Thepatteringoftherainhadlongagoannouncednightfall;andIwassitting[footnote1]inthecompanyofmywife,musingontheeventsofthepastandtheprospectsofthecomingyear,thecomingcentury,thecommingMillennium.
MyfourSonsandtwoorphanGrandchildrenhadretiredtotheirseveralapartments;andmywifealoneremainedwithmetoseetheoldMillenniumoutandthenewonein.
Iwasraptinthought,ponderinginmymindsomewordsthathadcasuallyissuedfromthemouthofmyyoungestGrandson,amostpromisingyoungHexagonofunusualbrilliancyandperfectangularity.
HisunclesandIhadbeengivinghimhisusualpracticallessoninSightRecognition,turningourselvesuponourcentres,nowrapidly,nowmoreslowly,andquestioninghimastoourpositions;andhisanswershadbeensosatisfactorythatIhadbeeninducedtorewardhimbygivinghimafewhintsonArithmetic,asappliedtoGeometry.
TakingnineSquares,eachanincheveryway,IhadputthemtogethersoastomakeonelargeSquare,withasideofthreeinches,andIhadhenceprovedtomylittleGrandsonthat—thoughitwasimpossibleforustoseetheinsideoftheSquare—yetwemightascertainthenumberofsquareinchesinaSquarebysimplysquaringthenumberofinchesintheside:"andthus,"saidI,"weknowthatthree-to-the-second,ornine,representsthenumberofsquareinchesinaSquarewhosesideisthreeincheslong."
ThelittleHexagonmeditatedonthisawhileandthensaidtome;"Butyouhavebeenteachingmetoraisenumberstothethirdpower:Isupposethree-to-the-thirdmustmeansomethinginGeometry;whatdoesitmean?"
AndthenIbegantoshewtheboyhowaPointbymovingthroughalengthofthreeinchesmakesaLineofthreeinches,whichmayberepresentedbythree;andhowaLineofthreeinches,movingparalleltoitselfthroughalengthofthreeinches,makesaSquareofthreeincheseveryway,whichmayberepresentedbythree-to-the-second.
Uponthis,myGrandson,againreturningtohisformersuggestion,tookmeuprathersuddenlyandexclaimed,"Well,then,ifaPointbymovingthreeinches,makesaLineofthreeinchesrepresentedbythree;andifastraightLineofthreeinches,movingparalleltoitself,makesaSquareofthreeincheseveryway,representedbythree-to-the-second;itmustbethataSquareofthreeincheseveryway,movingsomehowparalleltoitself(butIdon'tseehow)mustmakeSomethingelse(butIdon'tseewhat)ofthreeincheseveryway—andthismustberepresentedbythree-to-the-third."
"Gotobed,"saidI,alittleruffledbythisinterruption:"ifyouwouldtalklessnonsense,youwouldremembermoresense."
SomyGrandsonhaddisappearedindisgrace;andthereIsatbymyWife'sside,endeavouringtoformaretrospectoftheyear1999andofthepossibilitiesoftheyear2000;butnotquiteabletoshakeofthethoughtssuggestedbytheprattleofmybrightlittleHexagon.
RousingmyselffrommyreverieIturnedtheglassNorthwardforthelasttimeintheoldMillennium;andintheact,Iexclaimedaloud,"Theboyisafool."
"Heisnosuchthing,"criedmyWife,"andyouarebreakingtheCommandmentsinthusdishonouringyourownGrandson."ButItooknonoticeofher.
LookingaroundineverydirectionIcouldseenothing;yetstillIfeltaPresence,andshiveredasthecoldwhispercameagain.Istartedup."Whatisthematter?"
Therewasnothing;andIresumedmyseat,againexclaiming,"Theboyisafool,Isay;three-to-the-thirdcanhavenomeaninginGeometry."
Atoncetherecameadistinctlyaudiblereply,"Theboyisnotafool;andthree-to-the-thirdhasanobviousGeometricalmeaning."
MyWifeaswellasmyselfheardthewords,althoughshedidnotunderstandtheirmeaning,andbothofussprangforwardinthedirectionofthesound.
AtthefirstglanceitappearedtobeaWoman,seensideways;butamoment'sobservationshewedmethattheextremitiespassedintodimnesstoorapidlytorepresentoneoftheFemaleSex;andIshouldhavethoughtitaCircle,onlythatitseemedtochangeitssizeinamannerimpossibleforaCircleorforanyregularFigureofwhichIhadhadexperience.
WiththeusualhastinessandunreasoningjealousyofherSex,sheflewatoncetotheconclusionthataWomanhadenteredthehousethroughsomesmallapeture."Howcomesthispersonhere?"
IseebymypowerofSightRecoginition—""Oh,IhavenopatiencewithyourSightRecognition,"repliedshe,"'Feelingisbelieving'and'AStraightLinetothetouchisworthaCircletothesight'"—twoProverbs,verycommonwiththeFrailerSexinFlatland.
Assuminghermostgraciousmanner,myWifeadvancedtowardstheStranger,"Permitme,Madamtofeelandbefeltby—"then,suddenlyrecoiling,"Oh!
"Iamindeed,inacertainsenseaCircle,"repliedtheVoice,"andamoreperfectCirclethananyinFlatland;buttospeakmoreaccurately,IammanyCirclesinone."
Thenheaddedmoremildly,"Ihaveamessage,dearMadam,toyourhusband,whichImustnotdeliverinyourpresence;and,ifyouwouldsufferustoretireforafewminutes—"ButmywifewouldnotlistentothepropsalthatouraugustVisitorshouldsoincommodehimself,andassuringtheCirclethatthehourofherownretirementhadlongpassed,withmanyreiteratedapologiesforherrecentindiscretion,sheatlastretreatedtoherapartment.
Footnote1.WhenIsay"sitting,"ofcourseIdonotmeananychangeofattitudesuchasyouinSpacelandsignifybythatword;foraswehavenofeet,wecannomore"sit"nor"stand"(inyoursenseoftheword)thanoneofyoursolesorflounders.
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