Boston Studies in the Philosophy and History of Science 327 Johannes Lenhard Martin Carrier Editors Mathematics as a Tool Tracing New Roles of Mathematics in the Sciences Boston Studies in the Philosophy and History of Science Volume 327 Editors AlisaBokulich,BostonUniversity RobertS.Cohen,BostonUniversity JürgenRenn,MaxPlanckInstitutefortheHistoryofScience KostasGavroglu,UniversityofAthens ManagingEditor LindyDivarci,MaxPlanckInstitutefortheHistoryofScience EditorialBoard TheodoreArabatzis,UniversityofAthens HeatherE.Douglas,UniversityofWaterloo JeanGayon,UniversitéParis1 ThomasF.Glick,BostonUniversity HubertGoenner,UniversityofGoettingen JohnHeilbron,UniversityofCalifornia,Berkeley DianaKormos-Buchwald,CaliforniaInstituteofTechnology ChristophLehner,MaxPlanckInstitutefortheHistoryofScience PeterMcLaughlin,UniversitätHeidelberg AgustíNieto-Galan,UniversitatAutònomadeBarcelona NuccioOrdine,UniversitádellaCalabria SylvanS.Schweber,HarvardUniversity AnaSimões,UniversidadedeLisboa JohnJ.Stachel,BostonUniversity BaichunZhang,ChineseAcademyofScience Moreinformationaboutthisseriesathttp://www.springer.com/series/5710 Johannes Lenhard (cid:129) Martin Carrier Editors Mathematics as a Tool Tracing New Roles of Mathematics in the Sciences 123 Editors JohannesLenhard MartinCarrier DepartmentofPhilosophy DepartmentofPhilosophy BielefeldUniversity BielefeldUniversity Bielefeld,Germany Bielefeld,Germany ISSN0068-0346 ISSN2214-7942 (electronic) BostonStudiesinthePhilosophyandHistoryofScience ISBN978-3-319-54468-7 ISBN978-3-319-54469-4 (eBook) DOI10.1007/978-3-319-54469-4 LibraryofCongressControlNumber:2017936971 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Dedicated to Ann Johnson (1965–2016) This volume owes much to Ann. It synthesizes the work of the cooperation group “Mathematics as a Tool” that gathered over several years at the Center for Inter- disciplinary Research (ZiF), Bielefeld. The core group consisted of P. Blanchard, M.Carrier,J.Jost,andJ.Lenhard.Theypartlyactedasauthors;mostofthechapters are by scholars who were involved in workshops or other events organized by the ZiF group. Ann, who sadly passed away shortly before the book came out, was more than a brilliant participant in a workshop. She and her work have been an important source of inspiration for the entire group. Our joint work on the historyandphilosophyofmathematization,includingearlierworkshopsattheZiF, motivatedMartinCarrierandmyselftosetuptheZiFcooperationgroup. My own work owes much to Ann. We enjoyed an unusual collaboration that was based on the stunning experience of thinking on the same wavelength – notwithstanding our different characters and different disciplinary backgrounds. Wequicklyagreedhowhistory,technology,mathematics,andphilosophycouldbe mixedinfortunateways.Maybe,wewereratherthinkingonwavelengthsinterfering in a way that many crests and no troughs remained. It is a marvellous experience thatis,Ibelieve,veryrareinaresearcher’scareer. Annhadthegifttotransformpersistenteffortintoupliftfornewthought.Ihope this volume can achieve something similar. If one or another chapter makes the readerstartthinkingaboutwhatcouldbefruitfullytakenup,changed,andamplified, thisisprettymuchwhatAnnwouldhaveliked.Letuscarryoninherspirit. Bielefeld,Germany JohannesLenhard Bielefeld,Germany MartinCarrier v Contents Introduction:MathematicsasaTool .......................................... 1 JohannesLenhardandMartinCarrier PartI OrganizingScience RationalandEmpiricalCulturesofPrediction............................... 23 AnnJohnson MathematizationinSyntheticBiology:Analogies,Templates, andFictions....................................................................... 37 TarjaKnuuttilaandAndreaLoettgers Trigonometry,ConstructionbyStraightedgeandCompass, andtheAppliedMathematicsoftheAlmagest................................ 57 IdoYavetz ShapingMathematicsasaTool:TheSearchforaMathematical ModelforQuasi-crystals ........................................................ 69 HenrikKraghSørensen PartII ConceptualRe-evaluation Boon and Bane: On the Role of Adjustable Parameters inSimulationModels ............................................................ 93 HansHasseandJohannesLenhard SystemsBiologyintheLightofUncertainty:TheLimits ofComputation................................................................... 117 MilesMacLeod TheVindicationofComputerSimulations.................................... 137 NicolasFillion EmpiricalBayesasaTool....................................................... 157 AnoukBarberousse vii viii Contents PartIII ReflectionsontheToolCharacter OntheEpistemicandSocialFoundationsofMathematicsas ToolandInstrumentinObservatories,1793–1846........................... 177 DavidAubin ApproachingRealitybyIdealization:HowFluidResistance WasStudiedbyIdealFlowTheory............................................. 197 MichaelEckert IdealizationsinEmpiricalModeling........................................... 213 JulieJebeile ForcingOptimalityandBrandt’sPrinciple................................... 233 DomenicoNapoletani,MarcoPanza,andDanieleC.Struppa ObjectOrientedModelsvs.DataAnalysis–IsThistheRight Alternative?....................................................................... 253 JürgenJost Contributors DavidAubin Institut de mathématiques de Jussieu-Paris rive gauche (CNRS, Paris-Diderot,UPMC),SorbonneUniversités,Paris,France AnoukBarberousse UniversitéParis-Sorbonne,Paris,France MartinCarrier Department of Philosophy, Bielefeld University, Bielefeld, Ger- many MichaelEckert DeutschesMuseum,München,Germany NicolasFillion DepartmentofPhilosophy,SimonFraserUniversity,Burnaby,BC, Canada HansHasse Laboratory of Engineering Thermodynamics (LTD), University of Kaiserslautern,Kaiserslautern,Germany JulieJebeile IRFU/Service d’Astrophysique, CEA Paris-Saclay, Gif-sur-Yvette, France AnnJohnson Science and Technology Studies Department, Cornell University, Ithaca,NY,USA JürgenJost Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany SantaFeInstitute,NM,USA TarjaKnuuttila UniversityofSouthCarolina,Columbia,SC,USA UniversityofHelsinki,Helsinki,Finland JohannesLenhard Department of Philosophy, Bielefeld University, Bielefeld, Germany AndreaLoettgers UniversityofBern,Bern,Switzerland UniversityofGeneva,Genève,4,Switzerland ix x Contributors MilesMacLeod UniversityofTwente,Enschede,TheNetherlands DomenicoNapoletani University Honors Program and Institute for Quantum Studies,ChapmanUniversity,Orange,CA,USA MarcoPanza CNRS, IHPST (UMR 8590 of CNRS, University of Paris 1 Panthéon-Sorbonne),Paris,France ChapmanUniversity,Orange,CA,USA Henrik KraghSørensen Section for History and Philosophy of Science, Department of Science Education, University of Copenhagen, Copenhagen, Denmark Daniele C.Struppa Schmid College of Science and Technology, Chapman University,Orange,CA,USA IdoYavetz Cohn Institute for History and Philosophy of Science and Ideas, Tel AvivUniversity,TelAviv,Israel