Table Of ContentBoston 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
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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
