Flatland

100 Pages·2016·0.95 MB·English

by  Edwin A. Abbot

Edwin A. Abbot
Flatland
A Romance of Many Dimensions
Secretary of Foreign Relations
OriginallywrittenbyEdwinA.Abbot,published1884bySeely&Co.
this edition published 2020 by secretary of foreign relations
thelocalyarn.com/excursus/secretary
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Firstprinting,July2020
Contents
PrefacetotheSecondandRevisedEdition 7
I ThisWorld 11
OftheNatureofFlatland. 13
OftheClimateandHousesinFlatland. 15
ConcerningtheInhabitantsofFlatland. 17
ConcerningtheWomen. 21
OfourMethodsofRecognizingoneanother. 25
OfRecognitionbySight. 29
ConcerningIrregularFigures. 33
OftheAncientPracticeofPainting. 37
OftheUniversalColourBill. 41
OftheSuppressionoftheChromaticSedition. 45
ConcerningOurPriests. 49
OftheDoctrineofourPriests. 53
II OtherWorlds 57
HowIhadaVisionofLineland. 59
HowIvainlytriedtoexplainthenatureofFlatland. 63
ConcerningaStrangerfromSpaceland. 67
4
HowtheStrangervainlyendeavouredtorevealtomeinwordsthemyster-
iesofSpaceland. 71
HowtheSphere,havinginvaintriedwords,resortedtodeeds. 77
HowIcametoSpaceland,andwhatIsawthere. 79
How,thoughtheSphereshowedmeothermysteriesofSpaceland,Istillde-
siredmore;andwhatcameofit. 83
HowtheSphereencouragedmeinaVision. 89
HowItriedtoteachthetheoryofThreeDimensionstomyGrandson,and
withwhatsuccess. 93
HowIthentriedtodiffusetheTheoryofThreeDimensionsbyothermeans,
andoftheresult. 97
5
To the Inhabitants of Space in General
and H. C. in Particular this Work
is Dedicated by a Humble Native of Flatland
in the Hope that Even as he was Initiated
into the Mysteries of Three Dimensions,
having been previously conversant with Only
Two, so the Citizens of that Celestial Region
may aspire yet higher and higher to the Secrets
of Four Five or Even Six Dimensions
thereby contributing to the Enlargement of
The Imagination and the possible Development
of that most rare and excellent Gift of Modesty
among the Superior Races of Solid Humanity

Preface to the Second and Revised Edition
If my poorFlatlandfriendretainedthevigourofmindwhichheenjoyed
whenhebegantocomposetheseMemoirs,Ishouldnotnowneedtorepre-
senthiminthispreface,inwhichhedesires,firstly,toreturnhisthanksto
hisreadersandcriticsinSpaceland,whoseappreciationhas,withunexpected
celerity,requiredasecondeditionofhiswork;secondly,toapologizeforcer-
tainerrorsandmisprints(forwhich,however,heisnotentirelyresponsible);
and,thirdly,toexplainoneortwomisconceptions. ButheisnottheSquare
heoncewas. Yearsofimprisonment,andthestillheavierburdenofgeneral
incredulityandmockery,havecombinedwiththenaturaldecayofoldageto
erasefromhismindmanyofthethoughtsandnotions,andmuchalsoofthe
terminology,whichheacquiredduringhisshortstayinSpaceland. Hehas,
therefore,requestedmetoreplyinhisbehalftotwospecialobjections,oneof
anintellectual,theotherofamoralnature.
Thefirstobjectionis,thataFlatlander,seeingaLine,seessomethingthat
mustbethicktotheeyeaswellaslongtotheeye(otherwiseitwouldnotbe
visible,ifithadnotsomethickness);andconsequentlyheought(itisargued)
toacknowledgethathiscountrymenarenotonlylongandbroad,butalso
(thoughdoubtlessinaveryslightdegree)thickorhigh. Hisobjectionis
plausible,and,toSpacelanders,almostirresistible,sothat,Iconfess,when
Ifirstheardit,Iknewnotwhattoreply. Butmypooroldfriend’sanswer
appearstomecompletelytomeetit.
“Iadmit,”saidhe—whenImentionedtohimthisobjection—“Iadmitthe
truthofyourcritic’sfacts,butIdenyhisconclusions. Itistruethatwehave
reallyinFlatlandaThirdunrecognizedDimensioncalled‘height,’justasitis
alsotruethatyouhavereallyinSpacelandaFourthunrecognizedDimension,
calledbynonameatpresent,butwhichIwillcall‘extra-height’. Butwe
cannomoretakecognizanceofour‘height’thenyoucanofyour‘extra-
height’. EvenI—whohavebeeninSpaceland,andhavehadtheprivilegeof
understandingfortwenty-fourhoursthemeaningof‘height’—evenIcannot
nowcomprehendit,norrealizeitbythesenseofsightorbyanyprocessof
reason;Icanbutapprehenditbyfaith.
“Thereasonisobvious. Dimensionimpliesdirection,impliesmeasure-
ment,impliesthemoreandtheless. Now,allourlinesareequallyand
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infinitesimallythick(orhigh,whicheveryoulike);consequently,thereis
nothinginthemtoleadourmindstotheconceptionofthatDimension. No
‘delicatemicrometer’—ashasbeensuggestedbyonetoohastySpaceland
critic—wouldintheleastavailus;forweshouldnotknowwhattomeasure,
norinwhatdirection. WhenweseeaLine,weseesomethingthatislong
andbright;brightness,aswellaslength,isnecessarytotheexistenceofa
Line;ifthebrightnessvanishes,theLineisextinguished. Hence,allmyFlat-
landfriends—whenItalktothemabouttheunrecognizedDimensionwhich
issomehowvisibleinaLine—say,‘Ah,youmeanbrightness’: andwhenI
reply,‘No,ImeanarealDimension,’theyatonceretort‘Thenmeasureit,
ortellusinwhatdirectionitextends’;andthissilencesme,forIcandonei-
ther. Onlyyesterday,whentheChiefCircle(inotherwordsourHighPriest)
cametoinspecttheStatePrisonandpaidmehisseventhannualvisit,and
whenfortheseventhtimeheputmethequestion,‘WasIanybetter?’ Itried
toprovetohimthathewas‘high,’aswellaslongandbroad,althoughhe
didnotknowit. Butwhatwashisreply? ‘YousayIam“high”;measuremy
“highness”andIwillbelieveyou.’ WhatcouldIdo? HowcouldImeethis
challenge? Iwascrushed;andhelefttheroomtriumphant.
“Doesthisstillseemstrangetoyou? Thenputyourselfinasimilarposi-
tion. SupposeapersonoftheFourthDimension,condescendingtovisityou,
weretosay,‘Wheneveryouopenyoureyes,youseeaPlane(whichisofTwo
Dimensions)andyouinferaSolid(whichisofThree);butinrealityyoualso
see(thoughyoudonotrecognize)aFourthDimension,whichisnotcolour
norbrightnessnoranythingofthekind,butatrueDimension,althoughI
cannotpointouttoyouitsdirection,norcanyoupossiblymeasureit.’ What
wouldyousaytosuchavisitor? Wouldnotyouhavehimlockedup? Well,
thatismyfate: anditisasnaturalforusFlatlanderstolockupaSquare
forpreachingtheThirdDimension,asitisforyouSpacelanderstolockup
aCubeforpreachingtheFourth. Alas,howstrongafamilylikenessruns
throughblindandpersecutinghumanityinallDimensions! Points,Lines,
Squares,Cubes,Extra-Cubes—weareallliabletothesameerrors,allalike
theSlavesofourrespectiveDimensionalprejudices,asoneofyourSpaceland
poetshassaid1— 1TheAuthordesiresmetoadd,thatthe
misconceptionofsomeofhiscriticson
OnetouchofNaturemakesallworldsakin. thismatterhasinducedhimtoinsert
inhisdialoguewiththeSphere,certain
remarkswhichhaveabearingonthepoint
Onthis,pointthedefenceoftheSquareseemstometobeimpregnable.
inquestion,andwhichhehadpreviously
IwishIcouldsaythathisanswertothesecond(ormoral)objectionwas omittedasbeingtediousandunnecessary.
equallyclearandcogent. lthasbeenobjectedthatheisawoman-hater;
andasthisobjectionhasbeenvehementlyurgedbythosewhomNature’s
decreehasconstitutedthesomewhatlargerhalfoftheSpacelandrace,I
shouldliketoremoveit,sofarasIcanhonestlydoso. ButtheSquareis
sounaccustomedtotheuseofthemoralterminologyofSpacelandthatI
shouldbedoinghimaninjusticeifIwereliterallytotranscribehisdefence
againstthischarge. Acting,therefore,ashisinterpreterandsummarizer,I
9
gatherthatinthecourseofanimprisonmentofsevenyearshehashimself
modifiedhisownpersonalviews,bothasregardsWomenandasregardsthe
IsoscelesorLowerClasses. Personally,henowinclinestotheopinionofthe
SpherethattheStraightLinesareinmanyimportantrespectssuperiorto
theCircles. But,writingasaHistorian,hehasidentifiedhimself(perhaps
tooclosely)withtheviewsgenerallyadoptedbyFlatland,and(ashehas
beeninformed)evenSpaceland,Historians;inwhosepages(untilveryrecent
times)thedestiniesofWomenandofthemassesofmankindhaveseldom
beendeemedworthyofmentionandneverofcarefulconsideration.
InastillmoreobscurepassagehenowdesirestodisavowtheCircular
oraristocratictendencieswithwhichsomecriticshavenaturallycredited
him. WhiledoingjusticetotheintellectualpowerwithwhichafewCircles
formanygenerationsmaintainedtheirsupremacyoverimmensemultitudes
oftheircountrymen,hebelievesthatthefactsofFlatland,speakingfor
themselveswithoutcommentonhispart,declarethatRevolutionscannot
alwaysbesuppressedbyslaughter;andthatNature,insentencingtheCircles
toinfecundity,hascondemnedthemtoultimatefailure—“andherein,”he
says,“IseeafulfillmentofthegreatLawofallworlds,thatwhilethewisdom
ofManthinksitisworkingonething,thewisdomofNatureconstrainsitto
workanother,andquiteadifferentandfarbetterthing.” Fortherest,hebegs
hisreadersnottosupposethateveryminutedetailinthedailylifeofFlatland
mustneedscorrespondtosomeotherdetailinSpaceland;andyethehopes
that,takenasawhole,hisworkmayprovesuggestiveaswellasamusing,to
thoseSpacelandersofmoderateandmodestmindswho—speakingofthat
whichisofthehighestimportance,butliesbeyondexperience—declineto
sayontheonehand,“Thiscanneverbe,”andontheotherhand,“Itmust
needsbepreciselythus,andweknowallaboutit.”