The World as a Mathematical Game: John von Neumann and Twentieth Century Science (Science Networks. Historical Studies)

215 Pages·2009·1.13 MB·English

by  Giorgio Israel

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Science Networks . Historical Studies
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J. Gray, Milton Keynes
Giorgio Israel
Ana Millán Gasca
The World as a
Mathematical Game

John von Neumann
and Twentieth Century Science
Birkhäuser
Basel · Boston · Berlin
Authors:
Giorgio Israel Ana Millán Gasca
Dipartimento di Matematica Dipartimento di Matematica
Università di Roma “La Sapienza” Università Roma Tre
P.le A. Moro, 5 Largo S. Leonardo Murialdo, 1
00185 Roma 00146 Roma
Italy Italy
e-mail: [email protected] e-mail: [email protected]
Translated from the Italian by Ian McGilvray
2000 Mathematical Subject Classification: 01A60, 01A70, 03-03, 68-03, 93-03
Library of Congress Control Number: 2008941508
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ISBN 978-3-7643-9895-8 Birkhäuser Verlag AG, Basel - Boston - Berlin
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Contents
Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Ja´nosNeumann’sEarlyYears
1.1 AJewishfamilyinearlytwentiethcenturyBudapest . . . . . . . . 1
1.2 AyoungtalentinHungarianmathematicsbellee´poque . . . . . . . 2
1.3 Lightsandshadows.ThevonNeumanngeneration . . . . . . . . . 7
1.4 StudentyearsinGermany . . . . . . . . . . . . . . . . . . . . . . 13
2 VonNeumannandtheMathematicsofGo¨ttingen
2.1 TheGo¨ttingenmathematicians . . . . . . . . . . . . . . . . . . . . 19
2.2 Hilbert’smathematicaloptimism . . . . . . . . . . . . . . . . . . 22
2.3 Theproblemsofthefoundationsofmathematicsandthe
axiomaticapproach. . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Theaxiomatizationofquantummechanics
andfunctionalspaces. . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5 Acrucialcontributiontogametheory . . . . . . . . . . . . . . . . 39
3 AMathematicianBetweenPastandFuture
3.1 ContinuityandevolutioninvonNeumann’sthought . . . . . . . . 49
3.2 Axiomaticsandthetwentiethcenturyrenewal
ofmathematicalpractice . . . . . . . . . . . . . . . . . . . . . . . 53
3.3 VonNeumann’sconceptionofmathematics . . . . . . . . . . . . . 57
3.4 Thelanguageofmathematicsanddeterminism . . . . . . . . . . . 60
3.5 Theworldasastrategicgame:amathematicalidea
ofrationality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4 VonNeumannintheUnitedStates
4.1 PrincetonandtheAmericanmathematicalcommunity
inthe1930s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2 Aluckymigrant . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.3 ScientificcommitmentduringWorldWarII . . . . . . . . . . . . . 82
vi Contents
4.4 FromtheManhattanProjecttotheAtomicEnergy
Commission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.5 ScientificresearchandnationalsecurityduringtheColdWar . . . . 91
4.6 Freedomandlimitationsinthedevelopmentofscience
andtechnology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.7 Systems,information,control . . . . . . . . . . . . . . . . . . . . 104
4.8 VonNeumann’sfinalyears:averyengagedexpertand
thetimestealthilyborrowedforthescientist’sprojects . . . . . . . 115
5 BeyondMathematics:vonNeumann’sScientificActivity
inthe1940sand1950s
5.1 Fromrationaleconomytotheaxiomatizationof
economicbehaviour . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2 Thetheoryofgames:anewmathematicsforthe
socialsciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3 Decisions,organization,operationsresearch . . . . . . . . . . . . 133
5.4 Engineeringandmathematics:theprojectofan
electroniccalculator . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.5 Theuseofcomputerinscientificresearch . . . . . . . . . . . . . . 147
5.6 Thebrain-computeranalogy . . . . . . . . . . . . . . . . . . . . . 154
ConcludingRemarks:
vonNeumannandTwentiethCenturyScience . . . . . . . . . . . . . . . 167
Chronology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Bibliography
SourcesandscholarshiponJohnvonNeumann . . . . . . . . . . . . . . 175
JohnvonNeumann’spublishedworksandarchivedpapers . . . . . . . . 176
WorksbyvonNeumannmentionedinthebook . . . . . . . . . . . . . . 177
Generalbibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
IndexofNames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Abbreviations
AF AirForce
AEC AtomicEnergyCommission
AMP AppliedMathematicsPanel
AMS AmericanMathematicalSociety
AOD ArmyOrdnanceDepartment
BRL AODBallisticResearchLaboratory
CalTech CaliforniaInstituteofTechnology
CIA CentralIntelligenceAgency
ECP ElectronicComputerProject
EDVAC ElectronicDiscreteVariableComputer
ENIAC ElectronicNumerator,Integrator,AnalyserandComputer
FAS FederationofAmericanScientists
IAS InstituteofAdvancedStudy,Princeton
IBM InternationalBusinessMachines
ICBM IntercontinentalBallisticMissile
JNCW JohnvonNeumann:Collectedworks,editedbyA.Taub,
NewYork,Macmillan,6volumes,1961–63.
JNLC JohnvonNeumannPapers,ManuscriptDivision,Libraryof
Congress,WashingtonD.C.
MAA MathematicalAssociationofAmerica
MIT MassachusettsInstituteofTechnology
NBO NavyBureauofOrdnance
NDRC NationalDefenseResearchCommittee
NRC NationalResearchCouncil
ONR OfficeofNavalResearch
OSRD OfficeofScientificResearchandDevelopment
RAND ResearchandDevelopmentCorporation
RCA RadioCorporationofAmerica
SAGE SemiautomaticGroundEnvironment
SIAM SocietyforIndustrialandAppliedMathematics
UN UnitedNationsOrganization
Introduction
Matters atcourtdevourmy time & energies,as always. His Majestybe-
comes daily more capricious. At times he will forget my name, and look
atme with thatfrown,whichallwhoknowhimso well,as ifhedoesnot
recognize me at all; then suddenly will come an urgent summons, and I
mustscamperuptothepalacewithmystarcharts&astrologicaltables.
Forheputsmuchinnocentfaithinthisstarryscrying,which,asyouknow
well,Iconsideradingybusiness.Hedemandswrittenreportsuponvari-
ousmatters,suchasforinstancethenativityoftheEmperorAugustusand
of Mohammed,and the fate which is to be expected for the Turkish Em-
pire,and,ofcourse,thatwhichsoexerciseseveryoneatcourtthesedays,
theHungarianquestion:hisbrotherMatthiasgrowsevermorebrazenin
hispursuitofpower.
–JohnBanville,Kepler.
In thelands situatedin the heartof Europe,sweptby the conflictsof the early
twentieth century – just as they were three centuries before, at the time of Kepler
– beganthelife ofJohnvonNeumann,afigure whoperhapsmorethananyotheris
representativeoftwentiethcenturyscience.VonNeumannwasabrilliantscientist,the
author of fundamentalcontributions to mathematics and theoretical physics, and he
playedavitalroleintheextraordinarydisplayofpoweroftwentieth-centuryscience,
asexpressedbythedevelopmentofcomputers,automation,spacetravel,andtheuse
ofatomicenergy.
Infact,thetriumphsofscience–andalsoitsmiseries–whichsodeeplymark
our era, are actually the outcome of a long historical process that begins symboli-
cally with the work of Galileo. After the Scientific Revolution, the role of natural
philosophyinmodernsocietythinkingandlifebecameincreasinglyimportant.Even
when this role was expressed in essentially theoretical and intellectual forms – that
is, without any visible practical fall-out on everydaylife – scientific breakthroughs,
andaboveallthebest-knownofthemall,Newton’smechanicsandhistheoryofuni-
versal gravitation, formed the most solid basis for faith in progress, typical of the
Enlightenmentperiodandlaterofthewholeofmodernthought.1
1) Ontheprincipleofomnipotencecharacterizingmodernscientificthought,seeIsrael2001.
x Introduction
The links between von Neumann’sown epoch and the distant age of the birth
of modern science are closer than they might seem. In the first place – despite the
emergenceof relativistic and evenscepticalviews –, becausescience has continued
todrawinspirationfromtheidealofachievingaunitary,coherent,objectiveanduni-
versalimageoftheworld.Andsecondlybecause,exceptforafewimportantdiffer-
ences,Kepler’sdescriptionoftheservitudeanddifficultiesofhislifeasa“scientist”
also evokesthe delicaterole thatbefellthe so-called“experts”orscientific advisors
after World War II. Kepler was appointed imperial mathematician to the court of
KaiserRudolphIIin1601:inviewofhisknowledgeofastrology,hismaintaskwas
to advise the emperoron the managementof a wide range of personaland political
matters,andtodeliverhispropheciesintheformof“writtenreports”.VonNeumann,
although born in Budapest, in Hungary – that European frontier land between East
andWestonwhichtheconcernsofRudolphIIwerefocused–rosetothehighestrank
possiblefora scientistatthe serviceoftheUnitedStates government.Thedramatic
upheavalsthatbegantoshakeEuropeinthe1930sledhim,likemanyotherscientists,
tomovetotheUnitedStates,wherehebecameamemberoftheselectandexclusive
AtomicEnergyCommission.AnditmaywellbesaidthatseveralofvonNeumann’s
writings prompted by his government service could well be considered prophecies
concerningthetimesinwhichwelive.
Butheretheanalogiesceaseanddifferencesarise.Indeed,thegrowingroleof
science in society and the increasing interweaving of science and technical knowl-
edgewhich,towardstheendofthenineteenthcentury,culminatedintheburgeoning
oftechnology,allowedlessscopeforthefigureofthescientificscholarservingasan
advisoratthe mercyofthe “king’s”whims.The AgeofEnlightenmenthadputfor-
wardtheideathatthegovernmentofsocietymustbefoundedonscientificbases,and
indeeditisthescientifice´liteitselfwhoshouldleadsocietyinaccordancewiththese
principles.The Ide´ologuesschoolled bythe mathematicianCondorcet2 dreamedof
discoveringandapplyingthemathematicallawsthatwouldrationallyandjustlyreg-
ulate the makingofdecisionsin courtrooms,in assemblies,andin elections,orelse
wouldbeusedtogoverntheeconomy.3Thishighlyambitiousprojectcametonought:
significatively enough, Napoleon opposed the rights of human subjectivity and his-
torytotheEnlightenment’sclaimtobasethegovernmentofsocietyontheprinciples
ofpurerationality.4 Nevertheless,theseedshadbeensownofadialecticsthatisstill
2) OnthesetopicsseeMoravia1974,1986.
3) Condorcetwastheauthorofaprogramaimedattheestablishmentofa“socialmathematics”,thatis,
amathematicssuitablefortreatingalltheproblemsinvolvedinmanagingsocietyandtheeconomy.
Inthisconnection,seeBaker1975,Israel1993a,1996b.
4) InaspeechdeliveredtotheCouncilofStateon20December1812,NapoleonBonaparte,inthe
followingterms,attackedthemovementoftheIde´ologuesanditsclaimtoconstructascienceof
society:«Itisideology,thisshadymetaphysicsthat,subtlyseekingtheprimecauses,setsoutto
establishonthesebasesthelegislationofpeoples,insteadofappropriatinglawstotheknowledge
ofthehumanheartandlessonsofhistory,thatmustbeblamedforallthemisfortunesthathave
befallenourfairFrance.[...]Whenoneiscalledupontoregenerateastate,itisnecessarytofollow
constantlyopposingprinciples.Historypaintsthehumanheart:itisinhistorythatonemustseek
theadvantagesanddisadvantagesofthedifferentlegislations.»(N.Bonaparte,Correspondance,32