Critique of Computational Reason in the Natural Sciences

Giuseppe Longo

Description

Niveau: Supérieur
Critique of Computational Reason in the Natural Sciences? Giuseppe Longo Departement d'Informatique CNRS - Ecole Normale Superieure et CREA, Polytechnique, Paris September 8, 2009 Abstract In this text, we will attempt to shortly highlight certain constitutive principles of the particular form of knowledge provided by the digital ma- chine, the modern computer, in its relationship to Mathematics (from which it originates) and to the Natural Sciences (Physics and Biology). Our basic thesis is that the historical and conceptual richness of the the- ory which enabled the concrete realization of this extraordinary type of machine is far from being neutral or transparent with regard to reality. Specifically, we will see that the digital machine proposes causal struc- tures and the breakings of symmetry which generate them as being the central structures of the intelligibility of nature. This will enable to point out a distinction between “imitation and “modeling in terms of simula- tion or formalization, and therefore enable to highlight the limits and the potentialities of digital simulation. 1 From the alphabet to the machine The extraordinary innovation to which we are confronted today is a machine which is the result of a very specific historical evolution. This machine did not exist “before”, in the way in which there were no mammals on earth 300 million years ago. It is within the evolutive system's dynamic, which constantly pro- duces novelty, that mammals emerge: nothing miraculous, only a very complex mixture between invariance and variability, continuity and change, which are in part random, and in part not yet properly

• body cartesian


• tur- ing's alphabetic


• cartesian


• into shape


• alphabetic reading


• meaning emerges


• very complex


• universe into

Sujets

• Milano
• Cartesian

Informations

• Publié par: chaeh
• Nombre de lectures: 20
• Langue: English

Extrait

CritiqueofComputationalReasonintheNatural Sciences ∗ GiuseppeLongo De´partementd’Informatique CNRS-EcoleNormaleSupe´rieureetCREA,Polytechnique,Paris http://www.di.ens.fr/users/longo September8,2009 Abstract Inthistext,wewillattempttoshortlyhighlightcertainconstitutive principlesoftheparticularformofknowledgeprovidedbythedigitalma- chine,themoderncomputer,initsrelationshiptoMathematics(from whichitoriginates)andtotheNaturalSciences(PhysicsandBiology). Ourbasicthesisisthatthehistoricalandconceptualrichnessofthethe- orywhichenabledtheconcreterealizationofthisextraordinarytypeof machineisfarfrombeingneutralortransparentwithregardtoreality. Specifically,wewillseethatthedigitalmachineproposescausalstruc- turesandthebreakingsofsymmetrywhichgeneratethemasbeingthe centralstructuresoftheintelligibilityofnature.Thiswillenabletopoint outadistinctionbetween“imitationand“modelingintermsofsimula- tionorformalization,andthereforeenabletohighlightthelimitsandthe potentialitiesofdigitalsimulation. 1Fromthealphabettothemachine Theextraordinaryinnovationtowhichweareconfrontedtodayisamachine whichistheresultofaveryspecifichistoricalevolution.Thismachinedidnot exist“before”,inthewayinwhichtherewerenomammalsonearth300million yearsago.Itiswithintheevolutivesystem’sdynamic,whichconstantlypro- ducesnovelty,thatmammalsemerge:nothingmiraculous,onlyaverycomplex mixturebetweeninvarianceandvariability,continuityandchange,whichare inpartrandom,andinpartnotyetproperlyclassifiableintocurrentphysical categoriesofdetermination.Inasimilarormorecomplexfashion,humanhis- torydevelops,andwithinit,withacontinuity/discontinuitywhichisrichin termsofcommonpractices,oflanguage,andofsymbolicculture,weinvented thismachine,whichisintheprocessofchangingtheworld.Suchamachineis theculminatingpointofaveryspecificprocesswhichbeginswithlanguage,but ∗ In”FundamentalConceptsinComputerScience”(E.GelenbeandJ.-P.Kahane, eds.),ImperialCollegePress/WorldScientific,2009,TextoriginallywritteninItalian asLezioneGalileana,Pisa,25ottobre2006.AFrenchversionisalsodownloadable: http://www.di.ens.fr/users/longo 1

whichismainlyinfluencedbythebirthanddevelopmentofthealphabet:the digitalmachineisatfirstanalphabeticmachine,andthenalogicalandformal one.Inshort,itisaninventionwhichisbothextraordinaryandcontingentto ourculture,whichismarkedbythebirthofthealphabet,ofCartesianratio- nality,ofFregeanlogic,ofHilbertianformalism. Soletsenunciatetheproblemofconsideringwhatistheimpactofsucha machineontheconstructionofknowledge.Themachineisindeednotneutral; itimposesupononewhousesitahistoryandalogic,anorganizingviewof phenomena.Themostdeleteriousculturalattitudesareofthosewhoremain naivebeforethenoveltybroughtonbyevolutionandhistory(orthatwebring intoit):notknowinghowtoliveaccordingtoourownknowledge,notknowing howtoappreciatetheoriginalityofourownknowledge,andprojectingourlatest inventionontothepast,asif,whilerichinhumanhistory,itwasalreadyinthe world,orifitwereanaccurateimageofit.Andcontinuingtosay:theuniverse isabigcomputer,or...eachphysicalorbiologicalprocessisacomputation. OrthatTuringstheoryis“complete”and“maximal”:evenacellsactivityor quantumcomputingcanbereducedtoit.Thisisapretensetohavingthe “Definitivetheory”,inanAristoteliansense. And,mostofall,wedonotconsidertheoriginalityofthisextraordinary scienceandofthistechnologywhich,byorganizingourviewuponphenomena intheirownway(andintheirownimage),helpandguideusintheacquisition ofknowledge.Themachine,asotherinstrumentsinthepastdidandevenmore so,deeplyimpactsourrelationshiptoscience,asthealphabetandtheprinting presshavetransformedandimpactedoursocieties,eventhewayinwhichwe constructknowledge.Iwillnotdwellonallthethemeswehaveevoked,andI willonlypointouttheviewwhichcomputerscienceproposes,oneimbuedbya veryeffectiveorganizationofknowledgeintolittleboxes,intobits,intopixels, intoadiscreteorsometimesabsoluteexactitude,withnosmoothness,nofuzzi- ness,nogestalt,noalea.Orwithatbestsomeveryimportantimitations(ina sensetobespecifiedbelow)ofsuchcomponentsoftheworldandofknowledge, butoneswhichareforcedorbiasedbytheirownlogic. SoIwouldliketoreaddressthefactthattherootsofthismachinearevery oldandcanbefoundinthealphabet.Firstofall,5000-6000yearsago,the alphabetwas,fordifferentreasons,aninventioncomparabletothecomputer- mediateddiscretizationofknowledgewehavenowperformed.Thinkofthe originalityofthesefirstsocialgroupsfromMesopotamiawhofractionedthe linguisticflux,acontinuousspokensong,markingcertainpitchesasfirstconso- nants[HerrenschmidtC.etal.1996].Itwastheonsetofadevelopmentandof aculturewhichwerequitedifferenttothoseinherenttothehieroglyphicwriting ofideogramswhichproposedconceptsorevokedwholeimages,situations,or feelings,bymeansofdrawings.Conversely,thealphabetdiscretizes,subdivides continuouslanguageintoinsignificantatoms,intothebitswhichareletters. Thisconstitutesanextraordinaryleapofabstractionbyman,awayofrepre- sentinglinguisticinteractionwhichabsolutelydidnotexistbeforeandwhichwill markhumanculturebythe(re-)constructionofmeaningfromelementaryand simplesignswithoutmeaning,signsthatwerehighlyabstractassuch.More- over,andthisiscrucial,meaningisreconstructedthroughsound:thealphabet isphonetic.Meaningisprovidedbythereproductionofsound,andnotbythe evocationofanimageorofaconcept,ahugerevolution.Incomputerscience 2