flatland-第16节

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r　churches；　your　very　chests　and　safes；　yes　even　your　insides　and　stomachs；　all　lying　open　and　exposed　to　my　view。

I。　　Such　assertions　are　easily　made；　my　Lord。

STRANGER。　　But　not　easily　proved；　you　mean。　　But　I　mean　to　prove　mine。

When　I　descended　here；　I　saw　your　four　Sons；　the　Pentagons；　each　in　his　apartment；　and　your　two　Grandsons　the　Hexagons；　I　saw　your　youngest　Hexagon　remain　a　while　with　you　and　then　retire　to　his　room；　leaving　you　and　your　Wife　alone。　I　saw　your　Isosceles　servants；　three　in　number；　in　the　kitchen　at　supper；　and　the　little　Page　in　the　scullery。　　Then　I　came　here；　and　how　do　you　think　I　came？

I。　　Through　the　roof；　I　suppose。

STRANGER。　　Not　so。　　Your　roof；　as　you　know　very　well；　has　been　recently　repaired；　and　has　no　aperture　by　which　even　a　Woman　could　penetrate。　　I　tell　you　I　come　from　Space。　　Are　you　not　convinced　by　what　I　have　told　you　of　your　children　and　household？

I。　　Your　Lordship　must　be　aware　that　such　facts　touching　the　belongings　of　his　humble　servant　might　be　easily　ascertained　by　any　one　in　the　neighbourhood　possessing　your　Lordship's　ample　means　of　obtaining　information。

STRANGER。　　（TO　HIMSELF。）　　What　must　I　do？　　Stay；　one　more　argument　suggests　itself　to　me。　　When　you　see　a　Straight　Line　　your　wife；　for　example　　how　many　Dimensions　do　you　attribute　to　her？

I。　　Your　Lordship　would　treat　me　as　if　I　were　one　of　the　vulgar　who；　being　ignorant　of　Mathematics；　suppose　that　a　Woman　is　really　a　Straight　Line；　and　only　of　One　Dimension。　　No；　no；　my　Lord；　we　Squares　are　better　advised；　and　are　as　well　aware　as　your　Lordship　that　a　Woman；　though　popularly　called　a　Straight　Line；　is；　really　and　scientifically；　a　very　thin　Parallelogram；　possessing　Two　Dimensions；　like　the　rest　of　us；　viz。；　length　and　breadth　（or　thickness）。

STRANGER。　　But　the　very　fact　that　a　Line　is　visible　implies　that　it　possesses　yet　another　Dimension。

I。　　My　Lord；　I　have　just　acknowledged　that　a　Woman　is　broad　as　well　as　long。　　We　see　her　length；　we　infer　her　breadth；　which；　though　very　slight；　is　capable　of　measurement。

STRANGER。　　You　do　not　understand　me。　　I　mean　that　when　you　see　a　Woman；　you　ought　　besides　inferring　her　breadth　　to　see　her　length；　and　to　SEE　what　we　call　her　HEIGHT；　although　that　last　Dimension　is　infinitesimal　in　your　country。　If　a　Line　were　mere　length　without　〃height〃；　it　would　cease　to　occupy　Space　and　would　become　invisible。　　Surely　you　must　recognize　this？

I。　　I　must　indeed　confess　that　I　do　not　in　the　least　understand　your　Lordship。　　When　we　in　Flatland　see　a　Line；　we　see　length　and　BRIGHTNESS。　　If　the　brightness　disappears；　the　Line　is　extinguished；　and；　as　you　say；　ceases　to　occupy　Space。　But　am　I　to　suppose　that　your　Lordship　gives　to　brightness　the　title　of　a　Dimension；　and　that　what　we　call　〃bright〃　you　call　〃high〃？

STRANGER。　　No；　indeed。　　By　〃height〃　I　mean　a　Dimension　like　your　length：　　only；　with　you；　〃height〃　is　not　so　easily　perceptible；　being　extremely　small。

I。　　My　Lord；　your　assertion　is　easily　put　to　the　test。　You　say　I　have　a　Third　Dimension；　which　you　call　〃height〃。　Now；　Dimension　implies　direction　and　measurement。　　Do　but　measure　my　〃height〃；　or　merely　indicate　to　me　the　direction　in　which　my　〃height〃　extends；　and　I　will　become　your　convert。　　Otherwise；　your　Lordship's　own　understanding　must　hold　me　excused。

STRANGER。　　（TO　HIMSELF。）　　I　can　do　neither。　　How　shall　I　convince　him？　　Surely　a　plain　statement　of　facts　followed　by　ocular　demonstration　ought　to　suffice。　　　Now；　Sir；　listen　to　me。

You　are　living　on　a　Plane。　　What　you　style　Flatland　is　the　vast　level　surface　of　what　I　may　call　a　fluid；　on；　or　in；　the　top　of　which　you　and　your　countrymen　move　about；　without　rising　above　it　or　falling　below　it。

I　am　not　a　plane　Figure；　but　a　Solid。　　You　call　me　a　Circle；　but　in　reality　I　am　not　a　Circle；　but　an　infinite　number　of　Circles；　of　size　varying　from　a　Point　to　a　Circle　of　thirteen　inches　in　diameter；　one　placed　on　the　top　of　the　other。　　When　I　cut　through　your　plane　as　I　am　now　doing；　I　make　in　your　plane　a　section　which　you；　very　rightly；　call　a　Circle。　　For　even　a　Sphere　　which　is　my　proper　name　in　my　own　country　　if　he　manifest　himself　at　all　to　an　inhabitant　of　Flatland　　must　needs　manifest　himself　as　a　Circle。

Do　you　not　remember　　for　I；　who　see　all　things；　discerned　last　night　the　phantasmal　vision　of　Lineland　written　upon　your　brain　　do　you　not　remember；　I　say；　how；　when　you　entered　the　realm　of　Lineland；　you　were　compelled　to　manifest　yourself　to　the　King；　not　as　a　Square；　but　as　a　Line；　because　that　Linear　Realm　had　not　Dimensions　enough　to　represent　the　whole　of　you；　but　only　a　slice　or　section　of　you？　　In　precisely　the　same　way；　your　country　of　Two　Dimensions　is　not　spacious　enough　to　represent　me；　a　being　of　Three；　but　can　only　exhibit　a　slice　or　section　of　me；　which　is　what　you　call　a　Circle。

The　diminished　brightness　of　your　eye　indicates　incredulity。　　But　now　prepare　to　receive　proof　positive　of　the　truth　of　my　assertions。　You　cannot　indeed　see　more　than　one　of　my　sections；　or　Circles；　at　a　time；　for　you　have　no　power　to　raise　your　eye　out　of　the　plane　of　Flatland；　but　you　can　at　least　see　that；　as　I　rise　in　Space；　so　my　sections　become　smaller。　　See　now；　I　will　rise；　and　the　effect　upon　your　eye　will　be　that　my　Circle　will　become　smaller　and　smaller　till　it　dwindles　to　a　point　and　finally　vanishes。




There　was　no　〃rising〃　that　I　could　see；　but　he　diminished　and　finally　vanished。　　I　winked　once　or　twice　to　make　sure　that　I　was　not　dreaming。　　But　it　was　no　dream。　　For　from　the　depths　of　nowhere　came　forth　a　hollow　voice　　close　to　my　heart　it　seemed　　〃Am　I　quite　gone？　　Are　you　convinced　now？　　Well；　now　I　will　gradually　return　to　Flatland　and　you　shall　see　my　section　become　larger　and　larger。〃

Every　reader　in　Spaceland　will　easily　understand　that　my　mysterious　Guest　was　speaking　the　language　of　truth　and　even　of　simplicity。　　But　to　me；　proficient　though　I　was　in　Flatland　Mathematics；　it　was　by　no　means　a　simple　matter。　The　rough　diagram　given　above　will　make　it　clear　to　any　Spaceland　child　that　the　Sphere；　ascending　in　the　three　positions　indicated　there；　must　needs　have　manifested　himself　to　me；　or　to　any　Flatlander；　as　a　Circle；　at　first　of　full　size；　then　small；　and　at　last　very　small　indeed；　approaching　to　a　Point。　　But　to　me；　although　I　saw　the　facts　before　me；　the　causes　were　as　dark　as　ever。　All　that　I　could　comprehend　was；　that　the　Circle　had　made　himself　smaller　and　vanished；　and　that　he　had　now　reappeared　and　was　rapidly　making　himself　larger。

When　he　regained　his　original　size；　he　heaved　a　deep　sigh；　for　he　perceived　by　my　silence　that　I　had　altogether　failed　to　comprehend　him。　　And　indeed　I　was　now　inclining　to　the　belief　that　he　must　be　no　Circle　at　all；　but　some　extremely　clever　juggler；　or　else　that　the　old　wives'　tales　were　true；　and　that　after　all　there　were　such　people　as　Enchanters　and　Magicians。

After　a　long　pause　he　muttered　to　himself；　〃One　resource　alone　remains；　if　I　am　not　to　resort　to　action。　　I　must　try　the　method　of　Analogy。〃　Then　followed　a　still　longer　silence；　after　which　he　continued　our　dialogue。

SPHERE。　　Tell　me；　Mr。　Mathematician；　if　a　Point　moves　Northward；　and　leaves　a　luminous　wake；　what　name　would　you　give　to　the　wake？

I。　　A　straight　Line。

SPHERE。　　And　a　straight　Line　has　how　many　extremities？

I。　　Two。

SPHERE。　　Now　conceive　the　Northward　straight　Line　moving　parallel　to　itself；　East　and　West；　so　that　every　point　in　it　leaves　behind　it　the　wake　of　a　straight　Line。　　What　name　will　you　give　to　the　Figure　thereby　formed？　　We　will　suppose　that　it　moves　through　a　distance　equal　to　the　original　straight　Line。　　　What　name；　I　say？

I。　　A　Square。

SPHERE。　　And　how　many　sides　has　a　Square？　　How　many　angles？

I。　　Four　sides　and　four　angles。

SPHERE。　　Now　stretch　your　imagination　a　little；　and　conceive　a　Square　in　Flatland；　moving　parallel　to　itself　upward。

I。　　What？　　Northward？

SPHERE。　　No；　not　Northward；　upward；　out　of　Flatland　altogether。

If　it　moved　Northward；　the　Southern　points　in　the　Square　would　have　to　move　through　the　positions　previously　occupied　by　the　Northern　points。　But　that　is　not　my　meaning。

I　mean　that　every　Point　in　you　　for　you　are　a　Square　and　will　serve　the　purpose　of　my　illustration　　every　Point　in　you；　that　is　to　say　in　what　you　call　your　inside；　is　to　pass　upwards　through　Space　in　such　a　way　that　no　Point　shall　pass　through　the　position　previously　occupied　by　any　other　Point；　but　each　Point　shall　describe　a　straight　Line　of　its　own。　　This　is　all　in　accordance　with　Analogy；　surely　it　must　be　clear　to　you。

Restraining　my　impatience　　for　I　was　now　under　a　strong　temptation　to　rush　blindly　at　my　Visitor　and　to　precipitate　him　into　Space；　or　out　of　Flatland；　anywhere；　so　that　I　could　get　rid　of　him　　I　replied：　

〃And　what　may　be　the　nature　of　the　Figure　which　I　am　to　shape　out　by　this　motion　which　you　are　pleased　to　denote　by　the　word　'upward'？　I　presume　it　is　describable　in　the　language　of　Flatland。〃

SPHERE。　　Oh；　certainly。　　It　is　all　plain　and　simple；　and　in　strict　accordance　with　Analogy　　only；　by　the　way；　you　must　not　speak　of　the　result　as　being　a　Figure；　but　as　a　Solid。　But　I　will　describe　it　to　you。　　Or　rather　not　I；　bu