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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(xué)天才、理性行為理論創(chuàng)立者、預(yù)見會(huì)思考的機(jī)器出現(xiàn)的預(yù)言者,已經(jīng)和他的同樣是數(shù)學(xué)家的來(lái)訪者一起坐了差不多半個(gè)小時(shí)。那是1959年春季一個(gè)工作日的傍晚時(shí)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(huì)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(méi)有系皮帶的長(zhǎng)褲上。他的魁梧身軀現(xiàn)在就像一個(gè)布娃娃一樣缺乏活力,他的線條優(yōu)美細(xì)致的五官?zèng)]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(yuǎn)的地方,除了一次次重復(fù)著將垂在前額的略長(zhǎng)的黑發(fā)撥開的動(dòng)作,他幾乎一動(dòng)不動(dòng)。麥基正襟危坐,被沉默壓得透不過(guò)氣來(lái),并且非常清楚地意識(shí)到會(huì)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(yǔ)氣溫和,但聽上去仍有些慍怒。“你,一個(gè)數(shù)學(xué)家,”他開始說(shuō)道,“一個(gè)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(lái)自太空的外星人選中要來(lái)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(dòng)聲色的目光,緊緊盯著麥基?!耙?yàn)椋彼鼗卮?,帶著溫和適度的南方人特有的慢條斯理的語(yǔ)氣,好像自言自語(yǔ)一般,“我的有關(guān)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(xué)思想一樣的,所以我會(huì)認(rèn)真對(duì)待?!盵3]這個(gè)來(lái)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(xué)界。在接下來(lái)的十年,在那既以對(duì)人類理性抱有無(wú)上信念而著稱,又以對(duì)人類生存懷有無(wú)盡憂慮而聞名的十年,納什,用知名幾何學(xué)家米克哈爾?格羅莫夫的話說(shuō),證明了自己是“20世紀(jì)后半葉最杰出的數(shù)學(xué)家”。策略博弈、經(jīng)濟(jì)競(jìng)爭(zhēng)、計(jì)算機(jī)建筑學(xué)、宇宙的形狀、虛構(gòu)空間的幾何學(xué)、素?cái)?shù)的神秘,都是他廣闊的想象力涉獵的領(lǐng)域。他的想法屬于那種非常深?yuàn)W而又完全出人意料的類型,無(wú)疑會(huì)推動(dòng)科學(xué)思考進(jìn)入新的方向。[4]數(shù)學(xué)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(wú)論如何也無(wú)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(lè)和藝術(shù)而非與最古老的科學(xué)緊密相連的神奇異稟。這不僅僅是指他的頭腦運(yùn)轉(zhuǎn)更加靈敏,記憶力更加出眾,或是他更能集中精力。事實(shí)上,直覺(jué)的火花稍縱即逝,不能用常理解釋。就像其他偉大的數(shù)學(xué)直覺(jué)大師格奧爾格?費(fèi)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(gè)結(jié)論,然后才開始構(gòu)筑耗費(fèi)心力的證明過(guò)程。不過(guò),即便在他嘗試解釋某個(gè)令人震驚的結(jié)論之后,對(duì)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(gè)謎。20世紀(jì)50年代就在麻省理工學(xué)院認(rèn)識(shí)納什的唐納德·紐曼曾經(jīng)這樣描述他:“其他人通常會(huì)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(guò)來(lái)從那個(gè)遙遠(yuǎn)的山峰用探照燈照射這座山?!盵5]沒(méi)有人比納什更對(duì)原創(chuàng)力著迷、更蔑視權(quán)威、更珍惜自己的獨(dú)立性。早在青年時(shí)代,他的身邊就不乏20世紀(jì)最偉大的科學(xué)權(quán)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(méi)有加入任何一個(gè)學(xué)派,不是任何人的門徒,基本上是在既沒(méi)有引導(dǎo)者,也沒(méi)有跟隨者的狀況下前進(jìn)。在他所做的從博弈論到幾何學(xué)等多個(gè)學(xué)科的幾乎所有工作之中,他對(duì)廣為接受的知識(shí)、公認(rèn)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(dú)立工作。通常他一邊散步,不時(shí)用口哨吹出巴赫的作品,一邊進(jìn)行思考。納什掌握的數(shù)學(xué)知識(shí),主要并非來(lái)源于學(xué)習(xí)其他數(shù)學(xué)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(yùn)藏的真理。他迫切希望取得一鳴驚人的成就,因此隨時(shí)準(zhǔn)備捕捉真正重大的問(wèn)題。當(dāng)他全神貫注地思考某個(gè)新的難題時(shí),會(huì)留意到那些精通這個(gè)領(lǐng)域的人(他從來(lái)不認(rèn)為自己已經(jīng)精通某個(gè)領(lǐng)域)最初認(rèn)為是幼稚或錯(cuò)誤從而不予考慮的角度。即便是在學(xué)生時(shí)代,他對(duì)旁人的懷疑

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