English
WhenIsawmypoorbrotherledawaytoimprisonment,IattemptedtoleapdownintotheCouncilChamber,desiringtointercedeonhisbehalf,oratleastbidhimfarewell.
ButIfoundthatIhadnomotionofmyown.
IabsolutelydependedonthevolitionofmyGuide,whosaidingloomytones,"Heednotthybrother;haplythoushalthaveampletimehereaftertocondolewithhim.Followme."
Oncemoreweascendedintospace."Hitherto,"saidtheSphere,"IhaveshewnyounaughtsavePlaneFiguresandtheirinteriors.
NowImustintroduceyoutoSolids,andrevealtoyoutheplanuponwhichtheyareconstructed.
Behlodthismultitudeofmoveablesquarecards.
See,Iputononanother,not,asyousupposed,Northwardoftheother,butontheother.Nowasecond,nowathird.
See,IambuildingupaSolidbyamultitudeofSquaresparalleltooneanother.
NowtheSolidiscomplete,beingashighasitislongandbroad,andwecallitaCube."
"Pardonme,myLord,"repliedI;"buttomyeyetheappearanceisasofanIrregularFigurewhoseinsideislaidopentoview;inotherwords,methinksIseenoSolid,butaPlanesuchasweinferinFlatland;onlyofanIrregularitywhichbetokenssomemonstrouscriminal,sothattheverysightofitispainfultomyeyes."
"True,"saidtheSphere;"itappearstoyouaPlane,becauseyouarenotaccustomedtolightandshadeandperspective;justasinFlatlandaHexagonwouldappearaStraightLinetoonewhohasnottheArtofSightRecognition.
ButinrealityitisaSolid,asyoushalllearnbythesenseofFeeling."
HethenintroducedmetotheCube,andIfoundthatthismarvellousBeingwasindeednoPlane,butaSolid;andthathewasendowedwithsixplanesidesandeightterminalpointscalledsolidangles;andIrememberedthesayingoftheSpherethatjustsuchaCreatureasthiswouldbeformedbytheSquaremoving,inSpace,paralleltohimself:andIrejoicedtothinkthatsoinsignificantaCreatureasIcouldinsomesensebecalledtheProgenitorofsoillustriousanoffspring.
ButstillIcouldnotfullyunderstandthemeaningofwhatmyTeacherhadtoldmeconcerning"light"and"shade"and"perspective";andIdidnothesitatetoputmydifficultiesbeforehim.
WereItogivetheSphere'sexplanationofthesematters,succinctandclearthoughitwas,itwouldbetedioustoaninhabitantofSpace,whoknowsthesethingsalready.
Sufficeit,thatbyhislucidstatements,andbychangingthepositionofobjectsandlights,andbyallowingmetofeeltheseveralobjectsandevenhisownsacredPerson,heatlastmadeallthingscleartome,sothatIcouldnowreadilydistinguishbetweenaCircleandaSphere,aPlaneFigureandaSolid.
ThiswastheClimax,theParadise,ofmystrangeeventfulHistory.
HenceforthIhavetorelatethestoryofmymiserableFall:—mostmiserable,yetsurelymostundeserved!
Forwhyshouldthethirstforknowledgebearoused,onlytobedisappointedandpunished?
Myvolitionshrinksfromthepainfultaskofrecallingmyhumiliation;yet,likeasecondPrometheus,Iwillendurethisandworse,ifbyanymeansImayarouseintheinteriorsofPlaneandSolidHumanityaspiritofrebellionagainsttheConceitwhichwouldlimitourDimensionstoTwoorThreeoranynumbershortofInfinity.
Awaythenwithallpersonalconsiderations!
Letmecontinuetotheend,asIbegan,withoutfurtherdigressionsoranticipations,pursuingtheplainpathofdispassionateHistory.
Theexactfacts,theexactwords,—andtheyareburntinuponmybrain,—shallbesetdownwithoutalterationofaniota;andletmyReadersjudgebetweenmeandDestiny.
TheSpherewouldwillinglyhavecontinuedhislessonsbyindoctrinatingmeintheconformationofallregularSolids,Cylinders,Cones,Pyramids,Pentahedrons,Hexahedrons,Dodecahedrons,andSpheres:butIventuredtointerrupthim.NotthatIwasweariedofknowledge.
Onthecontrary,Ithirstedforyetdeeperandfullerdraughtsthanhewasofferingtome.
"Pardonme,"saidI,"OThouWhomImustnolongeraddressasthePerfectionofallBeauty;butletmebegtheetovouchsafethyservantaslightofthineinterior."
Sphere.Mywhat?
I.Thineinterior:thystomach,thyintestines.
Sphere.Whencethisill-timedimpertinentrequest?AndwhatmeanyoubysayingthatIamnolongerthePerfectionofallBeauty?
I.MyLord,yourownwisdomhastaughtmetoaspiretoOneevenmoregreat,morebeautiful,andmorecloselyapproximatetoPerfectionthanyourself.
Asyouyourself,superiortoallFlatlandforms,combinemanyCirclesinOne,sodoubtlessthereisOneaboveyouwhocombinesmanySpheresinOneSupremeExistence,surpassingeventheSolidsofSpaceland.
Andevenaswe,whoarenowinSpace,lookdownonFlatlandandseetheinsidesofallthings,soofacertaintythereisyetaboveussomehigher,purerregion,whitherthoudostsurelypurposetoleadme—OThouWhomIshallalwayscall,everywhereandinallDimensions,myPriest,Philosopher,andFriend—someyetmorespaciousSpace,somemoredimensionableDimensionality,fromthevantage-groundofwhichweshalllookdowntogetherupontherevealedinsidesofSolidthings,andwherethineownintestines,andthoseofthykindredSpheres,willlieexposedtotheviewofthepoorwanderingexilefromFlatland,towhomsomuchhasalreadybeenvouchsafed.
Sphere.Pooh!Stuff!Enoughofthistrifling!
Thetimeisshort,andmuchremainstobedonebeforeyouarefittoproclaimtheGospelofThreeDimensionstoyourblindbenightedcountrymeninFlatland.
I.Nay,graciousTeacher,denymenotwhatIknowitisinthypowertoreform.
Grantmebutoneglimpseofthineinterior,andIamsatisfiedforever,remaininghenceforththydocilepupil,thyunemacipableslave,readytoreceiveallthyteachingsandtofeeduponthewordsthatfallfromthylips.
Sphere.Well,then,tocontentandsilenceyou,letmesayatonce,IwouldshewyouwhatyouwishifIcould;butIcannot.Wouldyouhavemeturnmystomachinsideouttoobligeyou?
I.ButmyLordhasshewnmetheintestinesofallmycountrymenintheLandofTwoDimensionsbytakingmewithhimintotheLandofThree.
WhatthereforemoreeasythannowtotakehisservantonasecondjourneyintotheblessedregionoftheFourthDimension,whereIshalllookdownwithhimoncemoreuponthislandofThreeDimensions,andseetheinsideofeverythree-dimensionedhouse,thesecretsofthesolidearth,thetreasuresoftheminesofSpaceland,andtheintestinesofeverysolidlivingcreature,eventhenobleandadorableSpheres.
Sphere.ButwhereisthislandofFourDimensions?
I.Iknownot:butdoubtlessmyTeacherknows.
Sphere.NotI.Thereisnosuchland.Theveryideaofitisutterlyinconceivable.
I.Notinconceivable,myLord,tome,andthereforestilllessinconceivabletomyMaster.
Nay,Idespairnotthat,evenhere,inthisregionofThreeDimensions,yourLordship'sartmaymaketheFourthDimensionvisibletome;justasintheLandofTwoDimensionsmyTeacher'sskillwouldfainhaveopenedtheeyesofhisblindservanttotheinvisiblepresenceofaThirdDimension,thoughIsawitnot.
Letmerecallthepast.WasInottaughtbelowthatwhenIsawaLineandinferredaPlane,IinrealitysawaThirdunrecognizedDimension,notthesameasbrightness,called"height"?
Anddoesitnotnowfollowthat,inthisregion,whenIseeaPlaneandinferaSolid,IreallyseeaFourthunrecognizedDimension,notthesameascolour,butexistent,thoughinfinitesimalandincapableofmeasurement?
Andbesidesthis,thereistheArgumentfromAnalogyofFigures.
Sphere.Analogy!Nonsense:whatanalogy?
I.YourLordshiptemptshisservanttoseewhetherherememberstherevelationsimpartedtohim.
Triflenotwithme,myLord;Icrave,Ithirst,formoreknowledge.
DoubtlesswecannotseethatotherhigherSpacelandnow,becauswewehavenoeyeinourstomachs.
But,justastherewastherealmofFlatland,thoughthatpoorpunyLinelandMonarchcouldneitherturntoleftnorrighttodiscernit,andjustastherewascloseathand,andtouchingmyframe,thelandofThreeDimensions,thoughI,blindsenselesswretch,hadnopowertotouchit,noeyeinmyinteriortodiscernit,soofasuretythereisaFourthDimension,whichmyLordperceivesawiththeinnereyeofthought.
AndthatitmustexistmyLordhimselfhastaughtme.
Orcanhehaveforgottenwhathehimselfimpartedtohisservant?
InOneDimension,didnotamovingPointproduceaLinewithtwoterinalpoints?
InTwoDimensions,didnotamovingLineproduceaSquarewithfourterminalpoints?
InThreeDimensions,didnotamovingSquareproduce—didnotthiseyeofminebeholdit—thatblessedBeing,aCube,witheightterminalpoints?
AndinFourDimensionsshallnotamovingCube—alas,forAnalogy,andalasfortheProgressofTruth,ifitbenotso—shallnot,Isay,themotionofadivineCuberesultinastillmoredivineOrganizationwithsixteenterminalpoints?
BeholdtheinfallibleconfirmationoftheSeries,2,4,8,16:isnotthisaGeometricalProgression?Isnotthis—ifImightquotemyLord'sownwords—"strictlyaccordingtoAnalogy"?
Again,wasInottaughtbymyLordthatasinaLinetherearetwoboundingPoints,andinaSquaretherearefourboundingLInes,soinaCubetheremustbesixboundingSquares?
BeholdoncemoretheconfirmingSeries,2,4,6:isnotthisanArithemticalProgression?
AndconsequentlydoesitnotofnecessityfollowthatthemoredivineoffspringofthedivineCubeintheLandofFourDimensions,musthave8boundingCubes:andisnotthisalso,asmyLordhastaughtmetobelieve,"strictlyaccordingtoAnalogy"?
O,myLord,myLord,behold,Icastmyselfinfaithuponconjecture,notknowingthefacts;andIappealtoyourLordshiptoconfirmordenymylogicalanticipations.
IfIamwrong,Iyield,andwillnolongerdemandaFourthDimension;but,ifIamright,myLordwilllistentoreason.
Iasktherefore,isit,orisitnot,thefact,thaterenowyourcountrymenalsohavewitnessedthedescentofBeingsofahigherorderthantheirown,enteringclosedrooms,evenasyourLordshipenteredmine,withouttheopeningofdoorsorwindows,andappearingandvanishingatwill?
OnthereplytothisquestionIamreaedytostakeeverything.Denyit,andIamhenceforthsilent.Onlyvouchsafeananswer.
Sphere(afterapause).Itisreportedso.
Butmenaredividedinopinionastothefacts.
Andevengrantingthefacts,theyexplainthemindifferentways.
Andinanycase,howevergreatmaybethenumberofdifferentexplanations,noonehasadoptedorsuggestedthetheoryofaFourthDimension.
Therefore,prayhavedonewiththistrifling,andletusreturntobusiness.
I.Iwascertainofit.Iwascertainthatmyanticipationswouldbefulfilled.
Andnowhavepatiencewithmeandanswermeyetonemorequestion,bestofTeachers!
Thosewhohavethusappeared—nooneknowswhence—andhavereturned—nooneknowswhither—havetheyalsocontractedtheirsectionsandvanishedsomehowintothatmoreSpaciousSpace,whitherInowentreatyoutoconductme?
Sphere(moodily).Theyhavevanished,certainly—iftheyeverappeared.
Butmostpeoplesaythatthesevisionsarosefromthethought—youwillnotunderstandme—fromthebrain;fromtheperturbedangularityoftheSeer.
I.Saytheyso?Oh,believethemnot.
Orifitindeedbeso,thatthisotherSPaceisreallyThoughtland,thentakemetothatblessedRegionwhereIinThoughtshallseetheinsidesofallsolidthings.
There,beforemyravishedeye,aCubemovinginsomealtogethernewdirection,butstrictlyaccordingtoAnalogy,soastomakeeveryparticleofhisinteriorpassthroughanewkindofSpace,withawakeofitsown—shallcreateastillmoreperfectperfectionthanhimself,withsixteenterminalExtra-solidangles,andEightsolidCubesforhisPerimeter.
Andoncethere,shallwestayourupwardcourse?
InthatblessedregionofFourDimensions,shallwelingeratthethresholdoftheFifth,andnotentertherein?Ah,no!
Letusratherresolvethatourambitionshallsoarwithourcorporalascent.
Then,yieldingtoourintellectualonset,thegatesoftheSixDimensionshallflyopen;afterthataSeventh,andthenanEighth—
HowlongIshouldhavecontinuedIknownot.
InvaindidtheSphere,inhisvoiceofthunder,reiteratehiscommandofsilence,andthreatenmewiththedirestpenaltiesifIpersisted.
Nothingcouldstemthefloodofmyecstaticaspirations.
PerhapsIwastoblame;butindeedIwasintoxicatedwiththerecentdraughtsofTruthtowhichhehimselfhadintroducedme.
However,theendwasnotlongincoming.
Mywordswerecutshortbyacrashoutside,andasimultaneouscrashinsideme,whichimpelledmethroughspacewithavelocitythatprecludedspeech.Down!down!down!
Iwasrapidlydescending;andIknewthatreturntoFlatlandwasmydoom.
Oneglimpse,onelastandnever-to-be-forgottenglimpseIhadofthatdulllevelwilderness—whichwasnowtobecomemyUniverseagain—spreadoutbeforemyeye.Thenadarkness.
Thenafinal,all-consummatingthunder-peal;and,whenIcametomyself,IwasoncemoreacommoncreepingSquare,inmyStudyathome,listeningtothePeace-CryofmyapproachingWife.
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