Historical perspectives on science, II; Impact of science...

Historical perspectives on science—II

Impact N o . 160

279 Past and present links between history and philosophy of science William R. Shea

289 S o m e methodological problems in the history of contemporary life sciences Bernadino Fantini

303 Mathematics education: a historical view Geoffrey Howson

315 Preparations for Zaragoza—the X I X International Congress on the History of Science Mariano Hormigón

321 Publishing complete works of the great scientists: an international undertaking D . Speiser and P. Radelet-de Grave

349 Science during the Ming and Qing dynasties: contact between Chinese and western civilizations Du Shi-ran

357 The scientific revolution of the 17th century: new perspectives Pietro Redondi

369 The history of mathematics and ethnomathematics—how a native culture intervenes in the process of learning science Ubiratan D'Ambrosio

379 Journals on history of science: a brief guide

385 Conclusions Jean Dhombres

387 Readers' forum

389 Erratum

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Past and present links between history and philosophy of science

William R. Shea

Co-operation between historians and philosophers of science has often been honoured more in the breach than in the observance. Historians of science have sometimes locked themselves within the narrow confines of a strictly expository accumulation of the details of past science, while philosophers of science, under the influence of logical positivism, have frequently advocated a model of science as value-free, history-free: free, indeed, of almost everything but the tools of logic and semantics. In recent years, communication has been established between the disciplines, and we find an increasing number of philosophers who examine historical cases in the sciences in order to uncover the structure of scientific reasoning and understand scientific concepts as they actually emerged in the process of history.

Philosophers of science are interested in the nature and justification of scientific knowledge in general; historians of science in the development of science as it actually occurred over the centuries. This rough and ready distinction between two related disciplines should not obscure the fact that it is not always easy, at a first glance, to k n o w whether a given publication is a philosophical essay that draws on historical examples or an historical enquiry that is guided by philosophical considerations.

T h e tradition of philosophical-historical writing goes back to the Enlightenment and was particularly prominent in the nineteenth century with such figures as William Whewell in England, Charles Sanders Pierce in the United States, Ernst M a c h in Austria, and Arthur Hannequin in France. In the first half of the twentieth century, French philosophers wrote several outstanding works on the genesis of scientific ideas. N a m e s that leap to mind are Léon Brunschvig, Gaston Milhaud, Paul M o u y , Abel Rey, Alexandre Koyré, Hélène Metzger and Georges Ganguilhem. Pierre D u h e m came to

William R . Shea is Professor of History and Philosophy of Science and a m e m b e r of the Centre for Medicine, Ethics and L a w at McGill University, Montreal, President of the International Union of History and Philosophy of Science, and a Fellow of the Royal Society of Canada. H e is a graduate of the University of Cambridge, and a former Fellow of Harvard University and the Institute for Advanced Study in Berlin. H e is the author of Galileo's Intellectual Revolution, and The Magic of Numbers and Motion: the Scientific Career of René Descartes and the editor of several books including Reason, Experiment and Mysticism in the Scientific Revolution, Basic Issues in the Philosophy of Science, Otto Hahn and the Rise of Nuclear Physics, and Scientists and their Responsibility.

Professor Shea m a y be contacted at the following address: McGill Centre for Medicine, Ethics and L a w , 2020 University, Suite 2410, Montreal, Quebec H 3 A 2A5, Canada.

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the history of science from physics, and Emile Meyerson was originally trained in chemistry, but both m a k e important contributions to history and philosophy of science. In Germany, Ernst Cassirer wrote works that continue to be widely read for their penetrating study of the interplay between philosophical and scientific currents of thought.

But in spite of the work done by philosophers w h o wrote on historical subjects or turned to the history of science for their major examples, the mainstream of the philosophy of science, from roughly the second quarter of this century to the 1960s, was dominated by an a-historical movement k n o w n as 'logical empiricism' or 'logical positivism'. In this article I propose to examine this school of thought and show w h y it failed. I shall then consider the implication of this failure for the partnership between history and philosophy of science.

The region of logical positivism

In 1905 Albert Einstein published his special theory of relativity, and shortly thereafter quantum theory issued a second challenge to classical physics. Scientists, w h o had glibly accepted a form of uncritical realism, were shaken in their beliefs and began to ponder h o w familiar language can be used to describe entities and mechanisms that cannot be seen and behave in unexpected ways. The logical positivists met this problem by retreating to the basis of the immediately observable ('this is red', 'this is 10 centimetres long'), which they assumed was clear to everyone. This was sometimes expressed by saying that the question of meaning ('What do theories mean?') and the question of acceptability ( ' H o w do w e k n o w what theories are true?') hinge on the question of reference ('What are theories about?') which, in turn, was taken to raise no difficulty. Another w a y of making the same point was to stress the distinction between self-evident 'observation terms' and derivative 'theoretical terms'. This methodological assumption constituted the first or empirical component of logical empiricism.

The second or logical component consisted in reliance on mathematical logic for formulating the problems of the philosophy of science, often rechristened 'the logic of the sciences' to emphasize two of its main features. First, philosophy of science was to concern itself with the logical structure rather than the content of scientific statements, just as formal logic, since Aristotle, dealt with the form rather than the content of propositions. The job of the philosopher was conceived as the formal representation of scientific expressions in general, leaving to the practising scientist the task of confronting his conclusions with actual scientific procedure. Important advantages were said to result from this analogy with formal logic. Philosophy of science, thus disengaged from the specific tenets of particular scientific theories, was i m m u n e from the vicissitudes of change and the overthrow of current beliefs. Since the philosopher of science could, in principle at least, outline the characteristics of all possible explanations, he could, by the same stroke, give the formal characteristics of all future explanations. This was one of the most attractive aspects of the logical empiricist programme: it appealed to the administrative machinery of our minds accustomed to reduce understanding to arguments and classifications capable of development by deductive logic. The second and closely related feature of the 'logic of the sciences' was its conception of scientific theories as formal systems that can be formulated with the tools of mathematical logic. The philosopher of science concentrated on fully

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developed or idealized systems, and took for granted that science grew by incorporating old hypotheses into new ones, where they became special cases applicable in a limited domain of experience. For instance, Newton's First L a w , for which mass is invariant, was assumed to be quite simply a limiting case of the special theory of relativity, where mass varies with velocity, namely the state of affairs that obtains when velocity is small enough to be negligible.

The empirical and the logical aspect of logical empiricism can be summarized therefore by saying that theoretical terms are: (a) grounded in self-evident observation terms, and (b) open to exhaustive manipulation through modern mathematical logic. Observational statements ('this is green', 'this is w a r m ' , 'this is hard') were taken to be immediately decidable and to offer a basis for instituting a comparison between theories. As Rudolf Carnap, a leading Austrian positivist w h o emigrated to America, put it:

W e assumed that there was a certain rock bottom of knowledge, the knowledge of the immediately given, which was indubitable. Every other kind of knowledge was supposed to be firmly supported by this basis and therefore likewise decidable with certainty.1

Observation and theoretical terms

In view of the importance logical positivists gave observational statements in assessing the relative merits of rival theories, they were surprisingly vague about their nature. Even Ernest Nagel, whose Structure of Science became the standard textbook of logical positivism, presupposed that the distinction between observation and theoretical terms was unproblematic:

no precise criterion for distinguishing between experimental laws and theories is available, and none will be proposed here. It nevertheless does not follow that the distinction is spurious because it is vague, any more than it follows that there is no difference between the front and the back of a man ' s head just because there is no exact line separating the two.2

The most explicit statement is in Rudolf Carnap's classic paper, 'Testability and Meaning', where he makes the following two points. First, he holds that what it is to be 'observable' is a question for psychology and the behaviourist theory of language, not philosophy. Next, in approximate replacement of a definition, Carnap describes the concept of observability as follows: a predicate ' F is observable for a person N if for some object b, N can under suitable circumstances come to a decision to accept or reject 'P(b)' with the help of a few observations. H e continues:

This explanation is necessarily vague. There is no sharp line between observable and non-observable predicates because a person will be more or less able to decide a certain sentence quickly, i.e. he will be inclined after a certain period of observation to accept the sentence. For the sake of simplicity w e will here draw a sharp distinction between observable and non-observable predicates... Nevertheless the general philosphical, i.e. methodological question about the nature of meaning and testability will, as w e shall see, not be distorted by our over-simplification. Even particular questions as to whether or not a given sentence is confirmable, and

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whether or not it is testable by a certain person, are affected, as w e shall see, at most to a very small degree by the choice of the boundary line for observable predicates.3

A n untenable distinction

Carnap presupposed, therefore, that an initial distinction between observables and non-observables on pragmatic grounds leads to no distortion in the subsequent discussion of the relation of theory to observation. But there is no such guarantee. W h a t was overlooked in his account of observability is that the pragmatic conditions themselves are theory-laden, namely they are always formulated against a background of current scientific opinions and tenets. Furthermore, it is by no means obvious on Carnap's account that any predicate is, in principle, non-observable. Perception depends on training, past experience, and contemporary hypotheses, and there are circumstances in which suitably educated persons can come to a quick decision about any predicate, however apparently theoretical, such as 'meson' or 'positron'. His recourse to psychology or physiology to determine what an 'observable' is offers no easy w a y out. Even if these sciences could provide us with a clear answer to the question, w e would not escape the problem of a vicious regress. For what is it to be accepted as an 'observable' for psychology and physiology, and hence to be an empirical basis for their theories of 'observability'?

B y the 1950s the allegedly firm basis of observation language had become shaky, but the crisis of logical positivism was delayed because attention was shifted from the empirical to the logical aspect of the problem. For over a decade, philosophers of science, and most prominently Carl G . Hempel , focused on the deductive character of theories, and discussed various strategies to show h o w evidence could confirm or disprove statements arrived at deductively.4 A s the discussion progressed, it became increasingly clear that no satisfactory criteria could be found, and that the deductivist account was unable to solve the problem of the meaning or the truth of scientific theories. A strong reaction was inevitable, and by the end of the fifties the complaint was increasingly voiced that in their concentration on technical problems of logic, the logical empiricist movement had lost contact with real science.

The rediscovery of history

It was naive to read the past, as the positivists did, as the record of great m e n throwing off the shackles of a dark inheritance and heralding the d a w n of scientific objectivity. M a n y older theories that were derided as naive, for instance medieval mechanics and the phlogiston theory, were found to contain far more than simple-minded error and prejudice. It was discovered that N e w t o n not only framed non-empirical hypotheses but that he was strongly influenced by the alchemical tradition, and that Galileo, the father of'empirical science', neither dropped balls from the Leaning Tower of Pisa nor cared for experiments as m u c h as had hitherto been believed. A s closer attention was paid to the framework of theories it became apparent that the theoretical context determined not only the questions that were raised but the terms in which the answers had to be expressed to be judged acceptable. This was a direct challenge to the logical empiricist position that there is an absolute, theory-independent observation language

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whose terms have the same core of c o m m o n meaning for all competing theories. According to the new view, the meaning of all scientific terms, whether factual or theoretical, is governed by the general background (often called paradigm) which underlies them and in which they are imbedded.

This new interpretation was urged with considerable vigour by T h o m a s K u h n and Paul Feyerabend. 'The meaning of every term w e use', Feyerabend writes, 'depends upon the theoretical context in which it occurs. Words do not " m e a n " something in isolation; they obtain their meanings by being part of a theoretical system.' Whereas the logical empiricists considered theoretical terms as wholly dependent on observation ones, from the new viewpoint the exact reverse is true. Feyerabend stresses this point:

The philosophies w e have been discussing so far assumed that observation sentences are meaningful per se, that theories which have been separated from observations are not meaningful, and that such theories obtain their interpretation by being connected with some observation language that possesses a stable interpretation. According to the point of view I a m advocating, the meaning of observation sentences is determined by the theories with which they are connected. Theories are meaningful independent of observations; observational statements are not meaningful unless they have been connected with theories... It is therefore the observation sentence that is in need of interpretation and not the theory.5

It follows that a basic shift in the theoretical viewpoint entails a change in what counts as a real problem, a correct method, an acceptable explanation, and even a fact, since the meaning of observational terms is determined by the theory in which they occur. A philosophy of science that does not attend to the history and the actual practice of science condemns itself to the irrelevancy of abstract logic.

The inadequacies of logical empiricism, so mercilessly exposed by Feyerabend, led to a renewed interest in what could be learned from the development of science. In his influential book, The Structure of Scientific Revolutions, T h o m a s K u h n argued that the science of a given period can only be understood in the light of the general framework or paradigm that provides a scientific community with its conceptual tools and its criteria of relevance, validity, and confirmation.6 The meaning of terms is not fixed in some noetic heaven but is dependent on the paradigm in which it is imbedded. Scientific terms cannot be divorced from their historical context.

Theory-ladenness

Kuhn 's sweeping solution brought a new series of problems in its wake. For instance, does the mere extension or application of a theory m a k e a difference to the theoretical content and hence to the meaning of the terms involved? If the meaning observational terms depends completely on the theoretical framework, h o w can w e ascribe any continuity to the different usages of the same terms in successive theories? H o w can rival hypotheses be said to contradict one another, since in order for two sentences to be contradictory, what is denied by one must be affirmed by the other, and this is meaningless unless they have something in c o m m o n . K u h n and Feyerabend established the bankruptcy of a philosophy of science based on the allegedly firm foundation of 'observations', but their alternative account eventuates in a complete relativism in which it becomes impossible to compare any two scientific theories, and to

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choose between them on any but the most subjective grounds. If observation itself shares the uncertainties of theories, w e are adrift in a sea of hypotheses. Without a solid observational basis, w e have no moorings, no plan, and no science.

Various attempts have been m a d e in the last two decades to steer a fresh course between the Scylla of positivism and the Charybdis of relativism.7 It is generally accepted that the paradigm of disciplinary matrix of a given period, school or age determines to a large extent what questions can be raised and what kind of solutions can be entertained as likely answers. It is also generally felt that the claim that theories are incommensurable (i.e. cannot be compared) is a distortion of the very nature of the scientific enterprise. This extreme form of relativism is not as it claims the result of an investigation of what actually goes on in science but a purely logical consequence of a narrow preopposition about what 'meaning' is. These writers hold that if scientific terms do not retain precisely the same meaning over the history of their incorporation into more general theories, then these theories cannot be compared, and the similarities they exhibit must be considered, at the best, as superficial and, at the worst, as deceptive and misleading. This claim rests on the assumption that two expressions or sets of expressions must either have exactly the same meaning or else must be completely different. The only possibility left open by this rigid dichotomy of 'meanings' is that history of science, since it is not a process of development by accumulation, must be a completely noncumulative process of replacement.

The inherent weakness of this position turns out to be its retention of a positivistic concept of 'meaning'. If anything the revolution is not radical enough. K u h n and Feyerabend, in spite of their spirited attack on the positivist view that 'theories' are parasitic on 'observations', nevertheless approach their problems with that distinction in mind. They have applied the old classification to a n e w purpose rather than invented new conceptual tools for dealing with old problems. They have merely inverted the respective roles of the two members of the classical distinction: it is n o w the 'theory' that determines the meaning and acceptability of the 'observation', rather than the other way round.

It is m u c h more radical to call the distinction itself into question and to escape from the horns of the dilemma by breaking them. It m a y well be that several problems that bedevil contemporary philosophy of science are heightened (if not created) by the deficiencies of the distinction between a theoretical and an observational language. If this is the case, it is no longer the solution that is seen to be problematic but the very w a y in which the question is framed. For instance, the notorious problem of the ontological status of theoretical entities or the question whether a realistic interpretation of scientific theories can be upheld m a y be partly generated by an inadequate concept of the working of theories. It is all too easy to view the distinction between observational and theoretical as paralleling a distinction between existent and non-existent. If observation terms are said to have a clear and direct reference to entities that exist while theoretical terms do not, it becomes difficult to k n o w what theories are about. This is not due to any intrinsic opaqueness of the concept of existence, but to the sharpness of the distinction between theory and observation. As long as it was believed that theoretical terms could be exhaustively described via observational ones, theories could be handled as a convenient shorthand. W h e n it became apparent that such a reduction was only possible in part, the extra meaning of theoretical terms was sought in the position they occupied in the context of the system they belonged to. Thus theoretical entities could not exist in the same sense as tables and chairs, and it became

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a first-class puzzle to k n o w in what sense they could not be said to exist, short of being merely useful fictions.

The reaction of writers such as K u h n and Feyerabend was to claim that this indicates that observations are governed by theories, which are, in the last resort, irrational guesses at what the universe really looks like. But this did not solve the problem of meaning; it merely replaced the positivist thesis of meaning invariance with the doctrine of incommensurable meanings. A less rigid interpretation is possible: meanings can be considered similar or analogous, namely comparable in some respects while differing in others. By taking this path, w e can hope to preserve the fact that theories, for instance, Newtonian and relativistic dynamics, are not incommensurable, although they are more fundamentally different than the most usual logical empiricist views m a k e them. A n interesting case is the transition from Aristotelian mechanics to inertial physics in the seventeenth century. Aristotle assumed that motion required the constant application of force whereas Descartes and N e w t o n denied this and postulated that, once set in motion, a body would continue to m o v e in a straight line at a uniform velocity. In inertial physics, force does not produce speed as such, but a change of speed, namely acceleration or deceleration. The two theories m a y be far apart but it makes sense to compare them with the impetus theory, which was formulated in the Middle Ages, and is transitional in character. O n the one hand, the impetus theory shares with the Aristotelian theory the notion that motion cannot continue without the presence of an active cause, in this case the 'impetus' present in the moving body. O n the other hand, the impetus theory tends towards the modern view inasmuch as it makes the cause of motion internal and incorporeal instead of external and material.

The impact theory encouraged a fresh approach to problems by removing longstanding conceptual barriers. This was the case, for instance, in dealing with the hypothesis that the rising and setting of the sun was merely apparent, and resulted from the physical rotation of the earth on its axis in twenty-four hours. The Aristotelians rejected the suggestion outright because the physical assumptions of their system entailed that the air and the clouds would not share in this motion, and that w e would therefore experience a strong wind from the east if the earth rotated. By affirming that the air would receive an impetus and would be carried around as though nothing has happened, the impetus theory m a d e it possible to entertain the idea that the earth might move . Likewise by internalizing the cause of motion it shifted attention to a new set of possibilities. Since air could no longer be the force producing motion but merely an impediment, motion in a vacuum ceased to be implausible, and thus the impetus theory cleared the ground for thinking about the idealized case of a body moving in the absence of impeding forces. Furthermore, by treating all cases of motion, whether terrestrial or celestial, natural or constrained, in terms of one kind of cause, namely impetus, it paved the way for a unified account of all motion and provided an alternative approach to the traditional Aristotelian division.

O n the Kuhn-Feyerabend view one is practically driven to describe scientific change in revolutionary terms: to speak, for instance, of the overthrow of Aristotelian mechanics by the impetus theory and of the latter by Newtonian science. But a more balanced description seems possible. The Aristotelian-Scholastic tradition applied, as a template, an intricately connected w e b of concepts and propositions to the data of perception and everyday experience. In laying d o w n this system of interpretation, it simultaneously set up obstacles or limitation, both by theoretical precept and by suggestion, to thinking in certain other ways. The vacuum and the actual infinite, for

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example, appeared self-contradictory, while the motion of the earth seemed physically impossible. Scientific advance is related to a reassembling of the pattern of our experiences, and there is immense resistance to this. 'In this sense', writes the American philosopher of science, Dudley Shapere,

w e can speak of the Aristotelian view as having involved certain 'presuppositions' specifying [for example] what could and what could not count as an explanation. T o this extend K u h n and Feyerabend have m a d e an important point. But these 'presuppositions' were not mysterious, invisible, behind-the-scene 'paradigms' [ K u h n ] or 'high-level background theories' [Feyerabend], but were involved in the straight-forward scientific statements themselves, even though there were disagreements about details (and even about fundamentals), and even though the way in which they restricted thought, or the importance of these restrictions, could not be seen so easily.8

After all, they were seen by Oresme, Buridan and other medieval natural philosophers w h o reassembled the facts in a different pattern.

The difficulty in generalizing this strategy is the concept of similarity or degrees of likeness of the shifting meanings of the terms that are transformed as they pass from theory to theory.9 It is only too tempting to distinguish, against the background of a particular theory, between what is and what is not an essential part of the meaning of a term. For instance, it seems obvious (in the light of subsequent developments) that Newton's absolute space and absolute time are 'irrelevant features' of his mechanical theory. Yet those very features, for some purposes, m a y prove to be the very ones that are of central importance in comparing two uses. A n absolute distinction between essential and accessory features could only rest on an a priori conception of scientific understanding and would reintroduce the fallacy of the theoretical-observational dichotomy. It would thus seem wiser to allow all features of the use of a term to be equally potentially relevant in comparing the usage of the term in different contexts, but whether these post-positivistic strategies can be shown to be more faithful to the history of science and more adequate to the logic and theoretical inference remains to be seen. The discussion involves a critical examination of the assumption that most scientific inferences rest on analogy, and, if so, in what sense. Whatever the final outcome of the debate, the benefits already accrued from this radical reappraisal of the theoretical-observational distinction m a k e this venture one of the most promising in contemporary philosophy of science.

While this debate goes on, a very close link has been forged between philosophers and historians in Italy. The Florentine School, headed by Paolo Rossi, has published over thirty important monographs in the last fifteen years.10 These works, largely by young scholars, are remarkable for their sensitivity to conceptual as well as experimental problems in the genesis of modern science. A n excellent introduction to history of science, as it is practised in this school, is the recent Storia della Scienza in four volumes edited by Paolo Rossi and published by U T E T in Turin in 1988. The Italian school was never mesmerized by the apparently straightforward distinction between theoretical and empirical claims, and they consistently argued that scientific theories cannot properly be understood except in terms of their history. They insisted that various scientific structures or models, whether across time or contemporary, must be investigated in the light of philosophical assumptions that are often taken for granted. These structures must also be seen as the products of real h u m a n beings, in constant

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interaction with other h u m a n beings w h o share the same intellectual, cultural, religious and political world. T h e science of a given age cannot be divorced from the period in which it w a s born. T h e capacity for perceiving the relations of particular cases to law, instance to general rule, theorems to axioms, varies with the laws, the rules and the axioms. Philosophers and historians w h o discuss the nature or the emergence of science complement one another. T h e changing fabric of science and scientific arguments is not a seamless role, and there is an increasing feeling that the garment of philosophical and historical knowledge is best woven out of mutually supporting strands. •

Notes

1. C A R N A P , R U D O L F (1963) Intellectual Autobiography, in Schilpp, P. A . (ed.), The Philosophy of Rudolf Carnap. Open Court, Lasalle, 111., p. 57. For a critical analysis of neopositivism see Barone, Francesco (1986), // neopositivismo lógico, 2nd éd., 2 vols. Laterza, Roma-Bari.

2. N A G E L , E R N E S T (1961) The Structure of Science. Routledge & Kegan Paul, London, p. 83. 3. C A R N A P , R U D O L F (1953) Testability and Meaning, in Feigl, Herbert and Brodbeck, M a y

(eds.), Readings in the Philosophy of Science. Appleton-Century-Crofts, N e w York, pp. 63-64. 4. H E M P E L , C A R L G . (1945) Studies in the logic of Confirmation, originally published in Mind,

54, pp. 1-26,97-121. This article was reprinted in Hempel's Aspects of Scientific Explanation. Free Press, N e w York, 1965, pp. 3-51. It is still widely discussed, e.g. in the essays edited by Archinstein, Peter (1983) The Concept of Evidence. Oxford University Press, Oxford.

5. F E Y E R A B E N D , P A U L (1965) Problems in Empiricism (Part I), in Colodny, Robert G . (éd.), Beyond the Edge of Certainty. Prentice-Hall, Englewood Cliffs, N.J. p. 180. Feyerabend's essays have been conveniently edited in a two-volume set entitled Philosophical Papers. Cambridge University Press, Cambridge, 1981. His most famous book is Against Method. N e w Left Books, London, 1975.

6. K U H N , T H O M A S S. (1962) The Structure of Scientific Revolutions. Chicago University Press, Chicago. The second edition, published in 1970, contains an important postscript. Kuhn's views are developed in a collection of essays entitled The Essential Tension. Chicago University Press, Chicago, 1977.

7. For a survey of these attempts, see N E W T O N - S M I T H , W . H . (1981) The Rationality of Science. Routledge & Kegan Paul, London. See also the survey by Frederick Suppe in the introductory essay to the volume he edited, The Structure of Scientific Theories, 2nd edition. University of Illinois, Urbana, 1977, pp. 3-241.

8. S H A P E R E , D U D L E Y (1966) Meaning and Scientific Change, in Colodny, Robert G . (éd.), Mind and Cosmos. Pittsburgh University Press, Pittsburgh, pp. 78-79.

9. O n this problem, see H E S S E , M A R Y B. (1980) Revolutions and Reconstruction in the Philosophy of Science. Harvester Press, Brighton. See also H A C K I N G , I A N (1983) Representing and Intervening. Cambridge University Press, Cambridge, and C A R T W R I G H T , N A N C Y (1983) How the Laws of Physics Lie. Clarendon Press, Oxford. For an empiricist alternative to both scientific realism and logical positivism, see V A N F R A A S S E N , B A S C . (1980) The Scientific Image. Clarendon Press, Oxford. Recent reassessments by historians and philosophers of science will be found in S H E A , W I L L I A M R . (ed.) (1988) Revolutions in Science: Their Meaning and Relevance. Science History Publications, Canton, M A .

10. Most of these works have been published by Loescher in Milan. Rossi's influential views on the interaction between history and philosophy of science are well illustrated in one of his latest books, I ragni e leformiche. II Mulino, Bologna, 1986.

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S o m e methodological problems in the history of contemporary life sciences

Bernadino Fantini

The contemporary sciences pose scientific problems and difficulties for the historian. Because of the lack of perspective the history of contemporary events may become simply a chronical, a record of events in the order of their happening, a simple description of facts rather than an attempt to explain them. Only a cross-cultural, interdisciplinary, broad approach can give a deep understanding of the dynamics of the contemporary biomedical sciences and of their role in philosophy, culture and society.

T h e aim of this article is to analyse the trends and methodological problems of the history of contemporary biological and medical sciences. It does not pretend to be a survey of the existing historical literature, or a bibliographical analysis. Its only aspiration is to outline the major trends and to isolate the critical and specific methodological issues discussed by historians working on contemporary life sciences. As a consequence, references will be given only to papers and books considered as central to a methodological or theoretical issue.

The first question w e should ask is: W h a t is contemporary history? W h a t does the adjective 'contemporary' mean?

A n immediate answer could be that contemporary designates what is happening right n o w , in front of us. But this definition is really too naive. Even a purely chronological criterion does not work. W e can assume a conventional starting point, which could easily be the year 1900, because of its symbolic status, being the year of the rediscovery of Mendel's papers, and the first year of our century. W e could therefore define 'contemporary life sciences' as the science of our century. But in this w a y one risks introducing an artificial discontinuity between 19th- and 20th-century life

Bernardino Fantini works as an historian of biology and medicine at the Department of Genetics and Molecular Biology at the University of R o m e 'La Sapienza'. H e is presently spending a year as a visiting professor at the Institute of the History of Medicine, University of Geneva. His main interests are the history of biochemistry, genetics, microbiology, molecular biology, and the history of infectious diseases. In 1986 he spent a year at the Institut Pasteur, organizing the Service des Archives and working on the M o n o d papers. H e is Associate Editor of the journal History and Philosophy of the Life Sciences and Scientific Secretary of the Internationa] School of the History of Biological Sciences in Naples.

D r Fantini m a y be contacted at the following address: Dipartimento di Genética e Biología Molecolare, Université di R o m a 'La Sapienza', 00185 R o m e , Italy.


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sciences that in reality are in a state of continuity. Conversely, this criterion can easily overlook the discontinuities that biological sciences have undergone during our century, i.e. molecular biology and other revolutionary breakthroughs such as the synthetic theory of evolution, the emergence of ethology and the development of antibiotics in medicine.

Looking at other domains, w e can find the same problem. Contemporary art can be defined as the product of the 20th-century, but during the last decade the work of Picasso and Bracque has been considered as classical rather than contemporary. The same happened in music, where the contemporary music was defined as the music that followed the N e w Vienna School (Schoenberg, Berg and Webern) and Stravinsky, though these composers are n o w considered as 'classics' at the same level as Mozart, Brahms and Mahler and, as such, part of the standard repertoire of symphony orchestras and the like. Nowadays nobody would say that their music is 'contemporary music'.

A more elaborate answer to our question suggests that paradigms or research programmes used in the past are shared by scientists of today. This definition is indeed effective, and corresponds to the actual use of the term contemporary. In fact, w e can consider as 'our contemporary' a philosopher or a scientist of the distant past, when his theories can be used as part of our present theorization. Thus the physicist M a x Delbruck was able to consider Aristotle as one of the founders of molecular biology.1

M a n y historians interested in contemporary biology, especially from an epistemolog-ical point of view, often refer to Aristotle's philosophy and biology as a component of present theoretical development.2 The history of disciplines and problems that are connected with our present concerns, belong to the same intellectual tradition, paradigm or research programme, whatever one would chooses to call it.

A s w e will see this definition can help in explaining the relevance of the history of contemporary sciences and its specific characteristics.

The growth of the history of contemporary life sciences

In quantitative terms, the growth in the history of contemporary biological and medical sciences during the last twenty years can be easily measured. The number of papers devoted to this subject in the specialized journals exclusively devoted to the history and philosophy of life sciences, the composition of national and international professional history of science societies, the proportion of symposia on different aspects of the history of contemporary biology and medicine in the international congresses of history of science show the spread of this kind of historical research.

The phenomenon is obviously an aspect of the professionalization of the history of science and medicine that has occurred during the last three decades and has increased the opportunities for positions in universities and research centres. Nevertheless, the specific, differential growth in the history of contemporary biomedical sciences must be traced to different causes. First of all, it is a consequence of the growth of the biomedical disciplines themselves during this century, especially in the last 40 years. The 'biological revolution' indeed caused widespread historical interest in what happened and h o w

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Problems in contemporary life sciences

and w h y it happened. Furthermore, the social and ethical problems posed by these revolutionary advances have raised various historical questions, because m a n y of the present concerns (over animal experimentation, the definition of life and death, social attitudes towards n e w technological development, and so on) can be found in other historical contexts and thus comparative analysis can isolate what has changed and what is really new. Finally, the philosophical facets of contemporary biology, which challenge the standard definitions of life, have produced epistemological inquiries necessarily grounded on the historical analysis of the growth of knowledge.

This growth is not only quantitative, in the number of scholars, publications and symposia, but is rather analogous to embryonic development: as the number of scholars have increased, so the problems studied and the various approaches used have rapidly differentiated, producing a complex 'organism' and giving rise to difficult problems of coordination, communication and integration.

Specific problems of the history of contemporary sciences

Contemporary historians try to describe the roots and the characters of events that are taking place right n o w , in front of them. In a sense they are actually 'in' these events themselves, participating in the facts they describe. Using the classic model of Gestalt shift as a model of scientific discovery, the historian sees the image changing, in a state of flux, and he is merged into that same flux, sharing the 'paradigmatic shift'. If the image is still changing in front of us w h e n w e try to understand it, it is that m u c h more difficult to clearly distinguish its borders, its constitutive lines.

This difficulty was clearly perceived by Thucydides when describing the Peloponnesus W a r in the very years in which it was happening: 'difficult was the inquiry because those w h o participated to the events were not saying the same things about the same facts. Instead they spoke according to their memories or to their sympathy for one of the two sides' (I, 22).

Because of the lack of historical perspective, the history of contemporary events m a y become simply a chronicle, a record of events in the order of their happening, a simple description of facts instead of an attempt to explain them. Moreover, the participation of the historian in the facts he describes can easily produce distortions caused by preconceived general ideas or images. Epistemological analysis has shown the role played in scientific activity by 'patterns of expectation', which usually produce distortions of an ideological nature. The same mechanism is also at work in historical activity, where a preconceived idea often anticipates the historical inquiry. This can be considered as inevitable, because, being a theoretical activity, the history of science necessarily shares with science itself the well-known relationship between theories and facts. The historian needs always to interpret documents, because they are 'historical fact' that needs to be interpreted by 'historical theory', in the same way that an 'experimental fact' is always interpreted or created by 'scientific theory'. History is not the absolutely objective mirror of what really happened, but it is a rational reconstruction. It establishes links and proposes 'explanation' involving a philosophical or ideological reading frame, which reflects general ideas on the nature of knowledge or on the w a y it is acquired.3 The historian should be constantly aware of

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the presence of a 'pattern of expectation' and his critical tools should be always at work. Even without taking into account the instrumental view of history as the official reconstruction that can be used in scientific and commercial battles, the tendency to select and reinterpret historical problems as a function of the present questions and interests can produce deformations, especially in the evaluation of the relative weight of a theory or a discipline in a given historical context.

T h e first level at which this happens is the selection of sources. For the distant historical periods a sort of Natural Selection of ideas, theories, and discoveries takes place. At the beginning of historical research, the scholar usually knows what was relèvent in a given historical period and he can use that knowledge as a starting point for his critical study. Furthermore, a large portion of the documentation has been lost, luckily for the historian some would say, because a large place is thus left to his fantasy and exegesis. History can then really be the study of the traces of the past in the present.

In contemporary history, by contrast, there are no clear and unquestionable reference points and paradoxically there are too m a n y sources, a great abundance of surviving documentation. Moreover, this documentation accumulates under the eyes of the historian and in certain cases he can also contribute towards producing it. T h e increased interest in history, combined with the exponential growth of the scientific activity, is producing in m a n y scientific institutions and archive centres an enormous amount of often non-standardized and non-classified documentation.

Because of the redundancy of information, the historian cannot pursue the objective of total knowledge of all the sources available on the history of a given subject (for example, the theory of the gene or the etiology of cancer), something that is, on the contrary, a methodological imperative for the historian of a m o r e distant past. Drastic selection is necessary, but such a selection can easily become casual, the subject of expectations and preconceived ideas: the lack of a historical perspective can easily project into the past present concepts, theoretical connections and interpretations. T h e main difficulty of contemporary history is therefore to establish a specific and original method, a precise and correct criterion for selecting and exploiting the sources. T h e real problem is therefore to ask the right questions and to select the best tools for answering them.

Very often this selection is functional to the aim of retracing the precursors of a scientific theory, the origins of a discipline. But in such a w a y the historian can produce an endless search, a m a z e of confusing networks of connections and interwoven references, because in a highly dynamic situation, typical of the sciences of the 20th century, it is always possible to demonstrate that every discipline, every single experiment could have contributed a piece to the complex, three-dimensional puzzle of a great scientific discovery. This situation is complicated by the style of contemporary scientific literature, from which all references to the creative process are deliberately eliminated. Scientific publications are usually concerned with what results a scientist or a group of scientists have achieved, not h o w they have found them. Whilst addressing their scientific peers to inform them about the state of their research (as in the surveys of the history of the research and discoveries in m a n y scientific publications), authors acknowledge the influence exerted on them by their predecessors' work and opinions, but this historical reconstruction aims at a better explanation of the content, not to an analysis of the actual process of their discovery, vécu de la découverte ('the experience of discovery'), as M . D . G r m e k called it.4 These documents therefore do not by themselves convey the picture of the process which interests the historian of science.

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Different types of historie»

Redundancy of available information is not only quantitative, but also qualitative. M a n y different aspects of scientific activity are well documented, with a typical coalescence of theoretical, technical, institutional, socio-economical and h u m a n aspects (competition, personal collaboration, friendships or professional envies, etc). This h u m a n factor plays a relevant role in the spread of information, since communication in contemporary science is quite often verbal and interpersonal within a small community, rather than formalized in a published paper or at a conference.

A s a consequence, the structural relationships of scientific activity cannot be represented adequately, nor studied in their fullness, if their manifold historical articulations are not taken into account. A certain degree of separation of the various aspects of this articulation is possible for a distant problem, isolating a particular aspect and considering its background as fixed. For example, w e can study the details of Spallanzani's experimental procedures without referring to his social context or to that of his relations with other scientists of the time, sufficiently k n o w n through other historical analysis. Such a procedure is difficult to apply in contemporary history, w h e n each aspect changes continuously. The methodological danger inherent in focussing only on local problems can be overcome by the collaboration or eventually the contrast between m a n y différent specialties and historical interests. History of contemporary biological and medical sciences pertain necessarily to scholars of different formation: general historians, scientists, sociologists and philosophers that have produced m a n y different sorts of history, more differentiated than the history of the more distant past, because it is more difficult to establish the connections between different aspects and contexts. A s a consequence m a n y different 'histories' have been produced: histories of theories and 'research programmes', histories of disciplines and scientific communities, histories of single scientists or institutions, and histories of the social aspects of science. If 'local history' remains dominant in a large part of the history of biology and especially in the history of medicine, only a cross-cultural, interdisciplinary, broad approach can give a deeper understanding of the dynamics of contemporary sciences and of their role in philosophy, culture and society. Even someone interested only in the history of a specific scientific problem or of a particular institute, trying to isolate it from the texture of general history, must work out an overall picture of the flux of scientific ideas, as well as take into account economical, political, social and psychological factors.

T h e specific weight of different specialties is nevertheless different in contemporary history. For example, philology, which is a fundamental tool for historical research on the ancient and modern science to the 18th century, is a relatively minor concern for the contemporary historian. Notwithstanding a series of revolutionary processes in the life sciences (cellular theory, Darwinian evolution, scientific medicine—produced by the development of physiology, microbiology and immunology, biochemistry, genetics and molecular biology) the dictionaries have changed very little since the first half of the 19th century, which illustrates there is a continuity in the general problems addressed. O n e can read a medical textbook of 1840, for example, without the aid of sophisticated philological analysis. There is a fundamental stability of the dictionaries, even if the permanence of a term can hide changes in its meaning and particular attention should be given to that 'meaning shift'. Because of this fundamental stability, the introduction

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of a new word charged with theoretical significance, such as 'information' or 'programme', acquires per se a revolutionary impact.

A particular epistemológica! problem

F r o m the epistemological point of view, one of the important aspects of contemporary history is that disciplines, paradigms or research programmes are often considered as structural wholes. This puts emphasis on the separation between disciplines and communities, and the proximity of the historian to the events he is studying tends to emphasise discontinuities, because usually a scientific community, for various theoretical and sociological reasons, tends to stress the differences with the recent past rather than the similarities. However, sciences have a complex and mutable configuration and the choice between continuity and discontinuity is one of the classic dichotomies that cannot be solved, like function/structure or reduction/integration. Even in the most revolutionary periods it is always possible to find different sorts of continuity between the pre- and post-revolutionary periods. A s a consequence, giving an absolute preeminence to continuity or discontinuity will lead to historical illusions.

Nevertheless, to define a scientific discovery requires necessarily a laceration of the complex spatio-temporal reality, the isolation of certain events with a symbolical value which encompasses not just one point but a whole field of action. A s a consequence a certain degree of schematization becomes inevitable, although the naive desire to characterize a scientific discovery at all costs with a n a m e and an exact date can transform an historical reconstruction into an oversimplification. Let us take an extreme example. T o the question, W h o discovered the double helix of D N A ? most people would answer: James Watson and Francis Crick in 1953. This answer is correct, but only partially. The double helix is indeed a symbol of a new discipline, molecular biology, and in order to be significant the question should be reformulated and disaggregated. O n e question could then be: W h o discovered the crystallographic structure of D N A ? The answer to this question is: probably Rosalind E . Franklin,5 even if only Watson and Crick fully appreciated the biological implications of that peculiar structure. The question should then become: W h o discovered that the double helix structure can be the carrier of genetic information? The answer is again Watson and Crick, though one could note that the concept of information is not implied in the 1953 papers, and conversely that the idea of a complementary structure of the chemical basis of the gene was implied, on a theoretical basis, in classical genetical thinking6 and in the template model for protein synthesis.7 It is often illusory to try to assign a precise date to what is in fact a long process, m a d e up of m a n y stages, a series of discontinuities in a spatio-temporal continuity. The answer to this kind of question depends on the question itself and on the level of historical explanation.

Social studies of science

The introduction of a sociological approach to the history of science resulted in a large interest in institutions, schools, national styles and scientific communities. This relates to an objective aspect, the growing relevance even in biology and medicine of 'big

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science', in which more and more scientific research is a collective enterprise. But that could also be a byproduct of the lack of historical perspective, which does not allow one to isolate the specific and original contribution of an individual scientist as characterizing a discipline. Present paradigms seem collective paradigms, to be analysed with the tool of sociology rather than with that of psychology, and the individual creative process seems less important that the exchange of information and cooperative work. W e usually associate past revolutions with the work of a single scientist or physician (such as Aristotle, Galen, William Harvey, Georges Cuvier, Charles Darwin, Xavier Bichat, Claude Bernard, Gregor Mendel and Louis Pasteur) but w e tend to view contemporary science in the light of disciplines as a whole (biochemistry, ethology, genetics, molecular biology, immunology, endocrinology, virology, etc.).

The social history of restricted communities of specialists, of groups restricted in historical time and in social space, with well-defined spatio-temporal coordinates, is therefore a specific trend of contemporary history of science. It has already produced m a n y significant case studies, for example on the establishment of biochemistry as an autonomous discipline,8 on the beginnings of genetics as a particular blend of science, agriculture and politics, especially in the case of eugenics,9 and on the social impact of contemporary medicine and pharmacology that has produced a dramatic change in the pattern of disease distribution and in life expectancy, breaking the barrier of infant mortality.10

Particular attention has been given to the scientific styles that flourish when intellectual traditions develop in an adequate institutional context.11 R . Kohler, for example, studied the changing styles in biochemical tradition, from the birth of physiological chemistry in a medical context to the remarkable expansion in biochemists' interests in biological oxidation, intermediary metabolism, biosynthesis and macromolecules in the late 1930s. The biochemists' institutions and disciplinary rules provided m a n y opportunities and support for their expanding interest in cell physiology, but also set limits to their pace of change, in stark contrast with the unexpected discoveries of the molecular biologists, a contrast that was to be absorbed only in the 1960s after a fundamental reorientation of the biochemical tradition.12

History of disciplines

Because of the particular nature of contemporary history, interest focuses on disciplines and scientific communities rather than on single discoveries, institutions or theories. But this interest is not equally distributed. A few disciplines enjoy a remarkable historical activity, often as a part of the activities of the disciplines themselves, especially w h e n their development has raised important philosophical or ethical problems (such as genetics, molecular biology or evolution theory) or w h e n the scientists are aware of the need to stress the originality and the relevance of their discipline against a supposed imperialism of other disciplines (an attitude that can explain in part the historical activities promoted by biochemists).

Other disciplines or research programmes that have been equally relevant have been m u c h less studied from a historical point of view (for instance, ethology, embryology and cell biology, neurobiology, microbiology, virology, immunology, parasitology, pharmacology and epidemiology) and have usually been left to an

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'internal history' accomplished by the scientist themselves, with a somewhat lower level of critical rigour.13

The major conceptual theme in this context is the origin of a discipline or its fusing with other disciplines or research traditions, because in both cases this step marks a clear discontinuity.

T o identify the origins of a discipline implies a theoretical and historical definition, because it entails the definition of its theoretical core. This is more difficult for contemporary sciences, w h e n the disciplinary status is still being worked out. The main historiographical problem is to determine what should be considered as the real origin of a discipline: a new discovery? the existence of a scientific community with an institutional status and specialized journals and congresses? a new paradigmatic theory? or a new technical framework? The disparate character of these questions goes to explain w h y the problem of establishing the date and place of origin of a contemporary discipline can lead to different and even contradictory solutions. For example, the book Phage and the Origins of Molecular Biology,14 published in 1966 as a Festchrift to M a x Delbrück, considers the Phage G r o u p at the California Institute of Technology and the symposia it organized at Cold Spring Harbor as being the true disciplinary origin of molecular biology. A s a consequence in the book there is no contribution devoted to the history of crystallographic studies of proteins and nucleic acids or to the history of cellular physiology and enzymatic adaption. Conversely, James Watson's autobiography, The Double Helix,15 and Robert C . Olby's book The Path to the Double Helix16 contain m a n y differences but share the opinion that the true origin of molecular biology must be considered as being the discovery of the double helix structure of D N A at the Medical Research Council Laboratory in Cambridge. Robert Olby wrote two other papers on the same subject, with the titles 'The Origin of Molecular Genetics' and 'The Origins of Molecular Biology at Cambridge and Caltech'.17 However, if one looks to the book Origins of molecular biology: a tribute to Jacques Monod,18 one is quickly convinced that the origins of this discipline are to be located at the Institut Pasteur in Paris, in particular in the laboratories where A . Lwoff, J. M o n o d and F. Jacob studied the control of genetic expression and produced the innovative idea of the operon. According to A . Lwoff, Jacques M o n o d must be considered as 'the architect of molecular biology', because 'between 1948 and 1963 the main problems of the induced synthesis of enzymes were solved and molecular biology was created ex nihilo'.19 M a n y other authors, scientists and historians have proposed other origins or relevant contributions to the establishment of the new discipline.20

Given that science is a continuum, it is an impossible task to complete a m a p of the infinite number of contributions to the origins of a theory or a discipline. The problem is to specify the singularities of the new scientific reality which specifically distinguish it from others. F r o m this point of view, one can enumerate for molecular biology a few specific characteristics: (a) a new model of scientific explanation in biology, based on the concept of programme and information transfer; (b) a synthesis between genetics, biochemistry, microbiology, macromolecular chemistry and physics, and cellular theory; (c) a sharp separation between information transfer and the chemical processes that support it; (d) the explanatory role of the morphological concept of form and 'comparative anatomy' at the molecular model; (e) the formation of a n e w scientific community with specific characteristics. If one accepts this multithematic theory, then it follows that there cannot have been a single place or a single work that gave origin to molecular biology. It was the result of a long process, to which m a n y scientists,

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disciplines and institutions m a d e a fundamental contribution over a period of at least 20 years, from 1945 to 1965.

The same kind of analysis can be applied to the origin and the transformation of other disciplines. For example, microbiology has played a relevant role in contemporary biological and medical sciences as an analytical tool for genetics and pharmacology, and a theoretical basis for parasitology and preventive medicine. This was the result of the convergence of microbiology with general biology.21 After biochemists and physical chemists had treated the bacterial cell as simple a colloidal system or a 'bag of enzymes', the merging of different approaches to bacterial morphology, metabolism and genetics (nutrition research, comparative biochemistry, microbial genetics, chemotherapy, cytology, taxonomy and virology) transformed the bacterium into a fully blown biological object. This transformation therefore marks a concurrent shift across a whole range of different subjects and only an interdisciplinary historical analysis can reveal the reasons for this event. Studying individual disciplines or discoveries can hide important interdisciplinary and intertheoretical connections, as well as social and institutional influences. Furthermore, concentrating on the history of the contemporary discipline can easily mask the historical relevance of failed research programmes that have not been incorporated into the new disciplines, but which nevertheless played a relevant historical role. T o give an example: before the origins of molecular biology, during the 1940s, the plasmagene theory spread widely within the biological and medical sciences, as an attempt to provide a unified explanation of the self-replicating phenomena in microbiology, genetics, biochemistry and medicine. This theory dominated a large part of biological thinking in that period, and certainly had a remarkable impact on the development of m a n y biological disciplines, though it is today little k n o w n , even to the historian of science. The same could be said for the history of cytoplasmic inheritance, which has been studied in detail by J. Sapp.2 2

Autobiographies

As was stated before, the main problem facing the contemporary historian is the selection of sources. During the last decades a great deal of documentation has been produced by scientists creating their o w n history or the history of their discipline. This has produced a large amount of very impressive historical material, even if sometimes the work was justified by a negative attitude towards professional historians (with comments of the kind: 'Let w e doing the hard work, get rid of these historians that are too philosophically or sociologically oriented'). O n the contrary, the best results have been obtained through close cooperation between scientists and professional historians, as in the case of biochemistry.23

The recruitment of an active scientist to write on the history of a period has some evident advantages, in particular the detail of personal recollections thus m a d e available. However, the hazards of personal bias are obvious, and these are overcome only when, as for instance in the case of M . McCarty's book on the discovery that 'genes are m a d e of D N A ' , 2 4 instead of limiting themselves to sketching autobiographical notes from m e m o r y , the scientists go back to old laboratory notes and archives, correspondence and official reports, approaching events with caution, with a careful review of the various sources and an accurate interpretation of the factual data and

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chronology, and testing personal recollections with all the documentary evidence available.

In contemporary sciences there is an abundance of writing of a biographical nature on the researchers and their work. There is nothing new in this, a large number of biologists and physicians having left us this kind of literature, including in the 19th century H . von Helmoltz, O . Loewi, C . Nicolle, W . B . Cannon, C . Darwin, R . Kólliker, R . Virchow and m a n y others. W h a t is perhaps new is their spread and their success. This kind of writing is often dressed up to comply with the demands of a new kind of hagiography, particularly connected with Nobel Prize winners, producing a sort of 'How-I-did-it syndrome' typical of the 'heroic' view of scientific research that idealizes historic reality. The general public is particularly interested in 'heroic lives' and scientists are often cast as modern heroes fighting against the evils of obscurantism and ignorance.

But these autobiographies or biographies produced by scientists often combine a list of anecdotes with superficial documentation which lacks critical appraisal. Unfortunately, there is a widely held belief that accurate reconstructions of the experience of discovery can be found in the writings of the scientists concerned. However, an accurate analysis of a few historical cases for which an extensive documentation is available, has shown instead that with regard to events which have important social connections and emotional components, an autobiographical account is certainly valuable but cannot be accepted as definite. Autobiographical notes and books are far from being objective, because m e m o r y is a dynamic reality and inevitably some reorganization takes place in it (such a change in the temporal order, the a posteriori establishing of causal links, etc.). The names, dates and places are often accurate but the relationship between them is often not. As was noted by Thucydides in the passage quoted earlier, testimony, direct or indirect, is a kind of raw datum which must not be used beyond its immediate and superficial significance. Such information is not history, but it produces fundamental elements for a future history.

The contribution of this literature to the history of science is, however, invaluable, because such recollections contain unique information. A n 'inside story' is revealing, from the psychological and epistemological points of view, because it shows a logic of justification of its o w n action and theorization. Even the collection of the half-truths, myths and prejudices that are to be found in m a n y autobiographical records is extremely valuable for the historian if they are adequately evaluated and placed in the context of a detailed history.

Oral history

The same considerations can be applied to oral history. This is a fundamental and original tool, because for the first time the historian can create his o w n sources, producing them as the scientist produces facts in his laboratory. At the same time it gives rise to m a n y methodological problems. E . C . Clark25 lists four dominant features of oral history interviews: they are oral, autobiographical, the results of m e m o r y , and are a joint intellectual endeavour because with this technique the historian can create historical evidence through conversation with a person whose life experiences are considered memorable. The historian and interviewee bring differing perspectives to

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the past events they discuss, and this positive conflict gives the oral history interview a creative potential. However, the idea that in such interviews the truth is verbatim is an illusion. Oral history is an intersubjective experience of conversation and the oral historian must intervene as interpreter, writing about that a conversation means and heightening the shared meaning of the joint intellectual endeavour. This method is therefore very difficult to manage and often 'in oral history w e have used the simplest and most naive theory and method to ask the most significant questions'.26

Archives

A fundamental concern of the contemporary historian is the improvement of methods of collecting and preserving present-day evidence of scientific activity, establishing the primary materials on which the scholars of tomorrow will work. The fundamental sources on which any historical reconstruction of a scientific discovery must draw will remain documents originating from research directly involved in the various stages of its realization. Only these sources (publications, correspondence, note-books, laboratory records, recorded statements, recollections of conversations, and so on) can provide reliable information about the working of science.

M a n y scientific institutions have n o w established a policy for preserving their historically valuable records, provide facilities for their storage and have a positive attitude towards outside access to them. W o r k is being carried out: (a) to draw up inventories of the already deposited material by contacting research sites, libraries, archives, societies and individuals w h o might have such documents; (b) to document, collect and encourage the collection, deposition and use of archival materials; (c) to allow the use of the archival resources and to exchange information about them; and (d) to ask leading scientists to deposit their papers and documents. The publication of descriptions and catalogues of collected materials has already furnished the historian with an invaluable source of primary information.

M a n y theoretical problems must be solved in the process of documenting contemporary biomedical sciences. In particular, the enormous amount of existing documentation makes a rigid selection almost inevitable and a series of questions immediately arises: W h a t must w e save? W h o will save it? W h o will pay to maintain it? W h e r e to maintain it? H o w to maintain it?

The main and more difficult problem remains: H o w can w e choose what w e have to save? N o simply answer is available to such questions, in part because the interests of archivists and historians differ. They have different tools, methodologically and institutionally, and their respective aims need to be kept separate.

Science is n o w an international enterprise. The history of science and the collecting of archives can also be an international enterprise. The establishment of international guidelines to assist archivists and scholars in appraising, processing and describing scientific records of value can be useful in documenting the history of science. The establishment of an international policy for the standardization of procedures and c o m m o n rules for increasing the availability of documents could greatly increase their usefulness.

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The role of historical research in present debates

The methodological and theoretical difficulties discussed in the previous paragraphs should not hide the m a n y positive opportunities that the history of contemporary biomedical sciences offer to present debates on the practical and ethical consequences of scientific and technological developments. A large part of present concerns over the serious issues brought about by the biotechnologies were already present in the past. The lessons to be learnt from the historical inquiries include the knowledge that old material can be of benefit in motivating new research, in analysing social aspects, in answering fundamental questions about life and death, and in exposing the myths behind present attitudes. In the field of medical sciences, the dramatic impact of the A I D S pandemic, when historically reconstructed and analysed, serves to underline the extraordinary complacency on the part of public opinion following the introduction of antibiotics during the 1940s. Progress in medical sciences during the last century has obscured the enduring vulnerability of h u m a n populations to possible large-scale infections, owing to the expectation that hygiene, medicine and therapy would cope with any global epidemics.

In such a way the contemporary historian, bringing a knowledge of the past to present debates, collecting and preserving the memories of contemporary science, stresses the continuity of m a n y of our present concerns and at the same time the novel and sometimes revolutionary nature of m a n y advancements. While he enjoys his profession through the experience of retracing the roots and the ways of scientific creativity, the historian can feel a sense of efficacy, because, as Thucydides would say, he can be satisfied if what he is saying 'will be considered useful by someone w h o wishes to understand past events, that, owing to h u m a n nature, will be similar to future events'.

Notes

1. D E L B R U C K , M . , 'Aristotle-totle-totle', in Of Microbes and Life, M o n o d , J., Borek, E . (eds), N e w York: Columbia University Press, 1971, 50-55.

2. See C A N G U I L H E M , G . , 'La nouvelle connaissance de la vie' in Etudes d'histoire et de philosophie des sciences, Paris: Vrin, 1975,335-364. See also Rosenfield, L . W . , Aristotle and information theory, The Hague: Mouton, 1971.

3. G R M E K , M . D . , ' A plea for freeing the history of scientific discoveries from myth', in On Scientific discovery, M . D . Grmek, R . S. Cohen, G . Cimino (eds), Dordrecht: Reidel, 1981, 9^12.

4. G R M E K , M . D . , Raisonnement expérimental et recherches toxicologiques chez Claude Bernard, Geneva: Droz, 1973.

5. K L U G , A . , 'Rosalind Franklin and the Double Helix', Nature, 248, 1974, 787-88; J U D S O N , H . F., The Eighth Day of Creation. Makers of the Revolution in Biology. London: Jonathan Cape, 1979.

6. C A R L S O N , E . A . , The Gene: A Critical History, Philadelphia: W . B . Saunders, 1966. 7. D A L G L I E S H , C . E . , 'The template theory and the role of transpeptidation in protein synthesis',

Nature, 171, 1953, 1027-28. H A U R O W I T Z , F., 'Biological Problems and Immunochemistry'. Quart. Rev. Biol., 24, 1949, 93-123. For a critique of the circular nature of the template hypothesis see: D O U N C E , A . L. , 'Nucleoproteins (round-table discussion)'. J. Cell Comp. Physiol, 47, Suppl. 1,1956,103-112; P O N T E C O R V O , G . , 'Template and stepwise processes in heredity', Broc. Roy. Soc. B , 164, 1966, 167-9; P O N T E C O R V O , G . , 'Template Processes in Heredity and Evolution, in Devons, S. (éd.), Biology and the Physical Sciences', N e w York: Columbia University Press, 1969, 26-37.

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8. K O H L E R , R . E . , 'The History of Biochemistry: A Survey', J. Hist. Biol, 8, 1975, 275-318. K O H L E R , R . E . , From Medical Chemistry to Biochemistry. The making of a Biomedical Discipline, London: Cambridge University Press, 1982. F L O R K I N , M . , A History of Biochemistry, Part I-V, Amsterdam: Elsevier, 1972-1980. F R U T O N , I. S., Molecules and Life. Historical*Essays on the Interplay of Chemistry and Biology, N e w York: Wiley, 1972.

9. A L L E N , G . E . , 'Genetics, Eugenics and Society: Internalists and externalists in contemporary history of science', Soc. Stud. Sci., 6, 1976, 105-22; K E L V E S , D . J., In the name of eugenics. Genetics and the use of human heredity. N e w York: Knopf, 1985; K I M M E L M A N , B . A . , 'Genetics and eugenics in an agricultural context: the American Breeders' Association 1903-1913', Soc. Stud. Sci, 13, 1983, 163-204; S E A R L E , G . R . , 'Eugenics and Politics in Britain in the 1930s', Ann. Sci., 36,1979,159-216; W E I N D L I N G , P . , 'We imar eugenics: the Kaiser Wilhelm Institute for anthropology, h u m a n heredity and eugenics in social context', Ann. Sci., 42, 1985, S O S -SIS; L U D M E R E R , K . , Genetics and American Society: A Historical Appraisal, Baltimore: Johns Hopkins University Press, 1972. M A C K E N Z I E , D . , 'Eugenics in Britain', Soc. Stud. Sci., 6, 1976, 499^152.

10. P A R A S C A N D O L A , J. (éd.), 'The History of Autobiotics: A Symposium', Amer. Inst. Hist. Pharmacy, 1980; L I L I E N F E L D , A . M . (éd.), Times, Places, and Persons: Aspects of the History of Epistemology, Baltimore: Johns Hopkins University Press, 1980.

11. C R O M B I E , A . , 'Stili scientifice e livelli storiografici', in Livelli di realsà, Piattelli-Palmarini. M . (e cura di). Milano: Feltrinelli, 1983, 234-255.

12. K O H L E R , R . E . , From Medical Chemistry to Biochemistry. The making of a Biomedical Discipline, London: Cambridge University Press, 1982.

13. But there are of course m a n y valuable exceptions, for instance B O V E T , D . , Une chimie qui guérit. Histoire de la découverte des sulfamides, Paris: Payot, 1989; C A R P E N T E R , K . J., The History of Scurvy & Vitamin C, Cambridge, Cambridge University Press, 1986; K E I L I N , D . , The History of Cell Respiration and Cytochrome, Cambridge, Cambridge University Press, 1966; R A T H E R , L . J., The Genesis of Cancer: A Study in the History of Ideas, Baltimore: Johns Hopkins University Press, 1978; S I L V E R S T E I N , A . M . , A History of Immunology, San Diego, 1989.

14. C A I R N S , J., S T E N T , G . S., W A T S O N , J. D . (eds.), Phage and the Origins of Molecular Biology, Cold Spring Harbor Laboratory, 1966. For a different view see K E N D R E W , J. C , ' H o w molecular biology started? Review of Phase and the Origins of Molecular Biology', Sci. Amer., 216, 1967, 141-3. See also H A Y E S , W . , ' M a x Delbrück and the birth of molecular biology', Social Research, 51, 1984, 641-673. M U L L I N S , N . C , 'The development of a scientific specialty: the Phage Group and the origins of molecular biology', Minerva, 10,1972, 51-82; F I S C H E R , E . P., and L I P S O N , C , Thinking about science, Max Delbrück and the origins of molecular biology, N e w York: Norton, 1988; K A Y , L . E . , 'Conceptual Models and Analytical Tools: The Biology of the Physicist M a x Delbrück', J. Hist. Biol, 18, 1985, 207-246.

15. W A T S O N , J. D . , The Double Helix: A Personal Account of the Discovery of the Structure of D N A , N e w York: Atheneum, 1969; S T E N T , G . S. (éd.), The Double Helix: Text, Commentary, Reviews, Original Papers, N e w York: Norton, 1981. S T O K E S , T . D . , 'The Double Helix and the warped slipper—an exemplary tale', Soc. Stud. Sci., 12, 1982, 207-240.

16. O L B Y , R . C , The Path to the Double Helix, London: MacMillan, 1974. See also C R I C K , F . H . C , 'The double helix: a personal view', Nature, 248, 1974, 766-769.

17. O L B Y , R . C , 'The Origins of Molecular Genetics'. J. Hist. Biol, 7,1974,93-100; O L B Y , R . C , 'The Origins of Molecular Biology at Cambridge and Caltech', in Proceedings of the Conference on the History of Biochemistry and Molecular Biology. J. T . Edsall (éd.), Brookline, Mass.: A m . Acad. Arts and Sciences, 1970, 60-95. See also O L B Y , R . C , 'Historiographical Issues in the History of Genetics'. Riv. Stor. Sci., 1,1984; P E R U T Z , M . F. , 'Origins of molecular biology', New Sci., 1980, 326-329.

18. L W O F F , A . , and U L L M A N N , A . (eds.), Origins of Molecular Biology. A Tribute to Jacques Monod, N e w York: Academic Press, 1979.

19. Ibid., p. 17.

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20. See for example C A R L S O N , E . A . , ' A n Unacknowledged Founding of Molecular Biology: H . J. Muller's Contributions to Gene Theory 1910-1936', J. Hist. Biol, 4,1971,149-170; C O H E N , S. S., 'The origins of molecular biology: A review of Olby's The Path to the Double Helix', Science, 187, 1975, 827-830; C O H E N , S. S., 'The Biochemical Origins of Molecular Biology (Introduction)', Trends Biochem. Sci., 9, 1984, 334-6. See Olby's answer to the last paper: O L B Y , R . C , 'Biochemical origins of molecular biology: a discussion', Trends Biochem. Sci., 11, 1986, 303-305.

21. L E D E R B E R G , J., The history of microbiology 1930-1950, in History of the 20th Century, R o m a : Istituto dell'Enciclopedia Italiana, in press.

22. S A P P , J., Beyond the Gene. Cytoplasmic Inheritance and the Struggle for Authority in Genetics, Oxford University Press, 1987.

23. E D S A L L , J. T . (éd.), Proceedings of the Conference on the History of Biochemistry and Molecular Biology, Brookline, Mass. : A m . Acad. Arts and Sciences, 1970, 140-149; S R I N I V A S A N , P . R . , F R U T O N , J. S., and E D S A L L , J. T.(eds.), The origins of modern biochemistry. A retrospect on proteins, N e w York: N e w York Academy of Science, 1979; H O L M E S , F . L . , 'Hans Krebs and the discovery of the ornithine cycle', Fed. Amer. Soc. Exp. Biol. Proc, 39, 1980, 216-225.

24. M C C A R T Y , M . , The Transforming Principle: discovering that genes are made of D N A , London: Norton, 1986.

25. 'The Oral History Interview', in Effective Interviewing, (A. Tolor, éd.), T h o m a s : Springfield, Illinois, 1986.

26. G R E L E , R O N A L D J., ' C a n Anyone Over Thirty be Trusted? A Friendly Critique of Oral History', in Envelopes of Sound: The Art of Oral History (R. J. Grele, éd.), Chicago: Precedent Publishing, 1985, p. 205.

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Mathematics education: a historical view

Geoffrey Howson

A knowledge of the history of mathematics education can help us identify those key questions which must be answered, in ever-changing contexts, by each new generation of educators. Only through its study can we come to appreciate and begin to confront the great, yet vital, problems of effecting changes within educational systems.

Mathematics has a place in the curriculum of almost every school in all countries. Indeed, providing for the teaching of the subject must account for at least 10 per cent of all educational budgets—a vast s u m when aggregated around the globe. The abstract, symbolic sentence '1 + 1 = ' could be read and completed by millions of people w h o share no other verbal or written means of communication.

There would seem little need of arguing that considerable study should be devoted to the teaching of mathematics. It is given great emphasis worldwide, at correspondingly enormous cost, and is very widely, and in m a n y ways correctly, viewed as an essential springboard to national scientific and technological advancement and well-being.

Yet, for a variety of reasons, whole areas of mathematics education are given scant recognition. Surprisingly little, for example, is done systematically within the field of comparative education. Rather, considerable emphasis is placed on developmental work and on psychological research related, in particular, to the problems of learning mathematics. The reasons for these biases are obvious. Although mathematics is taught everywhere, there is universal dissatisfaction with its teaching. This unease has m a n y sources: curricula have not adapted sufficiently to the great widening of educational opportunities as enrolment and staying-on rates have everywhere soared, neither have they been able to respond to the opportunities offered by technological advances. There is a growing mismatch between hopes and attainments. Yet new goals are constantly being set, and possible n e w technological aids to teaching continue to come onto the market: no wonder that curriculum development should assume such importance. The

Geoffrey H o w s o n is Professor of Mathematical Curriculum Studies at the University of Southampton. F r o m 1983 to 1990 he was Secretary of the International Commission on Mathematical Instruction. H e is the author of m a n y books and articles on curriculum development and the history of mathematics education, including Mathematics: Society and Curricula (with H . B . Griffiths), Curriculum Development in Mathematics (with C . Keitel and J. Kilpatrick), A History of Mathematics Education in England, and School Mathematics in the 1990s (with B. J. Wilson). H e m a y be contacted at the following address: Faculty of Mathematical Studies, University of Southampton, Southampton S 0 9 5 N H , U K .


G. Howson

curriculum together with the teacher and the learner comprise the quintessential triad of education. That the teacher has received less attention than the other two members can be ascribed to the particular difficulties of studying, evaluating and comparing the work of teachers. It is also true that the researcher in learning can draw upon well-established theories which provide not only support but also a degree of academic 'respectability' denied their colleagues.

W h a t , though, has all this to do with the history of mathematics education? H o w will the study of that promote curriculum development, or contribute to better teaching and learning? It is, surely to these problems that the educator's efforts should be addressed, rather than to 'scholarly' pursuits such as history.

Similar arguments can, of course, be advanced concerning most of the topics covered in this and the previous issue of Impact. W h y , say, study the history of chemistry when one could be advancing the frontiers of that subject? The answers that the various authors would supply would have m u c h in c o m m o n . However, I believe that in the case of the history of education, other, more utilitarian arguments can be advanced.

W h a t are rarely studied within mathematics education are educational systems and h o w they respond to change. Yet it is on 'change' that w e wish to focus: change in the curriculum, in the use of technology, in pupils' levels of attainment and motivation, and in teachers' aims and efficiency. Such changes affect, and occur because of the effort of, individuals. However, if developments are to be successful then the effects on the system as a whole must be considered. If not, a minority of individuals will take advantage of new opportunities, but the majority are likely to accept the innovation in a garbled and often worthless form.

This is only one of the insights which a study of the history of mathematics education can help us develop. Elsewhere, I have referred to this history as 'the laboratory of the curriculum developer'. Here one can study the results of past experiments, and, for example, see what worked and what was rejected, what problems of implementation arose, come to understand h o w initial success can soon turn to disappointment, and appreciate the crucial role of the teaching force. It provides a bank of knowledge which should guide us when w e come to plan new initiatives. For here it must be remembered that unsuccessful experiments in education do not merely result in a loss of money and materials: they m e a n deprived students, and discouraged teachers and parents w h o will view further proposed innovations with very jaundiced eyes. History, alas, will m a k e us less sure of our ability to m o v e educational mountains. It m a y , however, help guide the task of earth-removal!

S o m e key questions

History not only teaches us about change, and the time scale for changes, but w e also learn from it that most of our key problems are not essentially new. Studying h o w these problems were answered in different times and in other contexts m a y still yield lessons for us today. Below w e shall give examples to illustrate these points and will also draw attention to some of the hazards which beset historians of mathematics education.

The history of mathematics stretches back for thousands of years and doubtless, since existing knowledge had to be passed on to novitiates, so does that of mathematics education. However, sources are such that little can be inferred about the way in which

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the transfer of mathematical knowledge took place. Plato's famous dialogue concerning Menon's slave is by far the best k n o w n of early examples of'mathematics education' in practice. It has been quoted on m a n y occasions and the Socratic dialogue used as an example of 'good teaching'. (One often wonders, though, h o w m a n y of the advocates have actually studied the dialogue and, in particular, the boy's contributions and the learning likely to have taken place.) But to what extent was Socrates' method typical or extended to form the basis of a curriculum? W e cannot tell.

It is only with the growing institutionalisation of learning that answers, and new doubts, emerge. The growth of Christianity led in the second half of the first millenium A D to the establishment of schools attached to religious institutions. N o w w e have evidence of curricula: for example, that of the school at York, England at which the scholar Alcuin taught.

Nowadays , w e are very m u c h aware of the distinction that must be m a d e between the 'intended' curriculum as set out by governments and other authorities and the curriculum 'implemented' by teachers. (That actually 'attained' by students is yet another matter.) Obtaining information about the implemented and attained curricula is very far from easy. W e do not k n o w exactly what was taught at York. Even where w e have 'evidence', for example Roger Bacon's observation that there were few, if any, in thirteenth-century Oxford w h o had read more geometry than Euclid's definitions and the first five propositions of Book 1, doubt remains. Is it fact, or a choleric outburst?

The reliability of sources and their interpretation present recurring problems in all disciplines. Those within the history of education would seem far greater than those within that of the pure sciences, particularly as one comes nearer the present times when education assumes such great political importance. ( H o w is one to interpret the recently set goal of the U S National Governors' Assocation: that 'by the year 2000, U S students will be the first in the world in mathematics and science achievement'? Is it to be interpreted as a serious statement on what is possible within the field of curriculum development, or as a target which is to be seriously sought (even though it is appreciated that it cannot be achieved), or is it simply a political utterance that will be forgotten come the year 2000?

But even the early records of the church institutions and the charters of the medieval universities suffice to demonstrate the importance of the question ' W h y teach mathematics?' The answer is implicit in the curricula. There the claims of mathematics as a utilitarian tool, as a key to understanding other sciences, and as a subject worthy of study for its o w n sake are all displayed—not necessarily concurrently. The reasons for not teaching mathematics—or, at least, ensuring that students did not see too m u c h of the subject—were also set out. It 'leads away from the things of life, and estranges m e n from perception of what conduces to the c o m m o n weal [good]', wrote the Spaniard Vives. The 16th century Englishman Ascham was more outspoken, ' M a r k all Mathematical heads which be wholly and only bent on these sciences, h o w solitary they be themselves, h o w unfit to live with others, h o w unapt to serve the world.' That mathematicians need to pay attention to their image is, then, but one of the early lessons of history.

Let us, however, consider briefly one set of reasons for studying mathematics: that supplied by Richard Mulcaster, a London schoolmaster and contemporary of Ascham's.

Such studies require concentration, and demand a type of mind that does not seek to m a k e public display until after mature contemplation... The Mathematical

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Sciences show themselves in m a n y professions and trades... whereby it is well seen that they are really profitable; they do not m a k e outward show, but our daily life benefits greatly by them. . . Mathematics are the first rudiments for young children, and are the sure means of direction for all skilled w o r k m e n , w h o without such knowledge can only go by rote, but with it might reach genuine skill... In the manner of their teaching [they] also plant in the mind of the learner a habit of resisting the influence of bare probabilities, of refusing to believe in light conjectures, of being moved only with infallible demonstrations.

(Just to underline the difference between what is 'intended' and what is 'implemented', it should be pointed out that neither of the schools of which Mulcaster was head included mathematics in its curriculum!)

Mulcaster's list is surprisingly comprehensive, particularly if one presents his aims in modern language:

the study of mathematics inculcates desirable personal traits, mathematics has utilitarian value, both in life and in the pursuit of other disciplines, a knowledge of mathematics can free one from dependence on remembered procedures and on other persons.1

In succeeding centuries n e w claims were m a d e for mathematics teaching. For one brief period, following Newton's revelation of a 'system' of celestial mechanics which 'could only proceed from the counsel and dominion of an intelligent and powerful Being... [the] Lord over all', it was argued that the study of mathematics would lead students to G o d . This claim was soon denied. Isaac Watts, an eighteenth century divine, w h o at one time was an advocate of teaching mathematics, grew to feel that 'having no tendency to rectify the will, to sweeten the temper, or m e n d the heart, [mathematical studies] often leave a stiffness, a positiveness and sufficiency on weak minds, which is m u c h more pernicious to society... than all their advantages can recompense... They are apt to beget a secret and refined pride, an overbearing vanity... This tempts [mathematicians] to presume a kind of omniscience in respect to their fellow creatures... [Mathematical studies are not] fit to be trusted in the hands of any but those w h o have acquired a humble heart, a lowly spirit, and a sober and teachable temper.'

W e have no space here to pursue the question, ' W h y teach mathematics?', or to consider further the arguments advanced against its teaching. Perhaps it should be emphasised, however, that there are genuine lessons to be learned from considering this question and, in particular, from seeing the different degrees of success which have attended past attempts to attain specific goals. For example, one commonly accepted aim is to teach mathematics so as to demonstrate its applicability within other disciplines. This has led on numerous occasions to calls for cross-curricula teaching. (A most interesting attempt to m o v e away from a subject-centred curriculum took place in the Soviet Union in the early post-revolutionary years. Then, the curriculum in the elementary school was presented through the three themes, nature, work and society. It was an initiative meriting further detailed historical study.) Yet if w e consider past experiences in a variety of countries w e see that although there have been m a n y successes in the primary grades, problems have arisen further up the school. Clearly, cross-curricula work can provide motivation and also desirable educational links. However, there are doubts as to whether by itself it can provide a sufficient base for

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mathematical learning in the secondary school. There are non-trivial lessons to be learned from the past.

Let us, however, turn briefly to another, m u c h related problem, ' W h y learn mathematics?', for this introduces us to other aspects of the history of mathematics education.

W h y learn mathematics?

Compulsory school attendance is relatively new in all countries; in England it did not come until 1880, in Mississippi until 1918. Even the general provision of schools teaching mathematics is fairly recent. A famous judgement delivered in 1805 in the English High Court decreed that grammar schools were for 'teaching grammatically the learned languages'. Schools wishing to teach mathematics or a modern language could only offer these subjects as optional extras for which fees were charged. Only in 1840 were endowed schools finally given permission to deviate from the classical, humanistic curriculum laid d o w n by their founders.

Yet there was a great need for utilitarian mathematics well before this was readily available in educational institutions. H o w was this need met? Here a most interesting area of mathematics education is opened up.

The rise of commerce began in Italy some five hundred years ago and soon there was a demand in m a n y European countries not only for what w e might term commercial arithmetic, but also for that knowledge of navigational mathematics which was becoming ever more essential. N o w new manuscripts and, more importantly, printed books became available which appealed to users rather than scholars. It was essential that these works were available in the vernacular and so, for the first time, there appeared 'popular' books in, for example, German and English by authors such as Ries and Recordé.2 The latter, in fact, identified two types of reader w h o might find his books of benefit: those ' w h o study principally for learning' and those w h o wished to acquire the knowledge for some particular, vocational purpose. Soon there arose 'mathematical practitioners' or 'reckoning masters' w h o were able to supply lessons to those requiring mathematics. S o m e idea of the need, and the way in which it persisted, is provided by the example of Samuel Pepys, the great diarist and the President of the Royal Society, whose n a m e appears on the title page of Newton's Principia. Pepys had studied at a leading school in London (one at which Mulcaster had been Head) before graduating at Cambridge University. Nevertheless, as a senior official in the Admiralty, he felt m u c h handicapped by a great gap in his education. H e knew scarcely any arithmetic! His diary for 1662 records h o w he therefore employed a tutor to help him learn the multiplication table.

The work of the English practitioners in the 17th and 18th centuries has been well documented and researched by such authors as E . G . R . Taylor and P . J. and R . Wallis. Through their work we are able to see h o w the demand for mathematics gradually spread throughout the country, h o w special series of lectures were given by either resident or peripatetic teachers and h o w , for instance, in-service courses for private teachers of mathematics were organised in Northern England in the 1760s. It is interesting to note here h o w the mathematical practitioner has been reincarnated in a slightly different form: the freelance tutor of computing w h o plies his or her trade with individuals and companies. Not only has conventional education not been able to

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respond quickly enough to changing needs, but w e n o w have such rapidly changing demands on workforces that schooling and higher education will, of necessity, prove quickly out-of-date. W e are entering a well-defined new era in education, but once again the established 'system' cannot produce a coherent response. The demands are having to be catered for elsewhere. O n e result is that U S industry n o w spends nearly as m u c h each year on the mathematical education of its employees as is spent on mathematics education in the nation's schools.3

The motivations of those learning mathematics, and those forced—often against their will—to learn mathematics, are constantly changing. History emphasises the need to continually study and respond to these changes.

N e w directions in mathematics teaching can, however, influence people's view of the subject. The mere utility of mathematics was to prove somewhat prejudicial in the early 17th century: '[such studies were] scarce looked upon as Academical studies, but rather mechanical; as the business of Traders, Merchants, Seamen, Carpenters, Surveyors of Lands, or the like, and perhaps some Almanack Makers in London. A n d among more than two hundred students (at that time) in our college [at Cambridge University], I do not k n o w of any two . . . w h o had more mathematics than I... which was then but little; and but few in the university. For the study of Mathematicks was at that time more cultivated in London than in the universities.' (John Wallis, writing of England in the 1630s and 1640s).

Balancing and respecting the claims of mathematics as both a utilitarian tool and also as a discipline in its o w n right has, of course, proved a continuing problem within mathematics education. False dichotomies between 'Pure' and 'Applied' mathematics have frequently complicated the matter even further.

Teachers of mathematics

The first 'teachers of mathematics' in Western Europe were not, then, primarily to be found in schools. They were often self-taught mathematicians w h o developed their knowledge as they pursued their trade. The story of the emergence of the professionally trained, institutionally educated teacher is a long and interesting one. (Recent writings in England have demonstrated that it is still not universally accepted that teachers should be professionally trained—the story is an on-going one.) It is also reasonably well documented, for it is post-1789. National systems of education were founded in France and Prussia about that time, governments came to link education with industrial advancement and, as a result, comparative accounts of education began to appear. For example, in 1831 the French commissioned a report on public education in Prussia. Later there were publications on Continental education by, among others, the American Barnard and the Englishman Kay-Shuttleworth. Particular interest was shown in the Swiss teacher-training institutions and, as a result, the work of Pestalozzi gained speedy international recognition. Research work on education in that period and, in particular, the influences of Prussia and France on the educational systems of other countries is currently being carried out by, for example, Schubring. (Another interesting feature of mathematics education in that period was the introduction of algebraic methods into geometry teaching. This raised similar problems to those currently being encountered with respect to the introduction of calculators into schools. W h a t would be the result of casting aside old methods, modes of thought and

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techniques that had been so prized? Accounts of the way in which changes were proposed and opposed, for example by the G e r m a n O h m , whose work has n o w been overshadowed by that of his better-known, law-giving brother, have been provided by a number of authors, such as Jahnke.)

N o sooner did the 'professionalisation' of teachers begin than questions began to be asked about their status in society. In 1838 the Committee of the Central Society of Education, London, offered a prize of £105, a considerable sum in those days, for the best essay on 'The Expediency and Means of Elevating the Profession of the Educator in Public Estimation'. The winner considered the proposal 'to connect with each of the Universities a professor of education, whose duty it would be to deliver lectures', but rejected this suggestion as unlikely to produce m u c h of benefit. Since then the battle has been fought, not only to raise (and, more recently in m a n y countries, to maintain) the status of teachers, but also to gain recognition for education as a university discipline.

The special contribution of professional associations of mathematics teachers is already well chronicled, for example the N C T M ' s History of Mathematical Education in the United States and Canada, published in 1970, and the history issued to mark fifty years of the Mathematical Association of America. The story of what is probably the oldest subject association, the Mathematical Association (of the U K ) , is currently being prepared.

If hard-won ground is not to be lost, than it is essential that the benefits of professionalism can be clearly demonstrated. This will only be done through historical and comparative studies. Here, of course, it must be stressed that in education, history has a nasty habit of starting last week. For, although the examples I have given have tended to be from the nineteenth century and earlier, some of the most relevant lessons are to be learned from recent history. Here one must mention, for example, those to be drawn from the wave of reforms which swept through the world in the 1960s and 1970s. So m u c h was hoped, and so little appears to have been achieved (indeed, some of what was achieved has already been lost). Attempts have been made to chronicle the battles and movements of those years, but often they have only served to illustrate the difficulties of writing histories—particularly if these are based only on 'official' written sources. Attempting to research, describe and compare the work of projects, sometimes working in a variety of countries within very different conditions, would, for example, hardly seem appropriate work for P h D students. Such work demands m u c h more experience and knowledge.

S o u r c e s for the historian

This serves to introduce us to s o m e of the problems of researching the history of mathematics education a n d in particular to the range of sources that is available to the historian. Let us list s o m e of these:

(i) statements concerning the a ims of mathematics education from individuals, government commissions, professional associations, . . . ;

(ii) legislation affecting the organisat ion o f m a t h e m a t i c s teaching in schools ; (iii) proposals, advertisements a n d syllabuses relating to mathematics courses; (iv) guides for classroom m a n a g e m e n t a n d accounts of mathematics teaching; (v) textbooks a n d examination papers;

(vi) pupils' w o r k b o o k s ;

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(vii) apparatus and aids available to the pupils and teachers; (viii) statistical data relating to mathematics education, its provision and to

student attainment; (ix) teacher education and the professional and social status of teachers; (x) theories and findings relating to the learning of mathematics.

It is, I believe, important that weight should be given to this full range of sources. Individual types of material m a y have m u c h to offer, but leave m a n y important questions unanswered. The recently published History of the School Mathematics Curriculum in Japan illustrates through the use of official documents and reports h o w the national curriculum has changed over the century. It is a fascinating document. Yet, for all its virtues, w e cannot learn h o w the curriculum was translated into practice, h o w it was taught and to what proportions of the country's male and female youth. Finding answers to these questions would not be easy. Textbooks are, of course, a wonderful source. These take bare phrases from a curriculum and flesh them out with explanations, examples and problems. They, it might be thought, can reveal what was taught. Textbooks lend themselves to systematic analysis and it is, for example, good that an analysis of books published in the decades immediately following the French Revolution is currently being undertaken by an international group with particularly strong French and G e r m a n representation. Close examination and comparisons reveal m u c h about h o w new mathematics creeps into textbooks and is disseminated. W e learn h o w a piece of academic mathematics is 'transposed' into a suitable form for the curriculum, h o w exercises are constructed around it, whether or not applications based on it enter texts and so on. Light is thrown on the influence of particular institutions and of the authors drawn from them. The influence of the Ecole Polytechnique and 19th-century Cambridge, for example, are clearly revealed. But w e must resist what Glaeser has called the tendency to 'linger over books'. They can tell us a great deal, but still leave m u c h unanswered.

T h o m a s Carlyle's translation of Legendre's Geometry tells us less about the influence of Legendre on English education than do its abysmal sales figures, and to learn of these w e must pick up a chance remark by one of his biographers. Again, a best-selling English school text of the 1870s contains one chapter which would be enthusiastically received by any critical mathematican or educator. The only pity is that no schoolteacher appears to have attempted to teach it! W e must be aware, then, of what is not revealed by texts.

Accounts of mathematics teaching are harder to find. There are reports written by nineteenth-century inspectors of schools and comparative educators, but these describe atypical classrooms, namely those in which a visiting dignitary is fleetingly to be found. 'Biographical' accounts exist, but these are often written in old-age with literary effect in mind rather than educational accuracy. There are few accounts of mathematics lessons in fiction and again their accuracy is often suspect—nevertheless one can, I believe, obtain certain insights into the way mathematics was taught. Perhaps the most reliable source is the student's workbook, or the hand-written marginal notes to be found in texts. F e w analyses of these last sources are to be found in the literature, yet they would seem to tell us m u c h . Happily, research reports, films and other sources will help future historians to form a better impression of h o w some mathematics classes operated in the late 20th century.

The mention of research prompts another observation. Mathematics has been taught for centuries. However, it is only in the 20th century that 'mathematics

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ARITHMETICAL QUESTIONS, ON A N E W PLAN: -

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Figure 1. Title page of a n early attempt to teach arithmetic in a cross-curricula setting. N o t e the intended audience.

311

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Figure 2. Calligraphy or mathematics? A n extract from an 18th-century (teacher's?) school workbook.

education' has emerged as a field of study and for research. The history of research in mathematics education has been admirably described by Kilpatrick (to appear); a paper which, through its documentation of the development of research interests and techniques, vividly illustrates the benefits of a historical understanding of where one is, h o w one arrived there and in which directions social, mathematical, educational and political forces are taking us.

Past v. present

It is, then, essential that w e c o m e to understand more of the past, that w e m a k e use of the lessons it offers, that time is not spent reinventing the wheel or following courses of

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action that experience can tell us are d o o m e d to failure. Yet here I must express s o m e misgivings. Mathematics education lacks, and is b o u n d to lack, that certainty which, say, mathematics possesses. There are few 'theorems' about h o w to teach mathematics and anyone involved in the training of teachers must occasionally look enviously at those w h o teach mathematics and possess one hundred per cent faith in the validity and accuracy of what they are teaching. Mathematics education, too, is all too often seen as pragmatic and vocationally oriented rather than scholarly. T h e result of this is a possibility that the history of mathematics education will be studied because it does allow one to display that scholarship which is prized by colleagues in other faculties and to deal in 'harder' facts than usual. O n e could, for example, write scholarly P h D theses, replete with facts, on the place of mathematics in the curricula of seventeenth century English g r a m m a r schools. I hope though that such delights will not prove too attractive to alert, young minds. There are m o r e pressing problems to be investigated within mathematics education. Nevertheless, history is, I believe, most important. There are numerous ways in which it can help us comprehend and respond to today's problems (see Glaeser (1984) for one example). It would be a pity, then, if its study were to be approached only in a 'traditional historical' manner . In the present crisis state of mathematics education, historical studies m a y be a luxury w e cannot afford unless they not only throw light on the past, but also illumine our present situation. •

Notes

1. It is interesting to compare Mulcaster's aims with those to be found in, say, Steen's article 'Numeracy' in the Spring 1990 issue of Daedalus.

2. There are intriguing parallels to be found between the switch from Latin to the vernacular as the medium of instruction in 16th century universities, and that from, say, English to the vernacular in newly-independent developing countries in the 1970s and 1980s. In this paper little has been said about education in the developing countries or in non-Christian societies. However, it must be stressed that the reasons for this are lack of space and, on occasion, lack of references, rather than lack of relevance. For it must be emphasised that interest in the history of mathematics education is still relatively limited and in many countries no large-scale histories exist.

3. National Research Council—quoted in Steen op cit.

References

G L A E S E R , G . (1984) A propos de la pédagogie de Clairaut, Recherches en Didactique des Mathématiques, 4, 332-344.

H O W S O N , A . G . (1982) A History of Mathematics Education in England, Cambridge University Press, Cambridge.

J A H N K E , H . N . and O T T E , M . (eds.) (1981) Epistemological and Social Problems of the Sciences in the Early Nineteenth Century, Reidel, Dordrecht.

K I L P A T R I C K , J. (in press) A history of research in mathematics education, in Handbook of Research on Mathematics Teaching and Learning (éd. Grouws, D . A . ) , Macmillan, N e w York.

N A G A S A K I , E . (ed.) (1990) A History of the School Mathematics Curriculum in Japan, N.I .E.R. , Tokyo.

N A T I O N A L C O U N C I L O F T E A C H E R S O F M A T H E M A T I C S (1970) A History of Mathematical Education in the United States and Canada, N C T M .

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Preparations for Zaragoza The X I X International Congress on the History of Science

Mariano Hormigón

The world's major international gathering devoted to the history of science will next meet in 1993 in Zaragoza, Spain. The person at the centre of the organizational effort needed to ensure its success talks here about the background and the present philosophy behind the preparations.

The XVIII General Assembly of the International Union of History and Philosophy of Science/Division of History of Science decided, at its session held in Munich on 7 August 1989, that the next International Congress on the History of Science would be held in Zaragoza, Spain, in 1993. It designated Professor Jean D h o m b r e s as President of the International Programme Committee, and myself as President of the Organizing Committee.

The General Assembly is thus relying on the Spanish scientific community of historians of science and technology and on the increasing interest of the Spanish authorities to develop this field of knowledge. The Spanish Society for the History of Science and Technology, created at the end of Franco's dictatorship and legalized in 1976—during the first democratic transition— has grown and has n o w four hundred members distributed in all the Spanish universities and higher educational and research centres, in secondary schools and in other institutions concerned with history of science and technology, Llull, the Journal of the Spanish Society for the History of Science and Technology, has produced up to the present 24 issues—issues appearing each M a y and November—in 14 volumes. The policy of the Ministry of Education also deserves some explanation. Since 1986 the history of science and technology has been a field of knowledge which has received special treatment, placing it on a similar plane to that of disciplines such as biogenetics, micro-electronics or applied mathematics. This

Mariano Hormigón teaches mathematics and history of science at the University of Zaragoza. His research interests are on Spanish science in the late 19th and the 20th century, a subject on which he has been publishing over the last fifteen years. H e is presently directing the section of the Department of Mathematics of the University of Zaragoza devoted to the history of science and has been, since 1984, the President of the Spanish Society of History of Science and Technology and, since 1981, the Editor of its journal Llull. H e can be contacted at the following address: Sociedad Española de Historia de las Ciencias y de las Técnicas, Facultad de Ciencias (Matemáticas), Ciudad Universitaria, 50009 Zaragoza, Spain.


M. Hormigón

special treatment, which has been designed mainly to train historians of science and technology coming from scientific fields, has enabled the university research groups to consolidate their work initiatives.

The Spanish community of historians of science and technology, which naturally hopes that the X I X International Congress on the History of Science will become a strengthening point for the development of this discipline in Spain, has a major responsibility as well as m u c h hard work before it. So, w e are presently starting to create the organs that will take charge of the preparations and development of the Congress.

A scientific meeting is valued for its debates and scientific advancements. Such glittering results are only achieved after hard organizational work, even if this m a y at first sight appear to stray from strictly scientific concerns. The Organizing Committee will be formed from the governing body of the Spanish Society for the History of Science and Technology, one representative of the Association for the History of Spanish Science and two representatives of the Seminar of the History of Science and Technology at the University of Zaragoza. Several members of this Seminar will constitute the Secretaryship of the Congress. Representatives of the more important Spanish research groups in the history of science and technology will also take part in the meetings of the Organizing Committee as assessors. Next autumn the Organizing Committee will discuss the schedule of plenary meetings for the next three years and then m a k e the first worldwide announcement of the X I X International Congress. Within the Scientific Committee the International Programme Committee, presided over by Professor Jean Dhombres , will be in charge of the executive share. The aim of this organ will be to channel and structure the scientific collaboration—plenary lectures, symposia, scientific sections—at the Zaragoza meeting.

The X I X International Congress on the History of Science is a challenge because of the high level of the previous eighteen (see Annex). The international community of historians of science and technology has experienced major structural changes during the last decades. While earlier international meetings were small and selective, the last two already had about one thousand participants. The congresses of Berkeley (1985) and H a m b u r g - M u n i c h (1989) represented steps of increasing progression, and this leads us to think in terms of about two thousand people for the Zaragoza meeting in 1993. This number naturally poses some very serious problems of organization and planning.

O n this particular point the suggestion of the XVIII General Assembly to shorten the next Congress is relevant; bearing in mind that the last two congresses covered an average of ten days and were dense, busy meetings full of hustle, there m a y be m a n y difficulties associated with having so large a number of participants in even more activities per day.

There is a trend in opinion, shared by some distinguished scientists, that calls into question the efficacy of any kind of scientific meeting. Its defenders argue that knowledge prospers thanks to that original research work whose quality is guaranteed by being refereed before its publication in some prestigious journal. D u e to the k n o w n quality control deficiencies of well attended congresses, they reject the unavoidable bad contributions, the good ones and even the very congresses themselves. But today, it goes without saying that it is more necessary that ever for any researcher to keep up to date in the most outstanding works appearing in his field of knowledge, as well as to k n o w the works' authors. It is almost impossible to read every interesting paper and, at

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the same time, be active in research, teaching, and scientific management. Either one's specialized topic is ridiculously scanty or most threads of the hank of knowledge one pretends to straighten out will necessarily escape one's notice. That is w h y , since the last century, when some European national scientific communities created the national Associations for the Advancement of Sciences, the idea of science as a c o m m u n a l action requiring periodical contact between the different groups took shape. That has been the practice in every active academic discipline: an area of knowledge not generating any kind of meeting is not an essential part of h u m a n knowledge: it is at most a subject. Congresses—especially international ones—are indispensable checkpoints for m e n and w o m e n producing living science to listen to, debate or refute other colleagues' theoretic and positions, learn about what has been and is being done, and articulate future fruitful joint ventures. The 'anti-congress' positions recall, with wearisome insistence, a decadent and obsolete scientific conception based on the view that knowledge concerns essentially the social group of the self-styled genius, generally established in a few selective academic centres around the world. Fortunately, the dominant trend towards international cooperation is isolating such elitist positions.

In the specific domain of the history of science and technology, the remarkable increase in size of the scientific community has brought about a change that has taken place without excessively sudden shocks. In spite of certain economic difficulties, representatives of more than seventy countries were able to attend the H a m b u r g -Munich Congress. If world politics carry on along the path of general relaxation, if the international economic situation improves, and if we , as organizers, get the necessary support, those two thousand or so participants from more than one hundred countries will have their stay in Zaragoza in 1993 guaranteed comfortable and pleasant.

Neither the Organizing Committee, the Scientific Committee nor the Executive Council of the International Union of History and Philosophy of Science/Division of History of Science, have given their final opinion on an important subject which is still to be exhaustively discussed: the Congress theme. The history of the Congresses of History of Science has not been uniform. The last two meetings illustrate two a m o n g the various ways of approaching this question. The Berkeley Congress offered symposia and scientific sections for the different periods and thematic areas. This structure provided the widest possibilities of participation for most researchers, whatever their geographical origin or research topic. The G e r m a n organizers of the XVIII International Congress chose a formula of proven effectiveness: the concentration of scientific contributions about a single theme. Such an approach puts obstacles in the w a y of participation, but undoubtedly favours the profound study of the chosen subject which, like that of the last Congress—Science and political order— should be of general concern for the international community. The debates which started at that very Congress in the Federal Republic of G e r m a n y and are still alive, seem to incline most historians of science and technology towards an open structure, in order to foster the biggest attendance and the widest thematic variety. This generous and flexible attitude m a y facilitate the submission of papers of low general concern as well as an increase in the already usual thematic dispersion of such large congresses, but our philosophy is to introduce every new research project and every new research group: that is, every new development in our discipline.

M a n y other things are at present under discussion. The Organizing Committee of the X I X International Congress on the History of Science will pay the most close attention to them all. A n y suggestions will be welcomed and carefully studied.

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M. Hormigón

As I have said before, the Spanish community of historians of science and technology is looking forward to such an important event. This is especially true of the members of the Seminar of History of Science and Technology of Aragon, w h o work at the Faculty of Sciences of the University of Zaragoza, because this group will be in charge of the concrete arrangements for the Congress. Zaragoza, the capital of the ancient kingdom of Aragón, is a town with more than two thousand years of history, of which m a n y vestiges remain. Primarily an Iberian town, Zaragoza is k n o w n as the 'town of the four cultures': R o m a n s , Muslims, Jews and Christians built throughout its history the present Zaragoza, a dynamic and tolerant town of seven hundred thousand inhabitants. The University of Zaragoza, founded in 1583, n o w has centres in five provinces with over two thousand professors and thirty thousand students. D o w n t o w n , in its main campus, is situated the Faculty of Sciences, with three close buildings—devoted to Geology, Mathematics and Physics/Chemistry—where about thirty lecture halls and twenty rooms will be used for the holding of the Congress. Nearby, a municipal sport centre, hotels and halls of residence and a neighbouring park of half a million square metres, will serve to provide a comfortable stay for participants. F r o m 1992, w e will have at our disposal a large Congress Hall with hotel facilities for one thousand four hundred people, and this is where the plenary sessions will be held.

I should like to end with one reflection. Although Mediterranean people are well-k n o w n for their ability to improvise, the Organizing Committee of the X I X International Congress on the History of Science will try not to give the faintest sign of this. W h a t w e will try to show clearly is a virtue that distinguishes Spanish people: hospitality. •

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Annex. The previous International Congresses on History of Science and the subsequent publication of their proceedings

Congress Venue Publication

I Paris, 20-25 M a y 1929 II L o n d o n , 30 June-4 July 1931

III Portugal, 30 Sept.-6 Oct. 1934 IV Prague, 22-27 Sept. 1937

V Lausanne, 30 Sept.-6 Oct. 1947

VI Amsterdam, 14-21 August 1950 VII Jerusalem, 4-12 August 1953

VIII Florence-Milan, 3-9 Sept. 1956 IX Barcelona-Madrid, 1-7 Sept. 1959

X Ithaca, 26 August-2 Sept. 1962 XI Warsaw, 24-31 August 1965

XII Paris, 25-31 August 1968 XIII M o s c o w , 18-24 August 1971 XIV Tokyo-Kyoto, 19-27 August 1974

X V Edinburgh, 10-19 August 1977

XVI Bucarest, 26 August-3 Sept. 1981

XVII Berkeley, California, 31 July-8 August 1985

XVIII Hamburg-Munich, 1-9 August 1989

Archeion, vol. 11, pp. I-CIX, 1929 Archeion, vol. 13-14, 1932 Archeion, vol. 16, 1934

Not published Coll. de travaux de l'Académie

intern, d'histoire des sciences, no. 2, Hermann & Cie, Paris, 1948

Idem, no. 6, 1951 Idem, no. 8, 1954 Idem, no. 9, 1958 Idem, no. 12, 1960 Hermann, Paris, 1964 Polish Academy of Sciences,

Warsaw, 1968 A . Blanchard, Paris, 1970 Nauka, Moscow, 1974 Science Council of Japan, 1975 Human Implications of Scientific

Advance, E . G . Forbes (éd.), Edinburgh, 1978

Academy of the Soc. Rep. of Romania, 1981

Office for the History of Science and Technology, Univ. of California, Berkeley, 1985 (Abstracts only)

Science and political order, F . Krafft & C h . J. Scriba (eds.), H a m b u r g - M u n i c h , 1989 (Abstracts only)

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Publishing complete works of the great scientists: an international undertaking

D . Speiser and P. Radelet-de Grave

Far from regarding editions of the complete works of great scientists as monuments or museum pieces testifying to the glory of a nation, the authors of this article consider that such editions provide the most direct access to the scientific knowledge of the past.

The importance of publishing complete editions of the works of the great scientists of the past m a y be perceived more clearly through comparison of the world's two great heritages: the artistic and the scientific. Everyone is in direct contact with the artistic heritage: w e can all visit churches and at least see from the outside the great palaces and castles. Most sculptures and paintings are accessible through m u s e u m s . Musical works are kept alive through the m a n y music schools and opera houses and m a y even be heard at h o m e thanks to the radio and recordings. Bookshops and libraries give us easy access to literary works of all countries and all periods.

This situation is in singular contrast with that relating to our scientific heritage. It is generally very difficult, even under the best conditions, to gain access to the great discoveries that constitute the masterpieces of our scientific past. They are buried in libraries, lost in books and journals, in m a n y cases hidden in manuscripts. W h a t is more, even if one of these texts is found, it is very difficult to read, perhaps obscure.

T h o u g h educated people today m a y be keenly interested in the great discoveries of the past, they are usually obliged to learn about them in popular works whose authors only too often k n o w the originals at second, third or even fourth hand.

Yet no one would deny the profound influence of science on our thinking, still less the extent to which technology permeates our lives. Their influence is so great that one is led to ask h o w science and technology, which always go hand in hand, have become what they are today. The answer, always coloured by philosophical, political or other

D . Speiser is Professor at the Institute of Theoretical Physics of the Catholic University of Louvain and is General Editor of the complete works of Bernoulli. P. Radelet-de Grave teaches at the same university and directs the publication of the works of the Bernoulli family. They m a y be contacted at the following address: Institut de Physique théorique (Unité F Y M A ) , Université Catholique de Louvain, 2, Chemin du cyclotron, B-1348 Louvain-la-Neuve, Belgium.


D. Speiser and P. Radelet-de Grave

interests, is frequently in contradiction with the historical facts. In science books footnotes intended to refer to such and such a discovery are all too often incorrect, and m a n y a theorem does not bear the n a m e of the person w h o actually discovered it first: hence the need to go back to the original texts and m a k e early studies accessible to people today.

W h a t exactly is meant by 'making scientific research accessible'? Newton's Principia, published in 1687, is probably the most famous work in the history of science. M a n y people imagine that this book, which is about 500 pages in length, contains the basic principles of the whole of modern mechanics as taught in the universities today. M a n y people also imagine that this book was read, studied and understood by all physicists in Newton's time and by a large number in later times.

These beliefs are quite wrong. In fact, it would probably not be an exaggeration to say that only about a dozen scholars read and understood the work during the 50 years following its publication, and that few have studied it during two and a half centuries that have since elapsed. It is not that the book lacked significance. The reason is the extreme difficulty of the subject-matter and the obscurity of the language: perhaps, too, the inadequacy—not always unintentional—of some of Newton's explanations. It is not surprising therefore that the descriptions of the contents of this book are often full of errors. T o take just three examples:

— Newton confines his study to the systems of point-masses, deals very little with rigid bodies and not at all with elastic bodies.

— The famous equations attributed to Newton are not contained in the book in the form in which w e k n o w them today. It was only in 1750 that they were expressed in that form by Euler.

— Lastly, the work contains very few infinitesimal formulations. It is therefore not sufficient to give even a physicist or an engineer of our time a copy of the Principia. The text would remain inaccessible, most of the chapters requiring detailed annotation.

Furthermore, the reader might be interested in purely historical questions such as: W h a t was k n o w n before Newton? W h a t new knowledge did he add? H o w and through what research were Newton's assertions transformed so that they could be formulated as they are today? and W h a t knowledge was added by his successors?

T o reply to these questions a detailed introduction and careful annotation would be required. (Many answers have, in fact, already been provided by D . T . Whiteside in his editing of the works of Newton.)

W h a t w e have just said concerning this particularly famous book is a fortiori true for m a n y others, perhaps less well k n o w n , but in fact just as, or almost as, important and often just as difficult. Even in the case of an author as lucid and clear as Euler, notes are essential to guide the reader through his labyrinthine work, of which the complete edition n o w totals 72 volumes.

W h a t follows is an attempt to explain the importance of editions of complete works and answer questions such as: W h a t is their special role? H o w is such an edition produced? The need for international collaboration will be stressed and a few of the most important editions will be mentioned. In conclusion the relations between science history and science teaching and between complete editions and non-European countries will be considered.

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Publishing complete works of the great scientists

A brief survey of a few editions of complete works

At all the times complete works have been published (see Annex). According to the philosophers, w e possess all the works of Plato—and this only because they were put together systematically. In 1744, Johann Bernoulli published a complete edition of his o w n works in four volumes, introduced by a quatrain attributed to Voltaire himself. Four years later an edition of the complete works of his elder brother Jakob, w h o had died 40 years earlier, was published thanks to the nephew of Johann and Jakob, Nikolaus Bernoulli, and the mathematician G . Carmer. Such editions were expensive and often paid for by subscription, particularly in England. They have been invaluable and although they no longer meet present critical demands, they are still appreciated.

W h e n education was organized at all levels within a public education system, States also began to use the system to promote this type of edition as a tribute to their great m e n and to enhance national prestige. In this way a number of editions of complete works were published, including those of Galileo in Italy, Descartes, Lagrange and Laplace in France and Gauss in Germany . Such editions were often prepared by distinguished scholars: for example, the works of Descartes were edited by P . Tannery, those of Fourier by G . Darboux, and those of Newton , as w e mentioned earlier, by D . T . Whiteside.

The smaller countries of Europe of course tended to lag behind, but their contribution was also important. W e are in possession today of an edition of the complete works of Huygens, which the science historian A . Koyré described as 'beyond all praise'. It was produced by the Academy of Sciences of the Netherlands, which spared neither h u m a n nor financial resources. The result of an immense amount of work, it includes a large number of records and tables which are of considerable assistance to the researcher. It m a y be regretted that each volume does not contain a plan of the whole edition. In fact, since most libraries will only lend two or three volumes at a time out of the total of 22, the reader m a y have difficulty in locating the topic studied. This criticism is m a d e only to show that there is room for improvement in the art of publishing. It might also be noted that it would be conceivable today for the members of the famous Academy to work anonymously. However that m a y be, this edition has always served as a reference for those that followed.

A plan for an edition of the complete works of Euler, probably the largest scientific work ever produced, was prepared by three G e r m a n mathematicians, F . Rudio, N . Kratzer and P . Staeckel, before the First World W a r . The edition was based on a catalogue of all Euler's works (some 800 titles), which had been prepared shortly before by the Swede G . Enestroem. So the original plan ran to some 54 volumes. The first volume, for which the famous mathematician H . Weber assumed responsibility, was published just before the war, in 1913. Later, it was realized that the original plan was quite inadequate and a n e w plan comprising 74 volumes was drawn up by the Swiss mathematician, A . Speiser.

Three features of this edition are worth mentioning:

(a) Geographically the edition was based in Switzerland, but it benefited from international collaboration, with scholars from at least six countries participating. It is clearly not by chance that the tradition of basing editions on international collaboration was born in a small country. S o m e years ago the initial plan was extended to

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include Euler's letters a n d manuscripts. This n e w part of the edition, prepared b y Switzerland in collaboration with the U S S R , will consist of be tween 12 a n d 2 0 vo lumes .

(b) In this part—and this is another n e w feature as compared with the very first volumes—Euler's works will be annotated and accompanied by an introduction. This critical apparatus will of course increase the value of the edition considerably, for it makes the writings and the work as a whole m o r e accessible.

(c) Certain texts b y Euler have also been accompan ied b y texts of other authors, to w h o s e a rguments he w a s replying.

T h e edition of the w o r k s of Leibniz is a special case. T h e total v o l u m e of his scientific a n d philosophical w o r k s exceeds that of the solely scientific w o r k of Euler. In addition, the vast quantity of Leibniz's manuscript notes still extant raises infinitely complex problems.

In 1935, the Swiss mathematician O . Spiess began w o r k o n the Bernoulli edition. T h e edition was reorganized in 1982 and the work continues today with the collaboration of scholars from at least eight different countries. A m o n g them are scientists and historians as eminent as B . L . van der Waerden , A . Weil, C . A . Truesdell, H . Goldstine and G . Mikhailov, all of w h o m consider that the work of a science historian deserves all their efforts. O f the 45 or so volumes of which the edition will be composed, seven have been published and four are n o w in press or in preparation.

This is not all, however. In m a n y countries today a growing interest in such editions m a y be observed. France has decided to pay tribute not only to A . Clairaut and J. d'Alembert, but also to M o n g e and Désargues. Italy is preparing a n u m b e r of editions and in Belgium it has been decided to publish the works of G . Mercator.

T h e time required to complete such editions should not c o m e as a surprise. For example, the edition of the works of Cauchy took over 50 years to complete. This m a k e s it particularly difficult to organize the work and maintain continuity.

W h y publish complete works?

M u c h of what has been said so far applies to the publication of any scientific text. W h a t aspects are specific to complete editions?

O n e aspect that must be mentioned is the overwhelming importance and interconnection of the works of a relatively small n u m b e r of scholars w h o m w e describe as 'great'. It is these scholars w h o have often guided the others and opened n e w horizons for them. They have generally done this by making a synthesis of what is already k n o w n in a certain field and supplementing it by their personal findings, thus opening up n e w avenues of research. O n e has only to mention Copernicus, Kepler, Galileo, N e w t o n and Euler. T h e reader will find in this article the names of other authors whose works should be studied anew, for they could guide us in our research into the history of science.

Another aspect specific to complete editions is that the work of the science historian is greatly facilitated thereby. All too often research papers or articles are studied in isolation or in relation to too few other texts. Their special significance in the general development of the history of science is thus lost sight of. Theoretically, all or at least large parts of what has already been published should be republished and worked on again, so as to provide an overall view. Yet this is out of the question and almost absurd.

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Complete editions therefore have the great advantage of presenting us with a full series of studies through which w e can follow developments in a given field, the emergence and elaboration of the concepts relating to that field and the gradual progress in understanding, sometimes right up to complete understanding. It often suffices to compare this panorama with that to be gained from a study of the complete works of two or three other authors in order to acquire an overall view. O n e m a y see more clearly in this context the importance of including in the complete works writings which stimulated the thought of the author in question or which were a direct consequence of the published work. Thus the first volume of the complete works of Euler includes the famous marginal notes by J. L . Lagrange and another volume contains a reference to the work of the Italian L . Mascheroni. O n e has to acknowledge that these editions are not only essential instruments for the science historian but in fact form the very basis of the history of science.

W h o should and can work on these editions?

It seems clear that the responsibility for such joint editions devolves first on the scholars of the author's native country. It is there that most of the manuscripts are generally to be found and it is accordingly there too that the essential financial assistance is likely to be obtained. Nevertheless, as already pointed out, international collaboration is necessary, for science is carried on today on a world scale and this should apply also to the history of science.

Actually, the foundations of modern science were laid in a small number of western European countries. However, these early scientists based their research on the work of the Greeks and the Arabs and, through those two peoples, on that of the Egyptians, Babylonians, Sumerians, Indians, Chinese and others. The development of science is therefore a world phenomenon which it would hardly be appropriate to treat at regional or even continental level.

Another reason for associating all continents in this work is best explained once again by a parallel with art. Erwin Panofsky, the great art historian w h o emigrated to the United States in 1933, used to say that the position of the U S A opened up possibilities for the art historian of which he never dreamed before. In Europe one was always restricted to national confines, which often distorted one's views. But from America one had a totally unprejudiced view of European art. The great distance meant that one saw European art as a vast panorama.

This is equally true of the history of science. For instance, at least four of the scientists to w h o m the American C . A . Truesdell gave due credit came from small countries, namely: Simon Stevin, Belgium; Christiaan Huygens, the Netherlands; Jakob Bernoulli and Leonhard Euler, Switzerland. Other examples are to be found in the work by A . Weil, which presents in Olympian fashion the discoveries m a d e in the field of the theory of numbers by—in chronological order—a Greek, Diophantes; a Frenchman, Pierre de Fermât; a Swiss, Leonhard Euler; a Savoyard, Joseph Louis de Lagrange and another Frenchman, Adrien Marie Legendre.

So let us hope that these editions will find collaborators in all countries and all continents and particularly in what is n o w called the Third World. All those w h o have contributed to this work have profited from it, and for those coming from another continent the benefit will also be incalculable.

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H o w is a complete edition produced?

Such a vast undertaking can only be carried out in stages: the first stage is the most difficult because it is the least gratifying. It is also generally the longest. It consists of collecting everything that the author has written, even if it is intended not to publish everything but to limit the edition to one or other of the following four types of material:

— published texts, namely, books and papers issued separately, or articles published in journals;

— manuscripts written with a view to the preparation of an article; — diaries and manuscript notes; — letters.

Clearly, when it is decided to publish only part of a work, the choice falls generally on the first and the last of these types of material. However, in order to m a k e a judicious choice, it is essential to have seen the whole of the author's production. Unfortunately, one can never be sure of having all the material to hand. This is understandable in the case of letters, but even whole works are often difficult to track d o w n . There comes a point at which the quest is no longer profitable and it is necessary to call a halt, at least provisionally, and to decide to pass on to the next stage.

The next stage consists of making a plan of the edition. A w a y of classifying the texts must be selected, then a way of distributing them in volumes. At this stage, too, the number of volumes and their size must be estimated. It should be noted that the principles of classification and distribution are different for each of the types of material mentioned. It should also be stressed that these principles m a y vary from one author to another and that the few ideas put forward here are given by w a y of example.

Published texts are often better rearranged according to subject-matter—mainly because the reader is generally interested in research on a particular subject and this arrangement makes it easier to locate that subject in an often vast work. Then, however, the question that arises is whether the subject-matter should be divided up according to current criteria or according to those of the author's time. The first course is generally more convenient for the present-day reader, but it must be borne in mind that the subdivision of science into different branches has not always been the same and that it is constantly changing.

For more distant periods it is difficult or even impossible to hesitate between two sets of criteria; one is forced to m a k e do with the classification of the period.

In any case the principles selected must be m a d e clear to the reader in the introduction to the first volume of the edition and also in the first volume of each series. It is essential that the reader have ready access at all times to a general plan which will serve as a guide for an edition consisting of 20, let alone 85 volumes. This plan m a y often be set out in a one-page summary appearing in each volume. After all, these editions are not only for general reading; they are working tools, which must therefore be functional and enable the researcher to find at once the text sought for analysis. (In fact a classification according to current categories is almost inevitable—for reasons which will again be stressed.)

T o revert to the classification of the different types of material, within each group of texts concerning one subject, the chronological order almost automatically becomes imperative. However, it must be decided in each case to what extent categories should be subdivided and where the chronological classification should begin. Compromises

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will be inevitable. With manuscripts and diaries, it all depends on their size and on their relation to the other material.

With correspondence, on the other hand, the criteria are quite different. A s several subjects m a y be dealt with in the same letter, classification by subjects is impossible and the chronological order has to be followed.

If justified by their number, the letters exchanged between two persons can of course be grouped together in a single subcategory. Within that subcategory, nevertheless, a chronological arrangement is customary. In any case it is essential to publish the letters of both correspondents together. If the number of correspondents is limited, the letters m a y be put together and the whole series therefore merely reproduced in chronological order.

The foregoing considerations concerning the organization of the edition would be incomplete if the question of which part of the work should be published first were not posed. The views of scientists consistently diverge with those of historians. The former are interested mainly in the published texts because these have determined the development of science, whereas the latter prefer to begin with the manuscripts and letters so as to follow the emergence of ideas.

The authors of this article are strongly in favour of the former solution, for the reason expressed as follows by J. Dieudonné: 'It is in the published texts that one normally finds the most maturely considered and clearest formulations.' Moreover, if these texts are published first, they will be of use to the editors of the manuscript parts of the work. A s to the deep understanding of an author's work and intellectual development, experience shows that it is reached only after long and arduous efforts on the part of several researchers.

Professional historians or philologists often criticize those w h o published complete works of scientists for having begun their task at the wrong end. They want the publication of the texts to be preceded by that of all the notes and papers that led up to the final published work. In the case of papers written before the invention of printing, they consider that one should begin by establishing the exact filiation of the manuscripts, as philologists have always done w h e n editing the classic works of literature. In advocating this, they forget that w e k n o w these classics, which have been read and reread over the centuries and, even if not fully understood, at least assimilated.

Imagine that the manuscript of an u n k n o w n masterpiece by Dante, Shakespeare or Goethe is discovered in a monastery, an attic or a cellar. W h a t would be the use in this case of beginning by setting up critical apparatus? Surely the most important thing would be to m a k e the work accessible to the general public. O n c e the specialists and the general public have grasped the essentials of the work, the task of the editor and of the annotator will be facilitated. Let us have no illusions, however. W h a t is exceptional in literature—namely, the discovery of an important u n k n o w n text—is the rule in science, where very few of the outstanding works are k n o w n and appreciated by readers today. It is in their final version that scientific works are most easily understood and that the author's ideas emerge most clearly.

Lastly, an observation relating to the practical aspects of the edition is in order. T w o aspects of the work involved in making texts accessible have been mentioned: their putting together, reproduction and arrangement and their annotation. Whereas the former activity remains objective, the latter is clearly m o r e subjective. It is therefore important to keep the two apart and not to introduce annotations into the original texts, which should be reproduced as historical documents with none but the

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unavoidable changes. Footnotes should contain only biographical or bibliographical information and explanations of symbols or vocabulary essential to the understanding of the text. The annotator's comments and observations m a y be grouped together in an annex to the work.

The third stage consists of finding editors w h o are specialists in the subject dealt with in the group of texts they will have to annotate—which means that they must have worked actively on the texts. It is for this reason too that the texts have to be classified according to current criteria. A n y other method of classification would increase the number of annotators working on the same volume. This is not practical and might lead to additional delays in publication. That is not the only factor which complicates this often very exciting stage. First of all the editor must be interested in the history of science and must k n o w or at least be able to read the languages used by the author: Latin, in particular. It has to be admitted that the number of scientists w h o k n o w Latin is steadily decreasing.

A n y one volume of an edition m a y of course contain several groups of texts on different subjects and therefore be annotated by different authors of various nationalities. As a result, it usually has to be printed in several languages. The present-day reader should not be put off by a certain heterogeneity. O n the contrary, it should be welcomed as proof of true international collaboration.

It might be added that the role of the historian is very different from that of the scientist (as actor in the field of the natural sciences) and calls for certain practical skills which the scientist usually lacks and has to acquire the hard way.

The principles for publishing correspondence diverge here because the historical difficulties often take precedence over the scientific. The collaboration of professional historians or of scientists experienced in this work is often essential.

Lastly, the publication must be financed. Only a few aspects are mentioned here since this stage varies considerably from one case to another.

Human resources

In all cases qualified staff must be paid. This problem would be m u c h easier to solve if more universities possessed institutes of science history. Collaboration in projects of this kind provides invaluable training, whether for students preparing theses or for assistant lecturers, and this type of institute can also provide the secretariat required. The work involved here is not that of the annotator, but the preparation of texts and manuscripts for the printer, the maintaining of liaison between the annotator, the publisher and the printer, the establishing of the principles of the edition and the monitoring of their application. The tasks are numerous and require qualified researchers or small groups attached to a scientific institute, with which close contact is essential.

Material resources

Undertaking the publication of an author's complete works would be unthinkable today without the tools of modern technology such as photocopying machines, word processors, computers, and so on.

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Financial resources

Apart from personnel and administrative costs, it is those of printing which m a k e these editions expensive. The number of institutions or individuals able to purchase these volumes is not large enough to m a k e the editions profitable. Fortunately, government bodies are showing more and more readiness to take their share of responsibility. However, without private sponsorship (through foundations, for example) such undertakings are not usually possible.

Means of distribution

The edition m a y be entrusted to a publisher with the necessary intellectual, artistic and financial resources. The publishing house must show great understanding and one cannot emphasize enough the merit of those publishers w h o are prepared to put energy into accomplishing this task. O n e might mention as an example the Opera Omnia of Euler, n o w in the hands of a third publisher and managed by a fourth generation of science editors.

Artistic resources are of the first importance, since not only do they do a great deal to m a k e a book attractive, but they also can and indeed must increase the clarity of its presentation. Taking ancient texts written in unfamiliar language and using a formal style quite different from our o w n and making them accessible to a modern scientist is an arduous task which can only be achieved through long and close collaboration between graphic artists and scientists, and which goes far beyond the scope of the complete edition. Moreover, the possibilities opened by computers will certainly lead publishers to reorganize, though this is beyond the scope of the present article.

As for financial resources, there is little more to add. The reader will have understood that this type of undertaking is long and exacting, extending over decades and involving several generations of participants, and that continuity is a problem.

T h e number of difficulties to be overcome before the means of publishing these editions are found should not prevent us from taking on the task and making every effort to complete it. For the great scientific works are part of the world heritage and it is our duty to hand them d o w n to the researchers of the future. •

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Annex. List of complete works of scientists

The following list of complete works was established by P. Radelet-de Grave and J. Dhombres by adopting as a criterion the exhaustive nature of the publications in question. However, we have applied this criterion less rigorously for those publications brought out during, or slightly after, the lifetime of the author, especially with respect to the present era. Certain publications are complementary and together form a whol;, these we have indicated by (a), (b),... By contrast, books which we might describe us parallel, rival publications are shown with a dash.

Several publications mentioned below were used in our work, and in addition we received the help of the publishing house of Springer Verlag. The information we obtained was supplemented by consulting the records of several libraries.

The History of Classical Physics, A selected, Annotated Bibliography, R . W . H o m e with the assistance of M a r k J. Gittins, N e w York & London, Garland Publishing,1984.

The History of Mathematics from the Antiquity to the Present, A Selective Bibliography, Joseph W . Dauben, , N e w York & London, Garland Publishing, 1985.

Dictionary of Scientific Biography, ed. C h . C . Gillispie, N e w York, C h . Scribner's Sons, 1970.

Biographisch-Literarisches Handwôrterbuch zur Geschichte der exakten Wissenschaften, J.C. Poggendorff, Leipzig, J.A. Barth, 1863.

"Edizioni entiche e storia della matemática" .Centro Internazionale per la ricerca matemática, published by E T S in 1986.

Guida alio studio della storia delle matematiche, G . Loria, Milan, Ulrico Hoepli, 1946.

Abbe, Ernst (1840-1905) Gesammelte Abhandlungen von Ernst Abbe, 5 vols, Jena, G . Fischer Verlag, 1904-1940.

Abel, Niels Henrik (1802-1829) - Œuvres complètes de N.H. Abel mathématicien, ed. B . Holmboe, 2 vols, Oslo, Christiania, 1838. - Œuvres complètes de N.H. Abel mathématicien,nouvelle édition, ed. L . Sylow & S. Lie, 2 vols, Oslo, Christiania, 1881.

A d a m s , John Couch (1819-1892) The Scientific Papers of John Couch Adams, ed. William Grylls A d a m s & R . Allen, with a Mémoire by J . W . Glaisher, 2 vols, Cambridge, 1896-1900.

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Ahlfors, Lars Valerian (1907) Collected Papers, 2 vols, Contemporary Mathematicians, Basel, Boston & Stuttgart, BirkhSuser, 1983.

Ajima, Naonobu (1732-1798) Ajima Naonobu zenshu [Collected works of Ajima Naonobu], ed. Hirayama Akira & Matsuoka Motohisa, Tokyo, Fufi Tanki Daigaku Chuppanbu, 1966.

Apollonius de Perga (ca. 262-ca. 190 B . C . ) Apollonii Pergaei quae graece extant..., ed. Heiberg, Leipzig, Teubner, 1891-1893.

Arago, Dominique François Jean (1786-1853) Œuvres complètes de François Arago, ed. J. A . Barrai, 17 vols, Paris, 1854-62. Republished, Paris 1865

Archimède (ca. 287-212 B . C . ) Opera Omnia cum Commentariis eutocii, ed. J.L. Heiberg, Leipzig, Teubner, 1880-1881. Republished, 3 vols, Leipzig, 1910-1915.

Artin.Emil (1898-1962) Collected Papers of Emit Artin, ed. Serge Lang & John T . Tate, N e w York, Addison-Wesley Publishing Company , 1965. Republished, Heidelberg, Springer, 1982.

Babbage, Charles (1792-1871) The works of Charles Babbage, ed. by Martin Campbell-Kelly, 11 vols, London, William Pickering, 1989.

Baire, René (1874-1932) Œuvres, ed. P . Dugac & P. Lelong, Paris, C N R S , 1990.

Ball, Sir Robert Stawell (1840-1913) Reminiscenses and letters, ed. Valentine Ball, London, 1915.

Banach, Stefan (1892-1945) Œuvres avec des commentaires, P W N - Polish Scientific Publishers, Warsaw, 1967-

Barrow, Isaac (1630-1677) The collected works, ed. Whewell, Cambridge, 1860. The geometrical works of J. Barrow, ed. J . M . Child, Chicago, 1916.

Bergman, T o b e m (1735-1784) Tobern Bergman's Foreign Correspondance, ed. Carled-Nordstrôm, Stockholm, 1965.

Berkeley, Georges (1685-1753) Oeuvres, ed. Geneviève Brykman, Paris, Presses Universitaires de France, vol. I, 1985, vol., II1986 & vol. Ill, 1989; other vols to follow.

Beltrami, Eugenio (1835-1899) Opere matematiche, 4 vols, Milan, 1902-1920.

Bernoulli, Daniel (1700-1782) die Werke von Daniel Bernoulli, ed. D . Speiser, Basel, BirkhSuser, 1982- , in progress.

Bernoulli, Jacob (1654-1705) - Jacobi Bernoulli Basiliensis Opera, ed. Gabriel Cramer, 2 vols, Geneva, 1744. Republished, Bruxelles, Editions Culture et Civilisation, 1967. - Die Werke von Jakob Bernoulli, ed. J .O. Fleckenstein & D . Speiser, Basel, BirkhSuser, 1969- En cours.

Bernoulli, Johann I (1667-1748) a) Opera omnia, ed. Gabriel Cramer, 4 vols, Lausanne, Geneva, 1742.

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Republished, Hildesheim : Georg Olms Verlag, 1968, with an introduction by J.E. Hofmann. b) Der Briefwechsel von Johann Bernoulli, ed. Otto Spiess & D . Speiser, Basel, Birkhâuser, 1955-, in progress.

Bernstein, Sergei Natanovich (1880-1968) Sochinenia akademika SU. Bernshteina, 4 vols, Moscow, 1952-1964.

Bessel, Friedrich Wilhelm (1784-1846) Abhandlungen von Friedrich Wilhelm Bessel, ed. R . Engelmann, 3 vols, Leipzig, 1875.

Betti, Enrico (1823-1892) Opere Matematiche di Enrico Betti, publícate per cura della R . Academia de' Linca, 2 vols, Milan, Hoepli, 1903-1915.

Beurling, Arne Karl August (1905) Collected Works of Arne Beurling, ed. Lennart Carleson, Paul Malliavin & John Neuberger, 2 vols, Contemporary Mathematicians, Basel, Boston & Stuttgart, Birkhâuser, 1989.

Bianchi, Luigi (1856-1928) Opere, Edizioni Cremonese, 11 vols, R o m e , 1952-1959.

Birkhoff, George David (1884-1944) Collected Mathematical Works of George David Birkhoff, American Mathematical Society, 3 vols, Providence, R.I., 1950.

Bohr, Harald August (1887-1951) Collected Mathematical Works, 3 vols, Copenhagen, 1952.

Boltzmann, Ludwig (1844-1906) Wissenschaftliche Abhandlungen, ed. Fritz Hasenóhrl, 3 vols, Leipzig, J.A. Barth, 1909.

Bolzano, Bernard (1781-1848) - Gesammelte Schriften, 12 vols, Vienna 1882. - Bernard Bolzano's Schriften, 5 vols, ed. Kôniglichen Bôhmischen Gesellschaft der Wissenschaften, Prague, 1930-1948.

Borchardt, Carl Wilhem (1817-1880) Gesammelte Werke, ed. G . Hettner, Berlin, 1888.

Borel, Armand (1923- ) Œuvres - Collected Papers, 3 vols, Heidelberg, Springer, 1983.

Vol. 1: 1948-1958. Vol. 2: 1959-1968. Vol. 3: 1969-1982. Borel, Emile (1871-1956)

Œuvres, 4 vols, Paris, C N R S , 1972. Brahe, Tycho (1546-1601)

Tychonis Braje Dani Opera omnia, ed. J.L.E. Dreyer, 15 vols, Copenhagen, 1913-1929.

Brendel, Johann Gottfried (1712-1758) Opusculi mathematici et medid argumenti, ed. H . A . Wrisberg, 3 vols, 1769-1775.

Brioschi, Francesco (1824-1897) Opere matematiche, ed. Ascoli et al., 5 vols, Milan, 1901-1908.

Brouwer, Luitzen Egbertus Jan (1881-1966) Collected works, ed. H . Freudenthal, Amsterdam, Oxford & N e w York, North Holland, 1975-1976.

Bruno, Giordano (1548-1600) Jordani Bruni Noleni opera latina conscripta...recensebat F. Fiorentino..., Neapoli, Apud D o m . Morano, 1879,8 vols.

Biichi, J. Richard (1924-)

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The Collected Works, ed. Saunders MacLane & Dirk J. Siefkes, Heidelberg, Springer, 1990.

Buffon, Georges Louis Leclerc Comte de (1707-1788) Œuvres complètes de Buffon, ed. J.L. Lanessan, 14 vols, Paris, A . Le Vasseur, 1884-1885.

Bunsen, Robert Wilhelm Eberhard (1811-1899) Gesammelte Abhandlungen, ed. W . Ostwald & E . Bodenstein, 3 vols, Leipzig, Wilhelm Engelmann, 1904.

Cantor, Georg (1845-1918) a) Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, ed. E . Zermelo, Berlin, 1930. Republished, Hildesheim, 1962; Heidelberg, Springer, 1980. b) Briefe, ed. Herbert Meschkowski & Winfried Nielson, Heidelberg, Springer, 1980.

Carathéodory, Constantin (1873-1950) Gesammelte mathematische Schriften, 5 vols, Munich, 1954-1957.

Cardano, Gerolamo (1501-1576) Opera omnia, ed. C . Sponi, 10 vols, Leiden, 1663.

Cartan, Elie Joseph (1869-1951) Œuvres complètes, 6 vols, Paris, 1952-1955.

Cartan, Henri (1904) Œuvres - Collected Works, 3 vols, R . Remmert & J.P. Serre, Heidelberg, Springer, 1979.

Casorati, Felice (1835-1890) Opere, vol I (1951)

Catalan, Eugène Charles (1814-1894) Mélanges mathématiques, 3 vols, Liège, 1887.

Cauchy, Augustin, Louis (1789-1857) Œuvres complètes, 27 vols, Paris, Gauthiers-Villars, 1882-1974.

Cavendish, Henry (1731-1810) The Scientific Papers of the Honourable Henry Cavendish, 2 vols, Vol. 1. The Electrical Researches, ed. James Clerk Maxwell, revised by Joseph Larmor, Cambridge, 1879. Republished, London, Cass, 1979. Vol. 2. Chemical and Dynamical Works, ed. T . E . Thorpe, Cambridge University Press, 1921.

Cayley, Arthur (1821-1895) Collected Mathematical Papers, 14 vols, Cambridge University Press, 1889-1898.

Chaplygin, Sergei Aleksandrovich (1869-1942) Sobranie sochinenia, 4 vols, Moscow & Leningrad, 1948-1950.

Chebyshev, Pafnutü' L'vovich (1821-1894) - Sochinenia, ed. A . A . Markov & N . Y . Sonin, 2 vols, St. Petersburg, 1899-1907. - Polnoe sobranie sochineny, 5 vols, Moscow & Leningrad, 1944-1951.

Chen, Jiangong (1893-1971) Chen Jiangong wenji [Works of Chen Jiangong], Pekin, Kexue chubanshe, 1981.

Chern, Shing-shen (1911) Selected Papers, 4 vols. Springer, Heidelberg, 1990.

Christoffel, Elvin Bruno (1829-1900) Gesammelte mathematische Abhandlungen, ed. L . Mauer, 2 vols, Leipzig & Berlin, 1910.

Clavius, Christoph (1536-1612)

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Opera matemática, 5 vols, Mainz, 1611-1612. N e w edition in preparation.

Clifford, William Kingdon (1845-1879) The mathematical Papers, ed. R . Tucker, London, 1882. Lectures and Essays, 2 vols, London, 1879.

Copernicus (1473-1543) Nicolas Copernicus, Complete works, intro. by E . Rosen, Warsaw, Krakow, Polish Academy of Sciences, 1978.

Cournot, Antoine-Augustin (1801-1877) Œuvres complètes, ed. A . Robinet, 10 vols, Bibliothèque des textes philosophiques, Paris, Vrin, 1973.

Cremona, Luigi (1830-1903) Opere matematiche di Luigi Cremona, ed. L . Bertini, 3 vols, Milan, 1914-1917.

Curie Sklodowska, Marie (1867-1934) Prace ... Zebrane przez Irene Joliot Curie, [Works ... collected by Irène Joliot Curie], Polska Akademia Nauk, Warsaw, 1954.

Curie, Pierre (1859-1906) Œuvres de Pierre Curie, published under the direction of La Société Française de Physique, Paris, Gauthier-Villars, 1908.

Darwin, George Howard (1845-1912) The scientific papers, 4 vols, Cambridge, 1908-1911.

Davy, Humphry (1778-1829) The Collected Works, ed. John Davy, 9 vols, London, 1839-40.

Dedekind, Richard (1831-1916) a)Gesammelte mathematische Werke, ed. R . Fricke, E . Noether & O . Ore, 3 vols, Brunswick, 1930-1932. b)Briefwechsel Cantor-Dedekind, ed. E . Noether & J. Cavaillès, Paris, 1937.

Delsarte, Jean (1903 -1966) Œuvres complètes, 2 vols, Paris, Editions du C N R S , 1969.

Desargues, Girard (1591-1662) - Œuvres réunies et analysées par M. Poudra, Paris, 1864. - N e w edition in preparation, ed. J. Dhombres & R . Taton, 2 vols, Paris, Blanchard, 1992.

Descartes, René (1596-1650) Œuvres de Descartes, ed. C h . A d a m & P. Tannery, 12 vols, Paris, Vrin, 1897-1913, updated 1964-1974.

Dini, Ulisse (1845-1918) Opere, Unione Matemática Italiana, 2 vols, R o m e , 1953-1954.

Diophante (fl. ca. 250 A . D . ) Diophanti Alexandrini Opera omnia..., ed. P. Tannery, 2 vols, Leipzig, Teubner, 1883-1888.

Dirichlet, Gustav Lejeune (1805-1859) G. Lejeune Dirichlets Werke, herausgegeben auf Veranlassung der Kôniglichen Preussichen Akademie der Wissenschaft, ed. Kornecker & L . Fuchs, 2 vols, Berlin, 1889-1897.

Dolbnja, Ivan P. (1853-1912) Œuvres mathématiques de J. Dolbnja, publiées sous les auspices de l'école supérieure des mines de l'impératrice Catherine II, 1 vol, St. Petersburg, 1913.

Ehrenfest, Paul (1880-1933) Collected Scientific Papers, Amsterdam, 1959.

Ehresmann, Charles (1905-1979)

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Œuvres complètes et commentées, Amiens, 1980-1984. Encke, Johann Franz (1791-1865)

Astronomische Abhandlungen, 3 vols, Berlin, 1868. Gesammelte mathematische una astronomische Abhandlungen, 2 vols, Berlin, 1888-1889.

Euclide (fl. ca. 300 B . C . ) Euclide Elementa, ed. J.L. Heiberg, Lipsiae, Teubner, 1883-1888.

Euler, Leonhard (1707-1783) Leonhardi Euleri Opera omnia, Turici, Orell Fiissli ; Basel, Boston & Stuttgart, Birkhauser, 1911-, in progress. Ser. 1: Opera mathematical Ser. 2: Opera mechanica et astronómica; Ser. 3: Opera physica et miscellanea, in progress; Ser. 4: Commerc ium epistolicum et Manuscripta, in progress.

Fagnano, Giulio Carlo (Márchese deToschi) (1682-1766) Opere matematiche del Márchese Giulio Carlo de' Toschi di Fagnano, ed. V . Volterra, G . Loria & D . Gambioli, 3 vols, R o m e , 1912.

Fejér, Leopold (1880-1959) Fejer Lipôt ôsszegyiijtôtt Munkai - Leopold Fejer, Gesammelte Arbeiten, 2 vols, Budapest, 1970.

Fermât, Pierre (1601-1665) Œuvres de Fermât, ed. P . Tannery & C h . Henry, 5 vols, Paris, Gauthier-Villars,1891-1922. Republished, ed. C . Houzel, Christol, R . Rashed, Paris, Blanchard, in preparation.

Fermi, Enrico (1901-1954) Collected Papers, ed. E . Segré, E . Amaldi, H . L . Anderson, E . Pérsico, F . Rasetti, C . S . Smith & A . Wattenberg, 2 vols, Chicago, 1962-1965.

Ferraris, Galileo (1847-1897) Opere, 3 vols, Milan, Associazione Elettrotechnica Italiana, 1902-1904.

Fibonacci, Leonardo, of Pisa (ca. 1180-<ra. 1250) Scirtti di Leonardo Pisano, ed. B . Boncompagni, 2 vols, R o m e , 1857-1862.

FitzGerald, George Francis (1851-1901) The Scientific Writings of the late George Francis Fitzgerald, ed. Joseph Larmor, Dublin, Hodges, Figgis & C o . ; London, Longmans, Green and C o . , 1902.

Fontenelle, Bernard Le Bovier de (1657-1757) - Œuvres de Ai. de Fontenelle, 6 vols, Paris, 1742. - Œuvres de Ai. de Fontenelle, 8 vols, Paris, 1751-1752. - Œuvres de M. de Fontenelle, 6 vols, Amsterdam, 1754. - Œuvres de M. de Fontenelle, 10 vols, Paris, 1758. - Œuvres de M. de Fontenelle, 11 vols, Paris, 1761,1766. - Œuvres de M. de Fontenelle, 12 vols, Amsterdam, 1764. - Œuvres de M. de Fontenelle, 7 vols, London, 1785.

Foucault, Jean Bernard Léon (1819-1868) Recueil des travaux scientifiques de Léon Foucault, ed. M m e Foucault & C M . Gariel, 2 vols, Paris, Gauthier Villars, 1878.

Fourier, Jean-Baptiste-Joseph (1768-1830) Œuvres de Fourier, ed. Gaston Darboux, 2 vols, Paris, Gauthier-Villars, 1888-1890.

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Science during the Ming and Qing Dynasties: contact between Chinese and western civilizations

D u Shi-ran

The history of China is characterized by periods during which the country was open to ideas and learning coming from the west, and those when its borders were strictly closed to outside knowledge. It is against such a backdrop that the integration of foreign science and technology and its influence must be judged.

The Ming and Qing Dynasties in Chinese history covered a period of roughly five and half centuries, from 1368 to 1911. For China, and any other country in either east or for that matter west, five and a half centuries is a long time in terms of the history of h u m a n society. Naturally, science played a more important role in promoting social development in this period than in any other previous ones, and this was especially true during the latter three hundred years.

The development of science during the M i n g and Qing Dynasties can be divided into four periods: pre-late Ming (1368-1582); late Ming and early Qing (1582-1744), which witnessed the first encounter with western science and technology; mid-Qing (1744-1850), which was characterized by the policy to close the country to international intercourse; and late Qing (1850-1911), which represented the second encounter with western science and technology. F r o m the late Ming and early Qing to the beginning of this century, contact with western science and technology (introduction, integration, resistance and conflicts) was an important part of the history of Chinese science and technology.

The pre-late Ming period

Science and technology in China has had a very long history. Astronomy, mathematics, medical science, materia medica, agriculture, metallurgy, textiles, porcelain, paper,

D u Shi-ran is Professor of the Institute of History of Natural Science of the Academia Sinica. Born at Jilin City in China in 1929, he graduated from the above-mentioned Institute in 1960. H e is currently Visiting Professor at Tohoku University, Sendai, Japan, and as of April 1991 will be Professor at Bukyo University, Kyoto, Japan (on the history of ancient Chinese science and technology, and the history of ancient Chinese thought). His main publications are: The History of Ancient Chinese Mathematics, 2 volumes (with Li Yan), 1963-64, Zong H u a Press, Beijing (an English version, 1986, Clearton Press, Oxford); and A Draft History of Chinese Science and Technology, 2 volumes, 1982, Science Press, Beijing. H e m a y be contacted at the following address: Research Institute for Japanese Culture, Faculty of Arts and Letters, Tohoku University, 980 Sendai, Japan.


Du Shi-ran

architecture, navigation and most other sciences and technologies began to take shape gradually during the Warring States Period (475-221 B . C . ) and the two H a n Dynasties (206 B . C - 2 2 0 A . D . ) . They were to reach the peak about 1000 years later in the Song and Yuan Dynasties (960-1368). However, in the first two hundred years of the Ming Dynasty, apart from ship-building, porcelain-making and textiles (especially silk fabrics), the development of science and technology was on the whole stagnant. This was especially true for astronomy and mathematics. The main reasons had to do with Ming society.

In the first place, unlike the commodity economy that was growing rapidly in Europe, the economy in the Ming Dynasty was still a small-scale peasant one based on self-sufficiency. A n d this small-scale peasant economy had limited demands on advanced science and technology.

Secondly, the Ming Dynasty had a very ruthless political system. There were spies everywhere and control over the mind was extremely tight. This, plus the imperial examination system, smothered people's creative ideas.

Thirdly, the major school of philosophical thought at the time was lixue, a type of Confucian philosophy. In particular, during the mid-Ming period, the N e w School represented by W a n g Yangming tried to integrate Confucianism, Buddhism and Taoism, stressed the power of the mind in understanding the ancient classics and frowned upon any practical knowledge that has to do with people's livelihood.

Finally, the Ming Court placed strict limitations on the development of science in general and on that of astronomy in particular. Legislation was passed in early Ming which contained strict penalties for people w h o privately studied astronomy and the calendar system. As a result, when the government became aware towards the end of the Ming Dynasty that forecasts on the solar and lunar eclipses were extremely inaccurate and therefore wanted to change the calendar, there was a serious scarcity of people w h o understood the calendar system. In ancient China, mathematics and the calculation of the calendar were closely linked, and as a result, there was not m u c h progress in the area of mathematics either.

The rise of shixue

The two things that had a major impact on science and technology in late Ming and early Qing were, (a) the rise of shixue, and (b) the introduction into China of western learning.

Shixue was a type of pragmatism which gradually took shape as a criticism and opponent of lixue and especially of the xinxue represented by L u Jiuyuan and W a n g Yangming. First, shixue was very critical of the empty talk and uselessness that were the trademarks of lixue and xinxue. Secondly, shixue took a sceptical attitide to accepted conventions and was eager to pursue truth regarding nature and patterns of social development. Thirdly, it emphasized the application of knowledge to practical problems. Fourthly, it held that science and technology was useful knowledge, and argued for the use of experiments in truth-finding. Finally, in terms of economic thought, shixue advocated that 'industry and commerce were both essential fo a state' and opposed the traditional policy that stressed agriculture at the expense of commerce. Politically, shixue attacked feudal authoritarianism and advocated democracy. With respect to literary thought, shixue was against the feudal ideology and for individualism.

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As representatives of the shixue school, there appeared m a n y outstanding thinkers such as Fang Yizhi (1611-1671), G u Y a n w u (1613-1682), W a n g Fuzhi (1619-1692) and Huang Zongxi (1610-1695). At the same time, there also appeared m a n y scientists such as the pharmacologist Li Shizhen (1518-1593), the agriculturalist and astronomer X u Guangqi, the encyclopaedist Song Yingxing (1587-1666?), the geographer X u Xiake, and the astronomers and mathematicians W a n g Xichan (1628-1682) and Mei Wending (1633-1721). As a result, science in the Ming Dynasty, which had been stagnant, witnessed a turn for the better.

The arrival of western learning

In addition to the rise of shixue, another important factor influencing the development of science and technology in late Ming and early Qing was the introduction into China of western learning. With the development of modern western civilization and especially with the worldwide activities of the early western colonialists, Jesuits came to the Far East. China and Japan started to have contacts with the west at more or less the same time. The most famous of the early Jesuits w h o came to China was the Italian Mateo Ricci (1552-1610), w h o arrived in 1582. Thanks to Ricci, western science and technology, which was completely different from the traditional science and technology of ancient China, began to arrive. This is why 1582 has been chosen as a dividing line in the periodization scheme of this article.

Most of the early missionaries to China were Jesuits, and the majority of their work in China was of course related to religion. Yet there is no denying the fact that Jesuits' activities the world over were also related to western colonialism. The introduction of western learning into China was an inevitable result of modern western colonialism. O n the other hand, it also responded to the need of the Oriental countries at the time. As far as China was concerned, it urgently needed astronomical knowledge in order to change its calendar system and gun-making technology to defend itself on the northeast against the invasion of the Qing troops. All this provided opportunities for missionaries to come to China. As Ricci himself said: 'There are no better examples to show that G o d is using science to convert Chinese scholars.' (Ricci, Notes from China, Vol. 2, p. 594. This is a retranslation of the Chinese translation of the original work.) U p o n Ricci's request, the R o m a n Court sent missionaries w h o were familiar with science and technology in general and with astronomy and calendar in particular. O f the more than four hundred missionaries sent before mid-Qing, those w h o were closely related to the spreading of science and technology included:

Nicolaus Longobardo (1559-1654, Italian, arrived in 1597); Didaco de Pantoja (1571-1618, Spanish, arrived in 1599); Sabbathinus de Ursis (1575-1620, Italian, arrived in 1606); Emmanuel Diaz (1582-1649, Portuguese, arrived in 1610); Julius Aleni (1582-1649, Italian, arrived in 1613); Joannes Terrenze (1576-1630, Swiss, arrived in 1621); Joan A d a m Schall von Bell (1591-1666, German, arrived in 1622); Jacobus R h o (1593-1638, Italian, arrived in 1624); Nicolas Smogolenski (1611-1656, Polish, arrived in 1646); and Ferdinandus Verbiest (1623-1688, Belgian, arrived in 1659).

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Those w h o came to China in early Qing (mostly sent by Louis XIV) included:

Joan Francisus Gerbillon (1654-1701, French, arrived in 1687); Joach Bouvet (1656-1730, French, arrived in 1687); Joan Bapt Regis (1663-1738, arrived in 1698); Dominicus Parennin (1665-1741, French, arrived in 1698); Petrus Jartoux (1668-1720, French, arrived in 1701); Ignatius Kogler (1680-1746, German, arrived in 1716); and Michael Benoist (1715-1774, French, arrived in 1744).

These missionaries did contribute to the spreading of western science and technology and the development of Chinese science and technology. In collaboration with Chinese scholars in the area of astronomy, they compiled the Chungzhen Calendar and took part in the reform of the calendar system. In the area of mathematics, they introduced western calculations to China and translated Euclid's Elements of Geometry. In addition, the missionaries introduced geography, map-making, autopsy, various animals and plants, machines, irrigation technology, telescope, clocks, acid-making, painting theories, music and various other kinds of knowledge into China. O f these, the compiling of the calendar system and the drawing of maps in early Qing were perhaps the most significant. The two large maps drawn during the reign of Kangxi and Qianlong were first class by standards at the time.

O n the issue of h o w to treat western science and technology, X u Guangqi (one of the people w h o welcomed it) suggested that the Chinese government adopt the policy of 'translating, integrating and surpassing'. It is a policy that might equally well be implemented today.

However, as part of western culture, western science and technology was distinctly different from that of the traditional Oriental culture. Moreover, the spreading of western knowledge in the east was linked with missionary and colonial activities. In this process of spreading western learning to the east, there were therefore bound to be strong reactions from some Oriental countries (i.e. resistance and conflicts as well as absorption and integration). For instance, there were major conflicts in China regarding knowledge of astronomy and the calendar coming from the west. The first major episode occurred during the reign of Chungzhen, Emperor of the Ming Dynasty (1629-1643). There was a fierce debate between those represented by X u Guangqi, Li Zhizao and Li Tianjing w h o were for the western calendar system and those like Wei Wenkui w h o were against it. The former finally w o n the debate, thanks to the accuracy of the western system in forecasting solar and lunar eclipses. However, the Ming Dynasty was soon to be overthrown and the reform of the calendar system consequently not completed.

In the Qing Dynasty that followed, the missionaries renamed the Chungzhen Calendar, which had been compiled in collaboration with X u Guangqi and others, as a N e w Book on the Western Calendar and then presented it to the Qing Emperor. The Qing Court decided to rely upon missionaries for their calendar reform, and this led to an even fiercer conflict. This time Yang Guangxian was the major opponent to the western system. H e wrote a report to the Emperor in which he accused the missionaries of 'agitating our people', and said that 'there must not be westerners in China, even if this means that China does not have a good calendar system'. As a result, Joan A d a m Schall von Bell and Ferdinandus Verbiest and five Chinese officials, including Li Zubai, w h o were for the western system, were sentenced to death. The two

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missionaries were later pardoned, but the Chinese officials gave their lives for the spreading of science and technology. O n the other hand, Yang Guangxian did not k n o w m u c h about the calendar. H e w o n the battle, but in the end, as he could not accurately forecast solar and lunar eclipses, was also sentenced to death, for the crime of deceiving the Emperor (only to be pardoned later). It was only after this that the western system became accepted.

The closing of China to the outside world

In the mid-18th century, two important changes took place that were to affect the development of science and technology in China. The first was the adoption of the policy to close China to international contact and the second was the rise of the Qain Jai scholarly school.

Because of the protocol issues raised by the Vatican (i.e. Catholics could only worship G o d but not their ancestors nor Confucius as was done according to traditional Chinese custom) and especially because of the missionaries' ill-fated intervention in the succession of the Qing emperors, the overwhelming majority of missionaries were expelled to H o n g K o n g or Macao . Only very few were allowed to stay on in Peking to continue their work on astronomy and the calendar. After the death of Michael Benoist in 1774, the Qing Court did not hire any new missionaries, so from then on none were involved in the astronomical and calendar work in China. The introduction of western scientific and technological knowledge into China practically ceased. The Qing Court was implementing the policy of closing China to international intercourse.

O n the other hand, there arose a new scholarly school—the Qian Jia School. Once the Qing Dynasty was established, and in order to suppress the anti-Qing forces, the government imprisoned and executed m a n y scholars for writing things considered unacceptable. At the same time, the government ordered the compilation of Si Ku Quan Shu, which was a collection of ancient Chinese classics consisting of over 3000 books. This encouraged most intellectuals to devote their energy to textual research and the sorting out of the ancient Chinese classics. Because of these two policies (suppression on the one hand and enticement on the other), academic life in China underwent great changes. Textual research involving the cataloguing of the ancient classics became very popular. It peaked during the reigns of the Qianlong and Jiaqing Emperors, and thus became k n o w n as the Qian Jia School.

Scientific work in this period also consisted primarily of the cataloguing of ancient science books. In the area of astronomy, research was carried out on the various calendar systems in Chinese history. At the same time, the western calendar that had been introduced into China earlier was improved. (Oval orbits were used, but the earth was still regarded as a focus of movement. The heliocentric theory was not really accepted by Chinese astronomers until after the O p i u m War . ) In the area of mathematics, ancient maths books were catalogued, and Chou Ren Zhuan, which was a collection of biographies of astronomers and mathematicians in Chinese history, was compiled. W o r k was also carried out on the cataloguing of ancient medical books.

Methodologically, there was something to be learned from the Qian Jia School. However, they relied mainly on textual research and looked d o w n upon scientific experiment. Consequently, there was a tendency to neglect science and technology. At

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the same time, the Qia Jia School also argued that western knowledge really originated from the east. This arrogant point of view certainly constituted an obstacle to the study of western scientific and technological knowledge. However, it was precisely in this period that western science and technology and economy was undergoing such rapid development, and as a result, China was left far behind.

The Westernization Movement

After the mid-19th century, the Qing Dynasty declined even further. In addition to the rampant red tape and official corruption, peasant uprisings became more and more serious. After the O p i u m W a r in 1840, the imperialist powers increased their activities in China, and the country was in danger of being partitioned.

Under these circumstances, even though the Qian Jia School was still quite influential, there was more and more criticism, in academic circles, about the impracticality of textual research, and the shixue school which had advocated the practical usefulness of knowledge became popular once more.

The O p i u m W a r opened China's doors and western scientific and technological knowledge again came to China on a large scale. F r o m the 1860s on, under the general policy of 'retaining the essential Chinese system while taking advantage of western techniques', the Qing government embarked upon a Westernization Movement which was the first government-led modernization drive in modern Chinese history. Various kinds of factories, mines and military industries were set up. Most of western advanced technologies, from steam engines to various machine tools, from metallurgical technologies to trains, ships, the telegraph and the electric light, came to China during this period. In addition, the government set up special institutions to translate western books (Peking's Tongwen House and Shanghai's Yishu House being the most famous of these). According to the records, a total of 468 western science and technology books were translated into Chinese from 1853 to 1911. Major westerners w h o took part in this translation included: Alexander Wylie (1815-1887, English, came to China in 1847); John Fryer (1839-1928, English); and Joseph Edkin (1823-1905, came to China in 1848). Major Chinese figures included: Li Shanlan (1811-1882); X u Shou (1818-1884); H u a Hengfang (1833-1902); and Y a n F u (1853-1921).

O n the whole, China engaged mainly in learning and absorbing western knowledge in this period; with the possible exception of Li Shanlan's research work on mathematics, there was little creative work being done by Chinese scholars themselves. Unlike the late Ming and early Qing period when western learning was first introduced into China, this was a time of no major conflicts.

As of the 1880s, China began to send students to study in the west. In the first decade of this century, the number of students sent abroad reached a peak. In 1905, the Qing government abolished the imperial examination system and new schools began to spring up throughout China.

However, the large-scale introduction of western science and technology into China did not really alter its backwardness. Most Chinese historians believe that the Westernization Movement , the first modernization drive in China, was a failure. There were m a n y reasons for this, probably the most important one being the general policy of 'retaining the essential Chinese system while taking advantage of western techniques'. The Qing Court's attempt to use western science and technology to

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maintain its feudal political and economic system was d o o m e d to failure. Consequently, more and more people joined the camps of the reformers and even the revolutionaries, the Qing Dynasty being finally overthrown in the revolutionary wave of 1911.

The question that history has left to China is still h o w to m a k e the country rich and strong as soon as possible.

The history of Chinese science and technology during the M i n g and Qing periods also presented a question to the world as a whole: h o w should the developing countries best use advanced western science and technology in order to modernize as quickly as possible? This is still one of the issues whose solution statesmen the world over are trying to bring about. •

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T h e scientific revolution of the 17th century: n e w perspectives

Pietro Redondi

The constant succession over the last twenty-five years of discoveries, interpretations and approaches in the study of the scientific revolution of the 17th century—particularly that of the relations between magic and science and the conflicts between religion and science— have not only totally transformed the science historian's trade, they have completely changed our image of scientific knowledge. The debate prompted by the arguments put forward to explain this great phenomenon of civilization has spread beyond the circle of the professional historian and aroused general interest in this 'revolution' and in the crucial heritage it has bequeathed to modern society.

T h o u g h in the form of differing, even conflicting, interpretations, the past twenty-five years have seen one of the most closely-knit attempts yet m a d e to understand the so-called 'scientific revolution'.

Hallowed theme of the general history of science and classic chronological term for the period astride the 16th and 17th centuries and spanning the years between Copernicus's De revolutionibus orbium coelestium (1543) and Newton's Philosophia naturalis principia mathematica (1687), the 'scientific revolution' used to call up the image of a decisive turning-point in the thinking of western civilization: 'the Scientific Revolution was the result of a truly unique series of innovations in ideas and methods that furnished the key to an understanding of the structure of things and the relations between them' (Hall, 1963). Copernican astronomy and physical experimentation on the one hand and analytical geometry and infinitesimal calculation on the other had caused the 'bible', Aristotle's opinions and pre-scientific animism, to be replaced by the understanding of the mechanical laws of nature. T h e church's interdict on Copernicus in 1616 and the retraction forced out of Galileo in 1632 were clear pointers to the subversive force of the n e w science: 'this revolution undermined the authority of

Pietro Redondi, whose first research post was at Milan University, is currently a research scientist with the C N R S working at the Alexandre Koyré Centre of the School of Higher Social Science Studies in Paris, of which he was Deputy Director from 1984 to 1989. His published works include L'acceuii des idées de Sadi Carnot et la technologie française (Vrin, 1980), Galileo erético (Einaudi, 1983, translated into several languages) and the collection of Alexandre Koyré lectures and papers published under the title De la mystique à la science (Editions de la E H E S S , 1986). Since 1983 he has been director of the periodical History and Technology. In 1984 he was awarded the C N R S bronze medal. H e m a y be contacted at the following address: Centre Alexandre Koyré, M u s é u m d'histoire naturelle, Pavillon Chevreul, 57 rue Cuvier, 75231 Paris, France.


Pietro Redondi

medieval science and its importance exceeded that of any other event since the birth of Christendom' (Butterfield, 1957).

In its philosophical sense the 'scientific revolution' concept has played a fundamental role in the history of science, not simply in terms of the philosophy of science but also in relation to political science. The metaphor, incidentally, was invented at the time of Les Lumières, when it was xised by Clairaut the astronomer and Bailly the first historian of astronomy to describe Newton's achievement. Scientist-cum-revolutionary, Bailly—like Lavoisier, eponymous hero of another revolution of science, the so-called 'chemical revolution'—was a victim of the Terror (Cohen, 1985). O n the eve of the French revolution a famous reference by Kant to the Copernican astronomic system in the preface to the second edition of his Critique of pure reason (1787) left posterity an influential analogy when he described critical rationalism as a 'Copernican revolution'.

However, supplying a historical definition—following the image that the participants in the so-called revolution had of themselves in terms of its time and causes—has always been problematic. Progress in the rationalization of experimental science lagged too far behind for any clear-cut designation of the completion of the 'scientific revolution' and the difficulty was just as great with regard to the way it developed. A s the positivist thinkers became skilled in the techniques of erudition and went back to the original sources, anticipations of modern science appeared. Pierre D u h e m ' s discovery early this century of mediaeval precursors of Galilean physics and his paradoxically presented characterization which overturned the traditional image of both the scholastic Middle Ages and the century of Galileo and Descartes suggest that the birth of modern science goes back as far as the 13th century.

D u h e m ' s argument for continuity between the scholastic thinking of the Middle Ages and 17th century science has received support and been developed in recent decades by studies on mediaeval perceptions and methodology (Crombie, 1953) and on the tradition of the teaching of Aristotelian logic in Padua (Randall, 1961) and in the Renaissance universities (Schmitt, 1981). Recently the prospect of a new interpretation has been opened up by a discovery relating to the courses of logic and natural philosophy given by the Jesuits at the turn of the 16th century in their famous colleges, that at R o m e in particular: the sources of Galileo's philosophical manuscripts on the logic of demonstration have been identified in the notes for these courses. N o w , if the date of these documents coincided, as is supposed, with Galileo's maturity, they would constitute the missing link in the chain of logical thought connecting the Middle Ages with modern science via the Jesuits (Wallace, 1981 and Crombie and Carugo, 1983).

The reduction of complex combinations to their simple elements and the proving or disproving of theories by deduction and comparison with the facts or even the empirical method that used to be presented as the revolutionary epistemological contribution of Galileo and Bacon, was not a modern invention at all. It began with Aristotle and his commentators, held its ground up to the age of the masters of logic in the 12th and 13th centuries and then triumphed during the Catholic counter-reformation by proposing rational knowledge as an answer to the scepticism, astrology and magic of the Renaissance. The apologetic problem, linked as it is with the supernatural value of miracles, is today a decisive problem in the history of the 'scientific revolution' and still largely unresolved. Its understanding would probably enable us to define more clearly the tensions between the occultist and atomist traditions of the Renaissance on the one hand and the experimental formulation taken

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by Galilean science in Italy and France on the other. Thus the history of the great quarrel between the Jesuits, Pascal and Mersenne on Torricelli's vacuum experiment yet has to be written in terms of the theological and philosophical debate that, in France, accompanied the flowering of modern science and culminated in the interdict on Cartesianism issued in R o m e in 1663 and adopted in Paris in 1671. Whilst the Jesuits expressed their fundamental apologetic ideal in the form of Aristotelian-Thomist rationalization, Pascal linked the spirit of geometry with Augustinian apologetics and Mersenne, in opposition to both the wonders of the magicians and the mechanism of his friend Descartes, and proposed a completely experimental mechanism with a clearcut separation between science and metaphysics (Lenoble, 1943).

However, it is n o w agreed that, after the discoveries m a d e by the exponents of the 'continuist theory', it is difficult to talk about a 'revolution' in the 17th century in the sense of the invention of a methodology. But the truth is that a purely methodological definition of the 'scientific revolution' had never been legitimized by the historians. It could only be defended if science were viewed independently of philosophical, religious and social ideas. O n the other hand, the continuist theory which traces Galilean thought back to mediaeval or Jesuit logical Aristotelianism comes up against a historical paradox: 'an essentially Aristotelian methodology generating—three centuries later—a science that is fundamentally anti-Aristotelian' (Koyré, 1966).

The problem as raised by Koyré concerned the danger of anachronism in applying epistemological categories from modern science to the history of science. According to Koyré, contrary to the significance attached to them by epistemology, abstract logic and methodology are of relatively little importance in the concrete development of 'scientific thought' where what mainly counts is the use m a d e of the principles of logic.

Koyré, for his part, had the intellectual dimension of science in view, which is a matter of looking at two questions: what, for the theories of the 17th century, were the limits of the thinkable at that time and why , within those limits, had this—rather than some other—thinkable c o m e to be? His proposal was that the 'scientific revolution' should be seen as a spiritual transformation, a change in conception of the world in which the attributes of perfection and inifinity previously reserved for G o d since the Middle Ages were transferred to nature. For him, this change was largely the result of two substitutions that were m a d e in the 17th century: the replacement of the closed cosmos by an infinite universe and that of concrete, hierarchized space by geometrized and completely homogenized space (Coumet, 1987).

O n the basis of his research on Paracelsus and Copernicus and his o w n Etudes galiléennes, Koyré attempted to trace infinitization and the principle of inertia from Bruno to Galileo, Kepler to Descartes and N e w t o n to Laplace and insisted that the thread had to be followed right up to Cantor, Maxwell and Einstein whose space-time geometry he sees as the culmination of the 'scientific revolution'. As for its origins, whilst the idea of the infinite went back to the 14th century from Nicholas of Cusa to the G e r m a n mystics and neo-Platonism, the geometerization of nature could be traced back to the atomism of Democritus. Koyré's 'scientific revolution' was everywhere and nowhere between Democritus and Einstein—constantly about to appear and for ever delayed. For us today it is a transcendental idea that cannot be reduced to historical periodization, though it does permit a history of science with interweaving conceptual levels opening and closing on one another and whose course is a subtly qualified and unstable process.

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The debate that this transformation of the history of the 'scientific revolution' sparked off in the late 1960s is still in progress.

It began when American historian T h o m a s Kuhn' s book The Structure of Scientific Revolutions, published in 1962, explained the 'revolution' as the theoretical interreg n u m that a scientific community which is battling with a theoretical system that is increasingly inadequate and therefore has to be replaced has to go through. Since the alternative theoretical systems stem from differing metaphysical and methodological assumptions, the adoption of a n e w 'paradigm' is a choice between theoretical systems that are incommensurable. The transformation of metaphysical conceptions advanced by Koyré descended from the world of abstract ideas to the very core of personal and institutional options, challenging traditional rationalist epistemology. A n essay in 1970 by Paul Feyerabend, the American epistemologist, on the religious and aesthetic rhetorical methods used by Galileo in defence of the Copernican theory drew criticism of all kinds, including that of obscurantism (Machamer, 1973).

Are not metaphysical beliefs and social, biographical and institutional factors all intrinsically irrational? Is it not essential to draw a clear line separating this ragbag of external accidents from the realm of pure science? Since the time of the Greeks, has not rationality implied atemporal and absolute criteria and formal systems of logic (Hesse, 1973)? Conversely, if this positivist methodological continuism is replaced by the equivalence of paradigms, then what becomes of the idea of rational progress (Rossi, 1975)?

Abandoning these questions which had, up to then, held it to a philosophy of science and history, the study of the 'scientific revolution', on the contrary, took a firmly anthropological turn, being content to observe that the criteria of rationality developed over time according to the cultural and social dimensions of science (Righini-Bonelli and Shea, 1975).

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T h e argument was that 'traditions of thought', 'metaphysical assumptions' and 'religious convictions' had to be embodied in the sociological notions of 'scientific community ' and 'social role' to become the key concepts of a re-appraisal of the problem of scientific knowledge. In her book Giordano Bruno and the hermetic tradition, published two years after K u h n ' s study and hotly debated at the philosophical level, the British historian Frances Yates rehabilitated the occultist thinking tradition of Hermetism and showed that the historical, religious and philosophical conditions justifying the description 'scientific revolution' would be enigmatic if n o account were taken of the intellectual m o v e m e n t of Renaissance magic preceding and accompanying mechanism.

According to her interpretation, the 'scientific revolution', though a unitary process, took place in two stages: a magic-occultist stage during the Renaissance in which the vision of the world is based on the universal laws of magical animism and a classical stage corresponding to the birth of mechanism. T h e central argument around which Yates built her case was the n e w perception of m a n , spread abroad by the magical thought of the Renaissance, as the operator and master of the natural forces. It w a s this mastery that encouraged hermetic philosophers like Bruno, Patrizi and Campanella to nurture thoughts of religious and political reform under the banner of a n e w religion of nature with the sun representing G o d using a symbolism that w a s also the basis of Kepler's trinitarian cosmology (Koyré, 1961). This religious Utopia w a s suppressed but it left an intellectual heritage to the thinkers of the 17th century because, in the figure of m a n the magician, possessor of the secrets of nature and versed in those of the

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In his Du monde clos à jythspmt. ¿ c runivers infini Koyré recognized in this version of Copernican cosmology which extended the star sphere to infinity a religious rather than astronomical view. Thomas Digges, pupil of mathematician and hermetic philosopher John Dee, was an astronomer, a military engineer and a fervant puritan. The infinite of the universe and the puritan ethic gave to Koyré and Merton, during the same period, in 1938-39, two different characterizations of the 17th century scientific revolution. From T . Digges, A Perfit Description of the Caelestiall Orbes, 1576.

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Figure 3.

In the astronomical errors in this diagram of Bruno, Yates found indications of an adherance to Copernicanism on the part of Bruno inspired more by the hermetic suggestions than by mathematical arguments. From G . Bruno, La cena dette ceneri, London, 1584.

mechanistic arts, were enshrined the characteristic features of the mechanistic natural philosopher.

Yate's second argument concerned the role of Utopias and secret societies as embryonic forms of the scientific academies of the 17th century, and her third highlighted hermetism's contribution to the progress of mathematics since the magicians' use of the Pythagorian tradition placed the number at the summit of natural learning. She also argued—the only aspect of the book to have been contested on the philological level (Westman, 1977)—that hermetic philosophy influenced the adoption of the heliocentric system and that the Copernican astronomic reform was seen by the hermetist philosophers as a celestial sign announcing an age of reform in the history of religion.

O n e advantage of Yates' study from the historical viewpoint is that it arrived at fairly precise dates for the beginning and end of the 'scientific revolution' phenomenon: the magical universe was born at the end of the 15th century with Ficino's neo-Platonic reinterpretation of magic and the hermetic age came to an end in 1614 w h e n the scholar Casaubon proved that the hermetic texts originated in the Christian era, thus confounding the belief that the occultist doctrines went back to antiquity. The discredit then thrown on the sources was followed by the polemic led by Kepler and Mersenne against the natural philosophies of the magicians and in favour of the mechanistic conception.

The traditions of thought that Yates had simply juxtaposed in her two-stage model of the revolution were combined into a unitary theory for the 'scientific revolution' by American historian Allen Debus (1965, 1978). In his new interpretation, the central historiographie hub, the ideal viewpoint, for understanding the role of Renaissance hermetism in the formation of modern science, is the chemistry of Paracelsus—both

COPERNICVS,

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Figure 4. The divisions and the harmonies, the correspondences and the oppositions of the natural elements and the ideals belonging to magic Platonism of the Renaissance—from Dee to Fludd, from Campanella to Kepler—define in a new way the Aristotelian world. From G . Bruno, De umbris idearum, Paris, 1582.

before and after 1614, i.e. the date at which the Yates study puts the end of the development of the hermetic programme. Whereas, for Koyré (1955), Paracelsus was the witness of the mystical m o v e m e n t and, for Hélène Metzger (1923), the inspiration of chemical doctrines in France up to the 18th century, for D e b u s — w h o had discovered his influence in England as well—Paracelsus was the incarnation of the image that Yates constantly refers to of the magician as nature's minister. His neo-Platonic and at the same time empiricist ideal came d o w n to looking at nature as it is (natura naturans) and his programme, aimed at relating medicine to the practical tradition of alchemy, met with success. T h e iatrochemical physicians were experimenters and their vitalism and biblically inspired mysticism and the profound significance that the mathematical harmonies of the analogies between microcosm and macrocosm had for them entitled them to be identified with the m o v e m e n t of the hermetic reformers studied by Yates. In this w a y the innovative importance attached to the Paracelsian school because of its input of vitalist and organicist ideas in chemistry, life sciences and physics disposed of this apparently irrational gap between the 'scientific revolution' and the 'Lavoisier chemical revolution' that traditional historiography had been obliged to accept by showing that characterising modern science in terms of

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Copernican astronomy and Galilean dynamics was historically reductive (Debus, 1977).

Moreover, these perspectives enabled the portraits of the classical authors including Bacon and his role in the transition from magic to a mechanistic philosophy close to artisans' practices (Rossi, 1957) and Harvey and the question of the mystical symbolism of the circle in the discovery of the circulation of the blood (Pagel, 1957), to be set in a broader context. Later studies (Maclean, 1972) confirmed the influence of a Platonic and experimental current of Paracelsian thought on science in England both in the Royal Society and in court medicine. However, while empiricist neo-Platonism m a y have reigned in chemistry and medicine, what was its role in mathematical physics and astronomy, aside from the well-known example of Kepler's mysticism of the secret harmonies of the universe?

T o the role of hermeticism and alchemy was added, in the 1970s, the study of the context of the discovery of mathematical physics in Newton's Principia. The genesis of the Newtonian laws was still outside the scope of positivist historiography because it could be reconstituted neither by Newton's quantitative research nor by logical connection to his predecessors' physics. Apart from this problem there was the equally awkward question of Newton's competence in alchemy, his lifelong pursuit. Analysis and chronological classification of all his writing on alchemy has m a d e it possible to suggest a possible connection between the two fields of Newtonian thought (McGuire and Rattansi, 1966; Dobbs , 1975). The importance attached in these writings to the reciprocal action of active spiritual agents in relation to passive matter in transmutations m a y lie behind his conception of attractive and repulsive forces acting between particles. A quantitative concept of universal attraction would thus have carried over the animist language of alchemy, where the conflict between opposite elements plays a dominant role, into physical mathematics (Westfall, 1975).

This fine problem, the theories advanced to solve it and the debate that has followed (McGuire, 1977) show h o w m u c h broader the notion of 'scientific revolution' has become. Admittedly it is n o w less linear but it is also far richer. In the late seventies it would have been out of the question to sum up the history of the birth of modern science in terms of continuity under the n a m e of methodology or by a discontinuous definition starting with the advent of mathematization. For a new post-Koyré generation of science historians, writing the history of the 'scientific revolution' meant studying a multiplicity of conflicts between cultural elements which dislocated each other on differing intellectual registers.

However, for the history of the 'scientific revolution', too, to become a history in its o w n right, taking its inspiration more from the h u m a n sciences and the past civilizations they study than from the philosophy of today's exact sciences, w e had to wait for the studies on the intellectual origins of the Glorious Revolution (Hill, 1965) and the work by science sociologist Robert King Merton in 1938 challenging the Weberian theory about the impetus given to science and technology by the puritan ethic.

Recent research on representative milieux such as the systematic analysis of the religious affiliations of the Royal Society (Purver, 1967) and the studies of the Platonic tradition of Cambridge (Webster, 1975) and the Anglican current drawing its inspiration from Newtonianism (Jacob, 1976) have shown that a unilateral sociological explanation of science in England in terms of a Puritan religious character or radical political ideal would be illusory. The experimental science adopted within the Royal

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Society has been the subject of a more qualified historical evaluation because it was, in fact, the cultural fruit of the English society of the time of the Restoration looking for a w a y out after a civil and religious conflict (Mulligan, 1973). This sociological history approach proved fruitful and enabled English historians Steven Shapin and Simon Schaeffer (1985) to relaunch the debate on the tension between scientific revolution and political revolution in 17th-century England and even on the tension embodied in Boyle and Hobbes.

Shapin and Schaeffer interpreted experimental practice as the expression of learning in which a philosophy of science is integrated with political thought. According to their analysis of the polemic between Boyle and H o b b s , the arguments involved with regard to the existence of a vacuum were also at play in their thinking with regard to the constitution of the English kingdom. Whereas the materialist mechanism of Hobbes, focussing on the real structures of nature, reflects a mechanistic doctrine of society and an absolutist doctrine of royal power, Boyle's p r o g r a m m e of testable experimental demonstrations reflects an organization of representative political power in a framework of religious tolerance.

T h e interest that the interpretation of the influence of religious conditioning and social roles on the development of modern science attracts today is also evident from the discussion that followed the publication of m y book Galileo erético which reveals the conflict between Galileo and the Jesuit college in R o m e regarding the atomist philosophy which the Italian thinker defended in opposition to Aristotelianism, thus exposing himself to the Jesuit accusation of Eucharistie heresy. This conflict, eclipsed in the traditional history of the 'scientific revolution' by the Copernican interdict, offered a window, exceptional in the richness of its theological and philosophical connotations, through which no reconstitute the relationship between political opening (or crisis) and cultural innovation (or restoration) within the R o m a n intellectual and religious community in which Galileo played out the role of Urban VII's learned protege (Redondi, 1983).

Yet more recent studies have begun to throw light on the contribution of reformed theology in favour of an atomistic mechanism, both through the absence of the tridentine d o g m a of the Eucharist and the presence of an Augustinian idea of natural passivity in the face of divine legislation (Deason, 1987).

A s for the history of Catholic science, Jesuit thought battling with the Reformation and the decline of traditional Catholic conceptions is also, at last, beginning to be restored to the religious paradigm that inspired it (Feldhay, 1987). Fusing science and the Catholic faith together in a n e w way , revolutionary Molinist theology stimulated the freedom of research of the Jesuit thinkers by encouraging the use of observation and mathematics in astronomy and natural philosophy and even the development of hermetist ideas.

Thus, with the development of modern science two research traditions— phenomenist and realist—have formed, one whose image is nature free of any kind of determinism with h u m a n salvation as its objective and another following the mechanistic idea of nature governed by the necessary laws of divine providence (Redondi, 1988).

These topics, together with the vocabulary and iconography, instruments and collections and patronage and rhetoric of science, are so m a n y fields of study in what w e still call the 'scientific revolution of the 17th century', while recognizing that it is a cultural adventure which cannot be simplified and that the idea that one single

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scientific revolution could have permanently transformed our history is a myth. In any case, the experimental disciplines compel us to recognize a 'second scientific revolution' (Kuhn, 1975) in a world completely different from that of the 17th century. •

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The history of mathematics and ethnomathematics H o w a native culture intervenes in the process of learning science

Ubiratan D'Ambrosio

Ethnomathematics is a programme which looks into the generation, transmission, institutionalization and diffusion of knowledge with emphasis on the socio-cultural environment. By drawing on the cultural experiences and practices of individuals and of communities, ethnomathematics allows for an easier flow of scientific ideas with children, reducing the effects of cultural blocks.

Ethnomathematics is a concept resulting from the perception of m a n as an animal in search of survival and of continuation of the species but with a plus over the other animal species. This plus is the drive to transcend one's o w n existence (the sense of past and future, sense of religion and art, sense of explaining and of understanding) and to transcend, by giving to it an extra dimension, the search for survival and procreation, which in Homo sapiens results from a different perception of the other, thus giving rise to senses of love, shareability, generosity, charity and the like. I call mathema the actions of explaining and understanding in order to transcend and of managing and coping with reality in order to survive. Throughout all our o w n life histories and throughout the history of mankind, technés (or tics) of mathema have been developed in very different and diversified cultural environments, i.e. in the diverse ethnos. So, in order to satisfy the drives towards survival and transcendence, h u m a n beings have developed and continue to develop, in every new experience and in diverse cultural environments, their ethno-mathema-tics. These are communicated vertically and horizontally in time and for the reason of being more or less effective, more or less potent and sometimes even for political reasons, these various tics have either lasted and spread (e.g. counting, measuring) or confined themselves to restricted groups and even disappeared. This is m y approach to the history of ideas.

A s a pedagogical programme, ethnomathematics stems from love, respect and solidarity for children and for adults: respect for each person's differences and solidarity with their needs. There have been m a n y examples of ethnomathematics and its use in

Ubiratan D'Ambrosio is Professor of Mathematics in the Institute of Mathematics, Statistics and Computer Science of the State University of Campinas, and Coordinator of the research institutes of the Secretary of Health of the State of Sâo Paolo, Brazil. H e is also President of the Latinoamerican Society of History of Science and Technology.

Professor D'Ambrosio m a y be contacted at the following address: R u a Peixoto Gomide 1772 A p . 83, 01409 Sâo Paolo, S.P. Brazil.


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school systems. I recall when, in the early fifties, I used to introduce the circumference of circles by looking at different bicycle wheels and measuring their trajectories in the road and dividing these lengths by the diameters. In the early seventies, I was responsible for a major curriculum development project in Brazil.1 The approach was an experimental one, with geometry starting from forms, measurements and properties, beginning with concrete, three-dimensional geometry and then moving into the two- and the one-dimensional. Theoretical reflections would be a next step, through the process of experimentally recognizing regularities, classifications and qualities. O u r approach was an integrated science approach,2 which is essential to the ethnomathematics programme, as will become clear later in this article. This was a typical example of what I was eventually to call ethnomathematics. Several other units in the project dealt with movement , forces and plant growing, always drawing on doing, rather than on laboratory work in the traditional sense. These were situations dealing with mathematics and science, with students designing and building their o w n instruments and apparatus out of their environmental reach.3

Let m e clarify from the onset that I understand environment in its most general sense: everything that surrounds us, natural, artificial and cultural. W e moved away from traditional laboratories since they bring a sense of artificiality to the early steps in scientific thinking. A child m a y be dominated by the idea that an instrument is designed and produced to perform a certain task, and this brings an artificiality to the process. Our reasoning in moving away from the traditional laboratory bears some similarities to recent philosophers w h o look into the fictional character of science. Thus, the basic pedagogic ideas behind such projects are for children to draw on observation and experimentation, dealing with situations and phenomena that belong to their environment, which is indeed a portion of reality, and to derive explanations, understanding, generalizations, abstractions and theories. Indeed, the project has the following steps as objectives: (a) observations and ad-hoc practices; (b) experimentation and methods; (c) reflections and abstractions; and (d) theories and invention. It is our belief that these are the steps leading to creativity, a major goal of our pedagogical project, and that these four steps derive from our approach to the history of ideas, particularly to the history of science.4

Background

The main ideas behind such considerations and what I later decided to call ethnomathematics, came out of close to 40 years of experience in the teaching of sciences, mathematics, reading and writing, hygiene, values, art, technological awareness, ecology and so on in the most diverse cultural environments, and in the most diverse ways: effective classroom action, teacher training, generating and directing projects, chairing and participating in commissions and mostly conducting and supervising research. W h e n I first started talking about ethnomathematics and ethnoscience I was also moved by some examples which, in themselves, are no more than successful and sometimes inspired ways of conducting classroom teaching. S o m e use real-life problems and situations and modelling, others use concrete materials, toys and games; some use history, often getting closer to stories and thus drawing upon fantasy and imagination. All this is valid; all these approaches fit perfectly well into the concept of ethnomathematics.

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The history of mathematics and ethnomathematics

But ethnomathematics is a more ambitious project, which depends on a new understanding of history and epistemology, essentially a new way of looking into the process of generation, transmission, institutionalization and diffusion of knowledge. It calls for looking at every facet of h u m a n understanding, of creativity, of socio-emotional and political factors and m a n y more, and this involves what w e n o w k n o w as arts, religion, science and so on but before they are (in one's existence) and were (in history) called as such. These ideas gave rise to a research programme which comprises theoretical concerns relevant to the explanation of nature as a whole and to h u m a n behaviour in the environment. This comes from h u m a n beings' unique characteristics of codification and symbolization of their practices to survive and to transcend. The approach to the body and to disease through distinct cultural environments, or ethnomedicine as it has been called, is gaining importance.5 The same is true when w e look into modes of identification and reckoning time. W e see in the history of mathematics, in practically every chapter of the development of modern mathematical ideas (Huygens, Newton and Einstein) the importance of time. W h e n w e ask rural communities about these modes w e see totally original mathematical ideas, which are elaborated from absolutely elementary ideas and which developed, through generations, into very sophisticated tics to explain and help the people to cope with their rural environment, i.e. to develop the mathema appropriate to their ethno. These are examples of ethnomathematics which abound in this world, and which are obviously the result of, and surely will continue to mark their participation in, the ceaseless cultural dynamic. There is an interesting example showing the intimate relation of this with literacy a m o n g the rural Tamil N a d u in India.6

S o m e historical remarks

Let us look briefly into some aspects of science and mathematics through history, mainly from the point of view of their transmission and institutionalization. W e need some sort of periodization for this overview, which corresponds, to a certain extent, to major turns in the socio-cultural composition of western history. W e disregard for the m o m e n t other cultures and civilizations. For reasons which w e shall not discuss here, mathematics appears universally as the earliest structured form of scientific knowledge. It was recorded, in all civilizations, before other forms of scientific understanding of the world had been structured. For this reason, m u c h of what follows will refer to mathematics.

W e rely upon the accounts of Plato for our information on the beginnings of mathematics, and these point to two clearly distinct branches: what w e might call 'scholarly mathematics', which was incorporated in the ideal education of Greeks, and another, which w e m a y term 'practical mathematics', reserved mainly for manual workers. Since the Egyptians there had been a space reserved for mathematical practices to be taught to workers. This is carried on to the Greeks, though Plato clearly states that 'all these studies [ciphering and arithmetic, measurements, relations of planetary orbits] into their minute details is not for the masses but for a selected few' and ' w e should induce those w h o are to share the highest functions of State to enter upon that study of calculation and hold it,... not for the purpose of buying and selling, as if they were preparing to be merchants or hucksters'.7 This distinction between scholarly and practical mathematics, reserved for different social classes, was adopted

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by the R o m a n s through the 'triviurri and 'quadrivium' and through a practical training for labourers. In the Middle Ages w e begin to see a convergence of both forms, scholarly and practical; that is, practical mathematics begins to use some ideas of scholarly mathematics in the field of geometry. Practical geometry becomes a subject in itself in the Middle Ages. The approximation of practical to theoretical geometry is achieved after the translation from the Arabic of Euclid's Elements by Adelard of Bath (early in the 12th century). Dominicus Gondissalinus, in his classification of sciences, says that 'it would be disgraceful for someone to exercise any art and not k n o w what it is, and what subject matter it has, and the other things that are premised of it'.8 With respect to ciphering and counting, change started to occur with the introduction of Arabic numerals. The treatise of Fibonacci9 is probably the first to present practical and theoretical aspects of arithmetic in a mixed way.

The next stage in our story is the Renaissance, where a new labour structure occurred in the domain of architecture with the appearance of technical drawing, thus making it accessible to bricklayers. The description of machinery was facilitated thanks to the emergence of drawing, and this allowed techniques to be reproduced by people other than their inventors. In painting, schools became more efficient, and treatises began to be available. The closing of the gap between scholars and the general public was evident, and scholars started to use vernacular for their scholarly works, and to write in a non-technical language and in a style accessible to non-scholars. Galileo provides a good example, and it is interesting to see the explanations of Isaac Newton about the publication of his Optiks in English, to look into the reasons for the Encyclopédie, and m a n y other examples.

The coming together of practical science and mathematics and scholarly science and mathematics increased in pace in the industrial era, not only because of the need to deal with increasingly complex machinery and understand instructional manuals, but also for social reasons. Exclusively scholarly training would not suffice for the children of an aristocracy which had to be prepared to keep its social and economic predominance in a new order. But the matter was not only of production, but rather of consumption, which was a major force behind education. Inevitably, the approximation of scholarly and practical science and mathematics begins to enter the then incipient school systems.

Finally, w e gain a last step in this rough history by reaching the 20th century and the widespread concept of mass education. Even more fundamentally than in the time of Plato, the question as to what science and mathematics should be taught in mass educational systems is posed. For those in power, it must be the science and the mathematics that keeps the economic and social structure, remanent from the aristocracy, determined by better training of subjects, which is essential for preparing the elite (as advocated by Plato) and at the same time allowing this elite to assume effective management of the productive sector and—what was essential—to develop consumption habits and capabilities. In the case of mathematics, this gave way to a 'scholarly practical' mathematics which w e shall call from n o w on 'academic mathematics', i.e. the mathematics which is taught and learnt in schools. But by contrast, ethnomathematics continues to be practised a m o n g identifiable cultural groups, such as national-tribal societies and even in metropolitan centres in the developed world through labour groups, children of a certain age bracket, professional classes, and so on. This is equally true with science in general. M u c h of the practices such as plant growing, building and divination fit into the category of ethnoscience, as

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opposed to 'academic science'. This depends largely on focuses of interest and motivation and on certain codes and jargon which do not belong to the realm of academic science and mathematics. W e go even further in these concepts of ethnomathematics and ethnoscience to include m u c h of the mathematics and physics that are currently practised by engineers and physicists, mainly calculus, which do not respond to the concept of rigor and formalism developed in academic mathematics courses. A s an example, w e refer to the Sylvanus T h o m p s o n approach to calculus, which fits into this category of ethnomathematics.10 Masons and well-diggers and shack raisers in slums are all practitioners of ethnomathematics and ethnoscience.

A n example: the concept of time

Time is without any doubt a fundamental concept in science and mathematics, although courses in both mathematics and the history of mathematics do not give m u c h importance to the development of the concept of time. As a cultural element time influences so m a n y aspects of life. In the approach of ethnomathematics to the history of mathematics w e look into the importance of time in explaining phenomena, in understanding the behaviour of nature and of h u m a n beings, and the importance of astronomy in the construction of scientific knowledge. But w e do not go into its purely descriptive aspects. Instead, w e try to do things, always trying to recapture the history of the actions. In other words, in doing things related to time, there is less to each than the traditional school might expect. It is a very difficult, almost impossible, task to teach the concept of the hour and h o w to read the hours on a clock to a child, or to an adult w h o has no previous experience of this kind of time measurement. Instead w e draw on the daily experiences of children related to time, such as the routines created by the immediate society, usually the family. These routines are normally wake-up time, breakfast time, lunch time, school time, dinner time and go-to-bed time. It is not difficult to associate these to solar movement and even to the construction of a solar clock. O f course, this draws on the experiences of every community. In order to better examine experiences, observations and codifications related to the observation of the skies w e have developed at U N I C A M P , under the direction of Professor Marcio D 'Olne C a m p o s , a multicultural naked-eye observatory. Drawing on characteristics of Stonehenge, of M a c h u Pichu, of the Suvay-Japur, students discuss the movement of the celestial bodies and are introduced to the concepts of time, culminating in the construction of sun-clocks.

A remarkable example is also given by L . S. Saraswathi (see note 6) in rural Tamil N a d u . The basic principle is that time is identified or reckoned and measured with the objective of performing actions, mostly agricultural, and organizing and conducting events, mostly rituals. There w e see measuring and counting as a means of satisfying both the managing of reality, the drive to survive, through agriculture and the explanation of reality, the drive to transcend, through rituals. Thus the Tamil N a d u population has developed tics for these complex mathema. W h a t they do for reckoning time is to use a simple device for measuring shadow. They take a piece of straw of any length and divide it into 16 equal parts by folding it in half eight times. The straw is then bent like a ' L ' and held on the ground with the vertical portion towards the Sun, so that the shadow of the upright portion falls on the horizontal portion kept on the ground. The vertical portion is adjusted in such a way that the length of its shadow is equivalent

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to the length of the horizontal portion. In this way the number of parts of the upright portion indicate the number of units of time that have passed since sun-rise if it is forenoon or the number that have passed since noon if it is the afternoon. People in this community are reported to tell time and to reckon with the precision of a minute. H o w did these practices originate? Where do w e see, in practices like these, indicators of cultural dynamics? In other words, what is the history of time measurement in this community?

Most of examples like this, dealing with the concept of time, of movement, measurement, counting, decoration and so m a n y practices of a mathematical nature, as well as processes of curing, of energy use, of agriculture and those associated with values, such as justice and sovereignty and political representation, all of them relying in a direct or indirect way on notions and practices of a scientific and mathematical nature, are part of the generation-after-generation accumulation of knowledge in particular cultural and natural environments. Cultural dynamics, resulting from mutual exposure, are k n o w n practically everywhere and in every epoch of the history of mankind, and have been incorporated within this process of accumulation of knowledge. They surely cannot be avoided, yet w e feel it essential that these cultural encounters be acknowledged in the proper perspective.

School systems

Education reforms, particularly in mathematics education, are missing the point. M o r e attention should be paid to students and teachers as h u m a n beings,11 and w e have to realize that mathematics—the same is true with respect to other disciplines—are epistemological systems in their socio-cultural and historical perspective and not finished and static entities of results and rules.12 O n the other hand, w e have to face the fact that schools are systems at the service of society, to which evaluation and testing are subordinated,13 and there is no point in trying to cover up this fact. It is recognized that negative self-esteem is particularly strong a m o n g minority students in the case of mathematics. The cultural image of mathematics recalls the most successful chapter in the history of European thought and contributes to negative cultural self-esteem, particularly a m o n g children from black, native American and Hispano backgrounds.

Ethnomathematics avoids this negative self-esteem. Success in ethnomathematics depends on h o w you manage the situation you have to face. Thus the social aspect is minimized and the cultural achievements are always present. Every single manifestation of art, production, behaviour, leisure, planning, walking and so on, covering all activities of a h u m a n being, brings with it numbers, figures, symmetries, harmonies, regularities, direction, design, logic, and so on, and all of this builds on into ethnomathematics. Every single culture, tribe, community and individual develops its o w n way of coping with everyday needs, with its environment, with its fellow h u m a n beings, always trying to understand what is going on, to explain what is seen and felt, and thus contributing to the building up of knowledge.

Knowledge is the cumulative product of mankind since the first appearance of Homo sapiens on our planet. M o d e s of thought differ from individual to individual, from community to community, from culture to culture; they are interchangeable and modifiable as the result of mutual exposition throughout time and thanks to the dynamics of interactive behaviour; every individual has the potential to learn what the

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other knows, every community and culture can absorb the behaviour of others. If w e want to bring these principles to the school, modelling and ethnographical methods appear as appropriate practices.14 There is no permanent, finished and absolute knowledge, neither in time or in cultural spaces. There are no superiority criteria a m o n g cultures, communities and individuals. All these belong to civilization in another, non-colonialist, definition of the term, as being 'the whole of the advances of h u m a n culture and aspirations beyond the purely animal level' (Webster's Third New International Dictionary, 1971). Aspirations that go beyond the purely animal level include explaining and understanding, i.e. the mathema.

A new approach to the curriculum

Several paragraphs in this paper carry, implicitly, a curricular proposal, both for pre-and in-service teacher training. There is not m u c h hope if w e do not change, radically, our approach to teacher training.15 The essence is to look at schooling not as a mere transmitter of knowledge, but primarily as playing a social, political and psycho-emotional role. Traditional and modern media are our repositories of knowledge. They are certainly better equipped and more efficient in transmitting accumulated knowledge, both 'finished' knowledge and knowledge 'in the making'. The fast pace of growth of knowledge, its amplitude, variety and need of updating, m a k e its transmission impossible via traditional methods alone. Equally, it is not possible to m a k e it the responsibility of the teacher. The teacher him/herself has to rush for his/her updating of knowledge, and this poses increasing problems, as w e all k n o w , with the concept of accreditation.16 There is a new role for schools and teachers which is reflected in the concept of curriculum itself, and this can best be summarized in figure 1.

The new role for schools and teachers here resides in the essential function of generating and managing the dynamics for the interactive behaviour expected in the classroom. Rather than being there to teach as traditionally defined ('to give instruction', 'to impart knowledge'), teachers should see themselves as partners in a c o m m o n search, in the c o m m o n and shared process of building up knowledge. The clear edge that the teacher most often has over the student should be adapted into a congenial partnership, building up into positive self-esteem for the student, and should never reflect an arrogant, imposing, authoritative attitude, which does no more than reinforce negative self-esteem. Particularly in science and mathematics education, accumulated, finished, stored knowledge remains far from the very nature of science and mathematics, whose main characteristic is their dynamic capacity for explaining and for coping with an ever-changing environment. W e expect students to be able to perform scientifically and mathematically. Thus, science and mathematics education means action. Simply accumulated knowledge in science and mathematics, which easily falls into rote learning, comes closer to history than to true science and mathematics. Descriptions of theories, of explanations and even of methods, have no more than exemplary value and should never be placed outside the context of social and cultural relativism. Thus, the ethnomathematics programme matches perfectly these ideas of the school. The historical approach asks that instead of building up history on heroes, on visionaries, on the giants of science and mathematics, which inevitably carries a Eurocentric bias, ethnomathematics builds upon the c o m m o n individual as the builder of scientific and mathematical knowledge and emphasizes the

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Figure I.

A new interactive curriculum concept.

I N S T R U M E N T A T I O N

Use of language, gestures, counting, drawing, retrieval of information, ethnography

CONTENTS

Accumulated in books, periodicals.newspapers, T V and media in general; in museums, monuments as popular practices

Group work, projects "show-and-tell", seminars, panel discussions and debates, reports

socio-cultural and natural environment as proposing directions for research through the d e m a n d on the imagination and the creativity of individuals and communities for the benefit of mankind as a whole. Even w h e n teaching certain basics, which w h e n properly contextualized are obviously needed, this should be done as an instrumentation for action and for the social construction of further knowledge. It is done with the purpose of preparing the student for action in his reality. T h e instruments, the tools, are not the object of science and mathematics education in this first stage. N o doubt, eventually they m a y constitute the object of reflection and of study, i.e. of academic scholarship, and this should be done in a broader socio-cultural and philosophical context; otherwise it is pure descriptive history, or should w e say story! •

Notes

1. The project was called 'Novos Materias para o Ensino de Matemática' and was aimed at developing modular material for the elementary school curriculum (ages 7 through 15). It was a major, nationwide curriculum development project sponsored by the Ministry of Education through a grant to the Institute of Mathematics, Statistics and Computer Science of the State University of Campinas ( U N I C A M P ) , Sâo Paulo, Brazil. At that time the project was a very advanced one, since we introduced educational technology, including open-circuit T V , video-taping, micro-teaching, calculators and computers. Smaller children were exposed to 'logo' in the very beginning of the development of these ideas. But much attention

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was given to socio-economic and cultural diversity. S o m e attention was also given to adult education. The approach was what we have called an experimental mathematics approach and the research for the project was important in the development of the basic ideas for ethnomathematics and to what is n o w known as 'science, technology and society'.

2. D ' A M B R O S I O , U B I R A T A N (1974) Sobre a Integraçâo do Ensino de Ciencias e Matemática, Ciencia e Cultura, 26, 11, pp. 1003-1010.

3. In Grenada, in a multinational project sponsored by the Organization of American States on 'Scientific Literacy and Technological Awareness' (1979-1982), middle school students were proposed to assess the water reserves of the country. This was motivated by the exodus of tourists during a crisis in water supply in the summer of 1980. Their measurement of the capacity of reservoirs made appeal to strategies which were devised on the spot, such as attaching a stone to a string to reach the bottom of the reservoir and discovering sampling as a technique to evaluate water use by families in the area. A group of students carried out research on the history of the construction of such reservoirs. This was an early example of the idea of social history of science and technology in the peripheral countries, an essential step for the broad programme of ethnomathematics. W e later found similar ideas in the Project FOXFIRE, being conducted by Eliot Wiggington in the U S A .

4. The importance of an epistemological posture underlying science education was stressed in U B I R A T A N D ' A M B R O S I O : Non-formal educational modules and the development of creativity, in Creativity and the Teaching of Sciences, ed. L . D . G ó m e z , Asociación INTERCIENCIA/CONICIT , San José, Costa Rica, 1983, pp. 79-90.

5. F A B R E G A , H O R A C I O , JR. (1975) The need for an ethnomedical science, Science, 189, 19 September, pp. 969-975.

6. S A R A S W A T H I , L . S. (1979) Functional Approach to W o m e n ' s Literacy, Problems of Women's Literacy, Central Institute of Indian Languages, Mysore, pp. 13-32.

7. Plato, The Complete Dialogues, org. E . Hamilton and H . Cairns, Bollinger Series, Pantheon Books, N e w York, 1966; respectively: Laws VII, p. 818 and Republic VII, p. 525 (b) and (c).

8. As cited in V I C T O R , S T E P H E N , K . (ed.) (1979) Practical Geometry in the High Middle Ages, The American Philosophical Society, Philadelphia, p. 8.

9. See elaboration on this in D ' A M B R O S I O , U B I R A T A N , Mathematics and society: some historical considerations and pedagogical implications, International Journal of Mathematics Education, Science and Technology, 11, 4, pp. 479-488.

10. T H O M P S O N , S Y L V A N U S (1984) Calculus Made Easy, St. Martin Press, N e w York (orig. edn. 1910).

11. See the excellent approach of G A R B A R I N O , J A M E S , et al. (1989) What Children Can Tell Us, Jossey-Bass Publ.

12. See in this respect D ' A M B R O S I O , U B I R A T A N (1987) Etnomatematica, Raizes Socio-Culturais da Arte ou Técnica de Explicar e Conhecer (A Collection of Five Essays), U N I C A M P , Campinas.

13. See the excellent research of A M A B I L E , T E R E S A (1983) The Social Psychology of Creativity, Springer-Verlag, N e w York.

14. See for example, D E C A R V A L H O B O R B A , M A R C E L O (1987) Um Estudo de Etnomatematica. Sua incorporaçâo na elaboraçâo de urna proposta pedagógica para o Nücleo-Escola dafavela de Vila Nogueira-Sào Quirino, Dissertacâo de Mestrado, U N E S P , Rio Claro; R O B E R T O N O B R E , S E R G I O (1989) Aspectos Sociais e Culturáis no Desenho Curricular da Matemática, Dissertacâo de Mestrado, U N E S P , Rio Claro; B U R I A S C O , R E G I N A , L . C . (1989) Matemática de Dentro e de Fora da Escola, Dissertacâo de Mestrado, U N E S P , Rio Claro, and the Project F O X F I R E by Eliot Wigginton, Anchor Press/Doubleday, Garden City, N . Y . , mainly Foxfire n.6, 1980, and Sometimes a Shining Moment, 1988.

15. D ' A M B R O S I O , U B I R A T A N (1985) Environmental influences, Studies in Mathematical Education, *• U N E S C O , Paris, pp. 29-46, for a proposal of an alternative curricular model. See also figure 1.

16. There is a growing need for making in-service training a regular activity for teachers. In fact, the dichotomy between the pre-service and in-service preparation of teachers is obsolete. Very attractive is the concept of not giving final degrees or accreditation for teachers. Teacher training is a professional life process.

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Journals on history of science: a brief guide

We present below a certain number of journals dealing with history of science: a list which is, of course, not exhaustive. The titles and the odd remarks that go with them were provided by the authors of the articles in these last two issues of Impact. They are, however, to be regarded as general indications; we do not pretend to have described in any depth either the spirit or the editorial policy of any particular review. There follows a longer list of other reviews presented without commentary. We have not given the titles of journals dealing with the history of technology, for this important area was not covered in the two issues.

Isis, Philadelphia The major professional journal. Edited in the U S A whose research workers it primarily serves, this review covers the whole spectrum of history of science, from the point of view of themes as well as periods. T h e critical reviews of a variety of published works are very useful, as is its cumulative annual bibliography which serves as a good working tool.

Osiris, Philadelphia A research journal devoted to the history of science and its cultural influences. T h e n e w series offers very useful thematic issues devoted to G e r m a n or American science.

British journal for the history of science, Cambridge Annals of science, Taylor & Francis, L o n d o n & Washington Revue d'histoire des sciences, Paris These three reviews largely cover the field of history of science, including the history of medicine as well as technology. O f a high level, the Revue d'histoire des sciences has published for a n u m b e r of years thematic issues in addition to its usual numbers (recently two were devoted to the history of science in China).

Nuncius, Florence N e w version of the Annali delVIstituto e Museo di Storia della Scienza di Firenze, this Italian review contains painstaking international w o r k highly specialized in the history of the Scientific Revolution: intellectual aspects, scientific instruments, history collections and archives. T h e journal is linked with exhibitions and cataloguing sponsored by the prestigious Museo di Storia della Scienze of Florence.

Studies in history and philosophy of science, Oxford & N e w York O n e of the most distinguished journals on the history of science. Thanks to the systematic publication of critical analyses of important work it serves as a forum for


Journals on the history of science

high-level debate on n e w methodologies and for the confrontation between problems of epistemology and history.

Physis, Florence Relaunched by the Enciclopedia Italiana, under the direction of V . Cappelletti, this review largely covers the whole field of the history of science.

Archives for history of exact sciences, Springer-Verlag, Berlin & N e w York Professional journal edited by Truesdell. Covers all periods of history, from Antiquity to the present day. M a n y of its contributors are mathematicians and the articles are generally very technical.

Centaurus, Copenhagen Journal of the Danish Society for History of Science, covering all aspects of history of science. Regularly features studies on technical aspects of ancient and medieval exact sciences.

Archives internationales d'histoire des sciences, R o m e A general vehicle for history of science, issued by the Académie Internationale d'histoire des sciences.

Historia mathematica, N e w York Review specializing in the history of mathematics.

Bollettino di storia delle scienze matematiche, Florence Since commencing publication in 1981, has stimulated study of the sources of Italian mathematics since the Renaissance. The journal covers the whole domain of history of mathematics, however, and has regularly published studies on the ancient and medieval periods.

Journal of the history of biology, Kluwer, Boston Edited by Everett Mendelsohn, the JHB (as it is colloquially k n o w n ) is a specialist journal which publishes articles dealing with all aspects of the history of biology, concentrating (although not exclusively) on the modern period. In particular it has published m a n y articles on the development of evolution theory and genetics, some of which relate their subjects to wider issues in social history and the history of ideas. The JHB thus provides a good illustration of the kind of work that is being done by academic historians of biology.

History and philosophy of life sciences, Naples Journal of the Zoological Station of Naples, publishing its historical studies.

Historical studies in the physical and biological sciences, Berkeley, U S A Journal which has become the reference in this domain.

Bulletin signalétique histoire des sciences et des techniques, C N R S , Paris Provides a bibliographical benchmark of worldwide production with very brief notes.

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Sciences et techniques en perspective, Nantes Journal published since 1981 by the Centre d'histoire des sciences et techniques of the University of Nantes and specializing in the sciences developed during the period 1750-1850, and their relations with philosophy.

Cahier d'histoire des sciences et des techniques, Paris Each issue devoted to a single theme. A publication of the French Society for the History of Science and Technology, it carries texts as well as commentaries, providing pedagogic materials or facilitating research.

Janus, Amsterdam International journal on the history of medical sciences, pharmacy and technology.

History of science, a review of literature and research in the history of science, medicine and technology in its intellectual and social context, Cambridge.

Historia Scientiarum, Tokyo Japanese journal on the history of science covering all areas.

Istorico-matematitcheskie Issledovanija, (Historicomathematic research) M o s c o w Publishes Russian material as the history of science

Ambix, Cambridge Journal of the Society for the study of alchemy and early chemistry, Cambridge.

Hull (Boletín de la Sociedad expanola de Historia de las Ciencias y de las Técnicas), Zaragoza Publishes Spanish material, and articles translated into Spanish

Rivista di storia della scienza, R o m e Generalist journal, but favouring mathematical sciences

Mathesis, Mexico Information and popularization journal on the philosophy and history of mathematics.

Social studies of science, Sage Publications, London Research journal on the social dimensions of science and technology.

Social epistemology, Taylor & Francis, Washington & London A journal of knowledge, culture and policy under the editorship of Professor Steve Fuller, Center for the Study of Science in Society, Virginia Polytechnic Institute, Blacksburg, U S A , provides a forum for the interdisciplinary research into the relations between science and society. O p e n to broad cultural enquiry, the journal is of some relevance to history and philosophy of science, particularly to ethnomathematics.

History of computing Reference journal.

Recherches didactiques des mathématiques, Paris For the learning of mathematics, Dept. of Math . , Concordia University, Montreal, Canada.

381


The Mathematical Intelligence These three journals occasionally publish articles devoted to the history of ma thematics education, the latter being at a higher mathematical level. A most useful guide to recent papers in the area is also contained in the newsletter of the International Study Group on the Relations between History and Pedagogy of Mathematics. This is obtained free on request from distributors throughout the world. For a list of distributors contact Professor Victor Katz, Department of Mathematics, University of the District of Columbia, 4200 Connecticut Avenue, N W , Washington, D C 20008, USA.

Other journals Acta historiae rerum naturalium necnon technicarum, Prague. Acta histórica medicinae stomatologiae pharmaciae veterinae, Prague. Acta medicae historiae patavina, Padua. A G U Committee on the history of physics newsletter, Greenbelt, U S A . Annals of the history of computing, Reston, U S A . Archiv der Geschichte der Naturwissenschaften, Vienna. Archive of natural history, London. Archiwum historii medycyny, W a r s a w . Beitràge zur Geschichte der Pharmazie, Stuttgart. Berichte zur Wissenschaftgeschichte, Wiesbaden. Boletín de la sociedad española de historia de la farmacia, Madrid. Bulletin de la Société française d'histoire des sciences et des techniques, Paris. Bulletin d'histoire de l'électricité, Paris. Bulletin of the history of dentistry, U S A . Bulletin of the history of medicine, Baltimore, U S A . Cadernos de histórica efilosofía da ciencia, Centro de lógica epistemologiia e historia da

ciencia, Universidade estadual de Campinas, Brazil. Cahiers du Séminaire d'histoire des mathématiques, Paris. Clio medica, Amsterdam. Earth science history, Washington, U S A . Fundamenta scientiae, Sâo Paulo. Gesnerus, Aarun. Histoire de ^Education, Paris. Histoire et Nature, Cahier de l'Association pour l'histoire des sciences de la Nature,

Paris. History and philosophy of logic, London. History and technology, London. Jonas, Elboeuf-sur-Andelle, France. Journal for the history of arabic science, Aleppo, Syria. Journal for the history of astronomy, U K . Journal of Japanese history of pharmacy, Tokyo. Journal of the history of medicine and allied sciences, U S A . Koroth, quarterly devoted to the history of medicine and science, Jerusalem. Kwartalnik historii nauki i techniki, W a r s a w . La vie des sciences, Académie des sciences, Paris. Lychnos Làrdomshistoriska Samfindets Arsbok, Stockholm. Medical history, London.

382


Medicina e historia, Barcelona. Medizinhistorisches Journal, Stuttgart. Newsletter of the Center for history of physics, U S A . N T M , Scriftenreihen fur Geschichte des Naturwissenschaften, Technik und Medezin,

Leipzig. Notes and records of the Royal Society of London, London. Organon, W a r s a w . Pharmaceutical historian: Newsletter of the British Society for the History of

Pharmacy, London. Philosophia Naturalis, Meisenheim-am-Glan, Germany . Quipu, Latino-american journal on the history of science and technology, Mexico. Revue d'histoire de la médecine hébraïque, Paris. Revue d'histoire de la pharmacie, Paris. Revue de synthèse, Paris. Science in context, Cambridge. Scientia, Milan. Sudhoffs Archiv, Zeitschrift fur Wissenschaftgeschichte, Wiesbaden. Studia histórica Academiae scientiarum hungaricae, Budapest. Studies in history and philosophy of science, London. Studies in history of biology, London & Baltimore. Studia leibnitiana, Zeitschrift für Geschichte der Philosophie und der Wissenschaften,

Stuttgart. Theoria, revista de teoría, historia y fundamentos de la ciencia, San Sebastian. Tijdschrift voor Geschiedenis der Geneeskunde, Natuurwetenschappen Wiskunde en

Techniek, Amsterdam.

383

Conclusion

After these two issues of Impact and at the conclusion of this historical and multifaceted inquiry into science, it would have been only natural to ask similar questions about technology. However, the history of technology arguably calls for an even larger assembly of experts, involves a greater number of people and institutions in society and brings a considerable number of economic forces into play. It therefore seemed best to limit ourselves just to science, especially since our aim was to demonstrate the different approaches which are possible in the history of science.

While w e have touched on the variety of ways in which the subject is tackled, and brought out the undeniable vitality of the last ten years in the history of science, w e have perhaps not emphasized strongly enough that for large-scale works serving the scientific community, our century has tended to favour teamwork (the admirable edition of Newton's papers produced by D . T . Whiteside* working alone being a notable exception). The series of complete works which have been listed in the annex to the article by Speiser and Radelet are generally the achievements of organized and international groups.

It is certainly more difficult to organize transverse studies involving large numbers of researchers if the great n a m e of some past scientist is not there to galvanize people's energies. There are, however, a few remarkable and effective examples which are worth mentioning, concerning the state of physics at the end of the nineteenth century, American science, etc., and it is possible to imagine that one future for the history of science might involve such forms of cooperation. Perhaps U N E S C O could find a role to match its ambitions in this international field, working in close cooperation with international scientific organizations? This would certainly not m e a n the disappearance of the lone researcher, and w e can be sure that the history of science will always attract different characters with varied educational backgrounds.

Perhaps, when all is said and done, w e should have touched on the role of the theatre and literature, which also illustrate in their way the place of science in the life of society. Bertold Brecht, with his forceful style, compels us to look at Galileo in a certain way and, whether one likes it or not, contributes to the image Galileo has. A remarkable play currently being staged in Paris, Les palmes de Monsieur Schutz, is providing a broad cross-section of the public with a particular view of the Curie family. While some choices have been open to question—one thinks of the pitiful fate inflicted on French scientists of the revolutionary period by a recent entertainment at L a Villette—we should surely see in this, above all, a renewal of interest at the present time in scientists themselves, individuals w h o m w e have been led all too rapidly to regard as of no further significance.

* The mathematical papers of Isaac Newton, Cambridge University Press, Cambridge.


Conclusion

T o conclude, w e should re-emphasize that there is a very strong element of pleasure in the vocation of all historians of science—the pleasure of being able to converse with scientists of all times.

Jean Dhombres

386

Readers' forum

An invitation Reasoned letters that comment , pro or con, on any of the to readers articles printed in Impact or which present the writer's

view on any subject discussed in Impact are welcomed. They should be addressed to the Editor, Impact of science on society, 7, place de Fontenoy, 75700 Paris (France).

The following letter received from reader V. G. Pushkin represents a personal reaction to the article 'Autonomous man' by Albert van Eyken published in Impact, no. 154 {1989), pp. 163—169. Dr Pushkin is Professor of Philosophy at the Herzen State Institute of Education, Leningrad, USSR.

The article by Albert van Eyken caught m y attention because it was unusual. W h a t it says is dictated by the author's intuitions, his view of the world and his profound subjectivity. Everything he asserts has an absolute value for him because it has been arrived at by his o w n thinking and is permeated by associations with life. This is w h y he attaches such great weight and importance to free will, dignity and individual reason. H e considers individuals in relation to the demands m a d e by the real and frequently complicated life situation in which they find themselves. V a n Eyken does not accept biologism in any of its forms or manifestations. In particular, he rejects the 'scientific' biologism whose advocates attempt to provide proof not for a person's strictly individual understanding but for what is determined by heredity, by the subconscious manifestation of personal experience or by an all-powerful environment.

The author of the article lays great stress on the autonomy of individuals, their freedom and dignity. These are very attractive concepts that people have been acquainted with for a long time. The author, in defending them, produces n e w arguments based on his o w n observations. H e speaks with good reason about acute social problems and the threat of antisocial behaviour. H e speaks out against moral laxity, erosion of the ethical foundations of social life, the cult of the ideas of aggression and violence and against everything that undermines in a person the basis of what is rational, reasonable and conscious. It is characteristic that he speaks out against the idea that the laws of h u m a n behaviour should be deduced from observations of animals, and this perhaps, is, the most important point he is making.

The individual is autonomous and fundamental. As the individual is, so is society too. The individual cannot be a part; it is a whole. The relationship of individual to society is possible only as the relationship of a whole to a whole. It was precisely in this way that Hegel understood the individual, as did the Russian philosopher N . A . Berdyayev. So it is that Albert van Eyken understands the individual. H e correlates that concept with contemporary society and its ethical and philosophical problems. The originality of the author's position is that it is based not on sociality but on individual subjectivity. Its orientation is towards the interior, intellectual universe, towards a person's dignity and ego. F r o m this there flows and becomes a reality the


acute problem of personal responsibility—the responsibility of each person for the state of society and its disposition. Every individual is, ideally, an autonomous personality with freedom of will. The author is not the slave of any approach or any doctrine. H e goes from the problem as experienced in life to its philosophical interpretation. ' W e m a y well suspect', he says, 'that autonomous m a n , living in a society where an influential body of scientific theory brings him d o w n to the level of an automaton and dismisses his mind as a superfluity, will often be dispirited or complaisant by turns' (p. 168).

The article dethrones such authorities as Freud and Skinner. Its author is correct in his criticism of the weak aspects of Freudianism, sociobiology and behaviourism and their adverse influence on the understanding of the individual. O n the other hand, in keeping with established canons, he could be taken tó task for excessive onesidedness and reproached for the fact that, having criticized influential psychological (and partly philosophical) schools, he did not do justice to them for the long and laborious path they trod, on which the truth revealed itself to them too. They did in fact raise important questions, even though they did not solve them. Both Freud and Skinner did m u c h that was valuable for the science of psychology. The author knows this, too, noting that Freud's ideas are not without substantial foundations. H e cannot reconcile himself, however, to the transfer of instinctive animal biologism to the h u m a n personality. It has to be acknowledged that an unjustified transfer of this kind distorts both the individual and society. Following this logic, he raises the important question of the responsibility of a scientist for his ideas towards society and towards every individual! Indeed, the author cannot accept the explanation of free thought as being an illusion, its place being supplanted by nature and nurture.

By his clear and convincing reasoning, the author of the article inclines the reader to support him. The reader feels cheered and becomes imbued with the lofty thinking of the author's idea. The wish involuntarily makes itself felt to become acquainted with the concepts of van Eyken not in fragmented form but fully, as expounded in his book.

V. G. Pushkin

388

Erratum

The publishers regret the following error. In the paper 'Science in the service of religion: the case of Islam' by D . A . King, Vol. 40, N o . 3 (1990 N o . 159) pp. 245-262, figure 8 was printed as the mirror image of its correct form. Figure 8 ought to have appeared as shown on the following replacement page.


D. A . King

Figure 8. A late scheme of sacred geography in which localities all over the Islamic world are arranged around the Kaaba. Their positions are derived by tradition not by calculation and in m a n y cases are not in accord with geographical reality. (Reproduced from M S Paris B.N.ar.2278 with kind permission of the Bibliothèque Nationale, Paris).

256

Looking ahead . . . The next issues of Impact of science on society will deal with:

No. 161 Prospects in contemporary biology Contributors include: François Gros (Paris) on the human genome and the responsibility of scientists; Giorgio Bernardi (Paris) on the role of the basic sciences in the H u m a n Genome Project; Kenichi Matsubara (Tokyo) and A . A . Bayev and A . D . Mirzabekov (Moscow) on the organization of the Project in Japan and the U S S R respectively; Santiago and James Grisolia (Valencia and San Diego) on the ethical, social and philosophical implications of the H u m a n Genome Project; Charles Pasternak (London) on the molecular biology of environmental stress: and Angelo Azzi and Daniel Boscoboinik (Berne) on the control of cell growth.

N o . 162

N o . 163

N o . 164

N o . 165

N o . 166

N o . 167

Science, technology and transport

Chernobyl: five years on

N e w trends in science education

Science and environmental choices

The image in science

Ergonomics

N o . 168 The meeting of worlds in science

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Annals of Science EDITOR G . L'E. Turner History of Science and Technology Group, Level 4, Sherfield Building, Imperial College, London S W 7 2 A Z , U K

SCOPE A N N A L S O F SCIENCE was launched in 1936 as an independent review dealing with the development of science since the Renaissance. N o w firmly established, its field of interest has widened to cover developments since the thirteenth century and to include articles in French and German. Contributions from Australia, Canada, China, France, Germany, Greece, Hungary, Italy, Japan, USA and USSR bear testimony to its international appeal. Each issue includes a comprehensive book reviews section and essay reviews on a group of books on a broader level. The editor is supported by an active international board. A cumulative index covering the period 1970-1986 was published recently.

RECENT CONTENTS The mercury clock of the Libros del Saber, A.A. Mills (UK) I Newton and Goethe on colour: physical and physiological considerations, M.J. Duck (UK) I Varignon ou la théorie du mouvement des projectiles 'comprise en une Proposition générale', M. Blay (France) I The introduction and development of continental drift theory and plate tectonics in China: a case study in the transference of scientific ideas from West to East, Yangjing Yi and D. Oldroyd (China and Australia) I Some aspects of Japanese science, 1868-1945, Eikob Shimao (Japan)/ Poincaré's role in the Crémieu-Pender controversy over electric convection, L. Indorato and G. Masotto (Italy) I Catholic astronomers and the Copernican system after the condemnation of Galileo, / I. Russel, SJ (UK) I Zu einigen Aspekten der Berufung von Mathematikem an die Technischen Hochschulen Deutschlands im letzen Drittel des 19. Jahrhunderts, S. Hensel (DDR) I Negotiating notation: chemical symbols and British Society, 1831-1835, T.L.Alborn (USA) I Benjamin Franklin and earthquakes, D.R.Dean (USA) I Huygen's designs for a simple microscope, M. Fournier (The Netherlands) IThe introduction of scientific rationality into India, SJ. Habib and D. Raina (India).

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Journal of the History of Education Society

History of Education EDITOR Roy Lowe Faculty of Education, University of Birmingham, PO Box 363, Birmingham B15 2TT, UK

SCOPE H I S T O R Y O F E D U C A T I O N has attracted considerable attention a m o n g social historians and others interested in the development of education in all parts of the world. The journal publishes original research, correspondence and major reviews of books on the history of education, whether in formal institutions or informal situations. Articles range from schooling at different periods and the teaching of specific subjects in schools, universities and colleges, to government policy, administration and philosophies of education. Special issues have focused on w o m e n and schooling, transatlantic influences on education, and the Second World War.

RECENT CONTENTS Thatcherism and English education: breaking the mould, or confirming the pattern? Richard Johnson (UK) I From Board to Ministry: the impact of the War on the education department, P. H. f, H. Gosden (UK) I What w o m e n learned from the Second World War, Penny Summerfield (UK) I The progressive educator and the Third World: a first look Hjohn Dewey, Ronald K, Goodenow (USA)/ Policy, politics and pragmatism: the State and the rural school in colonial N e w South Wales, NoelineJ. Kyle (Australia)/ Nationalists' demand for university education in Nigeria and Government's response, 1920 - 1948, S. S. Obidi, Nigeria I Conservative feminism and female education in the eighteenth century, JaneMcDermid(UK)/ Historiography of compulsory schooling: what is the problem? Pavla Miller (Australia) I Sex or class: the education of working class w o m e n , 1800 -1870 - 3 discussion papers, Keith Flett, June Purvis and Meg Gomersall (UK).

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