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ABeautifulMindSylviaNasar[1]

JohnForbesNash,Jr.

—mathematicalgenius,inventorofatheoryofrationalbehavior,

visionary

ofthethinkingmachine—hadbeensittingwithhisvisitor,alsoamathematician,fornearlyhalfanhour.Itwaslateonaweekdayafternooninthespringof1959,and,thoughitwasonlyMay,uncomfortablywarm.Nashwas

slumped

inanarmchairinonecornerofthehospitallounge,carelesslydressedinanylonshirtthathunglimplyoverhisunbeltedtrousers.Hispowerfulframewasslackasa

ragdoll's,hisfinelymoldedfeaturesexpressionless.Hehadbeenstaringdullyataspotimmediatelyinfrontoftheleftfootof

Harvard

professor

GeorgeMackey,hardlymovingexcepttobrushhislongdarkhairawayfromhisforeheadina

fitful,repetitivemotion.Hisvisitorsatupright,oppressedbythesilence,acutelyconsciousthatthedoorstotheroomwerelocked.Mackeyfinallycouldcontainhimselfnolonger.Hisvoicewasslightly

querulous,buthestrainedtobegentle."Howcouldyou,"beganMackey,"howcouldyou,amathematician,amandevotedtoreasonandlogicalproof...howcouldyoubelievethat

extraterrestrials

aresendingyoumessages?Howcouldyoubelievethatyouarebeingrecruitedbyaliensfromouterspacetosavetheworld?Howcouldyou...?"[2]NashlookedupatlastandfixedMackeywithan

unblinking

stareascooland

dispassionate

asthatofanybirdorsnake."Because,"Nashsaidslowlyinhissoft,reasonablesouthern

drawl,asiftalkingtohimself,"theideasIhadaboutsupernaturalbeings

cameto

methesamewaythatmymathematicalideasdid.SoItookthemseriously."[3]TheyounggeniusfromBluefield,WestVirginia—handsome,arrogant,andhighlyeccentric—burstontothemathematicalscenein1948.Overthenextdecade,adecadeasnotableforitssupremefaithinhumanrationalityasforitsdarkanxietiesaboutmankind'ssurvival,Nashprovedhimself,inthewordsofthe

eminentgeometerMikhailGromov,"themostremarkablemathematicianofthesecondhalfofthecentury."Gamesofstrategy,economicrivalry,computerarchitecture,theshapeoftheuniverse,thegeometryofimaginaryspaces,themysteryof

primenumbers—allengagedhiswide-rangingimagination.Hisideaswereofthedeepandwhollyunanticipatedkindthatpushesscientificthinkinginnewdirections.[4]Geniuses,themathematician

PaulHalmos

wrote,"areoftwokinds:theoneswhoarejustlikeallofus,butverymuchmoreso,andtheoneswho,apparently,haveanextrahumanspark.Wecanallrun,andsomeofuscanrunthemileinlessthan4minutes;butthereisnothingthatmostofuscandothatcompareswiththecreationofthe

GreatG-minorFugue

."Nash'sgeniuswasofthatmysteriousvarietymoreoftenassociatedwithmusicandartthanwiththeoldestofallsciences:Itwasn'tmerelythathismindworkedfaster,thathismemorywasmore

retentive,orthathispowerofconcentrationwasgreater.Theflashesofintuitionwerenonrational.Likeothergreatmathematicalintuitionists—GeorgFriedrichBernhardRiemann,JulesHenriPoincaré,SrinivasaRamanujan—Nashsawthevisionfirst;constructingthe

laborious

proofslongafterward.Butevenafterhe'dtrytoexplainsomeastonishingresult,theactualroutehehadtakenremainedamysterytootherswhotriedtofollowhisreasoning.

DonaldNewman,amathematicianwhoknewNashatMITinthe1950s,usedtosayabouthimthat"everyoneelsewouldclimbapeakbylookingforapathsomewhereonthemountain.Nashwouldclimbanothermountainaltogetherandfromthatdistantpeakwouldshinea

searchlight

backontothefirstpeak".[5]Noonewasmoreobsessedwithoriginality,more

disdainful

ofauthority,ormorejealousofhisindependence.Asayoungmanhewassurroundedbythe

highpriests

oftwentieth-centuryscience—AlbertEinstein,JohnvonNeumann,andNorbertWiener—buthejoinednoschool,becamenoone's

disciple,

gotalong:largelywithoutguidesorfollowers.Inalmosteverythinghedid—from

gametheory

togeometry—he

thumbedhisnoseat

thereceivedwisdom,currentfashions,establishedmethods.Healmostalwaysworkedalone,inhishead,usuallywalking,oftenwhistling

Bach.Nashacquiredhisknowledgeofmathematicsnotmainlyfromstudyingwhatothermathematicianshaddiscovered,butbyrediscoveringtheirtruthsforhimself.Eagertoastound,hewasalways

onthelookoutfor

thereallybigproblems.Whenhefocusedonsomenewpuzzle,hesawdimensionsthatpeoplewhoreallyknewthesubject(heneverdid)initiallydismissedasnaiveorwrong-headed.Evenasastudent,hisindifferencetoothers'

skepticism,doubt,andridiculewasawesome.[6]Nash'sfaithinrationalityandthepowerofpurethoughtwasextreme,evenforaveryyoungmathematicianandevenforthenewageofcomputers,spacetravel,andnuclearweapons.Einsteinonce

chided

himforwishingtoamend

relativitytheory

withoutstudyingphysics.Hisheroesweresolitarythinkersandsupermenlike

Newton

and

Nietzsche.Computersandsciencefictionwerehispassions.Heconsidered"thinkingmachines",ashecalledthem,superiorinsomewaystohumanbeings.Atonepoint,hebecamefascinatedbythepossibilitythatdrugscouldheightenphysicalandintellectualperformance.Hewas

beguiled

bytheideaofalienracesofhyper-rationalbeingswhohadtaughtthemselvestodisregardallemotion.

Compulsively

rational,hewishedtoturnlife'sdecisions—whethertotakethefirstelevatororwaitforthenextone,wheretobankhismoney,whatjobtoaccept,whethertomarry—intocalculationsofadvantageanddisadvantage,

algorithms

ormathematicalrulesdivorcedfromemotion,convention,andtradition.EventhesmallactofsayinganautomatichellotoNashinahallwaycouldelicitafurious"Whyareyousayinghellotome?"[7]Hiscontemporaries,onthewhole,foundhimimmenselystrange.Theydescribedhimas"aloof","haughty","withoutaffect","detached","spooky","isolated",and"queer".Nashmingledratherthanmixedwithhispeers.

Preoccupied

withhisownprivatereality,heseemednottosharetheir

mundane

concerns.Hismanner—slightlycold,abitsuperior,somewhatsecretive—suggestedsomething"mysteriousandunnatural".Hisremotenesswas

punctuated

byflightsof

garrulousness

aboutouterspaceandgeopoliticaltrends,childish

pranks,andunpredictableeruptionsofanger.Buttheseoutburstswere,

moreoftenthannot,as

enigmatic

ashissilences."Heisnotoneofus"wasaconstant

refrain.AmathematicianattheInstituteforAdvancedStudyremembersmeetingNashforthefirsttimeatacrowdedstudentpartyatPrinceton:Inoticedhimverydefinitelyamongalotofotherpeoplewhowerethere.Hewassittingonthefloorinahalf-circlediscussingsomething.Hemademefeeluneasy.Hegavemeapeculiarfeeling.Ihadafeelingofacertainstrangeness.Hewasdifferentinsomeway.Iwasnotawareoftheextentofhistalent.Ihadnoideahewouldcontributeasmuchashereallydid.[8]Buthedidcontribute,inabigway.Themarvelousparadoxwasthattheideasthemselveswerenotobscure.In1958,

Fortune

singled

Nash

out

forhisachievementsingametheory,

algebraic

geometry,and

nonlinear

theory,callinghimthemostbrilliantoftheyoungergenerationofnew

ambidextrous

mathematicianswhoworkedinbothpureandappliedmathematics.Nash'sinsightintothedynamicsofhumanrivalry—histheoryofrationalconflictandcooperation—wastobecomeoneofthemostinfluentialideasofthetwentiethcentury,transformingtheyoungscienceofeconomicsthewaythat

Mendel'sideasofgenetictransmission,

Darwin'smodelofnaturalselection,andNewton's

celestial

mechanicsreshapedbiologyandphysicsintheirday.第六課美麗心靈西爾維亞?納薩爾[1]小約翰?福布斯?納什,數(shù)學天才、理性行為理論創(chuàng)立者、預見會思考的機器出現(xiàn)的預言者,已經(jīng)和他的同樣是數(shù)學家的來訪者一起坐了差不多半個小時。那是1959年春季一個工作日的傍晚時分,雖然才是5月,天氣卻很熱,令人不太舒服。納什頹然坐在醫(yī)院會客室一角的扶手椅上,身上隨意穿著的那件尼龍襯衫,松松垮垮地蓋在他沒有系皮帶的長褲上。他的魁梧身軀現(xiàn)在就像一個布娃娃一樣缺乏活力,他的線條優(yōu)美細致的五官沒有任何表情。他一直目光呆滯地盯著哈佛教授喬治?麥基左腳前方不遠的地方,除了一次次重復著將垂在前額的略長的黑發(fā)撥開的動作,他幾乎一動不動。麥基正襟危坐,被沉默壓得透不過氣來,并且非常清楚地意識到會客室的所有門都鎖上了。麥基再也控制不住自己。他盡量使語氣溫和,但聽上去仍有些慍怒?!澳?,一個數(shù)學家,”他開始說道,“一個致力于研究理性和邏輯證明的人,怎么能相信外星人正在給你發(fā)送消息呢?怎么能相信你被來自太空的外星人選中要來拯救世界呢?怎么能……”[2]納什終于抬起頭,用類似某種鳥類或者蛇一樣冰冷而不動聲色的目光,緊緊盯著麥基?!耙驗?,”他慢慢地回答,帶著溫和適度的南方人特有的慢條斯理的語氣,好像自言自語一般,“我的有關超自然生物的想法出現(xiàn)在我的腦海里的方式,是和我的數(shù)學思想一樣的,所以我會認真對待。”[3]這個來自西弗吉尼亞州布盧菲爾德的年輕天才——英俊、傲慢,而且非常古怪——在1948年闖入數(shù)學界。在接下來的十年,在那既以對人類理性抱有無上信念而著稱,又以對人類生存懷有無盡憂慮而聞名的十年,納什,用知名幾何學家米克哈爾?格羅莫夫的話說,證明了自己是“20世紀后半葉最杰出的數(shù)學家”。策略博弈、經(jīng)濟競爭、計算機建筑學、宇宙的形狀、虛構(gòu)空間的幾何學、素數(shù)的神秘,都是他廣闊的想象力涉獵的領域。他的想法屬于那種非常深奧而又完全出人意料的類型,無疑會推動科學思考進入新的方向。[4]數(shù)學家保羅?哈莫斯寫道,天才“分為兩種:一種就像我們大家一樣,只是更為出色;另一種則是那些明顯具備超凡人類靈感的人。我們都能跑步,有些人還能在四分鐘內(nèi)跑完一英里;但是我們大多數(shù)人所做的一切無論如何也無法與譜寫出G小調(diào)賦格曲相提并論”。納什的天分就屬于那種常與音樂和藝術而非與最古老的科學緊密相連的神奇異稟。這不僅僅是指他的頭腦運轉(zhuǎn)更加靈敏,記憶力更加出眾,或是他更能集中精力。事實上,直覺的火花稍縱即逝,不能用常理解釋。就像其他偉大的數(shù)學直覺大師格奧爾格?費里德里希?伯恩哈德?黎曼、朱爾斯?亨利?龐加萊、斯里尼瓦薩?拉馬努金一樣,納什先看到一個結(jié)論,然后才開始構(gòu)筑耗費心力的證明過程。不過,即便在他嘗試解釋某個令人震驚的結(jié)論之后,對于那些企圖跟隨他的邏輯的人而言,他所選擇的真正途徑卻始終是一個謎。20世紀50年代就在麻省理工學院認識納什的唐納德·紐曼曾經(jīng)這樣描述他:“其他人通常會在山上尋找攀登頂峰的道路。納什卻干脆爬上另外一座山,再反過來從那個遙遠的山峰用探照燈照射這座山?!盵5]沒有人比納什更對原創(chuàng)力著迷、更蔑視權威、更珍惜自己的獨立性。早在青年時代,他的身邊就不乏20世紀最偉大的科學權威,比如艾伯特?愛因斯坦、約翰?馮?諾伊曼、諾伯特?維納,但是他沒有加入任何一個學派,不是任何人的門徒,基本上是在既沒有引導者,也沒有跟隨者的狀況下前進。在他所做的從博弈論到幾何學等多個學科的幾乎所有工作之中,他對廣為接受的知識、公認的方式以及根深蒂固的規(guī)律都持懷疑態(tài)度。他差不多一直是獨立工作。通常他一邊散步,不時用口哨吹出巴赫的作品,一邊進行思考。納什掌握的數(shù)學知識,主要并非來源于學習其他數(shù)學家已經(jīng)取得的成果,而是自己重新發(fā)現(xiàn)這些成果中蘊藏的真理。他迫切希望取得一鳴驚人的成就,因此隨時準備捕捉真正重大的問題。當他全神貫注地思考某個新的難題時,會留意到那些精通這個領域的人(他從來不認為自己已經(jīng)精通某個領域)最初認為是幼稚或錯誤從而不予考慮的角度。即便是在學生時代,他對旁人的懷疑

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