness names extension in a direction that Flatland's inhabitants cannot ordinarily identify. Brightness is a perceptible quality of their luminous lines. The Preface distinguishes these rather than treating brightness as simply another name for the missing dimension. This sense also differs from the measurable planar breadth that §16 allows Women as very thin parallelograms: a popular Straight Line need not be a mathematical line of zero breadth. Extra-height is the Square's provisional term for a corresponding unrecognised fourth direction in Spaceland. **In the work.** The objection is elementary and serious: a visible line appears to require some thickness. The revised Preface answers by conceding an unrecognised height to Flatland, while denying that its inhabitants have the means to conceive or measure it. Their lines are equally and infinitesimally thick. A lexicon that describes the revised world simply as physically zero-thickness erases the revision's central move. The reply turns attention from the existence of a property to the conditions under which it becomes a concept. Dimension implies direction, measurement and differences of more and less. If all lines present the same infinitesimal thickness and no observer can indicate the relevant direction, supplying a more delicate instrument does not settle what it should measure. The problem is partly one of orientation and available distinctions, not merely insufficient optical resolution. Brightness complicates the argument because it is both necessary for seeing and variable enough to help recognition. Flatlanders can ask whether a line is brighter, and they can interpret fading along its apparent extent. When the Square attempts to speak of a further visible aspect, they assimilate it to the familiar quality. The dispute shows a language absorbing an unfamiliar claim into a known category and then declaring the remainder meaningless. The Preface extends the situation to readers asked to recognise a fourth dimension. This extension is a thought experiment. It does not demonstrate that colour or brightness is secretly spatial depth, and it does not license treating every unmeasured quality as an additional dimension. The Chief Circle's demand to measure his high-ness combines epistemic challenge with social authority. Height is a missing direction; Highness is a style of elevated rank; the question is put by a High Priest to a prisoner. A small verbal joke makes the refusal of a dimension inseparable from the unequal situation in which it is demanded. **The places.** - **Preface.** “Third unrecognized Dimension” concedes what the objection says must be present - **Preface.** “equally and infinitesimally thick” describes the special limit of the answer - **Preface.** “what to measure, nor in what direction” identifies the conceptual obstacle - **Preface.** “Ah, you mean brightness” absorbs the unfamiliar claim into an available term - **Preface.** “measure my ‘high-ness’” makes social rank part of the pun **In this edition.** The Note on the Text identifies the two related insertions in §§16 and 19 as second-edition additions answering the thickness objection. This lexicon follows that revised text and does not silently harmonise it into an entirely different modern physical model of a two-dimensional universe. **See also.** [Dimension](#entry-dimension) (p. 39) · [Eye and the visible line](#entry-eye-retina) (p. 50) · [Recognition by sight](#entry-recognition-sight) (p. 94) · [The Editor and the revised Preface](#entry-editor-preface) (p. 45) ## Thoughtland and the changing use of an imagined place {#entry-thoughtland} *Thoughtland; Through Flatland to Thoughtland* **The word.** Thoughtland names a country of thought, but its referent changes. In §19 the Square uses it for the further region he hopes may lie beyond Spaceland. In §22 it becomes the guarded name for a theoretical vantage above Flatland. A shared name therefore does not identify the same number of dimensions in both places. **In the work.** The first use arises from a dispute over alleged appearances and disappearances. The Sphere proposes that they come from the brain, while acknowledging uncertainty about the facts. The Square seizes upon Thoughtland as another way of approaching the higher world his analogy has made imaginable. What the teacher presents as a dismissal of apparitions becomes, for the eager pupil, a possible designation of a further domain. That rhetorical reversal does not prove the domain exists. The Square is trying out the consequences of a pattern and asking a teacher who has no confirming knowledge. Thoughtland at this point belongs to his fourth-dimensional aspiration. Treating it as the final metaphysical realm that Abbott asserts would suppress the dialogue's uncertainty and the Sphere's refusal. In §22 the term serves a practical literary strategy. The Square wants to discuss a figure surrounded by six Squares and containing eight terminal Points, seen from a place where Flatland's interiors are visible. These are features of his account of the three-dimensional Cube and Space. He calls the place theoretical so that his treatise might evade a law against physical dimensional revelation. The word marks a protective change of presentation, not a claim that a Cube has become four-dimensional. The disguise fails to solve his main communicative problem. He cannot provide the necessary diagrams on Flatland's linear tablets, and cannot feel sure that readers will understand. A name can offer legal cover or conceptual room without supplying a usable representation. The later public speech likewise begins as fiction but turns into personal testimony under the pressure of enthusiasm. Thoughtland consequently links imagination, censorship and genre. The book the reader holds is itself fiction attributed to A Square, while the inner treatise tries to make dangerous knowledge speak as hypothesis. This resemblance is suggestive rather than an instruction to identify every inner and outer text. The treatise Through Flatland to Thoughtland is one work within the narrator's history; the memoir addressed to other dimensions is another. **The places.** - **§ 19.** “Thoughtland” is the Square's proposed name during speculation beyond Space - **§ 19.** “the brain” belongs to the Sphere's tentative account of alleged apparitions - **§ 22.** “not of a physical Dimension” describes the treatise's evasive presentation - **§ 22.** “six Squares” and “eight terminal Points” specify a three-dimensional Cube - **§ 22.** “Through Flatland to Thoughtland” is the title of the inner treatise **In this edition.** The annotation compares the inner title with Abbott's Through Nature to Christ. That resemblance helps a reader notice the language of passage and ascent. It does not make Thoughtland an explicit doctrine of Platonic Forms, or erase the local shift from speculative fourth dimension to hypothetical three-dimensional explanation. **See also.** [Fourth Dimension](#entry-fourth-dimension) (p. 57) · [Cube](#entry-cube) (p. 33) · [Diagrams and the position of the reader](#entry-diagrams) (p. 38) · [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99) · [Philosophical comparisons and their limits](#entry-philosophical-comparisons) (p. 85) ## Time and the millennium {#entry-time-millennium} *Long Vacation; half-hour glass; Millennium; millenary* **The word.** A millennium or millenary is a period of a thousand years. In Part II, time is measured at several scales: holiday and bedtime, half-hours and the turn of a year, the thousand-year interval of revelation, months of attempted writing and seven years of prison. These measures give a speculative narrative a stubbornly practical chronology, while exposing differences between a moment of insight and the long work of retaining it. **In the work.** The Lineland dream occurs on the last day but one of the 1999th year, at the beginning of the Long Vacation. The next evening the Sphere arrives. The narrator's legal holiday thus opens an interval in which private geometry can displace ordinary professional work. Later, however, the displacement becomes damaging: clients and business are neglected as he attempts to recover and transmit the new knowledge. The half-hour glass localizes the grand calendar. Because Flatland's attraction acts southwards, turning it northward resets it. The last falling sand marks the new period just as the visitor secures a private audience. Time is registered through a material object obedient to this world's physical conditions, rather than through a clock imported unchanged from the reader's world. The supplied 1884 reading says that the second Millennium has begun, although the surrounding dates and the Council's meetings at years zero, one thousand and two thousand point to the third thousand-year period. The inconsistency is textual evidence, not an invitation for the lexicon to silently correct Abbott. The narrator's world explicitly possesses a year zero, so its dating should not be forced into the conventional Christian era's sequence. At the Council, historical time has become precedent. Earlier minutes do not prompt reconsideration of earlier errors; they authorize the same response at the same calendrical point. The officers preserve enough knowledge to anticipate revelation while withholding it from the public. Repetition here stabilizes power rather than increasing collective understanding. Personal duration works differently. A few hours bring the Square from dogmatic rejection to new sight, but months of writing fail to reproduce that sight for anyone else. After about eleven months he can no longer confidently visualize the Cube; after seven years in prison he still has no converts. The widening disparity between the instantaneous event and its protracted aftermath is central to the ending. The book gives more than an ascent: it records the cost of having to live, work and remember after the extraordinary moment has passed. **The places.** - **§13:** “the first day of the Long Vacation” — The dream begins in professional leisure - **§15:** “I turned the glass Northward” — Timekeeping follows Flatland's local physics - **§15:** “The second Millennium had begun” — The retained 1884 reading conflicts with the surrounding count - **§18:** “the first hour of the first day of the year 0” — The calendar includes a zero-year meeting - **§22:** “Seven years have elapsed” — Narrative retrospect belongs to a long confinement **In this edition.** The note explicitly preserves *second* against later printings' *third* and explains the discrepancy. It also remarks on the loose *very few months* of the trial account after a sequence already exceeding eleven months. The lexicon reports those tensions instead of repairing the chronology without notice. **See also.** [Millennial visit](#entry-millennial-visit) (p. 78) · [Memory and forgetting](#entry-memory-forgetting) (p. 76) · [Prison and silence](#entry-prison-silence) (p. 90) · [Wives and household](#entry-wives-household) (p. 126) ## Touch and bodily proof {#entry-touch-belly} *Feeling; feel and be felt; touch; shooting pain* **The word.** Feeling means recognition by bodily contact as well as the more general capacity for sensation. Part II places several kinds of touch beside one another: a socially regulated introduction, a prohibited act in Lineland, a necessary lesson in solidity and an unconsented invasion of the Square's interior. Their shared vocabulary does not make them ethically or epistemically equivalent. **In the work.** The King of Lineland rejects touching as illegal, coarse and unnecessary. Contact could shatter a Point-Woman, and the law therefore prohibits the removal of the interval between any two inhabitants. The Square's suggestion that neighbours feel one another is deliberately provocative and, by his own admission, would not solve the proposed difficulty. Familiar bodily practices cannot simply be exported to a world whose dimensions alter their effects. In the sitting-room, however, the Wife's demand to feel the stranger yields useful information. Her tactile introduction establishes the absence of angles and corrects her first supposition that a Woman has entered. The Square later repeats the procedure because dry indoor conditions make Sight Recognition unreliable. His shame at touching someone apparently of Circular rank demonstrates how etiquette can discourage an effective means of inquiry. The Sphere transforms this ordinary contact into an alarming new possibility. He reaches the Square's stomach without crossing the outline that the Square understands as his bodily boundary. Announcing that slight pain will be outweighed by mental benefit, he proceeds before the pupil can remonstrate. The proof is real within the encounter, but its result is terror and renewed attack. More intimate evidence does not necessarily persuade better, particularly when it arrives as a violation. In Spaceland, touch becomes constructive rather than coercive. The Cube's visual appearance at first resembles an irregular plane figure. Handling it helps the Square learn that it has six plane faces and eight solid angles. The Sphere also lets himself be felt during the subsequent instruction in light, shade and perspective. Sensory cooperation, not simply one superior sense replacing another, produces understanding. This pattern complicates the hierarchy of Part I. The method associated with women and lower classes becomes indispensable to the geometer's highest discovery, while the supposedly commanding visual faculty repeatedly misleads him when deprived of training. Yet the novel does not romanticize touch as infallible: feeling the Sphere's section correctly establishes a Circle within the plane without disclosing the whole Sphere. Every method has a range, and the ethics of using it upon another person remains a separate question. **The places.** - **§14:** “illegal and unnatural excess of approximation” — Lineland condemns bodily contact - **§15:** “Feeling is believing” — The Wife asserts her preferred method of verification - **§16:** “My Wife was right” — The Square confirms her tactile finding - **§17:** “Before I could utter a word of remonstrance” — The internal touch precedes possible objection - **§19:** “as you shall learn by the sense of Feeling” — Touch is necessary to recognize a Solid **In this edition.** The notes explain both Flatland's etiquette and the geometry of the internal touch. Their historical discussion of coercive language illuminates the Sphere's justification but does not make the inflicted pain a neutral or automatically successful educational technique. **See also.** [Interior and exterior](#entry-interior-exterior) (p. 64) · [Cube](#entry-cube) (p. 33) · [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) · [Wives and household](#entry-wives-household) (p. 126) ## Universal Colour Bill {#entry-universal-colour-bill} *Universal Colour Bill; Bill; Code; new Legislation.* **The word.** A *Bill* is a proposed law, not an enacted statute merely because it has a title. *Universal* declares that the programme extends even to the previously unpainted Women and Priests. *Code* describes the specified scheme by which bodies are to be marked. The proposal makes visible identity a matter for collective legislation. **In the work.** The Bill follows an established custom of painting differentiated sides. Its innovation is to reach two classes whose supposed lack of sides has exempted them: straight-line Women and the socially designated Circles. The reformers replace counting sides with a distinction common to both, front and hinder halves. Red marks the half containing eye and mouth; green marks the other half. The scheme redefines the relevant common property instead of accepting the inherited criterion of difference. That shift produces the narrator's alarming comparison. Viewed side-on, a Woman appears as a line divided between red and green. Viewed along the diameter separating his coloured halves, a Priest also presents a divided line. The resemblance is conditional, not complete identity from every viewpoint. The Circle's line may be shorter and fade more quickly towards its ends. The narrator fears that observers accustomed to colour will neglect such details and that women will imitate the fading. His argument depends on the social training of attention as much as on geometry. The political implications are correspondingly precise. Women might receive the respect habitually given to Priests, overhear restricted information, or issue commands in a privileged name. These imagined abuses reveal that deference is attached to recognized appearance rather than to independently tested wisdom. The same sensory uncertainty already protects Circles from close examination; extending uncertainty downwards suddenly becomes a constitutional emergency. The second alleged purpose is the weakening of Circular training. Painted priestly homes would no longer give children uninterrupted practice in colourless sight recognition. The narrator calls the resulting intellectual loss demoralization, joining cognitive and moral decline. His anxiety also admits that elite intelligence depends partly on an environment and a curriculum, rather than solely on inherited sides. The Bill is defeated, but its specificity remains important. It is neither simply “everyone may use colour” nor merely a metaphor for equal rights. It is a compulsory public coding of bodies embedded in a larger reform movement. By following its actual clauses and visual consequences, readers can see how an everyday identifying convention becomes constitutional law, how equality can demand a changed criterion of recognition, and how a threatened monopoly can present the instability of its signs as the collapse of society itself. **The places.** - §9: “the Priests and the Women not excepted” - §9: “the front half of every human being” - §9: “half red, half green” - §9: “an immediate impression of identity of Class” - §9: “their pure and colourless homes” **In this edition.** The figure in §9 belongs to Abbott's illustrated argument, here reproduced through a modern redrawing. Modern note 95 explains its labelled lines and the fading distinction; note 93 supplies the Reform context. The drawing demonstrates a particular visual alignment, not an unrestricted equivalence between straight lines and circles. **See also.** [Colour](#entry-colour) (p. 28); [Reform and equality](#entry-reform-equality) (p. 95); [Dodecagon](#entry-dodecagon) (p. 40); [Chromatistes](#entry-chromatistes) (p. 23). ## Unreliability testimony and the burden of telling {#entry-unreliability-testimony} *Readers; memoirs; truth; defence; honestly* **The word.** Unreliability is an interpretive term for reasons to test a narrator's account rather than receive every judgement as authoritative. Testimony is an account offered by a witness. The two do not exclude one another: a biased narrator can witness something extraordinary, and a sincere witness can struggle to interpret or remember it. **In the work.** Several different tests apply to A Square. His account of Women is explicitly partisan in vocabulary and repeatedly makes inference from shape do the work of moral judgement. His political admiration exposes the interests of his class. His later admission that the explanation he gave his Wife was not wholly truthful supplies a direct instance of concealment. These are stronger grounds for criticism than a general assumption that first-person fiction is deceptive. A different problem concerns the events in Part II. The narrative labels the journeys to Lineland and Pointland as visions associated with sleep, while telling the visit to Spaceland as an experience brought about by the Sphere. The reader should preserve that distinction even when the ending expresses doubt. The dream in §20 includes a repentant Sphere; it does not establish that the waking teacher returned to retract its refusal. Memory imposes a further limit. The narrator has trouble reproducing a Cube in mental vision and later cannot confidently recover its exact shape. This does not retrospectively prove that there was no experience. It shows the difficulty of maintaining a representation without the perceptual and social resources that once supported it. The Preface adds a second witness-like voice whose role is itself mediated. The fictional Editor reports, interprets and summarises; he also grades the persuasiveness of the Square's defences. No single layer stands outside every qualification. This arrangement invites discriminating trust: attend to exact claims, circumstances, admissions and differences between report and judgement. The ending's suffering gives this discrimination an ethical dimension. Dismissing a prisoner because his description is imperfect can repeat the institution's cruelty. Treating everything he believes as demonstrated would erase the intellectual caution the book also asks of its readers. The memoir seeks a hearer capable of listening closely without converting sympathy into certainty. **The places.** - **Preface.** “interpreter and summarizer” discloses a layer of mediation - **§ 20.** “Vision” in the heading marks the status of the encouraging scene - **§ 21.** “not quite so consistent with truth” admits the concealment practised upon the Wife - **§ 22.** “everything that I had seen and heard in fact or vision” distinguishes kinds of reported experience - **§ 22.** “I cannot honestly say I am confident” makes a limitation part of the witness's candour **In this edition.** The modern Afterword discusses narrator, prejudice and the ending. Those analyses are helpful companions, but they do not replace the scene-by-scene evidence. In particular, neither a wholly redeemed narrator nor an all-a-dream solution is treated here as a fact established by the primary text. **See also.** [A Square and the voice of the memoir](#entry-a-square) (p. 11) · [Women](#entry-women) (p. 128) · [Dream and vision](#entry-dream-vision) (p. 43) · [Memory and forgetting](#entry-memory-forgetting) (p. 76) · [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) ## Upward and Northward {#entry-direction-upward} *upward; Northward; Upward, not Northward* **The word.** *Northward* names movement within Flatland; the Sphere's *upward* names movement out of its plane. Because Flatland's slight attraction acts southwards, the ordinary vocabulary of up and down already has a local meaning. The problem is not that the Square lacks the word *up*, but that he cannot detach it from the direction experience has taught him to associate with it. **In the work.** The difficulty is prepared in Lineland. The King translates left and right into north and south, the only two opposed directions he knows. The Square grows impatient with this mistranslation before committing its exact counterpart when the Sphere addresses him. What looks from outside like a foolish refusal is, from within, the almost irresistible assimilation of unfamiliar language to a known spatial system. The Sphere's explanation in §16 is more exact than the eventual slogan. Moving a Square northward makes some of its points pass through positions previously occupied by other points. Moving it out of the plane would give every point its own new path. This describes the relevant independence of the new direction without actually enabling the Flatlander to perform the movement. The pupil's repeated demand for an indication exposes the gap between a structural account and an available gesture. For a time bodily experience closes that gap. In Spaceland the Square sees cards laid on one another rather than northward of one another, and learns the construction of a Cube. After returning, he tries to preserve the discovery by repeating words. In §20 the several forms of the phrase become a charm, mechanically recited before sleep. Its survival in language initially feels like a guarantee that the experience can be recovered. The phrase then fails as a teaching instrument. The grandson ridicules it after hearing the Council's proclamation, and the Square shakes a moveable Square purposelessly, unable to enact the direction. The comic awkwardness matters: a teacher possessing true testimony can still fail to give a pupil either intelligible language or a reproducible demonstration. The formula is not worthless, but its brevity hides the practical knowledge it was intended to recall. At trial it becomes the President's first question. In prison it becomes a Sphinx-like riddle that threatens rather than guides. The movement of the phrase from explanation through mnemonic charm to torment gives the narrative a verbal history of diminishing command. The words have not changed their reference; the narrator's capacity to inhabit their meaning has altered. Abbott makes a compact expression carry the difference between remembering that something is true and still knowing how to think it. **The places.** - **§16:** “No, not Northward; upward; out of Flatland altogether” — The original correction is spatially explicit - **§19:** “not, as you supposed, Northward of the other, but on the other” — Construction supplies practical clarification - **§20:** “mechanically repeating, like a charm” — Explanation contracts into a mnemonic - **§21:** “I move it somewhere” — The attempted demonstration loses its direction - **§22:** “like a soul-devouring Sphinx” — The clue becomes a riddle that consumes its keeper **In this edition.** The notes connect the phrase to Flatland's southward attraction and retain its varying formulations rather than standardizing every occurrence. That variation distinguishes the original lesson, the sleeper's repetition and the final catch-phrase. **See also.** [Dimension](#entry-dimension) (p. 39) · [Movement and section](#entry-movement-section) (p. 79) · [Memory and forgetting](#entry-memory-forgetting) (p. 76) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) ## Voice and hearing {#entry-voice-hearing} *voice; hearing; voice-discrimination; Peace-cry; vocal organs* **The word.** *Hearing* is the first of Flatland's three stated means of recognition. A familiar voice can identify an individual; vocal distinctions can also suggest class. *Voice-discrimination* is a trained capacity, while the *Peace-cry* is a compulsory audible warning. Sound is evidence, communication and social regulation at once. **In the work.** The initial account gives hearing a real advantage: Flatlanders possess an unusually developed auditory sense. Its prestige does not follow its utility, however. Voice-discrimination is called a plebeian virtue, insufficiently cultivated among aristocrats. A faculty is devalued partly because the wrong people excel in it. The phrase allows the reader to separate perceptual competence from the social esteem attached to competence. Imitation complicates the evidence. An Isosceles can reproduce a Polygon's voice, and with training even a Circle's. The capacity undermines any simple expectation that rank must announce itself truthfully in sound. It also grants the supposedly intellectually deficient class an ability demanding sensitivity and practice. The narrator records the fact without substantially revising his judgement of the people who possess it. Women's compulsory sound has a different function. The Peace-cry compensates for a body that may become difficult to see. The law requires continuous vocal presence, yet the narrator subsequently complains about women's unending discourse. The society makes silence dangerous and then treats female sound as an affliction. The distinction between warning and speech remains, but the surrounding rhetoric turns the audible woman into a problem either way. A low female voice can nevertheless attract a Circle in §12, outweighing the pedigree considerations the same society declares essential. Hearing can disclose an attachment not governed by the official scale of angles and ancestry. The attraction exposes a limit to the claim that configuration alone explains judgement. The Lineland episodes reverse the hierarchy once more. There hearing supplies the information that vision cannot, and the King treats the voice as the essence of a person. The Square suggests mimicry precisely because he knows its possibility in Flatland; the King declares such deception impossible. Each world is tempted to convert its most useful sense into an unquestionable authority. Their disagreement does not show that hearing is inherently unreliable or inferior. It shows how a genuine faculty becomes dogmatic when its users refuse to imagine conditions beyond their habitual experience. **The places.** - “The first means of recognition is the sense of hearing” (§5) - “a plebeian virtue” (§5) - “an Isosceles can easily feign the voice of a Polygon” (§5) - “the humming sound of the continuous Peace-cry” (§4) - “the charms of a low voice” (§12) - “the Voice, being the essence of one’s Being” (§14) **In this edition.** Note 48 contextualises the Peace-cry, while note 115 identifies the *King Lear* phrase attached to a low voice. Notes 129–135 accompany Lineland's gendered and auditory assumptions. Those comparisons are editorial guidance; the contrast between imitable Flatland voices and the King's assertion of unchangeability is supplied directly by Abbott's narrative. **See also.** [Women](#entry-women) (p. 128); [Language and gender](#entry-language-gender) (p. 71); [Feeling and touch](#entry-feeling-touch) (p. 53); [Class and caste](#entry-class-caste) (p. 27). ## Voice and selfhood {#entry-voice-selfhood} *Voice; essence of one’s Being; Audition; Thinker, Utterer, Hearer* **The word.** Voice is the audible means by which these worlds announce persons, distinguish identities and sometimes misclassify the source of an utterance. In Lineland the King calls it the essence of being. In Pointland an external voice cannot be recognized as external at all. Between them, the Sphere's voice persists when his body is invisible, separating audible presence from the range of the listener's sight. **In the work.** Lineland gives hearing an extraordinary cognitive and social role. Vision cannot distinguish a Line from a Point, but voices identify age and sex, and the delay between a man's two voices measures his length. Harmony binds distant spouses and makes reproduction possible without contact. The King's claim that voice cannot be changed at will makes personal identity acoustically secure, at least within his account of the world. The Square cannot share this auditory richness. What the King enjoys as a meaningful totality sounds to the visitor like confused chirping. The failure is reciprocal: the King cannot imagine the Square's sight, and the Square cannot discriminate the King's sound. Dimensional advantage therefore does not automatically confer mastery of every faculty cultivated in the lower world. The narrator can see more while hearing less meaningfully. Voice also crosses boundaries that sight cannot cross. Before the Square enters the Line, the King hears speech as an inexplicable disturbance in his intestines. Before the Sphere's section appears in Flatland, the household hears him; after he vanishes, he continues speaking from nowhere the Square can locate. The audible evidence is unsettling precisely because it lacks a body where ordinary experience says a body should be. Pointland radicalizes the problem of attribution. The Point's utterance joins speaker, thought and listener into one enclosed circuit. When the Square speaks to it, the Point receives the content but treats the thought as its own invention. The failure lies neither in volume nor in syntax; the being cannot conceive another speaker. An apparently communicative exchange becomes a monologue because the hearer has no category for an independent source. The story's repeated voices therefore ask what is required to recognize someone else. Accurate hearing involves more than receiving sound, just as sight involves more than receiving a visible line. It requires a model of bodies, distances, sources and possible others. Where that model is rigid, a voice from outside can be dismissed as noise, magic or self-generated thought. The romance uses an ordinary medium of relation to show how difficult relation becomes when another world has to be admitted before its speaker can be heard. **The places.** - **§13:** “Only by the sound of the voice” — Hearing distinguishes what sight cannot - **§14:** “the essence of one’s Being” — The King makes voice foundational to identity - **§14:** “no better than a tiny chirping” — The visitor fails to hear the King's meaningful world - **§16:** “from the depths of nowhere came forth a hollow voice” — Audible presence outlasts visible section - **§20:** “Its own Thought coming to Itself” — An outside speaker is absorbed into the Point's selfhood **In this edition.** The notes explain auditory measurement and distinguish the Point's self-enclosed creed from the philosophical comparisons it invites. The lexicon treats the actual speeches as primary and does not convert the King's theory of immutable voice into a general law endorsed by Abbott. **See also.** [Lineland](#entry-lineland) (p. 74) · [King of Lineland](#entry-king-lineland) (p. 69) · [Pointland](#entry-pointland) (p. 87) · [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) ## Wives and household {#entry-wives-household} *Wife; Wives; household; Daughter; domestic individuality* **The word.** A household is a domestic group and the space of its daily relations. Part II places revelation inside such a group rather than in an isolated laboratory. The narrator's Wife, sons, orphan grandsons, daughter, servants, butler and page supply both the subjects of new vision and the people to whom he might have to explain what he has learned. Lineland's plural Wives provide a contrasting domestic arrangement shaped by another geometry. **In the work.** The Wife is the first person to answer the Square's dismissal of the grandson. She defends the boy by invoking the Commandments, before the Sphere independently confirms his mathematical insight. Her own encounter with the stranger is governed by practical concerns: how did someone enter a house promised to have no ventilators, and what can contact establish about the visitor? The narrator dismisses her as jealous and unreasoning, but her insistence on Feeling produces a result he later explicitly acknowledges as correct. Her retirement is secured by deference to apparent Circular rank. The Sphere says his message cannot be delivered in her presence, and she yields rather than require the important visitor to move. An extraordinary intellectual event thus begins inside ordinary gendered and class-based arrangements of access. The private audience is not free of social structure merely because its subject exceeds Flatland's world. From above, the Square sees his Wife anxiously searching for him while the rest of the house is exposed in its individuality. He wishes to reassure her but cannot move without his guide. The panoramic privilege is accompanied by helplessness towards someone he cares about. The daughter's first explicit appearance in the account is fleeting, and the house diagram gives her a room even though earlier verbal inventories had omitted her. That discrepancy can support attention to domestic invisibility without pretending that Abbott narrates her thoughts or a separate story. After returning, the Square withholds his experience from his Wife on the declared assumption that women cannot understand it. Her sensible response to his implausible cellar story is solicitude rather than argument. His later resolution to teach her is quickly postponed, and he ultimately gives an elaborate, admittedly untruthful account that sends her back to household duties. His enlightenment has not dissolved his habits of exclusion. The family is also a potential arm of the state. The narrator fears that his respectable sons may value patriotism and reverence for Circles above affection and hand him over. The supposedly safe grandson recants after hearing the law. Domestic life therefore surrounds revelation with care, prejudice, intellectual promise and danger. It is neither merely a comic interruption nor an uncomplicated refuge from public authority. **The places.** - **§15:** “He is no such thing” — The Wife defends the grandson before the visitor speaks clearly - **§15:** “you promised me, my dear” — Domestic arrangements govern the first explanation of the intrusion - **§18:** “Only my affectionate Wife” — New sight reveals her anxiety - **§18:** “Servants, Butler, Daughter” — The expanded household inventory briefly includes the daughter - **§20:** “my Wife, whose good sense far exceeds” — Praise still retains the narrator's hierarchy of sex - **§21:** “return quietly to her household duties” — The account restores an exclusion it had briefly promised to overcome **In this edition.** The notes identify the daughter in Abbott's house plan and mark her absence from earlier inventories. The author's own note to §15 explains that bodily words such as *sitting* indicate Flatland states of volition rather than ordinary human posture; that adaptation belongs to the fiction's domestic language, while the explanatory note should not be misregistered as main narrative vocabulary. **See also.** [Grandson](#entry-grandson) (p. 58) · [Touch and bodily proof](#entry-touch-belly) (p. 118) · [Interior and exterior](#entry-interior-exterior) (p. 64) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) ## Women {#entry-women} *Women; Female; Frail Sex; Thinner Sex; Straight Lines* **The word.** Flatland's Women are defined as Straight Lines and placed outside the male succession of increasingly many-sided bodies. The recurrent substitutes *Female*, *Frail Sex* and *Thinner Sex* shift between legal category, patronising description and physical measurement. These are the narrator's terms for a governed group, not neutral authorial judgements of women. **In the work.** Section 4 combines fear and contempt. Women are described as intellectually negligible yet capable of immediate destruction. The needle image makes that combination possible: a body reduced to almost nothing in breadth becomes formidable as a point. The narrator's account moves from this hazard to controls over movement, sound, entrances and illness. A woman must be continuously detectable, and involuntary motion can become grounds for execution. The supposed naturalness of respectable behaviour is manufactured through fashion. Upper-class back-motion is copied by wives lower down the hierarchy until an enforced precaution appears as an instinct of breeding. The passage distinguishes physical sex from class performance even while claiming that all women share one form. Their rank-dependent behaviour is learned and imitated, not simply given by being a line. Domestic peace is similarly qualified. Apartments can prevent women from turning, and tactful husbands make promises they do not intend to keep. The narrator praises these techniques as practical management. His admission that peace may mean only the absence of slaughter opens a gap between safety and a flourishing shared life. Neither partner's domination nor a truce based on deceit produces the harmony the word *peace* ordinarily promises. The conclusion of §4 denies women the prospect available to the lowest male lineage. “Once a Woman, always a Woman” fixes their social future, while the claim that they lack memory and foresight supposedly protects them from recognising its misery. Oppression is justified through an attributed inability to understand oppression. The narration's assurance is itself part of what the reader must examine. Section 12 makes that examination unavoidable. Women's education was removed by decree, and their capacities declined thereafter. Their exclusion from books also enables men to conceal the contempt expressed in male language. The law that produces ignorance then depends on its continuance. The narrator proposes reform for the sake of boys' intellectual strength, a restricted concern that nonetheless supplies evidence against his earlier account of immutable female nature. The second-edition Preface reports that imprisonment has altered the Square's views. That qualification matters, but it does not cancel the sustained misogyny of his social account. Reading the satire requires holding together the speaker's prejudices, their exposure through his own evidence, and the text's refusal to supply an entirely purified spokesman. **The places.** - “Our Women are Straight Lines” (§3) - “a Female, in Flatland, is a creature by no means to be trifled with” (§4) - “under penalty of death” (§4) - “the absence of slaughter” (§4) - “Once a Woman, always a Woman” (§4) - “they sensibly declined during each generation in intellectual power” (§12) **In this edition.** Notes 44–53 contextualise the rhetoric and laws of §4; notes 117–119 treat non-education and Abbott's support for women's education. The “Editor” defending the Square in the Preface is Abbott's fictional voice, not Diotimos speaking. Distinguishing those levels prevents modern annotation from being used as the narrator's own recantation. **See also.** [Straight line](#entry-line-straight) (p. 109); [Language and gender](#entry-language-gender) (p. 71); [Doors and houses](#entry-doors-houses) (p. 42); [Voice and hearing](#entry-voice-hearing) (p. 123). # Defined vocabulary register {#defined-register} Each headword has a contextual definition, an actual printed form and a primary-text reference. Some headwords group more than one local use. Forms come from Abbott’s text or his explicitly labelled notes, not from the modern editor’s explanatory prose. The full articles develop major subjects; this register supplies additional lexical access, including subsidiary and older senses that can be easy to miss. ### A Square {#register-001} The narrator's assumed name, simultaneously his geometrical form and his professional-class identity. The title page also assigns him the illustrations; this fictional authorship is distinct from Abbott's. **Printed form:** A Square (Title Page). See [A Square and the voice of the memoir](#entry-a-square) (p. 11). ### Abrogation {#register-002} Formal repeal or abolition of a law. Advocates seek the abrogation of the Irregular Penal Laws, so their challenge is directed at the legal structure of persecution rather than merely at individual acts of unkindness. **Printed form:** abrogation (§ 7). See [Irregularity](#entry-irregularity) (p. 65). ### Accost {#register-003} To address someone, especially a stranger. The Square accosts the apparent Woman before learning that his Flatland assumptions have misidentified Lineland's King. **Printed form:** accosted (§ 13). See [King of Lineland](#entry-king-lineland) (p. 69). ### Acquiesce {#register-004} Accept or submit without active resistance. The Circles tolerate reduced fertility as a consequence of their supposedly superior development. **Printed form:** acquiesce (§ 12). See [Fertility and extinction](#entry-fertility-extinction) (p. 54). ### Adage {#register-005} A familiar maxim or saying. Here the colour movement circulates a brief formula linking distinction of sides to distinction of colours. **Printed form:** adage (§ 8). See [Colour](#entry-colour) (p. 28). ### Aides-de-camp {#register-006} Military officers serving as assistants to a commanding officer. The painted Pentagons and Hexagons move across the field in these and other professional roles. **Printed form:** aides-de-camp (§ 8). See [Painting](#entry-painting) (p. 84). ### Alliance {#register-007} Marriages considered as unions between families and their social interests. University failures have difficulty forming suitable alliances because their educational deficiency is believed likely to reappear as bodily irregularity in their offspring. **Printed form:** alliances (§ 6). See [Birth and ascent](#entry-birth-ascent) (p. 19). ### Alphabet of angles {#register-008} A graded series of bodily examples used to teach the discrimination of angles, analogous to letters used in learning to read. The educational metaphor conceals the fact that its smallest signs are living people confined as teaching apparatus. **Printed form:** Alphabet of angles (§ 5). See [Education and schools](#entry-education-schools) (p. 46). ### Analogy {#register-009} Reasoning by carrying a known relation into a corresponding unfamiliar case. The method predicts properties of the Cube and later becomes the pupil's means of challenging his teacher's refusal of a fourth dimension. **Printed form:** Analogy (§ 16). See [Analogy](#entry-analogy) (p. 12). ### Anarchical {#register-010} Disorderly or opposed to established government. The word politicizes the narrator’s moral condemnation of the colour period. **Printed form:** anarchical (§ 8). See [Chromatic Sedition](#entry-chromatic-sedition) (p. 21). ### Animosity {#register-011} Active hostility or resentment. Political disagreement is described as turning into hostility within noble households. **Printed form:** animosity (§ 10). See [Chromatic Sedition](#entry-chromatic-sedition) (p. 21). ### Antagonistic {#register-012} Operating in opposition to one another. The two natural decrees increase bodily development while reducing reproductive capacity. **Printed form:** antagonistic (§ 11). See [Fertility and extinction](#entry-fertility-extinction) (p. 54). ### Antiquarian {#register-013} A student or collector of old remains and customs. The observer who might discover a surviving square house treats recent building forms like archaeological survivals, reinforcing the narrator’s confidence that pentagonal construction is a civilised advance. **Printed form:** antiquarian (§ 2). See [Doors and houses](#entry-doors-houses) (p. 42). ### Apostle {#register-014} A person sent to carry a message. The Sphere selects the Square to transmit the Gospel of Three Dimensions, turning geometrical discovery into a difficult public commission. **Printed form:** apostle (§ 17). See [Revelation and teaching](#entry-revelation-teaching) (p. 98). ### Apprehend {#register-015} To retain some grasp of a truth one cannot presently comprehend or reproduce in perception. The Square uses it for his faith in height after losing his former ability to realise it. **Printed form:** apprehend (Preface). See [Faith reason and the reach of experience](#entry-faith-reason) (p. 51). ### Approximation {#register-016} An approach towards another body. In the King's legal explanation, approaching so closely that no interval remains becomes a dangerous, punishable act of contact. **Printed form:** approximation (§ 14). See [Touch and bodily proof](#entry-touch-belly) (p. 118). ### Approximations {#register-017} Successive movements towards a closer fit. Repeated courtship choruses gradually bring the three lovers’ four voices into harmony, giving the love story a mathematical vocabulary of convergence. **Printed form:** approximations (§ 13). See [Wives and household](#entry-wives-household) (p. 126). ### Arbitrary visitations {#register-018} Intrusions dependent on another's unrestricted will. The Square fears repeated attacks upon his interior, making resistance a response to vulnerability as well as unbelief. **Printed form:** arbitrary visitations (§ 17). See [Touch and bodily proof](#entry-touch-belly) (p. 118). ### Aristocratic {#register-019} Favouring the rule or privileges of the highest class. The Square's reported disavowal of these tendencies is obscure and mediated by the fictional Editor, not an unqualified rewriting of the memoir. **Printed form:** aristocratic (Preface). See [The Editor and the revised Preface](#entry-editor-preface) (p. 45). ### Aristocratic Legislature {#register-020} The law-making authority organized around noble privilege. Its feared destruction is the narrator’s final measure of the Bill’s danger. **Printed form:** Aristocratic Legislature (§ 9). See [Law and sanction](#entry-law-sanction) (p. 72). ### Arithmetical {#register-021} Increasing by a fixed added amount when applied to the progression here. Zero, two and four boundaries lead to six square faces for the Cube. **Printed form:** Arithmetical (§ 16). See [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15). ### Assimilated {#register-022} Made similar or brought into likeness. Aristocratic voices are said to be assimilated, which weakens hearing as a means of determining rank and makes another sensory method necessary. **Printed form:** assimilated (§ 5). See [Voice and hearing](#entry-voice-hearing) (p. 123). ### Attraction {#register-023} The steady physical pull toward the South that enables Flatlanders to orient themselves without a sun. Its varying strength links geography to bodily experience, while the narrator uses women’s supposed weakness under it to justify a rule of gentlemanly behaviour. **Printed form:** attraction (§ 2). See [Attraction and climate](#entry-attraction-climate) (p. 18). ### Audition {#register-024} Hearing or an act of listening. The King boasts that one moment of audition yields an almost complete census of Lineland, far surpassing touch in speed and scope. **Printed form:** audition (§ 14). See [Voice and selfhood](#entry-voice-selfhood) (p. 125). ### August {#register-025} Dignified, venerable or imposing. Apparent Circular rank makes the visitor august in the household before anyone understands his true nature. **Printed form:** august (§ 15). See [Sphere](#entry-sphere) (p. 107). ### Averse {#register-026} Opposed or strongly disinclined. Pantocyclus’s speech renders most groups neutral towards or hostile to the Bill. **Printed form:** averse (§ 10). See [Reform and equality](#entry-reform-equality) (p. 95). ### Avocation {#register-027} Ordinary occupations or duties, here household tasks, rather than hobbies pursued apart from one’s main work. Poorer wives may turn away while engaged in these avocations, giving their husbands the silence that upper-class etiquette prevents. **Printed form:** avocations (§ 4). See [Women](#entry-women) (p. 128). ### Avowed {#register-028} Openly declared or acknowledged. Women publicly announce their change from support for the Bill to opposition. **Printed form:** avowed (§ 10). See [Cunning and policy](#entry-cunning-policy) (p. 35). ### Barbarism {#register-029} An expression condemned as violating accepted linguistic usage. Here the charge falls on feel used transitively to mean introduce; the narrator’s objection is to fashionable grammar, not to the bodily contact that the formula arranges. **Printed form:** barbarism (§ 5). See [Language and gender](#entry-language-gender) (p. 71). ### Barren {#register-030} Producing no offspring. The narrator attributes it to marriages he considers poorly chosen, within his own hereditary ideology. **Printed form:** barren (§ 12). See [Fertility and extinction](#entry-fertility-extinction) (p. 54). ### Beatitude {#register-031} Supreme happiness or blessedness. The Point calls its isolated existence infinitely blessed, so exalted religious language expresses complete self-satisfaction. **Printed form:** beatitude (§ 20). See [Pointland](#entry-pointland) (p. 87). ### Belauded {#register-032} Much or extravagantly praised. The Sphere contrasts the narrator's belauded Circles with his despised Straight Lines, challenging the ranking of intellect above affection. **Printed form:** belauded (§ 18). See [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82). ### Betters {#register-033} People of higher social rank, presumed by the conventional term to be superior. Avoiding collisions with one’s betters is a matter of etiquette as well as safety, and their privilege includes being spared a request for tactile identification. **Printed form:** betters (§ 6). See [Class and caste](#entry-class-caste) (p. 27). ### Beyond experience {#register-034} Outside the reach of experience presently available to the speaker. The phrase frames a caution against both declaring the unknown impossible and claiming exact knowledge of its nature. **Printed form:** beyond experience (Preface). See [Faith reason and the reach of experience](#entry-faith-reason) (p. 51). ### Bi-lingual {#register-035} Using two languages or distinct vocabularies. Flatland’s men speak an emotional and moral language to women while privately substituting a supposedly scientific vocabulary, so linguistic difference becomes a means of controlling access to knowledge. **Printed form:** bi-lingual (§ 12). See [Language and gender](#entry-language-gender) (p. 71). ### Bi-mental {#register-036} Having, as it were, two modes of mind. The narrator’s extension of bi-lingual suggests that maintaining the public moral vocabulary and the private deterministic one requires conflicting habits of thought, not merely different words. **Printed form:** bi-mental (§ 12). See [Language and gender](#entry-language-gender) (p. 71). ### Blot on her escutcheon {#register-037} A stain on a family’s honour or ancestry, expressed through the image of a heraldic shield. The narrator means a recorded irregular ancestor. **Printed form:** blot on her escutcheon (§ 12). See [Marriage and selection](#entry-marriage-selection) (p. 75). ### Breeding {#register-038} Good upbringing and cultivated manners, rather than reproduction in this occurrence. Giving a Lady the north side of a street becomes a test of breeding, so the vocabulary of social refinement already surrounds a bodily hierarchy that later depends heavily on literal breeding. **Printed form:** breeding (§ 2). See [Class and caste](#entry-class-caste) (p. 27). ### Brightness {#register-039} The familiar visible quality to which Flatlanders assimilate the Square's unfamiliar claim about height. The Preface distinguishes a real direction of extension from a quality of luminous appearance. **Printed form:** brightness (Preface). See [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113). ### Burnt umber {#register-040} A darkened reddish-brown earth pigment produced by heating umber. It completes the Square artillerymen’s four-colour palette. **Printed form:** burnt umber (§ 8). See [Painting](#entry-painting) (p. 84). ### By courtesy {#register-041} By social convention or respectful concession rather than demonstrated entitlement. The Chief Circle’s alleged ten thousand sides and a successful child’s Circular title receive this qualification. **Printed form:** by courtesy (§ 11). See [Chief Circle](#entry-chief-circle) (p. 20). ### Carnage {#register-042} Large-scale slaughter. The narrator substitutes it for battle, acknowledging the attack’s radically unequal conditions. **Printed form:** carnage (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Castigation {#register-043} Chastisement or punishment. The grandfather conjectures, without evidence, that it may strengthen the child’s Configuration. **Printed form:** castigation (§ 12). See [Conformity and obedience](#entry-conformity-obedience) (p. 32). ### Casual {#register-044} Accidental or arising by chance, rather than informal or relaxed. Casual motions are grouped with involuntary movements as dangers supposedly intensified by southern gravitation, helping turn climatic explanation into an argument for harsher control of women. **Printed form:** casual (§ 4). See [Attraction and climate](#entry-attraction-climate) (p. 18). ### Catch-phrase {#register-045} A compact, readily repeated formula. The narrator recognizes that the words about upward movement cannot alone carry the understanding he wants to communicate. **Printed form:** catch-phrase (§ 22). See [Upward and Northward](#entry-direction-upward) (p. 122). ### Celerity {#register-046} Speed or swiftness, here the unexpectedly rapid demand for a second edition. The formal word sustains the fictional Editor's courteous public voice. **Printed form:** celerity (Preface). See [The Editor and the revised Preface](#entry-editor-preface) (p. 45). ### Celestial region {#register-047} A heavenly-sounding designation of ordinary three-dimensional Space from the lower world's point of view. The flattering elevation of the reader's world is also an invitation to imagine something beyond it. **Printed form:** Celestial Region (Dedication). See [Dedication and the reader being addressed](#entry-dedication) (p. 36). ### Certifiable {#register-048} Capable of receiving official certification as equal-sided. The apparently mathematical fact must be ratified by an institution before it creates social rights; the word stresses that birth alone does not complete admission to a superior class. **Printed form:** certifiable (§ 3). See [Regularity](#entry-regularity) (p. 97). ### Certified pedigree {#register-049} An officially authenticated ancestry record. A Woman cannot legally marry without one. **Printed form:** certified pedigree (§ 12). See [Marriage and selection](#entry-marriage-selection) (p. 75). ### Charm {#register-050} A formula repeated as though it had a securing or magical power. The Square uses the words about upward movement to retain an experience he is already finding difficult to reconstruct. **Printed form:** charm (§ 20). See [Upward and Northward](#entry-direction-upward) (p. 122). ### Cheap system {#register-051} The educational arrangement that keeps specimens alive by feeding them for longer use. The narrator associates it with elected School Boards, but prefers the more expensive replacement system because he regards worn angles and surplus population as costs to be reduced. **Printed form:** cheap system (§ 5). See [Education and schools](#entry-education-schools) (p. 46). ### Chief Circle {#register-052} The chief office of Flatland’s ruling priestly order. Pantocyclus holds it during the Colour Revolt; the office and its later incumbents must not be collapsed into that one historical person. **Printed form:** Chief Circle (§ 10). See [Chief Circle](#entry-chief-circle) (p. 20). ### Chief Clerk {#register-053} The official who reads the Council's earlier minutes, identified as the narrator's brother. His direct exposure to the Sphere leads to perpetual imprisonment but later does not produce belief in a Sphere. **Printed form:** Chief Clerk (§ 18). See [Prison and silence](#entry-prison-silence) (p. 90). ### Chirruped {#register-054} Made a short chirping sound. The narrator's word reduces the King's sophisticated two-voiced demonstration to the kind of noise a Flatlander hears without its full significance. **Printed form:** chirruped (§ 14). See [Voice and selfhood](#entry-voice-selfhood) (p. 125). ### Chromatistes, inventor {#register-055} The Pentagon credited by tradition with inventing painting. He must be distinguished from the later Irregular Circle who leads the colour movement under the same name. **Printed form:** Chromatistes (§ 8). See [Chromatistes](#entry-chromatistes) (p. 23). ### Chromatistes, revolutionary {#register-056} The leader of the colour movement, identified through the preceding account with its Irregular Circle strategist. He is distinct from the Pentagon inventor of painting described in §8. **Printed form:** Chromatistes (§ 10). See [Chromatistes](#entry-chromatistes) (p. 23). ### Circular Neo-Therapeutic Gymnasium {#register-057} The institution in which infant high Polygons undergo dangerous reshaping to increase their sides and gain Circular status. Its therapeutic name contrasts with the very low survival rate. **Printed form:** Circular Neo-Therapeutic Gymnasium (§ 11). See [Fertility and extinction](#entry-fertility-extinction) (p. 54). ### Circumspection {#register-058} Cautious attention to surrounding risks. Dangerous corners are permitted on state buildings because approaching those places is supposed to require circumspection: an apparent safety exception makes architecture itself enforce the government’s authority. **Printed form:** circumspection (§ 2). See [Doors and houses](#entry-doors-houses) (p. 42). ### Civic rights {#register-059} The rights belonging to recognised members of the political community. The lowest-angle figures possess none, a denial that allows the state to treat them as disposable educational instruments while continuing to describe them as individuals. **Printed form:** civic rights (§ 5). See [Class and caste](#entry-class-caste) (p. 27). ### Cognizance {#register-060} Awareness or perceptual notice. Because the low Isosceles eye lies far from his sharp vertex, he may scarcely take cognizance of contact there, making bodily arrangement part of the narrator’s explanation of recognition accidents. **Printed form:** cognizance (§ 5). See [Eye and the visible line](#entry-eye-retina) (p. 50). ### Colligation {#register-061} Bindings or fastening together, particularly as a surgical treatment. Its place among compressions, extensions, and trepannings gives technical specificity to the effort to force irregular bodies into approved forms. **Printed form:** colligations (§ 7). See [Surgery and extermination](#entry-surgery-extermination) (p. 112). ### Colour Recognition {#register-062} Identification of bodies through their painted hues rather than difficult inference from angles and fading brightness. Its practical accessibility weakens the higher classes’ monopoly of expertise. **Printed form:** Colour Recognition (§ 9). See [Colour](#entry-colour) (p. 28). ### Commandment {#register-063} The scriptural injunction concerning honour to parents. The Circles reverse its direction by teaching reverence for more highly developed descendants. **Printed form:** Commandment (§ 12). See [Circular doctrine](#entry-circular-doctrine) (p. 25). ### Compensative Laws of Nature {#register-064} The alleged natural mechanisms keeping the classes in balance. In the ruler’s argument they justify restrictions and lethal practices that reduce the lower population. **Printed form:** Compensative Laws of Nature (§ 10). See [Compensation](#entry-compensation) (p. 29). ### Comprehend {#register-065} To grasp or understand fully. The imprisoned Square distinguishes a comprehension he once possessed from the faith by which he now holds on to height. **Printed form:** comprehend (Preface). See [Faith reason and the reach of experience](#entry-faith-reason) (p. 51). ### Conceit {#register-066} Both an opinion or conception and excessive self-importance. The narrator resists the Conceit that declares a fixed number of dimensions exhaustive, combining an intellectual mistake with the vanity that sustains it. **Printed form:** Conceit (§ 19). See [Fourth Dimension](#entry-fourth-dimension) (p. 57). ### Concession {#register-067} The yielding of a disputed point or demand. Pantocyclus announces acceptance of the Bill as part of a manoeuvre that ends in the opposition’s destruction. **Printed form:** Concession (§ 10). See [Cunning and policy](#entry-cunning-policy) (p. 35). ### Conclave {#register-068} A private, closed assembly. The priestly Circles meet in solemn conclave to renew their policy of suppressing dimensional revelations. **Printed form:** conclave (§ 18). See [Millennial visit](#entry-millennial-visit) (p. 78). ### Concourse {#register-069} A large assembled crowd. Here it describes the extraordinary gathering at which Pantocyclus defeats the movement. **Printed form:** concourse (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). A gathering or crowd. The Square asks about the moving multitude before understanding that its single line is an entire inhabited universe. **Printed form:** concourse (§ 13). See [Lineland](#entry-lineland) (p. 74). ### Condescending {#register-070} Stooping to visit or address someone regarded as lower. In the proposed visit of a fourth-dimensional person, the word carries a spatial descent and a hierarchy of presumed superiority. **Printed form:** condescending (Preface). See [Solid humanity and superior races](#entry-solid-superior-races) (p. 105). ### Condole {#register-071} To express sympathy or share another's grief. The Square wants to reach his arrested brother, but the guide postpones that familial response while continuing the lesson. **Printed form:** condole (§ 19). See [Wives and household](#entry-wives-household) (p. 126). ### Configuration {#register-072} A figure’s bodily shape or disposition of sides and angles. In the discussion of recognition it names what an observer must discover; the same word’s later elevation into doctrine depends on treating this visible arrangement as the cause of character. **Printed form:** configuration (§ 5). See [Regularity](#entry-regularity) (p. 97). Bodily form elevated into an all-explanatory doctrine of conduct and rank. The Circles teach that it determines actions regardless of will, training, or encouragement. **Printed form:** Configuration (§ 12). See [Configuration](#entry-configuration) (p. 31). ### Conformation {#register-073} The bodily shape or arrangement of parts. The Square derives women’s alleged mental incapacity directly from their conformation, turning an anatomical description into an explanation that claims to settle questions of judgment, memory, and moral agency. **Printed form:** conformation (§ 4). See [Irregularity](#entry-irregularity) (p. 65). The arrangement or structure of parts. The Sphere proposes lessons in the conformation of Solids, while his pupil now wants to question the dimensional limit of the entire course. **Printed form:** conformation (§ 19). See [Revelation and teaching](#entry-revelation-teaching) (p. 98). ### Congenital {#register-074} Present from birth. The doctrine distinguishes such bodily defects from deformations caused later by accidents, exercise, or temperature. **Printed form:** congenital (§ 12). See [Configuration](#entry-configuration) (p. 31). ### Conjugal {#register-075} Pertaining to marriage or spouses. Conjugal fury names the violent domestic conflicts reported during the agitation. **Printed form:** conjugal (§ 10). See [Marriage and selection](#entry-marriage-selection) (p. 75). ### Conjugal union {#register-076} The relation of spouses in marriage. The Square wonders how marriage can operate where intervening neighbours cannot be passed, and discovers a wholly auditory domestic system. **Printed form:** conjugal union (§ 13). See [Wives and household](#entry-wives-household) (p. 126). ### Consort {#register-077} A spouse, here the wife of a Circle. The elevated word suits the high social rank of the husband who quiets her with lavish promises, lending courtly dignity to a plainly manipulative domestic practice. **Printed form:** consort (§ 4). See [Women](#entry-women) (p. 128). ### Constituents {#register-078} The ingredients or components of something. Chromatistes discovers the materials needed to produce simple colours. **Printed form:** constituents (§ 8). See [Painting](#entry-painting) (p. 84). ### Constitution {#register-079} Flatland’s established political and social order, rather than necessarily a single written document. The Circles invoke its safety when defending rank, suppressing reform, and restricting colour. **Printed form:** Constitution (§ 10). See [Law and sanction](#entry-law-sanction) (p. 72). ### Consumed {#register-080} Put to death, in the euphemistic vocabulary used for people whom the authorities judge unfit to survive. Joined to painlessly and mercifully, it makes the elimination of an irregular child sound like compassionate completion of a medical process. **Printed form:** consumed (§ 7). See [Surgery and extermination](#entry-surgery-extermination) (p. 112). Put to death. The euphemism conceals the annual killing of workmen who might disclose the secret of colour production. **Printed form:** consumed (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Consummate {#register-081} Complete or supremely achieved. The Square initially praises the Sphere's loveliness and wisdom as consummate before learning how much remains concealed and contested. **Printed form:** consummate (§ 18). See [Sphere](#entry-sphere) (p. 107). ### Consummated {#register-082} Brought to completion, here specifically marriage made effective. The King's account makes coordinated sound perform the role that bodily union would have in a familiar marriage. **Printed form:** consummated (§ 13). See [Wives and household](#entry-wives-household) (p. 126). ### Consummating {#register-083} Bringing a marriage to completion, ordinarily through sexual union. The word makes the reported deception an accomplished violation rather than merely a failed courtship. **Printed form:** consummating (§ 10). See [Marriage and selection](#entry-marriage-selection) (p. 75). ### Conversant {#register-084} Acquainted or familiar with a subject. The native was previously acquainted with only two dimensions, so ordinary familiarity becomes the baseline from which further initiation begins. **Printed form:** conversant (Dedication). See [Initiation and mysteries](#entry-initiation-mysteries) (p. 62). ### Conversazione {#register-085} An evening social gathering devoted to conversation, often with intellectual or artistic associations. In Flatland its moving company of distinguished Polygons becomes a demanding practical examination in reading rank from shifting patches of brightness. **Printed form:** conversazione (§ 6). See [Recognition by sight](#entry-recognition-sight) (p. 94). ### Convert {#register-086} Someone persuaded to accept a new belief. The Square offers to become one if the Sphere can measure or indicate the asserted height, linking religious vocabulary with a demand for demonstration. **Printed form:** convert (§ 16). See [Evidence and demonstration](#entry-evidence-demonstration) (p. 49). ### Corporal {#register-087} Bodily. The King includes bodily information among the local, mental and spiritual statistics he claims to acquire by listening. **Printed form:** corporal (§ 14). See [Voice and selfhood](#entry-voice-selfhood) (p. 125). ### Corporal ascent {#register-088} A bodily rising or journey upward. The Square wants imaginative ambition matched by physical movement through further dimensions, although the narrative supplies no such waking ascent beyond three. **Printed form:** corporal ascent (§ 19). See [Fourth Dimension](#entry-fourth-dimension) (p. 57). ### Corporal decoration {#register-089} Decoration of the body. Corporal is bodily here, without the rank implied by the military noun corporal. **Printed form:** corporal decoration (§ 8). See [Painting](#entry-painting) (p. 84). ### Correspondent {#register-090} Corresponding or proportionate. The lower orders’ vocal capacities are more than correspondent with their hearing: they can produce convincing imitations that outstrip the reliability of auditory identification. **Printed form:** correspondent (§ 5). See [Voice and hearing](#entry-voice-hearing) (p. 123). ### Court Martial {#register-091} A military tribunal. It orders the destruction of suspected Irregular Triangles without the normal exact bodily measurement. **Printed form:** Court Martial (§ 10). See [Law and sanction](#entry-law-sanction) (p. 72). ### Cube {#register-092} A three-dimensional solid with six square faces and eight corners. The narrator encounters it by construction, touch and trained sight, then gradually loses confidence in his ability to recall its exact shape. **Printed form:** Cube (§ 19). See [Cube](#entry-cube) (p. 33). ### Cut-throat {#register-093} A violent criminal or murderer. The Square initially fears a disguised attacker from the despised Isosceles class, reading an unexplained visitor through his society's habitual suspicions. **Printed form:** cut-throat (§ 16). See [Sphere](#entry-sphere) (p. 107). ### Dashing {#register-094} Fashionably spirited, showy, or boldly up-to-date. Applied to young gentlemen who shorten the formula of introduction, it marks a social style whose careless linguistic innovations offend the narrator’s conservatism. **Printed form:** dashing (§ 5). See [Language and gender](#entry-language-gender) (p. 71). ### Decimated {#register-095} Subjected to the killing of one in ten, in the strict punitive sense identified by the edition’s note. It qualifies the assertion that the Working Men were spared. **Printed form:** decimated (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Deference {#register-096} Respectful yielding or attention accorded to someone’s supposed superiority. The narrator fears that painted women will receive the deference ordinarily directed to Priests. **Printed form:** deference (§ 9). See [Universal Colour Bill](#entry-universal-colour-bill) (p. 119). ### Degradation {#register-097} Reduction in rank, coupled with the notion of diminished bodily and mental development. The ancestor’s punishment and his relatives’ shock supposedly reduce the next generation’s angle, making social disgrace literally inheritable. **Printed form:** degradation (§ 5). See [Birth and ascent](#entry-birth-ascent) (p. 19). ### Degraded {#register-098} Low in physical development and social estimation, with the moral disapproval of debasement carried into the description of a shape. The narrator’s language makes the narrow base of a poor Triangle seem evidence of an inferior kind of person. **Printed form:** degraded (§ 3). See [Class and caste](#entry-class-caste) (p. 27). ### Demoniacal {#register-099} Resembling or attributed to a demon. The laugh apparently arising inside the Square turns a geometrical intervention into the experience of bodily possession and terror. **Printed form:** demoniacal (§ 17). See [Touch and bodily proof](#entry-touch-belly) (p. 118). ### Demonstration {#register-100} A reasoned proof or intelligible showing. The Square hopes to replace legally dangerous testimony about revelation with a geometrical argument others can follow. **Printed form:** Demonstration (§ 21). See [Evidence and demonstration](#entry-evidence-demonstration) (p. 49). ### Demoralize {#register-101} To degrade or corrupt, here in intellectual as well as moral capacity. The narrator predicts that painted Circular households will weaken one another’s trained powers of recognition. **Printed form:** demoralize (§ 9). See [Universal Colour Bill](#entry-universal-colour-bill) (p. 119). ### Destitute of converts {#register-102} Entirely without persuaded followers. After seven years of imprisonment, even the narrator's repeatedly instructed brother refuses belief in a Sphere. **Printed form:** destitute of converts (§ 22). See [Prison and silence](#entry-prison-silence) (p. 90). ### Deterrent {#register-103} Effective in discouraging an action by its feared consequences. The reported reproductive risks fail to deter Circles from the marriages the narrator condemns. **Printed form:** deterrent (§ 12). See [Marriage and selection](#entry-marriage-selection) (p. 75). ### Diaetetic {#register-104} Relating to treatment through diet and regimen; an older spelling of dietetic. The word broadens the proposed cures beyond surgery, while retaining the assumption that an irregular child is an object to be corrected before being allowed to live. **Printed form:** diaetetic (§ 7). See [Surgery and extermination](#entry-surgery-extermination) (p. 112). ### Diameter {#register-105} The width of a circle measured through its centre. The Sphere names thirteen inches as the diameter of his largest circular section, giving his apparently supernatural visit a determinate geometrical scale. **Printed form:** diameter (§ 16). See [Sphere](#entry-sphere) (p. 107). ### Dimension {#register-106} An independent measurable extent or direction. The debate distinguishes adding a dimension from adding another name for an extent already familiar to the observer. **Printed form:** Dimension (§ 16). See [Dimension](#entry-dimension) (p. 39). ### Dimensional prejudices {#register-107} Assumptions imposed by one's accustomed range of perception and movement. The Preface distributes this limitation across Points, Lines, Squares and higher beings rather than restricting it to Flatland. **Printed form:** Dimensional prejudices (Preface). See [Imagination and modesty](#entry-imagination-modesty) (p. 61). ### Discursive {#register-108} Ranging over several topics rather than proceeding directly to the central subject. The narrator applies it to his long account of Flatland’s social institutions. **Printed form:** discursive (§ 11). See [History and revolution](#entry-history-revolution) (p. 60). ### Disrepute {#register-109} Loss of esteem or good standing. The narrator connects the neglect of mathematical study with a decline in its public reputation. **Printed form:** disrepute (§ 9). See [Science and institutions](#entry-science-institution) (p. 101). ### Divers {#register-110} Various or several. The Council's recorded resolution uses the formal older term for people accused of unsettling the state through revelations. **Printed form:** divers (§ 18). See [Prison and silence](#entry-prison-silence) (p. 90). ### Dodecagon {#register-111} A twelve-sided plane polygon and therefore a noble rank in Flatland. The impostor copies its twelve-colour signal without acquiring twelve actual sides. **Printed form:** Dodecagon (§ 10). See [Dodecagon](#entry-dodecagon) (p. 40). ### Domestic individuality {#register-112} The distinct persons and arrangements of the household seen together from above. The new perspective makes visible what the narrator formerly knew only through inference. **Printed form:** domestic individuality (§ 18). See [Wives and household](#entry-wives-household) (p. 126). ### Double Extra-Solids {#register-113} Figures one dimension beyond Extra-Solids, generated by their analogous motion. The dreamed lesson extends construction to five dimensions without supplying waking empirical confirmation. **Printed form:** Double Extra-Solids (§ 20). See [Fourth Dimension](#entry-fourth-dimension) (p. 57). ### Duly certified {#register-114} Officially attested in the prescribed manner. In the Female Code, certification of an illness involving involuntary movement authorises immediate destruction, so bureaucratic correctness supplies the warrant for killing rather than for care. **Printed form:** duly certified (§ 4). See [Women](#entry-women) (p. 128). ### Ecclesiastical {#register-115} Pertaining to the church or priesthood. Ecclesiastical secrets belong to the restricted information Women might overhear when mistaken for Priests. **Printed form:** ecclesiastical (§ 9). See [Circles and Priests](#entry-circle-priest) (p. 24). ### Editor {#register-116} The fictional Spacelander who represents the Square's explanations and qualifies their success. This character is distinct from the modern editor of the supplied annotated edition. **Printed form:** Editor (Preface). See [The Editor and the revised Preface](#entry-editor-preface) (p. 45). ### Egress {#register-117} An exit or means of getting out. The guards prevent the attacked soldiers from escaping. **Printed form:** egress (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Elicit {#register-118} To draw out information through questions. The narrator's patient inquiry initially extracts an account from a ruler who cannot imagine that familiar facts might be unknown. **Printed form:** elicited (§ 13). See [King of Lineland](#entry-king-lineland) (p. 69). ### Emanated {#register-119} Originated or issued from a source. The narrator locates the Bill’s political ingenuity in an Irregular Circle rather than a lower-class proposer. **Printed form:** emanated (§ 9). See [Cunning and policy](#entry-cunning-policy) (p. 35). ### Endowment {#register-120} Funds or property permanently assigned to support an institution or office. The complexity of recognising moving nobles is said to justify rich professorial endowments, tying academic prestige and expenditure to the social needs of the elite. **Printed form:** endowments (§ 6). See [Education and schools](#entry-education-schools) (p. 46). ### Endowments {#register-121} Funds or property assigned to support institutions, offices, or studies. The reformers demand their removal from established recognition and mathematical instruction. **Printed form:** endowments (§ 9). See [Science and institutions](#entry-science-institution) (p. 101). ### Ennobled {#register-122} Raised into a noble or privileged rank. The promise that rebellious leaders may eventually be ennobled encourages them to enter State Hospitals, making the language of honour an instrument for removing political opposition. **Printed form:** ennobled (§ 3). See [Class and caste](#entry-class-caste) (p. 27). ### Environed {#register-123} Surrounded or bounded. The theoretical figure environed with six Squares is a cautiously described Cube in the narrator's attempted treatise. **Printed form:** environed (§ 22). See [Cube](#entry-cube) (p. 33). ### Enwrap {#register-124} Wrap or envelop. A Circle surrounds the truth about his perimeter with a protective social mystery. **Printed form:** enwrap (§ 11). See [Circles and Priests](#entry-circle-priest) (p. 24). ### Esoteric {#register-125} Reserved for an initiated inner group. The Square reports only from hearsay that the highest university classes still use colour in advanced mathematics. **Printed form:** esoteric (§ 10). See [Science and institutions](#entry-science-institution) (p. 101). ### Essay {#register-126} To attempt or try. The narrator wants to essay his skill as a teacher partly because the experience is already slipping from memory. **Printed form:** essay (§ 21). See [Revelation and teaching](#entry-revelation-teaching) (p. 98). ### Eulogy {#register-127} Formal expressions of praise. The narrator calls his exaltation of Fog eulogies, drawing attention to the celebratory rhetorical style through which an apparently unpromising physical condition becomes the foundation of arts and sciences. **Printed form:** eulogies (§ 6). See [Fog](#entry-fog) (p. 55). ### Evangelize {#register-128} To proclaim a gospel or seek converts. The narrator briefly resolves to extend the dimensional message even to groups his society excludes from higher intellectual life. **Printed form:** evangelize (§ 21). See [Revelation and teaching](#entry-revelation-teaching) (p. 98). ### Expediency {#register-129} Practical advantage or suitability to an end. The reformers invoke it, together with Nature, to justify distinguishing everyone’s front from back. **Printed form:** Expediency (§ 9). See [Law and sanction](#entry-law-sanction) (p. 72). ### Extinguished {#register-130} Put to death, expressed through the image of quenching a light. In a world of luminous bodies the euphemism has physical resonance, but it also softens the proposal to kill failed university students in the name of mercy. **Printed form:** extinguished (§ 6). See [Surgery and extermination](#entry-surgery-extermination) (p. 112). ### Extra Cubes {#register-131} Figures belonging to the extension of the dimensional series beyond ordinary Cubes. Their inclusion among prejudiced beings turns the higher-dimensional analogy into an argument for shared fallibility. **Printed form:** Extra-Cubes (Preface). See [Solid humanity and superior races](#entry-solid-superior-races) (p. 105). ### Extra height {#register-132} The Square's provisional name for an unrecognised fourth direction in Space. The coined name helps formulate an analogy without supplying a direction the audience can measure. **Printed form:** extra-height (Preface). See [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113). ### Extra-solid angles {#register-133} The projected corners of the four-dimensional figure generated by a Cube. The Square predicts sixteen by analogy, but does not report a waking observation of them. **Printed form:** Extra-solid angles (§ 19). See [Fourth Dimension](#entry-fourth-dimension) (p. 57). ### Extra-Solids {#register-134} Four-dimensional figures constructed by moving Solids through a new independent direction. The instruction occurs in the Square's dream, not in a verified higher-dimensional journey. **Printed form:** Extra-Solids (§ 20). See [Fourth Dimension](#entry-fourth-dimension) (p. 57). ### Extremities {#register-135} The ends of a body or figure. A Lineland Man has a voice and an eye at each end, unlike the one-voiced visitor whom the King consequently misclassifies. **Printed form:** extremities (§ 13). See [Voice and selfhood](#entry-voice-selfhood) (p. 125). ### Extricating {#register-136} Freeing or disentangling oneself from a difficulty. The Square escapes a doctrinal dilemma by using an expedient that the Circles themselves also use. **Printed form:** extricating (§ 12). See [Circular doctrine](#entry-circular-doctrine) (p. 25). ### Faith {#register-137} The Square's surviving apprehension of a reality he can no longer fully comprehend. It belongs to the predicament of a witness with failing representational powers, not a universal substitute for reasoning. **Printed form:** faith (Preface). See [Faith reason and the reach of experience](#entry-faith-reason) (p. 51). ### Fall {#register-138} The narrator's name for his expulsion from Spaceland and the suffering that follows. The word combines literal descent with a biblical narrative pattern, without establishing that Abbott condemns the curiosity that provokes it. **Printed form:** Fall (§ 19). See [Prometheus Paradise and the cost of knowledge](#entry-prometheus-paradise) (p. 91). ### Family brain {#register-139} The registered angle treated as the hereditary measure of a family’s intelligence. Recording it in degrees gives a spurious precision to the account of how punishment and moral shock retard descendants’ ascent through the class system. **Printed form:** family brain (§ 5). See [Angle](#entry-angle) (p. 14). ### Fast society {#register-140} The fashionable pleasure-seeking set, with an implication of looseness or recklessness. Its approval legitimises an abbreviated use of feel that the narrator calls a barbarism, locating linguistic change in a morally suspect elite. **Printed form:** fast society (§ 5). See [Language and gender](#entry-language-gender) (p. 71). ### Fatuity {#register-141} Foolishness or lack of judgment. The narrator blames the bride’s relatives for allowing the fraudulent marriage to proceed. **Printed form:** fatuity (§ 10). See [Dodecagon](#entry-dodecagon) (p. 40). ### Fecundity {#register-142} Fertility or prolific reproduction. The Square attributes extraordinary fecundity to the criminalised poor, explaining their abundance as educational specimens and making their reproductive capacity a resource to be exploited or reduced. **Printed form:** fecundity (§ 5). See [Birth and ascent](#entry-birth-ascent) (p. 19). ### Feeler {#register-143} The person actively touching another figure’s angle to identify him. The capitalised role distinguishes the vulnerable examiner from the person examined, making the risks of a sneeze or movement central to the rules of the encounter. **Printed form:** Feeler (§ 5). See [Feeling and touch](#entry-feeling-touch) (p. 53). ### Feeling {#register-144} The practised identification of another figure by touching an angle. It is chiefly a test of class rather than personal identity, and its double role as physical contact and polite introduction exposes the social conventions embedded in a sensory act. **Printed form:** Feeling (§ 5). See [Feeling and touch](#entry-feeling-touch) (p. 53). ### Feeling is believing {#register-145} The Wife's maxim that touch establishes what sight may misjudge. Her examination correctly finds no angles, although feeling the section cannot yet disclose the whole Sphere. **Printed form:** Feeling is believing (§ 15). See [Touch and bodily proof](#entry-touch-belly) (p. 118). ### Felt {#register-146} The person whose angle is being touched during recognition. Used as a substantive, it names a temporary social role whose duty is complete stillness, since even an involuntary movement may fatally pierce the Feeler. **Printed form:** Felt (§ 5). See [Feeling and touch](#entry-feeling-touch) (p. 53). ### Fettered {#register-147} Bound with restraints so that movement is impossible. The capitalised occurrence begins the sentence describing classroom specimens: immobilisation protects pupils while rendering the human teaching material wholly subject to institutional use. **Printed form:** Fettered (§ 5). See [Education and schools](#entry-education-schools) (p. 46). ### Figure {#register-148} A geometrical form and, in this inhabited geometry, often a person. The Sphere corrects the Square's use of Figure for the prospective Cube, requiring the more specific dimensional term Solid. **Printed form:** Figure (§ 16). See [Dimension](#entry-dimension) (p. 39). ### Flagitious {#register-149} Grossly wicked or criminal. The word marks the extreme end of the misconduct that Pantocyclus attributes to bodily irregularity. **Printed form:** flagitious (§ 12). See [Configuration](#entry-configuration) (p. 31). ### Fog {#register-150} Atmospheric obscurity that progressively dims more distant portions of a figure. Unlike the obstructive fog familiar to the reader, it makes trained sight possible in Flatland by providing the tonal differences from which shape and rank can be inferred. **Printed form:** Fog (§ 6). See [Fog](#entry-fog) (p. 55). ### Foreland {#register-151} A headland or projecting stretch of coast. In the comparison with a sailor’s distant view, such projections disappear into a single apparent line: the example explains how a visible outline can conceal the shape that produces it. **Printed form:** forelands (§ 1). See [Recognition by sight](#entry-recognition-sight) (p. 94). ### Forsooth {#register-152} Indeed or truly, often used with irony. The Sphere's scornful use mocks Flatland's claim to call its plane Space, displaying impatience rather than a neutral definition. **Printed form:** forsooth (§ 16). See [Space and Spaceland](#entry-space-spaceland) (p. 106). ### Four in One {#register-153} The bass and tenor of one Man combined with the soprano and contralto of two Women. The King presents this four-part harmony as a necessary order of marriage rather than a local arrangement. **Printed form:** Four in One (§ 13). See [Wives and household](#entry-wives-household) (p. 126). ### Fourth Dimension {#register-154} An additional independent direction beyond Spaceland's three. It is reasoned about and sought, but the romance does not present a verified waking journey into it. **Printed form:** Fourth Dimension (§ 19). See [Fourth Dimension](#entry-fourth-dimension) (p. 57). ### Frail Sex {#register-155} A conventional collective designation of women as weak, both bodily and morally. Here it sits beside descriptions of women’s supposedly overwhelming lethal power, exposing the instability of a rhetoric that treats them as helpless and terrifying together. **Printed form:** Frail Sex (§ 4). See [Women](#entry-women) (p. 128). ### Franticly {#register-156} Madly or distractedly, in the Shakespearean motto about squaring one's talk. Its older spelling and double relation to speech and shape announce the risk that the Square's account will be heard as derangement. **Printed form:** franticly (Title Page). See [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103). ### Fraternal {#register-157} Pertaining to brothers or brotherly affection. The prison visits offer real familial care but no shared belief, separating kindness from intellectual conversion. **Printed form:** fraternal (§ 22). See [Prison and silence](#entry-prison-silence) (p. 90). ### Freeman {#register-158} A person released from serf condition and admitted to the Regular classes. Freedom is represented as the consequence of a sufficient angle rather than as a right possessed independently of bodily form. **Printed form:** freeman (§ 5). See [Class and caste](#entry-class-caste) (p. 27). ### Frugality {#register-159} Thrift and disciplined restraint in spending or consumption. It is made an ancestral prerequisite for an Equilateral birth, translating a conventional middle-class virtue into a supposed force that gradually reshapes descendants’ bodies. **Printed form:** frugality (§ 3). See [Birth and ascent](#entry-birth-ascent) (p. 19). ### Fruition {#register-160} Enjoyment or possession of what is desired. The dreamed Sphere leaves the Point to the ignorant enjoyment of its supposedly universal powers. **Printed form:** fruition (§ 20). See [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82). ### Full career {#register-161} At full speed or in the full course of motion. Lineland's inhabitants halt their rhythmic movement at the decisive instant of the marriage chorus. **Printed form:** full career (§ 13). See [Lineland](#entry-lineland) (p. 74). ### Furlong {#register-162} A measure of distance equal to one eighth of a mile, or 220 yards. Applying this substantial terrestrial measure to inhabitants only inches long gives their country an ordinary geographical scale despite the extraordinary bodies that occupy it. **Printed form:** furlongs (§ 2). See [Attraction and climate](#entry-attraction-climate) (p. 18). ### Gamboge {#register-163} A yellow pigment derived from a gum-resin, and the colour it produces. Here it is one of four colours assigned to the Square soldiers. **Printed form:** gamboge (§ 8). See [Painting](#entry-painting) (p. 84). ### Gentlemen {#register-164} Men of recognised social position, here grouped with the professional classes as Squares and Pentagons. The designation carries class entitlement beyond ordinary courtesy: being a gentleman is part of Flatland’s visible, hereditary arrangement of persons. **Printed form:** Gentlemen (§ 3). See [Class and caste](#entry-class-caste) (p. 27). ### Geometrical Progression {#register-165} A sequence with a constant multiplying ratio. The Sphere uses successive doubling to predict the Cube's eight terminal points from the earlier counts one, two and four. **Printed form:** Geometrical Progression (§ 16). See [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15). ### Gift of Modesty {#register-166} The intellectual and ethical humility the dedication hopes its supposedly superior readers may acquire. Calling it a gift does not make it an automatic consequence of inhabiting Space. **Printed form:** Gift of Modesty (Dedication). See [Imagination and modesty](#entry-imagination-modesty) (p. 61). ### Gospel of the Three Dimensions {#register-167} The visitor's message of a world beyond Flatland's plane. Its religious wording emphasizes transmission and conversion without establishing the messenger's divinity or infallibility. **Printed form:** Gospel of the Three Dimensions (§ 17). See [Revelation and teaching](#entry-revelation-teaching) (p. 98). ### Grandson {#register-168} The younger orphan Hexagon whose question about the third power anticipates a Cube. He later withdraws the suggestion after hearing the Council's proclamation against dimensional revelation. **Printed form:** Grandson (§ 15). See [Grandson](#entry-grandson) (p. 58). ### H C {#register-169} The individually addressed dedicatee within the general address to Space. The supplied editor generally identifies him as Howard Candler; the primary text gives initials only. **Printed form:** H. C. (Dedication). See [Dedication and the reader being addressed](#entry-dedication) (p. 36). ### Half-hour glass {#register-170} A sand-glass measuring thirty minutes. Its final run marks the millennium's turn, and turning it northward adapts timekeeping to Flatland's southward attraction. **Printed form:** half-hour glass (§ 15). See [Time and the millennium](#entry-time-millennium) (p. 116). ### Hand-alphabet {#register-171} An alphabet represented by finger positions, used in communication by or with deaf people. The narrator invokes it as the allegedly easier practice that obstructs lip-reading, an educational analogy reflecting a contested nineteenth-century preference for oral instruction. **Printed form:** hand-alphabet (§ 6). See [Language and gender](#entry-language-gender) (p. 71). ### Haply {#register-172} Perhaps or by chance. The Sphere's sombre prediction that the Square may later have time with his imprisoned brother hints at the similar confinement awaiting him. **Printed form:** haply (§ 19). See [Prison and silence](#entry-prison-silence) (p. 90). ### Harangue {#register-173} A forceful, extended public address or tirade. The Square attempts to educate the Point by denunciation, repeating an impatient style of teaching whose limits the episode reveals. **Printed form:** harangue (§ 20). See [Pointland](#entry-pointland) (p. 87). ### Hereditary level {#register-174} The inherited degree of bodily development and social status from which a child is thought liable to relapse. Fear of such relapse is used to justify permanently separating a newly certified Equilateral from his parents and relations. **Printed form:** hereditary level (§ 3). See [Birth and ascent](#entry-birth-ascent) (p. 19). ### Heresies {#register-175} Beliefs rejected by the ruling doctrinal authority. Here they include the ordinary belief that effort or education can influence conduct. **Printed form:** heresies (§ 12). See [Circular doctrine](#entry-circular-doctrine) (p. 25). ### Heterodox {#register-176} Departing from accepted belief. The narrator is already regarded as heterodox before his explicit public confession supplies the occasion for arrest. **Printed form:** heterodox (§ 22). See [Prison and silence](#entry-prison-silence) (p. 90). ### Hierarchy {#register-177} An ordered structure of authority, here especially the ruling priestly order. Its high status depends partly on distinction from other bodies. **Printed form:** Hierarchy (§ 9). See [Circles and Priests](#entry-circle-priest) (p. 24). ### High ness {#register-178} The Chief Circle's punning name for the height he challenges the Square to measure. It combines an unrecognised physical direction with the social language of Highness and high priesthood. **Printed form:** high-ness (Preface). See [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113). ### Hinder extremity {#register-179} The rear end of the line constituting a Woman’s body. The decorous anatomical circumlocution helps the narrator discuss bodily danger in a tone of polite detachment, even when that language precedes lethal legal restrictions. **Printed form:** hinder extremity (§ 4). See [Women](#entry-women) (p. 128). ### Historian {#register-180} The role through which the Square partly explains his adoption of customary exclusions and judgements. The Editor's qualification leaves open whether descriptive reporting has become allegiance. **Printed form:** Historian (Preface). See [A Square and the voice of the memoir](#entry-a-square) (p. 11). ### Historical pieces {#register-181} Paintings representing historical, legendary, or elevated narrative subjects. They belong to the list of pictorial genres whose variety Flatland’s ordinary vision cannot reproduce. **Printed form:** historical pieces (§ 8). See [Painting](#entry-painting) (p. 84). ### Homage {#register-182} An expression of submission, loyalty, or reverential respect. Compulsory painting would make every class acknowledge Colour’s authority. **Printed form:** homage (§ 9). See [Conformity and obedience](#entry-conformity-obedience) (p. 32). ### Honourable confinement {#register-183} Lifelong detention presented as a dignified privilege. The adjective conceals the loss of liberty suffered by rebel leaders enticed into State Hospitals, where prospective advancement becomes a pretext for permanent incapacitation. **Printed form:** honourable confinement (§ 3). See [Surgery and extermination](#entry-surgery-extermination) (p. 112). ### Horizon {#register-184} The limit or extent of vision. A Linelander's horizon is a Point because the eye can look only along the single line of its world. **Printed form:** horizon (§ 13). See [Lineland](#entry-lineland) (p. 74). ### Human diagonals {#register-185} A measure based on the cross-body extent of a Flatland figure. The narrator expresses the approach to Pointland in the bodily scale of his own world. **Printed form:** human diagonals (§ 20). See [Pointland](#entry-pointland) (p. 87). ### Idiom {#register-186} A characteristic form or manner of expression belonging to a community. The male scientific idiom is an exclusive social language whose meanings boys must learn while preserving the older vocabulary for conversations with their mothers. **Printed form:** idiom (§ 12). See [Language and gender](#entry-language-gender) (p. 71). ### Imagination {#register-187} The faculty whose enlargement the book desires, enabling readers to entertain a standpoint beyond familiar perception. Its desired companion is modesty, because imaginative reach alone need not overcome prejudice. **Printed form:** Imagination (Dedication). See [Imagination and modesty](#entry-imagination-modesty) (p. 61). ### Immunity {#register-188} Exemption from a burden or obligation. The narrator calls release from the school tribute an immunity while condemning the resulting survival and growth of the lower classes. **Printed form:** immunity (§ 9). See [Compensation](#entry-compensation) (p. 29). ### Immured {#register-189} Shut in or confined, literally enclosed within walls. The mildly Irregular survivor is immured in a Government Office, where employment is also compulsory residence, surveillance, and the denial of an independent adult life. **Printed form:** immured (§ 7). See [Irregularity](#entry-irregularity) (p. 65). ### Impartiality {#register-190} Freedom from bias between contending sides. The narrator describes Pantocyclus as presenting an appearance of it while conducting a partisan and lethal strategy. **Printed form:** impartiality (§ 10). See [Cunning and policy](#entry-cunning-policy) (p. 35). ### Impervious {#register-191} Not admitting or responding to something, here argument. The King applies the accusation to his visitor while treating his own conception of Space as beyond question. **Printed form:** impervious (§ 14). See [King of Lineland](#entry-king-lineland) (p. 69). ### Imposture {#register-192} Deception by assuming a false identity or status. An Isosceles can imitate a superior figure’s voice, so the possibility of imposture reveals that the supposedly natural social hierarchy requires continual verification. **Printed form:** imposture (§ 5). See [Voice and hearing](#entry-voice-hearing) (p. 123). ### Impregnable {#register-193} Unable to be breached or refuted. The Editor applies this confident judgement to the intellectual defence, then expressly refuses equivalent confidence about the moral defence. **Printed form:** impregnable (Preface). See [The Editor and the revised Preface](#entry-editor-preface) (p. 45). ### Inane {#register-194} Empty, pointless or lacking intelligible content. The Square's broken explanation ends in an inane gesture because he cannot enact the direction he is trying to teach. **Printed form:** inane (§ 21). See [Upward and Northward](#entry-direction-upward) (p. 122). ### Incommode {#register-195} To inconvenience or trouble. The Wife refuses to make the apparently exalted visitor move elsewhere and retires herself, showing how etiquette secures the private lesson. **Printed form:** incommode (§ 15). See [Wives and household](#entry-wives-household) (p. 126). ### Incredulity {#register-196} Unwillingness or inability to believe. General incredulity and mockery, as well as imprisonment and age, are said to have damaged the Square's mind. **Printed form:** incredulity (Preface). See [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120). Unwillingness or inability to believe. The Square's diminishing eye-brightness signals doubt, making an internal intellectual response visible within Flatland's bodily conventions. **Printed form:** incredulity (§ 16). See [Evidence and demonstration](#entry-evidence-demonstration) (p. 49). ### Indiscretion {#register-197} An imprudent or socially improper act. The Wife apologizes for treating the visitor as a Woman before discovering the smooth circular section that commands her deference. **Printed form:** indiscretion (§ 15). See [Wives and household](#entry-wives-household) (p. 126). ### Infecundity {#register-198} Lack of fertility. The Square's reported historical interpretation treats the Circles' reproductive decline as a limit upon their power, not as an extinction already completed in the narrative. **Printed form:** infecundity (Preface). See [Providence and the language of necessity](#entry-providence) (p. 93). Barrenness or lack of reproductive capacity. The Square fears that its continuation may make the Circular class unable to produce a Chief Circle. **Printed form:** infecundity (§ 12). See [Fertility and extinction](#entry-fertility-extinction) (p. 54). ### Infinitesimal {#register-199} Extremely small, here too small for the Flatlander to recognize and measure as a third dimension. The revised discussion distinguishes the body's slight height from the brightness through which the Square perceives it. **Printed form:** infinitesimal (§ 16). See [Dimension](#entry-dimension) (p. 39). ### Infinitesimally {#register-200} In an indefinitely minute degree. The revised defence grants all Flatland lines an equal minute thickness rather than making them absolutely without any third-dimensional extent. **Printed form:** infinitesimally (Preface). See [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113). ### Initiated {#register-201} Admitted into mysteries previously unavailable. The dedication uses religious and ceremonial language for a change in dimensional understanding and makes that change a model for further inquiry. **Printed form:** Initiated (Dedication). See [Initiation and mysteries](#entry-initiation-mysteries) (p. 62). ### Integrity {#register-202} Honesty and fidelity to duty. The doctrine attributes a lawyer’s integrity to exact right angles rather than a praiseworthy moral choice. **Printed form:** integrity (§ 12). See [Configuration](#entry-configuration) (p. 31). ### Intellectual Arts {#register-203} Learned methods and disciplines requiring mental training, particularly the recognition arts and mathematical sciences. Art here is not restricted to aesthetic production. **Printed form:** intellectual Arts (§ 9). See [Science and institutions](#entry-science-institution) (p. 101). ### Intercourse {#register-204} Ordinary social communication and dealings, without a specifically sexual sense here. The narrator claims that irregular bodies would make intercourse perilous or impossible, treating the convenience of familiar interaction as a justification for compulsory bodily conformity. **Printed form:** intercourse (§ 7). See [Regularity](#entry-regularity) (p. 97). ### Interpreter and summarizer {#register-205} The two roles claimed by the fictional Editor when transmitting the Square's moral defence. The phrase tells readers that they are receiving mediated interpretation rather than a literal transcript. **Printed form:** interpreter and summarizer (Preface). See [The Editor and the revised Preface](#entry-editor-preface) (p. 45). ### Intestines {#register-206} Internal organs, used here to locate the apparently bodiless voice. The King interprets a sound coming from an unrecognized lateral direction as arising within himself. **Printed form:** intestines (§ 13). See [Interior and exterior](#entry-interior-exterior) (p. 64). ### Introduction {#register-207} The formal presentation of one person to another through a mutual acquaintance. Flatland makes the convention materially testable: an introduction licenses reciprocal contact through which the parties establish each other’s geometric and social rank. **Printed form:** introduction (§ 5). See [Feeling and touch](#entry-feeling-touch) (p. 53). ### Invisible Cap {#register-208} A figurative cap of invisibility, the magical concealment device familiar from myth and fairy tale. The narrator assigns its function to a Woman’s dim rear point, translating a marvellous object into Flatland’s optical conditions. **Printed form:** Invisible Cap (§ 4). See [Women](#entry-women) (p. 128). ### Iota {#register-209} An extremely small part, from the name of a Greek letter. The promise not to alter an iota asserts exact testimony that later failures of memory make difficult to sustain. **Printed form:** iota (§ 19). See [Memory and forgetting](#entry-memory-forgetting) (p. 76). ### Isosceles Hospital {#register-210} An institution for correcting the unequal sides of a malformed Isosceles. Pantocyclus prescribes it as bodily treatment for what would otherwise appear as moral failure. **Printed form:** Isosceles Hospital (§ 12). See [Configuration](#entry-configuration) (p. 31). ### Jostled {#register-211} Knocked or pushed in a crowd. Painting reduces such collisions by making a body easier to recognize. **Printed form:** jostled (§ 8). See [Colour](#entry-colour) (p. 28). ### Juggler {#register-212} A conjurer or deceptive performer, rather than only someone who tosses objects. The Square uses the explanation to accommodate strange visible effects without accepting another dimension. **Printed form:** juggler (§ 16). See [Evidence and demonstration](#entry-evidence-demonstration) (p. 49). ### Kinetic {#register-213} Concerned with motion. Wentbridge’s Kinetic Geometry addresses the changing appearances of figures that move and rotate, giving an imposing academic title to the practical art of navigating elite company. **Printed form:** Kinetic (§ 6). See [Recognition by sight](#entry-recognition-sight) (p. 94). ### Kinetics {#register-214} The study of bodies in motion and the forces associated with motion. The chapter pairs it with Statics among the studies displaced by colour recognition. **Printed form:** Kinetics (§ 9). See [Science and institutions](#entry-science-institution) (p. 101). ### Last resource of civilization {#register-215} The Sphere's euphemism for resorting to coercion. Failure to persuade is made a reason to force the pupil into the new experience. **Printed form:** last resource of civilization (§ 17). See [Revelation and teaching](#entry-revelation-teaching) (p. 98). ### Latent {#register-216} Hidden or not directly observable. The narrator imagines an unproved latent effect to reconcile punishment with official bodily determinism. **Printed form:** latent (§ 12). See [Configuration](#entry-configuration) (p. 31). ### Legislature {#register-217} The lawmaking authority, presented as capable of regulating both buildings and permissible inquiry. Its move from taxing investigations of light to prohibiting them exposes the political enforcement behind the appearance of settled natural knowledge. **Printed form:** Legislature (§ 2). See [Nature and law](#entry-nature-law) (p. 81). ### Licentious {#register-218} Unrestrained, especially by accepted moral rules. It is one of the hostile labels the narrator concedes against the age whose beauty he admires. **Printed form:** licentious (§ 8). See [Painting](#entry-painting) (p. 84). ### Line of Lines {#register-219} The Square's description of his own construction from a moving Line. He turns a valid generative relation into a claim that he completes and infinitely surpasses the King. **Printed form:** Line of Lines (§ 14). See [Movement and section](#entry-movement-section) (p. 79). ### Lineland {#register-220} The one-dimensional world the Square visits in a dream. Its inhabitants cannot pass one another, see only Points along their horizon, and organize identity and marriage through hearing. **Printed form:** Lineland (§ 13). See [Lineland](#entry-lineland) (p. 74). ### Lip-speech {#register-221} Speech articulated with the lips, here part of the oral education of deaf people and paired with lip-reading. The narrator prizes it above manual communication in order to justify withholding the supposedly easier art of Feeling from elite children. **Printed form:** lip-speech (§ 6). See [Language and gender](#entry-language-gender) (p. 71). ### Local Speculative Society {#register-222} The discussion society where the narrator finally recounts his journey openly. A paper defending the restriction to two dimensions provokes the speech that leads to his arrest. **Printed form:** Local Speculative Society (§ 22). See [Prison and silence](#entry-prison-silence) (p. 90). ### Logical anticipations {#register-223} Predictions reached through reasoning before direct factual confirmation. The Square asks the Sphere to test these anticipations rather than claiming already to have witnessed a fourth-dimensional world. **Printed form:** logical anticipations (§ 19). See [Analogy](#entry-analogy) (p. 12). ### Logical dialect {#register-224} The supposedly rational vocabulary reserved for males and their books. Its secrecy underwrites the men’s authority, and the narrator fears that a child might disclose it to a mother and expose the duplicity of their deferential speech. **Printed form:** logical dialect (§ 12). See [Language and gender](#entry-language-gender) (p. 71). ### Long Vacation {#register-225} The extended holiday during which the lawyer-narrator pursues geometry. The story locates it at the end of Flatland's year without establishing an earthly season. **Printed form:** Long Vacation (§ 13). See [Time and the millennium](#entry-time-millennium) (p. 116). ### Lucid {#register-226} Clear and intelligible. The King demands a lucid description of the new world, exposing the gap between the visitor's confidence and his ability to make an unfamiliar direction understood. **Printed form:** lucid (§ 14). See [Evidence and demonstration](#entry-evidence-demonstration) (p. 49). ### Luminary {#register-227} A source or organ of light, here the Square's eye. He points to its proper position at an angle, while the Sphere means an eye in an entirely different dimensional location. **Printed form:** luminary (§ 16). See [Interior and exterior](#entry-interior-exterior) (p. 64). ### Luminous {#register-228} Giving out light, as the edges of Flatland’s inhabitants do. Their visibility is built into their bodies rather than supplied by a sun; differences of brightness will therefore carry information about living bodies and their positions. **Printed form:** luminous (§ 1). See [Eye and the visible line](#entry-eye-retina) (p. 50). ### Luminous wake {#register-229} A shining trace left by movement. The Sphere asks the Square to imagine such a trace so that familiar Lines and Squares can lead towards a generated Cube. **Printed form:** luminous wake (§ 16). See [Movement and section](#entry-movement-section) (p. 79). ### Lunatic asylum {#register-230} An institution confining people deemed insane. Flatland’s unsuccessful investigators of the origin of light crowd these establishments, preparing the connection between intellectual nonconformity and coercive custody that the narrator later experiences himself. **Printed form:** lunatic asylums (§ 2). See [Nature and law](#entry-nature-law) (p. 81). ### Lustre {#register-231} Brightness or brilliance of appearance. It is a feminine attraction for which a Circle may disregard his professed concern about pedigree. **Printed form:** lustre (§ 12). See [Marriage and selection](#entry-marriage-selection) (p. 75). ### Lustrous {#register-232} Shining or luminous. The Point-like beings are visible presences, but the Square must learn that their role within Lineland differs from what his own world would suggest. **Printed form:** lustrous (§ 13). See [Lineland](#entry-lineland) (p. 74). ### Mainstays {#register-233} Principal supports. The Circles are represented as the supporting pillars of the Constitution. **Printed form:** mainstays (§ 11). See [Circles and Priests](#entry-circle-priest) (p. 24). ### Manufactory {#register-234} A manufacturing establishment or factory. The single colour manufactory is kept secret by annually killing and replacing its workers. **Printed form:** manufactory (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Many in the One {#register-235} The Sphere's account of himself as a body composed of many circular sections. A grand philosophical formulation receives a specific geometrical application. **Printed form:** Many in the One (§ 18). See [Sphere](#entry-sphere) (p. 107). ### Marshal’s baton {#register-236} The ceremonial staff signifying high military command. The legendary Circle gives it up, together with his crown, for the painter’s brush. **Printed form:** marshal’s baton (§ 8). See [Painting](#entry-painting) (p. 84). ### Mauve {#register-237} A pale purple colour, one of the Square artillerymen’s four hues. The modern annotation identifies its strikingly recent Victorian dye-history. **Printed form:** mauve (§ 8). See [Painting](#entry-painting) (p. 84). ### Meanest capacity {#register-238} The least intellectual ability or weakest understanding; meanest does not mean the cruellest. The narrator claims even such a reader must recognise women’s danger, using a patronising appeal to obviousness to forestall examination of his conclusions. **Printed form:** meanest capacity (§ 4). See [Women](#entry-women) (p. 128). ### Memoirs {#register-239} A retrospective account by the participant whose experiences are told. The prison narrative and its fictional editorial mediation distinguish these memoirs from the earlier inner treatise titled Through Flatland to Thoughtland. **Printed form:** Memoirs (Preface). See [A Square and the voice of the memoir](#entry-a-square) (p. 11). ### Mercurial versatility {#register-240} Quick, lively adaptability. It describes the young Tradesman’s early practical abilities, which failed aristocratic students lack along with the trained powers of graduates, leaving them excluded from the advantages of either class. **Printed form:** mercurial versatility (§ 6). See [Education and schools](#entry-education-schools) (p. 46). ### Methought {#register-241} It seemed to me. The archaic form marks the dreamer's report of the King's threat and helps carry the grand martial fantasy into the waking breakfast-bell. **Printed form:** methought (§ 14). See [Dream and vision](#entry-dream-vision) (p. 43). ### Micrometer {#register-242} An instrument for measuring very small distances. Its proposed use does not solve the Square's problem because the Flatlanders cannot identify what direction the instrument should measure. **Printed form:** micrometer (Preface). See [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113). ### Military review {#register-243} A ceremonial display or inspection of troops. The coordinated movement of differently painted bodies makes this an especially rich artistic spectacle. **Printed form:** military review (§ 8). See [Painting](#entry-painting) (p. 84). ### Millenary {#register-244} A thousand-year period or its turn. The Council orders renewed searches at each millenary, converting revelation's rare timetable into a schedule for suppression. **Printed form:** millenary (§ 18). See [Time and the millennium](#entry-time-millennium) (p. 116). ### Millennium {#register-245} A thousand-year period. The supplied 1884 text calls the newly opening period the second, despite the surrounding year-numbering; that reading should be reported rather than silently repaired. **Printed form:** Millennium (§ 15). See [Time and the millennium](#entry-time-millennium) (p. 116). ### Miscarriage {#register-246} An unfortunate accident or disastrous failure, not a lost pregnancy in this context. It denotes the narrator’s ancestor accidentally piercing a Polygon during Feeling, an event whose consequences extend through the family’s inherited status. **Printed form:** miscarriage (§ 5). See [Feeling and touch](#entry-feeling-touch) (p. 53). ### Modesty {#register-247} Restraint in judging one's own knowledge and superiority. It asks a reader to admit a possible limit without forbidding active speculation. **Printed form:** Modesty (Dedication). See [Imagination and modesty](#entry-imagination-modesty) (p. 61). ### Molest {#register-248} To trouble or disturb, without the later specifically sexual implication. The visitor uses it in his apology after discovering he has addressed a monarch as a Woman. **Printed form:** molested (§ 13). See [King of Lineland](#entry-king-lineland) (p. 69). ### Monarch of the world {#register-249} The King of Lineland's title for himself. His claim makes the single line he rules coextensive with the whole world, joining political authority to a limit of conception. **Printed form:** Monarch of the world (§ 13). See [King of Lineland](#entry-king-lineland) (p. 69). ### Monopolising {#register-250} Reserving a benefit or practice to a restricted group. The reformers use the term for arts whose institutional support maintains aristocratic advantage. **Printed form:** monopolising (§ 9). See [Reform and equality](#entry-reform-equality) (p. 95). ### Monstrosity {#register-251} A supposedly malformed being. The King treats one unfamiliar voice as evidence of defective femininity, turning the Square's own classificatory prejudices against him. **Printed form:** Monstrosity (§ 13). See [King of Lineland](#entry-king-lineland) (p. 69). ### Moral obliquity {#register-252} Crookedness of conduct or departure from what is right, drawing on obliquity’s literal sense of slanting. Flatland fuses the figurative and geometrical senses by treating an irregular bodily outline as equivalent to moral fault and criminality. **Printed form:** moral obliquity (§ 7). See [Irregularity](#entry-irregularity) (p. 65). ### Moral terminology {#register-253} The vocabulary for describing and judging conduct. The Square's unfamiliarity with Spaceland's moral language is the Editor's reason for mediating his defence against the charge of misogyny. **Printed form:** moral terminology (Preface). See [The Editor and the revised Preface](#entry-editor-preface) (p. 45). ### Must needs {#register-254} Must necessarily. In the rejected assertion that the unknown must have precisely a certain form, the idiom intensifies a certainty the book asks its readers to resist. **Printed form:** must needs (Preface). See [Providence and the language of necessity](#entry-providence) (p. 93). ### Myriads {#register-255} Extremely large numbers of people. The term anticipates the multitude killed after the revolutionary leader’s defeat. **Printed form:** myriads (§ 9). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Mysteries {#register-256} Truths or experiences to which the speaker has been admitted through initiation. In this setting the religious register gives dimensional discovery dignity while leaving further mysteries possible. **Printed form:** Mysteries (Dedication). See [Initiation and mysteries](#entry-initiation-mysteries) (p. 62). ### Nature {#register-257} The larger order that the Square believes can redirect the Circles' policies to unintended ends. This providential use must be distinguished from the narrator's local invocations of natural law to justify oppression. **Printed form:** Nature (Preface). See [Providence and the language of necessity](#entry-providence) (p. 93). ### Neo-Therapeutic Cemetery {#register-258} The burial ground crowded by children who die during attempts at surgical promotion. It supplies the material counter-image to the successful children’s celebratory processions. **Printed form:** Neo-Therapeutic Cemetery (§ 11). See [Fertility and extinction](#entry-fertility-extinction) (p. 54). ### Non-dimensional Gulf {#register-259} The Point's realm without length, breadth or height. The word Gulf makes a spatial image of a condition that lacks internal extension. **Printed form:** non-dimensional Gulf (§ 20). See [Pointland](#entry-pointland) (p. 87). ### O yes! O yes! {#register-260} The herald's call demanding attention before a public proclamation. Its interruption of a private lesson makes the state's prohibition audible inside the family. **Printed form:** O yes! O yes! (§ 21). See [Grandson](#entry-grandson) (p. 58). ### Objection {#register-261} A challenge requiring an answer. The Preface separates a problem about visibility and thickness from a moral problem about the narrator's treatment of women, and grants the two replies different degrees of success. **Printed form:** objection (Preface). See [The Editor and the revised Preface](#entry-editor-preface) (p. 45). ### Ocular demonstration {#register-262} A showing directed to the eye. The Sphere expects visible changes in his section to establish their cause, but the Square sees the effects without understanding the new direction. **Printed form:** ocular demonstration (§ 16). See [Evidence and demonstration](#entry-evidence-demonstration) (p. 49). ### Omnipresence {#register-263} Presence everywhere. Applied ironically to the Point, it is a vacuous achievement because the being recognizes no world beyond itself. **Printed form:** omnipresence (§ 20). See [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82). ### Omniscience {#register-264} Knowledge of everything. The Point's claim depends on treating itself as the only thing there is; it differs from the visual omnividence debated in §18. **Printed form:** omniscience (§ 20). See [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82). ### Omnividence {#register-265} All-seeing, the rare word the Square applies to his new view of Flatland. The Sphere denies that visual access makes anyone more just, loving or divine. **Printed form:** omnividence (§ 18). See [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82). ### Order {#register-266} The restored rule of the existing hierarchy. Its triumphant capitalization attaches a legitimating name to the outcome of an organized massacre. **Printed form:** Order (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Ordinance {#register-267} An authoritative decree or prescribed arrangement. Calling the relation between intelligence and blunter angles an ordinance of Nature lends the vocabulary of government to biology, as though the natural world had legislated for aristocratic security. **Printed form:** ordinance (§ 3). See [Nature and law](#entry-nature-law) (p. 81). ### Palled {#register-268} Lost their power to interest or delight. Ordinary pleasures fade after the dimensional visit, as everyday sights continually remind the narrator of an inaccessible larger view. **Printed form:** palled (§ 22). See [Memory and forgetting](#entry-memory-forgetting) (p. 76). ### Pantocyclus {#register-269} The Chief Circle who orchestrates the defeat of the Colour Revolt and is later credited with the doctrine of Configuration. The modern annotation glosses his Greek-derived name as All-Circle. **Printed form:** Pantocyclus (§ 10). See [Chief Circle](#entry-chief-circle) (p. 20). ### Paradise {#register-270} The Square's name for the height of his happiness when he learns to recognize Solids. Its pairing with his subsequent Fall frames intellectual discovery in the language of an attained and lost blessed condition. **Printed form:** Paradise (§ 19). See [Prometheus Paradise and the cost of knowledge](#entry-prometheus-paradise) (p. 91). ### Parallelogram {#register-271} A quadrilateral with opposite sides parallel. The educated Square insists that a visible Woman is scientifically a very thin Parallelogram, not a perfectly breadthless abstract line. **Printed form:** Parallelogram (§ 16). See [Dimension](#entry-dimension) (p. 39). ### Pasteboard {#register-272} Stiff card made from layers of paper, proposed as material for the reader’s model figures. The familiar schoolroom material turns an abstract claim about vision into an experiment: lower the eye to the table and the model’s distinct outline becomes a line. **Printed form:** pasteboard (§ 1). See [Recognition by sight](#entry-recognition-sight) (p. 94). ### Patent {#register-273} Plainly evident or open to observation. By declaring the consequences of irregularity patent to Spaceland readers, the Square presses his assumptions into the form of common knowledge rather than demonstrating that they warrant the policies he supports. **Printed form:** patent (§ 7). See [Regularity](#entry-regularity) (p. 97). Plain, open or readily intelligible. The narrator's assertion that the dream's higher methods are patent even to women preserves his gender prejudice inside apparent intellectual liberation. **Printed form:** patent (§ 20). See [Wives and household](#entry-wives-household) (p. 126). ### Peace-cry {#register-274} The continuous warning sound every Woman must make in a public place on pain of death. Its peaceful name contrasts with both the bodily danger it signals and the state violence that enforces its uninterrupted production. **Printed form:** Peace-cry (§ 4). See [Voice and hearing](#entry-voice-hearing) (p. 123). ### Pedigrees {#register-275} Records of family descent. State-supervised pedigrees claim to reveal women’s otherwise invisible potential to produce irregular offspring. **Printed form:** pedigrees (§ 12). See [Marriage and selection](#entry-marriage-selection) (p. 75). ### Penal Laws {#register-276} Laws imposing penalties and civil disabilities on a defined group. The Irregular Penal Laws institutionalise suspicion of bodily difference through restrictions on work, marriage, movement, and survival, making exclusion part of the constitution of ordinary life. **Printed form:** Penal Laws (§ 7). See [Irregularity](#entry-irregularity) (p. 65). ### Pencil {#register-277} A fine paintbrush in the older sense. The Circle’s adoption of the artist’s pencil represents the abandonment of command for painting. **Printed form:** pencil (§ 8). See [Painting](#entry-painting) (p. 84). ### Perdition {#register-278} Utter ruin or destruction, with religious associations of damnation. Pantocyclus applies it to the supposed coming loss of domestic happiness and constitutional order. **Printed form:** perdition (§ 10). See [Cunning and policy](#entry-cunning-policy) (p. 35). ### Perimeter {#register-279} The enclosing boundary of a plane figure. The Square's eye sits on it and looks along Flatland, unlike the hypothetical eye on his exposed flat side imagined by the Sphere. **Printed form:** Perimeter (§ 16). See [Interior and exterior](#entry-interior-exterior) (p. 64). ### Peroration {#register-280} The concluding, usually heightened portion of a formal speech. His fervent appeal abandons the disguise of fiction and asks the audience openly to believe in three dimensions. **Printed form:** peroration (§ 22). See [Prison and silence](#entry-prison-silence) (p. 90). ### Perspective {#register-281} The visual relations through which depth and spatial position are inferred. The newly arrived Square must learn it, along with light and shade, before he can recognize Solids reliably. **Printed form:** perspective (§ 19). See [Cube](#entry-cube) (p. 33). ### Perturbed angularity {#register-282} Disordered mental activity expressed in Flatland's geometrical vocabulary. The Sphere reports an explanation that attributes apparitions to the seer's brain instead of an external higher world. **Printed form:** perturbed angularity (§ 19). See [Dream and vision](#entry-dream-vision) (p. 43). ### Perusal {#register-283} Reading or examination of a written work. A single book could expose the contrast between men’s private beliefs and their language to Women. **Printed form:** perusal (§ 12). See [Science and institutions](#entry-science-institution) (p. 101). ### Perversity {#register-284} Stubborn or wilful wrongheadedness. The Square interprets the King's failure to understand as perversity, foreshadowing the Sphere's impatience with him. **Printed form:** perversity (§ 14). See [King of Lineland](#entry-king-lineland) (p. 69). ### Phalanx {#register-285} A close, formidable formation of armed bodies. Convicts form an impassable barrier at every entrance to the hall. **Printed form:** phalanx (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Phantasmal vision {#register-286} A dreamlike or spectral sight. The Sphere uses the phrase for the Square's previous dream of Lineland, claiming to have read it upon his exposed brain. **Printed form:** phantasmal vision (§ 16). See [Dream and vision](#entry-dream-vision) (p. 43). ### Philanthropy {#register-287} Concern for human welfare, here organised humanitarian advocacy for changing the treatment of Irregulars. Calling it falsely named lets the narrator dismiss sympathy as mistaken sentiment while presenting the suffering of a minority as necessary policy. **Printed form:** Philanthropy (§ 7). See [Irregularity](#entry-irregularity) (p. 65). ### Picturesque incidents {#register-288} Striking events capable of vivid telling and strong emotional effect. The narrator recommends that statesmen exploit, anticipate, and sometimes perhaps manufacture them. **Printed form:** picturesque incidents (§ 10). See [Cunning and policy](#entry-cunning-policy) (p. 35). ### Placability {#register-289} Readiness to be appeased or reconciled. The Sphere's placability belongs to the Square's dream and must not be treated as an independently witnessed waking change of mind. **Printed form:** placability (§ 20). See [Dream and vision](#entry-dream-vision) (p. 43). ### Plausible {#register-290} Apparently persuasive. The Editor concedes this quality to the thickness objection before presenting the Square's answer, giving the difficulty more seriousness than a dismissive caricature would allow. **Printed form:** plausible (Preface). See [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113). ### Plebeian {#register-291} Belonging to the common people or lower social orders. Voice-discrimination is called a plebeian virtue, showing that an ability may be genuinely useful while remaining socially discredited because of the people who chiefly possess it. **Printed form:** plebeian (§ 5). See [Class and caste](#entry-class-caste) (p. 27). ### Plume yourself {#register-292} To take pride in or congratulate oneself on something. The Square attacks the King's satisfaction with inferring a Line while boasting about his own broader, still limited range. **Printed form:** plume yourself (§ 14). See [King of Lineland](#entry-king-lineland) (p. 69). ### Pointland {#register-293} The zero-dimensional world of a single self-satisfied Point, encountered in a dream. It cannot recognize another being and interprets external correction as its own thought. **Printed form:** Pointland (§ 20). See [Pointland](#entry-pointland) (p. 87). ### Polygonal {#register-294} Many-sided, but specifically an honourable designation acquired by the upper ranks of Flatland’s nobility. The transition from a geometrical adjective to a title makes social prestige appear to follow naturally from increasing numbers of sides. **Printed form:** Polygonal (§ 3). See [Polygon](#entry-polygon) (p. 88). ### Portent {#register-295} An ominous or extraordinary occurrence. A high-born Woman’s turning her back on her husband is described as a portent, exaggerating a bodily movement into a threat to the orderly status of the household. **Printed form:** portent (§ 4). See [Women](#entry-women) (p. 128). ### Posterity {#register-296} A person’s descendants or later generations. For an Isosceles, improvement is chiefly a hope for posterity, allowing a prospect too remote to benefit the individual to sustain loyalty to the hierarchy that degrades him. **Printed form:** posterity (§ 3). See [Birth and ascent](#entry-birth-ascent) (p. 19). Future descendants considered as a line or collective. The number of their sides and their ability to reproduce determine the ruling class’s prospects. **Printed form:** posterity (§ 11). See [Fertility and extinction](#entry-fertility-extinction) (p. 54). ### Powder-magazine {#register-297} Buildings for storing gunpowder and military explosives. They occur among the state structures exempted from the ban on sharp triangular corners, where an injurious shape becomes a useful deterrent rather than an unacceptable public danger. **Printed form:** powder-magazines (§ 2). See [Doors and houses](#entry-doors-houses) (p. 42). ### Prattle {#register-298} Light or supposedly childish talk. The grandfather calls the boy's geometrical speculation prattle even while remaining unable to dismiss the question it has raised. **Printed form:** prattle (§ 15). See [Grandson](#entry-grandson) (p. 58). ### Prearrangement {#register-299} An arrangement supposedly made in advance by a wise governing power. The Square praises it for denying women the memory or expectation that would let them dwell on their oppression, converting deprivation into a consoling evidence of providence. **Printed form:** Prearrangement (§ 4). See [Nature and law](#entry-nature-law) (p. 81). ### Precipitated {#register-300} Hurled or flung suddenly and violently. The Square rushes at his teacher when the proposed Cube seems intolerable mockery, making intellectual impasse erupt into bodily action. **Printed form:** precipitated (§ 16). See [Sphere](#entry-sphere) (p. 107). ### Preclude {#register-301} To prevent or make impossible. The President promises no unnecessary discomfort beyond what is required to preclude escape, narrowing concern to confinement's administration rather than its justice. **Printed form:** preclude (§ 22). See [Prison and silence](#entry-prison-silence) (p. 90). ### Precocious {#register-302} Unusually advanced for one's age. The grandson's early mathematical ability makes him the hoped-for first pupil, but civic fear interrupts what intelligence alone might permit. **Printed form:** precocious (§ 21). See [Grandson](#entry-grandson) (p. 58). ### Preconcerted {#register-303} Arranged or agreed in advance. The final words of Pantocyclus’s speech are an agreed signal for the attack. **Printed form:** preconcerted (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Presence {#register-304} The sensed nearness of someone not yet visible. The chill and whisper precede the Sphere's visible section and give a geometrical arrival the atmosphere of a supernatural visitation. **Printed form:** Presence (§ 15). See [Sphere](#entry-sphere) (p. 107). ### Pretext {#register-305} A professed ground for action, with an implication that it may excuse rather than fully justify it. The narrator treats many-sidedness as the innovators’ pretext for giving different sides different colours. **Printed form:** pretext (§ 8). See [Colour](#entry-colour) (p. 28). ### Priestly order {#register-306} The highest rank, comprising figures whose numerous tiny sides cannot be distinguished from a circular outline. The name joins religious office to the summit of inherited social power; the apparent Circle is both priest and ruler. **Printed form:** Priestly order (§ 3). See [Class and caste](#entry-class-caste) (p. 27). ### Priests {#register-307} Members of Flatland’s highest, supposedly Circular order. Their authority extends over government, commerce, education, and science as well as theology. **Printed form:** Priests (§ 11). See [Circles and Priests](#entry-circle-priest) (p. 24). ### Pristine {#register-308} Original and unimpaired. The Circles are said to preserve their intellectual clarity while other classes abandon difficult recognition skills. **Printed form:** pristine (§ 9). See [Science and institutions](#entry-science-institution) (p. 101). ### Professional Men {#register-309} Members of occupations treated as requiring specialised learning and carrying gentlemanly status. They occupy the Square and Pentagonal ranks, so professional distinction is represented as an inherited bodily form rather than simply an acquired qualification. **Printed form:** Professional Men (§ 3). See [Class and caste](#entry-class-caste) (p. 27). ### Progenitor {#register-310} An ancestor or originating parent. The Square imagines himself progenitor of a Cube because a Square's movement through a new direction can generate it. **Printed form:** Progenitor (§ 19). See [Cube](#entry-cube) (p. 33). ### Progenitors {#register-311} Ancestors or forebears. Surgery is fancifully said to double their number by conferring the rank that would ordinarily require many generations. **Printed form:** progenitors (§ 11). See [Fertility and extinction](#entry-fertility-extinction) (p. 54). ### Prometheus {#register-312} The mythic giver of fire punished for benefiting humanity. The Square invokes him for his own rebellious search, then bitterly contrasts the Titan’s useful gift with his own failure to bring his countrymen any accepted knowledge. **Printed form:** Prometheus (§ 19). See [Prometheus Paradise and the cost of knowledge](#entry-prometheus-paradise) (p. 91). ### Promulgators of paradoxes {#register-313} People publicly advancing propositions that contradict received belief. This dismissive designation introduces reformers who argue that persecution produces the Irregular’s hostility; the label prejudges their case even while the text gives their argument considerable force. **Printed form:** promulgators of paradoxes (§ 7). See [Irregularity](#entry-irregularity) (p. 65). ### Proof positive {#register-314} Supposedly decisive evidence. The visitor announces the changing section as proof positive, but the subsequent failure distinguishes seeing an effect from accepting its explanation. **Printed form:** proof positive (§ 16). See [Evidence and demonstration](#entry-evidence-demonstration) (p. 49). ### Propagation {#register-315} Reproduction and continuation of a lineage. The laws of Circular propagation combine faster increase of sides with reduced fertility. **Printed form:** propagation (§ 11). See [Fertility and extinction](#entry-fertility-extinction) (p. 54). ### Prosecution {#register-316} Sustained pursuit or carrying through of an undertaking, not criminal proceedings. The prosecution of Sight Recognition requires time and money, identifying the material resources concealed beneath the language of a naturally superior art. **Printed form:** prosecution (§ 6). See [Education and schools](#entry-education-schools) (p. 46). ### Prospect {#register-317} The view presented to the eye, rather than a future possibility. Here every prospect resolves into a visible line. **Printed form:** prospect (§ 8). See [Painting](#entry-painting) (p. 84). ### Prostrating {#register-318} Bowing or casting oneself down in submission; here the act is explicitly mental. The narrator's reverence for his guide exceeds the geometrical discovery it follows. **Printed form:** Prostrating (§ 18). See [Sphere](#entry-sphere) (p. 107). ### Proximity {#register-319} Nearness in space. Lineland's marriages dispense with bodily proximity, showing how an institution can be reimagined around a different physical constraint. **Printed form:** proximity (§ 13). See [Lineland](#entry-lineland) (p. 74). ### Purged {#register-320} Cleared of persons treated as an impurity or dangerous excess. In context it is a cleansing euphemism for organized elimination of the lower orders. **Printed form:** purged (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Quietism {#register-321} Enforced mental inactivity, used here for the system that withholds education from women. The term’s associations with passive repose acquire a coercive turn: the policy produces the intellectual decline that supposedly validates the original exclusion. **Printed form:** quietism (§ 12). See [Language and gender](#entry-language-gender) (p. 71). ### Rapt {#register-322} Carried away or transported. The marriage account describes the triplet as vocally transported into union, making an ecstatic term do the work of impossible bodily movement. **Printed form:** rapt (§ 13). See [Wives and household](#entry-wives-household) (p. 126). ### Reactionary {#register-323} Favouring a return to, or defence of, the established order against reform. The Circles arrange the attendance of Women committed to opposing the colour movement. **Printed form:** reactionary (§ 10). See [Cunning and policy](#entry-cunning-policy) (p. 35). ### Realise {#register-324} To make something fully present to understanding or sight, rather than merely know the statement that it exists. The Square can no longer realise height as he once did. **Printed form:** realise (Preface). See [Faith reason and the reach of experience](#entry-faith-reason) (p. 51). ### Redundant population {#register-325} People represented as surplus to the requirements of society. Applied to the lower Isosceles classes, the phrase enables their deaths in domestic violence to be counted as a public benefit rather than a calamity. **Printed form:** redundant population (§ 4). See [Surgery and extermination](#entry-surgery-extermination) (p. 112). ### Reform {#register-326} Alteration of an existing institution presented as improvement. Pantocyclus appears to accept its principle while organizing opposition to the Colour Bill and preparing violence. **Printed form:** Reform (§ 10). See [Reform and equality](#entry-reform-equality) (p. 95). ### Regular Hospitals {#register-327} Institutions intended to correct irregularities in Triangles, Squares, and Polygons. Treatment is set against the threatened alternatives of prison or execution. **Printed form:** Regular Hospitals (§ 12). See [Configuration](#entry-configuration) (p. 31). ### Remonstrance {#register-328} An objection or protest. The visitor touches the Square's interior before he can remonstrate, so an announced educational benefit is imposed rather than accepted. **Printed form:** remonstrance (§ 17). See [Touch and bodily proof](#entry-touch-belly) (p. 118). ### Responsive note {#register-329} A vocal pitch that answers another in harmony. Lineland's distant lovers recognize their intended spouses through sound rather than sight or contact. **Printed form:** responsive note (§ 13). See [Voice and selfhood](#entry-voice-selfhood) (p. 125). ### Retinue {#register-330} The attendants surrounding an important person. The King dismisses the Square's accurate description of his retinue because the facts need not have been obtained by the impossible sight being claimed. **Printed form:** retinue (§ 14). See [Evidence and demonstration](#entry-evidence-demonstration) (p. 49). ### Retirement {#register-331} Recesses or parts that draw back, here indentations of a coastline rather than withdrawal from employment. Contrasted with projections, the word names relief that ordinary light and shadow may reveal but Flatland’s uniformly luminous world cannot display. **Printed form:** retirements (§ 1). See [Recognition by sight](#entry-recognition-sight) (p. 94). ### Retrograde {#register-332} Moving backwards. A Woman’s retrograde movement can drive her rear point into another figure, showing how a seemingly simple direction of travel acquires a gendered political significance in the account of domestic safety. **Printed form:** retrograde (§ 4). See [Women](#entry-women) (p. 128). ### Retrogression {#register-333} Movement backwards to a supposedly lower state. Pantocyclus predicts bodily and social decline if distinctions of rank disappear. **Printed form:** retrogression (§ 10). See [Reform and equality](#entry-reform-equality) (p. 95). ### Retrospect {#register-334} A backward view or review. The Square's retrospective thoughts at the year's end are interrupted by a child's prospective extension of geometry and the Sphere's arrival. **Printed form:** retrospect (§ 15). See [Time and the millennium](#entry-time-millennium) (p. 116). ### Reverie {#register-335} Absorbed thought or daydreaming. The narrator emerges from it to turn the glass, still troubled by the grandson's question immediately before the visitor announces himself. **Printed form:** reverie (§ 15). See [Grandson](#entry-grandson) (p. 58). ### Romance {#register-336} An imaginative narrative of extraordinary events. The title joins this literary kind to mathematical dimensions, inviting wonder and interpretation rather than promising a modern love story. **Printed form:** Romance (Title Page). See [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99). ### Rude health {#register-337} Vigorous, robust health: rude here means strong and unaffected, not discourteous. The healthy man hardly feels the southern pull and may consequently find it difficult to perform the courtesy of giving a woman the north side of the road. **Printed form:** rude health (§ 2). See [Attraction and climate](#entry-attraction-climate) (p. 18). ### Rudimentary {#register-338} Elementary or imperfectly developed. The inventor’s first painting method has not yet become a refined art. **Printed form:** rudimentary (§ 8). See [Painting](#entry-painting) (p. 84). ### Rustication {#register-339} Temporary exclusion from a university, traditionally a sending away into the country. Wentbridge imposes it for a first act of Feeling, turning a familiar academic punishment into enforcement of the elite’s preferred sensory habits. **Printed form:** Rustication (§ 6). See [Education and schools](#entry-education-schools) (p. 46). ### Sagacity {#register-340} Practical shrewdness and sound judgment. Even the sagacity of an educated Square is taxed by a crowd, a difficulty the narrator enlarges into an argument that bodies outside predictable forms would destroy social order. **Printed form:** sagacity (§ 7). See [Recognition by sight](#entry-recognition-sight) (p. 94). ### Sanctioned {#register-341} Officially permitted or approved. The sense is permission, not punishment, in the reported university exception to the ban on colour. **Printed form:** sanctioned (§ 10). See [Law and sanction](#entry-law-sanction) (p. 72). ### Sanitary and Social Board {#register-342} The examining authority that decides whether a child born to Isosceles parents qualifies for the Equilateral class. Its compound title treats social rank as a matter of bodily health and makes the state the arbiter of legitimate improvement. **Printed form:** Sanitary and Social Board (§ 3). See [Regularity](#entry-regularity) (p. 97). ### Scion {#register-343} Descendants of a distinguished family, originally a term for shoots or grafts. The scions of rich houses alone can afford prolonged visual training, so hereditary promise is sustained by inherited money and leisure. **Printed form:** scions (§ 6). See [Birth and ascent](#entry-birth-ascent) (p. 19). ### Scourge {#register-344} To whip or flog. The decree combines this punishment with imprisonment for regular Triangles, making the response to alleged revelation explicitly dependent on rank. **Printed form:** scourge (§ 18). See [Prison and silence](#entry-prison-silence) (p. 90). ### Scouted {#register-345} Rejected with contempt, not reconnoitred. An Irregular is scouted by his parents from birth, placing family repudiation at the start of the reformers’ account of how organised mistreatment may deform character. **Printed form:** scouted (§ 7). See [Irregularity](#entry-irregularity) (p. 65). ### Seasonable simulations {#register-346} Timely pretences or feigned expressions, recommended as a means of pacifying wives. The approving phrase reveals that upper-class domestic tact includes deliberate deception, while the lower-class husband’s insistence on literal truth is condemned as stupidity. **Printed form:** seasonable simulations (§ 4). See [Women](#entry-women) (p. 128). ### Second Nature {#register-347} An acquired practice so habitual and effective that it functions like an original natural condition. Colour recognition is said to have changed the practical basis of social distinctions. **Printed form:** second Nature (§ 9). See [Colour](#entry-colour) (p. 28). ### Secret archives {#register-348} Restricted records of earlier manifestations. The President's exclusive access lets him know enough to anticipate events while preventing that knowledge from becoming public. **Printed form:** secret archives (§ 18). See [Millennial visit](#entry-millennial-visit) (p. 78). ### Section {#register-349} The intersection of a higher-dimensional body with a lower-dimensional region. The Sphere appears in Flatland through a circular section, which the Square sees edgewise as a line. **Printed form:** section (§ 16). See [Movement and section](#entry-movement-section) (p. 79). ### Sedition {#register-350} Resistance or agitation classified as an offence against established authority. The narrator’s use of the term presents the colour movement through the rulers’ judgment of it. **Printed form:** Sedition (§ 10). See [Chromatic Sedition](#entry-chromatic-sedition) (p. 21). ### Seditious heresy {#register-351} A belief treated as both political rebellion and religious error. In Flatland the same Circles govern state and doctrine, so the Third Dimension can be prosecuted in both registers. **Printed form:** seditious heresy (§ 21). See [Prison and silence](#entry-prison-silence) (p. 90). ### Semicircle {#register-352} Half a circle or its circumference. The Bill uses front and hinder semicircles as the two coloured regions of a priestly body. **Printed form:** semicircle (§ 9). See [Universal Colour Bill](#entry-universal-colour-bill) (p. 119). ### Seminary {#register-353} Educational establishments, not necessarily institutions for training clergy. The higher Seminaries provide exclusive early schooling for aristocratic children, distinguishing their preparation in Sight Recognition from the tactile instruction of public elementary schools. **Printed form:** Seminaries (§ 6). See [Education and schools](#entry-education-schools) (p. 46). ### Sensibly {#register-354} Perceptibly or noticeably, rather than prudently. The statement that untaught women sensibly declined makes the effect of denied education observable, unsettling the claim that their inferior condition is simply a fixed natural fact. **Printed form:** sensibly (§ 12). See [Language and gender](#entry-language-gender) (p. 71). ### Sensuous {#register-355} Appealing to or developing the senses. The term describes the age’s intensified experience of beauty, without necessarily asserting sexual sensuality. **Printed form:** sensuous (§ 8). See [Painting](#entry-painting) (p. 84). ### Serf-born {#register-356} Born into the dependent, unfree labouring class. The adjective gives the Isosceles ancestry a political condition as well as a shape, clarifying that ascent out of the class involves release from inherited subjection. **Printed form:** serf-born (§ 3). See [Artisan and soldier](#entry-artisan-soldier) (p. 16). ### Serfdom {#register-357} The dependent, unfree condition assigned to the Isosceles labouring class. Reaching sixty degrees releases a figure from serfdom, so an exact geometric threshold also functions as a boundary of civic status. **Printed form:** serfdom (§ 5). See [Artisan and soldier](#entry-artisan-soldier) (p. 16). ### Seven score thousand {#register-358} One hundred and forty thousand, since a score is twenty. This is the stated death toll, not the earlier total of 120,000 people hissing the Chief Circle. **Printed form:** seven score thousand (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Simulate {#register-359} To pretend or feign. The King assumes the stranger is only pretending not to know Lineland's customs, making genuine difference of experience difficult to discuss. **Printed form:** simulating (§ 13). See [King of Lineland](#entry-king-lineland) (p. 69). ### Solid {#register-360} A three-dimensional body in the Sphere's usage. This differs from the Flatland use for a plane figure enclosed on its sides, a verbal disagreement central to the lesson. **Printed form:** Solid (§ 16). See [Dimension](#entry-dimension) (p. 39). ### Solid angles {#register-361} The corners where the Cube's faces meet. There are eight; they are not the six plane faces that bound the body. **Printed form:** solid angles (§ 19). See [Cube](#entry-cube) (p. 33). ### Solid Humanity {#register-362} Three-dimensional humankind, addressed with the overtones of substantiality and respectability. The phrase makes the reader's physical privilege sound like a moral distinction and then asks that reader for modesty. **Printed form:** Solid Humanity (Dedication). See [Solid humanity and superior races](#entry-solid-superior-races) (p. 105). ### Soliloquizing {#register-363} Speaking to oneself. The Point can conceive no independent listener, and even the Square's interruption is absorbed into its solitary circuit of thought. **Printed form:** soliloquizing (§ 20). See [Voice and selfhood](#entry-voice-selfhood) (p. 125). ### Sonorousness {#register-364} Resonant or continuously audible sound. The narrator’s contrast between a Woman’s deadly silent point and her safe but noisy speaking end makes audibility a bodily safety mechanism and a target of his misogynistic irritation. **Printed form:** sonorousness (§ 4). See [Voice and hearing](#entry-voice-hearing) (p. 123). ### Sophism {#register-365} A plausible but supposedly misleading argument. The narrator applies the term to the claim that distinct sides naturally imply distinct colours. **Printed form:** sophism (§ 8). See [Colour](#entry-colour) (p. 28). ### Soul-devouring Sphinx {#register-366} The narrator's image for the once-helpful precept about upward movement. Its unanswered riddle now threatens his mind, reversing the phrase's earlier function as a guide. **Printed form:** soul-devouring Sphinx (§ 22). See [Upward and Northward](#entry-direction-upward) (p. 122). ### Spaceland {#register-367} The three-dimensional world of the Sphere and the addressed reader. The Square's bodily visit enlarges his sight without granting autonomous movement or unlimited knowledge. **Printed form:** Spaceland (§ 19). See [Space and Spaceland](#entry-space-spaceland) (p. 106). ### Specimens {#register-368} Living low-angle Isosceles treated as representative examples for schoolchildren to handle. The impersonal scientific label effaces their personhood, preparing the narrator’s calculation of the costs and advantages of feeding them or letting them starve. **Printed form:** Specimens (§ 5). See [Education and schools](#entry-education-schools) (p. 46). ### Sphere {#register-369} The three-dimensional visitor whose intersections with Flatland are circles. He teaches genuine new geometry while remaining impatient, coercive and unwilling in waking life to accept his pupil's extrapolation beyond three dimensions. **Printed form:** Sphere (§ 16). See [Sphere](#entry-sphere) (p. 107). ### Sphinx {#register-370} The mythic monster whose unanswered riddle destroys its hearers. The narrator compares the haunting phrase about upward movement to a Sphinx when the former clue has become a question he can no longer master. **Printed form:** Sphinx (§ 22). See [Prometheus Paradise and the cost of knowledge](#entry-prometheus-paradise) (p. 91). ### Square as a verb {#register-371} To shape or frame one’s speech. The Shakespearean motto turns that ordinary verbal sense into a pun on the narrator’s geometrical body and invites the question of how his available form constrains what he can say. **Printed form:** square my talk (Title Page). See [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103). ### St Vitus’s Dance {#register-372} The traditional name for a disorder involving involuntary movement, included among the conditions for which the Female Code orders immediate destruction. In this context the name exposes a law that treats an unchosen bodily condition as a danger warranting execution; it is not a diagnosis or medical recommendation by this companion. **Printed form:** St. Vitus’s Dance (§ 4). See [Women](#entry-women) (p. 128). ### State-craft {#register-373} Skill in directing political affairs. The narrator recognizes the Bill’s strategic design while condemning its aims. **Printed form:** state-craft (§ 9). See [Cunning and policy](#entry-cunning-policy) (p. 35). ### Static {#register-374} Concerned with figures at rest, as one branch of the Geometry taught at Wentbridge. Paired with Kinetic, it makes the academic distinction directly relevant to the everyday challenge of recognising stationary or moving people. **Printed form:** Static (§ 6). See [Recognition by sight](#entry-recognition-sight) (p. 94). ### Statics {#register-375} The branch of mechanics concerned with equilibrium and bodies at rest. It is one of the intellectual studies neglected when colour simplifies practical recognition. **Printed form:** Statics (§ 9). See [Science and institutions](#entry-science-institution) (p. 101). ### Status {#register-376} Recognised social standing. Its threatened loss makes an upper-class Woman’s orientation toward her husband more than a safety practice: the posture becomes an enforceable sign of the family’s distinction. **Printed form:** status (§ 4). See [Class and caste](#entry-class-caste) (p. 27). ### Stipend {#register-377} A fixed regular payment for service. The miserable stipend of the confined government clerk makes the ostensibly spared Irregular’s life one of coerced labour rather than ordinary employment. **Printed form:** stipend (§ 7). See [Irregularity](#entry-irregularity) (p. 65). ### Sub-lustrous {#register-378} Only faintly luminous. A Woman’s rear end is sub-lustrous enough to approach the dimness of an inanimate object, a physical condition that permits near-invisibility and supplies the professed rationale for intrusive safety regulations. **Printed form:** sub-lustrous (§ 4). See [Eye and the visible line](#entry-eye-retina) (p. 50). ### Substantial realities {#register-379} The apparently solid, dependable objects of ordinary experience. During periods of doubt even Flatland's wall and writing tablets lose their certainty, so the ending is not a simple discovery that only Spaceland was dreamed. **Printed form:** substantial realities (§ 22). See [Dream and vision](#entry-dream-vision) (p. 43). ### Subversion {#register-380} The undermining or overthrow of an established system. The narrator interprets confusion in public rank as a threat to the Constitution. **Printed form:** subversion (§ 9). See [Chromatic Sedition](#entry-chromatic-sedition) (p. 21). ### Suffused {#register-381} Spread over or permeated with a quality. The language of the colour period is imagined as itself tinted with richer feeling or thought. **Printed form:** suffused (§ 8). See [Colour](#entry-colour) (p. 28). ### Superficial {#register-382} Belonging to a surface. The Sphere applies it geometrically to what Flatlanders call solid, while the ordinary suggestion of shallowness lends the correction a cutting social tone. **Printed form:** superficial (§ 17). See [Interior and exterior](#entry-interior-exterior) (p. 64). ### Superfluous {#register-383} Unnecessary or exceeding what is needed. Older studies come to seem superfluous because the new visual code makes their daily applications less demanding. **Printed form:** superfluous (§ 9). See [Science and institutions](#entry-science-institution) (p. 101). ### Superior Races {#register-384} The collectively honoured inhabitants of Space. The phrase borrows the language of ranking populations while the dedication questions whether a higher dimension brings a higher character. **Printed form:** Superior Races (Dedication). See [Solid humanity and superior races](#entry-solid-superior-races) (p. 105). ### Surreptitiously {#register-385} Secretly and without authorization. The Square fears that a Woman might learn to read and discover the men’s restricted discourse. **Printed form:** surreptitiously (§ 12). See [Science and institutions](#entry-science-institution) (p. 101). ### Sweetmeats {#register-386} Sugared delicacies or confectionery. The grandson proposes them as the bodily strengthening treatment supposedly required for his disobedient Configuration. **Printed form:** sweetmeats (§ 12). See [Configuration](#entry-configuration) (p. 31). ### Tablets of accounts {#register-387} Written records of financial dealings. Removing one from the locked cupboard makes a familiar, identifiable household object into evidence of dimensional access. **Printed form:** tablets of accounts (§ 17). See [Evidence and demonstration](#entry-evidence-demonstration) (p. 49). ### Terminal Points {#register-388} Endpoints or corners used in the dimensional sequence. Their number doubles from Point through Line and Square to Cube, and is distinguished from the count of lower-dimensional boundary faces. **Printed form:** terminal Points (§ 16). See [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15). ### Terminology {#register-389} The specialised words needed to describe a domain. The Square's loss of terminology is part of his declining ability to keep the experience of Space available. **Printed form:** terminology (Preface). See [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120). ### Thick {#register-390} Extended in the dimension the Square calls height. The revised defence concedes this quality to Flatland lines while arguing that its equal infinitesimal presence supplies no usable scale of differences. **Printed form:** thick (Preface). See [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113). ### Third power {#register-391} A number multiplied by itself twice, as three times three times three. The grandson asks for the geometrical meaning of an operation he has already learned arithmetically. **Printed form:** third power (§ 15). See [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15). ### Thoughtland {#register-392} A region the Square imagines through thought when the Sphere questions extraordinary appearances. In §19 it answers his desire for a fourth-dimensional view; in the later treatise it names a theoretical three-dimensional vantage over Flatland intended to evade the law. **Printed form:** Thoughtland (§ 19). See [Thoughtland and the changing use of an imagined place](#entry-thoughtland) (p. 115). ### Through Flatland to Thoughtland {#register-393} The theoretical treatise composed after the return, using a hypothetical region to evade the law. It is distinct from the later prison memoir that the reader is receiving. **Printed form:** Through Flatland to Thoughtland (§ 22). See [Revelation and teaching](#entry-revelation-teaching) (p. 98). ### Torrid zones {#register-394} The very hot climatic regions, where Fog does not prevail. Their clearer atmosphere paradoxically restricts visual knowledge, linking the narrator’s hierarchy of civilised regions to an optical resource unavailable everywhere. **Printed form:** torrid zones (§ 6). See [Attraction and climate](#entry-attraction-climate) (p. 18). ### Touch of Nature {#register-395} A shared characteristic linking beings across worlds. In the adapted Shakespearean saying, what they share is prejudice and persecution, not only affectionate fellow-feeling. **Printed form:** touch of Nature (Preface). See [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103). ### Tradesman {#register-396} A member of the respectable commercial middle class, represented by an equal-sided Triangle. The term denotes social standing as well as occupation; its geometric equivalent allows the narrator to describe a commercial hierarchy as if it were simply a classification of shapes. **Printed form:** Tradesman (§ 1). See [Equilateral](#entry-equilateral) (p. 47). ### Transfixed {#register-397} Pierced right through by a sharp point, rather than merely rendered motionless by surprise. Loyal Isosceles troops transfix their leaderless class fellows, turning the labouring population’s bodily weapon against itself. **Printed form:** transfixed (§ 3). See [Artisan and soldier](#entry-artisan-soldier) (p. 16). Pierced through by a pointed weapon or body. Chromatistes is physically killed, not merely rendered motionless by amazement. **Printed form:** transfixed (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Transmuted {#register-398} Changed into another form or substance. Moral words are transmuted when love becomes anticipated benefit and duty becomes necessity or fitness, suggesting a systematic conversion of ethical relations into calculations and constraints. **Printed form:** transmuted (§ 12). See [Language and gender](#entry-language-gender) (p. 71). ### Trepanning {#register-399} Operations boring or cutting an opening in the skull. Listed among the attempted cures of Irregularity, the procedure imports the vocabulary of serious surgery into a state programme that treats deviation of shape as a remediable social disease. **Printed form:** trepannings (§ 7). See [Surgery and extermination](#entry-surgery-extermination) (p. 112). ### Tribute {#register-400} A compulsory contribution imposed on a subordinate population. Here the contribution consists of low Isosceles supplied as educational specimens, with lethal consequences. **Printed form:** tribute (§ 9). See [Science and institutions](#entry-science-institution) (p. 101). ### Triennial {#register-401} Lasting three years in this context. It describes the duration of the agitation, not an event recurring every third year. **Printed form:** triennial (§ 10). See [History and revolution](#entry-history-revolution) (p. 60). ### Ultra-marine {#register-402} A deep blue pigment or colour. The hyphenated form belongs to this copy-text’s list of the artillerymen’s hues. **Printed form:** ultra-marine (§ 8). See [Painting](#entry-painting) (p. 84). ### Undulation {#register-403} A smooth, wave-like movement. The cultivated swaying of upper-class women’s backs is distinguished from the monotonous swinging of poorer women, transforming a compulsory warning movement into an elaborate mark of social refinement. **Printed form:** undulation (§ 4). See [Women](#entry-women) (p. 128). ### Unemancipable {#register-404} Unable to be freed from dependence or bondage. The Square promises to remain his teacher's unemancipable slave if granted further knowledge, expressing aspiration in the language of submission. **Printed form:** unemancipable (§ 19). See [Revelation and teaching](#entry-revelation-teaching) (p. 98). ### Universal Colour Bill {#register-405} The proposed law extending compulsory painting to all classes. It assigns red and green halves to Women and Priests, threatening their established visual distinction. **Printed form:** Universal Colour Bill (§ 9). See [Universal Colour Bill](#entry-universal-colour-bill) (p. 119). ### Vacuum {#register-406} An empty region or void. The dream's flight through a Vacuum emphasizes the Point's isolation; the scene remains a visionary fiction rather than a consistent physical account of sound transmission. **Printed form:** Vacuum (§ 20). See [Pointland](#entry-pointland) (p. 87). ### Vantage-ground {#register-407} A position giving an advantage of view. The Square projects a higher vantage from which the interiors of Spaceland's bodies would become exposed as Flatland's are from three dimensions. **Printed form:** vantage-ground (§ 19). See [Fourth Dimension](#entry-fourth-dimension) (p. 57). ### Variegated {#register-408} Marked with different colours. The inventor’s multicoloured frame makes his identity and movements readily legible. **Printed form:** variegated (§ 8). See [Colour](#entry-colour) (p. 28). ### Vent their spleen {#register-409} Discharge anger or ill temper, spleen carrying its older emotional sense. The narrator uses the phrase for women’s violent reactions to restrictive laws, partly acknowledging that the danger invoked to justify confinement can be aggravated by confinement itself. **Printed form:** vent their spleen (§ 4). See [Women](#entry-women) (p. 128). ### Ventilators {#register-410} Openings for air. The Wife fears that a Woman has entered through one, and invokes the husband's promise that their new house would have none. **Printed form:** ventilators (§ 15). See [Wives and household](#entry-wives-household) (p. 126). ### Vermilion {#register-411} A brilliant red pigment or colour. In the military tableau it colours the guns, distinct from the four colours worn by their Square operators. **Printed form:** vermilion (§ 8). See [Painting](#entry-painting) (p. 84). ### Vertex {#register-412} The corners at which a triangle’s sides meet, especially the acute point opposite the short base of an Isosceles. In the social account this mathematical feature becomes a weapon, a measure of intelligence, and an index of rank. **Printed form:** vertices (§ 3). See [Angle](#entry-angle) (p. 14). ### Via media {#register-413} A middle course between opposed positions. The narrator’s compromise rejects some immediate infant killings but allows later destruction after medical review, so the language of moderation disguises the continuity of the coercive principle. **Printed form:** via media (§ 7). See [Surgery and extermination](#entry-surgery-extermination) (p. 112). ### Vigour {#register-414} Mental strength or energy. The Editor contrasts the Square's former vigour with the condition produced by imprisonment, public disbelief and age. **Printed form:** vigour (Preface). See [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120). ### Visibly incorporate {#register-415} Embodied in visible form. What the Square had only inferred as circular perfection now appears before him as a three-dimensional being, though he still misreads its surface. **Printed form:** visibly incorporate (§ 18). See [Sphere](#entry-sphere) (p. 107). ### Visitations {#register-416} Official inspection rounds, here systematic searches of lower-class homes. The administrative word covers the continuing purge after the assembly massacre. **Printed form:** visitations (§ 10). See [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### Volition {#register-417} The act or power of willing. The Sphere initially says that sufficient volition could let the Square leave his plane, although the later journey shows the pupil dependent on the guide's will. **Printed form:** volition (§ 17). See [Movement and section](#entry-movement-section) (p. 79). ### Vouchsafed {#register-418} Granted or bestowed, often by a superior. The Square describes Flatland's visible lines as privileges granted to his people, making a perceptual difference sound like rank or favour. **Printed form:** vouchsafed (§ 14). See [Space and Spaceland](#entry-space-spaceland) (p. 106). ### Vulgarise {#register-419} To make common, less exclusive, or less socially distinguished. Exceptional promotions are welcomed because they do little to vulgarise aristocratic privileges: the benefit to the excluded is assessed by how little it costs those already admitted. **Printed form:** vulgarise (§ 3). See [Class and caste](#entry-class-caste) (p. 27). ### Wane {#register-420} To diminish or grow weaker. The Soldiers’ penetrating power wanes as their intelligence waxes, creating the compensating exchange on which the narrator bases his praise of the aristocratic constitution. **Printed form:** wane (§ 3). See [Artisan and soldier](#entry-artisan-soldier) (p. 16). ### Wax {#register-421} To increase or grow stronger. Set against wane, it describes increasing mental ability in a Soldier whose widening angle simultaneously diminishes his capacity to pierce; intellectual advancement is thus said to remove the physical threat it might have organised. **Printed form:** wax (§ 3). See [Artisan and soldier](#entry-artisan-soldier) (p. 16). ### Woman hater {#register-422} The hostile characterization levelled at the narrator by critics. The Editor does not simply dismiss it: he admits the defence is less convincing than the answer to the geometrical objection. **Printed form:** woman-hater (Preface). See [The Editor and the revised Preface](#entry-editor-preface) (p. 45). ### Wonted {#register-423} Usual or customary. The habitual weekly chorus provides the setting for a particular marriage, joining repetitive communal practice to individual fulfilment. **Printed form:** wonted (§ 13). See [Lineland](#entry-lineland) (p. 74). ### Æsthetic {#register-424} Pertaining to beauty and its appreciation. The Square separates Flatland’s artistic dullness from the intellectual interest of its mathematical life. **Printed form:** æsthetic (§ 8). See [Painting](#entry-painting) (p. 84). # Expressions and motifs {#contextual-glosses} These glosses dwell on compact expressions whose force depends on a scene, idiom or double meaning. The quoted words belong to the cited primary passage; the explanation is this companion’s interpretation. They supplement the full articles without replacing their longer accounts. ### A humble native addressing superior readers {#phrase-humble-native} **Dedication: “a Humble Native of Flatland”.** Humility is announced from a position that the reader can easily regard as inferior. Yet the address goes on to ask those superior readers for modesty, exposing the gap between receiving deference and deserving moral authority. Native also gives the speaker the role of a local guide explaining a strange society to visitors. Such a guide can know his world intimately without seeing the arrangements he has naturalised. The phrase therefore establishes both authority and limitation: he can teach outsiders, and those outsiders can recognise failings in him. The dedication asks whether the same reversal could happen to them. See [Dedication and the reader being addressed](#entry-dedication) (p. 36) and [A Square and the voice of the memoir](#entry-a-square) (p. 11). ### But he is not the Square he once was {#phrase-not-square-once} **Preface: “he is not the Square he once was”.** The idiom usually marks a change in strength, character or ability; here its noun also names a geometrical class. The Editor does not report that the prisoner's body has acquired another number of sides. He reports the decline of a person whose class-name appears to promise a fixed identity. Imprisonment, mockery and ageing have reduced the witness's ability to express what he learned. The joke is quiet, and its human cost is not cancelled by the geometrical pun. It warns a reader that a later account may combine remembered revelation with damaged resources of recollection. See [The Editor and the revised Preface](#entry-editor-preface) (p. 45) and [Memory and forgetting](#entry-memory-forgetting) (p. 76). ### Measure my high ness {#phrase-measure-highness} **Preface: “measure my ‘high-ness’”.** The Chief Circle's challenge is not only a demand for evidence. The hyphen exposes an elevated social title as if it named a measurable property, while the office of High Priest supplies another hierarchical echo. The prisoner claims a kind of height that the official cannot conceive; the official already enjoys a kind of high status that the prisoner cannot challenge effectively. This alignment does not make measurement itself oppressive. It shows how a reasonable evidential demand can be administered from a position that refuses the conceptual changes necessary to meet it. A pun carries both a problem of knowledge and a scene of unequal authority. See [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113). ### One touch of Nature makes all worlds akin {#phrase-worlds-akin} **Preface: “One touch of Nature makes all worlds akin!”** The adapted saying extends likeness across dimensions. Its preceding list includes Points, Lines, Squares, Cubes and Extra-Cubes; its subject is their liability to dimensional prejudice. The common touch is consequently not a guarantee of kindness. It can be the shared tendency to persecute anyone who speaks beyond familiar experience. Recognizing the phrase without reading its immediate context would turn its sharper argument into a reassuring sentiment. The edition explains the Shakespearean source and its own less comforting sense; Abbott's change from a single world to all worlds makes the reader's supposed superiority part of the joke. See [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103). ### Both kinds of dogmatism {#phrase-two-dogmatisms} **Preface: “This can never be” and “It must needs be precisely thus”.** These opposite claims are paired as refusals of a properly limited mind. One closes inquiry by denying possibility; the other closes it by dictating the exact contents of the unknown. The alternative is not indifference between truth and falsehood. It is a willingness to distinguish what is experienced, what can be demonstrated, what analogy makes thinkable and what remains conjecture. The Square and Sphere exchange roles under this test: each can expose one boundary and protect the next. The reader is not asked to approve every imaginative assertion but to notice when a confident verdict exceeds its grounds. See [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) and [Imagination and modesty](#entry-imagination-modesty) (p. 61). ### My country and my universe {#phrase-country-universe} **§ 1: “my country” and “my universe”.** The narrator corrects the second phrase into the first retrospectively. What he once called the whole of reality has become a region within a larger field. The modest verbal revision records an immense conceptual change. It also sets a recurring trap: a world newly recognised as larger can become another universe if its inhabitants refuse to imagine beyond it. Calling Spaceland a country instead of a final cosmos helps preserve the possibility that its horizon is provisional too. The opening sentence thus does philosophical work without introducing a special technical vocabulary; two ordinary possessive expressions carry the difference between belonging somewhere and exhausting everything. See [A Square and the voice of the memoir](#entry-a-square) (p. 11) and [Space and Spaceland](#entry-space-spaceland) (p. 106). ### Poor Flatland Prometheus {#phrase-flatland-prometheus} **§ 22: “poor Flatland Prometheus”.** The Square explicitly names the mythic benefactor punished for bringing fire to mortals. He immediately injures the flattering comparison by saying that he has brought his countrymen nothing they can receive. The problem is not simply whether he possesses a gift; it is whether a gift becomes useful knowledge in the absence of understanding or converts. His self-description can sound heroic and self-pitying at once. The myth is therefore an instrument of self-measurement rather than a certificate of success. It also recalls the earlier Promethean ambition of §19, where the wish to bring down knowledge helped drive speculation beyond the Sphere's limit. See [Prison and silence](#entry-prison-silence) (p. 90) and [Revelation and teaching](#entry-revelation-teaching) (p. 98). ### The soul devouring Sphinx {#phrase-sphinx} **§ 22: “a soul-devouring Sphinx”.** The remembered instruction Upward, not Northward has become a riddle the narrator cannot solve in practice. The named monster transforms a successful clue into a torment. The Square still has the words, and knows that their distinction mattered, but cannot consistently recover the direction or mental image they once opened. The failure is therefore neither ordinary forgetfulness of a formula nor proof that the formula was always meaningless. It is a broken relation between language and a once-available conception. By setting this image beside the fluctuating Cube, the ending makes the price of revelation a problem of continued intelligibility as well as of punishment. See [Memory and forgetting](#entry-memory-forgetting) (p. 76) and [Upward and Northward](#entry-direction-upward) (p. 122). ### Give her the North side of the way {#phrase-north-side-courtesy} “give her the North side of the way” (§ 2) This is Flatland’s formula for a gentleman’s street courtesy to a Lady. Since the natural pull is southward, directions have bodily consequences, and etiquette makes the north side a concession to someone assumed less able to resist that pull. Yet the narrator admits that a healthy man in a temperate region may barely feel the force that is supposed to guide his conduct. The result is a small comedy of manners built into the physics: the better equipped he is physically, the less certain he may be how to behave politely. The supplied editorial note compares the convention with giving a woman the wall side of an English pavement. The comparison clarifies the social code without making Flatland’s rule identical to it. See [Attraction and climate](#entry-attraction-climate) (p. 18), [Class and caste](#entry-class-caste) (p. 27), and [Women](#entry-women) (p. 128). ### Stifle sedition in its very cradle {#phrase-sedition-cradle} “stifle sedition in its very cradle” (§ 3) The phrase means to suppress resistance before it can develop, imagining political opposition as an infant that can be smothered. It follows the account of the Law of Compensation, under which increasing intelligence supposedly diminishes the poor man’s bodily power to injure. The state then supplements this convenient natural arrangement by promoting some leaders, confining others, and executing those who remain intractable. Birth imagery therefore joins two scales of government: the long management of hereditary improvement and the immediate disabling of a rebellion. What the narrator admires as prevention depends on dividing ambitious individuals from their class. His metaphor also makes violence sound like prudent intervention at an early stage, before the later description reveals the bodies on which it operates. See [Birth and ascent](#entry-birth-ascent) (p. 19), [Artisan and soldier](#entry-artisan-soldier) (p. 16), and [Surgery and extermination](#entry-surgery-extermination) (p. 112). ### In a becoming and respectful manner {#phrase-becoming-respectful} “in a becoming and respectful manner” (§ 4) The Female Code requires women to use a separate eastern entrance and to enter with this prescribed display of deference. Becoming means fitting or socially proper: the law governs the meaning of an action as well as its physical route. Abbott’s own attached note links the rule to a clerical demand in Spaceland that villagers, farmers, and Board School teachers approach by a separate entrance. That authorial comparison makes the humiliation of Flatland’s women legible as an everyday practice of class exclusion, not merely a fantastic safety device. The architecture distinguishes admitted persons before they even begin to speak. Courtesy consequently operates as an obligation imposed from above, while its decorous wording obscures the unequal standing the doorway announces. See [Doors and houses](#entry-doors-houses) (p. 42), [Class and caste](#entry-class-caste) (p. 27), and [Women](#entry-women) (p. 128). ### Once a Woman, always a Woman {#phrase-once-woman} “Once a Woman, always a Woman” (§ 4) The proverb-like balance gives exclusion the sound of an unquestionable truth. It is immediately named a Decree of Nature, placing a social limit beyond any apparent possibility of revision. Its force depends on the contrast with the Isosceles man: he may at least imagine his descendants acquiring better angles, while no comparable prospect is offered to women. The sentence therefore marks the boundary of Flatland’s promised progress. Biological ascent is not a universal law benefiting every inhabitant, but a selectively distributed hope. The narrator’s next consolation is still more revealing: he praises the arrangement that allegedly prevents women from remembering or anticipating their misery. Instead of challenging the prohibition, he imagines the oppressed as fortunately incapable of comprehending it. See [Women](#entry-women) (p. 128), [Birth and ascent](#entry-birth-ascent) (p. 19), and [Nature and law](#entry-nature-law) (p. 81). ### Feel and be felt by {#phrase-feel-and-be-felt} “feel and be felt by” (§ 5) The older formula of introduction spells out reciprocal action: each stranger will inspect the other’s angle and submit to the same examination. Its balanced active and passive verbs make equality within the encounter audible, even though the purpose is to discover unequal rank. Successive urban shortenings omit the explicit passive half and eventually make feel mean introduce. The narrator complains of linguistic degeneration, but the transformation also shows how a bodily procedure can become conventional social shorthand. A courteous introduction grants access to information that cannot be read directly from an apparent outline. Because an unexpected movement may kill the examiner, the formal words are backed by an exacting discipline of stillness. Etiquette here manages physical exposure as well as reputation. See [Feeling and touch](#entry-feeling-touch) (p. 53), [Angle](#entry-angle) (p. 14), and [Language and gender](#entry-language-gender) (p. 71). ### Expense is the truest economy {#phrase-expense-economy} “expense is the truest economy” (§ 5) The maxim ordinarily defends paying more for better quality or greater durability. The Square applies it to replacing living classroom specimens instead of keeping them fed. Frequent replacement preserves accurate angles for the pupils to handle and, in his account, slightly reduces the supposedly redundant Isosceles population. A recognisable household principle thus carries the reader across an appalling shift in what counts as an expense and what counts as a benefit. Neither the specimen’s life nor its suffering appears as a cost in the calculation. The cheap system is not innocent either, since it still confines people as apparatus, but the narrator’s preferred economy makes their deaths an additional advantage. The smooth proverbial ending presents that judgment as practical wisdom. See [Education and schools](#entry-education-schools) (p. 46), [Feeling and touch](#entry-feeling-touch) (p. 53), and [Artisan and soldier](#entry-artisan-soldier) (p. 16). ### Perfect propriety in Polygonal society {#phrase-polygonal-propriety} “to comport oneself with perfect propriety in Polygonal society” (§ 6) The alliterative phrase joins respectable conduct to a particular bodily and social class. Comport oneself means behave or carry oneself; propriety requires knowing how to move among high-ranking figures without collisions or unwelcome requests to touch them. The Square concludes that one should ideally be a Polygon oneself. This is more than a joke about snobbery: prolonged schooling and habitual practice give the rich an informational advantage over a visitor who cannot interpret their changing outlines. The apparently effortless grace of superior breeding has expensive conditions. The narrator’s own difficulty is useful evidence, since he possesses education and respectability yet still feels outmatched. Membership in the fashionable circle depends on embodied training that formal knowledge alone cannot supply. See [Recognition by sight](#entry-recognition-sight) (p. 94), [Polygon](#entry-polygon) (p. 88), and [Education and schools](#entry-education-schools) (p. 46). ### The interests of the Greater Number {#phrase-greater-number} “the interests of the Greater Number” (§ 7) The phrase makes numerical predominance a warrant for the suffering of a minority. It follows the reformers’ account of the Irregular’s exclusion from family, marriage, meaningful work, and ordinary trust. Rather than refuting that account, the narrator answers that the majority requires such a life to be hard. Greater Number consequently changes the question from whether the treatment is just to whether accepted arrangements should be inconvenienced. The subsequent examples include doors, theatre admission, military service, and commercial credit, all organised around predictable bodies. The supplied editorial note identifies the language of utilitarianism; the passage’s particular distortion lies in treating existing conveniences as decisive while excluding the minority’s welfare from serious comparison. A claim about general benefit licenses very particular harms. See [Irregularity](#entry-irregularity) (p. 65), [Regularity](#entry-regularity) (p. 97), and [Doors and houses](#entry-doors-houses) (p. 42). ### Painlessly and mercifully consumed {#phrase-mercifully-consumed} “painlessly and mercifully consumed” (§ 7) Consumed means put to death, but its passive form leaves the executioner and the physical act unnamed. Painlessly describes the proposed manner of killing; mercifully assigns it a moral character before the reader can judge the policy. The phrase completes the Square’s advertised middle course between immediate destruction at birth and unrestricted tolerance. He would postpone the decision until the body begins to set and medical recovery is judged improbable. That delay looks moderate only because the child’s right to survive remains conditional on achieving an approved shape. The Medical Board supplies procedural authority, while the soft adverbs convert a political decision into a supposed act of care. The passage exposes how a reform in timing can preserve the underlying principle of elimination. See [Surgery and extermination](#entry-surgery-extermination) (p. 112), [Irregularity](#entry-irregularity) (p. 65), and [Nature and law](#entry-nature-law) (p. 81). ### A bi-lingual and bi-mental existence {#phrase-bi-mental-existence} “a kind of bi-lingual, and I may almost say bi-mental, existence” (§ 12) The qualifying phrases make the narrator sound cautious while he describes a profound division between public and private thought. Men use love, duty, and moral judgment in speaking to women, then replace those terms with calculations of benefit, necessity, and fitness among themselves. Bi-mental suggests that this division cannot remain a harmless change of vocabulary: boys must acquire incompatible ways of explaining action and learn when to display each. The Square’s stated worry is the injury to male intellectual strength, although his examples also expose systematic deception of women. His fear that a mother might learn the logical dialect reveals how much the arrangement depends on restricted literacy and controlled transmission. The language policy therefore preserves authority by making knowledge unevenly available within the household. See [Language and gender](#entry-language-gender) (p. 71), [Women](#entry-women) (p. 128), and [Education and schools](#entry-education-schools) (p. 46). ### pure from the pollution of paint {#phrase-pollution-paint} Exact wording: “pure from the pollution of paint” (§8). The repetition of *p* makes the verdict memorable, almost proverbial. *Pure* turns the absence of pigment into moral cleanliness, while *pollution* makes an applied colour sound like contamination. The narrator assigns this purity to Women and Priests together, even though their shared exemption arises from very different social positions. What the Women confess as deficiency, the Priests proclaim as perfection: neither is conventionally credited with distinct sides requiring distinct colours. The phrase therefore exposes how the same visual condition can carry opposite social values before receiving one convenient moral name. It also jars with the narrator’s delight in the lost painted world. His evaluative vocabulary condemns what his description makes desirable. Related: [Colour](#entry-colour) (p. 28); [Painting](#entry-painting) (p. 84); [Universal Colour Bill](#entry-universal-colour-bill) (p. 119). ### a second Nature {#phrase-second-nature} Exact wording: “a second Nature” (§9). An acquired habit becomes *second nature* when it seems as immediate as an original disposition. Flatland gives the idiom constitutional force. Colour recognition has changed what ordinary people can do, so the reformers argue that legal distinctions should change too. The capitalized *Nature* brings the new practice into competition with the authority constantly invoked for inherited rank. The phrase does not mean that painting literally alters the number of anyone’s sides. It means that a cultural invention can transform the practical consequences of those sides. This distinction is crucial: the new code makes competence more widely available while remaining capable of imitation. Its political strength and its vulnerability arise from the same detachment of visible signs from bodily form. Related: [Colour](#entry-colour) (p. 28); [Reform and equality](#entry-reform-equality) (p. 95); [Dodecagon](#entry-dodecagon) (p. 40). ### the perimeter of the whole subject {#phrase-perimeter-subject} Exact wording: “the perimeter of the whole subject” (§10). Pantocyclus proposes to review a debate as though it were a figure whose boundary could be surveyed. The ordinary metaphor of looking around a subject becomes pointedly literal in a society that identifies people by perimeters. *Whole* promises completeness and balance: the speech will acknowledge defects and advantages alike. Its actual design is selective, directing each class towards the loss most likely to frighten it. The phrase also hints at enclosure. While the speaker purports to survey the subject’s boundary, his agents control the audience’s physical boundaries and eventually seal the exits. That spatial correspondence is an interpretive echo, not a stated pun, but it makes the language of comprehensive understanding fit an operation of comprehensive control. Related: [Cunning and policy](#entry-cunning-policy) (p. 35); [Suppression and massacre](#entry-suppression-massacre) (p. 110). ### the greatest number {#phrase-greatest-number} Exact wording: “the greatest number” (§10). Pantocyclus equates the greatest number with the Criminal Classes and converts a possible democratic justification into an alarm. The modern annotation connects the wording with the utilitarian language of the greatest happiness of the greatest number, already invoked in §7. In this speech, however, numbers establish a threat rather than a claim to welfare. The argument relies on the ruler’s prior classification of an entire population as criminal; it does not demonstrate each person’s criminal act. Artisans are encouraged to identify with the honour they hope to acquire rather than with the numerical majority to which they belong. The phrase therefore marks a change of political perspective: counting people can expose exclusion, or it can make their abundance a reason to suppress them. Related: [Compensation](#entry-compensation) (p. 29); [Reform and equality](#entry-reform-equality) (p. 95); [Isosceles rebels](#entry-isosceles-rebel) (p. 68). ### spared but decimated {#phrase-spared-decimated} Exact wording: “spared but decimated” (§10). The conjunction permits the narrator to preserve a claim of mercy while reporting collective killing. The modern note reads *decimated* in its strict punitive sense: one in ten put to death. Most of the Working Men survive, but those selected do not, and the group’s cooperation with the Circles offers no immunity. *Spared* is comparative, measured against the complete destruction of another crowd rather than against an ordinary right to live. The phrase condenses the moral arithmetic of the regime: a smaller proportion killed can be presented as clemency. It also exposes the inadequacy of treating the suppressed movement as one undifferentiated population. Artisans receive a different punishment from soldiers, but the distinction remains within a policy of coercive reduction. Related: [Suppression and massacre](#entry-suppression-massacre) (p. 110); [Isosceles rebels](#entry-isosceles-rebel) (p. 68); [Compensation](#entry-compensation) (p. 29). ### the Workmen are annually consumed {#phrase-annually-consumed} Exact wording: “the Workmen are annually consumed” (§10). *Consumed* means killed, not exhausted by hard labour or consumed figuratively by enthusiasm. Its passive grammar suppresses the immediate killer, while *annually* makes death a routine feature of production. New workers replace the murdered ones so that colour manufacture can continue without allowing its knowledge to circulate. The pairing of a factory with consumption gives the labourers the status of expendable material. The sentence also changes the scale of the chapter’s violence: after the spectacular massacre comes an administrative cycle that needs no new revolt to justify it. The state's fear survives its victory. A secret said to belong to one ruler remains dependent on other people's work, and killing those people conceals that dependency rather than removing it. Related: [Suppression and massacre](#entry-suppression-massacre) (p. 110); [Chief Circle](#entry-chief-circle) (p. 20); [Science and institutions](#entry-science-institution) (p. 101). ### doing nothing themselves {#phrase-doing-nothing} Exact wording: “doing nothing themselves” (§11). The participial phrase sits within a grand catalogue of priestly direction. At first it could sound like praise of pure supervision: others perform the work while the Circles provide its organizing cause. Read less deferentially, it exposes a governing class that takes credit without labour. The following qualification, restricting their causation to everything “worth doing,” lets authority decide in advance which accomplishments deserve recognition. The modern note compares the paradox to the philosophical First Cause, but the social meaning does not depend on that allusion. The Circles rule commerce, science, education, and theology without a corresponding account of their own productive acts. Syntax allows praise and indictment to occupy the same sentence, leaving readers to hear what the admiring narrator does not adequately judge. Related: [Circles and Priests](#entry-circle-priest) (p. 24); [Chief Circle](#entry-chief-circle) (p. 20); [Science and institutions](#entry-science-institution) (p. 101). ### assumed, by courtesy {#phrase-assumed-courtesy} Exact wording: “assumed, by courtesy” (§11). The inserted qualification quietly removes the Chief Circle’s ten thousand sides from the category of measured fact. The numerical claim sounds exceptionally precise, but *assumed* identifies its evidentiary weakness and *courtesy* supplies its social justification. The prohibition on feeling a Circle prevents routine verification. This is not an argument that ten thousand sides would make a true mathematical circle: a finite polygon would still remain polygonal. The phrase instead shows how a convention receives the outward form of scientific certainty. It also prepares the later description of surgically promoted children as Circles “at least by courtesy.” At the summit and threshold of rank alike, the title depends partly on authorized recognition rather than on literal fulfilment of its geometric name. Related: [Chief Circle](#entry-chief-circle) (p. 20); [Circles and Priests](#entry-circle-priest) (p. 24); [Fertility and extinction](#entry-fertility-extinction) (p. 54). ### Configuration makes the man {#phrase-configuration-man} Exact wording: “Configuration makes the man” (§12). The maxim places bodily shape where a moral proverb would put conduct or character. The modern note identifies the reversal of “Manners makyth man.” *Makes* is stronger than *influences*: it claims a complete explanatory relation between physical form and the person. In the surrounding argument, will, teaching, encouragement, and praise lose causal standing. Yet the sentence’s authority rests on Pantocyclus, whose strategic success has involved rhetoric, deception, fear, and the redirection of hope. The history itself has shown people responding to circumstances and persuasion. That tension need not prove a formal logical contradiction, since a determinist could seek bodily mechanisms for such responses; it does reveal how little the slogan explains the political processes the narrative has actually described. Related: [Configuration](#entry-configuration) (p. 31); [Circular doctrine](#entry-circular-doctrine) (p. 25); [Cunning and policy](#entry-cunning-policy) (p. 35). ### no blot on her escutcheon {#phrase-blot-escutcheon} Exact wording: “no blot on her escutcheon” (§12). An escutcheon is a heraldic shield, so a blot figuratively stains a family’s honour. Here the supposed stain is an irregular ancestor entered in a Woman’s pedigree. The metaphor makes descent look like a visible surface that can be inspected, compensating for the fact that women’s straight bodies disclose no such irregularity. It also transfers the social prestige of heraldry into the bookkeeping of reproductive governance. The phrase states what the narrator expects a prudent Circle to seek; he immediately complains that Circles often prefer lustre or a low voice. The standard is therefore neither universally obeyed nor independently verified as beneficial. It reveals the narrator’s evaluative language and the class system’s genealogical anxieties, not an actual moral stain upon a woman or her forebears. Related: [Marriage and selection](#entry-marriage-selection) (p. 75); [Fertility and extinction](#entry-fertility-extinction) (p. 54); [Configuration](#entry-configuration) (p. 31). ### Once neighbours, always neighbours {#phrase-once-neighbours} **§13.** “Once neighbours, always neighbours.” The maxim condenses a geometrical constraint into the sound of proverbial wisdom. No inhabitant of Lineland can step aside to pass another, so an initial position fixes a lifelong relation. The next sentences compare that relation with marriage and borrow the language of permanent vows. Yet actual marriage in Lineland does not require neighbouring bodies: voices join lovers separated by enormous distances. The juxtaposition distinguishes unavoidable spatial attachment from chosen or harmonized affection. It also invites comparison with Flatland's sayings that turn an inherited condition into an apparently self-evident law. A proverb's reassuring balance can make confinement sound natural before anyone asks whether another direction would release it. **See also.** [Lineland](#entry-lineland) (p. 74) · [Wives and household](#entry-wives-household) (p. 126) ### A feminine Monstrosity with a bass voice {#phrase-feminine-monstrosity} **§13.** “a feminine Monstrosity with a bass voice” The King's diagnosis follows from a confident rule: a Man has two voices, whereas the visitor has only one. The unfamiliar being is consequently interpreted as a defective Woman rather than evidence that the rule has a limited field of application. The insult also reverses the Square's opening mistake, when he assumed that the King must be a Woman because he looked like a Straight Line. Both speakers convert their own society's bodily conventions into universal classifications. The scene does not merely expose the King's ignorance. It makes the respectable geometer experience the humiliating treatment he habitually accepts when Flatland declares an unusual form irregular, unintelligent or socially inferior. **See also.** [King of Lineland](#entry-king-lineland) (p. 69) · [Voice and selfhood](#entry-voice-selfhood) (p. 125) ### The completion of your incomplete self {#phrase-completion-incomplete} **§14.** “the completion of your incomplete self” The Square makes dimensional extension sound like the fulfilment of another being's deficient nature. His next explanation, that he is a Line of Lines, has a geometrical basis: a Line moving sideways can generate a Square. The moral and social judgment does not follow with equal necessity. To possess one more dimension is to have powers the King lacks; it does not establish that the King exists merely as an unfinished version of the visitor. The grand claim appears in an angry, unsuccessful attempt at instruction. It anticipates the narrator's later readiness to worship the Sphere and the Sphere's explicit correction that greater visual access does not make a person more divine. **See also.** [Movement and section](#entry-movement-section) (p. 79) · [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) ### Go to bed {#phrase-go-to-bed} **§15.** “Go to bed” The ordinary parental command abruptly ends an extraordinary question. The grandson has carried a construction forward from Point to Line and Square, suggesting an unknown result for the third power while acknowledging that he cannot visualize it. The grandfather answers neither the numerical analogy nor that candid uncertainty. He uses his authority over the child's routine to terminate the exchange. Its domestic scale is important: intellectual limits are enforced before the police enter the story, by a respected teacher who believes he is restoring good sense. The Sphere's subsequent defence of the boy exposes the lost opportunity. Later, when the grandfather tries to resume the lesson, the state supplies the child with a new reason to withdraw. **See also.** [Grandson](#entry-grandson) (p. 58) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) ### Dimension implies direction and measurement {#phrase-direction-measurement} **§16.** “Dimension implies direction and measurement.” The Square asks for a criterion rather than another prestigious assertion. If the new height is a dimension, he wants it measured or its direction indicated. On the pupil's present terms, the Sphere admits that he can do neither. The demand is therefore more serious than the surrounding comedy of an eye in the stomach may suggest. Yet it is not the last word: a subject confined to a plane may lack the practical access required to satisfy a test that presupposes movement outside it. The passage stages a genuine tension between intelligible evidence and the enlargement of the framework within which evidence is intelligible. Neither credulity nor simple contempt for the request captures its force. **See also.** [Dimension](#entry-dimension) (p. 39) · [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) ### One Dimension behind the thing {#phrase-dimension-behind} **§16.** “one Dimension behind the thing” The Sphere uses *behind* metaphorically for a decrease in dimensional degree, not for a position to the rear. The boundary of a Line consists of Points, that of a Square of Lines, and that of a Cube of square faces. This is why the same word *side* cannot keep an identical geometrical object as its referent through the lesson. The phrase lets familiar language carry a general relation, but the guide repeatedly has to explain that his sides are what the Square would call solids. In §19 the pupil extends this relation to eight bounding Cubes for a four-dimensional figure. The construction is coherent even though the proposed world is not witnessed. **See also.** [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15) · [Fourth Dimension](#entry-fourth-dimension) (p. 57) ### Deeds, and not words, shall proclaim the truth {#phrase-deeds-words} **§17.** “Deeds, and not words, shall proclaim the truth.” The declaration promises an escape from verbal misunderstanding. The Sphere will remove a tablet from a locked cupboard and then reach the Square's bodily interior. These deeds certainly disturb the pupil's account of what is possible, but they do not immediately establish the visitor's explanation. Instead they produce fear of a magician and another attack. The contrast between words and deeds therefore fails to settle the deeper problem: an event has to be interpreted, and several interpretations may initially seem possible to someone lacking a new spatial concept. The maxim also conceals an ethical escalation. A demonstration using a household object becomes an invasion of the pupil's body before he can object. **See also.** [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) · [Touch and bodily proof](#entry-touch-belly) (p. 118) ### What you think you see, you see not {#phrase-think-you-see} **§18.** “What you think you see, you see not” The guide corrects the Square precisely when the new world seems to have replaced inference with direct vision. Looking at the Sphere, the pupil imagines that his interior lies open and asks why the organs are missing. He is actually seeing the surface. The sentence thus interrupts any simple opposition between deceptive inference and self-explanatory sight. Newly enlarged vision remains an activity interpreted through habits that can misidentify its object. Its correction is also limited: the Sphere can explain this error without possessing an exhaustive account of every possible dimension. The line invites disciplined adjustment of a particular judgment, not surrender to the teacher as an authority incapable of error. **See also.** [Interior and exterior](#entry-interior-exterior) (p. 64) · [Sphere](#entry-sphere) (p. 107) ### I am become as a God {#phrase-become-as-god} **§18.** “I am become as a God.” The narrator converts a changed viewpoint into a claim about changed status. From above Flatland he can see interiors previously concealed, and his country's wise men reserve all-seeing for God. The Sphere's answer inserts the missing moral question: ordinary criminals in Spaceland possess the same access, so why should it make anyone divine? The exaltation is not simply mocked as false perception; the Square really does see more. What fails is the inference that power, knowledge and goodness must increase together. The biblical resonance identified by the edition strengthens the drama of newly opened eyes, but the immediate dialogue also supplies its own correction through the vocabulary of justice, mercy, selfishness and love. **See also.** [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) · [Scripture gospel and prophetic speech](#entry-scriptural-language) (p. 102) ### The Progenitor of so illustrious an offspring {#phrase-progenitor-offspring} **§19.** “the Progenitor of so illustrious an offspring” The Square's pleasure at encountering the Cube borrows the language of family advancement. His own movement through a new direction could generate this more complex being; he therefore imagines himself as an ancestor who might be proud of a superior descendant. The analogy resonates with Flatland's hereditary increase in sides, but the geometrical operation is different: it adds a dimension, not merely a side. This distinction matters to the next turn. If a Square can generate a Cube, the pupil asks, why should a Cube not generate a further figure? A flattering account of his place in the new order becomes a means of refusing that order's finality. **See also.** [Cube](#entry-cube) (p. 33) · [Analogy](#entry-analogy) (p. 12) ### I cast myself in faith upon conjecture {#phrase-faith-upon-conjecture} **§19.** “I cast myself in faith upon conjecture” The Square's avowal combines commitment with an explicit admission of incomplete evidence. He immediately says that he does not know the facts and asks his guide to confirm or deny his logical anticipations. The sentence should therefore not be quoted as an assertion that the Fourth Dimension has already been demonstrated by experience. His counts and analogies give the conjecture structure, while his appeal seeks a factual response. The surrounding rhetoric nonetheless grows increasingly ecstatic, and the later rush towards higher dimensions risks outrunning that stated discipline. The passage's interest lies in the conjunction: a mind may have reason to pursue what it cannot yet verify without having earned certainty about everything it hopes to find. **See also.** [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) · [Fourth Dimension](#entry-fourth-dimension) (p. 57) ### To aspire is better than to be blindly and impotently happy {#phrase-aspire-better} **§20.** “to aspire is better than to be blindly and impotently happy” The dreamed Sphere offers this lesson while displaying Pointland's complete self-contentment. The Point's happiness is not questioned because it lacks intensity: its hymn celebrates existence ecstatically. The difficulty is that no independent being or corrective thought can enter its account of the world. Aspiration names an opening towards something beyond the self's present circumference. Yet the setting qualifies the authority of the moral. The waking Sphere had just punished his pupil's aspiration beyond three dimensions; only the dreamed figure now endorses it and acknowledges error. The statement is consequently both an instruction to the Square and an imagined correction of the teacher whose real conduct had contradicted it. **See also.** [Pointland](#entry-pointland) (p. 87) · [Dream and vision](#entry-dream-vision) (p. 43) · [Imagination and modesty](#entry-imagination-modesty) (p. 61) ### Its own Thought coming to Itself {#phrase-thought-coming-itself} **§20.** “Its own Thought coming to Itself” The Point describes the Square's hostile address as an achievement of its own mind. The correction has been heard, but its source has been eliminated: because the hearer cannot conceive another being, the apparent objection must be self-generated. The phrase reveals a particularly strong form of closed conviction. It does not need to silence criticism, since criticism can be absorbed as fresh proof of creative power. Repeated capitalized pronouns make this circuit of self-reference visible in the sentence. The episode is more exact than a general joke about egotism: it identifies the condition under which no reply can count as a reply, because the existence of a respondent is excluded in advance. **See also.** [Voice and selfhood](#entry-voice-selfhood) (p. 125) · [Pointland](#entry-pointland) (p. 87) ### Patent even to the Female Sex {#phrase-patent-female-sex} **§20.** “patent even to the Female Sex” The small word *even* preserves a hierarchy at the climax of apparent intellectual liberation. The Square has dreamed a teacher who admits his error and shows constructions beyond three dimensions; he then measures their simplicity by claiming that women could understand them. The compliment to the method depends on a familiar disparagement of women. This matters beside the Wife's earlier accurate reliance on touch and sensible response to his return. The narrator's expanded geometrical imagination has not automatically corrected his social judgments. Nor does his next resolution to preach to women and soldiers erase the qualification: the promised inclusiveness is quickly interrupted, and the Wife still receives an evasive account rather than a serious lesson. **See also.** [Wives and household](#entry-wives-household) (p. 126) · [Revelation and teaching](#entry-revelation-teaching) (p. 98) ### The Truth might be trusted {#phrase-truth-might-be-trusted} **§22.** “the Truth might be trusted” The President borrows the prisoner's final appeal and turns it into an argument for leaving him confined. If Truth intends his release and future teaching, it can bring those events about; meanwhile the Council will impose perpetual imprisonment. The apparent agreement conceals opposed practical conclusions. The Square entrusts a vulnerable claim to something beyond immediate power, while the official uses that trust to exempt power from changing its conduct. The promise of tolerable conditions completes the displacement from the justice of the sentence to its orderly administration. This is an especially cold form of silencing because it does not answer the testimony directly: it adopts the witness's own language and makes that language support the closure of his case. **See also.** [Prison and silence](#entry-prison-silence) (p. 90) · [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) # Lexical index {#lexical-index} This index links to the full articles, defined headwords and subsidiary expressions. Repeated access points are navigation, not additional definitions. The register preserves precise forms and references; article headings can be broader thematic categories. ## Articles by subject {#index-articles} - [A Square and the voice of the memoir](#entry-a-square) (p. 11) - [Analogy](#entry-analogy) (p. 12) - [Angle](#entry-angle) (p. 14) - [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15) - [Artisan and soldier](#entry-artisan-soldier) (p. 16) - [Attraction and climate](#entry-attraction-climate) (p. 18) - [Birth and ascent](#entry-birth-ascent) (p. 19) - [Chief Circle](#entry-chief-circle) (p. 20) - [Chromatic Sedition](#entry-chromatic-sedition) (p. 21) - [Chromatistes](#entry-chromatistes) (p. 23) - [Circles and Priests](#entry-circle-priest) (p. 24) - [Circular doctrine](#entry-circular-doctrine) (p. 25) - [Class and caste](#entry-class-caste) (p. 27) - [Colour](#entry-colour) (p. 28) - [Compensation](#entry-compensation) (p. 29) - [Configuration](#entry-configuration) (p. 31) - [Conformity and obedience](#entry-conformity-obedience) (p. 32) - [Cube](#entry-cube) (p. 33) - [Cunning and policy](#entry-cunning-policy) (p. 35) - [Dedication and the reader being addressed](#entry-dedication) (p. 36) - [Diagrams and the position of the reader](#entry-diagrams) (p. 38) - [Dimension](#entry-dimension) (p. 39) - [Dodecagon](#entry-dodecagon) (p. 40) - [Doors and houses](#entry-doors-houses) (p. 42) - [Dream and vision](#entry-dream-vision) (p. 43) - [The Editor and the revised Preface](#entry-editor-preface) (p. 45) - [Education and schools](#entry-education-schools) (p. 46) - [Equilateral](#entry-equilateral) (p. 47) - [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) - [Eye and the visible line](#entry-eye-retina) (p. 50) - [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) - [Feeling and touch](#entry-feeling-touch) (p. 53) - [Fertility and extinction](#entry-fertility-extinction) (p. 54) - [Fog](#entry-fog) (p. 55) - [Fourth Dimension](#entry-fourth-dimension) (p. 57) - [Grandson](#entry-grandson) (p. 58) - [History and revolution](#entry-history-revolution) (p. 60) - [Imagination and modesty](#entry-imagination-modesty) (p. 61) - [Initiation and mysteries](#entry-initiation-mysteries) (p. 62) - [Interior and exterior](#entry-interior-exterior) (p. 64) - [Irregularity](#entry-irregularity) (p. 65) - [Isosceles](#entry-isosceles) (p. 67) - [Isosceles rebels](#entry-isosceles-rebel) (p. 68) - [King of Lineland](#entry-king-lineland) (p. 69) - [Language and gender](#entry-language-gender) (p. 71) - [Law and sanction](#entry-law-sanction) (p. 72) - [Lineland](#entry-lineland) (p. 74) - [Marriage and selection](#entry-marriage-selection) (p. 75) - [Memory and forgetting](#entry-memory-forgetting) (p. 76) - [Millennial visit](#entry-millennial-visit) (p. 78) - [Movement and section](#entry-movement-section) (p. 79) - [Nature and law](#entry-nature-law) (p. 81) - [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) - [Painting](#entry-painting) (p. 84) - [Philosophical comparisons and their limits](#entry-philosophical-comparisons) (p. 85) - [Pointland](#entry-pointland) (p. 87) - [Polygon](#entry-polygon) (p. 88) - [Prison and silence](#entry-prison-silence) (p. 90) - [Prometheus Paradise and the cost of knowledge](#entry-prometheus-paradise) (p. 91) - [Providence and the language of necessity](#entry-providence) (p. 93) - [Recognition by sight](#entry-recognition-sight) (p. 94) - [Reform and equality](#entry-reform-equality) (p. 95) - [Regularity](#entry-regularity) (p. 97) - [Revelation and teaching](#entry-revelation-teaching) (p. 98) - [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99) - [Science and institutions](#entry-science-institution) (p. 101) - [Scripture gospel and prophetic speech](#entry-scriptural-language) (p. 102) - [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103) - [Solid humanity and superior races](#entry-solid-superior-races) (p. 105) - [Space and Spaceland](#entry-space-spaceland) (p. 106) - [Sphere](#entry-sphere) (p. 107) - [Straight line](#entry-line-straight) (p. 109) - [Suppression and massacre](#entry-suppression-massacre) (p. 110) - [Surgery and extermination](#entry-surgery-extermination) (p. 112) - [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113) - [Thoughtland and the changing use of an imagined place](#entry-thoughtland) (p. 115) - [Time and the millennium](#entry-time-millennium) (p. 116) - [Touch and bodily proof](#entry-touch-belly) (p. 118) - [Universal Colour Bill](#entry-universal-colour-bill) (p. 119) - [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120) - [Upward and Northward](#entry-direction-upward) (p. 122) - [Voice and hearing](#entry-voice-hearing) (p. 123) - [Voice and selfhood](#entry-voice-selfhood) (p. 125) - [Wives and household](#entry-wives-household) (p. 126) - [Women](#entry-women) (p. 128) ## Defined words and expressions {#index-words} - [A Square](#register-001) (p. 130) - [Abrogation](#register-002) (p. 130) - [Accost](#register-003) (p. 130) - [Acquiesce](#register-004) (p. 130) - [Adage](#register-005) (p. 130) - [Aides-de-camp](#register-006) (p. 130) - [Alliance](#register-007) (p. 131) - [Alphabet of angles](#register-008) (p. 131) - [Analogy](#register-009) (p. 131) - [Anarchical](#register-010) (p. 131) - [Animosity](#register-011) (p. 131) - [Antagonistic](#register-012) (p. 131) - [Antiquarian](#register-013) (p. 131) - [Apostle](#register-014) (p. 131) - [Apprehend](#register-015) (p. 132) - [Approximation](#register-016) (p. 132) - [Approximations](#register-017) (p. 132) - [Arbitrary visitations](#register-018) (p. 132) - [Aristocratic](#register-019) (p. 132) - [Aristocratic Legislature](#register-020) (p. 132) - [Arithmetical](#register-021) (p. 132) - [Assimilated](#register-022) (p. 132) - [Attraction](#register-023) (p. 133) - [Audition](#register-024) (p. 133) - [August](#register-025) (p. 133) - [Averse](#register-026) (p. 133) - [Avocation](#register-027) (p. 133) - [Avowed](#register-028) (p. 133) - [Barbarism](#register-029) (p. 133) - [Barren](#register-030) (p. 133) - [Beatitude](#register-031) (p. 134) - [Belauded](#register-032) (p. 134) - [Betters](#register-033) (p. 134) - [Beyond experience](#register-034) (p. 134) - [Bi-lingual](#register-035) (p. 134) - [Bi-mental](#register-036) (p. 134) - [Blot on her escutcheon](#register-037) (p. 134) - [Breeding](#register-038) (p. 134) - [Brightness](#register-039) (p. 135) - [Burnt umber](#register-040) (p. 135) - [By courtesy](#register-041) (p. 135) - [Carnage](#register-042) (p. 135) - [Castigation](#register-043) (p. 135) - [Casual](#register-044) (p. 135) - [Catch-phrase](#register-045) (p. 135) - [Celerity](#register-046) (p. 136) - [Celestial region](#register-047) (p. 136) - [Certifiable](#register-048) (p. 136) - [Certified pedigree](#register-049) (p. 136) - [Charm](#register-050) (p. 136) - [Cheap system](#register-051) (p. 136) - [Chief Circle](#register-052) (p. 136) - [Chief Clerk](#register-053) (p. 136) - [Chirruped](#register-054) (p. 137) - [Chromatistes, inventor](#register-055) (p. 137) - [Chromatistes, revolutionary](#register-056) (p. 137) - [Circular Neo-Therapeutic Gymnasium](#register-057) (p. 137) - [Circumspection](#register-058) (p. 137) - [Civic rights](#register-059) (p. 137) - [Cognizance](#register-060) (p. 137) - [Colligation](#register-061) (p. 138) - [Colour Recognition](#register-062) (p. 138) - [Commandment](#register-063) (p. 138) - [Compensative Laws of Nature](#register-064) (p. 138) - [Comprehend](#register-065) (p. 138) - [Conceit](#register-066) (p. 138) - [Concession](#register-067) (p. 138) - [Conclave](#register-068) (p. 138) - [Concourse](#register-069) (p. 139) - [Condescending](#register-070) (p. 139) - [Condole](#register-071) (p. 139) - [Configuration](#register-072) (p. 139) - [Conformation](#register-073) (p. 139) - [Congenital](#register-074) (p. 140) - [Conjugal](#register-075) (p. 140) - [Conjugal union](#register-076) (p. 140) - [Consort](#register-077) (p. 140) - [Constituents](#register-078) (p. 140) - [Constitution](#register-079) (p. 140) - [Consumed](#register-080) (p. 140) - [Consummate](#register-081) (p. 141) - [Consummated](#register-082) (p. 141) - [Consummating](#register-083) (p. 141) - [Conversant](#register-084) (p. 141) - [Conversazione](#register-085) (p. 141) - [Convert](#register-086) (p. 141) - [Corporal](#register-087) (p. 141) - [Corporal ascent](#register-088) (p. 141) - [Corporal decoration](#register-089) (p. 142) - [Correspondent](#register-090) (p. 142) - [Court Martial](#register-091) (p. 142) - [Cube](#register-092) (p. 142) - [Cut-throat](#register-093) (p. 142) - [Dashing](#register-094) (p. 142) - [Decimated](#register-095) (p. 142) - [Deference](#register-096) (p. 143) - [Degradation](#register-097) (p. 143) - [Degraded](#register-098) (p. 143) - [Demoniacal](#register-099) (p. 143) - [Demonstration](#register-100) (p. 143) - [Demoralize](#register-101) (p. 143) - [Destitute of converts](#register-102) (p. 143) - [Deterrent](#register-103) (p. 143) - [Diaetetic](#register-104) (p. 144) - [Diameter](#register-105) (p. 144) - [Dimension](#register-106) (p. 144) - [Dimensional prejudices](#register-107) (p. 144) - [Discursive](#register-108) (p. 144) - [Disrepute](#register-109) (p. 144) - [Divers](#register-110) (p. 144) - [Dodecagon](#register-111) (p. 144) - [Domestic individuality](#register-112) (p. 145) - [Double Extra-Solids](#register-113) (p. 145) - [Duly certified](#register-114) (p. 145) - [Ecclesiastical](#register-115) (p. 145) - [Editor](#register-116) (p. 145) - [Egress](#register-117) (p. 145) - [Elicit](#register-118) (p. 145) - [Emanated](#register-119) (p. 145) - [Endowment](#register-120) (p. 146) - [Endowments](#register-121) (p. 146) - [Ennobled](#register-122) (p. 146) - [Environed](#register-123) (p. 146) - [Enwrap](#register-124) (p. 146) - [Esoteric](#register-125) (p. 146) - [Essay](#register-126) (p. 146) - [Eulogy](#register-127) (p. 146) - [Evangelize](#register-128) (p. 147) - [Expediency](#register-129) (p. 147) - [Extinguished](#register-130) (p. 147) - [Extra Cubes](#register-131) (p. 147) - [Extra height](#register-132) (p. 147) - [Extra-solid angles](#register-133) (p. 147) - [Extra-Solids](#register-134) (p. 147) - [Extremities](#register-135) (p. 147) - [Extricating](#register-136) (p. 148) - [Faith](#register-137) (p. 148) - [Fall](#register-138) (p. 148) - [Family brain](#register-139) (p. 148) - [Fast society](#register-140) (p. 148) - [Fatuity](#register-141) (p. 148) - [Fecundity](#register-142) (p. 148) - [Feeler](#register-143) (p. 148) - [Feeling](#register-144) (p. 149) - [Feeling is believing](#register-145) (p. 149) - [Felt](#register-146) (p. 149) - [Fettered](#register-147) (p. 149) - [Figure](#register-148) (p. 149) - [Flagitious](#register-149) (p. 149) - [Fog](#register-150) (p. 149) - [Foreland](#register-151) (p. 150) - [Forsooth](#register-152) (p. 150) - [Four in One](#register-153) (p. 150) - [Fourth Dimension](#register-154) (p. 150) - [Frail Sex](#register-155) (p. 150) - [Franticly](#register-156) (p. 150) - [Fraternal](#register-157) (p. 150) - [Freeman](#register-158) (p. 150) - [Frugality](#register-159) (p. 151) - [Fruition](#register-160) (p. 151) - [Full career](#register-161) (p. 151) - [Furlong](#register-162) (p. 151) - [Gamboge](#register-163) (p. 151) - [Gentlemen](#register-164) (p. 151) - [Geometrical Progression](#register-165) (p. 151) - [Gift of Modesty](#register-166) (p. 152) - [Gospel of the Three Dimensions](#register-167) (p. 152) - [Grandson](#register-168) (p. 152) - [H C](#register-169) (p. 152) - [Half-hour glass](#register-170) (p. 152) - [Hand-alphabet](#register-171) (p. 152) - [Haply](#register-172) (p. 152) - [Harangue](#register-173) (p. 153) - [Hereditary level](#register-174) (p. 153) - [Heresies](#register-175) (p. 153) - [Heterodox](#register-176) (p. 153) - [Hierarchy](#register-177) (p. 153) - [High ness](#register-178) (p. 153) - [Hinder extremity](#register-179) (p. 153) - [Historian](#register-180) (p. 153) - [Historical pieces](#register-181) (p. 154) - [Homage](#register-182) (p. 154) - [Honourable confinement](#register-183) (p. 154) - [Horizon](#register-184) (p. 154) - [Human diagonals](#register-185) (p. 154) - [Idiom](#register-186) (p. 154) - [Imagination](#register-187) (p. 154) - [Immunity](#register-188) (p. 154) - [Immured](#register-189) (p. 155) - [Impartiality](#register-190) (p. 155) - [Impervious](#register-191) (p. 155) - [Imposture](#register-192) (p. 155) - [Impregnable](#register-193) (p. 155) - [Inane](#register-194) (p. 155) - [Incommode](#register-195) (p. 155) - [Incredulity](#register-196) (p. 155) - [Indiscretion](#register-197) (p. 156) - [Infecundity](#register-198) (p. 156) - [Infinitesimal](#register-199) (p. 156) - [Infinitesimally](#register-200) (p. 156) - [Initiated](#register-201) (p. 156) - [Integrity](#register-202) (p. 156) - [Intellectual Arts](#register-203) (p. 157) - [Intercourse](#register-204) (p. 157) - [Interpreter and summarizer](#register-205) (p. 157) - [Intestines](#register-206) (p. 157) - [Introduction](#register-207) (p. 157) - [Invisible Cap](#register-208) (p. 157) - [Iota](#register-209) (p. 157) - [Isosceles Hospital](#register-210) (p. 158) - [Jostled](#register-211) (p. 158) - [Juggler](#register-212) (p. 158) - [Kinetic](#register-213) (p. 158) - [Kinetics](#register-214) (p. 158) - [Last resource of civilization](#register-215) (p. 158) - [Latent](#register-216) (p. 158) - [Legislature](#register-217) (p. 158) - [Licentious](#register-218) (p. 159) - [Line of Lines](#register-219) (p. 159) - [Lineland](#register-220) (p. 159) - [Lip-speech](#register-221) (p. 159) - [Local Speculative Society](#register-222) (p. 159) - [Logical anticipations](#register-223) (p. 159) - [Logical dialect](#register-224) (p. 159) - [Long Vacation](#register-225) (p. 159) - [Lucid](#register-226) (p. 160) - [Luminary](#register-227) (p. 160) - [Luminous](#register-228) (p. 160) - [Luminous wake](#register-229) (p. 160) - [Lunatic asylum](#register-230) (p. 160) - [Lustre](#register-231) (p. 160) - [Lustrous](#register-232) (p. 160) - [Mainstays](#register-233) (p. 160) - [Manufactory](#register-234) (p. 161) - [Many in the One](#register-235) (p. 161) - [Marshal’s baton](#register-236) (p. 161) - [Mauve](#register-237) (p. 161) - [Meanest capacity](#register-238) (p. 161) - [Memoirs](#register-239) (p. 161) - [Mercurial versatility](#register-240) (p. 161) - [Methought](#register-241) (p. 161) - [Micrometer](#register-242) (p. 162) - [Military review](#register-243) (p. 162) - [Millenary](#register-244) (p. 162) - [Millennium](#register-245) (p. 162) - [Miscarriage](#register-246) (p. 162) - [Modesty](#register-247) (p. 162) - [Molest](#register-248) (p. 162) - [Monarch of the world](#register-249) (p. 162) - [Monopolising](#register-250) (p. 163) - [Monstrosity](#register-251) (p. 163) - [Moral obliquity](#register-252) (p. 163) - [Moral terminology](#register-253) (p. 163) - [Must needs](#register-254) (p. 163) - [Myriads](#register-255) (p. 163) - [Mysteries](#register-256) (p. 163) - [Nature](#register-257) (p. 163) - [Neo-Therapeutic Cemetery](#register-258) (p. 164) - [Non-dimensional Gulf](#register-259) (p. 164) - [O yes! O yes!](#register-260) (p. 164) - [Objection](#register-261) (p. 164) - [Ocular demonstration](#register-262) (p. 164) - [Omnipresence](#register-263) (p. 164) - [Omniscience](#register-264) (p. 164) - [Omnividence](#register-265) (p. 165) - [Order](#register-266) (p. 165) - [Ordinance](#register-267) (p. 165) - [Palled](#register-268) (p. 165) - [Pantocyclus](#register-269) (p. 165) - [Paradise](#register-270) (p. 165) - [Parallelogram](#register-271) (p. 165) - [Pasteboard](#register-272) (p. 165) - [Patent](#register-273) (p. 166) - [Peace-cry](#register-274) (p. 166) - [Pedigrees](#register-275) (p. 166) - [Penal Laws](#register-276) (p. 166) - [Pencil](#register-277) (p. 166) - [Perdition](#register-278) (p. 166) - [Perimeter](#register-279) (p. 166) - [Peroration](#register-280) (p. 167) - [Perspective](#register-281) (p. 167) - [Perturbed angularity](#register-282) (p. 167) - [Perusal](#register-283) (p. 167) - [Perversity](#register-284) (p. 167) - [Phalanx](#register-285) (p. 167) - [Phantasmal vision](#register-286) (p. 167) - [Philanthropy](#register-287) (p. 167) - [Picturesque incidents](#register-288) (p. 168) - [Placability](#register-289) (p. 168) - [Plausible](#register-290) (p. 168) - [Plebeian](#register-291) (p. 168) - [Plume yourself](#register-292) (p. 168) - [Pointland](#register-293) (p. 168) - [Polygonal](#register-294) (p. 168) - [Portent](#register-295) (p. 168) - [Posterity](#register-296) (p. 169) - [Powder-magazine](#register-297) (p. 169) - [Prattle](#register-298) (p. 169) - [Prearrangement](#register-299) (p. 169) - [Precipitated](#register-300) (p. 169) - [Preclude](#register-301) (p. 169) - [Precocious](#register-302) (p. 169) - [Preconcerted](#register-303) (p. 170) - [Presence](#register-304) (p. 170) - [Pretext](#register-305) (p. 170) - [Priestly order](#register-306) (p. 170) - [Priests](#register-307) (p. 170) - [Pristine](#register-308) (p. 170) - [Professional Men](#register-309) (p. 170) - [Progenitor](#register-310) (p. 170) - [Progenitors](#register-311) (p. 171) - [Prometheus](#register-312) (p. 171) - [Promulgators of paradoxes](#register-313) (p. 171) - [Proof positive](#register-314) (p. 171) - [Propagation](#register-315) (p. 171) - [Prosecution](#register-316) (p. 171) - [Prospect](#register-317) (p. 171) - [Prostrating](#register-318) (p. 171) - [Proximity](#register-319) (p. 172) - [Purged](#register-320) (p. 172) - [Quietism](#register-321) (p. 172) - [Rapt](#register-322) (p. 172) - [Reactionary](#register-323) (p. 172) - [Realise](#register-324) (p. 172) - [Redundant population](#register-325) (p. 172) - [Reform](#register-326) (p. 172) - [Regular Hospitals](#register-327) (p. 173) - [Remonstrance](#register-328) (p. 173) - [Responsive note](#register-329) (p. 173) - [Retinue](#register-330) (p. 173) - [Retirement](#register-331) (p. 173) - [Retrograde](#register-332) (p. 173) - [Retrogression](#register-333) (p. 173) - [Retrospect](#register-334) (p. 173) - [Reverie](#register-335) (p. 174) - [Romance](#register-336) (p. 174) - [Rude health](#register-337) (p. 174) - [Rudimentary](#register-338) (p. 174) - [Rustication](#register-339) (p. 174) - [Sagacity](#register-340) (p. 174) - [Sanctioned](#register-341) (p. 174) - [Sanitary and Social Board](#register-342) (p. 174) - [Scion](#register-343) (p. 175) - [Scourge](#register-344) (p. 175) - [Scouted](#register-345) (p. 175) - [Seasonable simulations](#register-346) (p. 175) - [Second Nature](#register-347) (p. 175) - [Secret archives](#register-348) (p. 175) - [Section](#register-349) (p. 175) - [Sedition](#register-350) (p. 175) - [Seditious heresy](#register-351) (p. 176) - [Semicircle](#register-352) (p. 176) - [Seminary](#register-353) (p. 176) - [Sensibly](#register-354) (p. 176) - [Sensuous](#register-355) (p. 176) - [Serf-born](#register-356) (p. 176) - [Serfdom](#register-357) (p. 176) - [Seven score thousand](#register-358) (p. 177) - [Simulate](#register-359) (p. 177) - [Solid](#register-360) (p. 177) - [Solid angles](#register-361) (p. 177) - [Solid Humanity](#register-362) (p. 177) - [Soliloquizing](#register-363) (p. 177) - [Sonorousness](#register-364) (p. 177) - [Sophism](#register-365) (p. 177) - [Soul-devouring Sphinx](#register-366) (p. 178) - [Spaceland](#register-367) (p. 178) - [Specimens](#register-368) (p. 178) - [Sphere](#register-369) (p. 178) - [Sphinx](#register-370) (p. 178) - [Square as a verb](#register-371) (p. 178) - [St Vitus’s Dance](#register-372) (p. 178) - [State-craft](#register-373) (p. 179) - [Static](#register-374) (p. 179) - [Statics](#register-375) (p. 179) - [Status](#register-376) (p. 179) - [Stipend](#register-377) (p. 179) - [Sub-lustrous](#register-378) (p. 179) - [Substantial realities](#register-379) (p. 179) - [Subversion](#register-380) (p. 180) - [Suffused](#register-381) (p. 180) - [Superficial](#register-382) (p. 180) - [Superfluous](#register-383) (p. 180) - [Superior Races](#register-384) (p. 180) - [Surreptitiously](#register-385) (p. 180) - [Sweetmeats](#register-386) (p. 180) - [Tablets of accounts](#register-387) (p. 180) - [Terminal Points](#register-388) (p. 181) - [Terminology](#register-389) (p. 181) - [Thick](#register-390) (p. 181) - [Third power](#register-391) (p. 181) - [Thoughtland](#register-392) (p. 181) - [Through Flatland to Thoughtland](#register-393) (p. 181) - [Torrid zones](#register-394) (p. 181) - [Touch of Nature](#register-395) (p. 182) - [Tradesman](#register-396) (p. 182) - [Transfixed](#register-397) (p. 182) - [Transmuted](#register-398) (p. 182) - [Trepanning](#register-399) (p. 182) - [Tribute](#register-400) (p. 182) - [Triennial](#register-401) (p. 183) - [Ultra-marine](#register-402) (p. 183) - [Undulation](#register-403) (p. 183) - [Unemancipable](#register-404) (p. 183) - [Universal Colour Bill](#register-405) (p. 183) - [Vacuum](#register-406) (p. 183) - [Vantage-ground](#register-407) (p. 183) - [Variegated](#register-408) (p. 183) - [Vent their spleen](#register-409) (p. 184) - [Ventilators](#register-410) (p. 184) - [Vermilion](#register-411) (p. 184) - [Vertex](#register-412) (p. 184) - [Via media](#register-413) (p. 184) - [Vigour](#register-414) (p. 184) - [Visibly incorporate](#register-415) (p. 184) - [Visitations](#register-416) (p. 184) - [Volition](#register-417) (p. 185) - [Vouchsafed](#register-418) (p. 185) - [Vulgarise](#register-419) (p. 185) - [Wane](#register-420) (p. 185) - [Wax](#register-421) (p. 185) - [Woman hater](#register-422) (p. 185) - [Wonted](#register-423) (p. 185) - [Æsthetic](#register-424) (p. 185) ## Subsidiary expressions {#index-phrases} - [A bi-lingual and bi-mental existence](#phrase-bi-mental-existence) (p. 191) - [A feminine Monstrosity with a bass voice](#phrase-feminine-monstrosity) (p. 195) - [A humble native addressing superior readers](#phrase-humble-native) (p. 186) - [a second Nature](#phrase-second-nature) (p. 192) - [assumed, by courtesy](#phrase-assumed-courtesy) (p. 194) - [Both kinds of dogmatism](#phrase-two-dogmatisms) (p. 187) - [But he is not the Square he once was](#phrase-not-square-once) (p. 186) - [The completion of your incomplete self](#phrase-completion-incomplete) (p. 196) - [Configuration makes the man](#phrase-configuration-man) (p. 194) - [Deeds, and not words, shall proclaim the truth](#phrase-deeds-words) (p. 197) - [Dimension implies direction and measurement](#phrase-direction-measurement) (p. 196) - [doing nothing themselves](#phrase-doing-nothing) (p. 194) - [Expense is the truest economy](#phrase-expense-economy) (p. 190) - [Feel and be felt by](#phrase-feel-and-be-felt) (p. 189) - [Give her the North side of the way](#phrase-north-side-courtesy) (p. 188) - [Go to bed](#phrase-go-to-bed) (p. 196) - [the greatest number](#phrase-greatest-number) (p. 193) - [I am become as a God](#phrase-become-as-god) (p. 198) - [I cast myself in faith upon conjecture](#phrase-faith-upon-conjecture) (p. 198) - [In a becoming and respectful manner](#phrase-becoming-respectful) (p. 189) - [The interests of the Greater Number](#phrase-greater-number) (p. 190) - [Its own Thought coming to Itself](#phrase-thought-coming-itself) (p. 199) - [Measure my high ness](#phrase-measure-highness) (p. 186) - [My country and my universe](#phrase-country-universe) (p. 187) - [no blot on her escutcheon](#phrase-blot-escutcheon) (p. 195) - [Once a Woman, always a Woman](#phrase-once-woman) (p. 189) - [Once neighbours, always neighbours](#phrase-once-neighbours) (p. 195) - [One Dimension behind the thing](#phrase-dimension-behind) (p. 197) - [One touch of Nature makes all worlds akin](#phrase-worlds-akin) (p. 187) - [Painlessly and mercifully consumed](#phrase-mercifully-consumed) (p. 191) - [Patent even to the Female Sex](#phrase-patent-female-sex) (p. 199) - [Perfect propriety in Polygonal society](#phrase-polygonal-propriety) (p. 190) - [the perimeter of the whole subject](#phrase-perimeter-subject) (p. 192) - [Poor Flatland Prometheus](#phrase-flatland-prometheus) (p. 187) - [The Progenitor of so illustrious an offspring](#phrase-progenitor-offspring) (p. 198) - [pure from the pollution of paint](#phrase-pollution-paint) (p. 191) - [The soul devouring Sphinx](#phrase-sphinx) (p. 188) - [spared but decimated](#phrase-spared-decimated) (p. 193) - [Stifle sedition in its very cradle](#phrase-sedition-cradle) (p. 188) - [To aspire is better than to be blindly and impotently happy](#phrase-aspire-better) (p. 199) - [The Truth might be trusted](#phrase-truth-might-be-trusted) (p. 200) - [What you think you see, you see not](#phrase-think-you-see) (p. 197) - [the Workmen are annually consumed](#phrase-annually-consumed) (p. 193) # Passage index {#passage-index} The primary frame and all twenty-two numbered sections are represented. Each entry points to articles discussing that passage and to relevant subsidiary glosses. Register definitions carry their own exact attestations. A passage reference identifies Abbott’s text; accompanying page numbers identify this companion. ## Title Page {#passage-title} - [A Square and the voice of the memoir](#entry-a-square) (p. 11) - [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99) - [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103) ## Dedication {#passage-dedication} - [Dedication and the reader being addressed](#entry-dedication) (p. 36) - [Imagination and modesty](#entry-imagination-modesty) (p. 61) - [Initiation and mysteries](#entry-initiation-mysteries) (p. 62) - [Solid humanity and superior races](#entry-solid-superior-races) (p. 105) ## Preface {#passage-preface} - [A Square and the voice of the memoir](#entry-a-square) (p. 11) - [The Editor and the revised Preface](#entry-editor-preface) (p. 45) - [Eye and the visible line](#entry-eye-retina) (p. 50) - [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) - [Imagination and modesty](#entry-imagination-modesty) (p. 61) - [Providence and the language of necessity](#entry-providence) (p. 93) - [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99) - [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103) - [Straight line](#entry-line-straight) (p. 109) - [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113) - [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120) - [Women](#entry-women) (p. 128) ## Part I epigraph {#passage-part-one} - [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103) ## Part II epigraph {#passage-part-two} - [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103) ## Section 1 {#passage-1} - [A Square and the voice of the memoir](#entry-a-square) (p. 11) - [Diagrams and the position of the reader](#entry-diagrams) (p. 38) - [Equilateral](#entry-equilateral) (p. 47) - [Eye and the visible line](#entry-eye-retina) (p. 50) - [Imagination and modesty](#entry-imagination-modesty) (p. 61) - [Philosophical comparisons and their limits](#entry-philosophical-comparisons) (p. 85) - [Recognition by sight](#entry-recognition-sight) (p. 94) - [Straight line](#entry-line-straight) (p. 109) Expressions: [My country and my universe](#phrase-country-universe) (p. 187). ## Section 2 {#passage-2} - [Attraction and climate](#entry-attraction-climate) (p. 18) - [Diagrams and the position of the reader](#entry-diagrams) (p. 38) - [Doors and houses](#entry-doors-houses) (p. 42) - [Nature and law](#entry-nature-law) (p. 81) Expressions: [Give her the North side of the way](#phrase-north-side-courtesy) (p. 188). ## Section 3 {#passage-3} - [A Square and the voice of the memoir](#entry-a-square) (p. 11) - [Angle](#entry-angle) (p. 14) - [Artisan and soldier](#entry-artisan-soldier) (p. 16) - [Birth and ascent](#entry-birth-ascent) (p. 19) - [Chief Circle](#entry-chief-circle) (p. 20) - [Circles and Priests](#entry-circle-priest) (p. 24) - [Class and caste](#entry-class-caste) (p. 27) - [Compensation](#entry-compensation) (p. 29) - [Equilateral](#entry-equilateral) (p. 47) - [History and revolution](#entry-history-revolution) (p. 60) - [Isosceles](#entry-isosceles) (p. 67) - [Isosceles rebels](#entry-isosceles-rebel) (p. 68) - [Marriage and selection](#entry-marriage-selection) (p. 75) - [Nature and law](#entry-nature-law) (p. 81) - [Polygon](#entry-polygon) (p. 88) - [Regularity](#entry-regularity) (p. 97) - [Solid humanity and superior races](#entry-solid-superior-races) (p. 105) - [Straight line](#entry-line-straight) (p. 109) - [Surgery and extermination](#entry-surgery-extermination) (p. 112) - [Women](#entry-women) (p. 128) Expressions: [Stifle sedition in its very cradle](#phrase-sedition-cradle) (p. 188). ## Section 4 {#passage-4} - [Artisan and soldier](#entry-artisan-soldier) (p. 16) - [Attraction and climate](#entry-attraction-climate) (p. 18) - [Class and caste](#entry-class-caste) (p. 27) - [Doors and houses](#entry-doors-houses) (p. 42) - [Eye and the visible line](#entry-eye-retina) (p. 50) - [Language and gender](#entry-language-gender) (p. 71) - [Nature and law](#entry-nature-law) (p. 81) - [Straight line](#entry-line-straight) (p. 109) - [Voice and hearing](#entry-voice-hearing) (p. 123) - [Women](#entry-women) (p. 128) Expressions: [In a becoming and respectful manner](#phrase-becoming-respectful) (p. 189) · [Once a Woman, always a Woman](#phrase-once-woman) (p. 189). ## Section 5 {#passage-5} - [Angle](#entry-angle) (p. 14) - [Attraction and climate](#entry-attraction-climate) (p. 18) - [Birth and ascent](#entry-birth-ascent) (p. 19) - [Diagrams and the position of the reader](#entry-diagrams) (p. 38) - [Education and schools](#entry-education-schools) (p. 46) - [Equilateral](#entry-equilateral) (p. 47) - [Eye and the visible line](#entry-eye-retina) (p. 50) - [Feeling and touch](#entry-feeling-touch) (p. 53) - [Isosceles](#entry-isosceles) (p. 67) - [Polygon](#entry-polygon) (p. 88) - [Recognition by sight](#entry-recognition-sight) (p. 94) - [Surgery and extermination](#entry-surgery-extermination) (p. 112) - [Voice and hearing](#entry-voice-hearing) (p. 123) Expressions: [Feel and be felt by](#phrase-feel-and-be-felt) (p. 189) · [Expense is the truest economy](#phrase-expense-economy) (p. 190). ## Section 6 {#passage-6} - [Angle](#entry-angle) (p. 14) - [Class and caste](#entry-class-caste) (p. 27) - [Diagrams and the position of the reader](#entry-diagrams) (p. 38) - [Education and schools](#entry-education-schools) (p. 46) - [Equilateral](#entry-equilateral) (p. 47) - [Eye and the visible line](#entry-eye-retina) (p. 50) - [Feeling and touch](#entry-feeling-touch) (p. 53) - [Fog](#entry-fog) (p. 55) - [Polygon](#entry-polygon) (p. 88) - [Recognition by sight](#entry-recognition-sight) (p. 94) - [Straight line](#entry-line-straight) (p. 109) - [Surgery and extermination](#entry-surgery-extermination) (p. 112) Expressions: [Perfect propriety in Polygonal society](#phrase-polygonal-propriety) (p. 190). ## Section 7 {#passage-7} - [Doors and houses](#entry-doors-houses) (p. 42) - [Irregularity](#entry-irregularity) (p. 65) - [Isosceles](#entry-isosceles) (p. 67) - [Law and sanction](#entry-law-sanction) (p. 72) - [Nature and law](#entry-nature-law) (p. 81) - [Regularity](#entry-regularity) (p. 97) - [Surgery and extermination](#entry-surgery-extermination) (p. 112) Expressions: [The interests of the Greater Number](#phrase-greater-number) (p. 190) · [Painlessly and mercifully consumed](#phrase-mercifully-consumed) (p. 191) · [the greatest number](#phrase-greatest-number) (p. 193). ## Section 8 {#passage-8} - [Chromatic Sedition](#entry-chromatic-sedition) (p. 21) - [Chromatistes](#entry-chromatistes) (p. 23) - [Colour](#entry-colour) (p. 28) - [Dodecagon](#entry-dodecagon) (p. 40) - [History and revolution](#entry-history-revolution) (p. 60) - [Painting](#entry-painting) (p. 84) Expressions: [pure from the pollution of paint](#phrase-pollution-paint) (p. 191). ## Section 9 {#passage-9} - [Chromatic Sedition](#entry-chromatic-sedition) (p. 21) - [Chromatistes](#entry-chromatistes) (p. 23) - [Colour](#entry-colour) (p. 28) - [Cunning and policy](#entry-cunning-policy) (p. 35) - [Isosceles rebels](#entry-isosceles-rebel) (p. 68) - [Law and sanction](#entry-law-sanction) (p. 72) - [Reform and equality](#entry-reform-equality) (p. 95) - [Science and institutions](#entry-science-institution) (p. 101) - [Universal Colour Bill](#entry-universal-colour-bill) (p. 119) Expressions: [a second Nature](#phrase-second-nature) (p. 192). ## Section 10 {#passage-10} - [Chief Circle](#entry-chief-circle) (p. 20) - [Chromatic Sedition](#entry-chromatic-sedition) (p. 21) - [Chromatistes](#entry-chromatistes) (p. 23) - [Colour](#entry-colour) (p. 28) - [Compensation](#entry-compensation) (p. 29) - [Cunning and policy](#entry-cunning-policy) (p. 35) - [Dodecagon](#entry-dodecagon) (p. 40) - [History and revolution](#entry-history-revolution) (p. 60) - [Isosceles rebels](#entry-isosceles-rebel) (p. 68) - [Law and sanction](#entry-law-sanction) (p. 72) - [Reform and equality](#entry-reform-equality) (p. 95) - [Science and institutions](#entry-science-institution) (p. 101) - [Suppression and massacre](#entry-suppression-massacre) (p. 110) Expressions: [the perimeter of the whole subject](#phrase-perimeter-subject) (p. 192) · [the greatest number](#phrase-greatest-number) (p. 193) · [spared but decimated](#phrase-spared-decimated) (p. 193) · [the Workmen are annually consumed](#phrase-annually-consumed) (p. 193). ## Section 11 {#passage-11} - [Chief Circle](#entry-chief-circle) (p. 20) - [Circles and Priests](#entry-circle-priest) (p. 24) - [Circular doctrine](#entry-circular-doctrine) (p. 25) - [Fertility and extinction](#entry-fertility-extinction) (p. 54) - [Initiation and mysteries](#entry-initiation-mysteries) (p. 62) Expressions: [doing nothing themselves](#phrase-doing-nothing) (p. 194) · [assumed, by courtesy](#phrase-assumed-courtesy) (p. 194). ## Section 12 {#passage-12} - [Circular doctrine](#entry-circular-doctrine) (p. 25) - [Configuration](#entry-configuration) (p. 31) - [Conformity and obedience](#entry-conformity-obedience) (p. 32) - [Dodecagon](#entry-dodecagon) (p. 40) - [Fertility and extinction](#entry-fertility-extinction) (p. 54) - [Language and gender](#entry-language-gender) (p. 71) - [Law and sanction](#entry-law-sanction) (p. 72) - [Marriage and selection](#entry-marriage-selection) (p. 75) - [Voice and hearing](#entry-voice-hearing) (p. 123) - [Women](#entry-women) (p. 128) Expressions: [A bi-lingual and bi-mental existence](#phrase-bi-mental-existence) (p. 191) · [Configuration makes the man](#phrase-configuration-man) (p. 194) · [no blot on her escutcheon](#phrase-blot-escutcheon) (p. 195). ## Section 13 {#passage-13} - [Dream and vision](#entry-dream-vision) (p. 43) - [Interior and exterior](#entry-interior-exterior) (p. 64) - [King of Lineland](#entry-king-lineland) (p. 69) - [Lineland](#entry-lineland) (p. 74) - [Time and the millennium](#entry-time-millennium) (p. 116) - [Voice and selfhood](#entry-voice-selfhood) (p. 125) Expressions: [Once neighbours, always neighbours](#phrase-once-neighbours) (p. 195) · [A feminine Monstrosity with a bass voice](#phrase-feminine-monstrosity) (p. 195). ## Section 14 {#passage-14} - [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) - [King of Lineland](#entry-king-lineland) (p. 69) - [Lineland](#entry-lineland) (p. 74) - [Movement and section](#entry-movement-section) (p. 79) - [Space and Spaceland](#entry-space-spaceland) (p. 106) - [Touch and bodily proof](#entry-touch-belly) (p. 118) - [Voice and hearing](#entry-voice-hearing) (p. 123) - [Voice and selfhood](#entry-voice-selfhood) (p. 125) Expressions: [The completion of your incomplete self](#phrase-completion-incomplete) (p. 196). ## Section 15 {#passage-15} - [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15) - [Cube](#entry-cube) (p. 33) - [Dream and vision](#entry-dream-vision) (p. 43) - [Grandson](#entry-grandson) (p. 58) - [Sphere](#entry-sphere) (p. 107) - [Time and the millennium](#entry-time-millennium) (p. 116) - [Touch and bodily proof](#entry-touch-belly) (p. 118) - [Wives and household](#entry-wives-household) (p. 126) Expressions: [Go to bed](#phrase-go-to-bed) (p. 196). ## Section 16 {#passage-16} - [Analogy](#entry-analogy) (p. 12) - [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15) - [Dimension](#entry-dimension) (p. 39) - [Dream and vision](#entry-dream-vision) (p. 43) - [The Editor and the revised Preface](#entry-editor-preface) (p. 45) - [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) - [Initiation and mysteries](#entry-initiation-mysteries) (p. 62) - [Interior and exterior](#entry-interior-exterior) (p. 64) - [Memory and forgetting](#entry-memory-forgetting) (p. 76) - [Movement and section](#entry-movement-section) (p. 79) - [Space and Spaceland](#entry-space-spaceland) (p. 106) - [Sphere](#entry-sphere) (p. 107) - [Straight line](#entry-line-straight) (p. 109) - [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113) - [Touch and bodily proof](#entry-touch-belly) (p. 118) - [Upward and Northward](#entry-direction-upward) (p. 122) - [Voice and selfhood](#entry-voice-selfhood) (p. 125) Expressions: [Dimension implies direction and measurement](#phrase-direction-measurement) (p. 196) · [One Dimension behind the thing](#phrase-dimension-behind) (p. 197). ## Section 17 {#passage-17} - [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) - [Interior and exterior](#entry-interior-exterior) (p. 64) - [Millennial visit](#entry-millennial-visit) (p. 78) - [Revelation and teaching](#entry-revelation-teaching) (p. 98) - [Sphere](#entry-sphere) (p. 107) - [Touch and bodily proof](#entry-touch-belly) (p. 118) Expressions: [Deeds, and not words, shall proclaim the truth](#phrase-deeds-words) (p. 197). ## Section 18 {#passage-18} - [Chief Circle](#entry-chief-circle) (p. 20) - [The Editor and the revised Preface](#entry-editor-preface) (p. 45) - [History and revolution](#entry-history-revolution) (p. 60) - [Interior and exterior](#entry-interior-exterior) (p. 64) - [Law and sanction](#entry-law-sanction) (p. 72) - [Millennial visit](#entry-millennial-visit) (p. 78) - [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) - [Prison and silence](#entry-prison-silence) (p. 90) - [Revelation and teaching](#entry-revelation-teaching) (p. 98) - [Solid humanity and superior races](#entry-solid-superior-races) (p. 105) - [Space and Spaceland](#entry-space-spaceland) (p. 106) - [Sphere](#entry-sphere) (p. 107) - [Time and the millennium](#entry-time-millennium) (p. 116) - [Wives and household](#entry-wives-household) (p. 126) Expressions: [What you think you see, you see not](#phrase-think-you-see) (p. 197) · [I am become as a God](#phrase-become-as-god) (p. 198). ## Section 19 {#passage-19} - [Analogy](#entry-analogy) (p. 12) - [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15) - [Cube](#entry-cube) (p. 33) - [Dedication and the reader being addressed](#entry-dedication) (p. 36) - [Dimension](#entry-dimension) (p. 39) - [The Editor and the revised Preface](#entry-editor-preface) (p. 45) - [Fourth Dimension](#entry-fourth-dimension) (p. 57) - [Interior and exterior](#entry-interior-exterior) (p. 64) - [Memory and forgetting](#entry-memory-forgetting) (p. 76) - [Movement and section](#entry-movement-section) (p. 79) - [Philosophical comparisons and their limits](#entry-philosophical-comparisons) (p. 85) - [Prometheus Paradise and the cost of knowledge](#entry-prometheus-paradise) (p. 91) - [Revelation and teaching](#entry-revelation-teaching) (p. 98) - [Solid humanity and superior races](#entry-solid-superior-races) (p. 105) - [Space and Spaceland](#entry-space-spaceland) (p. 106) - [Sphere](#entry-sphere) (p. 107) - [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113) - [Thoughtland and the changing use of an imagined place](#entry-thoughtland) (p. 115) - [Touch and bodily proof](#entry-touch-belly) (p. 118) - [Upward and Northward](#entry-direction-upward) (p. 122) Expressions: [Poor Flatland Prometheus](#phrase-flatland-prometheus) (p. 187) · [One Dimension behind the thing](#phrase-dimension-behind) (p. 197) · [The Progenitor of so illustrious an offspring](#phrase-progenitor-offspring) (p. 198) · [I cast myself in faith upon conjecture](#phrase-faith-upon-conjecture) (p. 198). ## Section 20 {#passage-20} - [Dimension](#entry-dimension) (p. 39) - [Dream and vision](#entry-dream-vision) (p. 43) - [Fourth Dimension](#entry-fourth-dimension) (p. 57) - [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) - [Pointland](#entry-pointland) (p. 87) - [Sphere](#entry-sphere) (p. 107) - [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120) - [Upward and Northward](#entry-direction-upward) (p. 122) - [Voice and selfhood](#entry-voice-selfhood) (p. 125) - [Wives and household](#entry-wives-household) (p. 126) Expressions: [To aspire is better than to be blindly and impotently happy](#phrase-aspire-better) (p. 199) · [Its own Thought coming to Itself](#phrase-thought-coming-itself) (p. 199) · [Patent even to the Female Sex](#phrase-patent-female-sex) (p. 199). ## Section 21 {#passage-21} - [Diagrams and the position of the reader](#entry-diagrams) (p. 38) - [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) - [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) - [Grandson](#entry-grandson) (p. 58) - [Memory and forgetting](#entry-memory-forgetting) (p. 76) - [Philosophical comparisons and their limits](#entry-philosophical-comparisons) (p. 85) - [Revelation and teaching](#entry-revelation-teaching) (p. 98) - [Scripture gospel and prophetic speech](#entry-scriptural-language) (p. 102) - [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120) - [Upward and Northward](#entry-direction-upward) (p. 122) - [Wives and household](#entry-wives-household) (p. 126) ## Section 22 {#passage-22} - [A Square and the voice of the memoir](#entry-a-square) (p. 11) - [Analogy](#entry-analogy) (p. 12) - [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15) - [Cube](#entry-cube) (p. 33) - [Diagrams and the position of the reader](#entry-diagrams) (p. 38) - [Dimension](#entry-dimension) (p. 39) - [Dream and vision](#entry-dream-vision) (p. 43) - [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) - [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) - [Imagination and modesty](#entry-imagination-modesty) (p. 61) - [Initiation and mysteries](#entry-initiation-mysteries) (p. 62) - [Memory and forgetting](#entry-memory-forgetting) (p. 76) - [Millennial visit](#entry-millennial-visit) (p. 78) - [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) - [Philosophical comparisons and their limits](#entry-philosophical-comparisons) (p. 85) - [Prison and silence](#entry-prison-silence) (p. 90) - [Prometheus Paradise and the cost of knowledge](#entry-prometheus-paradise) (p. 91) - [Providence and the language of necessity](#entry-providence) (p. 93) - [Revelation and teaching](#entry-revelation-teaching) (p. 98) - [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99) - [Scripture gospel and prophetic speech](#entry-scriptural-language) (p. 102) - [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103) - [Thoughtland and the changing use of an imagined place](#entry-thoughtland) (p. 115) - [Time and the millennium](#entry-time-millennium) (p. 116) - [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120) - [Upward and Northward](#entry-direction-upward) (p. 122) Expressions: [Poor Flatland Prometheus](#phrase-flatland-prometheus) (p. 187) · [The soul devouring Sphinx](#phrase-sphinx) (p. 188) · [The Truth might be trusted](#phrase-truth-might-be-trusted) (p. 200). # Thematic index {#thematic-index} These groups gather related questions without claiming that every character supplies the same answer. An article can appear in more than one group because a word or episode can do several kinds of work. ## Words voices and the making of a narrator - [A Square and the voice of the memoir](#entry-a-square) (p. 11) - [The Editor and the revised Preface](#entry-editor-preface) (p. 45) - [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120) - [Romance satire and the refusal of a complete code](#entry-romance-satire) (p. 99) - [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103) - [Language and gender](#entry-language-gender) (p. 71) - [Voice and hearing](#entry-voice-hearing) (p. 123) - [Voice and selfhood](#entry-voice-selfhood) (p. 125) ## Geometry bodies and movement - [Angle](#entry-angle) (p. 14) - [Straight line](#entry-line-straight) (p. 109) - [Equilateral](#entry-equilateral) (p. 47) - [Polygon](#entry-polygon) (p. 88) - [Circles and Priests](#entry-circle-priest) (p. 24) - [Dodecagon](#entry-dodecagon) (p. 40) - [Dimension](#entry-dimension) (p. 39) - [Cube](#entry-cube) (p. 33) - [Movement and section](#entry-movement-section) (p. 79) - [Arithmetic and geometrical progression](#entry-arithmetic-geometric-series) (p. 15) - [Upward and Northward](#entry-direction-upward) (p. 122) - [Thickness brightness and an unrecognised dimension](#entry-thickness-brightness) (p. 113) ## Perception representation and evidence - [Eye and the visible line](#entry-eye-retina) (p. 50) - [Feeling and touch](#entry-feeling-touch) (p. 53) - [Fog](#entry-fog) (p. 55) - [Recognition by sight](#entry-recognition-sight) (p. 94) - [Diagrams and the position of the reader](#entry-diagrams) (p. 38) - [Interior and exterior](#entry-interior-exterior) (p. 64) - [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) - [Analogy](#entry-analogy) (p. 12) - [Touch and bodily proof](#entry-touch-belly) (p. 118) - [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) - [Voice and hearing](#entry-voice-hearing) (p. 123) ## Rank inheritance and the social body - [Class and caste](#entry-class-caste) (p. 27) - [Artisan and soldier](#entry-artisan-soldier) (p. 16) - [Isosceles](#entry-isosceles) (p. 67) - [Birth and ascent](#entry-birth-ascent) (p. 19) - [Compensation](#entry-compensation) (p. 29) - [Marriage and selection](#entry-marriage-selection) (p. 75) - [Fertility and extinction](#entry-fertility-extinction) (p. 54) - [Regularity](#entry-regularity) (p. 97) - [Irregularity](#entry-irregularity) (p. 65) - [Solid humanity and superior races](#entry-solid-superior-races) (p. 105) ## Gender households and unequal education - [Women](#entry-women) (p. 128) - [Wives and household](#entry-wives-household) (p. 126) - [Language and gender](#entry-language-gender) (p. 71) - [Doors and houses](#entry-doors-houses) (p. 42) - [Straight line](#entry-line-straight) (p. 109) - [Education and schools](#entry-education-schools) (p. 46) - [Grandson](#entry-grandson) (p. 58) - [Conformity and obedience](#entry-conformity-obedience) (p. 32) ## Government institutions and organised violence - [Law and sanction](#entry-law-sanction) (p. 72) - [Chief Circle](#entry-chief-circle) (p. 20) - [Circles and Priests](#entry-circle-priest) (p. 24) - [Science and institutions](#entry-science-institution) (p. 101) - [Education and schools](#entry-education-schools) (p. 46) - [Surgery and extermination](#entry-surgery-extermination) (p. 112) - [Suppression and massacre](#entry-suppression-massacre) (p. 110) - [Prison and silence](#entry-prison-silence) (p. 90) - [Millennial visit](#entry-millennial-visit) (p. 78) ## Art colour equality and revolution - [Painting](#entry-painting) (p. 84) - [Colour](#entry-colour) (p. 28) - [Chromatistes](#entry-chromatistes) (p. 23) - [Universal Colour Bill](#entry-universal-colour-bill) (p. 119) - [Chromatic Sedition](#entry-chromatic-sedition) (p. 21) - [Reform and equality](#entry-reform-equality) (p. 95) - [History and revolution](#entry-history-revolution) (p. 60) - [Isosceles rebels](#entry-isosceles-rebel) (p. 68) - [Cunning and policy](#entry-cunning-policy) (p. 35) ## Nature doctrine and political necessity - [Nature and law](#entry-nature-law) (p. 81) - [Configuration](#entry-configuration) (p. 31) - [Circular doctrine](#entry-circular-doctrine) (p. 25) - [Compensation](#entry-compensation) (p. 29) - [Providence and the language of necessity](#entry-providence) (p. 93) - [Attraction and climate](#entry-attraction-climate) (p. 18) - [Fertility and extinction](#entry-fertility-extinction) (p. 54) - [Conformity and obedience](#entry-conformity-obedience) (p. 32) ## The worlds and their boundaries - [Lineland](#entry-lineland) (p. 74) - [King of Lineland](#entry-king-lineland) (p. 69) - [Space and Spaceland](#entry-space-spaceland) (p. 106) - [Pointland](#entry-pointland) (p. 87) - [Sphere](#entry-sphere) (p. 107) - [Fourth Dimension](#entry-fourth-dimension) (p. 57) - [Interior and exterior](#entry-interior-exterior) (p. 64) - [Movement and section](#entry-movement-section) (p. 79) - [Solid humanity and superior races](#entry-solid-superior-races) (p. 105) ## Teaching conversion and resistance - [Revelation and teaching](#entry-revelation-teaching) (p. 98) - [Evidence and demonstration](#entry-evidence-demonstration) (p. 49) - [Grandson](#entry-grandson) (p. 58) - [Sphere](#entry-sphere) (p. 107) - [King of Lineland](#entry-king-lineland) (p. 69) - [Millennial visit](#entry-millennial-visit) (p. 78) - [Touch and bodily proof](#entry-touch-belly) (p. 118) - [Scripture gospel and prophetic speech](#entry-scriptural-language) (p. 102) - [Initiation and mysteries](#entry-initiation-mysteries) (p. 62) ## Imagination faith and philosophical inquiry - [Imagination and modesty](#entry-imagination-modesty) (p. 61) - [Faith reason and the reach of experience](#entry-faith-reason) (p. 51) - [Analogy](#entry-analogy) (p. 12) - [Philosophical comparisons and their limits](#entry-philosophical-comparisons) (p. 85) - [Dedication and the reader being addressed](#entry-dedication) (p. 36) - [Fourth Dimension](#entry-fourth-dimension) (p. 57) - [Providence and the language of necessity](#entry-providence) (p. 93) - [Omnividence and the limits of godlike sight](#entry-omniscience) (p. 82) - [Dream and vision](#entry-dream-vision) (p. 43) ## Writing memory time and the ending - [Memory and forgetting](#entry-memory-forgetting) (p. 76) - [Prison and silence](#entry-prison-silence) (p. 90) - [Time and the millennium](#entry-time-millennium) (p. 116) - [Diagrams and the position of the reader](#entry-diagrams) (p. 38) - [Unreliability testimony and the burden of telling](#entry-unreliability-testimony) (p. 120) - [A Square and the voice of the memoir](#entry-a-square) (p. 11) - [Dream and vision](#entry-dream-vision) (p. 43) - [The Editor and the revised Preface](#entry-editor-preface) (p. 45) - [Shakespeare epigraphs and the changing world](#entry-shakespeare-epigraphs) (p. 103) - [Prometheus Paradise and the cost of knowledge](#entry-prometheus-paradise) (p. 91) - [Thoughtland and the changing use of an imagined place](#entry-thoughtland) (p. 115) # Source guide and edition notes {#source-guide} ## The controlling edition Edwin A. Abbott, Flatland A Romance of Many Dimensions, annotated edition, Diotimos Editions, Literary Fiction Collection, 2026. The supplied Markdown, EPUB and PDF identify the same editorial project. The PDF has 211 physical pages. The Markdown provides the continuous note identifiers used in this companion's occasional references to notes; the EPUB and PDF preserve the illustrated reading edition. The EPUB, initially supplied with a generic binary media label, is a valid EPUB archive. The source's metadata and Note on the Text identify its copy-text as the revised second edition of 1884. They describe a modern transcription checked against that printing and the restoration of readings altered in later transmission. These are the edition's stated procedures. This lexicon has checked its quotations and references against the supplied edition; it has not undertaken a new bibliographical collation or silently substituted an online text. The primary literary work comprises the Title Page, Dedication, Preface to the Second and Revised Edition, the two part epigraphs and all twenty-two sections. Its four explicitly labelled authorial notes also belong to the primary layer. The source's Introduction, Key Words, How to Read It, Note on the Text, Afterword, Chapter Outline, Critical Reception, Things You May Not Know, Further Reading, Textual Notes, Notes on Sources, Sources and the remaining notes are modern apparatus. They explain the primary work but do not supply additional occurrences of Abbott's vocabulary. ## Textual points that affect reading - **The revised Preface:** Its fictional Editor reports a prisoner after seven years of imprisonment and answers two kinds of criticism. The main narrative is not silently rewritten to match every reported change of opinion - **Thickness:** The Preface and the added discussions in §§16 and 19 admit equally infinitesimal unrecognised height. This is distinct from women's very small but measurable breadth within the plane - **The retained Isosceles reading:** In §3 the edition retains the 1884 wording “emergence of an Isosceles” where the preceding argument concerns a rare Equilateral birth. Its textual note explains the apparent slip. The lexicon quotes the supplied form and does not build a different biological rule upon it - **The retained Millennium reading:** In §15 the edition retains “The second Millennium had begun” despite the surrounding chronology pointing to the transition after the 1999th year. The phrase is evidence of a local numerical problem, not a reason to invent a second visit chronology - **An emendation in §6:** The edition reports correcting the original misprint It to If. This companion follows that stated emendation - **Dodecagon:** The revised plane figure has twelve sides. The source records the correction of Dodecahedron, a solid figure, in the earlier printing; the two words are not interchangeable - **Before they are aware:** The supplied §13 wording about Lineland courtship is retained. It should not be replaced from a later printing by before they are awake - **Chromatistes:** The painter-inventor in §8 is described as a Pentagon. The leader in §§9–10 is described as an Irregular Circle. The recurrence of the name does not license identifying them as one continuously described person across the intervening centuries - **Spelling and capitals:** Mixed recognise and recognize, older shew and shewed, æsthetic, conspicuous social capitals and other stated 1884 forms remain meaningful source features. Article headings may use normal editorial case; exact quotations and cited forms preserve the wording they identify ## References and attribution A reference to §1–§22 identifies a numbered section of Abbott's work. Dedication, Preface, Title Page and Part epigraphs identify the unnumbered primary frame. Original page numbers mentioned inside the Preface refer to the 1884 printing, not to this lexicon. Links and page locators within the companion lead to its own articles or definitions. Short source snippets are chosen as evidence, not as substitutes for reading the full scene. The places is selective: an article may draw on a larger passage than the few words quoted there. The passage index consequently follows the actual scope of discussion and is not merely a count of quotation marks. Historical and comparative identifications taken from the supplied apparatus are described as such. In particular, an editorial parallel with Plato, Aristotle, Scripture, Shakespeare, Victorian education or political reform does not automatically establish a single intended allegory or a documented direct influence. Explicit names such as Prometheus and Sphinx have a different evidential status from a comparison that a later reader brings to the work. ## Reading the formats The PDF is the fixed-page reading copy; Word is editable; EPUB is reflowable; Markdown is the durable text source. They contain the same substantive articles, register, glosses and indexes. Reflow and the normal handling of notes can change where a paragraph appears. Internal navigation is therefore provided by links as well as by fixed-page locators where applicable. The source files are preserved unchanged. This companion is an interpretive reference work, not a corrected replacement for the supplied edition. Its scope is the source's entire primary work and the literary questions that the supplied apparatus makes relevant; its claims remain proportionate to that evidence.