Introduction: The Empirical and the FormalTensions in Scientific Knowledge In thc early modem period when many researchers wcre proposing new approaches for investigating nature. [hey put (WO different goals in thc forefront: On the one hand, (hey argued for braad empirieal inquiries supponed by massive data collections, while on the mheT they highlightcd the ideal of a thorough rnathematical trcatment and establ ishing of formal structures. How these {wO strands were related, ir al all , was not so d earwhal they shared was essentiall y thc claim [0 overcome former, purponedly barren traditions and to creale new approaches. Indeed, even a brief look into thc early years or the Philosophieni Transacrions suggests that broad empirieal data gathering (claimed 10 be Baconian) and mathematical structure (as in the studics of the laws of collision, for cxample) had little 10 do with each other. The..-.e two charncteristics of modem science have been with us ever sinee. While the focus on empiriea! research juslifies our expeclation that the basic statements of science be realistic, the mathemalical structure aims at guaranleeing them a high degree of rigor and reliability. When Thomas Kuhn introduced his famous dichotomy between 'mathemariea\' and 'Baconian' sciences, he drew attention to a di sti nction that had been visible for many centuries. Although his dichotomy has to be ' taken with a pinch of salt'. historians of science tend 10 agree thaI scientific dcvelopments differ widely when il comes 10 the relationship betwecn the empirical and thc fonnal. There are scientific doma.ins in which the empirical side was always prevait ing. Natural history, for example, represents a type of scientific knowledge that consists of huge bodies of delailed informalion about specific things in all their variations. typically with the claim of being comprehensive for the empirical domain in question. In other cases, such as chemistry, such knowledge is even formulated in quantitative laws. And in general the empirica l approach is high!y apt for practical use. Recipes describing how to handle specific things can often bc easily extracled from this kind of knowledge. It is nOI by chance, therefore, that major pans of the knowledge of engineering traditions are of an cmpirical nature. At the same time, Ihere have also been branches of research in which highly formali zed, but less empirieal knowledge formed the eore. i.e. in which mathem:ttical structures have CENT"'UIWS '2008 : VOl. 50: PP. 2! 12!J; doi: 1O_lllllj.l600*!}.198_200H.OOI29..<e () 2008 Tht AUlhors_ Joomal ~'Q1l1vilauOII C 2(1()8 BlackweJl Munl~gllllrd . 212 F. Sleinle (md G. Scl!ir,mllllli dominated at the cost of the empirical details. and empirical re$uhs wou ld only be used and searched selectiveJy. Traditional rmilhematical domains. such as musical hamlOny or traditional oplics as weil as the ' rational mechanics' of the 18th century provide ill ustrative cages. More rccentl y [he dcvelopment of string thcory. ~md also general ~volulionary th~ory. could be considered domains that have developed a formali sm. while their relation to empirieal research remains ralher open. Howcver, such a dichotomie ullderstanding ofmodem seienee and its hislOry has its limitations. There have always been domains and episodes thaI do not fil illto the Kulm -type distinct ion, but in which the empirieal :md the fonna! were tightly interwoven in different ways. Ir is research of this nature thaI is the focus of this special issue. In the earty modern period (and, in facl. lhroughout ilS early history), astronomy provides a striking ease of how the empirieal may beeome integrat~d with Ihe formal. Kepler. for ex.ample. used a large bulk of empirieal data 10 fundamentally reform a highly deveJoped mathematical domain . And for any modern astronomer, it was dear that empirical protedures as ' simple. ' as the detennination ofthe position of a star with some preeision were impossible without advanccd formal toots. such as a theory of almosphcric rcfraetion . Thc very lask of datu gat.hering could not be fulfilled without usi ng elaborate formal toob thaI thcmselves were refined in Ihc proeess of obtaining data. To jump 10 more recent limes, cosmology prov ides anolher case. While for a long time it was a field wi th meagre empirieal grounding, but with a highly deve!opcd mathematical struclUre, it is now Iiving through aperiod in whieh large bodies of new empirieal data are being gathered, often of a kind previously unlhought-oL such as quasar data or Ihe variations in microwave background. Here the power of mathematical formali sm comes imo tension wilh the bulk of new empirical input. For a somewhat comrasting ease, one may think of modem moleeular geneties, a domain in whieh the amount of empirical datu, produee<l by seientific machinery, has reache<! Ihe poi m that the need ror formali zation has become. essential. Without powerful means of formal izalion (maybc cve.n mathematical slruclUres), mueh oflhe dala could easily jusl getiosl within an ocean of Dlhers, or become meaningless. So in this instance. it is the empiriea! overload that is driving lhe need for a more fOrmal approach. In aU these cases, the 'empirieal' nnd the 'fonnat ' nre very elosely interlinkcd. although in different ways. And while there havc always been studics of the relation bctween Ihcory and empirical data (from the induetion problem to lhe reeent diseussion of the ro te of models), Ihere have been hard ly any attempls W ponray and allalyze Ihe panorama of vari ous fonns of these eonstellations of elose interaction. This state of research is allthe more unsati sfactory sinee both in hislory and in present day science there are numeTOUS and imponant cases of such interlinked depcndencies of empirieal and fomm[ aspects. Hence a research group, centered in Wuppenal/Germany, took the initiative to address these queslions. [n June 2007, the authors of this introduction, together with Moritz Epple. HeimUl Pulte and Erhard Scholz. jointly organized a workshop that focussed. in an ex p!oratory manner, on a beller underslanding of the various fonns of such dense inreractions, Four (1 2008 The AUlhors. l o"mar compi!alion C "2(X)8 B!acl."welt Munksgaard. 213 of the papers from the workshop that addressed parlicutar historienl episodes are :lSsemb1ed in thi s specialissue. lWo scientific domains are in the forefront here: hydrodynamics und geomagneti sm. In both cases. the papers address a time span Ihat covers 'Significant changes. FOT hydroc\ynamics, Olivier Darrigol discusses (he relation with regard 10 the 18th century and clearly shows the wide gutf betwecn the theoretical approaches and the empirical dal:!. [n order 10 aceount for punclual points of contact, he proposes the analytic notion of modularity. When Michael Ecker! Ihen presents the development ofwind tunnels in the 20th century, we see, by contrasI, a very elose intertwining or lhe processes uscd for obtaining dala and those needed for developing rnathematical structures that allow data handling, und which can even gtJide thc scarch for further data. A similar [(ansition from a wide gulf to elose intcrtwining becomes visible in the ease of geomagnetism. Art Jonkers analyses thc processes of dala gathering and theorizing in the 17th and 18th eenturies und finds that, in many eases, they were separate. However, he makes us aware that lalking of theorizing in general is too eoarse: the historieal case shows different types of theoretieal activilies that may weil huve different relations to the process of dutu-gathcring. Looking at [he 19th century, by contras!. Gregory Good prescnts a different scenario, with theoretical und empirieal aetivities beiog most cJoscly inlertwined , somelimes evcn politieally org:mized. In both fields we see the relation between empirieal and mathematical activities significantly changi ng around the [um of the 19th ce ntury, with their mutual depcndency drastically increasing. 11lis does nOi only lead 10 quest ions of how these changes ean be charaelerized in detail , but also of wh,l( made thern t.leveJop around roughly tbe same time-questions thllt can only be answered by further research. Moreover, it would be in* leresling to see 10 what degree a distinclion between various types oftheorizing, as we see in thc. geoll1agnclic casc. can also be found in lhe cases of hydroteehnics and hydrodynamics: for example, we do not yet know mucb about (he practitioners' way of concepruali zing and theoriz.ing Iheir problems. The four papers that make up Ihis special issue of Centall/"llS allempI, bolh individually and as a whole, 10 illustrate the variety of ways in wh ich the empirieal and Ihe fonna] may becomc intertwined. as weil as showing the richness of the research questions Ihal can reSult fro m this kind of nondichotomie consideration. Friedrich SlejT/fe mrd Gregor Schiemal1n University of Wuppertal, Gennany f,t 2U()8 Tlic Authors. Journal COrl1pilBtion 02008 ßlaüwclt MunksgaMd The Official Journal 01 Ihe European Sociely for the History of Science www.blackwellpublishing.com/ cnt