Kathryn M. Olesko *
Tacit Knowledge and School Formation
2nd Series, Volume 8
ALL SCHOOLS have pedagogic elements. The intellectual and investigative cohesiveness of a school is achieved by different avenues; all involve some form of training. Although possessing individual scientific styles, members of a school have learned, to a greater or lesser degree, to think and practice in like-minded ways. This holds for both main types of scientific schools: the research schools that have been at the center of historical inquiry for some time, and the more traditional schools associated initially with master-pupil relationships and later with more formal educational settings that only recently have attracted historical attention. Schools at centers of learning or institutions of higher education often exist by virtue of strong and well-defined training programs that successfully convey distinctive methods of scientific practice and judgment capable of distinguishing their participants from other investigators in the same discipline. Research schools, in contrast, often rely on more informal means of normalizing the investigative practices and mental habits of its members; apprenticeship under or imitation of older members, collaboration with peers, assistantships in research, and internal works-in-progress sessions are but a few of the social means whereby practitioners learn to be like one another. Creating a certain number of commonalities and sustaining them above a critical threshold are so important in a school that schools can neither form nor continue to exist without some mechanisms for instruction and reinstruction.
A key process in forming a school is transmitting craft skills of investigation from colleague to colleague, from master to pupil. Until recently, the process of skill transmission was notoriously ill defined, understood as one that took place largely unconsciously, by imitation, experience, emulation. This received understanding - based more on presumption and intuition than on actual empirical studies, either historical or sociological, of science pedagogy - shrouded the acquisition of skills in secrecy by classifying it as tacit knowledge: inarticulable and therefore invisible to the historical eye. Recently, however, historical studies of science pedagogy have suggested that the domain of tacit knowledge may be considerably smaller than hitherto assumed; while sociological studies of skill acquisition have argued that an element of tacitness remains in laboratory techniques even as they are rationalized and codified, and furthermore that this tacitness is desirable for the production of innovation.  The historical and socio-
* Department of History, Georgetown University, Washington, D.C. 20057-1058.
1. For historical studies see, e.g., Graeme Gooday, “Precision Measurement and the Genesis of Physics Teaching Laboratories in Victorian Britain,” British Journal for the History of Science, 1990, 23:25-51; and Kathryn M. Olesko, Physics as a Calling: Discipline and Practice in the Konigsberg [Seminar for Physics (Ithaca, N.Y./London: Cornell Univ. Press, 1991) (neither Gooday nor I explicitly address the nature of tacit knowledge). For sociological studies see Kathleen Jordan and Michael Lynch, “The Sociology of a Genetic Engineering Technique: Ritual and Rationality in the Performance of the ‘Plasmid Prep,’” in The Right Tools for the Job: At Work in Twentieth-Century Life Sciences, ed. Adele E. Clarke and Joan H. Fujimura (Princeton, N.J.: Princeton Univ. Press, 1992); and Jordan and Lynch, “The Mainstreaming of a Molecular Biological Tool: A Case Study of a New Technique,” in A Sociology of a New Technology, ed. Graham Button (London: Routledge & Kegan Paul, in press).]
HHC: [bracketed] displayed on page 18 of original.
logical approaches to skill acquisition do not contradict one another; for historical studies of science pedagogy have not argued that all of scientific practice is codified, only that a considerable portion of it is, including parts of those areas formerly thought most immune to explicit codification, such as data analysis.
Tacit knowledge is thus a strategic historiographic locus for understanding school formation. So is its opposite, explicit knowledge. Sociologists of science use a variety of terms to designate knowledge and skills that are explicit, including rationalized, codified, coherent, standardized, routine, “ready-made,” and stabilized. Explicit techniques and knowledge are articulable and generally exhibit great similarity from practitioner to practitioner. Both tacit and explicit knowledge explain how behavior is constrained in a scientific school; these constraints shape the identity of the school. The purpose of this essay is twofold: first, to raise questions about how historians have hitherto viewed skill and knowledge acquisition in school formation; and second, to suggest ways in which the pedagogic element in school formation can be reexamined so as to recast the role of tacit and explicit knowledge and practices in it.
Historians of scientific schools have acknowledged the pedagogic element in them. Gerald L. Geison’s influential and oft-quoted definition of a scientific school incorporates its function as an agent of advanced instruction. He defines a school as “small groups of mature scientists pursuing a reasonably coherent program of research side-by-side with advanced students in the same institutional context and engaging in direct, continuous social and intellectual interaction.” Geison furthermore emphasizes that a director must help new recruits make the transition “from learning to independent research.” Jerome Ravetz assigns a strong causal role to the pedagogic element in school formation: “The character of scientific work done by the graduates of different sorts of research schools will inevitably reflect their training.”  Marxist historiography of scientific schools, with its greater sensitivity to the fine distinctions that must be made when discussing the social organizations of modern society, assigns a prominent role to the pedagogic element. In a volume on scientific schools that has been influential in eastern European literature but is only now entering the West, Valerij Borisoviè Gasilov lists, as the first of thirty-five definitions of a scientific school, “a method or a system of teaching, instruction, diffusion of knowledge, transmission of knowledge, from teacher to pupil.” In the same volume A. M. Cukerman warns,
2. Gerald L. Geison, “Scientific Change, Emerging Specialties, and Research Schools,” History of Science, 1981, 9:20-40, on p.23 (emphasis added); and Jerome R. Ravetz, Scientific Knowledge and Its Social Problems (New York: Oxford Univ. Press, 1971), p. 100 (emphasis added).
though, that “the idea of a scientific school cannot be reduced to a purely formal teacher-pupil relationship” because of the wide variation in how students absorb and apply what is taught. But he still admits that it must have an educative function if it is to transmit a director’s “way of thinking.” 
Empirical studies of research schools have generally considered active engagement in research to be the means whereby the craft skills of investigation, especially experimental investigation, are transmitted. Hence Geison identifies as Michael Foster’s “single most important contribution” to the formation of the Cambridge school of physiology “his steadfast care and feeding of the research ethos,” which Foster accomplished by teaching an evolutionary approach to physiological phenomena and by transmitting by example certain tools and methods, all suited for treating problems linked to his study of the heartbeat, which became the center of gravity of the school’s investigations. In his study of the Munich school of metabolism, Frederic L. Holmes views the school’s formation largely through the contours of the research programs and the visions of its leaders; thus, “participation of the younger members in the research activity” of the school’s leader became simultaneously “training for future independent work.”  Other similar examples could be cited.  To date the literature on research schools has in general emphasized the dominant qualities of a director’s research style as the principal resource of the school’s craft skills of investigation, which are learned largely by imitation and experience.
But how, exactly, does that imitation and experience occur? The exact process is never fully articulated, although the factors facilitating imitation and experience are. Factors such as effective leadership, a well-equipped laboratory, and an environment conducive to early participation in research figure prominently in such descriptions. This lacuna is less the result of the lack of suitable source materials, it seems, than of the powerful (and often unacknowledged) influence upon historical analysis of certain older sociological and philosophical approaches to how scientists learn the art of investigation. Here Michael Polanyi’s notion of tacit knowledge has exerted considerable influence, despite the debatable nature of his evidence (he draws less upon the history or practice of science than upon other social and cultural activities, such as music and sport) and despite his at-times unconvincing style of presentation (key definitions are sometimes presented as tautologies).
3. Valerij Borisovië Gasilov, “Analyse der Interpretation des Terminus ‘wissenschaftliche Schule,’” in Wissenschaflliche Schulen, 2 vols., ed. Semem R. Mikulinsky et al. (Berlin: Akademie-Verlag, 1977-1979), Vol. I, pp. 291-321, on p. 294; and A. M. Cukerman, “Die Denkweise des Leiters - Ein bestimmender Faktor für die Bildung einer wissenschaftlichen Schulen,” ibid., pp. 429-436, on p. 429.
4. Gerald L. Geison, Michael Foster and the Cambridge School of Physiology: The Scientific Enterprise in Late Victorian Society (Princeton, N. J.: Princeton Univ. Press, 1978), p. 359 (see also pp. 224-235); and Frederic L. Holmes, “The Formation of the Munich School of Metabolism,” in The Investigative Enterprise: Experimental Physiology in Nineteenth-Century Medicine, ed. William Coleman and Holmes (Berkeley/Los Angeles: Univ. California Press, 1988), pp. 179-2 10, esp. pp. 180 (quotation), 202-206.
5. See, e.g., Leo J. Klosterman, “A Research School of Chemistry in the Nineteenth Century: Jean Baptiste Dumas and his Research Students,” Annals of Science, 1985, 42:1-40 (Part 1), 41-80 (Part II), esp. pp. 6-7, 21, 29; and James A. Secord, “The Geological Survey of Great Britain as a Research School, 1839-1855,” History of Science, 1986, 24:223-275, esp. p. 262 (although the pedagogic element is not as prominent in this school as in the others mentioned).
Polanyi’s fundamental premise is that scientists engaged in investigation, especially of the experimental sort, act according to rules that are only partially specifiable. Language, according to Polanyi, does not possess the power to articulate all that a scientist learns or does; “Rules of art can be useful,” he claims, “but they do not determine the practice of an art; they are maxims which can serve as a guide to an art only if they can be integrated in the practical knowledge of the art.” Polanyi’s belief that the craft skills of science are tacitly learned and known and largely inarticulable has had profound consequences in the study of skill learning, including in scientific schools, because it has often prefigured the historiographic categories used for thinking through such studies. Polanyi writes that “an art which cannot be specified in detail cannot be transmitted by prescription, since no prescription for it exists. It can be passed on only by example from master to apprentice. This restricts the range of diffusion to that of personal contacts, and we find accordingly that craftsmanship tends to survive in closely circumscribed local traditions.”  Within Polanyi’s framework the way in which the craftwork of science has been approached in the empirical study of scientific schools - by focusing on the research style of the master or leader - obtains its methodological justification.
Polanyi’s ideas and their methodological implications find expression in the writings of other seminal thinkers. Ludwik Fleck’s Genesis and Development of a Scientific Fact, not well known in the West until after the publication of Polanyi’s book, also supported the notion that the “technical skills required for any scientific investigation” cannot be “formulated in terms of logic.”  In an important and influential chapter, “Science as Craftsman’s Work,” Ravetz too asserts that the craft work of science is inaccessible, tacit, and unconscious, and hence incapable of being “specified in a formal account” and unable to surpass the simplest level of description. His ideas display an uncanny similarity to Polanyi’s: he believes that tacit knowledge of craft skills is transmitted “largely through the close personal association of master and pupil”; that it is “learned entirely by imitation and experience” but perhaps “without any awareness”; and that it is an important element in the creation of scientific schools.  It has been largely Ravetz’s discussion of tacit knowledge that has inspired historians to identify it as a subject worthy of investigation, despite its presumed unspecifiable character. Martin Rudwick has called for historians “to recover what... a network of individuals held tacitly in common.” Pertinent to present concerns, Geison has suggested that schools could be used fruitfully to understand “the transmission of ‘tacit’ knowledge in the actual ‘craft’ of science.” 
Despite the optimism of Rudwick and Geison, Polanyi’s philosophy of tacit knowledge qua historiographic strategy is in several respects problematic. The goal of scientific practice is creativity; yet Polanyi maintains that the learning of
6. Michael Polanyi, Personal Knowledge: Towards a Post-Critical Philosophy (Chicago: Univ. Chicago Press, 1958), pp. 50 (see also pp. 49, 53-63), 53.
7. Ludwik Fleck, Genesis and Development of a Scientific Fact, trans. Fred Bradley and Thaddeus J. Trenn (Chicago: Univ. Chicago Press, 1979), p. 35.
8. Ravetz, Scientific Knowledge (cit. n. 2), pp. 75, 76, 102-106, quoting from pp. 75, 103.
9. Martin J. S. Rudwick, The Great Devonian Controversy: The Shaping of Scientific Knowledge Among Gentlemanly Specialists (Chicago: Univ. Chicago Press, 1985), p. 10; and Geison, “Scientific Change” (cit. n. 2), p. 36.
craft skills necessitates the denial of the self in favor of submission to authority. “To learn by example,” he writes, “is to submit to authority.”  Polanyi’s scientist works, paradoxically, entirely within tradition. Polanyi’s insistence on the unconscious and inarticulate nature of craft skills denies the possibility that scientists or even novices can examine their thinking and practice in consciously critical and self-reflexive ways, and thus strips them of one of the most powerful mental techniques that Western intellectuals have exercised since the Reformation. Ravetz, in contrast, recognizes that there must be a balance between blind indoctrination and the cultivation of a critical perspective, but he still acknowledges that learning the craft skills of science is largely a conservative process.  The relatively closed nature of tacit knowledge is also apparent in sociological studies of craft skills. Although acknowledging that skills must be rationalized to a certain extent to be learned - thereby placing skills and knowledge in an arena where changes and permutations could occur - such studies still make local styles a matter of learning tacitly the inarticulable techniques that others already know. 
The broader historiographic implications of tacit knowledge - not in what it implies should be investigated, but in what cannot be examined under its aegis - are most problematic and troublesome. The presumed inarticulable nature of the tacit knowledge of craft skills helped to ground the historical view of school formation (and even more generally of scientific practice and initiation into it) in mystery and secrecy, so that historians depict the school as operating much like an early modern guild. This view of tacit knowledge became a framework for historical investigation and interpretation: it determined beforehand how the crucial intellectual and social processes of skill, knowledge, and even value acquisition were configured. School formation in particular came to be viewed as dependent upon a limited number of readily explicit factors, such as the research style of a school’s leader. A low priority was assigned to examining in fine detail such matters as the means by which school members learned from one another or, in the case of educationally based scientific schools, even the content of science courses and laboratory exercises that helped shape school members to begin with; for the skills and values of scientific practice were presumed unspecifiable. Thus the actual mechanisms for acquiring skills and values central to the formation of a school fell outside the domain of direct historical investigation. Labeled tacit a priori, the process of acquiring craft skills and their values, as it took place in the school, remained invisible to the historical eye.
Despite the existence of pertinent sources, little has been done to specify what must be tacitly learned and what can be acquired by more explicit or formal means, especially in the pedagogic settings in which schools sometimes took hold. Ravetz does cite “pitfalls” - places where the investigative procedure could go especially wrong - as a special instance where instruction in laboratory exercises must be explicitly given. He seems, however, to consider this an unusual instance of articulation because he drew attention to the fact “that the formal training of scientists has generally been carried on without any recognition of the craft character of scientific work.” “Explicit precepts,” Ravetz warns, “are insufficient,”
10. Polanyi, Personal Knowledge (cit. n. 6), p. 53.
11. Ravetz, Scientific Knowledge (cit. n. 2), p. 96.
12. See, e.g., Jordan and Lynch, “Sociology of a Genetic Engineering Technique” (cit. n. 1).
useful “only in the context of the solution of sophisticated technical problems.”  Recent sociological studies have not gone much further, identifying explicit precepts with routine practices, tacit ones with the “secrets” of performing a practice correctly. 
In general, assuming that craft skills are a form of tacit knowledge foreclosed even studying both the abstract body of knowledge and practical exercises that constituted science education, including the pedagogic element in school formation, and the sources (such as lecture and laboratory exercise notebooks of students, assistants, and professors) that could assist both in differentiating tacit and explicit knowledge and in defining the realm over which the latter rules. These are challenging issues in the study of scientific schools, not only because a deeper study of science teaching and learning could diminish the realm of the tacit, but also because if it is found that what is taught does not fully coincide with the dominant themes, topics, and techniques of a leader’s research, the entire historiographic tradition of defining the pedagogic element of a school primarily in terms of the imitation and adaptation of the research example set by its leader could collapse.
Teaching and its relationship to research have not, however, been ignored in the literature on scientific schools. The way in which Michael Foster assembled physiological knowledge for teaching, by assigning a prominent role to evolutionary principles, influenced the research work of his students. Frederic L. Holmes has examined the near fusion of teaching and research in Justus Liebig’s Giessen laboratory, where a well-known school of chemistry took shape. In the Konigsberg seminar for physics, where by several contemporary accounts a school of physics took shape, a minor technique in Franz Neumann’s research - exact experiment and the determination of constant and accidental errors - became a dominant theme in his science pedagogy, which strongly influenced the protocol and style of his students’ investigations.  In each of these cases, however, it was not primarily research but rather teaching that shaped the character of the school. Foster actually published little; Liebig’s early laboratory did not have as strong ties to his research as did his later laboratory; and what Neumann’s students considered indispensable techniques in physical investigation were not readily apparent in Neumann’s research.
As these examples and several others in this volume amply testify, leading centers of science education in nineteenth-century Germany are strategic and rich cases for reexamining the role of tacit knowledge in school formation. The eighteenth-century German university generally lacked the institutional conditions for close social and intellectual interaction between professors and students because lecture courses dominated university learning. Although new pedagogic techniques, such as exercises that applied what had been learned, appeared by the end of the century, classes were by and large run in traditional ways. In the
13. Ravetz, Scientific Knowledge, pp. 102, 99, 102, 103 (emphasis added).
14. Jordan and Lynch, “Sociology of a Genetic Engineering Technique.”
15. Geison, Michael Foster (cit. n. 4); Frederic L. Holmes, “The Complementarity of Teaching and Research in Liebig’s Laboratory,” Osiris, 1989, 5:121-164; and Olesko, Physics as a Calling(cit. n. 1).
early nineteenth century new pedagogic methods and new forums for learning science - exercise sessions, seminars, teaching laboratories, and, by the end of the century, full-fledged institutes - fostered such strong cognitive and affective bonds between professors and students that distinctive styles of scientific practice became associated with local settings. About one of those new forums for teaching and learning, the seminar, Wilhelm Schrader wrote that it allowed for the continuity of leadership that produced a clearly defined work discipline (Arbeitszucht) and a solid working tradition (Arbeitsüberlieferung).  The close personal relationship resulting from such bonding is evident in the moving affective language used in correspondence, in the mythical stories and mystical images that grew up around educational experiences, in the indistinct boundary between the public institutional space of education and the private domestic sphere of the professor’s home life, and in the ease with which moral qualities became affixed to the performance of scientific work.
The intellectual bonding that took shape in these forums depended on a strong pedagogic element that eventuated in shared characteristics of scientific thinking and practice. The complicated and creative nature of pedagogic activity in the natural sciences at the beginning of the nineteenth century made these new and intimate forums ideal breeding grounds for schools. The novelty of schools is apparent in the lexicon entries Schule and wissenschafiliche Schule from the first half of the century.  At that time natural philosophers were working out the pedagogic definition of the scientific disciplines; students were collaborators in that process, making known what worked in the classroom and what did not. The distinct identity of schools was aided by the insular nature of these new forums where well-defined curricula - local pedagogic definitions of the natural sciences - took shape. Students learned to apply scientific methods in practical exercises. These exercises as well as the proto-investigations based on them helped to shape the students’ identities as scientific practitioners, to create a sense of community among them, and to form schools whose intellectual coherence and cohesiveness largely resulted from the efficacy of science pedagogy.
Because teaching and research coexisted in the German university - and were equally strong - the meaning of the term school took several forms in German settings in the nineteenth century. At one end of the spectrum were research schools of the type created by Justus Liebig at Giessen in chemistry, by Carl Ludwig at Leipzig in physiology, by Wilhelm Wundt at Leipzig in psychology, and by August Böckh at Berlin in philology. Each of these schools had strong, distinctive, and innovative programs of instruction, but their distinguishing mark was the outstanding research productivity of their members.
Yet the term school was also used to describe educational settings where little research was done but where intense systematic teaching, often culminating in no more than organized practical exercises that broke down the elements of research methodologies into smaller problems, took place. Hence the physicist Gustav Kirchhoff could claim that as a result of his cooperation with the mathematician
16. Wilhelm Schrader, “Ueber akademische Seminare,” Lehrproben und Lehrgange aus der Praxis der Gymnasien undRealschulen, 1899, 60: 1-19, on p. 18.
17. C. Friedrich, “Wissenschaftliche Schule in der Pharmacie: Teil I,” Pharmacie, 1988, 43:274-277, on p. 274.
Leo Koenigsberger as codirector of Heidelberg University’s mathematico-physical seminar in the brief period between 1870 and 1874, “a mathematico-physical school has been built at our university, which is our pride and joy.”  That there are no other references to a school of physics at Heidelberg does not diminish the importance of Kirchhoff’s remark, which underscores the fact that special educational settings, such as the seminar, gave rise to schools whose origins and constitution we as historians have still insufficiently examined. Schools were also viewed in more personal terms, as desirable professional accomplishments, even before the goals of recent institutional and pedagogic reforms had been completely realized. The mathematician Carl Jacobi, anxious to trade his position at Konigsberg for another, wrote to the Prussian minister of education in 1835 that he wanted to go to Bonn University, where he believed that he could found a school.  Significantly, the strength of Jacobi’s school - at Konigsberg, after all, not Bonn - was partially founded on his teaching, which he used as a vehicle for working through his research interests.
As Alan Rocke emphasizes in his article on Hermann Kolbe’s school of chemistry in this volume, the power of science pedagogy to produce strong intellectual bonding should not be underestimated. Rocke’s description of Kolbe’s teaching and leadership at Marburg and Leipzig illustrates the factors that shape schools in educational settings: close personal contact between professors and students; the relaxation, periodically at least, of lines of intellectual authority between professors and students; a strong emphasis on practical laboratory work, completed in a graduated fashion; the assistance of the guiding hand of a master, but also the sense that independence is cultivated; self-instruction and even the articulation by the student of the techniques guiding scientific practice; and finally the explicit portrayal of steps in an investigative procedure. Schools based at educational institutes, such as Kolbe’s, inculcated techniques, values, and styles of interpretation and judgment until they became overriding precepts guiding scientific investigation, shaping the student’s image of scientific knowledge. At the advanced level, in research, a strong belief in a school’s techniques and ideas could lead to bitter controversy, as Steven Turner demonstrates for the case of the Helmholtz-Hering exchange over visual perception. But even before the upper levels of scientific practice were reached, the distinctive character of a school could guide behavior in unusual ways.
The application of what was learned could be taken to extremes. Ravetz, for instance, discusses the case of a student in Wilhelm Wundt’s Leipzig institute who doctored his data so as not to contradict the expectations of Wundt’s school. Robert Frank notes how crestfallen Carl Ludwig was when a student in his Leipzig physiological institute, realizing the effect of a disturbance in his apparatus, reversed his conclusion (which had been achieved initially by “rigging” the apparatus) so that it no longer supported Ludwig’s views.  It was difficult to extract oneself from such influence and bonding. In turning down Franz Neumann’s
18. Gustav Kirchhoff to Emil du Bois-Reymond, 27 Sept. 1874, quoted in Emil Warburg, “Zur Erinnerung an Gustav Kirchhoff,” Die Naturwissenschaften, 1925, 13:205-212, on p. 211.
19. Leo Koenigsberger, Carl Gustav Jacob Jacobi (Leipzig: Teubner, 1904), pp. 173-174.
20. Ravetz, Scientific Knowledge (cit. n. 2), pp. 96n-97n; and Robert G. Frank, Jr., “American Physiologists in German Laboratories, 1865-1914,” in Physiology in the American Context, 1850-1940, ed. Gerald L. Geison (Bethesda, Md.: American Physiological Society, 1987), pp. 11-46, on p. 35.
invitation to habilitate in physics at Konigsberg in 1861, Oskar Emil Meyer couched his decline in missionary terms. “Since the beginning of your instruction,” he explained, “I was guided by the notion that I would be trained as an apostle of your gospel in the world. I cannot give that up now because you have appointed me deacon of your congregation.” With embarrassment Meyer admitted that had he gone to Konigsberg he would only have been able to lecture from notes he had taken in Neumann’s courses. Yet buried deep in his letter was also a fear that, had he gone to Königsberg, “evil” people would say that he could not do anything without first seeking Neumann’s advice.  Like the students of Wundt and Ludwig, Neumann’s exhibited a distinctive investigative style. But that style’s dependency upon strictly tacit knowledge is debatable; for in these examples, as well as those taken from other German schools, students could, if pressed, self-consciously call upon the skills and values that defined the school by referring back to the educational experiences, elementary or advanced, that had shaped them. 
Strong instructional programs, however, did not always lead to school formation. For example, by all accounts Robert Bunsen had an extremely good program of instruction at Heidelberg, was an effective and inspiring teacher (especially in conveying the craft skills of chemistry), and supervised dozens of research projects undertaken by students in his laboratory, many of which were published. Yet contemporary observers did not identify Bunsen as having established a school. As to why, it appears that the methods and problems undertaken at Heidelberg were just not sufficiently distinct enough from those elsewhere in Germany to justify the epithet “school,” the identity of which rests at least in part on perceived differences between its practices and those elsewhere. One might therefore ask of Bunsen’s program whether the generalization or broad appeal of the skills it conveyed vitiated school formation. The intellectual profile of Bunsen’s example and other similar negative cases demands deeper historical examination in order to enhance our understanding of the pedagogic element in the formation and character of schools.
Of special interest to the history of schools and the role of the pedagogic element and tacit knowledge in them are German schools of physics in the nineteenth century. When he took over the editorship of the prestigious Annalen der Physik in 1890, Gustav Wiedemann identified three schools that had shaped German physics in the middle decades of the nineteenth century Wiedemann used the term “school” in a broad sense, meaning something akin to “school of thought,” but one with a permanent institutional base, a distinct investigative style (especially in the use of quantitative techniques), and a coherent instructional program. The first school, centered at Berlin University under Gustav Magnus, was largely experimental in character and drew its conceptual and methodological inspiration from chemistry. The second and third combined mathematical and experimental
21. Oskar Emil Meyer to Franz Neumann, 21 Nov. 1861, Franz Neumann Nachlass, 53.IIA: Briefe von Schülern, Niedersächsische Staats- und Universitätsbibliothek, Handschriftenabteilung.
22. See Olesko, Physics as a Calling (cit. n. 1), for examples of the affective bonding between Neumann and his students and of the characteristics of this school’s style.
methods and were more strongly influenced by the exact experimental methods of astronomy. These schools appeared at Gottingen University under Wilhelm Weber and at Konigsberg University under Franz Neumann. Of the two, Wiedemann viewed the Konigsberg school of physics as having cultivated a stronger mathematical orientation. 
The demographic constitution of these German schools of physics cannot be defined as rigorously as that of research schools because instruction was the primary function of the institutes associated with each school, and hence research productivity alone cannot be used as a reliable guide to either membership in or the identity of the school. In broad terms, however, the most productive school was Magnus’s, where from the 1840s to 1870 some eighty investigations issued from his Berlin laboratory; before 1870 student publication at Gottingen and Konigsberg combined did not equal that at Berlin.  Although Weber’s and Neumann’s research interests and styles were resources for the courses and practica each offered, at neither location was physics instruction completely dominated by the dictates of a research agenda. The schools at Gottingen and Konigsberg created their identities not from research but from teaching programs, and specifically from that part of their teaching that concerned quantification.
At Konigsberg and Gottingen, especially at the latter, the large domain of explicit knowledge passed on to students lay in instructional programs in exact experimental physics, particularly in areas that Polanyi and Ravetz consider to be most immune to articulation and explicit codification, and therefore to constitute a hard core of tacit knowledge: techniques of measurement and data analysis, including the values and judgments exercised in their use. The process of going from instrument readings to the magnitudes that appear in formulas, Polanyi argues, “rests on an estimate of observational errors which cannot be definitely prescribed by a rule.” Tacit knowledge, according to Polanyi, guides the scientist in computing those errors in order to move from experiment to theory. But, because “no strict relationship” exists between measured and reduced data, the process of data reduction, Polanyi argues, “remains... indeterminate.”  Ravetz too views data analysis as a craft skill, but one much more intricate: “The simple judgment of the ‘soundness’ of data is a microcosm of the complex of accumulated social experience and judgments which go into scientific endeavor.” Hence the well-known and common phenomenon of apparently similar sets of data being accepted by one researcher yet rejected by someone in the same field but from a different school, using different techniques. Craft knowledge is in Ravetz’s view
23. Gustav Wiedemann, “Vorwort,” Annalen der Physik, 1890, 39:ix-xii, on pp. x-xi, esp. p. xi. Wiedemann’s delineation of schools was confirmed by other contemporary observers, and not only those who had affiliations with either of these schools. See e.g., C. Voit, “Franz Ernst Neumann,” Sitzungsberichte der math.-physikal. Classe der k. b. Akademie der Wissenschaften zu München, 1896, 26:338—343, on p. 339.
24. A. W. Hoffmann, “Zur Erinnerung an Gustav Magnus,” Berichte der Deutschen Chemischen Gesellschaft, 1870, 3:993-1101, on pp. 1099-1101. Additional investigations not mentioned by Hoffmann are cited in A. Guttstadt, Die Anstalten der Stadt Berlin für die öffentliche Gesundheitspflege undflir den naturwissenschafllichen Unterricht: Festschrift dargeboten den Mit gliedern der Versammlung Deutschen Naturforscher und Aerzte von den städtischen Behörden (Berlin: Stuhr, 1886), p. 140.
25. Polanyi, Personal Knowledge (cit. n. 6), p. 19. See also his discussion of spurious results (p. 53) and self-regulating instruments (p. 20).
even needed to decide “which sort of functional relation is represented by the discrete set of points” obtained through measurement, thus making the graphical analysis of data a matter of deploying techniques and judgments tacitly learned. 
The cases of Gottingen and Konigsberg indicate, however, that not only was data and error analysis more explicit at these locations than either Polanyi or Ravetz would seem to allow, but also that styles in data and error analysis differentiated practitioners, including novices, in each school. Owing to the richness and variety of its sources, including notebooks of practical measuring problems assigned to students, Göttingen’s program is especially revealing of the ways in which esoteric techniques were made explicit not only for instructional purposes, but also for actual research in physics.  For the most part, professors directed practical laboratory exercises; but they also allowed advanced students to teach beginners, thereby weakening the strict hierarchy customarily associated with German institutes. Weber modeled Gottingen’s practical measuring exercises, at both the beginning and the advanced levels, largely on his and Carl Friedrich Gauss’s geomagnetic research, which strongly shaped the Gottingen organization, style, and approach for decades. 
The type of measurement in Gottingen’s exercises was one in which precision was achieved largely through the perfection of instruments, as had been done in the geomagnetic work. Trials were generally thin; corrections for errors were embodied in instruments; and precision was described in terms like “a truly mathematical precision,” “a microscopic precision,” and “a precision that leaves nothing to be desired.”  What Polanyi, Ravetz, and others considered the prime example of tacit knowledge - techniques of measurement and data analysis - was made explicit in instruction. Student notebooks indicate that instructors delineated how instruments and their errors should be handled. A key term was reliability. To call an instrument reliable meant that the instrument had been perfected as much as possible so as to minimize the analytic computation of costant (or systematic) errors. All corrections were thus, in a sense, embodied in the material perfection of the instrument so that the measurements in themselves, before being worked over, possessed a “fineness” (Feinheit) they might not have had
26. Ravetz, Scientific Knowledge (cit. n. 2), pp. 76-77, 8 1-84, 88-91, 93, quoting from pp. 82, 84.
27. These sources include reports for the Göttingen mathematico-physical seminar, where most of the practical exercises were held, student notebooks from the seminar, and Friedrich Kohlrausch’s instructional notebooks, which include exercises and student assignments kept while he was the assistant for practical exercises between 1866 and 1870. See Königliches Universitäts-Curatorium zu Göttingen, Akten betr. die Einrichtung eines mathematisch-physikalischen Seminars (1850-1883), Universitätsarchiv Göttingen, 4/Vh/20; Wilhelm Weber Nachlalss, Nr. 21: Seminar-Vorlesungen in Nachschrift v. K. Hattendorif, and Hermann Wagner Nachlass, Nr. 6: Vorträge von Wilhelm Weber über verschiedene Gegenstände der mathematischen Physik, gehalten im physikalischen Seminar der Georgia Augusta, 1860-63, both in Niedersächsische Staats- und Universitätsbibliothek, Handschriftenabteilung; and Friedrich Kohlrausch, Tagesbücher Nrs. 2500 and 2601, Sondersammiungen, Deutsches Museum, Munich.
28. Wilhelm Weber to Colonel Sabine, 20 Feb. 1845, rpt. in Wilhelm Weber’s Werke, 6 vols., ed. Königliche Gesellschaft der Wissenschaften zu Gottingen (Berlin: J. Springer, 1892-1894), Vol. II, pp. 274—276; and reports of the Göttingen mathematico-physical seminar, 1850-1870, Universitäts-archiv Göttingen, 4/Vh/20.
29. See such sources as the Göttingen seminar reports; C. F Gauss to Wilhelm Olbers, 2 Aug. 1832, C. F. Gauss Nachlalss, Niedersächsische Staats- und Universitätsbibliothek, Handschriftenabteilung; and especially the remarks about precision and accuracy made in Resultate aus den Beobachtungen des magnetischen Vereins im Jahre 1836-41, 6 vols., ed. C. F Gauss and W. Weber (Göttingen: Dieterich, 1837—1838; Leipzig: Weidemann, 1839-1843).
if less attention had been paid to refining instruments. Possessing such faith in their data, students more easily represented it in idealized images, such as maps or graphs, much in the same way that Gauss and Weber had used in their geomagnetic results. For the crucial area of data analysis, notebooks indicate that Weber instructed students to deal with “outliers” in a way consistent with the instrument-orientation of his exercises. In cases where the instrument was not yet properly calibrated (initial measurements) or where the calibration wore off (final measurements), students were told to eliminate data. Good data was thus tied to the perfect operating state of the instrument. 
It may seem self-evident that outliers should be eliminated, but it was not. Exercises that placed a higher value on the analytic determination of accidental errors by the method of least squares, such as those at Konigsberg, taught students to retain all (or almost all) data. Hence at Konigsberg precision was tied to the probability assessments in the method of least squares; results based on observations were believed not to possess mathematical certainty; and the analytic determination of both constant and accidental errors, not the perfection of instruments, was regarded as the best way to purify data.  Students at Gottingen, by contrast, questioned the ability of least squares to account for errors in the data. The material or instrument-oriented approach to data practiced at Gottingen was enhanced by keeping practical applications in view in laboratory exercises, a custom not observed at Konigsberg.  The practical purposes of the Gottingen exercises meant that an exact analysis of the data itself was less useful, because when a useful result was needed quickly, one just did not have the time to engage in elaborate and complex computations like those required in least squares. Gottingen’s pragmatic program of physics instruction thus remained relatively immune to the excessive skepticism concerning data and theory construction that was, at times, so crippling at Konigsberg.
That Wiedemann and others could identify a school at Gottingen only for the middle decades of the nineteenth century is significant. Between 1866 and 1870 Friedrich Kohlrausch codified Gottingen’s practical exercises. In 1870 he published a textbook of practical physics based on those exercises.  An explicit statement of the research values and techniques that had guided the school of physics at Gottingen, his textbook focused more on instruments than on data. It advocated using least squares only to establish the overall limits of error, and deemed the exhaustive analytic determination of constant errors “too laborious.” Kohlrausch’s textbook was accepted very quickly and on a wide scale throughout Germany, establishing a uniformity of practical exercises in physics hitherto not seen. But its popularity vitiated the maturation of the Göttingen school into what Joseph Fruton has called a “research group.”  Although fine distinctions in
30. Weber Nachlalss, Nr. 21, and Wagner Nachlass, Nr. 6 (both cit. n. 27).
31. Olesko, Physics as a Calling (cit. n. 1).
32. Seminar reports, Universitätsarchiv Gättingen, 4/Vh120. Practical applications included problems from navigation, geodesy, mine surveying, telegraphy, sacchirimetry, and medicine.
33. Kohlrausch, Tagesbücher Nrs. 2500 and 2601 (cit. n. 27); and Fnedrich Kohlrausch, Leitfaden der praktischen Physik (Leipzig: Teubner, 1870).
34. Joseph Fruton, “Contrasts in Scientific Style: Emil Fischer and Franz Hofmeister, Their Research Groups, and Their Theory of Protein Structure,” Proceedings of the American Philosophical Society, 1985, 129:313-370; and Fruton, “The Liebig Research Group: A Reappraisal,” ibid., 1988, 132:1-66.
experimental styles based on approaches to measurement continued to characterize differences between schools of physics until early in the twentieth century, the only schools that could realistically take shape were those that contrasted sharply with Kohlrausch’s general practices, such as the school of August Kundt. Hence the experimental physicist Friedrich Paschen could remark in 1925 that “as an assistant to [Wilhelm] Hittorf, I had the opportunity to learn what was insufficiently emphasized in the school of Kundt: namely to make precision measurements as they were done by [Victor Henri] Regnault.” Kundt’s school rejected not only precision measurement of the Gottingen type but also the kind of rigorous computation of errors that had been practiced earlier at Konigsberg. 
So we are left with somewhat of a paradox. The explicit codification of practices, including those of data analysis, helped to create a school at Gottingen. But the widespread popularity of the Gottingen style, following Kohlrausch’s publication of its characteristic practices in his textbook, diluted the distinctiveness of the school’s identity. From the beginning it had been the explicit statement, rendered in instruction, of exact experimental practices that had been so important in shaping the identity of the school. Students exhibited the same preference for instrument perfection over error analysis in their research that had been evident in their practical exercises. Pace Ravetz and Polanyi, craft knowledge of the sort associated with data and error analysis was not entirely ineffable.
As Rocke argues here for the case of Kolbe, tacit knowledge cannot be entirely eliminated from school formation; “cookbook knowledge” and precepts cannot guide scientific practice completely. In fact, prior to the codification of the Gottingen school’s practices in Kohlrausch’s textbook, residual tacit practices did remain a part of the school’s operation. Most of these tacit practices were found in the execution of geomagnetic measurements proper, as when Kohlrausch supervised advanced students in them, rather than in other types of exercises and projects involving precision measurement. The failure of the Gottingen school to mature and to sustain a distinct identity after the appearance of Kohlrausch’s textbook, however, can be attributed in large part to the inability of the school to maintain a distinct identity in the context of the widespread dissemination of its practices. The case of Gottingen physics, as well as others like it, suggests that a more nuanced understanding of the domains of the tacit and the explicit, as well as the boundaries between them, is essential for understanding not only the formation of scientific schools, but also more generally the formation of the scientist.
The burden of this brief essay has been that overemphasizing the role of tacit knowledge in school formation has entailed ignoring a key factor in school formation: learning by explicit precept. As the cases described in this volume illustrate, the precepts and assumptions guiding a school’s operation can be self-consciously
35. Friedrich Paschen, “Antrittsrede,” Sitzungsberichte der PreuJ3ischen Akademie der Wissenschaften, Phil.-hist. Klasse, 1925, pp. cii-civ on p. cii. Paschen could not, in fact, have chosen a more contentious example of precision measurement. Regnault’s measurements were accepted at Göttingen, but at Königsberg were considered flawed for their inadequate consideration of certain experimental errors. See Olesko, Physics as a Calling (cit. n. 1), pp. 297-298, 378-386.
deployed in arguments, debates, and controversies only when they are articulable, and hence explicit. In his article on the Helmholtz-Hering controversy in this volume, for instance, Steven Turner demonstrates the importance of a special set of explicitly recognizable characteristics, linguistic differences, in the definition and operation of a school as well as in scientific controversy. Explicit knowledge, such as these linguistic differences, lies at the basis not only of controversy between schools, but also of the identity, productiveness, and even continuity of a school. What the pedagogic element in school formation makes clear, however, is that a delicate balance must be maintained. If too much is made explicit in the scientific practice of a school, as when Kohlrausch codified Göttingen’s practices in his textbook, then either a school will not form or an existing one will neither mature nor be sustained. A school’s success thus depends on keeping some secrets, but neither too many nor too few.