flatland-第15部分

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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；　but　Analogy。

We　began　with　a　single　Point；　which　of　course　　being　itself　a　Point　　has　only　ONE　terminal　Point。

One　Point　produces　a　Line　with　TWO　terminal　Points。

One　Line　produces　a　Square　with　FOUR　terminal　Points。

Now　you　can　give　yourself　the　answer　to　your　own　question：　　1；　2；　4；　are　evidently　in　Geometrical　Progression。　　What　is　the　next　number？

I。　　Eight。

SPHERE。　　Exactly。　　The　one　Square　produces　a　SOMETHING…WHICH…　YOU…DO…NOT…AS…YET…KNOW…A…NAME…FOR…BUT…WHICH…WE…CALL…A…CUBE　with　EIGHT　terminal　Points。　　Now　are　you　convinced？

I。　　And　has　this　Creature　sides；　as　well　as　angles　or　what　you　call　〃terminal　Points〃？

SPHERE。　　Of　course；　and　all　according　to　Analogy。　　But；　by　the　way；　not　what　YOU　call　sides；　but　what　WE　call　sides。　You　would　call　them　SOLIDS。

I。　　And　how　many　solids　or　sides　will　appertain　to　this　Being　whom　I　am　to　generate　by　the　motion　of　my　inside　in　an　〃upward〃　direction；　and　whom　you　call　a　Cube？

SPHERE。　　How　can　you　ask？　　And　you　a　mathematician！　The　side　of　anything　is　always；　if　I　may　so　say；　one　Dimension　behind　the　thing。　　Consequently；　as　there　is　no　Dimension　behind　a　Point；　a　Point　has　0　sides；　a　Line；　if　I　may　say；　has　2　sides　（for　the　Points　of　a　Line　may　be　called　by　courtesy；　its　sides）；　a　Square　has　4　sides；　0；　2；　4；　what　Progression　do　you　call　that？

I。　　Arithmetical。

SPHERE。　　And　what　is　the　next　number？

I。　　Six。

SPHERE。　　Exactly。　　Then　you　see　you　have　answered　your　own　question。　The　Cube　which　you　will　generate　will　be　bounded　by　six　sides；　that　is　to　say；　six　of　your　insides。　　You　see　it　all　now；　eh？

〃Monster；〃　I　shrieked；　〃be　thou　juggler；　enchanter；　dream；　or　devil；　no　more　will　I　endure　thy　mockeries。　　Either　thou　or　I　must　perish。〃　And　saying　these　words　I　precipitated　myself　upon　him。




Section　17。　　How　the　Sphere；　having　in　vain　tried　words；　　　　　　　　　　　　　　　　resorted　to　deeds



It　was　in　vain。　　I　brought　my　hardest　right　angle　into　violent　collision　with　the　Stranger；　pressing　on　him　with　a　force　sufficient　to　have　destroyed　any　ordinary　Circle：　　but　I　could　feel　him　slowly　and　unarrestably　slipping　from　my　contact；　no　edging　to　the　right　nor　to　the　left；　but　moving　somehow　out　of　the　world；　and　vanishing　to　nothing。　　Soon　there　was　a　blank。　　But　still　I　heard　the　Intruder's　voice。

SPHERE。　　Why　will　you　refuse　to　listen　to　reason？　I　had　hoped　to　find　in　you　　as　being　a　man　of　sense　and　an　accomplished　mathematician　　a　fit　apostle　for　the　Gospel　of　the　Three　Dimensions；　which　I　am　allowed　to　preach　once　only　in　a　thousand　years：　　but　now　I　know　not　how　to　convince　you。　Stay；　I　have　it。　　Deeds；　and　not　words；　shall　proclaim　the　truth。　Listen；　my　friend。

I　have　told　you　I　can　see　from　my　position　in　Space　the　inside　of　all　things　that　you　consider　closed。　　For　example；　I　see　in　yonder　cupboard　near　which　you　are　standing；　several　of　what　you　call　boxes　（but　like　everything　else　in　Flatland；　they　have　no　tops　nor　bottoms）　full　of　money；　I　see　also　two　tablets　of　accounts。　　I　am　about　to　descend　into　that　cupboard　and　to　bring　you　one　of　those　tablets。　　I　saw　you　lock　the　cupboard　half　an　hour　ago；　and　I　know　you　have　the　key　in　your　possession。　But　I　descend　from　Space；　the　doors；　you　see；　remain　unmoved。　Now　I　am　in　the　cupboard　and　am　taking　the　tablet。　　Now　I　have　it。　Now　I　ascend　with　it。

I　rushed　to　the　closet　and　dashed　the　door　open。　　One　of　the　tablets　was　gone。　　With　a　mocking　laugh；　the　Stranger　appeared　in　the　other　corner　of　the　room；　and　at　the　same　time　the　tablet　appeared　upon　the　floor。　　I　took　it　up。　　There　could　be　no　doubt　　it　was　the　missing　tablet。

I　groaned　with　horror；　doubting　whether　I　was　not　out　of　my　senses；　but　the　Stranger　continued：　　〃Surely　you　must　now　see　that　my　explanation；　and　no　other；　suits　the　phenomena。　　What　you　call　Solid　things　are　really　superficial；　what　you　call　Space　is　really　nothing　but　a　great　Plane。　　I　am　in　Space；　and　look　down　upon　the　insides　of　the　things　of　which　you　only　see　the　outsides。　You　could　leave　this　Plane　yourself；　if　you　could　but　summon　up　the　necessary　volition。　　A　slight　upward　or　downward　motion　would　enable　you　to　see　all　that　I　can　see。

〃The　higher　I　mount；　and　the　further　I　go　from　your　Plane；　the　more　I　can　see；　though　of　course　I　see　it　on　a　smaller　scale。　For　example；　I　am　ascending；　now　I　can　see　your　neighbour　the　Hexagon　and　his　family　in　their　several　apartments；　now　I　see　the　inside　of　the　Theatre；　ten　doors　off；　from　which　the　audience　is　only　just　departing；　and　on　the　other　side　a　Circle　in　his　study；　sitting　at　his　books。　　Now　I　shall　come　back　to　you。　And；　as　a　crowning　proof；　what　do　you　say　to　my　giving　you　a　touch；　just　the　least　touch；　in　your　stomach？　　It　will　not　seriously　injure　you；　and　the　slight　pain　you　may　suffer　cannot　be　compared　with　the　mental　benefit　you　will　receive。〃

Before　I　could　utter　a　word　of　remonstrance；　I　felt　a　shooting　pain　in　my　inside；　and　a　demoniacal　laugh　seemed　to　issue　from　within　me。　A　moment　afterwards　the　sharp　agony　had　ceased；　leaving　nothing　but　a　dull　ache　behind；　and　the　Stranger　began　to　reappear；　saying；　as　he　gradually　increased　in　size；　〃There；　I　have　not　hurt　you　much；　have　I？　　If　you　are　not　convinced　now；　I　don't　know　what　will　convince　you。　　What　say　you？〃

My　resolution　was　taken。　　It　seemed　intolerable　that　I　should　endure　existence　subject　to　the　arbitrary　visitations　of　a　Magician　who　could　thus　play　tricks　with　one's　very　stomach。　　If　only　I　could　in　any　way　manage　to　pin　him　against　the　wall　till　help　came！

Once　more　I　dashed　my　hardest　angle　against　him；　at　the　same　time　alarming　the　whole　household　by　my　cries　for　aid。　　I　believe；　at　the　moment　of　my　onset；　the　Stranger　had　sunk　below　our　Plane；　and　really　found　difficulty　in　rising。　　In　any　case　he　remained　motionless；　while　I；　hearing；　as　I　thought；　the　sound　of　some　help　approaching；　pressed　against　him　with　redoubled　vigour；　and　continued　to　shout　for　assistance。

A　convulsive　shudder　ran　through　the　Sphere。　　〃This　must　not　be；〃　I　thought　I　heard　him　say：　　〃either　he　must　listen　to　reason；　or　I　must　have　recou