從統(tǒng)計(jì)物理到社會(huì)科學(xué)：如何從微觀推導(dǎo)出宏觀 From statistical physics to social sciences - the pitfalls of multi-disciplinarity

Complexity

JournalofPhysics:

PERSPECTIVE?OPENACCESS

Fromstatisticalphysicstosocialsciences:thepitfallsofmulti-disciplinarity

Tocitethisarticle:Jean-PhilippeBouchaud2023J.Phys.Complex.4041001Viewthe

articleonline

forupdatesandenhancements.

Youmayalsolike

-

Informationretrievalandstructural

complexityoflegaltrees

Yanik-PascalF?rster,AlessiaAnnibale,LucaGamberietal.

-

Hyper-diffusiononmultiplexnetworks

RezaGhorbanchian,VitoLatoraandGinestraBianconi

-

Sensitivitytonetworkperturbationsinthe

randomizedshortestpathsframework:

theoryandapplicationsinecological

connectivity

IlkkaKivim?ki,BramVanMoorterandMarcoSaerens

ThiscontentwasdownloadedfromIPaddress

41

on17/12/2024at00:09

?2023TheAuthor(s).PublishedbyIOPPublishingLtd

IoppublishingJ.Phys.Complex.4(2023)041001

/10.1088/2632-072X/ad104a

Journalofphysics:complexity

crossMark

OPENACCESS

RECEIVED

21September2023

ACCEPTEDFORPUBLICATION

28November2023

PUBLISHED

8December2023

OriginalContentfromthisworkmaybeusedunderthetermsofthe

CreativeCommons

Attribution4.0licence

.

Anyfurtherdistributionofthisworkmust

maintainattributionto

theauthor(s)andthetitleofthework,journal

citationandDOI.

PERSPECTIVE

Fromstatisticalphysicstosocialsciences:thepitfallsofmulti-disciplinarity

Jean-PhilippeBouchaud

?

CapitalFundManagement&AcadémiedesSciences,Paris,France

E-mail:

jean-philippe.bouchaud@institut-de-france.fr

Keywords:multidisciplinarity,econophysics,complexsystems

Abstract

ThisistheEnglishversionofmyinaugurallectureatCollègedeFrancein2021.Ireflectonthe

difficultyofmulti-disciplinaryresearch,whichoftenhingesonunexpectedepistemologicalandmethodologicaldifferences,forexampleaboutthescientificstatusofmodels.Whatisthepurposeofamodel?Whatareweultimatelytryingtoestablish:rigoroustheoremsorad-hoccalculationrecipes;absolutetruth,orheuristicrepresentationsoftheworld?Iarguethatthemain

contributionofstatisticalphysicstosocialandeconomicsciencesistomakeusrealisethat

unexpectedbehaviourcanemergeattheaggregatelevel,thatisolatedindividualswouldnever

experience.Crises,panics,opinionreversals,thespreadofrumoursorbeliefs,fashioneffectsandthezeitgeist,butalsotheexistenceofmoney,lastinginstitutions,socialnormsandstablesocieties,mustbeunderstoodintermsofcollectivebeliefand/ortrust,self-sustainedbyinteractions,oronthecontrary,therapidcollapseofthisbeliefortrust.Theappendixcontainsmyopeningremarkstotheworkshop‘MoreisDifferent’,asatributetoPhilAnderson.

Volantsuperomnes

1

1.Introduction

Ihavechosentodevotemyinaugurallecturetothechallengesposedbymulti-disciplinarity,inthehopethatmyexperienceasatheoreticalphysicistexploringeconomicsandfinancewillillustratetheissuesandpitfallsassociatedwithanapproachthatissupposedlyfruitfulandencouragedbythesupervisorybodies,butwhichcomesupagainstnumerousobstacleswhenwetrytoputitintopractice.

Inmanyways,venturingintoadisciplinethatisnotyourownislikeemigratingtoacountrywhereyouknowneitherthelanguagenortheculture,andwhichdoesnotexpectmuchfromnewcomers,especially

whentheyhavethearroganceandnaivetytobelievethattheywillbringanewperspective,differenttools,acomplementaryrepresentationoftheworld.Andyet,asRenéCharsaid,whatcomesintotheworldtodisturbnothingdeservesneitherconsiderationnorpatience.

Suchconfrontationofcultures,oftendifficultandsometimesbrutal,isneverthelessfertileifitisallowedtocontinueoverlongperiods.Italsoraisesquestionsaboutscienceingeneral,andsciencein

particular—whatareitsaims?Whatareitsmethodologicalpresuppositions,itssocialconventions,itscriteriaofexcellenceandscientifictruth,itseditorialpractices?Shouldtheoryprecedeconfrontationwithdata,as

someeconomistsbelieve,orshouldobservationinspiretheory,asisoftenthecaseinphysics?Andwhatisa

1TheCollègedeFrancehasalwaysrepresentedformeacompendiumofexcellenceandhighstandards,auniquelinkinthetransmissionofknowledgethatisbothcutting-edgeanduniversal,instantaneousandpermanent.ThecoursesgivenbyPierre-GillesdeGennes,ClaudeCohen-TannoudjiandPhilippeNozières,eachintheirownstyle,inspiredandprofoundlyinfluencedme.Idon’tthinkIwouldhavebecometheresearcherIamtodaywithouttheirteachings.That‘swhyI’msoexcitedattheprospectofteachingheremyself,ifonlyforayear,andI’dliketothanktheBettencourt-SchullerFoundationwarmlyforgivingmethisopportunity,aswellasmycolleagueswhoproposedanddefendedmyapplication,especiallyAntoineGeorgesandAlainProchiantz.I’dalsoliketosendmanythanks:toElisabeth,mylifelongmuse,tomychildrenandtheirstimulatingideas,tomycolleagues,collaboratorsandfriends,butalsotomystudentsandpost-docs.Afterall,researchisfirstandforemostacollectivephenomenon.

2

oppublishingJ.Phys.Complex.4(2023)041001J-PBouchaud

theory,amodel,alaw—termswhich,curiouslyenough,donothavethesamemeaningorthesamestatusindifferentdisciplines,asIwillcomebacktolater.

Thisdiscussionisparticularlyimportantbecausemodelsoftenserveasparadigms,asconceptualpillarsonwhichdisciplinesdevelop.Makenomistake:certainmodelsandtheories,whenweareexposedtothem,carvesuchadeepgrooveinourmindsthattheydetermine,inthelongterm,ourconceptionoftheworldandourprofessionalpractices.

However,aninterestingquestionisraisedfromtheoutset:whatlegitimacydoesonehavetocriticisea

disciplinetowhichonedoesnotbelong?Arelaycriticscredible,orevenaudible?Canonecastdoubtontheknowledgeofexpertsintheirfieldbyrelyingonexpertisefromoutsidethatfield?

2

Andyet,afresh

perspectiveissometimesneededtocastdoubtonaxiomsthataretoofamiliarortoquestiontheobviousthatistooconsensual.

Asfarasmethodologyisconcerned,suchinterferenceseemstometobeperfectlylegitimate,becausethepracticeofscientificresearchandtheproductionofknowledgecanundoubtedlybetransposedtoother

fields,beyondthepurelytechnicalaspects.It’snotuncommonfortheformalbeautyofatheory,its

mathematicalaesthetics,totakeprecedenceoveritsrelevancetodescribingtheworld;insuchcases,researchdevelopsoutsidetheground,inavacuum,wherethejustificationbecomesthesheerintellectualinvestmentalreadymade.Inthiscase,itisverydifficulttobreakthespell;onthispoint,forexample,Iwouldliketo

quotetheeconomistWillemBuiter,whowrotein2008,shortlyaftertheonsetofthegreatrecession

3

:Mostmainstreammacroeconomictheoreticalinnovationssincethe1970shaveturnedouttobeself-referential,

inward-lookingdistractionsatbest.Researchtendedtobemotivatedbytheinternallogic,intellectualsunk

capitalandaestheticpuzzlesofestablishedresearchprogrammesratherthanbyapowerfuldesiretounderstandhowtheeconomyworks.

2.Fromstatisticalphysicstosocialsciences

Idiscoveredstatisticalphysicsintheearly80s.Oneofthemajorresearchthemesatthattimewasphasetransitions(afteritsheydayinthe1970s),whichbroughttolighttheconceptsofcollectiveeffectsanduniversality,whichhadascopefarbeyondphysicsalone,asIwilldiscusslater.

Anewbodyoftheorywasthenbeingbuiltaroundthesomewhatvaguenotionof‘complexsystems’.Itwasdiscoveredthatsomephysicalsystemsneverreachthermodynamicequilibrium,becausereachingthatequilibriumwouldbelikesolvinganoptimisationproblemsocomplexthatnoalgorithm—noteventhe

dynamicsofthesystemitself—couldfindthesolutioninareasonableamountoftime.Wealsounderstoodthatthesesystemsarefragile,i.e.hyper-sensitivetodisturbances,andtheirdynamicsintermittent.Small

causescangiverisetomajorcatastrophes(avalanches,earthquakes),leadingtoabruptanddiscontinuousevolution.Thestatisticsofevents,farfrombeingGaussian,arecharacterisedbythickdistributiontails,

whichallowextremeeventstooccurwithanappreciableprobability.

AtellingexampleofsuchsituationsistheanomalousdiffusionoftheLévytype.WeareallfamiliarwithBrownianmotion,inwhichdiffusionresultsfromaverylargenumberofverysmallsteps.Brownianmotioniscontinuous,andthedisplacementstatisticsareGaussian.Incontrast,the‘Lévyflight’ismadeupofstepsofdifferentsizes,someverysmallandothersverylarge.Whateverthescaleatwhichweobservethis

movement,itisalwaysthefewlargestjumpsthatdominatethetotaldisplacement.ALévyflightisperfectlyself-similar,althoughitisdominatedbyextremeevents[

1

].

Suchanomalousdiffusionwasfirstobservedexperimentallyin1990attheLaboratoiredePhysique

Statistiquedel’ENS,inasolutionofso-called‘giant’micelles[

2

].Iwasluckyenoughtobeabletointerprettheseexperimentstheoretically,andthisworkwasoneofthetriggersformygradualmigrationtowardswhatisnowcalled‘econophysics’,aratherunfortunateneologismbutconstructedinthesamewayas‘biophysics’or‘geophysics’.

Becauseafewyearsearlier,inSeptember1987,thefirstconferencebringingtogethereconomistsand

physicistswasheldinSantaFe(NewMexico).Co-organisedbyPhilAnderson—inmyviewoneofthemostextraordinarytheoreticalphysicistsofthetwentiethcentury(NobelPrizeinPhysicsin1977)—KenArrow

(NobelPrizeinEconomicsin1972)andDavidPines(Quantumliquidphysicist),theconferencewasentitled‘TheEconomyasanEvolvingComplexSystem’[

3

]soughttoimbuetheoreticaleconomicswithrecent

ideas—perhapstoorecent—fromstatisticalphysics.

Unfortunately,despitesuchprestigiousgodfathers,thegraftdidnottake.ForreasonsthatIwilltrytoexplainlater,econophysicsdevelopedfor30yearsinarelativelyautarkicway,creatingveryfewbridgeswith

2Thisparadoxechoesthecurrentdebateaboutthevalueofexpertopinioninademocracy.

3WillemBuiter,Theunfortunateuselessnessofmost‘stateoftheart’academicmonetaryeconomics.VoxEU(2009).

/

article/macroeconomics-crisisirrelevance

.

3

oppublishingJ.Phys.Complex.4(2023)041001J-PBouchaud

theworldofeconomistsandalittlemorewiththeworldoftheoreticalfinance.Neo-classicaleconomics

seemedtohavewontheday;in2003—5yearsbeforethegreatrecessionof2008—RobertLucas,winnerofthe1995NobelPrizeinEconomics,declared:macroeconomics[...]hassucceeded:itscentralproblemof

depressionpreventionhasbeensolved,forallpracticalpurposes.

Andyet,ironically,on19October1987,justafewweeksaftertheSantaFeconference,theDow-Jones

indexexperienceditsworstdayever,falling22.6%inasingleday.Afineexampleofarareevent,totally

absentfromtheclassicaltheoryofsupposedlyGaussianmarkets.What’smore,thiscrashdoesnotseemtobelinkedtoanyeconomicnewsthatmightexplainitsscale.

Facedwithsuchaneventwithnoapparentcause,thephysicistimmediatelythinksofanendogenous

discontinuity,generatedbyfeedbackloopsinternaltothecomplexsystemthatisafinancialmarket,withitsthousandsofplayerswhoinfluenceeachother...butthisinterpretationwasalongwayfromthedominant

dogmaatthetime(orevennow),thatofrationalagents,whoseinfinitewisdomwouldallowthemarketstoalwaysdisplaythe‘true’price,theonethatreflectstheso-called‘fundamental’value,andthatonlyvariesifnewinformationjustifiesit.Thisisthetheoryofefficient,stablemarkets,whichdonotgetcarriedaway

spontaneously,donotgiveintounjustifiedpanicmovements,butstubbornlyprovideinformationaboutthevalueoftheworld.

Doyouguysreallybelievethis?wasPhilAnderson’sbluntandundiplomaticreactionwhenthistheorywaspresentedtohiminSantaFein1987[

3

].IadmitIhadthesamereactionwhen,afewyearslater,Ireadmy

firsttheoreticalfinancearticles,particularlythoseonthefamousBlack,Scholes&Mertonmodel.Thisseemstometobeaperfectexampleofthegulfthatcanexistbetweenscientificcultures.Itallowsmetodiscussindetailtotheessentialdifferencesbetweenpossibleinterpretationsoftheveryconceptof‘model’,andto

discussacrucialquestion:whatisagoodmodel?

3.Aparadigmaticmodel:Black,Scholes&Merton

AfterFisherBlack’suntimelydeathin1995,MyronScholesandRobertMertonwereawardedtheNobelPrizeinEconomicsin1997fortheirtheoryofoptionpricing[

4

],whichIhavetopresenthereverybrieflysothatitsparadigmaticnaturecanbeunderstood.

Anoptionisaninsurancecontractonthevalueofafinancialasset.Supposeyouwanttoinsureyour

shareportfoliosothatevenifpricesfallsignificantly,theinsurerundertakestobuyitbackataminimum

price,saytoday’sprice,foraperiodoftenyears.Whatpremiumistheinsurerentitledtocharge?Betweennowand—say—1yearfromnow,whatinvestmentstrategyshouldtheinsurerfollowtominimisetheriskitiscovering?

TheBlack–Scholes–Mertonmodelmakesitpossibletoanswerthesetwoquestionssimultaneouslyandunequivocally.Therearetwosurprises,whichareparticularlyrelevanttomypoint,becausetheyoffendtheintuitionofthephysicist,butseemnaturaltotheeconomistandtothemathematician.Whatis—orhas

become—obvioustosomemayremainobscureorevenquestionabletoothers.Thesediscrepanciescaneithergiverisetonewideasor,onthecontrary,breedmutualdistrust.

Thefirstsurpriseisthat,intheworldofBlack–Scholes,theinsurancepremiumdoesnotdependonthevalueoftheexpectedaveragereturnofthestockmarketoverthenextyear;whetherthestockmarketrisesorfalls,thepriceoftheoptionsisunchanged;noassumptionaboutthisaveragereturnisthereforenecessarytosetthepriceofinsuranceagainstfallingstockprices!

Thesecond,perhapsevenmoredisturbingsurpriseisthattheinsurercanfollowastrategyknownas

‘hedging’,whichallowsittotakenoriskatall.However,themodelexplicitlyassumesthatmarketpricesareunpredictable.Bywhatsleightofhand,then,canriskdisappearcompletely?

TheanswerliesintheveryspecialnatureoftheBlack–Scholes–Mertonhypotheses,whichassumethat

pricemovementsaredescribedbyacontinuous-timeBrownianmotion.AsImentionedearlier,Brownian

motioncanbeconstructedasthesuperpositionofaninfinitenumberofinfinitesimallysmallsteps.Insuchamodel,thepriceevolvescontinuously,withoutjumps;chanceis‘benign’,uncertaintycanbetamedand,inasense,disappears.

Butitisasingular,fragilemodel:assoonasonetakesintoaccountthefactthatthestatisticsofprice

variationsareheavy-tailed,thatpricejumpsofallsizesoccurinfinancialmarkets

4

,fromtheinsignificanttocentury-longcrashesliketheonein1987,thentheriskthatBlackandScholeshadsweptunderthecarpetreappears,anditisinfactfarfromnegligible.Moreover,thisriskisasymmetrical:theinsurer’spotential

lossesaremuchgreaterthanthoseoftheinsured.Ifthiswerenotthecase,theveryexistenceofinsurance

4Earthquakesofverydifferentmagnitudescoexist,someimperceptibleandothersdestructive.RememberthattheRichterscaleislogar-ithmic:+1onthisscalecorrespondstoanearthquake30timesmorepowerful.

4

oppublishingJ.Phys.Complex.4(2023)041001J-PBouchaud

contractsofthistypewouldbepointless,sinceinsurance,bydefinition,isatransferofrisk.Inaway,themodelcontradictstheveryexistenceofthecontractsitseekstotheorise.

Butitgetsevenworse.TheindiscriminateuseoftheBlack–Scholes–Mertonmodelcreatesadestabilisingfeedbackloop,whichconsiderablyamplifiedthe1987crashImentionedearlier.Sotheparadoxiscomplete:usingamodelinwhichcrashesdonotexistcanactuallytriggertheirexistence!Themodelitselfbecomesasystemicriskfactor.

MyfirstforayintotheoreticalfinanceowesagreatdealtoChristianWalter,whohadreadmyarticleonLévyflightsingiantmicelles[

2

].HesuggestedthatIshouldgeneralisetheBlack–Scholes–Mertonmodeltosituationsof‘wildrandomness’,asBeno?tMandelbrotcalledit,i.e.wheretherandomnessisheavy-tailed.TheresultofthisresearchleadtoanarticlepublishedinLeMonde,14March1995,entitledLesmarchés

dérivés,pourunepédagogiedurisque.

Theleastthatcanbesaidisthatmypiecedidnothelptoestablishacalmdialoguewithfinancial

mathematics.ButitdidleadtothecreationofScience&Finance,whichlatermergedwithCapitalFundManagement.Thisenabledustodevelopanalternative,‘physicist’sview’offinancialmarketsand,moregenerally,oftheoreticaleconomics.Lookingback,Istilldonotknowwhetheralessconfrontational

approachwouldhaveacceleratedtheinnovationprocess,orwhetheritwouldhavedilutedorevenstifledoriginalideas.That’spreciselytheconundrumofmulti-disciplinarity.

4.Phenomenologicalmodels

TheBlack–Scholes–MertonmodelbelongstoacategorythatIwouldcall‘phenomenological’models,tobedistinguishedfrom‘foundational’and‘metaphorical’models,whichIwilldiscusslater.Thepolysemyoftheword‘model’isinfactafirstobstacletomulti-disciplinarity:whatisthepurposeofamodel?Whatmakesitscientific?Whatareweultimatelytryingtoestablish:rigoroustheoremsorad-hoccalculationrecipes;

absolutetruth,orheuristicrepresentationsoftheworld?

‘Phenomenological’modelsattempttorepresentrealityinmathematicalterms.Usingafewformulasor‘laws’,theysummarisethebehaviourtheyaretryingtodescribe,forexampleasimplelinearregression.Themathematicalapparatusthentakestheselawsanddrawsallsortsoflogicalconsequencesfromthem.Frombeingdescriptive,themodelthenbecomespredictive.

Anexampleofthistypeofmodelisgivenbythelawofbehaviourofso-callednon-Newtonianfluids,

suchasmayonnaise,maizenaortoothpaste,whichstipulatesthatthestressσappliedisequaltoathresholdstressσc,increasedbyapowerlawcontributionfromtheshearrateγ.:

σ=σc+γ.x.(1)

Byinjectingthisbehaviourallawintothegeneralequationsdescribingtheflowofliquids,wecanpredict,forexample,theheadlossesinapipe,i.e.thecostofpumpingsuchafluid.Wethereforeobtainapredictionofthemodel,butnoexplanationoftheoriginofthepostulatedlawofbehaviour.

AsRenéThomoncenoted,topredictdoesnotnecessarilymeantounderstand.Thelawusedisatbestjustifiedbyempiricalobservationsthatareadjusted,withinacertainrangeofvariability,bythelawin

question.

Buttheselawsareoftenmotivatedonlybyconsiderationsofmathematicalconvenience.The

phenomenologicalmodelalwayscontainsacertainnumberofadjustableparameters,whicharechosentorepresentthephenomenon‘a(chǎn)swellaspossible’.Itisthusalwayspossibletofindtheoptimumvaluefortheseparameters,evenifthemodelistotallyunrealistic.Butifthemodeliswrong,suchaprocedurecanbe

disastrous,becausetheconsequencesdeducedfromthemodelmaybecompletelyatoddswithreality.

Thereareseveralmodelswidelyusedinfinancewhicharepreciselyinthissituation:onecanadjusttheobservationsperfectlyonagivenday,calculatetheconsequencesexactly,butendupbeingcompletelywrongaboutthesignofcertainderivatives,i.e.predictthatcertainquantitiesshouldincreasewheninrealitytheyaredecreasing!

5

Theproblemisthatthereisoftennojustificationforthesemodelsbasedonfundamentalprinciples.

Theseprinciplesarethesubjectofaconsensusbecausealltheconsequencesdrawnfromthemareconsistentwithallknownobservations—asisthecase,forexample,ofthermodynamicsorquantummechanics.To

returntonon-Newtonianliquids,wewouldliketojustifytherheologicallaw,equation(

1

),basedentirelyonthemovementofthemoleculesthatmakethemup,whichisgovernedbyquantummechanics.Whatisthecollectivemechanismbywhichathresholdconstraintσcarises,preventingtheliquidfromflowingifthe

5Theso-called‘localvolatility’modelisoneexample,see[

5

].

5

oppublishingJ.Phys.Complex.4(2023)041001J-PBouchaud

constraintisnotstrongenough?Thisistheheartofstatisticalphysics,andoneofthethemesofmyforthcominglectures:howcanwemovefromthemicroscopictothemacroscopic?

Thereasonwhysucha‘microscopic’justificationisessentialisthatitallowsustounderstandthelimitsofamodel,andwhenitispushedoutsidethenormaloperatingregime.Whathappensinextremesituations?Isthemodelstillvalid?Thisisobviouslyanessentialconcern,bothinconventionalengineeringandin

financialengineering;andalso,forexample,forthemonetarypolicyofcentralbanksintimesofcrisis

6

.

TheBlack–Scholes–Mertonmodelisaperfectcaseinpoint.Wepostulateanintellectuallyreasonable

model(thatoftheBrownianmotion)forwhichthemathematicaltoolsareelegant,efficientandplentiful,

andweturnthecrankthatallowsustocalculateallsortsofthings,whileturningablindeyetothemanifestlynon-Gaussianevents(atthebeginningofthe90s,itwasevenacceptedthatoneshouldremovetheso-calledaberranteventsfromthecalibration!)Thisestablishedaparadigmofzerorisk,whichledtothecrashof1987thatcontradicteditsverypremises.

AsIsaidearlier,theimportanceofparadigmsshouldnotbeunderestimated:theyinformourintuitionandshapeourvisionoftheworld.Thedangersofamodelwithout‘microscopic’foundationsaremagnifiedwhenitisperformative,i.e.whenitestablishesacertainnumberofprofessionalorinstitutionalpractices

basedonthemodelitself.

InthecaseoftheBlack-Scholes-Mertonmodel,amissingbutessentialingredientisthefeedbackofthehedgingstrategyonprices.Thepriceofafinancialassetdoesnotexistinitself,asthePlatonicvisionof

efficientmarketswouldhaveusbelieve(andasfinancialengineershavelongbelieved,andsometimesstill

believe).Thepriceisbuttheresultoftheveryactionsofbuyersandsellers.Transactionshaveanimpactonprices,andthisimpactcaninitiateafeedbackloopandleadtoinstability(seeforexample[

6

]).Itisbytryingtoformulateamore‘microscopic’theoryofpriceformation,insteadofpostulatinganex-nihilomodel,thatwemighthaveguessedtheintrinsiclimitationsoftheBlack–Scholes–Mertonmodel.

Inanycase,itseemstomecrucialthatthequalitativeconclusionsofamodelshouldberobusttosmallchangesinassumptions,becauserealityrarelyobeysperfectlytheequationswepostulate.Amodelisa

simplifiedrepresentationoftheworldthatallowsustoorientateourselvesandguideourintuition.Themapisnottheterritory,andweneedtomakesurethatthesimplificationisnotabetrayal.Agoodmodelshouldbeanon-paradoxicalrepresentationoftheworld:thereshouldbeasfewanomalies,paradoxes,exceptionsand‘blackswans’aspossible.

5.Fundamentaltheoriesand‘Metaphorical’models

Phenomenologicalmodelscoexistwith,andoftenfeedinto,twoothertypesofmodelwhoseaimsare

different

7

.‘Foundational’modelsaremoreambitious:theydonotproposeadhocequationstodescribea

phenomenon,butratheranaxiomatic,explanatoryandcoherentscheme.Ifitstandsuptovariouslogical

andempiricaltests,suchamodelbecomesafundamentaltheory.AgoodexampleistheBohr–Rutherford

modelofthehydrogenatom:itpostulatesthattheatomismadeupofapositivelychargednucleusandan

electronconstrainedtomoveinstableorbits,determinedonthebasisofaconditionforquantifyingangularmomentum.Thismodelcontainsthepremisesofquantummechanics.

Anotherexampleistherationalagentmodelineconomics,whichisthestartingpointforanambitioustheoryofhumandecisionsinthepresenceofuncertainty,fromwhichallsortsofeconomicconclusionscanbedrawn.Unfortunately,inthiscase,theexperimentalevidencefromnumerouscognitiveandbehaviouralbiasesonthepartofeconomicagentscastsstrongdoubtsonthevalidityoftheinitialmodel—unlesswe

considerthatattheaggregatescaleofaneconomy(orafinancialmarket),irrationalindividualbehaviourisaveragedoutanddisappears.Everythingwouldthenhappen‘a(chǎn)sif’agentswererational.Butisitreally

reasonabletomakethisadditionalassumption?

Inanycase,thisonceagainconcernsthequestionofthepathfrommicrotomacro:whatremainsof

individualbehaviourwhenweobservelargeensembles?Weshallseethatinthepresenceofinteractionsthesebiasesmay,onthecontrary,bereinforcedratherthanaverageouttozero.

Finally,Iwouldliketotalkaboutsomemodelsthatareparticularlyclosetomyheart,whichIproposetocall‘metaphorical’;theyarealsooftencalled‘toy-models’.Thesemodelsdonotseektoexplainan

observationindetail,butrathertohighlightmechanismsthatwoul