Science and Cultural Diversity

Filling a gap in the History of Science

Números anteriores de cuadernos Quipu Director de la colección: Juan José Saldaña 1. El perfil de la ciencia en América 2. Cross Cultural Diffusion of Science: Latin América 3. Descubrimientos del carbón mineral y petróleo en México 4. Los orígenes de la ciencia nacional

Science and Cultural Diversity

Filling a gap in the History

of Science

Juan José Saldaña Editor

Cuadernos de Quipu 5

México, 2001

DR © 2001, Sociedad Latinoamericana

de Historia de las Ciencias y la Tecnología Apartado postal 21-873, 04000 México, D.F., MÉXICO

Table of Contents Foreword 7

Part I. Articles Ethnomathematics as a new research field, illustrated by studies of

mathematical ideas in African history Paulus Gerdes 11

Ethnoscience and ethnomathematics: a historiographical proposal for

non-western science Ubiratan D'Ambrosio 37

Science at the edge of the Earth

Wesley M. Stevens 51 Intelligibilité et historicité (Science, ratíonalité, histoire)

Michel Paty 59 The savant's drama: two cultures and two shores

Antonio Lafuente and Tiago Saraiva 97 Western and non-western science: history and perspectives

Juan José Saldaña 123 Science and cultural diversity in a post-colonial context

S. lrfan Habib 145 Diversidad cultural en la memoria histórica y gráfica de México

Teresa Rojas Rabiela 151

Part II. Remarks to stimulate discussions on science and cultural diversity

A Letter from Madrid

A. Lafuente 163

A Letter from Australia R. MacLeod 167

A Letter from Paris

M. Paty 171 A Letter from Sweden

F. Flores 179

Part III. Statutes and By-Laws of the International Association for Science and Cultural Diversity

Statutes 185 By-Laws 189

Foreword On November 29th and 30th 2000, in the city of Pachuca (Mexico), the constitutive meeting of the International Association for Science and Cultural Diversity (IASCUD) as well as an international symposium on the theme of Science and Cultural Diversity took place. This was accomplished within the VII Mexican Congress of History of Science and Technology organized by the Mexican Society of History of Science and Technology (MSHST). Brought together by the MSHST to give birth to the IASCUD, historians of science assisted from Argentina, Canada, Colombia, France, India, Mexico and Mozambique, and several other colleagues from Australia, Brazil, South Korea, Spain and the US, that for private reasons could not be present, sent valuable contributions to the symposium. The initiative to convoke this meeting was intimately entailed to the decision of the organizers of the XXI International Congress of History of Science (Mexico City, 8-14 July 2001) to adopt "Science and Cultural Diversity" as the Congress theme, as well as to the general acceptance as a new investigation front that this proposal has received by the community of historians of science of the world. This is why our purposes are to firstly and fundamentally give guidance and continuity to this theme. To achieve this, IASCUD has converted itself into a permanent academic organization to be able to stimulate and coordinate international synergies. Our goal is the impulse of initiatives for the recovery of a true worldwide history of science, technology and medicine with social and cultural impacts in societies today. Secondly, IASCUD is expected to be a specialized organization of the International Union of History and Philosophy of Science/Division of History of Science for the improvement of its duties. Hence, the corresponding petition has been made and soon this international organization shall decided on this. Finally, during the Mexico Congress the IASCUD will organize a symposium that, benefiting from the contributions that the Congress will make to the development of the theme of science and cultural diversity, will be able to draw out some conclusions for the historiography of science as well as a work agenda. This book therefore constitutes a report of activities held until now by IASCUD-including its Statutes -, as well as a documentary testimony of the process of its integration. Indeed, as a way to give them ample distribution, several discussion documents are published which circulated by means of e-mail between the promoters of this initiative (with the obvious informality that this implies), and whose inclusion here should be considered as part of a live reflection on the theme that now occupies our attention. Of course, this reflection is not over, and this ¡s more that anything of an invitation to continue it. Likewise, included are various texts with the contributions made to the symposium of Pachuca, which I’m confident, are to stimulate discussions on the subjects

addressed as well as studies that allow us to advance in our comprehension of such a crucial theme for the understanding of what the history of science has been. Therefore, this is how we appear before the General Assembly of the IUHPS/DHS to obtain its approval as a new scientific section of the Union. But it is also in our interest to appear before the international community of historians of science, technology and medicine to invite them to incorporate themselves to this association and its duties. At the beginning of the XXI century, projects with participation of science and technology are being conceived. In these scenario buildings we intend to contribute with historical studies emphasazing the essential relationship between science and culture.

JUAN JOSÉ SALDAÑA Secretary Genera/ of the IASCUD

Part I Articles

Ethnomathematics as a new research field, illustrated by studies of

mathematical ideas in African history

PAULUS GERDES

Preliminary remarks The organisers of this conference on "New Trends in the History and Philosophy of Mathematics" asked me to "...view the history and philosophy of mathematics from the angle of studies in 'Ethnomathematics'", and "...hear about [my] methodological reflections, especially in case studies as examples, but not a review of general trends". As it is not easy to do justice to the proposed, partially opposite tasks, I should like to refer the reader, beforehand, to some of my earlier studies that review some general trends and/or present overviews. For a historical and philosophical reflection on the role of human, cultural activity ('Tätigkeit' in German) in the development of early geometrical thinking, I should like to refer to my study Zum erwachenden geometrischen Denken (1985), published in German under the title Ethnogeometrie (1990) with a preface by Peter Damerow. An English language version under the title Culture and the awakening of geometrical thinking with a preface by Dirk Struik is currently in press (Gerdes, 2000). For an introduction to mathematical ideas in the history of Africa south of the Sahara, see Claudia Zaslavsky's classical Africa Counts (1973), and for an update and literature overview see my paper in Historia Mathematica (Gerdes. 1994). For an overview of the development of ethnomathematics in relationship to concerns in mathematics education, see my paper in the International Handbook of Mathematics Education (Gerdes, 1996). For a reflection on ethnomathematics and mathematics teacher education, see my paper in the international journal of Mathematics Teacher Education (Gerdes, 1998). The organisers suggested as title for my talk "Ethnomathematics as a new research field illustrated by new discoveries in 'African Mathematics'". As can be seen, I changed the second part of the title a little bit "...illustrated by studies of mathematical ideas in African history". There are several complementary reasons to avoid in a meeting of historians and philosophers of mathematics the expression 'African Mathematics'. One reason is to avoid any connotation with expressions as 'German Mathematics', 'One reason is to avoid any connotation with expressions as 'German Mathematics', 'French Mathematics', ...and the political-ideological environment of nazism in which they were developed (cf. the contribution to this volume by Herbert Mehrtens). An other reason is not to be dragged into a debate like the one on African Philosophy (and ethnophilosophy) (cf. Houtondji, 1976,1997; Houtondji & Wiredu, 1984): What is philosophy?, Where ends wisdom

and starts philosophy?,... I prefer to speak about mathematical activities and ideas, about mathematical aspects of cultural phenomena, about mathematical elements in cultural contexts (cf. Gerdes, 1997a: 402). With this remark, we have already arrived at the notion of ethnomathematics. In this paper I will discuss ethnomathematics and related concepts, present two examples of studies of mathematical ideas in African history, and conclude with a reflection about ethnomathematics and mathematical thinking. Ethnomathematics / ethnomathematicology Ethnomathematics (or ethnomathematicology) is relatively new as a field of research. It may be described as the study of mathematical ideas and activities as embedded in their cultural context. As views of mathematics as "culture-free" and "universal" have been rather dominant in the academia, ethnomathematics emerged relatively late. Otto Raum with his Arithmetic in Africa (1938), Dirk Struik with his On the sociology o f mathematics (1942), Leslie White with his The locus of mathematical reality: an anthropological footnote (1947), and Raymond Wilder with his The cultural basis o f mathematics (1950) may be counted among the (relatively) isolated forerunners of ethnomathematicology. The Brazilian Ubiratan D'Ambrosio launched in the 1970's his ethnomathematical program (cf. D'Ambrosio, 1985, 1997), as a methodology to track and analyse the processes of generation, transmission, diffusion and institutionalisation of mathematical knowledge in diverse cultural systems (D'Ambrosio, 1990: 78). He developed his ideas inspired by a reflection about major problems of mathematics education in the 'Third World'. In contrast to "academic mathematics", i.e. the mathematics which is taught and learned in schools and universities, D'Ambrosio called ethnomathematics "the mathematics which is practiced among identifiable cultural groups, such as national-tribal societies, labor groups, children of a certain age bracket, professional classes, and so on" (D'Ambrosio, 1985a: 45). That so many children fail in mathematics is due to "the mechanism of schooling [that] replaces these practices by other equivalent practices which have acquired the status of mathematics, which have been expropriated in their original forms and returned in a codified version" (D'Ambrosio, 1985a: 47). Emergence of several concepts D'Abrosio's ethnomathematics was not the only concept that emerged in the context of reflections on mathematics education in the 'Trird World' and later found an echo in other parts of the globe. Colonial education had presented mathematics generally as something rather 'western', 'European', as an exclusive creation of 'white men'. The hasty curriculum transplantation —during the 1960's— from the highly industrialised nations to 'Third World' countries did not change fundamentally this image.

During the 1970's and 1980's, there emerged among teachers and mathematics educators in developing countries and later also in other countries a growing resistance to this presentation (cf. e.g. Njock, 1985; PoweII & Frankenstein, 1997), against the racist and (neo) colonial prejudices, against the eurocentrism, that it reflects. It was stressed that beyond the 'imported school mathematics' there have existed also other forms of mathematics. In this context, various concepts have been proposed to contrast with the 'academic mathematics' / 'school mathematics' (i.e., the school mathematics of the transplanted, imported curriculum):

• 'Indigenous mathematics' (cf. e.g. Gay & Cole, 1967; Lancy, 1978). Criticizing education of Kpelle children (Liberia) in 'western-oriented' schools —they "are taught things that have no point or meaning within their culture" (1967: 7) -Gay and Cole propose a creative mathematical education that uses the indigenous mathematics as starting point;

• Sociomathematics of Africa (Zaslavsky, 1973: 7): "the applications of mathematics in the lives of African people, and, conversely, the influence that African institutions had upon the evolution of their mathematics";1

• Informal mathematics (Posner, 1978, 1982; Ascher & Ascher, 1981): mathematics that is transmitted and that one learns out-side the formal system of education;

• Mathematics in the (African) socio-cultural environment (S. Doumbia, S. Touré (Côte d'lvoire), 1984): the mathematics of African games and craft work that belongs to the socio-cultural environment of the child should be integrated in the mathematics curriculum;

• Spontaneous mathematics (D'Ambrosio, 1982): each human being and each cultural group develops spontaneously certain mathematical methods;

• Oral mathematics (Carraher et al., 1982, 1987; Kane, 1987): in all human societies there exists mathematical knowledge that is transmitted orally from one generation to the next;

• Oppressed mathematics (Gerdes, 1982,1985a): in class societies (e.g., in the countries of the Trird World' during the colonial occupation) there exist mathematical elements in the daily life of the populations, that are not recognized as mathematics by the dominant ideology;

• Non-standard mathematics (Carraher et al., 1982; Gerdes, 1982, 1985á; Harris, 1987,1997): beyond the dominant standard forms of ‘academic' and 'school' mathematics, other mathematical forms have developed in the whole world and in each culture. Carraher (= Nunes) also uses the expression street mathematics for mathematical ideas developed in the 'streets', outside the school context (cf. Carraher, 1988);

• Hidden or frozen mathematics (Gerdes, 1982, 1985, 1986,1990, 2000): although, probably, the majority of mathematical knowledge of the formerly colonized peoples has been lost, one may try to reconstruct or 'unfreeze"

1 D'Ambrosio used in 1976 the same term in the context of Brazil. See U. D'Ambrosio (1976).

the mathematical thinking, that is 'hidden' or 'frozen' in old techniques, like, e.g., that of basket making

• Folk mathematics (Mellin-Olsen, 1986): the mathematics (although often not recognized as such) that develops in the working activity of each of the peoples may serve as a starting point in the teaching of mathematics;

• People's mathematics as a component of people's education in the context of the struggle against apartheid in South Africa (Julie, 1989);

• Mathematics codified in know-how (Ferreira, 1991); • Implicit and non-professional mathematics (Ascher & Ascher, 1981;

Zaslavsky, 1994).2 Various aspects illuminated by the aforementioned concepts have been gradually incorporated under the more general denominator of ethnomathematics. This process has been accelerated by the creation of the International Study Croup on Ethnomathematics [ISGEm] in 1985. First level of definition On the one hand, if ethnomathematics is considered as the mathematics of a certain (sub)culture, then 'academic mathematics' is also a concrete example of ethnomathematics. On the other hand, when all ethnomathematics is mathematics, why call it ethnomathematics? And not simply the mathematics of this and that (sub)culture? Doing so, ISGEm defines ethnomathematics also at another level, as a research field, that reflects the consciousness of the existence of many mathematics, particular in a way to certain (sub)cultures. Second level of definition As a research field, ethnomathematics (or ethnomathematicology like ethnomusicology) may be defined as the cultural anthropology of mathematics and mathematical education, or in the formulation of D'Ambrosio in 1977: "Ethnoscience as the study of scientific and, by extension, technological phenomena in direct relation to their social, economic and cultural background" 2 At the end of their book Code of the Quipu. Ascher & Ascher present the following interesting comments on the development of mathematics and of mathematical activities: "Mathematics arises out of, and is directly concerned with, the domain of thought involving the concepts of number, spatial configuration, and logic. In Western culture a professional class, called mathematicians,..., deals solely and exclusively with these concepts. Examples of other groups involved in mathematical endeavors are accountants, architects, bookies, construction engineers, landscape designers, navigators, and system analysts. Non-professional mathematics, as practiced by these groups... may often be implicit rather than explicit. When these mathematical endeavors are implicit, they are none the less, mathematics. Because of the provincial view of the professional mathematicians, most definitions of mathematics exclude or minimize the implicit and informal. It is, however, in the nature of any professional class to seek to maintain its exclusivity and to do this, in part, by recreating the past in terms of unilinear progress towards its own present" (Ascher & Ascher, 1981: 158-159).

(D'Ambrosio, 1987: 74). In this sense it includes "the study of mathematical ideas of non literate peoples", which was the Ascher's definition of ethnomathematics in 1986. Contrast with ‘ethnographers’ conceptualisations of ethnoscience Among ethnographers and anthropologists the concept of 'ethnoscience' is used sience the end of the 19th century. Their use of the concept seems to be either more restricted or differently ideologically loaded than the concept as it is used nowadays by mathematicians and mathematics educators. In the ethnological dictionary of Panoff and Perrin (1973) two definitions of the concept of ethnoscience are presented. In the first case, it is a "branch of ethnology that dedicates itself to the comparison between the positive knowledge of exotic societies and the knowledge that has been formalized in the established disciplines of western science" (Panoff & Perrin, 1973: 68). This definition raises immediately some questions, like: "What is positive Knowledge?"; "In what sense exotic?" and "Does there exist a western science?" In the second case, "each application of one of western scientific disciplines to natural phenomena which are understood in a different way by indigenous thinking" is called ethnoscience (Panoff & Perrin, 1973: 68). Both definitions belong to a tradition that traces back to the colonial time, when ethnography was born in the most 'developed' contries as a 'colonial science', that studied almost exclusively the cultures of subjected peoples, also as a 'science' than opposed the so-called 'primitive' thinking to the 'western' thinking as somehow absolutely different. Among ethnographers there exists also another current, that considers the prefix 'ethno' in a very different way. E.g., Favrod characterises ethnolinguistics in his Introduction to social and cultural anthropology as follows: "Ethnolinguistics tries to study language in its relationship to the whole of cultural and social life" (Favrod, 1977: 90). When we transfer this characterisation of ethnolinguistics to ethnomathematics, we obtain by analogy: "Ethnomathematics tries to study mathematics (or mathematical ideas) in its (their) relationship to the whole of cultural and social life". According to Crump the term ethnoscience became popular among ethnographers in the 1960's: "it may be taken to refer to the 'system of knowledge and cognition typical of a given culture'" (Crump, 1990: 160). In Crump's The anthropology of number (1990) there are only a few references to the work of 'ethnomathematicians'.3 Still in the 1990's anthropologists, historians of science and mathematicians have to find each other to develop together ethnomathematics as an anthropology of mathematics and mathematics education.4 3 He points out that "first, few professional mathematicians have any interest in the cognitive assumptions in their work; second, few anthropologists are numerate in the sense of being able to realize how significant the numbers that occur in the course of their field work might be in the local culture" (Crump, 1990: viii). 4 D'Ambrosio uses sometimes the expression "anthropological mathematics". See e.g. D'Ambrosio (1985a), cf. Gerdes (1 985b).

Broad concept The emergence of ethnomathematics (or ethnomathematicology) as a research field reflects the growing consciousness of the existence of many mathematics, particular in a certain way to (sub)cultures. In this sense, the following characteristics make part of the paradigm of ethnomathematics:

• Use of a broad concept of mathematics, including, in particular, counting, locating, measuring, designing, playing, explaining (cf. e.g Bishop, 1988);

• Emphasis and analysis of the influences of socio-cultural factors on the teaching, learning and development of mathematics;

• Mathematics (its techniques and truths) is considered a cultural product. Every people —every culture and every subculture— develops its own particular mathematics. Mathematics is considered to be a universal, pan-human activity. As a cultural product mathematics has a history. Under certain economic, social and cultural conditions, it emerged and developed in certain directions; under other conditions, it emerged and developed in other directions. In other words, the development of mathematics is not unilinear.

Implications for the historiography and philosopby o f mathematics The emergence of ethnomathematics as a research field has implications for the historiography and philosophy of mathematics. Historians and philosophers cannot anymore restrict themselves to a mere reflection on the history of philosophical problems arising from 'academic' mathematics. It seems necessary to reflect about other forms of mathematical production and activity in order to understand better the relationships between nature, culture and the development of mathematical thinking. Let me present two examples of ethnomathematical / historical studies of mathematical ideas in southern Africa. First example: Sona geometry (cf. Gerdes, 1988, 1991, 1991a, 1991b,1993/4, 1998a, 1995, 1997, 1997a, 1999; Ascher, 1988a) An example of a historical- ethnomathematical study is my tentative to analyse and reconstruct the sona tradition. This tradition was developed among the Chokwe of Northeastern Angola and related peoples. The Chokwe culture is well known for its decorative art that ranges from ornamentation on woven mats and baskets, iron works, ceramics, sculpture and engravings on calabash to tattooing, paintings on the walls of houses, and drawings in the sand called "sona" (singular: "lusona"). Each boy learnt the meaning and execution of the easier sona during the initiation rites. Drawing experts (akwa kuta sona) transmitted the more complicated sona to

their male descendants. These drawing experts were at the same time the storytellers who used the sona as illustrations, referring to proverbs, fables, games, riddles, animals. The drawings were executed in the following way: After cleaning and smoothing the ground, the drawing experts first set out with their fingertips a net of equidistant points and then they draw a line figure that embraces the points of the network. The experts execute the drawings swiftly. Once drawn, the designs are generally immediately wiped out. Figure 1 presents some examples of sona. Slave trade, colonial penetration and occupation provoked a cultural decline and the loss of a great deal of knowledge about sona. On the basis of an analysis of sona reported by missionaries, colonial administrators and ethnographers,5 I tried to contribute to the reconstruction of mathematical elements in the sona tradition. As the examples in figure 1 suggest, symmetry and monolinearity played an important role as cultural values: most Chokwe sona are sym-metrical and/or monolinear. Monolinear means composed of only one (smooth) line; a part of the line may cross another part of the line, but never a part of the line may touch another part.

FIGURE 1 Examples of symmetrical, monolinear sona

The drawing experts developed a whole series of geometric algorithms for the construction of monolinear, symmetrical designs. Figure 2 displays two monolinear sona belonging to the same class in the sense that, although the dimensions of the underlying grids are different, both sona are drawn applying the same geometric algorithm.

5 The most important collections of sona were published by: Hamelberger, 1952; Santos, 1961; Pearson, 1977; Fontinha, 1983, Kubik, 1988.

FIGURE 2 Two sona drawn with the same geometric algorithm

The drawing experts also invented various rules for building up monolinear sona. The following presents a first example. Figure 3 shows three, monolinear sona. They are similar to each other: each presents a basic design of triangular form. I suppose that the drawing experts who invented these sona probably began with triangular patterns and transformed them into monolinear patterns with the help of one or more loops (see the example in figure 4). The monolinear patterns so obtained were adapted (maybe later by others) topologically so that they could express the ideas the drawers wanted o transmit through them.

FIGURE 3

An eagle carrying a chicken A person dead to fatigue A thimunga bird in flight a b c

FIGURE 4 Transformation of triangular design into a monolinear design

Sona experts also discovered various rules for chaining monolinear sona to form bigger monolinear sona. Figure 5 displays an example of the use of a chain rule: it indicates how the appearance of the monolinear drawing in figure 5c may be explained on the basis of the monolinearity of the two patterns in figure 5a and the way they have been chained together (see Figure 5b).

FIGURE 5 Examples of the application of a chain rule

The monolinearity of the lusona in figure 6a may be explained on the basis of another chain rule: If one joins square grids (in the example: two grids of dimensions 2 x 2) to a rectangle with dimensions which are relative prime (in the example: 3 x 5), then the resulting grid leads to a monolinear drawing if one applies the same geometric algorithm as used in figure 6c with the rectangular grid of dimensions 3x5 ('diagonally plaited mat' algorithm).

FIGURE 6

When analysing and reconstructing elements of the sona tradition, I found that there are several reported sona, which clearly do not conform to the cultural values of symmetry and monolinearity. Sometimes the symmetry or monolinearity was broken in order to give the drawing a specific meaning (Figure 7 gives an example).

FIGURE 7

Lusona representing ‘kilu' or 'kalamba', the thinker (monolinear, but not symmetrical)

More often we seem to be dealing with mistakes or errors. Figure 8a gives an example of a reported lusona with mistakes and figure 8b the reconstructed drawing without mistakes. The drawing experts may have committed some of these mistakes, because they were contacted when they were already old men. They were saying that as young men they had been much better 'akwa kuta sona'. We may be dealing with errors in the transmission of the sona knowledge from one generation to the next, or with mistakes on the part of the reporter, who had little

time to make his copies, as traditionally the drawing experts wipe their drawings out immediately after concluding their story. The wiping out was one way to protect their knowledge, to maintain their monopoly of sona knowledge. Here we have another probable reason for mistakes in the reporting of sona: a form of cultural resistance; the experts made consciously mistakes to deceive the reporter —the white man, associated with slave trade, colonial administration and Christianity—, and so to protect their secret knowledge. In the secret and monopoly character of the sona tradition lies also a reason for its gradual extinction: as soon as a drawing expert is taken slave, the knowledge disappears from his community; some of the knowledge may have survived in one way or another in the 'New World'.6 In 1997, the author had the opportunity to learn about the survival of a sona type drawing in the United States of America. Figure 9 presents a sand drawing I received from a woman who grew up in Greenwood, Mississippi which is in the Delta near Greenville. She had learned this and other sona from Mary Reaves —of African descendance, born almost a hundred ago— who was her nurse (Susan Enger, personal communication, 1997).

FIGURE 8

6 Cf. the exceptional arithmetical knowledge of Thomas Fuller, who was brought in 1 724 as a slave from África to North America. See Fauvel & Gerdes (1990).

FIGURE 9 A lusona type drawing —that survived the slave trade— in the USA

The same line drawing also appears among the Tamil threshold designs in India and on decorated cloths from Sierra Leone and Ethiopia. Cf. P. Gerdes, "Ethnomathematik dargestellt...", o.c., pp. 374, 396, 397. The historical reconstruction of mathematical ideas incorporated in the sona tradition led me not only to mathematical and didactic re-search, but also to the study of traditions that from a mathematical-technical point of view display similarities with the sona tradition. So far I analysed some geometrical algorithms in Ancient Egypt (used for the decoration of scarabs, vases and walls), monolinear designs from Ancient Mesopotamia, threshold designs drawn by Tamil women in India (cf. Gerdes, 1989, 1995a), Celtic knot designs (cf. Cromwell, 1993; Gerdes, 1999b), sand drawings from the Vanuatu islands (Oceania) (cf. Ascher, 1988), and some designs motifs from other parts of Africa. I suppose that the methodology used in the reconstruction of the sona tradition may be further developed in the study of these other traditions that bear certain similarities with the sona tradition. Figure 10 presents examples of symmetrical, monolinear designs belonging to these traditions. Concerning the historiography of mathematics, the example of the sona raises the question of what type of sources and argumentation can be used. Also it shows —in the case of Ancient Egypt— that various traditions with mathematical 'ingredients' may co-exist in the same society, interrelated with each other or not. In that sense, it becomes difficult, if not impossible, to speak of the mathematics of Ancient Egypt, the mathematics of Greece, etc.

FIGURE 10 Examples of symmetrical and monolinear designs

Second example: Litema geometry (cf. Gerdes, 1995b, 1996a, 1998b: ch. 9) In Lesotho and neighbouring zones of South Africa, Sotho women developed a tradition of decorating the walls of their houses with designs. The walls are first neatly plastered with a mixture of mud and dung, and often colored with natural

dyes. While the last coat of mud is still wet, the women engrave the walls, using their forefinger. Their art is seasonal: The sun dries it and cracks it, and the rains wash it away. An entire village is redecorated before special occasions such as engagement parties, weddings, and important religious celebrations. The Sotho women call their geometric patterns, litema (singular: tema). The books The African Mural (Changuion et al., 1989) and African Painted Houses: Basotho Dwellings of Southern Africa (Wyk, 1998) contain beautiful collections of photographs of litema. The National Teacher Training College of Lesotho published a colection litema patterns, collected by its mathematics students (Mothibe, 1976). In his presentation, the coordinator underlines that "like other national traditions this one is in danger of dying out as more and more houses are built of concrete walls which are usually painted or white-washed. Also a growing number of women no longer like or know the art anymore" (Mothibe, 1976:2). Symmetry is a basic feature of the litema patterns. Figure 11 presents part of a tema pattern. As ¡s often the case, this tema pattern is built up from a basic square that constitutes the (unit) cell of the pattern. Figure 12 displays the cell for the tema in figure 11.

FIGURE 11

FIGURE 12

The Sotho women lay out a network of squares and then they reproduce the basic design in each square. The number of reproductions or repetitions of the unit cells depends, in practice, on the available space on the wall to be decorated. As in figure 11, a whole pattern is built up out of repetitions of a 2 x 2 square, in which the unit cell appears ¡n four positions, obtained by horizontal and vertical reflection about the axes of the 2 x 2 square. The symmetries of a whole pattern depend on the symmetries of the unit cell. The unit cell in figure 12 has two diagonal axes of symmetry. The unit cell of the litema pattern in figure 13 has no axial symmetry however is invariant under a half turn. The unit cell of the litema pattern in figure 14 has one axis of symmetry.

FIGURE 13

FIGURE 14

Several painted litema, and others whereby changes in the relief of the dung surface of the plater suggest two distint colors, may be represented on paper as black-and-white patterns. Some, as the one in the figure 15, are built up in the same way as the earlier patterns considered.

FIGURE 15

Others are two-color patterns, whereby in each horizontal or vertical reflection of the unit cell the colors are reversed. The image of a unit cell is the negative (in photographic terms) of the reflected cell (see the example in figure 16, leading to the tema pattern in figure 17). Figure 18 present further examples.

FIGURE 16

FIGURE 17

FIGURE 18

A different, and colorful style of geometric wall decoration has been developed by Ndebele women in south Africa (cf. Courtney-Clarke, 1986; PoweII & Lewis, 1995; Gerdes, 1995b, 1996a, 1998b, ch. 10). Suggestions for further research of female cultural activities in Southern Africa in which mathematical considerations are embedded, are presented in Women, Art and Geometry in Southern Africa (Gerdes, 1995b, 1996a, 1998b; cf. Gerdes & Bulafo, 1994). One question for the historiography of mathematics, raised by this example of ethnomathematical research, is the underrepresentation of women in the history of mathematics. Does this underrepresentation correspond to reality, or does it reflect certain views about mathematics? Does it reflect a view of mathematics as 'something' that can be 'easily' dissected from other cultural elements? Ethnomathematical research sems to show that mathematical ideas and activities are often 'interwoven' with other cultural ideas and activities. Underrepresentation of any cultural group in the history of mathematics, may tell us more about the historiography of mathematics than about the underrepresented cultural groups. Here lies also a challenge for the philosophy of mathematics: whose mathematics is the object of philosophical analysis?

Mathematical thinking and Ethnomathematics Conflicting views The question may be raised if the examples given are an expression of mathematical thinking? If one reads the ethnographer Santos on the mathematical knowledge of the Chokwe, his answer would be no: The Chokwe know some arithmetic, some time reckoning and some geo-metrical vocabulary (line, curve, point,...), but they do not know mathematics (Santos, 1960). The same author published, however, an interesting study on the sona (Santos, 1961), but he did not see any relationship with mathematics. His 'no' answer reflects the horizon of his ethnographic training and his school mathematics education in the colonial metropole. But does this school mathematics education give a real picture of what mathematics is all about? Are the concepts, are the construction and chaining rules, ...developed and invented by the 'akwa kuta sona' mathematical? Ever since my first personal contact with the sona, I 'felt' —trained in Europe as a research mathematician— that I was dealing with mathematical ideas, and speaking at professional gatherings of mathematicians I saw that the mathematical aspects and potential of the sona was quinckly absorbed by the mathematical community. This example may serve to raise the important question of who defines some activity, some idea, or some theory as mathematical. Who defines "What is m mathematical thinking?" What can be said about his/her socio-cultural background? Is it possible to discuss philosophical questions related to mathematics platonically outside the con-text of culture?

Intercultural intelligibility o f mathematical thinking As ethnomathematics (or ethnomathematicology) is the field of inquiry that studies mathematical ideas in their historical-cultural contexts, an ethnomathematician may be, for instance, interested in understanding the role and embodiment of mathematical thinking both in the invention and (re)production of decorative patterns. If no direct dialogue, physically or historically, with the inventors and/or (re)producers is possible, the researcher may try to reconstruct elements of mathematical thrinking probably involved in the invention and reproduction processes. These reconstructed elements may be called 'frozen' or 'hidden' math-ematics (cf. Gerdes, 1990, 2000). The reconstruction is not completely impossible as the researcher may have developed some feeling for mathematical ideas. Just like any musician (or even any human being) may develop a certain understanding of and feeling for musical expressions, and any linguist (or even any human being) may develop a certain understanding and recognition of language phenomena. In this sense, mathematical thrinking is as pan-human as using a language or involvement in music (playing, listening,...). This 'feeling for' is the result of an enculturation process (cf. Bishop, 1988). From an ethnomathematical perspective, mathematics becomes the product of all cultures, being the school mathematics experience of a researcher only one form of mathematical experience. Mathematics is not the product of a particular culture sphere, 'western', but a common human experience. In the process of studying mathematical ideas in diverse cultural contexts, the understanding of what mathematics is, or better of what constitutes mathematical activity, may be deepened. Mathematical thinking is only interculturally intelligible. And there lies a challenge for philosophy in general and for the philosophy of mathematics in particular: to contribute to the development of the means for intercultural intelligibility. Responsibility and urgency In other words, ethnomathematical studies may broaden the (intercultural) understanding of what are mathematics, of what are mathematical ideas and activities. There cannot be a sole, unified view of mathematics. For a monolinthic and dominant view there is no basis. At the same time, for the other extreme, a cultural relativism concerning mathematics, there is also no ground: intercultural intelligibility seems possible. Ethnomathematicians, historians and phylosophers of mathematics may arrive at these opinions, but, in this phase of 'globalisation' monolithic views seem still to be dominant among educators, professional mathematicians and administrators. This raises the question of the responsibility of ethnomathematicians, historians and philosophers of mathematics. Relative to research, it is my opinion that among the most urgent tasks is the study of mathematical elements in cultural spheres that are under siege, in particular of cultures in the "Third World", in the South. Humanity will loose an enormous source of knowledge, an enormous potential for

broadening the reflection on mathematical thinking if these elements are not studied today and in the near future.

Acknowledgments I thank the Danish Network on History and Philosophy of Mathematics for inviting me to take part in the conference, the Danish Natural Science Research Council for financing my travel and stay. I thank the Research Department (SAREC) of the Swedish International Development Agency for sup-porting financially the Mozambican Ethnomathematics Research Project.

References Ascher, Marcia, "Graphs in culture: a study in ethnomathematics". Historia

Mathematica 15:201-227, 1988. Ascher, Marcia, "Graphs in cultures (II): a study in ethnomathematics". Archive for

History of Exact Sdences 39(1), 75-95, 1988a. Ascher, Marcia. Ethnomathematics, a multicultural view of mathematical ideas.

Pacific Grove: Brooks & Colé, 1991. Ascher, Marcia and Robert Ascher, Code of the Quipu: a study in media,

mathematics and culture. Ann Arbor: The University of Michigan Press, 1981.

Ascher, Marcia and Robert, Ascher. "Ethnomathematics". History of Science 24: 125-144,1986.

Bishop, Alan, Mathematical enculturation, a cultural perspective on mathematics education. Dordrecht: Kluwer, 1988.

Carraher, Terezinha, "Street mathematics and school mathematics". Proceedings of the 12th International Conference on Psychology of Mathematics Education. Veszprem, 1-23, 1988.

Carraher, Terezinha; David Carraher and Analúcia Schliemann, "Na vida, dez; na escola, zero: os contextos culturais da aprendizagem de matemática". Cadernos de Pesquisa 42: 79-86, 1982.

Carraher, Terezinha; David Carraher and Analúcia Schliemann, "Written and oral mathematics". Journal of Research in Mathematics Education 8: 83-97, 1987.

Changuion, Paúl, T. Matthews, and A. Changuion, The African Mural. Cape Town: Struik, 1989.

Courtney-Clarke, Margaret, Ndebele: The Art of an African Tribe. New York: Rizzoli, 1986. Cromwell, Peter, "Celtic knotwork: Mathematical Art". The Mathematical Intelligencer 15(1): 36-47, 1993.

D'Ambrosio, Ubiratan, "Matemática e sociedade". Ciência e Cultura 28: 1418-1422, 1976. D'Ambrosio, Ubiratan, Mathematics for rich and for poor countries, Paramaribo: CARIMATH, 1982 (mimeo.).

D'Ambrosio, Ubiratan, Socio-cultural bases for mathematics education. Campiñas: UNICAMP, 1985.

D'Ambrosio, Ubiratan, "Ethnomathematics and its place in the history and pedagogy of mathematics". For the Learning of Mathematics 5(1): 44-48, 1985a.

D'Ambrosio, Ubiratan, Etnomatemática: arte ou técnica de explicar e conhecer. São Paulo: Editora Ática, 1990.

D'Ambrosio, Ubiratan. Ethnomathematics. Albuquerque: International Studygroup on Ethnomathematics, 1997.

Fauvel, john and Paulus Gerdes, "African Slave and Calculating Prodigy: Bicentenary of the Death ofThomas Fuller". Historia Mathematica 17(2): 141-151, 1990.

Favrod, C. A., Antropología. Lisbon: Pblicações Dom Quixote, 1977. Ferreira, Eduardo, "Por urna teoria da etnomatemática". BOLEMA 7: 30-35, 1991. Fontinha, Mario, Desenhos na areia dos Quiocos do Nordeste de Angola. Lisbon:

Instituto de Investigação Científica Tropipal, 1983. Gay, J. and M. Colé, The new mathematics and an old culture, a study of learning

among the Kpelle of Liberia. New York: Holt, Rinehart & Winston, 1967. Gerdes, Paulus, Mathematics for the benefit of the people, Paramaribo:

CARIMATH,1982 (mimeo). Gerdes, Paulus, Zum erwachenden geometrischen Denken. Maputo: Eduardo

Mondiane University, 1985 (mimeo). Gerdes, Paulus, "Conditions and strategies for emancipatory mathematics

education in underdeveloped countries". For the Learning of Mathematics 5(3): 15-20, 1985a.

Gerdes, Paulus, How to recognize hidden geometrical thinking? A contribution to the development of anthropological mathematics". For the Learning of Mathematics 6(2): 10-12, 17, 1986.

Gerdes, Paulus, "On possible uses of traditional Angolan sand drawings in the mathematics classroom". Educational Studies in Mathematics 19: 3-22, 1988.

Gerdes, Paulus, "Reconstruction and extensión of lost symmetries: examples from the Tamil of South India". Computers and Mathematics with Applications 17(4-6): 791- 813,1989.

Gerdes, Paulus, Ethnogeometrie. Kulturanthropologische Beiträge zur Cénese und Didaktik der Ceometrie, Bad Salzdetfurth: Verlag Franzbecker, 1990.

Gerdes, Paulus, Lusona: Geométrical Recreations of África /Recréations Géométriques d'Afrique. Maputo: Ethnomathematics Research Project, 1991.

Gerdes, Paulus, "On mathematical elements in the Tchokwe drawing tradition". Discovery and Innovation, lournal of the African Academy of Sciences 3(1): 29-36, 1991a.

Gerdes, Paulus, "On Mathematical Elements in the Tchokwe 'Sona tradition". Afrika Mathematika, lournal of the African Mathematical Unión, Series 2, 3:119-130,199 Ib.

Gerdes, Paulus, Geometría 5ona: Reflexões sobre a tradição de desenhos na areia en África ao sul do Equador. Maputo: Ethnomathematics Research Project, 1993/4 (3 volumes).

Gerdes, Paulus, "On Mathematics in the History of Sub-Saharan África". Historia Mathematica 21: 345-376, 1994.

Gerdes, Paulus, Sona Ceometry; Reflections on the tradition of sand drawings in África south of the Equator. Maputo: Ethnomathematics Research Project, Vol. 1, 1994a.

Explorations in Ethnomathematics and Ethnoscience in Mozambique. Gerdes, Paulus (ed.), Maputo: Ethnomathematics Research Project, 1994b.

Gerdes, Paulus, Une tradition géométrique en Afrique -Les dessins sur le sable. París: L'Harmattan, 1995, (3 volumes).

Gerdes, Paulus, "Extension(s) of a reconstructed Tamil ring-pattern." In The Pattern Book: Fractals, Art, and Nature, C. Pickover, ed. World Scientific, Singapore, 1995a.

Gerdes, Paulus, Women and geometry in Southern África: Suggestions for further research. Maputo: Ethnomathematics Research Project, 1995b.

Gerdes, Paulus, "Ethnomathematics and mathematics education: an overview". In International Handbook of Mathematics Education. A. Bishop, ed., Dordrecht: Kluwer, 909-944, 1 996.

Gerdes, Paulus, Femmes et Géométrie en Afrique Australe. París: L'Harmattan, 1996a.

Gerdes, Paulus, Ethnomathematik dargestellt am Beispiel der Sona Geometrie. Berlin, Heidelberg, Oxford: Spektrum Verlag, 1997.

Gerdes, Paulus, Recréations Géométriques d'Afrique -Lusona- Geométrical Recreations of África. París: L'Harmattan, Paris, 1997a.

Gerdes- Paulus, Women, art, and geometry in Southern África. Lawrenceville, NJ: África World Press, 1998b.

Gerdes, Paulus, "Culture and mathematics teacher education". Journal of Mathematics Teacher Education 1(1): 33-53, 1998c.

Gerdes, Paulus, Geometry from África. Mathematical and educational explorations, Washington DC: Mathematical Association of América, 1999a [Preface by Arthur B. PoweII].

Gerdes, Paulus, "On the geometry of Celtic knots and their Lunda-designs". Mathematics in School, 1999b, May 1999, 29-33.

Gerdes, Paulus, Culture and the awakening of geometrical trinking. Anthoropoligical, histórical, and philosophical considerations. An ethnomathematical study, Minneapolis: MEP Press, 2000 [Preface by Dirk Struik] (in press).

Gerdes, Paulus, Le cercle et le carré. crétivité géométrique, artistique et symbolique de vanniéres et vanniers d'Afrique, d'Amérique, d'Amérique, d'Asie et d'0céanie, París: L'Harmattan, 2000a [Preface by Maurice Bazin].

Gerdes, Paulus and Gildo Bulafo, Sipatsi: Technology, Art and Geometry in Inhambane. Maputo: Ethnomathematics Research Project, 1994.

Hamelberger, E., "A escrita na areia". Portugal em África 53: 323-330. 1952.

Harris, Mary, "An example of traditional women's work as a mathematics resource". For the Learning of Mathematics 7(3) 26-28, 1987.

Harris, Mary, Common Threads: Women, Mathematics and Work. Staffordshire: Trentham Books, 1997.

Houtondji, Paulin, African Philosophy: Myth & Reality. Bloomington: Indiana University Press, [1976] 1996.

Houtondji, Paulin, Combats pour le sens: un itineraire africain. Cotonou: Les Éditions du Flamboyant, 1997.

Teaching and research In philosophy: África. Houtondji, P. and K. Wiredu (eds.), París: UNESCO, 1984.

Kane, Abdoulaye, Les systémes de numération parlée des groupes ouest-atlantiques et Mande. Contribution á la recherche sur les fondaments et l'histoire de la pensée logique et mathématique en Afrique de l'Quest. (PhD thesis) Lille, 1987.

Kubik, Gerhard, Tusona-Luchazi ideographs, a graphic tradition as practiced by a people of West-Central África. Fohrenau: Verlag Stigimayr, 1988.

"The Indigenous Mathematics Project". Lancy, D. (ed.), Papua New Guinea Journal of Education 14: 1-217, 1978.

Mellin-Olsen, Stieg, "Culture as a key theme for mathematics education. Postseminar reflections". In Mathematics and Culture, a seminar report. Radal: Caspar Forlag, 99-121, 1986.

Litema, Designs collected by students of the National Teacher Training College of Lesotho. Mothibe, B. (ed.), Maseru: NTTC, 1976.

Njock, Georges, "Mathématiques et environnement socio-culturel en Afrique Noire". Presence Africaine 135(3): 3-21, 1985.

Panoff, M., and M. Perrin, Diccionario de Etnología. Sao Paulo: Lexis, 1973. Pearson, E., People of the Aurora. San Diego: Beta Books, 1977. Posner, J., "The development of mathematical knowledge in two west African

societies", Child Development 53: 200-208, 1982 [based on her Ph. D. thesis, 1978].

Ethnomathematics: Challenging Eurocentrism in Mathematics Education. PoweII, Arthur B. and Marilyn Frankenstein (eds.), Albany: State University of New York Press, 1997.

PoweII, Ivor and Mark Lewis, Ndebele: A people and their art. Cape Town: Struik, 1995.

Raum, Otto, Aríthmetic in África. London: Evans Brothers Ltd., 1938. Santos, Eduardo dos, "Sobre a matemática dos Quiocos de Angola". García da

Orta 3(2): 257-271, 1960. Santos, Eduardo dos, "Contribuição para o estudo das pictografías e ideogramas

dos Quiocos". Estudos sobre a etnología do ultramar Portugués 2: 17-131, 1961.

Struik, Dirk, "On the sociology of mathematics". Science and Society 6: 58-70, 1942.

Touré, Saliou, "Preface". In Mathématiques dans l'environnement socio-culturel Africain. Doumbia, Salimata (ed.), Abidjan: Institut de Recherches Mathématiques d'Abidjan, 1-2, 1984.

White, Leslie, "The locus of mathematical reality: an anthropological footnote." [1947] reproduced in j. Newman (ed.), The World of Mathematics, New York, Vol. 4: 2348- 2364, 1956.

Wyk, Cay van, African painted houses. Basotho dweilings of Southern África. New York: Harry Abrams, 1998.

Wilder, Raymond, "The cultural basis of mathematics". Proceedings International Congress of Mathematidans, 1: 258-271, 1950.

Zaslavsky, Claudia, África counts: Number and pattern in African culture. Brookiyn: Lawrence Hill Books, [1973] 1979, 1999.

Zaslavsky, Claudia, "Mathematics in África: explicit and implicit". In Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, I. GrattanGuinness, ed. London: Routledge, London, 1994.

Zaslavsky, Claudia, "África Counts and Ethnomathematics". For the Learning of Mathematics 14(2), 3-8, 1994a.

Ethnoscience and ethnomathematics:

a historiographical proposal for non-western science

UBIRATAN D/AMBROSIO

"Oriental philosophies and religions are of a very different kind from those of the West. I can therefore imagine that there might also exist different modes of thinking even in mathematics.

Yasuo Akizuki, 1960 This paper focus on the social, political and cultural factors in the dynamics of the transfer and the production of scientific and mathematical knowledge in the colonies, as well as on the recognition of non-European forms of science and mathematics, either extant or buried in the colonial process. This is a historiography proposal, which relies on the memory of people and events that survived in a literate era. The methodology puts together scraps of information in non-traditional historic sources and recognizes extant practices, normally called ethno-science and ethnomathematics. Knowledge and cultural encounters Science, as generally understood nowadays, emerged in a distinctive form of explaining, understanding and coping with the natural environment in the Mediterranean Basin, since early times. Every culture generated something equivalent to Science, which works satisfactorily in its context. These are corpora of knowledge that have been generated in a particular context, with specific motivations, and that have been and are subject to changes resulting from exposition to other cultures, particular during the colonial era. These corpora of knowledge, generally called ethnosciences and ethnomathematics, have been dealt with inappropriate historiography and equivocated criticism.7

7 Ubiratan 0'Ambrosio, "A Historiographical Proposal for Non-western Mathematics", Mathematics Across Cultures. The History of Non-Western Mathematics, Helaine Selin (ed.), Dordrecht, Kluwer Academic Publishers, 2000, pp. 79-92.

These are results of the major challenges facing the human species, which is driven towards survival and transcendence. To survive, which is an action needed in the encounter with the other and with nature as a whole. To transcend, which looks into before and after the moment, searching the past and probing into the future. In order to survive, man needs to generate ways of dealing with the immediate environment, which provides air, water, nourishment, the other and everything needed for the survival of the individual and of the species. These are techniques and styles of individual and collective behavior, which include communication and language. In search of transcendence, man developed perceptions of past, present and future and their enchaining, and means of explanation of facts and phenomena. These means are memories, individual and collective, myths and divinatory arts, which allow penetrating the future. In memory and myths are the traditions, which include history, religions and systems of values and explanations. The divinatory arts are practices, such as astrology, oracles, logics, such as, for example, the I Ching, numerology and the laws of nature (philosophia naturalis), or, using a comprehensive term, the sciences, which tell us what may happen. A historiography must look into all these categories, memories, myths and the divinatory arts (techniques, behavior, communication, language, traditions, history, religions, systems of values, sciences) to make sense of the past. Very much in line with the Annales proposal.8 Knowledge is the response to the drives for survival and transcendence. How is knowledge generated, organized intellectually and socially, and diffused? Particularly language and mathematics offer major challenges. Both have grown differently in different cultures. And both have been affected by cultural encounters throughout history. Particularly important for our analysis are the encounters which occurred after the 15th century between European and non-European cultures. I agree with Urs Bitterli when he reduces the encounter of European and non-European cultures to three basic phases: contact, collision and relationship. He shows that they do not occur necessarily ¡n this order, that they are not mutually excluding and that there has been occurrence of the three types. In some cases the contact lead directly to relationship.9 These types of encounter are convenient for understanding cultural dynamics of the encounters, from the beginning of European overseas conquest through early industrial relations. Current History and Philosophy of Science and of Mathematics focuses on ideas, which synthesize centuries of development in the Mediterranean Basin, enriched by contacts with Africa and the Far East. Historiography is largely based on written

8 See Encyclopedia of Historians and Historical Writing, Chicago, Fitzroy Dearborn Publishers, 1999, "Febvre, Luden", pp. 379-380. 9 Urs Bitterli, Cultures ¡n Conflict. Encounters Between European and Non-European Cultures, 1492-1800, Cambridge, Polity Press, 1989.

sources and relies on names, epochs, dates and places proposed by early historians. Contact, collision and relationship are moments of the same process of the modern European expansion. Although the conquered civilizations possessed scientific and mathematical knowledge, current historiography of science and mathematics is inadequate to recognize the cultural] dynamics of the contacts. Its nature and history are practically unknown. The collision phase resulted in the denial of the forms of knowledge of the conquered. The relationship is marked by an effort to transfer science and mathematics from the European tradition to the colonies.10 The condition of consumers of the knowledge produced in Europe continued in the colonies until the transition from the 19th through the 20th century, when a local production of science and mathematics originated in Europe, start to be delineated. Ethnoscience and ethnomathematics The great navigations since the 16th century mutually exposed forms of scientific knowledge from different cultural environments. The several ethnosciences, among them European sciences, have been subjected to great changes as a result of the encounters. I will examine some of the consequences of this mutual exposure of cultures. By ethnosciences I mean the corpora of knowledge established as systems of explanations and ways of doing, which are accumulated through generations in specific cultural environments. Particularly important for us is ethnomathematics, which is corpora of knowledge derived from quantitative and qualitative practices, such as counting, weighing and measuring, sorting and classifying. The same as Western science and mathematics, ethnosciences and ethnomathematics have a symbiotic relation. Both are not new disciplines. Rather, they are part of a research program on history and epistemology. The pedagogical implications are obvious. Both research and educational programs take into account all the forces that shape a mode of thought, in the sense of looking into the generation, organization (both intellectual and social) and diffusion of knowledge.11 The research program, typically interdisciplinary, brings together and interrelates, results from the cognitive sciences, epistemology, history, sociology and education. An essential component is the recognition that science and mathematics are intellectual constructs of mankind in response to needs of survival and transcendence.

10 Ubiratan D'Ambrosio, La Transferencia del Conocimiento Matemático a las Colonias: Factores Sociales, Políticos y Culturales, LLULL, Vol. 22, 1999, pp. 347-380. 11 Ubiratan D'Ambrosio, Several Dimensions of Science Education: A Latin American Perspective, Santiago, CIDE/REDUC, 1991, p. 119.

The need for an intellectual framework to organize the corresponding systems of codes, norms and practices gave rise to many aspects of science and mathematics.12 In the research program, particular attention is given to those dimensions of knowledge, which bear some relation to what became known as the several discipline of science and mathematics in European civilization after the 15th century. Ethnoscience, both as corpora of knowledge and as pedagogical practices, is supported by the history of science and reflect the dynamics of cultural acquisition. Some examples illustrate this. All over the World, much of the weather explanations and predictions, agriculture practices, processes of cure, dressing and institutional codes, culinary, and commerce, carne from the European tradition developed in the Middle Ages and the Renaissance. But we see, all over the World, practices performed in a very distinctive. These practices, which have their origins in native communities, are significantly modified as a result of mutual exposition of cultural forms since colonial times. For example, it is common to see indigenous peoples in the Americas using Indo-Arabic numerals, but performing the operations from bottom to top, explaining that this is the way trees grow. But it is also common to identify, in the more advanced notions, the influence of this mutual exposition in everyday life and practices. In daily life, practices, which are scientifically based, are easily recognized. This is evident by looking into professions that require some scientific knowledge and mathematical abilities. Practices and perceptions of learners are the substratum upon which new knowledge is built. Thus, new knowledge has to be based on the individual and cultural history of the learner and it has to recognize the diversity of extant cultures, present in specific communities, all over the world. This is the essence of a new educational posture called Multicultural Education. A new educational posture depends on a new historical attitude which recognizes the contribution of past cultures in building up the modern world and modern thought, and which avoids omissions and errors of the past treatment of cultural differences. We easily identify two categories of scientific knowledge:

• Scholarly (or "formal" or "academic") science, supported by a convenient epistemology, and whose practice is restricted to professionals with specialties;

• Cultural (or "practical" or "popular" or "street") science, or ethnosciences.

12 Ubiratan D'Ambrosio, "Ethno-mathematics, the Nature of Mathematics and Mathematics Education", Mathematics, Education and Philosophy: An International Perspective, Paúl Ernest (ed.), The Falmer Press, London, 1994.

These categories are closely related and their main distinction refers to criteria of rigor, to the nature, domain and breadth of its pursuits, which is "how well" they respond to the needs of survival and transcendence. For example, pre-Columbian cultures had different worldviews. This is inbuilt in their mythology, religion and, of course, in their complex of explanations, and as a consequence, different styles of doing their measurements and computations.13 These practices are still prevalent in some native communities. Land measurement, as practiced by peasants in Latin America nowadays, comes from ancient geometry transmitted to medieval surveyors, since land property and measurement (geometry) were strange to Pre-Columbian cultures. Most Amazonian tribes have counting systems that goes as "one, two, three, four, many". And that is all, since with these numbers they can satisfy all their needs.14 We also recognize important ways of dealing with pottery, tapestry and everyday knowledge with strong mathematics characteristics in several cultures.15 The same with African cultures.16 The people from these cultures have no problems at all in assimilating the current European number system and deal perfectly well with counting, measurement and money when trading with individuals of European culture. Another example comes from Africa, where the people deal with numbers and counting according to their specific cultural background.17 The high prestige of science comes mainly from its recognition as the basic intellectual instrument of progress. It is recognized that modern technology depends on science and that the instruments of validation in social, economic and political affairs, mainly through storing and handling data, are based on science and mathematics. Particularly important in this respect is statistics. This evidently brings to science an aura of essentiality in modern society. There is a general feeling that there are practically no limits to what can be explained by science. Many of the applications that give such a prestigious position to science are part of various forms of cultural dynamics. The same is, probably, more clearly seen in technology. The efforts of the early colonizers to adapt technology developed in Europe to the new lands is responsible for many advances, particularly in mining, agriculture and medicine.18 Another important example on how the cultural dynamics of the encounter is seen in the transfer of applied science and technology is the process of urbanization. How to meet the challenge of founding cities in the new lands?19

13 See the recent book by Andrea C. Schalley, Das mathematische Weltbild der Maya, Frankfurt am Main, Peter Lang, 2000. 14 Native American Mathematics, Michael Closs (ed.), University of Texas Press, Austin, 1986. 15 Marcia Ascher, Ethnomathematics. A Multicultural View of Mathematical Ideas, Pacific Grove, Brooks/Cole Publishing Company, 1991. 16 Paulus Gerdes, Ethnomathematics and Education in Africa, Institute of International Education/Stockholms Universitet, Stockholm, 1995. 17 Claudia Zaslavsky, Africa Counts: Number and Pattern for Teachers, Lawrence Hill, New York, 1979. 18 See the interesting paper by Nicolas Garcia Tapias, "The Repercussion of Spanish Technology in the Discovery of the American Continent", ICÓN, vol. 5, 1999, pp. 113-127.

Practices are generated, organized and transmitted informally, the same as language, to satisfy immediate needs of a population. They are incorporated in the pool of common knowledge that keeps a group of individuals, a community, a society together and operational, and this is what is called culture. Culture thus manifests itself in different, obviously interrelated, forms and domains. Cultural forms, such as sets of explanations, language, mathematical practices, religious feelings, values, family structure, dressing and behavior patterns, are thus diversified. They are of course associated with the history of the groups of individuals, communities and societies where they are developed. A larger community is partitioned into several distinct cultural variants, each owing to its own history and responsive to differentiated cultural forms. Some remarks on historiography History, as a major academic discipline, carries with it an intrinsic bias, which makes it difficult to explain the ever present process of cultural dynamics that permeates the evolution of mankind. This paves the way for paternalism and arrogance, for intolerance and intransigence. And clearly interferes with the understanding, for different cultural groups, of each other processes of building up their cultural realities when trying to satisfy their needs of survival and transcendence. These biases have been methodological as well as ideological, particularly in the History of Science. Helge Kragh says "History of Science has its own 'imperialism' that partly reflects the fact that viewed historically and socially science is almost purely a western phenomenon, concentrated on a few, rich countries. While science may be international, history of science is not.”20 This seems to be almost unavoidable in the framework of historiographies that rely on reductionist approaches, such as the case of the various supposedly autonomous histories, in particular in the History of Science. The mere fact that to pursue historical analyses one talks about the sciences, such as Physics, Chemistry, Mathematics, as distinct from Religion, Art, Politics, obviously impedes the understanding of the processes of evolution of ideas and methods, of reflection and action, which underlies man's struggle to find explanations, to understand and cope with its environment, and of conviviality with nature. Reductionism, which characterizes several of the so-called autonomous histories and also histories based on facts and names, on places and dates, naturally derives from the prevailing ideology and justify cur-rent actions. Even when we move a step further than narrative history and go to historiography, the facts prevail

19 See the important study of José Sala Cátala, Ciencia y Técnica en la Metropolización de América, Theatrum Machinae, Ediciones Doce Calles/CSIC, Madrid, 1996. 20 Helge Kragh, An Introduction to the Historiography of Science, Cambridge Univ. Press, Cambridge, 1987, p. 111.

over the processes and we may be led to be satisfied with the false impression of having approached the past because we have verified data and described facts. Historiography focused on a problem should never lose the view of all the forces, which play in the historical reality, thus avoiding the unilateral approach of the specialist and the reductionist flow to a few elements. Armando Saitta asks for the historian to look into "What to-day isn't but tomorrow will be".21 He clearly proposes a global history. When he refuses the history of the "if", he opens the way to an evaluation of all the alternatives which were present in the process and he claims that the one alternative which have succeeded should not imply the rejection of he others. E. H. Carr has the same opinion when he says that the historical moment in which several alternatives were open does not imply abandoning those that did not succeed, but rather looking into the reason for which some did not succeed and what was the cost of this decision.22 Paraphrasing Miguel León-Portilla, it is a matter of listening also to the loser.23 History has been mostly the history of the winners. Indeed, to remove the history of the loser was the most efficient intellectual tool of the colonizer. As recognized by Markus P.M. Vink, the development of science and technology in the 19th century gave material tools, such as quinine, vaccination, the machine gun, steamboat, railroad, telegraph, which became fully integrated in the knowledge brought by the colonizer (winner) to supersede the knowledge of the conquered (loser).24 This is particularly true in the history of the sciences of the losers. The mere fact is that science means power, since, as every other divinatory art, it anticipates what did not yet happen. This association of science with power is seen very clearly in the history of European science.25 The dawn of modern science is identified with the modern geography of the world, and the granting of privileges for those capable of mastering modern science and technology. How did this privileged role of scientists come into being? Why conquered and colonized still have problems in mastering science and technology? Why have science and technology progressed so rapidly and in this process have left aside, indeed eliminated, social and, above all, ethical concerns, thus paving the way for enormous social, political and environmental distortions? These questions are germane to the concept of knowledge itself.

21 Armando Saitta, II programma della Collezione storica, Laterza, Bari, 1955, p. 12. 22 E.H. Carr, What is History?, Penguin Books, Harmondsworth, 1968. 23 Miguel León-Portilla, "Visión de los Vencidos (Crónicas Indígenas Mexicanas)", Historia 16, 1985. 24 For a comprehensive view of the late Western colonial expansion, see Markus P.M. Vink, "New or High Imperialism, 1870-1914", Process and Patterns, World History bulletin, vol. XVII, núr. 1, Fall 2000, pp. 16-31. 25 The silence of European historians of science about John Flamsteed (1646-1 719) is an example. See David Clark and Stephen P.H. Clark, Newton's Tyranny. The Sup-pressed Scientific Discoveries of Stephen Cray and John Flamsteed, W.H. Freeman, New York, 2000.

Building-up scientific knowledge We see knowledge as emanating from the people, essentially generated by individual as a result of man's drive towards explaining, understanding and coping with the immediate environment and with reality in general, reality understood in its broadest sense and in permanent change as a result of man's own action. This drive, with the ultimate objectives of survival and transcendence, is obviously holistic and dynamically subjected to a process of exposure to other members of society, people. Thanks to communication, both immediate and remote in time and space, the knowledge thus generated goes through a process of codification, intertwined by an associated underlying logic, inherent to the people as a form of knowledge —some call wisdom. The modes of communication and the underlying logic are recognized as the result of the prevailing cognitive processes. Cognitive evolution, related to environmental specificity, gives rise to different modes of thought and different underlying logic, communication and codification. Hence knowledge is thus organized, intellectually, that is, structured and formalized subjected to specificities of cultural nature. And through the cultural process of sharing knowledge and according behavior, it is socially organized. It becomes a corpus in the cultural framework. Power structure, which itself rises from society as a form of political knowledge, appropriates, indeed expropriates, structured knowledge and organize them in institutions. In this form, and under the control of the establishment and the power structure, which mutually support each other, knowledge is given back to the people, who in the first instance generated it, through systems and filters which are designed to keep the established power structure. It is the diffusion of knowledge. The generation, organization and diffusion of knowledge is clearly a holistic process subjected to the dynamics of change. This is the essence of the research program on the history of science, which I call Ethnomathematics. It recognizes that mutual exposure of distinct approaches to knowledge, resulting from distinct environmental realities, is global, embracing the entire cycle of the generation, organization and diffusion of knowledge. The process of cultural dynamics which takes place in the encounters is based on mechanisms which balance the process of change, which I call acquiescence —that is, the capability of consciously accepting change (modernity)— and the cultural ethos —which acts as a sort of protective mechanism against change that produces new cultural forms. This behavior can be traced back throughout the entire history of mankind. These conceptual tools are close to the ethos and schismogenesis, introduced by Gregory Bateson in dealing with cultural contact and enculturation.26 In the encounter of the two worlds (Europe and America) this was violated in many instances. The origin of these violations may be related to distinct views of nature. A scientific conceptualization, which resulted from an intertwining of medieval 26 Gregory Bateson, 5teps to an Ecology of Mind, Ballantine Books, New York, 1972.

Judeo, Christian and Greco-Arabic thought, and developed in Europe, lead man to look at nature and at the universe as an inexhaustible source of richness and to exploit these resources with a mandatory drive towards power and possession.27 This behavior towards nature and life has lead man to favor a single model of development, hence to ignore the cultural, economical, spiritual and social diversities, which constitute the essence of our species. These reflections question the set of current concepts and models, and calls for the acceptance of the idea that survival depends of a global and holistic view of reality. This demands a radical change, which applies to all levels of knowing and doing. We are thus lead to look for radical changes in our models of development, of education and of civilization, based in the recognition of a plurality of models, of cultures, of spirituality and of social and economical diversity, with full respect for each one of the distinct options. Final remarks The conquest and colonization had, as a consequence, an enormous influence in the course of development of the civilization. The chroniclers of the conquest tell of they have seen and learnt. They mention absolutely different ways of explaining the cosmos and the creation, and ways of dealing with the surrounding environment. Religious systems, political structures, architecture and urban arrangements, sciences and values were, in a few decades, suppressed and replaced by those of the conqueror. A few remnants of the original behavior of these cultures were and still are outlawed or treated as folklore. But they surely integrate the cultural memory of the peoples descending from the conquered. Much of these behaviors are easily recognized in everyday life. Science and mathematics, as human endeavor, are not different. This is one focal point of the research program called, Ethnomathematics, which deals with the generation, the intellectual and social organization and the diffusion of different ways, styles, modes (tics) of explanation, understanding, learning, coping with and probing beyond (mathema) the immediate natural and socio-cultural environment (ethno).28 Obviously, ethnoscience is part of this. The early colonizers of the Americas, the Spanish and the Portuguese, paved the way for the French, the English and the Dutch colonizer and later on for Africans, Europeans and Asiatic immigrants. With them carne new forms of coping with the environment, of dealing with daily life, and new ways of explanation and learning. 27 It is a good theme to compare the efforts of historians of science to insert ecological concerns in the evolution of Western thought and these views on ethno-science. Particularly illustrative of these questions is the paper by Andrew Cunningham, "Science and Religion in the Thirteenth Century Revisited: The Making of St. Francis the Proto-Ecologist. Part I: Creature not Nature", Studies in History and Philosophy of Science, vol. 31A, núr. 4, December 2000, pp. 613-643. 28 Ubiratan D'Ambrosio, Etnomatemática. Arte ou Técnica de Explicar e Conhecer, Editora Ática, Sao Paulo, 1990. A translation is available, Ethnomathematics. The Art or Technique of Explaining and Knowing, Patrick B. Scott (tr.), NMSU/ISGEm, Las Cruces, 1998.

The result was the emergence of a synthesis of different forms of knowing and explaining which were generated by and available to the different communities, to workers and to the people. We recognize the emergence very soon of new religions, of new cuisine, new music, new arts and new languages. All of these absolutely interrelated as a synthesis of the cultural forms of the ancestors. Particularly in the Americas, the variety and peculiarity of the expositions of cultures and the specificity of the population migrations re-veal an effort of the colonizer to transfer, with minor adaptations, the forms of social, economical and political organization and administration prevailing in the metropolises, including schooling and scholarship (academies, universities, monasteries). The new institutions in the Americas were based on the styles prevailing in the metropolises, mostly under influence, and even control, of religious orders. This poses the following

Basic question: What are the relations between the producers and consumers of cultural goods?

This guides a proposal for a historiography of science and mathematics, which I have called "the basin metaphor".29 Although this is a question affecting the relations between academia and society in general, hence between the ruling elite and the population as a whole, it is particularly important for understanding the role of intellectuals in the colonial era. Curiously enough, the factors influencing the consumption of what we might call academic science and mathematics produced in an alien cultural environment, and what "outsiders" of the profession —that is, non-scientists— have to say about science and mathematics, which affect their everyday life, have not been given attention in the prevailing historiography.30 It is important to incorporate to the History of Science and Mathematics, in an essential way, not as mere anecdotes, the views of aliens —cultural and academic— about science and mathematics. This broader look, suggested by new historical scholarship, comes under severe at-tack, in what became to be known as the Science Wars.31 The essence of my historiographical proposal is the recognition that this cannot be done unless we examine simultaneously techniques, behavior, communication, language, traditions, history, systems of values, religions and the sciences. They come together. The recognition of other systems of generation, of intellectual and

29 Discussed in the paper in note 1 above. 30 See Ubiratan D'Ambrosio, Mathematics and Literature, Essays in Humanistic Mathematics, Alvin M. White (ed.), The Mathematical Association of America, Washington D.C., 1993, pp. 35-47. 31 See the issue devoted to the theme "Science Wars" of the 5oc;a/ Text, pp. 46-47, Spring/Summer 1996. The issue has very interesting papers. Regrettably, attention was given only to the hoax of Alan Sokal. As a consequence there were renewed attacks on Afrocentrism, warnings against a "new dark age of irrationalism" and other controversial disputes going on in the academic world. All this that might be interpreted as a form of intellectual fundamentalism is nothing but a defensive posture against the challenge, which the current epistemological order is facing.

social organization and of diffusion of ways, styles, modes of explanation, understanding, learning, coping with and probing beyond the immediate and the remote natural and socio-cultural environment, is the only possibility of escaping the arrogance associated with the Western concept of truth. Fundamentalism, which is the result of such arrogance, is best described by Sri Aurobindo (1872-1950):

For Western Philosophy a fixed intellectual belief is the most important part of a cult, it is the essence of its meaning and it is what distinguishes it of others. Thus, formulated beliefs make true or false a religion, according to agreeing or not with the beliefs of its critics.

Science at the edge of the Earth∗

WESLEY M. STEVENS Speaking during the early seventh century, an Irishman accused his fellows and their science of being like "a pimple on the face of the Earth." The writer was Cummian who lived near Durrow in the southern region of Ireland. He included Britons in his jeremiad; like most of the Irish, the Britons were of Celtic race who lived in Brittany, now a part of northwestern France, in Brittany on the northern coast of Espagne, and in Devon and Wales which are southwestern parts of what is now known as the United Kingdom of Great Britain. Cummian compared the Irish and Britons negatively with Hebrews, Greeks, Scythians, and Egyptians in a rather wide-ranging scope of cultural diversity. He was seeking the answer to a scientific problem for which Nature provides the text and History the context. The Epistola Cummiani was written in Latin about 632 A.C. It is a document which is concerned with the many and diverse systems used by Christians for determining the date of their chief feast in a long succession of years.32 A great number of books have been written about the date of Easter and the science required by different systems for predicting the dates of that movable feast of Christians. Each of those dating systems must coordinate cycles of Sun and of Moon with historical events in a way that would allow the prediction of future dates of Easter Sun-day in a long time series, perhaps in perpetuity. Those systems and their details will be left aside today, in order to consider two examples of science within diverging cultures.

I The problem which those Irishmen were discussing was set by their Saviour long ago. About the year 29 A.D. in Palestine and most likely using the Aramaic language, Jesus had prayed for his followers "that they may all be one" (Gospel John XVII: 22), or in the Latin version: ut omnes sint unum. Thereafter in the

∗ Universidad Autónoma del Estado de Hidalgo, Sala Pilar Licona, Pachuca, México 28 November 2000. 32 Ms. London British Library Cotton Vitellius A. XII (s. XII2) f. 79-83; ed. James Ussher, Veterum Epistolarum Hibernicarum Sylloge (Dublin 1632), pp. 24-35. See the analysis by W.M. Stevens, "Scientific instruction in early insular schools," in Insular Latin Studies, ed. Michael Herren (Toronto: Pontifical Institute of Mediaeval Studies, 1981), pp. 83-111, with further literature; rpr in Stevens, Cycles of Time and Medieval Scientific Learning in the Middle Ages (Aldershot, U.K.: Ashgate Publishing, 1995): item IV.

Gospel account were several analogies of union which became very attractive to the community of Christians. As the followers of Jesus the Christ tried to worship together, it happened that they may have remembered the earlier events and experiences of the Apostles with some variation, that they placed those events and experiences within the weekdays and months of local calendars, and that writers of the four Gospel Books therefore left records within their different cultures which appear to diverge ¡n detail when read out of context. These limited and incomplete records of days, weeks, and months were not questions of faith, though theological ideas were brought to support some of the explanations. Within the second and third centuries of the Christian era, many serious scholars tried to overcome those unnecessary and quite embarrassing divergencies of cultural detail and of historical context by referring back to the textbook of Hellenistic astronomy.33 If they were successful, that would be good history and it would also be good science, for certain elements of astronomy can be related to the regularities of Nature. That is what Cumian requires of the Irish and the Britons; it is what he finds with the Hebrews, Greeks, Scythians, and Egyptians. If Nature proviedes the text of an event, it will be found both in astronomy and in geography, and it will require a little help from mathematics. Those three scientific disciplines may vary in techniques as developed in different cultures and during different eras. Yet, we can agree (I expect) that each discipline has had the same purpose at all times and in all cultures: that purpose is a rational understanding of natural phenomena. On the other hand, thosee three scientific disciplines have not always been succesful in their methods. They have attempted the rational understanding of natural phenomena diversely in different times and places; so diversely that modern astronomers, geographers, and mathematicians often scoff at the notion that earlier knowledge was anything like science. To compensate for this self-indugence and pride of modern scientists, some will express an interest ¡n the achievements of one or another ancient culture which they have not studied, while retaining an open or even an empty mind about anything in their own culture more than one generation ald.

II Other cultures have memories, and the memory of any culture is limited (9 its own sources. Those cultural sources may take at least three forms: Present memory, Monuments and artifacts, and Writing.34

33 Stevens, "Cycles of Time: Calendrical and astronomical reckonings in early science", in Time and Process: The study of time VIl, ed. ).T. Fraser and L. RoweII (Madison, Conn.: International Universities Press, 1993), pp. 27-51; idem, "Sidereal time in Anglo-Saxon England", in Voyage to the other world: The legacy of Sutton Hoo, ed. C.B. Kendall and P.S. Wells (Minneapolis: University of Minnesota Press, 1992), pp. 125-152: rpr in Stevens, Cycles of Time, Op. cit.: Items I and V. 34 Mary j. Carruthers, The Book of memory: a study of memory ¡n medieval culture (Cambridge University Press, 1990).

1) Present Memory is short-term. At most, your memory and mine can take us back one or two generations; some experts may arise in any culture who are trained to recall a few, selected social events back to a third generation.35 Within that stretch there is usually much uncertainty, and beyond it there is serious deterioration of memory, so that assistance is required for even the most expert memories in the form of ceremonial liturgies, oral repetition of stories, verses, and especially those ceremonies, stories, and verses supported by music. 2) Monuments and Artifacts survive from ancient cultural activities. Some are standing, but they are mostly fallen and lay on the ground, ignored in any society; yet, they may be gathered unp and studied to help us recall earlier bits of knowledge. From remains of monuments and fragile artifacts, archaeologists may reconstruct pieces of the past into longer memories which, to be retained and consulted, must then be written. 3) Letters, Notes, and Written Records from past times fill out our short present memories, so far as they go. When available, such writings allow a richer history to be written and corrected, even about cultures of which no living person has an active memory.

III Let’s return now to that quotation from a letter written in seventh century. In the heat of debate, Cummian referred to Ireland as being "Like a pimple on the face of the Earth." What sort of pimple? Well, that is an analogy for a place, a region, or even an island. Imagine a protrusion on a human face and transfer that image to the whole Earth. But upon what sort of Earth? It must go beyond the usual range of Irish and Brits and include those other four cultures, however distant they may be. Implied is some experience in communicating at very great distances, North and South, East and West. How would that Irishman in the early seventh century have described the Earth, with such scope to include Hebrews, Greeks, Scythians, and Egyptians? On this question about the shape of the Earth assumed in ancient times, I dare say that your present memory is much like the memory of most Irishmen: uncertain, perhaps even void. But let’s go back one or two generations. How would your parents or your teachers have answered the question about ideas of the shape of the Earth in the seventh century? How about your grandparents and their teachers? As this is a question which I have addressed to many people, let me help you out, here: drawing upon present memory, it is commonly said that the Earth was not understood to be round in the olden days, so that an Irishman in the early seventh century must have thought that it was flat, if he thought at all. This is only a guess, but even old verses and songs provide no help to describe the Earth. In order to discover what the Irish and the Britons thought about the Earth in the seventh century, we should move on to the second category of sources: 35 Genealogies may perhaps extend to seven generations, in some cases.

monuments and artifacts. There are a lot of those in Ireland, and most seem to be relies of an old religion: that is, stone crosses and stone huts and walls for monastic enclosures. But we can-not expect the remains of religious communities to tell us or even imply anything to describe the Earth, whether in terms of astronomy, geography, or mathematics, now can we? This leaves us dependent upon writing as a source of knowledge. Here again, the sources from Ireland are quite limited, for there are very few written recors of any sort in the seventh century of our era. But at least there are some, of which the Letter of Cummian is a rare survival and is most interesting. While arguing the question of a proper dating system for Easter, Cummian draws upon religious imagery, but he wants agreement with his colleagues on a scientific basis. He is not satisfied with local sources but seeks a wider scope. He has some doubts about the adequacy of short-term memory and the support from ceremonial liturgy, story, verse, and song. On the other hand, he knows some Hellenistic science of Mediterranean origin. In this, he is not alone. Later in the same century, another Irishman named Augustinus drew upon some concepts of this Hellenistic type of thinking, in orden to describe various natural phenomena,36 and one result was a better account of the flux of the seas than any Greek or Roman ever knew. This developement was carried much further by others. Another half century later, an Angle in Northumbria also compared his location to "a pimple on the face of the Earth". That was the monk Beda at Jarrow-upon-Tyne.37 Jarrow is now overwhelmed by the storage tanks for crude oil, imported by ship through the North Sea and up the River Tyne to Newcastle, thence to be refined and distributed all over the United Kingdom. At Jarrow in the early decades of the eighth century, Beda did indeed use the writings by those Irishmen, Cummian and Augustine; and he also drew upon Greek culture mediated by Egyp-tians, Scythians, Romans, Africans, and Spaniards. From those sources and with rare skills of his own, Beda was able to provide a very sensible answer to the Easter problem which bothered Cummian; his answer is the standard Western calendar, used by most cultures and by all scientists in the world today, with minor

36 De mirabilibus Sacrae Scripturae libri was written by the Irish Augustine (s. VII med.), but due to similarity of name, it was published among the works by Augustine of Hippo 354-430 A.D., ed. Patrologia Latina XXXV (1845) 2149-2200. The edition prepared by Gerard McGinty for his dissertation at Trinity College, Dublin (1971), has not been published. See also Marina Smyth, Understanding the universe in seventh-century Ireland, Woodbridge, U.K.: Boydell Press, 1996. In her valuable book, Dr. Smyth has litte to say about tides, and she is quite mistaken about descriptive knowledge of the Earth in Ireland, as my review explained in American Historical Review 103 (1998) pp. 1233-1234. 37 Beda venerabilis (673-735 A.D.) is well known for his Historia ecclesiastica (translated into many languages), and he also wrote biblical commentaries, lives of the abbots of Jarrow, Wearmouth, and Lindisfarne, computistical tracts, and schoolbooks on gram-mar, verse, and natural phenomena. See P. Hunter Blair, the World of Bede, New York: St. Martin's Press, 1970; Stevens, Bede's scientific achievement (The Jarrow Lecture for 1985), revised edition in Cycles of Time, Op. cit.: item II, and a large literature noted in both books. Except for the essays and editions by jones cited below, most other discussions of this great writer ignore his many scientific works.

adjustments.38 In addition, he was able to write the best "Theory of Tides" ever conceived, prior to the seventeenth century. Although Isaac Newton's invention of a new "Theory of Gravity" forced some adjustments to Beda's theory, a harbour pilot in Dublin told me in 1986 that, in order to bring ships safely to dock, what Beda wrote is basically what he does today, when he consults the annual British Admiralty Tide Tables. Between all of those different cultures and all of those times with their differing contexts, there must be science.

IV Our earlier question remains: How did they describe the Earth long ago in those distant outposts of Irish, Britons, and Angles? From old written sources we may now understand better the monuments and artifacts of several cultures. But they are still not perhaps what we might expect. Anaximander, Anaxagoras, and other Greeks tried at first to describe the Earth as flat, but they also described the heavens as round. Socrates asked about new ideas of the Earth arising in his times but offered no explanation. By analogy with the heavens, first the Pythagoreans and then Plato and Aristotle imagined that the Earth too must be round. Thereafter, so did everyone else.39 When Cummian spoke of a pimple on a face, it was by analogy with a human face on a round skull. And his analogy referred to mental activity, to knowledge. What is a small speck of an idea worth in relation to knowledge shared by the whole world? When the Irish Augustine wrote of tides, he knew of ships coming into dock and departing only when the flux of waters assisted them. He could see ships going and coming over the horizon without fear of falling off: sailors know well that the surface on which they work is curved, whether or not they think about it, for the port rises to them as they come in and sinks from sight when they sail away. When Beda wrote about these matters, he specifically described the Earth is a globe, a sphere, round like a ball which boys play with. And so it goes without a break into all those cultures and into the science shared by all.40

V The Irishman Cummian in the early seventh century learned from some returning travellers what was done about the date of the Easter celebration by strange 38 Bedae Opera de temporibus, ed. Charles W. Jones, Cambridge, Mass.: The Medieval Academy of America, 1943, Latin text with introduction and annotations; English translation by Faith Wallis, Becfe: the reckoning of time, Liverpool University Press, 1999, with useful introduction and annotations. 39 Stevens, "The figure of the Earth in lsidore's De natura rerum", ISIS 71/257 (1980) pp. 268-277, rpr in Cycles of Time, Op. cit.: Ítem III. 40 Idem, "Earth, models of (before 1600)," in Sciences of the Earth. An encyclopedia of events, people, an phenomena, ed. Gregory A. Good, New York: Garland Publishing, 1998,pp. 182-188.

people in distant places. Dating systems required knowledge of astronomy and history. Thus, he argued that the knowledge which all those people held in common was to be trusted more than what some local Christians in Ireland thought, perhaps implying a new estandar for acceptable knowledge. In order to evaluate systems, on the basis of which one may predict dates in a long time series, Cummian appealed to what was held in common by Hebrew, Scythian, Greek, and Egyptian Christians, but not to Rome as a religious authority. That is, scientific knowledge cannot be known only here by ourselves, privately and intuitively, on the basis of present memory. It cannot be known only by present memory reinforced with ceremony, story, verse, and song. Neither can it be known only from great monuments or sacred artifacts. Those sources are valuable, but they are local, variable, short-lived, and may be uncertain in part. Reliable knowledge and its applications must be public and common, based upon information for which there are agreed standards of verification. So far as he went on the question of a proper system for predicting the date of Easter, Cummian was right but incomplete. A successful solution to that problem required more information, and better calculations than were available to him. Across the Irish Sea, Beda drew upon an even wider range of scholarship and himself supplied a large part of what was needed in terms of the lunar cycle and corrections for other systems of dating. But his work was also incomplete, requiring more information and better calculations, as he acknowledged, especially in terms of the astronomy of planetary orbits.41 Early descriptions of the Earth as a sphere, data tables for Christian celebration of Easter and thus creation of the western calendar, and a complete and reliable theory of tides during the seventh and eighth century were attempts at rational explanations of natural phenomena amongst peoples of divergent cultures who lived quite far away from each other. There was communication between them however and exchange of ideas. The history of their accomplishments in these examples suggests that reliable knowledge of natural phenomena must be public; it must be based in a rationality which may be commonly understood ¡n other cultures; and it must allow for continuing revision in the presence of additional evidence and ever more careful analysis. I am sure that astronomers, geographers, and mathematicians of all times and all cultures would agree. Otherwise, it cannot be science. Otherwise, such science would not be worthy of our diverse cultures, wherever and whomever we are.

41 Beda proposed a means of calculating planetary orbits, relative to the stars: sidereal time, but cited its uncertainties and asked his readers to improve upon his study. The date he received for the vernal equinox was incorrect, and he could not be more accurate. He didn't know about the so-called "precession of equinoxes," as explained in works of Hipparchos of Nicaea (ca. 190-120 B.C.) and Ptolemaios of Alexandria (ca. 100-165 A.D.) which were not known to any Latin writer on astronomy before the twelfth century. These matters are discussed by in more detail by Stevens, "Astronomy in Carolingian schools", in Kart der Crosse un sein Nachwirkenn. 1200 lahre Kulture und Wissenschaft in Europa, vol. I, ed. P.L. Butzer et al., Leiden: Brepols, 1995, pp. 41 7-487, esp. pp. 429-433.

Intelligibilité et historicité (Science, rationalité, histoire)

MICHEL PATY Conférence à la séance de clôture sur "l’Histoire des sciences dans le patrimoine mondial", du Colloque Les grands rendez-vous de la science et de l'histoire, Palais de la Découverte et UNESCO, Paris, 20-25 mars 2000 (le 25.3), et à la séance sur "Science et diversité culturelle - Ciencia y diversidad cultural - Science and Cultural Diversity", VII Congreso Mexicano de Historia de la Ciencia y la Tecnología, Pachuca, Mexique, 26-29 novembre 2000 (le 27.11). (Le second exposé, prononcé en espagnol, avait pour titre: Reflexiones sobre las relaciones entre la inteligibilidad y la historicidad en las transmisiones y las creaciones de conocimientos científicos). Résumé L'un des principaux objectifs de la science est de montrer que "le monde est intelligible" par la raison humaine. Cette tentative de compréhension rationnelle a une histoire, laquelle est étroitement liée à celle des sciences, mais aussi à celles des techniques et de la philosophie. Après avoir montré comment la considération des sciences dans l'histoire ouvre ou renouvelle un vaste champ de problèmes philosophiques, nous examinons la question de l'intelligibilité sous divers aspects qui vont de la rationalité (plus large et complexe que la seule logique) à l'action pratique (avec la pensée technique), à l'esthétique et aux choix éthiques, à la communicabilité des connaissances, dans le temps et dans l'espace, et aussi à la création scientifique. Nous analysons ensuite les rapports entre construction sociale et historicité, en faisant ressortir toute l'importance des contenus de connaissance, qui ne se laissent pas dissoudre dans les conditions externes de leur constitution. Toute la richesse de l'historicité se laisse voir dans la manière organique dont ces contenus sont tissés à partir de matériaux du monde empirique assimilés dans des constructions rationnelles. L'historicité elle-même nous devient intelligible, et permet de concevoir les élargissements de la rationalité qui permettent les ouvertures, les inventions et les progrès de la connaissance.

Introduction. Les sciences dans l'histoire, un champ de problèmes philosophiques Dans cette séance de clôture d'un Colloque de presque une semaine sur l'histoire des sciences au travers des siècles et des civilisations, je voudrais proposer quelques réflexions qui appartiennent à ce qu'on pourrait appeler la philosophie de l'histoire des sciences. Elles appartiennent, en vérité, autant à l'histoire des sciences qu'à la philosophie des sciences. Ces réflexions porteront sur quelques aspects bien circonscrits et je ne reprendrai pas les questions générales traditionnellement débattues sur les relations entre la philosophie des sciences et l'histoire des sciences, sinon pour indiquer d'emblée que ces réflexions veulent témoigner à leur manière de ce que l'histoire des sciences, comme d'ailleurs aussi bien les sciences en leur état actuel, constituent pour la philosophie des sciences un champ très riche et vivant de problèmes. Je dis bien un champ de problèmes (philosophiques et épistémologiques) à inventorier, et non un lieu d'application de thèses à illustrer, comme ce serait le cas pour une philosophie des sciences normative qui serait, en réalité, conçue comme séparée de l'histoire des sciences. Et ces problèmes, saisis sur le vif, concrètement pour ainsi dire, sont susceptibles de renouveler opportunément un domaine où l'on a souvent eu tendance, au long du siècle qui s'achève, à s'enliser dans des débats quelque peu scolastiques, sans doute parce que, précisément, quelque chose d'important manquait à une philosophie des sciences insistant de manière unilatérale sur les questions de langage, de logique des propositions et de significations. De telles questions sont, certes, fondamentales pour parler avec précision, mais elles étaient considérées seulement pour elles-mêmes, dans l'abstrait, et aussi dans l'intemporalité, en délaissant le plus souvent la considération des sciences telles qu'elles existent effectivement, avec leurs propositions, leurs procédures, leurs interprétations et controverses, pour ne retenir que des questions sur la pensée et le langage en général. Cette philosophie de la connaissance était trop coupée de la vie des sciences et sélectionnait ses problèmes en les idéalisant ; et quand elle s'intéressait effectivement aux sciences et non pas seulement à la pensée dans sa généralité, elle se cantonnait dans la zone pour ainsi dire sans risque des connaissances avérées, laissant de coté celles qui se font et qui se trouvent dans un processus de transformation. Si, d'aventure, changements et controverses étaient évoqués, ils étaient aussitôt renvoyés à d'autres instances que la philosophie, à la psychologie des individus et à l'histoire de communautés sociales, les deux étant supposées porter sur des séries d'événements échappant à la science proprement dite et à la saisie de la rationalité. Ceci valant surtout pour la philosophie des sciences de la tradition anglo-saxonne, dans le courant analytique, qui fut comme on le sait très influente, pour le meilleur et pour le pire, sur la philosophie de la connaissance de notre temps. C'est que l'histoire des sciences est assez encombrante pour des conceptions qui voudraient ramener la connaissance scientifique à une sorte de système logique plus ou moins fermé, rapporté à des catégories déjà fixées en référence à des

savoirs considérés comme acquis, et que l'on pourrait dès lors analyser en chambre. L'histoire des sciences enseigne immédiatement, en effet, à qui s'y intéresse, non seulement que les connaissances bougent et se modifient sans cesse, mais qu'elles ne sont pas uniformes et de nature semblable les unes par rapport aux autres, si l'on considère tant la variété des disciplines que l'hétérogénéité des systèmes de savoirs dans les différentes civilisations et aux diverses époques. Est-on sûr, d'ailleurs, que le même mot de science convienne à des configurations de savoirs et de pratiques prises dans des cultures très différentes ? Même si l'on trouve des raisons convaincantes de répondre affirmativement (ce qui est mon cas), la question mérite d'être posée. Elle est corrélative de la définition de ce que l'on entend par science, et les études comparatives sur des aires culturelles variées, comme celles qui ont été développées depuis deux ou trois décennies,42 obligent, en vérité, à revoir quelques certitudes simplificatrices: de celles, par exemple, qui feraient peu ou prou de la science au sens que nous connaissons pour le monde contemporain la norme de toute science, nous rendant alors aveugles à des pans entiers d'un riche patrimoine de l'humanité.43 Remarquons, en outre, que l'histoire des sciences, par nature, n'inventorie pas seulement les sciences acquises, elle voit se former des savoirs nouveaux, souvent non conscients encore d'eux-mêmes en tant que tels, car la nouveauté, au moment où elle surgit, ne dispose pour nos yeux que de l'espace de ce qui était connu, où elle était encore à proprement parler impensable. Pour que ces connaissances neuves nous deviennent explicites, il faut que les structures mêmes de nos représentations mentales se soient trouvées transformées à la faveur de leur assimilation progressive. En bref, l'histoire des sciences est l'histoire des connaissances qui, à travers l'espace et le temps, s'inventent, se transmettent, s'appliquent, se modifient, et aussi qui se réfléchissent sur elles-mêmes, par la pensée critique et philosophique, et par l'interpénétration avec d'autres instances de culture. C'est sous ces aspects divers, non fermés et vivants, que l'histoire des sciences nous donne à saisir ce qu'est, dans sa réalité effective, la science, aussi bien l'une des sciences particulières que l'ensemble des sciences dans leurs manifestations locales et différenciées. En ayant en vue ce paysage, dont il faudra détailler tant soit peu certains traits, je voudrais proposer les réflexions qui suivent sur quelques enseignements philosophiques de l'histoire des sciences, en les centrant autour de la question de la rationalité, ou du rationalisme - lié à la science par nature -, tout en considérant cette rationalité sous les éclairages qu'en procure l'histoire. Je me concentrerai donc, dans cette perspective, sur plusieurs problèmes des rapports entre science, rationalité et histoire, rapportés au double point de vue de l'intelligibilité et de l'historicité ; autant dire que j'ai modifié, dans le sens d'une explicitation, le titre qu'il

42 Cf. p. ex./ Jami, Moulin & Petitjean [1992], Habib & Raina [1999], et références bibliographiques dans Paty [1999b]. 43 Cf. Paty[1999aetb].

m'était initialement proposé de traiter, "La science et le rationalisme", en le faisant glisser vers une formulation plus précise et également plus actuelle, à savoir "Intelligibilité et historicité", avec en sous-titre "Science, rationalité, histoire". Dimensions de l'intelligibilité Explicitons donc quelques aspects du paysage qui s'offre à nous si nous tenons compte des travaux des historiens et des philosophes sur les sciences et la pensée scientifique en les rapportant à la question de I'intelligibilité, c'est-à-dire de l'appropriation par la raison, dans les pensées subjectives singulières, de tel élément de connaissance. Sans intelligibilité, il n'est pas de science, puisque la science est une production humaine, et, bien entendu, il n'est pas non plus d'histoire des sciences, puisque toutes les réceptions, transmissions, remaniements et nouveaux cours de sciences sont le fruit d'expériences vécues par ces mêmes subjectivités, fussent-elles rassemblées en "communautés", et considérant de toutes façons qu'elles participent d'une vie sociale. II n'est pas de communautés et de société sans sujets individuels, à moins de parler de robots (et même pas de clones). L'orientation des convictions intellectuelles selon des "paradigmes" dans le sens kuhnien,44 caractéristiques d'une époque et d'un contexte social, est une image bien trop schématique et même grossière, que l'on dirait calquée sur celle d'un champ magnétique orientant une limaille de fer au comportement uniforme, pour qu'elle puisse s'appliquer effectivement à des pensées humaines qui sont aussi conscience, raison et volonté. Toute autre est l'idée de "champ intellectuel" ou de "champ scientifique" proposée par Pierre Bourdieu, qui laisse aux individus la possibilité de s'orienter différemment les uns des autres, gardant leur capacité d'originalité créative.45 L'histoire des sciences nous apprend que les connaissances ne sont pas transmises de manière uniforme, la compréhension faisant appel à un ensemble complexe de dispositions et d'attitudes, comme les enseignants le savent bien. Elle nous apprend aussi que les savants ou les chercheurs eux-mêmes n'ont pas exactement la même lecture d'un fait, d'un problème, ou d'une proposition scientifiques, bien que ceux-ci soient présentés sous une formulation rationnelle et aussi objective que possible (nous reviendrons sur ces différences, liées aux "styles scientifiques"). Retenons, pour l'instant, que la rationalité, qui fait la science, en ce sens du moins qu'elle caractérise les contenus de science, car il faut tenir compte aussi du donné d'observation ou d'expérience constaté (mais cette constatation résulte elle-même d'un travail dans la rationalité: critique, procédure, vérification, etc.) ; que la rationalité, donc, n'est pas uniforme et univoque pour tous, même si tous ont la capacité de raison. Retenons encore que la rationalité dans la pensée d'un sujet n'est pas isolée et s'accompagne de la capacité d'émotion, du sentiment esthétique, de préoccupations métaphysiques, voire religieuses, de l'exercice de la volonté, de projets, de choix de valeurs, d'une culture, d'une représentation du 44 Kuhn [1962]. 45 Bourdieu [1966, 1976].

monde, selon des dispositions propres à chaque individu, qui guident d'ailleurs l'"intuition intellectuelle" comme perception synthétique immédiate... Cette "intuition" à laquelle tous les grands savants et philosophes de l'histoire de la pensée se réfèrent, même si les uns et les autres la conçoivent différemment, chacun à sa manière, pour rendre compte d'une constatation sur des faits d'intel-ligence dont ils ne savent pas donner de description détaillée par l'analyse. Autrement dit, le rationnel n'est pas univoque et déborde largement le logique ; il peut prendre, dans les modalités de la compréhension, appui sur l'intuition intellectuelle, qui fait intervenir des facteurs dont la complexité résiste à l'analyse. Il joue sur les registres du réel et du possible, et implique la prise en compte de données multiples et de situations compliquées qui multiplient les solutions concevables a priori. Et pourtant, malgré cette grande flexibilité, le rationnel peut être qualifié de manière positive, et opposé à l'irrationnel. Il permet de définir l'intelligibilité (l'intelligibilité rationnelle, justement), et constitue le moteur de la démarche scientifique. C'est lui qui donne la possibilité de décrire (et de communiquer) les connaissances scientifiques acquises, et il permet aussi, par sa flexibilité même, de concevoir que l'invention scientifique soit possible comme réponse originale et singulière à une exigence d'intelligibilité posée de manière particulière. Cette intelligibilité particulière elle-même n'est pas fermée dans sa singularité, puisqu'elle peut être transmise et adoptée par d'autres, sans devenir impersonnelle pour autant: elle reste toujours l'objet d'une adaptation idiosyncratique dans l'assimilation par une intelligence singulière. C'est un des traits de la rationalité de permettre la communication (discursive) et le partage des explications. Sans doute l'affirmation que la raison est la chose du monde la mieux partagée n'est-elle pas encore une idée dépassée... L'idée de science entretient donc avec la rationalité un lien de constitution, et avec elle aussi l'activité technique dont elle est issue, au moins à l'origine: la technique, qui est aussi une pensée (pratique) rationnelle,46 est sans doute aussi, comme la science, une pensée qui tient en quelque façon à l'esthétique et aux autres dimensions que nous avons mentionnées. Le lien de la pensée technique à l'esthétique semble attesté dès l'époque paléolithique, si l'on en croit les préhistoriens, qui font valoir que "les pierres taillées (le) sont beaucoup plus [taillées] (...) que leur usage ne le réclamait", et qu'elles présentent "une évidente recherche esthétique", due peut-être, d'ailleurs, à ce que ces outils "étaient investis d'une dimension sacrée". Sans doute est-ce "dans ses gestes d'artisan que l'homme s'est peu à peu découvert artiste...", et peut-être même l'art, qui est apparu indépendamment à peu près au même moment en divers endroits de la planète (de - 40 000 à - 12 000 ans, en Australie, en Europe et en Asie, en Afrique et en Amérique), serait-il antérieur à la pensée conceptuelle.47

46 Voir, sur le développement de la fabrication des outils, et celui corrélatif de la pensée, les ouvrages désormais classiques d'André Leroi-Gourhan (Leroi-Gourhan [1964, 1971]). Voir aussi Calder [1961]. Sur la philosophie de la technique, voir Simondon [1958]éd. 1989. 47 Lorblanchet [1999 a et b].

Soit dit en passant, rien n'oblige à opposer une explication fonctionnaliste classique des formes que nous qualifions d'art et l'attribution à leur propos d'un véritable sentiment esthétique, et l'on pourrait envisager que ce que nous concevons comme esthétique est issu de l'histoire de cette pratique primitive déjà très élaborée, qui était à la fois fonctionnelle et signifiante. La forme exprimait une exigence de sens, d'ailleurs liée à la pratique, à la fonction, et, par là, portait une esthétique. Fonction pratique, sens et esthétique étaient vraisemblablement présents et indistincts à l'origine, dans une pensée de toutes façons symbolique, et n'auront été conçus séparément et de manière réflexive que par la suite, très tardivement sans doute. On en trouverait encore la trace, plus près de nous, dans les temps historiques : le mot art signifiait jusque relativement récemment le travail utile et le savoir-faire par l'outil, dont l'expression, dans la forme, n'était peut-être que secondairement de la beauté.48 Il est en tout cas significatif que les arts et les beaux-arts aient une même origine (renvoyée par les Grecs à la "mimesis"). Il serait assez naturel que la pensée conceptuelle fût advenue bien après la pensée technico-esthétique, qui manifeste d'ailleurs plus directement le lien avec la nature, et même l'immersion dans la nature, pour la reproduire (par l'art), ou pour la prolonger (par l'outil). Quant à la science, elle se caractérise à l'origine (ou plutôt à ses origines, qui sont diverses), comme pratique et comme théorie ; et, d'une certaine manière, du moins dès qu'elle fut réflexive, avec la conscience d'être théorie, c'est-à-dire en admettant de raisonner dans l'abstraction même de la théorie, ayant distendu les liens qui l'avaient initialement formée sur le monde sensible et perceptible, comme on pourrait le reconstituer avec la genèse de la géométrie et l'arithmétique. Pratique ou théorique, la science est une activité qui se produit avant tout dans un univers de formes symboliques (mais déjà, d'ailleurs, chez l'être humain pensant, la sensation et la perception elles-mêmes transposent leurs éléments dans des signes et des formes symboliques).49 Les représentations symboliques de la science sont capables d'agir sur le monde. Et, avant elles, celles des grottes ornées, quelle que soit l'interprétation que l'on se donne de l'art pariétal, mais dont la signification était peut-être chamanique, si l'on en croit Jean Clottes et D. Lewis-Williams, dans leur livre sur Les chamans de la préhistoire.50 48 Dans les temps modernes, V Encydopédie de Diderot et d'Alembert, qui se définit comme Dictionnaire raisonné des sciences, des arts et des métiers, établit une distinction entre les art5 (c'est-à-dire ce qui a trait à la technique et à l'industrie) et les beaux-arts (les arts au sens contemporain). Cf. d'Alembert & Diderot [1751-1780]. 49 Sur les symboles comme éléments de la pensée et leur rapport à la perception, de nombreuses réflexions ont été développées dès le xvmè siècle (p. ex., Condillac) et surtout à partir du milieu du xixè, avec von Helmhoitz, Hertz, etc. Sur la pensée humaine dans ses différents domaines comme formes symboliques, voir l'ouvrage toujours fondamental d'Ernst Cassirer (Cassirer [1923-1925]). On pourrait aussi évoquer à ce sujet l'histoire de l'écriture (cf., p. ex., Zaïi & Berthier [1997]). 50 Clottes et Lewis-Williams [1996], Clottes [1998]. Selon cette conception, l'art rupestre serait la figuration d'expériences d'hallucinations et de transes faites par le chaman pour accéder au monde des esprits et des animaux-esprits. Le chamanisme est sans doute la plus ancienne religion du monde. L'interprétation de Leroi-Gourhan était différente, fondée sur une oposition sexuelle entre des principes masculins et féminins (Leroi-Gourhan [1965]).

Il existe fort probablement, depuis qu'il y a des représentations ou des productions d'objets par les hommes, un lien étroit entre l'action pratique (dans la forme et la finalité des instruments), la connaissance qui l'accompagne, ['esthétique (par la finition des outils, ou le dessin des animaux en mouvement, par exemple), les significations exprimées, et la conscience qui les explicite et les rend manifestes, et qui les organise ensemble. Ces relations nous sont mieux connues pour la période "historique", notamment par les documents écrits : du moins, pour ce qui est de la pensée des anciens Grecs et de leurs héritiers jusqu'à nous, mais elles le sont moins bien pour les autres civilisations ; il est cependant plus que vraisemblable que ces liens y aient existé aussi, sous des formes certes à première vue différentes de celles auxquelles nous avons nous-mêmes été initiés, et donc qu'ils aient été et soient universels. Notre science procède de plusieurs origines. Son caractère abstrait la rattache de façon privilégiée à la "source grecque", qui la fonde explicitement sur la raison, le logos, défini comme tel par sa fonction intellectuelle et qui lie, en les fondant ensemble, la science et la philosophie.51 Ce lien de nature et cette fonction, que caractérise l'exercice de la rationalité, s'est établi, ou du moins souvent accompagné, d'oppositions qui se sont succédées au long de l'histoire, selon du moins ce que nous savons des civilisations et des cultures méditerranénnes et européennes. Opposition, tout d'abord, de la science et de la pensée rationnelle contre le mythe (avec les physiciens ioniens, les philosophes présocratiques), puis contre l'opinion, par la philosophie, avec Socrate se heurtant aux sophistes, puis avec Platon, Aristote... Opposition, plus tard, contre l'autorité reçue, qui imposait à l'exercice de la rationalité des limitations étroites, celle de ['"Ecriture révélée" des religions, aussi bien que celle des auteurs anciens. En témoignent les affirmations de Galilée, de Descartes, de Pascal, sur la nécessité de juger par soi-même, par l'usage de la raison appuyée sur l'observation, dans les matières profanes et naturelles, et non plus par le recours à l'érudition,52 ce pour quoi on a pu dire, avec Henri Gouhier dans son ouvrage sur la Jeunesse de Descartes, qu'ils participaient de ['"anti-Renaissance".53 Opposition contre les abus des pouvoirs politiques et "spirituels", pour la liberté et la tolérance, aux XVIIè et XVIIIè siècles notamment54 et, d'une manière générale, pour l'autonomie et la liberté de la pensée.55 Ensuite, quand la science s'est trouvée intégrée aux structures de la société, avec l'industrialisation et l'avènement de l'âge du capitalisme et des impérialismes, la

51 Vernant [1965], Lloyd [1995]. 52 Cf. Paty[1997, 1999a]. 53 Gouhier [1958]. Voir aussi Mandrou [1973]. 54 "Faites naitre, s'il est possible", écrivait d'Alembert dans l'article "Géomètre" de {'Encyclopédie, "des géomètres parmi ces peuples [soumis à l'obscurantisme] ; c'est une semence qui produira des philosophes avec le temps et presque sans qu'on s'en aperçoive"; et avec la philosophie, l'idée de liberté... (d'Alembert et Diderot [1751-1780], vol. 7, 1757). Cf. Paty [1998a], p. 142. 55 Pierre Bourdieu montre, dans Les règles de l'art, comment, après des siècles de dépendance des pouvoirs, juristes, artistes, écrivains, savants ont acquis leur autonomie en parvenant à imposer leurs normes propres et leurs valeurs spécifiques, notamment celle de vérité, dans leur univers propre (Bourdieu [1992]). Voir aussi Bourdieu [1998], p. 106.

situation s'est faite plus complexe, et le lien de la rationalité scientifique (et technique) aux autres "valeurs universelles" (qui sont, en vérité, des conquêtes de l'homme dans son histoire) est apparu moins univoque et s'est distendu. La science (et sa rationalité) put servir aussi à promouvoir ou à justifier des contre-valeurs (de l'exploitation de l'homme à l'organisation de son oppression par des États totalitaires, et à son raval à l'état d'objet mercantile), cela au prix, il est vrai, le plus souvent, de perversions de sens. Pour se protéger de tout lien dans un sens ou dans l'autre, l'on proclama la "neutralité de la science" et, implicitement, celle de la rationalité. Et cependant, par-delà son fonctionnement dans des situations concrètes qui peuvent être les plus diverses, la rationalité (et la raison en général) quand elle se fait réflexive, se saisit comme une valeur, reconnue et librement choisie au même titre que les autres, et donc entretenant des liens avec ces autres valeurs. Par exemple, comprendre (dans la profondeur du sens de ce mot) a à voir avec liberté et dignité humaine (et, soit dit en passant, ce serait un terrible contre-sens de penser qu'il puisse y avoir un lien de nature entre rationalité et coercition).56 Dans ce sens, la rationalité, considérée dans sa dimension essentielle de valeur, ne manque pas de susciter aujourd'hui, comme elle le fera également demain, des oppositions en continuité avec celles dont nous venons de parler. Par exemple, contre les pouvoirs économiques sans partage qui visent à l'utilité ou au profit immédiat de quelques uns, sans égard pour l'intérêt général et le long terme, et mettent ainsi la planète en coupe réglée et en danger pour sa survie. Ce combat est aussi philosophique, contre les doctrines qui s'avèrente congruentes à cet état de choses, par exemple un certain pragmatisme nominaliste moderne qui rejette les notions générales et à vocation universelle comme celles d'humanité (et d'unité du genre humain), de vérité, de réalité, voire même, d'ailleurs, de rationalité, bien au-delà de ce qui est requis par la critique nécessaire de ces notions et de leur part d'idéalisme ou d'idéologie...57 (Mais il s'agit bien, au vrai, d'une autre idéologie, adéquate à une conception purement mercantile de la civilisation dont la valeur première et absolue, régulatrice des autres, serait le libre-échangisme au niveau mondial, à quoi tout le reste serait soumis : faisant du monde une collection d'objets à équivalent numéraire, dont la fonction est d'être acquis ou échangés). Ajoutons, enfin, l'opposition, toujours requise, contre les pouvoirs d'idéologies et d'ignorabimus de toutes sortes, fidéistes, sectaires ou fondamentalistes, auxquels on ajoutera, pour faire bonne mesure, les pouvoirs intellectuels et institutionnels des réductionnismes étroits (par exemple, disciplinaires).58 Ces oppositions rendent manifeste, par la négative, le lien qui existe entre, d'une part, la raison ou la rationalité et, d'autre part, la volonté et les choix éthiques. 56 Cette affirmation, qui m'apparait fondamentale, demanderait, bien entendu, de plus amples développements, contre de fréquentes allégations contraires. 57 Est ici visée, en particulier, la philosophie de Richard Rorty (Cf., p. ex., Rorty [1995]). 58 La catégorie sociale moderne de ['"intellectuel" s'est, pour une part, formée sur une ligne de comportement de l'ordre que nous venons d'indiquer, dans des oppositions qui ont porté sur les valeurs humaines en général, rassemblées autour de l'idée de raison. Sur l'histoire des intellectuels dans la période moderne en France, voir Charles [1990, 1996], Ory & Sirinelli [1992].

Notons, d'ailleurs, que la valorisation de la science, l'affirmation du désir de comprendre, est elle-même un choix d'ordre éthique.59 Le choix de la rationalité reste toujours, à chaque étape, une lutte (y compris dans la vie quotidienne, individuelle, sociale, politique) : lutte pour l'affirmation de la capacité de chacun à comprendre, c'est-à-dire pour l'affirmation de l'intelligibilité par les pensées individuelles, de Descartes à Kant, à Husserl, à Ricœur, et pour la liberté de comprendre, c'est-à-dire pour le libre-arbitre dans le jugement. Tant il est vrai qu'il ne peut être de connaissance authentique qu'acceptée de plein gré. Cette rapide évocation nous incite à nous demander quelles sont, aujourd'hui, /es figures de cette rationalité et à chercher si, bien qu'elle soit de nos jours souvent durement questionnée, à travers les grandes notions générales qui la sous-tendent, comme la vérité, l'universalité, la réalité (du monde), et bien que certains de ses traits puissent être remodelés, la rationalité ne comporte pas des caractères invariants, qui perdurent sous les transformations et - nous le verrons - sous les élargissements. L'abandon de certitudes anciennes qui, pensait-on, la fondaient, comme l'évidence divine au soubassement du cogito cartésien, ou l'an-crage dans le monde réel par l'expérience, ou son inscription dans les structures de la pensée du sujet (l'a priori kantien), ne l'annule pas pour autant, car elle continue d'être au cœur de l'expérience de la pensée, et notamment de la pensée scientifique. Mais elle réclame de nouveaux approfondissements. Des directions relativement neuves d'investigations sur la rationalité se présentent, grâce aux leçons de l'histoire des sciences, qui peuvent enrichir nos conceptions sur elle (la rationalité, le rationnel), et l'étayer non comme une hypothèse, optionnelle, mais comme un fait fondateur, avec des solidarités inédites pour une grande part. Par exemple, comme nous l'avons rappelé plus haut, que la rationalité n'est pas étrangère à la volonté. Et encore, qu'elle entretient des liens, qui commencent à peine à être inventoriés, avec \'esthétique (et cela, bien que le vrai ait été dissocié du beau, auquel l'antiquité grecque l'identifiait). Et aussi, qu'elle est féconde, plus encore que par l'explication, par l'invention. Voici, précisément, un thème plutôt nouveau, qui pourrait enrichir considérablement la philosophie des sciences, celui de invention dans /a rationalité, de la création scientifique, création de formes rationnelles et de connaissances objectives. L'invention scientifique, qui a partie liée, évidemment, à la croissance des sciences, qui en est, en quelque sorte, l'élément significatif que pourrait saisir une micro-histoire des sciences, en vue de comprendre comment se sont établis les contenus nouveaux des sciences qui se font jour, et rechercher des généralisations possibles. Il serait tentant, ici, de faire un parallèle avec la micro-histoire pour l'histoire sociale au sens de Carlo Ginzburg, qui s'intéresse aux

59 Plusieurs savants contemporains parmi les plus grands l'ont clairement affirmé: voir, par exemple, Albert Einstein (notamment dans un texte sur "Les motifs de la recherche", et le "temple de la science", en hommage à Max Planck, cf. Einstein [1989-1993],vol. 5, pp. 171-173, et commentaire dans Paty [1993], chap. 8), et Jacques Monod dans Le hasard et na nécessité (Monod [1970]), etc....

singularités, aux stratégies individuelles à l'intérieur d'un microcosme pour les rattacher à des significations plus larges, voire à des invariants historiques.60 La subjectivité, la singularité, des pensées et des actions humaines, demande la communication des unes aux autres pour qu'elles puissent s'inscrire (pour nous) dans l'histoire et, de manière effective, pour qu'elles puissent contribuer à faire l'histoire (l'histoire tout court, ou l'histoire des sciences, mais la seconde est inscrite dans la première, même si elle en constitue un chapitre très particulier, tout comme l'histoire de l'art, d'ailleurs, et sans fermeture, puisqu'elle tient aussi aux sciences elles-mêmes et à la philosophie).61 Ces subjectivités et ces singularités ne sont pas effacées ou abolies par le désir d'objectivité, qui marque le projet même de connaissance scientifique: leur prise en considération est essentielle si l'on veut que notre conception de la connaissance échappe à l'épure d'un schème abstrait, qui rejoindrait d'ailleurs l'idée d'explication universelle par un "consensus social" sur des contenus somme toute secondaires, "sécrétés par l'époque", pour ainsi dire, sans point d'application particulier significatif. Car il est question, fondamentalement, pour ce qui est de la science, d'intelligibilité, et celle-ci n'est réalisée que chez des individus tous particuliers. Cette intelligibilité n'est pas uniforme, puisque les savants euxmêmes comprennent chacun différemment (la plupart du temps, et jusqu'à un certain point) les questions discutées, les problèmes à résoudre, voire les propositions admises comme résolues. On voit bien, par là, que les inventions, même scientifiques, sont toujours des oeuvres individuelles, des "créations" au sens propre, comme on l'entend pour les arts.62 Sans l'aspect créatif, qui tient à la diversité des formulations et des réponses possibles à des questions ou des problèmes, à la diversité des "styles scientifiques" dont la caractérisation est complexe (idiosyncraties personnelles, "programmes épistémologiques" propres, inscription dans des "traditions scientifiques" diverses par l'enseignement, l'expérience ou la culture),63 il n'y aurait pas d'invention, pas de nouveauté, et partant pas de science comme réponse à la demande d'intelligibilité. Et enfin, pour en terminer avec le paysage qui s'offre à nous, on ferait grand profit de l'étude des formes de la rationalité selon d'autres configurations, qui apparaissent dans les sciences d'autres cultures, ainsi que de la communication entre ces formes différentes et de la possibilité de les traduire l'une dans l'autre, par exemple par leur rapport à l'utilité, à l'abstraction, à la preuve, etc... Il reste intéressant (et réconfortant) de constater que des connaissances formulées dans des cultures très différentes sont en grande partie communicables, et qu'il est possible de les identifier comme appartenant aux mathématiques, ou à la physi-que, ou à la botanique, etc.. Par exemple, ce qui est mathématique pour le savant jésuite européen qui vient en Chine au XVII è siècle a un correspondant dans la

60 Ginzburg [1989] ; Levi [1991]; Dosse [1999], p. 74. 61 Paty [1990]. 62 Sur la création scientifique, voir Paty [1999e]. 63 Sur ces notions, voir notamment Granger [1968] éd. 1988, Hacking [1992], Paty [1990, 1993, 1996].

pensée de son interlocuteur chinois, ce qui fait qu'ils sont conscients de parler sur un même terrain.64 Cette reconnaissance tacite est en elle-même un fait d'invariance et d'universalité quant à la rationalité, d'une importance sans aucun doute considérable. Construction sociale et historicité Les adeptes des conceptions "relativistes" sur la connaissance qui aboutissent, dans leurs versions extrêmes, à considérer les contenus scientifiques comme vides de sens, ont invoqué, pour justifier leurs conceptions, les changements de la rationalité, ou dans la rationalité, ou de notre conception de la rationalité. Mais que de tels changements aient effectivement lieu, comme des philosophes eux-mêmes l'ont indiqué, de Hegel à Bachelard, Granger et d'autres,65 cela ne signifie pas que la rationalité ne soit définie que comme étant "socialement construite", référence faite à une expression si commune en "nouvelle sociologie des sciences"66 que l'on n'attend plus que la parution d'un titre comme "Thé social construction of reason" ; nous venons bien d'avoir A Social History of Truth, qui porte quasiment cette interprétation par son titre même.67 L'idée va bien au-delà de celle d'une construction sociale de "la science", sur laquelle on peut argumenter, considérant la diversité des dimensions et des fonctions de cette dernière. Mais les idée de raison et de rationalité, liées au discernement du vrai et du faux, et qui sont la base de tout raisonnement et constituent l'outil intellectuel de la mise en relation, sont plus centrales, dépouillées, moins flexibles que celle de science, sauf à utiliser ces termes dans une acception laxiste et déjà "social-réductionniste", comme, par exemple, "la raison du plus fort". Mais on voit bien que ce serait là pur sophisme, et faire prendre un jeu de mots pour une démonstration. Le thème des changements de rationalité mérite mieux que de telles variations sur des miroitements de surface. Il est fondamental pour qui se préoccupe de la connaissance en la rapportant à la pensée. Si nous l'examinons d'une manière plus approfondie, en tentant de caractériser positivement de tels changements, nous pouvons les considérer, en fait, comme des élargissements de la rationalité, qu'il sera possible de décrire et de comprendre en les rapportant à des arguments de raison, saisis dans leur historicité même. Il ne s'agit en rien de sauts arbitraires d'un "paradigme" à un autre qui serait imposé socialement. Un tel examen, dont nous esquisserons plus loin quelques éléments, nous assure, malgré la défaite des absolus intemporels qui seraient fondés une fois pour toutes, de la capacité et de la puissance de la pensée à se représenter et à expliquer le monde, et aussi bien à se représenter elle-même. Mais il est utile, au préalable, de nous interroger sur ce que peut signifier, tant au plan de l'histoire qu'à celui de la science, ce que l'on qualifie de

64 Voir Jami [1992] et d'autres travaux du même auteur. Cf. Paty [1997, 1999aetb]. 65 Hegel [1965], Bachelard [1949], Granger [1955]. 66 lan Hacking en a fait récemment l'inventaire dans son livre Thé Social Construction of What ? (Hacking [1999]). 67 Shapin [1994].

"socialement construit". Le sens qui doit être éliminé d'emblée, c'est celui qui nierait la signification propre des contenus, sur les divers plans historiques ou scientifiques, c'est-à-dire la réduction de tout niveau de signification à un simple constat de fait social, autrement dit le réductionnisme social ou sociologique. Même "socialement construite", une pensée symbolique possède son niveau propre de signification. Il serait peut-être préférable, à cet égard, de parler de pensée, par exemple, de représentation, socialement "constituée", plutôt que "construite", qui implique une sorte de totalisation et paraît plus susceptible de favoriser les glissements réductionnistes. La notion de construction sociale n'est que faiblement explicative en ce qui concerne les matériaux, l'architecture et la signification propre donnée à la construction en question. Construite pour les besoins de la topographie, la géométrie fut, dès ses débuts, une science des figures et de leurs proportions, et non une science de la société qui a éprouvé la nécessité de mesurer des distances et des surfaces sur la Terre. La vérité, c'est que, dès qu'elle s'est trouvée ainsi formulée en référence à cette question, la géométrie définissait par là-même son objet, et celui-ci sortait aussitôt du domaine du social en tant que tel : sa rationalité propre, son /ogos, échappaient à l'opinion et faisaient sens directement. La rationalité ainsi conçue était en même temps consciente d'elle-même, et déterminait une conception précise de la science et de la philosophie. Lorsqu'on dit qu'une représentation symbolique, une science ou un élément particulier de savoir ont été élaborés ou construits "en société", on exprime, en réalité, l'idée qu'il l'ont été par les moyens et dans les formes propres de la pensée humaine, en l'état d'existence d'une société caractérisée dans le temps et dans l'espace, de ses savoirs acquis et de ses valeurs admises. Dire que ces éléments d'une forme culturelle sont "construits socialement" est une affirmation qui n'apporte en elle-même que peu d'éléments de connaissance (sauf quant aux cir-constances), prise entre les deux extrêmes de la tautologie ou du sophisme. En d'autres termes, si l'on porte ainsi utilement l'accent sur les relations entre ces représentations et la vie sociale, on ne saurait en tirer grand chose sur ce que sont ces éléments eux-mêmes, à plus forte raison s'ils peuvent être abstraits de significations directement sociales, comme ceux des contenus de sciences exactes ou de la nature, mais aussi, à un certain niveau de profondeur, ceux des productions artistiques. Or, ce sont pourtant ces éléments qui font la chair même de ces formes culturelles. Constitués, élaborés, construits, par des pensées organisées socialement, leur signification est à prendre à leur niveau propre, portant sur ce qu'ils désignent et sur la manière dont ils le désignent. Etant construits, ils ne sont pas donnés de tous temps, ils ont une origine, se transforment, et ne sont pas voués à l'éternité ou à l'absolu. Ils sont historiques. Il nous faut nous interroger sur ce que signifie cette historicité, étant acquis que le sens historique lui-même est un de ces éléments de connaissance qui sont apparus dans l'univers symbolique, historiquement situé comme les autres, et cependant porté, dès que l'on en prend conscience, à un certain rang d'universalité : tout est historique (j'entends, tout ce qui vient des humains est historique), ce qui

veut être un écho à la belle définition que Marc Bloch donnait de l'histoire : "la science des hommes dans le temps".68 Tout ce qui est des humains est historique, même s'ils n'en ont pas conscience. Il semble, par exemple, que les grandes civilisations de l'Inde, si riches philosophiquement et scientifiquement, n'aient pas eu le sens de l'histoire, ce qui se voit à l'exposition même de leurs récits fondateurs et de leurs systèmes de pensée. Il y aurait, bien sûr, beaucoup à dire sur la naissance du sens historique et de la conscience de l'historicité, sur les rivages de la Méditerranée et en Occident. Ce sens est beaucoup plus ancien, à coup sûr, que les prétentions arrogantes du réductionnisme social qui voudrait l'accaparer sous des formes appauvries. Car enfin, une fois le sens de l'histoire affirmé, tout le travail sur l'historicité reste à faire. Il faut examiner dans le détail, pour une société donnée (une culture, ou une civilisation, entendues dans le sens anthropologique le plus neutre possible), l'ensemble des modalités diverses qui la sollicitent : l'organisation sociale, la production technique, les idéologies et les systèmes de croyances et de valeurs, les formes d'expression, l'esthétique (voir, sur celle-ci, les remarques qui précèdent), les connaissances et les systèmes de savoir et de pensée, c'est-à-dire la science et, sans doute, la philosophie, ou ce qui en tient lieu sous un autre nom ou simplement de fait.69 L'historicité traverse toutes les formes de pensée et d'action humaine, et déjà cette diversité laisse voir que chaque forme possède ses modalités et ses justifications propres, qui non seulement ne se dissolvent pas dans ce caractère historique, mais qui ont pris naissance et se sont développées, se sont constituées, selon ce caractère même, qui a présidé à l'arrangement de leurs "matériaux" (symboliques et concrets). C'est au cours de ce développement que se sont créés et mis en place les éléments (conceptuels) d'intelligibilité qui permettent l'assimilation, à un état donné de connaissance, et ces éléments eux-mêmes informent ceux de l'état qui suivra, le rendant possible. C'est en ce sens que le mathématicien Jean Dieudonné, l'un des membres éminents du mouvement Bourbaki, écrivait : "Je pense qu'il n'est pas possible de comprendre les mathématiques d'aujourd'hui si l'on n'a pas au moins une idée sommaire de leur histoire".70 A cet égard, les mathématiques sont peut-être les plus visiblement historiques des sciences exactes, car le fil de cette histoire peut être suivi sur une longue durée, à la différence de l'astronomie, de la physique, de la chimie, de la géologie, de la biologie, par exemple, dont les développements et les remaniements récents tendent à effacer, vis-à-vis de leur sens actuel, leur histoire précédente. Ce qui, bien sûr, n'atténue en rien le fait qu'elles sont tout autant, elles aussi, le fruit et l'objet d'une histoire, et que les contenus conceptuels ont été constitués à la faveur de cette histoire, par strates d'organisations successives, qu'il est possible de retrouver sous le sol actuel, comme des couches géologiques malgré les

68 Bloch [1949], p. 4. 69 Que ces notions ne soient pas réflexives dans une culture donnée ne signifie pas pour autant qu'elles en soit absentes. 70 Dieudonné [1987], p. 10.

plissements des mouvements (des réorganisations) de terrain qui sont survenus depuis. Donc, une théorie mathématique (ou autre), comme une cathédrale, a été historiquement construite ou constituée : mais on n'a fait, en en prenant conscience et en l'énonçant, que prendre acte d'un fait, condition nécessaire à la réalisation d'une possibilité, et sa matrice. Cela ne nous amène pas plus loin qu'au seuil de cette construction, dans laquelle il nous faut pénétrer pour en saisir le sens. Il nous faut voir ce que représente, dans la pensée symbolique des hommes (ceux de ce temps-là, mais aussi ceux d'autres temps), cette théorie mathématique, ou cette cathédrale. Quelle en est la signification, pour eux et pour nous ? Signification pour eux : nous, de notre présent, tentons de comprendre ce que cela signifiait pour les hommes de ce temps-là. Nous tentons d'entrer dans /es contenus de sens, entendus selon les systèmes de pensée de l'époque, nous tentons de comprendre dans l'historicité, en établissant par là-même ce qu'est la discipline (la science) historique, au-delà du récit descriptif. Car il est question de comprendre, c'est-à-dire d'établir un pont entre nous et cette époque, concernant cet élément de représentation abstrait ou architectural, pour tenter de saisir la pensée des êtres humains de cette époque-là, du moins des créateurs qui cons-truisaient et vivaient ces formes, qui les concevaient (eux-mêmes inséparables des contemporains qui les recevaient ou les habitaient). Il est question de saisir cette pensée en elle-même, selon la "systématique" de ses significations propres, sans projeter sur elle nos exigences ou nos critères d'intelligibilité et de significations. Tel est le problème-clé de la méthode historique, sur lequel nous reviendrons. Signification pour nous : je l'entends de la manière suivante. Par rapport aux formes de pensée (mathématique, dans le cas indiqué), d'expression, ou de technique (architecturale, par exemple) que nous connaissons, en notre temps, quel est /e lien (s'il en est, et il est difficile de nier longtemps qu'il y en ait un), qui court de ces formes anciennes aux formes actuelles ; et surtout, quelle signification neuve les formes actuelles, qui étaient impensables à l'époque ancienne, confèrent à ces premiers achèvements ? Nous tentons, autrement dit, de concevoir comment nos contenus de sens, nouveaux par rapport à ceux qui les ont précédés, ont été rendus possibles. Nous tentons de comprendre, par une démarche rétrospective, comment ces formes qui nous sont signifiantes et qui correspondent à notre rationalité et à notre esthétique actuelles, ont pu être effectivement constituées. C'est-à-dire, de comprendre, non seulement les conditions de possibilité, mais la réalisation effective de telles possibilités, en ces contenus de connaissances ou en formes d'expression qui constituent aujourd'hui même notre univers intelligible et signifiant. La connaissance du passé, dans sa signification même, nous permet de concevoir la possibilité et les modalités de constitution de notre connaissance actuelle et, par là, sa signification, du moins en partie. Une telle démarche, qui constitue proprement la démarche historique (histoire sociale, histoire des sciences, des techniques, de l'art, des idées), pose en préalable le bien-fondé de s'intéresser aux contenus de sens, pour l'un ou l'autre des "objets" concerné et des disciplines correspondantes (leurs définition et leurs

frontières entre elles fussent-elles mobiles et fluctuantes dans le cours de l'histoire). J'ai évoqué surtout des connaissances, des techniques, ou des arts, mais on en dirait autant des conceptions sociales, des croyances et des valeurs, morales, éthiques ou spirituelles. Toute forme symbolique et tout système de telles formes suscite le regard historique et pose le problème du rapport de ^historicité et des contenus de sens. Je me contenterai dans la suite de considérer la connaissance, et singulièrement la connaissance scientifique, mais il est clair que l'histoire est une, comme la pensée, siège des actions humaines qui sont inscrites dans l'histoire et la tissent. Historicité des contenus de sens Représenter le déroulement historique, cela ne peut se faire en temps réel ou en grandeur nature. On connaît ce conte de Jorge Luis Borges dans lequel un géographe minutieux, pris d'un souci de réalisme intégral, se propose d'établir la carte d'une certaine région de la surface de la Terre le plus fidèlement possible : quand elle est achevée, elle vient recouvrir exactement l'étendue représentée. La carte est à la dimension même du terrain. D'un autre coté, comme l'écrivait Henri Poincaré, le cerveau de l'homme, qui est dans l'Univers, ne pourrait à lui seul contenir tous les éléments de l'Univers.71 La représentation de la réalité, de la réalité du monde naturel ou de la réalité historique, ne peut coïncider avec cette réalité (et, d'abord, parce qu'elle est de nature symbolique, transcrite en forme de signes, de mots ou d'images, qui ont, dans la pensée, la fonction de représenter cette réalité, mais qui sont d'une nature totalement différente). Les faits qui serviront de base à nos représentations ne peuvent être exhaustifs et doivent être choisis, en histoire comme en science, pour la signification de leurs contenus. Dans ce sens, Marc Bloch écrivait, dans Apologie pour l'histoire, ou Métier d'historien : "Face à l'immense et confuse réalité, l'historien est nécessairement amené à y découper le point d'application particulier de ses outils ; par suite, à faire en elle un choix qui, de toute évidence, ne sera pas le même [que celui d'un autre spécialiste dont l'objet serait autre, un biologiste, par exemple], et qui sera un choix d'historien" ; "ce qui est", ajoutait-il, "un vrai problème d'action", qui poursuit l'historien tout au long de ses recherches.72 C'est aussi pourquoi le regard d'après coup est utile, et permet de faire de /'histoire, et non pas des (petites) histoires, sans signification profonde. S'il est utile et nécessaire en histoire, ce regard rétrospectif ne l'est, à coup sûr, pas moins en histoire des sciences, permettant de considérer pour une même époque des éléments (des faits de savoir) dont le lien ne pouvait pas être aperçu sur le moment, mais dont la réunion s'avère par la suite structurellement signifiante pour

71 Poincaré [1909], éd 1918, chap. 2, p. 20. 72 Bloch [1949],p. 2.

une science donnée, et permet de caractériser factuellement, dans /e temps historique, le progrès d'un chapitre de la connaissance scientifique. Donnons-en un exemple particulièrement parlant et significatif, celui de deux résultats obtenus par Galilée, sans apparence de lien entre eux, et d'ailleurs mentionnés indépendamment l'un de l'autre, respectivement dans ses deux grands ouvrages, les Dialoghi et les Discorsi publiés à plusieurs années de distance : la relativité des mouvements, d'une part, et l'égalité de l'accélération due à la pesanteur pour tous les corps tombant à une hauteur donnée, d'autre part. La première, la relativité des mouvements (d'inertie, qui est une conséquence du principe d'inertie)73 est mise en avant et argumentée par Galilée dans les Dialogues sur les deux plus grands systèmes du monde, en faveur de la supériorité du système de Copernic : Galilée y réfute l'argument aristotélicien, repris par les scolastiques, pour l'absence de mouvement de la Terre, basé sur l'observation d'une flèche rapide, lancée à la verticale, qui retombe au même endroit, et non en arrière. Quant à la seconde, qui appartient à la loi de la chute des corps, selon laquelle l'accélération due à la pesanteur à hauteur donnée est indépendante de la nature et de la grandeur du corps qui tombe en chute libre, Galilée la démontre dans les Discours sur deux sciences nouvelles, ouvrage dans lequel il établit la première loi quantitative et temporelle de la mécanique et fonde, vu rétrospectivement, cette dernière comme science.74 Or, cette conjonction, qui ne pouvait être alors qu'inaperçue, puisqu'elle ne revêtait aucune signification particulière, et qui serait apparue au mieux comme purement fortuite à qui l'eût notée, prit, près de trois siècles plus tard, avec Einstein, une signification théorique précise, qui fut féconde et qui devait s'avérer fondamentale : elle fut le point de départ de son cheminement vers la théorie de la relativité générale. Einstein associa structurellement le principe de relativité (généralisé aux mouvements quelconques) et la loi de Galilée, qu'il formula comme "principe d'équivalence" : équivalence de la masse inertielle et de la masse gravitationnelle, ou encore équivalence (locale) d'un mouvement uniformément accéléré et d'un champ de gravitation homogène.75 Bien entendu, pour que cette conjonction aît pu devenir explicite et opératoire, des transformations de formulation avaient été nécessaires, tributaires des progrès de la science des mouvements (la mécanique). Ces transformations, qui correspondaient en fait à de véritables modifications conceptuelles, n'étaient pas à la disposition de Galilée ; Newton non plus, pour d'autres raisons historiques, ne pouvait pas les penser, bien qu'elles concernassent la "physique newtonienne" et, fondamentalement le concept de mas5e introduit et défini par Newton dans ses Principia.76 La masse figure de deux manières différentes dans la loi de la 73 Les mouvements d'inertie sont les mouvements rectilignes uniformes. Le principe d'inertie, incomplètement formulé par Galilée (qui ne l'abstrayait pas de la pesanteur), stipule que tout corps animé d'un tel mouvement le garde sauf si quelque cause l'oblige à en changer. 74 Galilée [1 632, 1638]. Cf. Koyré [1 935-1939], Geymonat [1957], Clavelin [1968], Drake [1980], Mariconda [à paraître]. 75 Einstein [1907]. Voir Paty [1993], chap. 5 ; [1999d]. 76 Newton [1687].

dynamique et dans celle de la gravitation universelle de Newton. Dans la première, qui exprime la force comme le produit de la masse par l'accélération, la masse d'inertie, pensée comme "quantité de matière des corps", figure comme le paramètre, ou coefficient, reliant la force et l'accélération (Newton en donnait une formulation moins précise, en termes de changement de la quantité de mouvement et ne disposait pas de la forme différentielle pour exprimer l'accélération). Des études critiques éclairantes de ces concepts ont été données notamment par Ernst Mach, Heinrich Hertz, Henri Poincaré, puis Albert Einstein, sans compter, bien auparavant, par Jean d'Alembert.77 Dans la seconde loi newtonienne, celle de l'attraction ou gravitation universelle, la masse du corps figure comme le coefficient de la loi d'attraction : elle ne s'identifie à la première que pour rendre compte de la loi de Galilée de la constance de l'accélération à hauteur donnée : les deux coefficients, qui figurent respectivement dans l'une et dans l'autre lois, sont éliminés de la formule de l'accélération s'ils sont égaux, ce qui donne la raison fondamentale de la loi de Galilée, la constance de l'accélératon pour tous les corps, indépendammennt de leur masse, à hauteur donnée.78 Cette propriété d'égalité, considérée par Newton comme une coïncidence, fut conçue par Einstein79 comme une identité, c'est-à-dire comme correspondant à un fait physique général et fondamental, susceptible d'être érigé en "principe physique : le "principe d'équivalence" entre la masse d'inertie et la masse gravitationnelle. L'égalité des deux coefficients de masse, reliés l'un au mouvement accéléré'(la masse d'inertie), l'autre au champ de pesanteur (la masse gravitationnelle), qu'Einstein proposa ainsi de considérer comme une identité, lui fit concevoir l'"expérience de pensée" (donnant à voir un phénomène physique) de l'accom-pagnement d'un mouvement de chute libre (tous les corps situés à l'intérieur d'un ascenseur sans câble tombent avec la même accélération, et sont donc au repos les uns par rapport aux autres). D'où l'équivalence locale du mouvement accéléré et du champ de pesanteur, dont l'explicitation à l'aide de l'outil mathématique du calcul tensoriel devait conduire à la théorie de la relativité générale.80 Cet exemple fait bien voir ce que l'on gagne à tenir pleinement compte de l'historicité des connaissances : on se donne ainsi les moyens de comprendre le mouvemment de leur constitution progressive, de la formation des nouvelles significations qu'elles engendrent. Quand on parle d'historicité des contenus (d'une science), ce n'est pas pour dire que l'historicité dissoudrait les contenus, mais au contraire qu'elle en tisse la forme avec des matériaux qui lui ont été donnés, et

77 D'Alembert [1 743], Mach [1883], Hertz [1894], Poincaré [1902, 1905], Einstein [1946]. Cf. Paty[1999f]. 78 La force de pesanteur peut s'écrire de deux manières, par l'une et l'autre lois. De l'égalité des deux formes on déduit l'expression de l'accélération comme propor-,. ,, , , m M m,. M tionnelle au rapport des deux masses. F = m, =C " ' i _ ——, d'où y = —— r2 m l'accélération y est constante localement (à r donné), on doit avoir 79 L'égalité des deux masses était constatée au temps d'Einstein avec une très grande précision, notamment par les expériences d'Eôtvos réalisées dans les premières années du xxè siècle. 80 Einstein [1907, 1916]. Voir Paty [1993].

dont la nature (de contenus conceptuels, contenus de pensée) résiste à toute réduction externe (sociale). Il parait légitime de dire, inversement, qu'il n'est d'historicité qu'en raison des contenus, puisque c'est la compréhension de la manière dont ceux-ci se sont constitués qui permet de concevoir, précisément, leur historicité. On pourrait transcrire cette remarque sur les contenus et l'historicité en termes de rapports entre l'épistémologie (conçue comme l'étude des sciences selon les contenus de sens) et l'histoire des sciences (l'étude des sciences selon le déroulement historique), par la formule connue: "L'épistémologie sans histoire des sciences est vide, l'histoire des sciences sans épistémologie est aveugle".81 L'intelligibilité sous le signe de la rationalité Du point de vue de l'histoire, les formes symboliques correspondant à la diversité des pensées et des actions humaines et, en particulier pour l'histoire des sciences, celles qui correspondent à des connaissances scientifiques, constituent un donné de fait qu'il s'agit de comprendre, c'est-à-dire d'interpréter ou d'expliquer. Cette compréhension suppose la possibilité d'une communication, fût-elle indirecte et partielle, entre ces formes du passé et celles qui habitent le sujet présent et dirigent son regard. La connaissance ou la science de l'histoire fait elle-même partie de ce "regard" actuel, informé de ce qu'il connait mais en même temps sachant se décentrer ou, du moins, conscient de cette nécessité. Concevoir ces formes comme produites dans le passé implique ce regard, sinon "scientifique" au sens propre (ce qui impliquerait de préciser quelle science est l'histoire), du moins à visée objectivante : comprendre ce qui était, au plus près possible de ce que cela était, c'est-à-dire de la signification que cela avait alors pour les sujets et les protagonistes de cette connaissance et, à cette fin, tenter de l'installer dans le système ancien de signification reconstitué. C'est cela que l'on veut dire quand on parle, pour une connaissance historique, de comprendre, d'interpréter, d'expliquer... Il s'agit d'établir le système de compréhension, historiquement pertinent, au sein duquel les éléments symboliques porteurs de contenus signifiants, par exemple les concepts, se donnent sens les uns aux autres par leurs relations et font sens dans le corps plus ample des connaissances de l'époque. Ce système peut alors être mis en relation avec le notre par rapport auquel nous aurons su nous décentrer, ou avec d'autres systèmes de connaissances correspondant à des étapes intermédiaires dans le cours de l'histoire. La notion d'explication elle-même subit des transformations au fur et à mesure que l'on a affaire à des exigences différentes pour la connaissance et que de nouvelles exigences se créent. Ce sont les références mêmes de l'explication qui changent avec d'autres demandes d'intelligibilité. Nul doute que la loi de la chute des corps fût, pour Galilée, en même temps qu'une description de comment tombent les 81 Transformée depuis Kant par, entre autres, Carnap, Einstein, Feyerabend.

corps (la loi étant donnée par des relations entre des grandeurs adéquatement choisies), une explication, au moins relative puisqu'elle rattachait entre elles les chutes de différents corps et les ramenait à upe même sorte de mouvement (uniformément accéléré, indépendamment d'ailleurs de la vitesse intiale, considérant le principe d'inertie et l'addition des vitesses, qui rendaient équivalentes les chutes verticale et parabolique): mouvement distinct d'autres mouvements possibles et existants, mais en rapport à eux, et cette explication fût-elle partielle, puisqu'elle ne donnait pas la forme de la loi. Mais opposer la "description" et une "explication", comme cela fut courant plus tard, apparaîtrait ici schématique et serait se concentrer arbitrairement sur l'un des aspects du problème. Du point de vue de l'historicité, la loi de Galilée de la chute des corps était explicative en ceci du moins qu'elle en donnait l'intelligibilité, qui n'était pas acquise jusqu'alors, quand la conception de la géométrie des trajectoires était en défaut : au lieu d'être imposée par une idée préalable comme dans la pensée antérieure (pour laquelle seules la ligne circulaire ou la ligne droite étaient concevables comme trajectoires naturelles),82 la courbe balistique suivie par le corps en chute libre était reconstituée à partir d'une pensée du mouvement et de son unification (entre les mouvements "naturels", continus, et "violents" ou par chocs). C'est dans ce sens qu'elle était explicative. Mais cette intelligibilité, ou cette explication, se heurtait aussitôt à de nouvelles questions, et tout d'abord sur la relation quantitative (le rapport des distances parcourues et des temps) qui déterminait les propriétés balistiques du mobile. L'explication n'en était donc une que jusqu'à un certain point, et l'intelligibilité du phénomène demandait une intelligibilité plus grande, sur la raison des relations constatées. Il fallait donc pousser au-delà, tenter de comprendre les causes, comme Descartes (qui concevait les causes par contacts et proposa sa théorie des tourbillons), ou comme Newton (avec sa théorie de la force instantanée d'attraction universelle pour la gravitation). Mentionnons, en passant, la rupture entre l'intelligibilité cartésienne et l'intelligibilité newtonienne qui survint alors, largement soulignée par Newton en conclusion du second livre des Principia (l'impossibilité de rendre compte du mouvement des planètes par des tourbillons de matière éthérée) et rendue nécessaire par la connaissance plus précise des phénomènes et des lois de la mécanique (exposée au livre 1 sur le mouvement des corps et mise en œuvre au Livre III sur le Système du Monde).83 L'attraction de gravitation newtonienne constituait un nouveau principe d'intelligibilité, sans être toutefois elle-même intelligible, c'est-à-dire sans pouvoir être expliquée par des termes connus. C'était une hypothèse, un saut conceptuel, justifiée empiriquement. Le concept d'attraction comportait cependant davantage qu'une simple hypothèse empirique, qui l'entraînait en fait en direction d'une conception rationnelle, celle d'une propriété physique fondamentale, attachée à la nature même des corps. C'est ce qui transparaît dans l'analyse 82 Cf. Paty[1999d]. 83 Newton [1687].

épistémologique qu'en fit d'Alembert au milieu du XVIIIè siècle, pour en rechercher une justification en raison.84 Cette justification de l'attraction universelle lui venait de ce que la physique des corps célestes pouvait être rationalisée autour d'elle. Il fallait donc bien la concevoir et, pour s'en faire ainsi une idée intelligible, abandonner l'idée de l'expliquer dans les termes connus et faussement évidents des actions de contact, tout en l'admettant, au contraire, comme un principe d'explication pour la science qui la faisait intervenir (l'astronomie) et, par une définition fondatrice, pour la loi empirique qui la manifestait (la loi de la force de gravitation comme inverse carré des distances). Admise comme une propriété générale des corps, elle fonctionnait ainsi comme un concept rationnel, sans toutefois être rationnelle au sens où ses raisons seraient analysables. Mais en cela, faisait remarquer d'Alembert, elle ne différait pas d'un autre concept de la mécanique newtonienne, l'impénétrabilité, qui fait la distinction entre les corps et l'étendue qu'ils occupent et maintient l'identité de ces corps dans leurs chocs entre eux. Cette propriété, postulée par Newton et qui ne choquait personne, n'était pas plus compréhensible, au fond, à bien y regarder, que celle de l'attraction universelle (et il en allait de même, en définitive, de tous les principes et propriétés physiques). D'Alembert trouvait, en quelque sorte, un compromis entre le rationne] et l'empirique : l'empirique (ou le contingent) est un rationnel qui s'ignore. L'attraction devait se rapporter, comme les autres principes physiques généraux de la mécanique, à quelque vérité nécessaire, même si elle avait d'abord pu être formulée, provisoirement, de manière contingente et toute empirique, en raison de notre ignorance. Sa rationalité n'était pas apparente, mais elle se manifesterait dans la configuration d'une physique plus perfectionnée où les faits et les lois isolés seraient réunis aux principes généraux et aux lois universelles acceptés et fondés en raison sous une même évidence. Le caractère empirique pour nous, pourrait-on dire dans ce cas, n'aura été que la manifestation, partielle et encore obscure, d'une rationalité supérieure, c'est-à-dire de quelque chose dont l'explication se trouve en avant, et non en arrière. Cet essai de justification par d'Alembert correspond, en fait, sous le point de vue de l'intelligible, à une extension du domaine de la rationalité. Cette extension n'est pas pure transparence, puisqu'elle admet que l'on prenne appui sur une base obscure, sur un concept qui s'impose à la pensée, mais qui est venu de ['"extérieur" (entendons : du monde extérieur à la pensée, qui l'impose à celle-ci), par l'"évidence des faits". L'élargissement du rationnel prend donc ici au début la voie, au moins apparente, de l'empirique. Mais cet empirique est appelé, pour d'Alembert, à être subsumé dans un rationnel ultérieur, dont il remplit déjà la fonction en étant hissé à la généralité et formulé comme une hypothèse théorique qui prend en pratique rang de principe. On doit remarquer que, même pour des conceptions moins uniment rationalistes que celles de d'Alembert, nombreux sont

84 D'Alembert, article "Attraction" dans l'Encyc/opédie (D'Alembert & Diderot [1751-1780], vol. 1), et D'Alembert [1758]. Voir Paty [1998a].

en physique les exemples de cette "rationalisation forcée" de concepts qui se sont imposés "par construction", mais sans explication de type analytique ou causal. Telle est peut-être, d'une manière analogue et générale, la leçon historique de la découverte et de la formulation des "principes physiques" (conservation de l'énergie, second principe de la thermodynamique, principe de relativité, etc.). On commenterait de manière assez semblable la "laïcisation" d'un principe d'expression plus formelle et de signification moins intuitive comme celui de moindre action, réalisée avec la mécanique de Hamilton et avec toutes les théories physiques ultérieures qui le mettent en œuvre, sans nulle référence à une finalité quelconque comme dans sa forulation originelle par Maupertuis. Le principe de moindre action est un principe "formel", devenu fondateur pour la physique mathématique et théorique, dont le contenu physique, qu'il exprime par sa forme et sa fonction, correspond à une sorte d'expression synthétique de la théorie, ramenée à ses traits essentiels, et embrassant l'ensemble des phénomènes du domaine correspondant.85 Le principe de moindre action exprime synthétiquement un ensemble complexe de relations imbriquées entre des grandeurs caractéristiques d'un système physique, ces relations ayant été révélées ou vérifiées à la faveur de l'expérience. Il porte en lui, à cet égard, en quelque sorte de manière emblématique, la signification de ce qu'est un système physique mathématisé. Ce principe nous fournit peut-être, par son caractère formalisé par excellence, et pleinement physique en même temps, une clé pour mieux comprendre la nature de ce que nous disons être intelligible et qui pose cependant une espèce d'énigme : comment ce qui vient, fût-ce en partie, de l'expérience, peut-il être assimilé dans la pensée par sa transformation en du rationnel ? Les extensions du rationnel D'une certaine manière, la formalisation mathématique de la physique permet de dépasser l'alternative de l'empirique et du rationnel. Par l'expression mathématique (théorique), la connaissance des nouveaux phénomènes dont la théorie rend compte ou qu'elle anticipe, tout en provenant de l'expérience du monde extérieur, se place dans l'espace de la connaissance rationnelle. Car cet empirique est assimilé dans des formes qui appartiennent au rationnel : de même, selon ce que nous avons vu plus haut, que des faits d'observation suffisamment généraux se voient érigés par la pensée en principes, qui peuvent être exprimés comme des axiomes, dont ils ont la fonction référentielle et organisatrice. C'est ainsi que procède, d'une manière générale, la physique théorique, qui se caractérise à la fois par son expression mathématisée et sa fidélité à la spécificité des phénomènes.86 A la différence de la physique mathématique entendue au sens restrictif de sa pure formalisation, qui ne fonctionne que selon la rationalité mathématique (interne pour

85 Sur ce sujet, voir, par exemple, les conceptions d'Henri Poincaré (Poincaré [1902], chap. 9 et 10 ; [1905], chapitres 7 et 8). Cf. Paty [1999e]. 86 Paty [1994, 1999e].

ainsi dire, mais elle aussi susceptible d'extensions), la physique théorique constitue sa forme (mathématisée) par l'assimilation rationnelle de phénomènes empiriquement donnés. Autrement dit, le rationnel s'est élargi grâce à l'assimilation de l'empirique, ou encore, c'est par l'expérience du monde naturel que se développe le théorique et l'intelligible, et que s'accroît l'espace du rationnel. Le rationnel fonctionne ici, en somme, de manière organique, restant lui-même tout en modifiant ses structures, en augmentant ses capacités, sans se dissoudre dans l'empirique dont il se nourrit. La mathématisation de la physique (plus précisément : de telle théorie physique), justifiée par les propriétés des concepts et des grandeurs, adéquatement définies, qui permettent de la caractériser,87 devient ainsi elle-même principe d'explication, comme on le voit d'une manière particulièrement nette et exemplaire au long de l'histoire des trois derniers siècles, avec l'"analytisation" des divers domaines de la physique par le calcul différentiel et intégral, celle-ci n'étant légitimée que dans la mesure où les grandeurs et les principes correspondant à la spécificité des phé-nomènes physiques ont été exactement formulés.88 Un tel "principe d'explication" rend compte de manière à la fois analytique et synthétique des relations les plus précises entre les concepts et les grandeurs qui tissent les propriétés du monde physique et expriment son unité sous-jacente. Cette évocation n'épuise pas les nombreuses questions qui restent en suspens, les questions épistémologiques, mais aussi celles de nature ontologique ou métaphysique. Je mentionnerai, au rang des questions épistémologiques ou relevant de la philosophie de la connaissance, d'abord la diversité des épistémies pour les diverses sciences (par exemple, la biologie, aux modes de rationalité en partie différents de ceux de la physique), et la nécessité de s'opposer aux réductionnismes injustifiés ; puis la non-univocité de la rationalité, considérant un problème scientifique donné, question qui est celle du débordement du logique par le rationnel, à laquelle répond la prise en compte de la variété des "styles scientifiques" et des "programmes épistémologiques", et la "liberté logique" du travail de la pensée, chère à Poincaré et à Einstein, qui leur est sous-jacente.89 Et encore, la question des interprétations et les effets d'interprétation sur la pensée des contenus, qu'ont illustrée en notre temps, comme on le sait de reste, des théories comme la mécanique quantique ou l'évolution darwinienne. Toute la question de l'interprétation de la mécanique quantique, dans ses options les plus diverses, se ramène au souci d'établir cette science sur une base d'intelligibilité rationnelle ; mais les avis diffèrent sur ce que doit être une telle base.90 A cet égard, la question de l'exigence de rationalité rencontre, mais d'une manière naturellement peu claire au début, celle des élargissements de la rationalité. Je l'entends dans le sens d'un élargissement de ce qui est admis comme explication

87 Paty [1998b, à paraître, a]. 88 Cf. Paty [1994]. 89 Poincaré [1902, 1905], Einstein [1946], Paty [1993], chap 9 ; Paty [1999e], 90 Paty [2000a].

rationnelle pour quelque chose d'existant, que ce soit des figures géométriques, des nombres, ou des entités physiques ou d'une autre nature. Quant aux questions ontologiques, je remarquerai seulement que l'élargissement du champ des explications et de la rationalisation n'annule | pas le domaine obscur qui demeure, changeant mais irréductible, au soubassement de toute connaissance (constatation pascalienne ou "relativité de l'ontologie" au sens de Willard Quine).91 Sur les questions métaphysiques, je m'en tiendrai à l'une d'elles, pascalienne aussi (liée, d'ailleurs, à la précédente), celle de notre ignorance par rapport à notre connaissance, question qui est à l'horizon de toute évocation de l'intelligible. Si le "livre de la connaissance" est voué à être toujours fini bien qu'il augmente sans cesse, et quels que soient nos efforts pour l'accroître, ne devrait-on pas considérer que la mesure de nos questions serait mieux prise en compte dans un "livre de notre ignorance" ? Car il pourrait sembler que, sachant ce que nous savons, nous mesurerions mieux le degré de notre ignorance que celui de notre connaissance. Mais on répondra à cela que le livre de notre ignorance est plus incertain encore, pouvant être aussi bien vu comme presque vide ou comme infini. C'est que notre ignorance, telle que nous en avons conscience, n'est jamais que relative à ce que nous connaissons. Il peut parfois nous sembler, comme ce fut le cas de plusieurs physiciens à la fin du XIXème siècle (et c'est aussi le cas de certains physiciens de la fin du XXème, sans parler des biologistes...), que le domaine des questions non résolues de telle science s'amenuise de jour en jour comme peau de chagrin : la physique, disaient-ils, explique désormais pratiquement tout et ne comporte plus que deux points obscurs, l'absence de vent d'éther et la loi du rayonnement thermique. Or ces deux phénomènes, précisément, loin d'être de portée limitée et circonscrits par les théories de la physique, signalaient ses gouffres profonds qui déterminèrent les deux "révolutions scientifiques" du XXème siècle, celles de la relativité et des quanta. Nous n'avons pas idée de ce que le futur nous réserve quant aux changements des fondements mêmes de nos connaissances. Aussi assurés les croyons-nous, ils peuvent toujours en principe être modifiés, car aucun élément de ces bases n'est intangible, puisqu'ils comportent tous une part d'arbitraire qui tient à ce qu'ils sont des produits de l'esprit humain, des formes symboliques. C'est pour cela que nous n'en n'aurons jamais fini avec la recherche des raisons des raisons, et c'est encore Pascal que nous retrouvons : le livre de notre ignorance est un infini insondable. Pourtant nous avançons, à mi-chemin entre ces deux ignorances, la presque nulle et l'infinie, ou entre ces deux connaissances, l'une dérisoire et l'autre immense (à deux moments subjectifs de notre jugement), avec, dans ces entre-deux, pour viatique /e sens de l'intelligible et pour guide la conscience d'historicité.

91 Pascal [1670], Quine [1969].

Conclusion provisoire. Intelligibilité de I' historicité Nous avons tenté d'éclairer la question du rapport entre deux instances de l'activité de connaissances, I'intelligibilité et l'historicité, souvent considérées à tort comme contradictoires ou divergentes. Mais nous avons laissé jusqu'ici de coté la question suivante, qui semble plus épineuse encore : comment la conscience de ['historicité des connaissances se juxtapose-t-elle au contenu de vérité des connaissances ? On admettra que ces contenus de vérité sont relatifs, mais que l'idée de vérité, sans connotation d'absolu, garde cependant une fonction de régulation qui n'est pas illusoire, c'est-à-dire qu'une vérité relative peut être opposée à une fausseté absolue. Nous l'admettrons sans entrer ici plus avant dans les problèmes philosophiques que ces notions suscitent. Il va sans dire alors que l'intelligibilité porte sur de tels contenus de vérité (relative). Que pouvons-nous dire à propos d'une telle question, en nous plaçant au seul point de vue de l'exigence d'historicité? Pour que les différentes représentations-explications proposées au cours du temps demeurent intelligibles, d'une manière ou d'une autre, fût-ce très imparfaitement, il aura fallu et il faut que des modifications aient été et soient possibles. C'est-à-dire que l'invention de nouvelles formes de représentation ait été et demeure possible, et qu'une compréhension des formes passées le reste aussi après elles, dans un autre univers de significations, comme, par exemple, dans le nôtre : et si nous voulons être un tant soit peu historiens, il nous faut acquérir la capacité de dépasser le sens immédiat que ces formes du passé pourraient avoir pour nous, par projection, et nous efforcer à la compréhension d'un sens propre à ce passé lui-même. Et, pour cela, il faut bien d'abord, comme le remarquait Marc Bloch, que nous ayons nous-mêmes expérimenté la connaissance de notre propre présent. La connaissance du présent aide à connaître le passé ; elle en est même la condition première.92 Il faut bien aussi que la compréhension de ces formes passées de connaissance ait un sens, qu'il y ait une sorte de continuité minimale, que les deux univers aient une commune mesure, sous des sytèmes de représentation différents. L'histoire des rapports de connaissances en succession dans le temps,93 et de manière éminente celle de transmissions culturelles, en particulier des transmissions des savoirs scientifiques, procure à cet égard une riche moisson de faits, malgré toutes nos inconnaissances concernant bien des situations complexes et des passés lointains.94 Dans le débat de certains philosophes et historiens des sciences sur l'incommensurabilité des systèmes conceptuels et théoriques, de Kuhn à Feyerabend,95 ceux-ci n'auront oublié qu'une chose, c'est que la transmission a existé et existe, et avec elles la communication, qui demandait quelque "mesure"

92 Bloch [1949]. 93 Par exemple, la physique de Newton et celle d'Einstein : Cf. Paty [1987]. 94 Cf., p. ex., Needham [1954-, 1969, 1974, 1993], Rashed & Morélon [199?], Habib & Raina [1999], Thapar [1999], Paty [1999b]. 95 Kuhn [1962, 2000], Feyerabend [1981].

commune, dans la pratique du travail des scientifiques, et que ce sont là des faits d'histoire. Des faits empiriques, peut-être, mais qui, en tant que faits, demandent eux-mêmes à être compris, tout comme ceux dont nous avons parlé pour l'histoire des sciences. Autrement dit, nous posons nécessairement par là l'intelligibilité de l'historicité. Par l'attention à ces faits d'histoire, et par les leçons de leur analyse, la question d'une "incommensurabilité" apparaît être seulement formelle, se posant pour des axiomatiques sur des corps (ou structures) de propositions fixées ; si elle peut avoir son intérêt à ce niveau, elle n'est pas pertinente du point de vue historique, où l'on s'efforce, dans le travail de recherche, de dépasser une théorie présentant des difficultés, mais dont on part, fût-ce pour lui faire violence... On pourrait en multiplier les exemples, pour des situations réelles, ayant été l'objet d'expériences vécues, concernant aussi bien des travaux scientifiques conduisant à des découvertes ou inventions, des situations de réception de théories nouvelles, ou encore des remaniements théoriques. Les discontinuités dans la pensée, comme dans les actions et les événements, se détachent toujours sur un fond de continuité. La leçon des faits d'histoire à ce sujet (des faits de l'histoire des sciences) est, au contraire, qu'il existe une commune mesure entre des connaissances inscrites dans des systèmes de pensée différents, et donc correspondant à des contenus conceptuels distincts, et malgré la difficulté à rendre compte du passage de l'une à l'autre, ou du dialogue entre elles ; il aura d'ailleurs pu s'agir d'une traduction seulement partielle, et transformée. Et l'on peut alors se demander si cela ne serait pas, précisément, par l'effet de la rationalité, et de la conscience de cette rationalité. On pourra, certes, objecter à cela que la rationalité des sciences n'est pas une, elle non plus, à travers les disciplines et les objets, les époques et les cultures ; et qu'elle n'est même pas univoque pour une science et un objet de science donnés, puisqu'elle admet des variantes quand elle est en formation, en élargissement ; et que la rationalité elle-même est modifiable et se modifie au long de l'histoire.96 Mais on voit bien que l'objection ne vaut pas impossibilité/quand, au contraire, elle distend les éléments des systèmes pris dans la comparaison, leur donnant plus de jeu, rendant leur agencement effectif moins rigide à nos yeux d'observateurs du passé. On peut parler, assurément, d'historicité de la rationalité elle-même : mais il restera à préciser ce que cela signifie, car de tels mots, s'ils correspondent à des réalités, ne sont bien entendu pas des sésames ouverts sur toutes les interprétations non fondées, voire fantaisistes, qui comprennent les réductions et les dissolutions. Car c'est, précisément, parce qu'une communication est constatée, comme une matière de fait, et qu'elle est donc en droit possible, quelles que soient ses transformations (et les trahisons - naturelles - de ses traductions) aussi bien que ses limitations, que nous pouvons continuer de parler de rationalité, comme ce qui désigne un noyau plus profond que les contenus de connaissances eux-mêmes, qui les rend possible et les constitue, et dont nous somme 96 Granger[1955], éd. 1967.

problablement loin d'avoir fait le tour ; noyau grâce auquel, en tout cas, nous pouvons accéder, de notre présent, à une compréhension toujours perfectible du passé, ou des ailleurs contemporains. Quant au futur, qui nous est en général largement imprévisible, s'il se révèle progressivement à nous, à la vitesse même (ou à peu près) de ses accomplissements, c'est à la faveur de la mise au point de nouveaux schémas de compréhension qui se fondent sur la rationalité et sur sa capacité d'extension, nécessitée par nos exigences successives d'intelligibilité, et qui permettent de concevoir (rationnellement) ce qui était jusqu'ici encore impensable. Notre conscience de l'historicité pose l'exigence de son intelligibilité, et elle la pose selon des conditions épistémiques qui sont celles spécifiques à l'histoire comme discipline. Par exemple, selon une conception propre du temps des hommes dans leurs sociétés et leurs cultures, qui est celui-là même de la conscience historique, le temps des distanciations et des mûrissements. "Réalité concrète et vivante rendue à l'irréversibilité de son élan", écrivait Marc Bloch, "le temps de l'histoire, au contraire [de celui des sciences de la mesure], est le plasma même où baignent les phénomènes et comme le lieu de leur intelligibilité".97 Cette conscience du temps de l'histoire fait concevoir de prendre en compte les changements de signification, en histoire aussi bien qu'en histoire des sciences. Invitant les historiens à éviter l'erreur "de confondre une filiation avec une explication", Marc Bloch leur rappelait que les idées qui contribuent à en former d'autres, qu'il s'agisse du régime féodal ou des idées de la Révolution, en passant d'un milieu à un autre, ou d'une génération à une autre, sont transformées, adaptées au conditions nouvelles, sociales ou intellectuelles.98 Il en va, pourrions-nous proposer, de la "filiation" prise pour une explication, dénoncée par le grand historien, comme de la "construction sociale" selon ce que nous en avons dit en commençant : elle laisse entier le problème de savoir pourquoi et comment ceci a été transmis ou construit, c'est-à-dire la question des significations et des contenus, même liés aux circonstances. "Jamais (...) un phénomène historique ne s'explique pleinement en dehors de l'étude de son moment", écrivait encore Marc Bloch.99 Cela signifie, pour nous, que l'historicité s'oppose aux algorithmes des reconstitutions intemporelles, et cela vaut en parti-culier pour l'histoire des sciences : ni réductionnisme social, ni algorithme rationnel intemporel n'ont rendu et ne rendront compte de la science qui s'invente dans la pensée humaine inscrite dans l'histoire.

97 Bloch [1949], p. 5. 98 Bloch [1949], p. 7. 99 Bloch [1949], p. 9.

Références bibliographiques D'Alembert, Jean le Rond, Traité de dynamique, David, Paris, 1743. 2ème éd.,

modif. Et augm., David, Paris, 1758. D'Alembert, Jean le Rond, "Essai sur les éléments de philosophie ou sur les

principes des connaissances humaines", Paris, 1758. In Oeuvres philosophiques, historiques et littéraires de d'Alembert, vol. 2, Bastien, Paris, 1805 [suivi des Êclaircissements]. Reed., Olms Verlag, Hildesheim, 1965.

D'Alembert, Jean le Rond, et Diderot, Denis, Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, 17 vols. + 11 vol. de planches, Briasson, David, Le Breton et Durant, Paris, 1751-1780.

Bachelard, Gaston, Le rationalisme appliqué, Paris, 1949. Bloch, Marc, Apologie pour l'histoire ou Métier d'historien, Cahiers des Annales,

1949 (Manuscrit original : 1941. 1ère publ., posthume préparée par Lucien Febvre) ; nlle éd. critique préparée par Etienne Bloch et Jacques le Goff, Armand Colin, Paris, 1993.

Bourdieu, Pierre, Champ intellectuel et projet créateur, Les Temps modernes, núm. 246, 1966, pp. 865-906.

Bourdieu, Pierre, Le champ scientifique, Actes de fa recherche en sciences sociales, núm. 2/3, 1976, pp. 88-103.

Bourdieu, Pierre, Les règles de l'art. Genèse et structure du champ littéraire, Minuit, Paris, 1992.

Bourdieu, Pierre, Contre-feux, Liber-Raisons d'agir, Paris, 1998. Thé French Historical Révolution : The Annales School 1929-1989, Burke, Péter

(éd.), London, 1990 ; trad. brésil por Nilo Odalia, A escola dos Annales, 1929-1989. A revolução francesa da historiografia, Editôra UNESP, São Paulo, 1991 (éd. utilisée).

New Perspectives on Historical Writing, Basil Blackwell, Burke, Péter (éd.), London, 1991 ; trad. brasil por Magda Lopes, A escrita da história. Novas perspectivas, Editera UNESP, Sâo Paulo, 1992 (éd. utilisée).

Calder, Richtie, Man and his techniques, 1961. Trad. fr. par Henri Delgove, L'homme et ses techniques, Pavot, Paris, 1963.

Cassirer, Ernst, Die Philosophie des symbolischen Formen, 1923, 1924, 1925. Trad. fr. par Ole Hansen-Love et Jean Lacoste, La philosophie des formes symboliques, Minuit, Paris, 3 vols., 1972.

Charles, Christophe, Naissance des intellectuels, Minuit, Paris, 1990. Charles, Christophe, Les intellectuels en Europe au XIXè siècle. Esssai d'histoire

comparée, Seuil, Paris, 1996. Clavelin, Maurice, La philosophie naturelle de Galilée, A. Colin, Paris, 1968. Clottes, Jean, Le voyage en préhistoire, Ed. La maison des Roches, Diffusion

Seuil, Paris,,1998. Clottes, Jean et D. Lewis-Williams, Les chamans de la préhistoire. Transes et

magies dans les grottes ornées, Seuil, Paris, 1996. Dieudonné, Jean, Pour l'honneur de l'esprit humain, Hachette, Paris, 1987. Dosse, François, L'histoire ou le temps réfléchi, Coll. Optiques, Hatier, Paris, 1999.

Drake, Stilman, Galileo (1980) ; trad. de l'anglais par Jean-Paul Sheidecker, Actes Sud; 1986.

Einstein, Albert, Elektrodynamik bewegter Körper, Annalen der Physik, ser. 4, XVII, 1905, 891-921. Republ. in C.P., vol. 2, pp. 276-306. Trad. fr., Sur l'électrodynamique des; corps en mouvement, in O.C., vol. 2, pp. 31-58.

Einstein, Albert, Ueber das Relativitätsprinzip und die aus demselben gezogenen Folgerungen, ]ahrbuch der Radioaktivität, IV, 1907, 411-462 ; V,1908, 98-99 (Berichtigungen, errata). Republ. in C.P., vol. 2, pp. 433-488. Trad. fr., Du principe de relativité et des conséquences tirées de celui-ci, in O.C., vol. 2, pp. 84-124.

Einstein, Albert, Die Grundlage der allgemeinen Relativitätstheorie, Annalen der Physik, ser. 4, XLIX, 1916, 769-822. Trad. fr., Les fondements de la théorie de la relativité générale, in O.C., vol. 2, pp. 1 79-227.

Einstein, Albert, Newtons Mechanik und ihr Einfluss auf die Gestaltung der theoretisherr Physik, Naturwissenschaften, pp. 15, 273-276 ; La mécanique de Newton et son influence sur l'évolution de la physique théorique, in O.C., vol. 5, pp. 235-241.

Einstein, Albert, Autobiographisches. Autobiographical notes, in Schilpp, P.A. (éd.), Albert Einstein , philosopher and scientist, The Library of living philosophers, Open Court, La Salle (III.), 1949, pp. 1-95. (Texte rédigé en I946).

Einstein, Albert, Thé Collected Papers of Albert Einstein, éd. by J. Stachel, D.C. Cassidy, R. Schulmann, M. Klein et al., Princeton University Press, Princeton, New jersey, 1987, 8 vols. parus jusqu à 1999. (C.P.)

Einstein, Albert, Oeuvres choisies, éd. par F. Balibar et al., Seuil/CNRS, Paris, 5 vols., 1989-1993. (O.C.)

Feyerabend, Paul, Philosophical Papers, 2 vols., Cambridge University Press, 1981.

Galilei, Galileo (Galilée), Dialogo sopra i due massime sistemi del mondo : tolemaico e copernicano ; trad. fr., Dialogues sur les deux plus grands systèmes du monde (1632), Seuil, Paris, 1992.

Galilei, Galileo (Galilée), Discorsi e dimostrazioni mathematiche in torno di due nuove scienze, Leyde, 1638 ; ré-éd., avec introd; et notes, par A. Carugo et L. Geymonat, Boringhieri, 1958. Trad. fr. par Maurice Clavelin, Discours sur deux sciences nouvelles (1638), A. Colin, Paris, 1970.

Geymonat, Ludovico, Galilée, trad. de l'italien par François-Marie Rosset, Laffont, Paris, 1968; Seuil, Paris 1992.

Ginzburg, Carlo, Miti, emblemi, spie : morfologia e storia, Torini, 1986 ; Trad. fr., Mythes, emblèmes, traces, Flammarion, Paris, 1989.

Gouhier, Henri, Les premières pensées de Descartes. Contibution à l'histoire de l'anti- Renaissance, Vrin, Paris, 1958.

Granger, Gilles-Gaston, La raison, Coll. Que sais-je ?, Presses Universitaires de France, Paris, 1955 ; 9ème éd., 1989.

Granger, Gilles-Gaston, Essai d'une philosophie du style, Armand Colin, Paris, 1968; rééd., Odile Jacob, Paris, 1988.

Situating thé history of science ; Dialogues with Joseph Needham, Habib, S. Irfan and Raina, Dhruv (eds.), Oxford University Press (New Delhi), 1999.

Hacking, lan, "Style" for Historians and Philosophers, Studies in History and Philosophy 23, 1992, pp. 1-20.

Hacking, lan, Thé social construction of what?, Harvard University Press, Cambridge (Mass.), 1999.

Hegel, Georg Wilheim Fiedrich, La raison dans l'histoire (Introduction aux leçons sur la philosophie de l'histoire), trad. nouvelle, intr; et notes par K. Papaioannou, Le monde en 10/18, Paris, 1965.

Hertz, Heinrich, Die prinziopien der Mechanik, in neuem zussammenhange, Teubner, Lepzig, 1894. Trad. angl. par D.E. Jones et J.T Walley, Thé principles of méchantes presented in a new form, Mac Millan, London, 1893; Dover, New York, 1956.

Jami, Catherine, Western mathematics in China, seventeenth century and nineteenth century, in Jami, Moulin, Petitjean [1992], pp. 79-88.

Science and Empires, Jami, Catherine, Moulin, Anne-Marie, Petitjean, Patrick (eds.), Kluwer, Dordrecht, 1992.

Koyré, Alexandre, Etudes galiléennes, Actual. se. industr., 3 fasc., Hermann, Paris, 1 935- 1939 ; 1 vol., Hermann, Paris, 1966.

Kuhn, Thomas, The Stucture of Scientific Révolutions, The University of Chicago Press, Chicago, 1962; 2nd éd., 1970.

Kuhn, Thomas, Dogma contra critica. Mondi possibili nella storia délia scienza, con due lettere di Paul K. Feyerabend, a cura di Stefano Gattei, Raffaello Cortina editore, Milano, 2000.

Faire l'histoire, Le Goff, Jacques et Nora, Pierre (eds.), Gallimard, Paris, 3 vols., 1974. Réé-éd., 1986.

Leroi-Gourhan, André, Le geste et la parole, 2 vols. Albin Michel, Paris. Vol. 1 : Technique et langage, 1964; Vol. 2: La mémoire et les rythmes, 1965.

Leroi-Gourhan, André, Evolution et techniques, 2 vols., Albin Michel, Paris. Vol. 1 : L'homme et la matière (1 ère éd., 1 943), nlle version, 1971. Vol. 2, Milieu et techniques, 1971.

Leroi-Gourhan, André, La préhistoire de l'art occidental, Mazenod, Paris, 1965. Levi, Giovanni, On micro-history ; trad. brés., "Sobre a micro-historia", in Burke

[1991], trad. br., 1992, pp. 133-161. Lloyd, Geoffrey E. R., Logos et vérité, L'Aventure humaine. Savoirs, libertés,

pouvoirs (Paris), núm. 5, Avril 1996, pp. 7-22. Lorblanchet, Michel, La naissance de l'art. Gensèse de l'art préhistorique, Ed.

Errance, Paris, 1999. Lorblanchet, Michel, Pourquoi l'art est-il apparu ?, entretien avec Eric Rohde, La Recherche, núm. 326, déc. 1999, pp. 107-109.

Mach, Ernst, Die Mechanik in ihrer Entwicklung historisch-kritisch Dargellstellt, Leipzig, 1883 ; trad. fr. (sur la 4 ème éd. allemande) par E. Bertrand, La mécanique. Exposé historique et critique de son développement, Hermann, Paris, 1904 ; ré-éd., 1923.

Mandrou, Robert, Histoire de la pensée européenne, vol. 3 : Des humanistes aux hommes de science, Seuil, Paris, 1973.

Mariconda, Pablo [à paraître]. Galilei, Galileo, Dialogo sui due Massimi Sistemi del Mondo, traduction en portugais (Brésil) et édition critique avec une introduction par Pabio Mariconda, Discurso Editorial, São Paulo, à paraître.

Monod, Jacques, Le hasard et la nécessité, Seuil, Paris, 1970. Needham, Joseph, Science and civilisation in China, Cambridge University Press,

Cambridge, 7 vols. en 34 tomes, 1954. Needham, Joseph, The Great Titration, 1969 ; trad. fr. par Eugène Jacob, La

science chinoise et l'Occident (Le Grand Titrage), Seuil, Paris, 1973. Needham, Joseph, La tradition scientifique chinoise (recueil d'articles trad. en fr.),

Hermann,. Paris, 1974. Needham, Joseph, Dialogues des civilisations Chine-Occident. Pour une histoire!

œcuménique des sciences. Recueil d'articles conçu par G. Métaillé, La Découverte, Paris, 1993.

Newton, Isaac, Philosophiae Naturalis principia mathematica, London, 1687 ; 2ème éd.,ï 1713 ; 3ème éd., 1726; éd. par Alexandre Koyré et I. B. Cohen, Cambridge.' University Press, Cambridge, 1972. Trad. angl. par A. Motte, The mathematical principles of natural philosophy, 1729 ; 3è éd., 1726 ; trad. rév. par F. Cajori, Berkeley, j Univ. California Press, 1934.

Ory, Pascal & Jean-François Sirinelli, Les intellectuels en France. De l'affaire Dreyfus à nos jours, Armand Colin, Paris, 1992.

Pascal, Biaise, Pensées, in B.P., Oeuvres complètes, Préface d'Henri Gouhier, Présentation et Notes de Louis Lafuma, Seuil, Paris, 1963.

Paty, Michel, "Einstein et la pensée de Newton", La Pensée, núm. 259, 1987, pp. 17-37.

Paty, Michel, L'analyse critique des sciences, ou le tétraèdre épistémologique (sciences, philosophie, épistémologie, histoire des sciences), L'Harmattan, Paris, 1990.

Paty, Michel, Einstein philosophe. La physique comme pratique philosophique, Presses | Universitaires de France, Paris, 1993.

Paty, Michel, "Le caractère historique de l'adéquation des mathématiques à la physique", in Garma, Santiago; Flament, Dominique; Navarro, Victor (eds.). Contra los titanes ; de la rutina.- Contre les titans de la routine, Comunidad de Madrid/C.S.I.C., Madrid, 1994, pp. 401-428.

Paty, Michel, "Remarques sur la production sociale des sciences et la question de la S vérité", in Malet, Emile et Le Bras, Hervé (éds.). Science et démocratie. Penser le XXIè siècle, Editions Passages, Paris, 1996, pp. 185-219.

Paty, Michel, "L'idée d'universalité de la science et sa critique philosophique et historique", in Arboleda, Luis Carlos y Carlos Osorio (éds.), Nacionalismo e internacionalismo en la historia de las ciencias y la tecnología en América latina, Memorias de/ IV Congresso Latino-Americano de Historia de las Ciencias y la Tecnología, Universidad del Valle, Cali (Colombia), 1997, p. 57-89. Egalement, Asclepio (Madrid), 49 (2), 1997, pp. 5-43.

Paty, Michel, D'Alembert ou la raison physico-mathématique au siècle des Lumières, Les Belles Lettres, Paris, 1998.

Paty, Michel, "La philosophie et la physique", in Jean-François Mattéi (éd.), Le Discours philosophique, volume 4 de l'Encyclopédie philosophique universelle, Presses Universitaires de France, Paris, 1998, chap. 123, pp. 2104-2122

Paty, Michel, "L'universalité de la science. Une idée philosophique à l'épreuve de| l'histoire", Mâat. Revue Africaine de Philosophie, 1ère année, núm. 1, avril 1999, pp. 1-26. Trad. angl., Universality of Science: Historical Validation of a Philosophical idea, as Chapter 12, in Habib & Raina [1999], pp. 303-324

Paty, Michel, "Comparative history of modem science and the context of dependency", transi, from French by Nicholas Flay, Science, Technology and Society. An International journal Devoted to the Developping World (New Delhi, Sage; Publications), 4, 2, 1999, pp. 1 71-204.

Paty, Michel, "La place des principes dans la physique mathématique au sens de Poincaré", in Sebestik, jan et Soûlez, Antonia (éds.), Actes du Colloque France-Autriche Paris, mai 1995, Interférences et transformations dans la philosophie française et autrichienne (Mach, Poincaré, Duhem, Boltzmann), Fundamenta philosophise (Nancy/ éd. Kimé, Paris) 3 (2), 1998-1999, pp. 61-74.

paty, Michel, "Les trois stades du principe de relativité", Revue des questions scientifiques, 170 (núm. 2), 1999 (les relativités. Première partie ), pp. 103-150.

Paty, Michel, "La création scientifique selon Poincaré et Einstein", in Serfati, Michel (éd.), La recherche de la vérité, Coll. L'écriture des Mathématiques, ACL-éditions du Kangourou, Paris, 1999, pp. 241-280.

Paty, Michel, "Masse (de Newton à Einstein)", in Lecourt, Dominique (éd.), Dictionnaire d'histoire et de philosophie des sciences, Presses Universitaires de France, Paris, 1999, pp. 613-616.

Paty, Michel, "Interprétations et significations en physique quantique", Revue Internationale de philosophie, núm. 212, 2-2000, pp. 1 7-60.

Paty, Michel [à paraître]. La notion de grandeur et la légitimité de la mathématisation en physique, Deuxième tournée de Philosophie des Sciences Jean Largeault, Universités de Paris-Sorbonne (Paris-4), Paris 1-Panthéon-Sorbonne, Marc Bloch-Strasbourg-2 et Institut Universitaire de France, Vendredi 7 Mai 1999.

Poincaré, Henri, La science et l'hypothèse, Flammarion, Paris, 1902 ; 1968. Poincaré, Henri, La valeur de la science, Flammarion, Paris, 1905 ; 1970. Poincaré, Henri, Science et méthode, Flammarion, Paris, 1908 ; 1918. Quine, Wllard V, Ontological Relativity and Other Essays, Columbia University

Press, New York, 1969 ; trad. fr. par Jean Largeault, Relativité ede l'ontologie et autres essais, Aubier-Montaigne, Paris, 1971.

Raina, Dhruv & S. Irfan Habib, "Technical content and social context", in Petitjean, Jami & Moulin [1992], pp. 121-136.

Histoire des sciences arabes, Rashed, Roshdi & Morélon, Régis (éd.), 3 vols., Seuil, Paris, 1997.

Rorty, Richard, L'espoir au lieu du savoir. Introduction au pragmatisme, trad. fr., Albin Michel, Paris, 1995.

Shapin, Steven, A Social History of Truth. Civility and Science in Seveteenth Century England, University of Chicago Press, Chicago, 1994.

Simondon, "Du mode d'exisstence des objets techniques", Aubier, Paris, 1958 ; nlle éd., 1989.

Thapar, Romila, "History of science and thé Oikoumene", in Habib & Raina [1999], pp. 16-28.

Vernant, Jean-Pierre, Mythe et pensée chez les Grecs, Maspéro, Paris, 1965; nlle éd. rev. augm., La Découverte, Paris, 1985.

L’Aventure des écritures. Naissances, Zali, Anne & Berthier, Annie (éds.), Bibliothèque nationale de France, Paris, 1997.

The savant’s drama: two cultures

and two shores

ANTONIO LAFUENTE AND TIAGO SARAIVA One of the attributes Italo Calvino recommends for writing in the coming millennium is lightness, a provision whose purpose is to clear away the obscurity of the world and to prevent our being crushed by matter, by chaos or by tradition. Lightness is not the same as simplicity, but it is similar. Nor does it, in this case, have the same type of outcome as the struggle between darkness and light or, more recently, between ancient and modern. They are different things, since gravitas is not a sign of the past, but one which is dominant in all centuries and all places. Poetry is the antidote, hence its purgative character. And what about science? Calvino bows down before this venerable icon, and admits that no human undertaking has been so efficient, so methodically and institution-ally efficient, in the effort to scrape the accumulated grime from things and to create the illusion that we can not only understand it but even control it and then possess it.100 Our relationship with science is ever-changing. No-one disputes its enormous powers of seduction, nor its undeniable ability to buoy up hopes. For centuries our cultural imagery has been full of images produced by this inexhaustible factory of dreams. It would seem that its ideal is self-sufficiency, the conquest of all types of knowledge and free unlimited movement. And so it becomes a historical undertaking which is more and more independent, versatile and mobile.101 Most people trust in its practicability, but many more have misgivings. There is a lightness in science which is associated to its closeness to the mysteries of the world, and it is hard not to yield to its appearance of truthfulness, honesty, freedom, altruism, solidarity and even beauty. But while it is sorting out all our problems and putting the pieces back in order, it is be-coming more and more remote from the people, from the ordinary world. And finally we all find ourselves pushed to the shore of a vast savage continent.102

100 Italo Calvino, Seis propuestas para el próximo milenio. Ediciones Siruela, Madrid, 1989. 101 Bruno Latour, Science in action, Harvard University Press, Cambridge, MA: 1973. 102 See Bertrand Labasse, Observations on the Communication of Scientific and Technological Knowledge, Reportto Directorate-General XII of the European Comission, 1999. AIso, Alan Irwin, Citizen Science, a study of People, Expertise and Sustainable Development, Routledge, London, 1995.

Illusions of the two cultures On the 8th of May 1794, three months before the downfall of Robespierre, Lavoisier was beheaded. The sentence was carried out after he had been refused permission to finish some experiments which would otherwise have been left incomplete. The answer from the appeal court was brief: "La République n'a pas besoin de savants". From that moment on we have had a perfect symbol to reflect on the difficult historical relation-ships between the two republics - the republic of letters and that of politicians. And the circumstances surrounding the case are captivating: for example, the presence of the guillotine, Joseph-Ignace Guillotin's dreadful new technique, invented at the request of the National Assembly to ease the work of the executioner, overwhelmed by the enormous number of condemned prisoners swelling the prison population.103 Surely what is most striking is the judge's brutal and absurd reply, because the Republic wanted to be enlightened and to set itself up as a structure capable of exercising rational control over the social and natural world. It was not an easy decision to close down the Académie des Sciences, but it was justified by the need to impose upon scientific institutions a form of democratic control more committed to the needs of the nation.104 Science, as the tiresome rhetoric of the day declared, was no longer an end in itself but an instrument of the new bourgeois state. Not that the revolutionaries invented the argument of the usefulness of science: the argument is as old as knowledge itself, and traces of it can be found as far back as the times of Archimedes. But what was novel now was the central role which the new rhetorical and practical politics gave to the scientists and the institutions. Suffice it to recall the impressive list of mathematicians, astronomers, engineers and physicists who carne to power after the French Revolution: Carnot led the Committee of Public Safety, Monge commanded the Navy, Bailly headed the City Council of Paris until he was guillotined, Laplace was a senator, Fourier a prefect, and Arago became a minister. A Geometrician, Bonaparte, seized civil and military power.105 The words that condemned Lavoisier confirm that what the Republic needed, in its role as representative of the people, was good republicans; and that, as a result, no branch of knowledge and no scholar could remain outside the control of the new democratic power.

103 It is nonetheless ironic that we are talking here of the same Guillotin who in 1 794, under Franklin's presidency and with the collaboration of Lavoisier himself, was a member of a Royal Commission set up to judge and repress the practice of Mesmerism. Mesmer's theories, based on supposed animal magnetism and hypnosis, had taken root in the popular imagination and were presenting a threat to the medical profession. Few examples so clearly sum up the networks connecting scientific activity with politics. See Lavoisier in European Context: Negotiating a New Language for Chemistry, Bernadette Bensaude-Vincent and F. Abbri (eds.), Science History Publications, Nantucket, Mass.: 1996. 104 See Roger Hahn, The Anatomy of Scientific Institution: The Paris Academy of Sciences, 1666-1803, The University of California Press, Berkeley: 1971. 105 Michel Serres, "Paris 1800", en Michel Serres (ed.), Elementos para una historia de las ciencias, Cátedra, Madrid: 1991.

The situation in 1800 represented a turning-point. The road ahead was the right one, but ¡t was full of obstacles. If we look at Tocqueville, the Frenchman who in 1831 travelled round the young American republic, marvelling at the enormous differences he found on either side of the Atlantic, we see someone who laments the lack of liberty in Europe and who unequivocally denounces the oligarchic nature of the French institutions. r-le was doubtless aware of the existence of the École Polytechnique and of the Musée d'Histoire Naturelle, perhaps the greatest concentrations of talent then existing in the world, but he deplores their élitist organisation. What makes America different is its fascination with utilitarianism: the ability to link technical knowledge to everyday needs, ensuring for the people a level of well-being and consumption unheard of in the Old Continent. And this is the crux of his comparison, for it unites the spirit of practicality with democracy.106 Something in this analysis reminds us of another, equally well-known: that of Voltaire and his exile in London. For Voltaire what explained the cultural and scientific hegemony of England and Holland was the development of trade and the generalisation of comfort, as a new social value alongside citizenship. The comparison between the severity of some and the tolerance of others ended in his scathing criticisms of European monarchies. The subject, as we can see, is an old one and, although its form changes, there was always an influential current of opinion in favour of a causal relation between tolerance and learning, and between democracy and science. For Tocqueville and the many intellectuals who carne after him the civilising equation was simple: individual liberties encourage practical knowledge, leading to cheaper production and a better standard of living. The formula is completed with another idealisation which sees the citizens in the middle of a mechanised utopia, part of a system which guarantees the combination of collective happiness and individual wellbeing.107 And the more technology, the greater the wealth and the more democracy. Very naïve, no doubt, but this was how they presented the tale of the little milkmaid defending liberalism and progress. We now have a huge range of examples with which to criticise such naïveté, or rather such utilitarian and industrial optimism. And although we are well aware of the cases of the former Soviet Union and the majority of Asian countries (such as China, India, Japan or Pakistan), the fact is that we are faced with a successful ideology which still has many followers, even in positions of political responsibility. The awareness of the power of science is not new. But it never reached such sublime heights as in the middle of the 19th century. And we are not just thinking of its military and industrial applications, but its more broadly cultural aspect. We are talking about the religion of progress which not only promised more efficient machines and panaceas for all ills, but the very vision of a truth revealed and not

106 Eda Kranakis, Constructing a Bridge. An Exploration of Engineering Culture, Design, and Research in Nineteenth-Century France and America, The MIT Press, Cambridge: T997. 107 See Leo Marx, The Machine in the Carden: Technology and the Pastoral Ideal in America. Oxford UP, New York: 1 964. David Nye, American Technological Sublime. Cambridge, MIT Press, MA: 1994.

inherited. While positivism gained followers and organised spectacular propaganda coups, like the Universal Exhibitions which drew huge crowds —the Paris Exhibition of 1900 attracted some 50 million visitors— the first misgivings began to be felt. Machines, once seen by the working class as a threat to the stability of their Jobs, stopped burning. They would be worshipped by the masses now that they had been won over to the cause of progress.108 Some intellectuals, however, were not so easily seduced and they imagined new dangers: Frankenstein is the symbol of this new trend. But who was this character? Most people would reply that it was a fictional monster created by Mary Shelley, and the subject of a host of films. Some may even remember that its deformation was due to a sudden electrical failure seconds before the corpse on which experiments were being done carne back to life. And, finally, there will be the vague image of a nightmarish laboratory, the horrified people, or the innocence of a little girl who is not frightened off by the difference of aesthetic values. But no. Frankenstein was the doctor who thought up the experiment, and not the result of the operations. It is strange, is it not, this transfer of identity between the subject of the action to the object he creates. Clearly, here is a novel which invites us to think about the dangers of this new emerging power which science represents. But the cultural turmoil is not caused by the results, since the risk lies in certain irresponsible scientists who unleash forces or processes which later they cannot, or will not, control.109 Mary Shelley seems to be saying to her readers that some scientists may be-come perverted, even by their own stupidity. But what the people, the public, remember is less high-minded, and it is scientific activity itself which bears the stigma. And this is one of the key arguments of the theory of two cultures, for while scientists "carry the future in their bones", traditional intellectuals such as Yeats, Pound and, for example, OrweII, were accused by Snow of being born Luddites: deaf to the good news of science and blind to technical progress. All the same it is interesting that the sect of the reactionaries, initially formed by laymen of the industrial and urban working class, should grow, according to Snow, to include the humanists a hundred years later.110 The shadows which began to appear in this 19th century literature become predominant in the rupturist works of Wells, for whom the novum announced by science is not a machine paradise but a night-mare in which beings from other worlds or devastating wars drag Humanity back to early brutish stages of their evolution. In Wells the story is normally built around an unexpected superhuman force which must be fought by the selfless and philanthropic hero, free of the usual self-righteousness and self-satisfaction, and who has to resist this disastrous biological regression towards destruction. In this sense all of Wells' work is an argument against the mindless Victorian society and against the arrogant and diabolical scientist, capable of unleashing forces which he then cannot control. 108 Paul Greenhalgh, Ephemeral Vistas. The Expositions Universales, Creat Exhibitions and World's Fairs, 1851-1939, Manchester University Press, 1988. 109 Antonio Lafuente and Alberto Elena, "Los científicos ante su imagen y su público", Claves de razón práctica, 67, November 1996, pp. 48-55. 110 Roger Kimball, "The two cultures today", The New Criterion, on line, February 1994. www.newcriterion.com.

With it comes the end of the brilliant certainties of Newtonian physics, and we begin to see terrible portents of wars between worlds, genetic alchemy or evolutionary accidents. This is the world which will slowly come to dominate in the literature of our century. Socialist paradises, described by William Morris and others, enlightened by socially-conscious and generous scientists, are replaced in films like Fritz Lang's Metropolis or novels like Aldous Huxley's Brave New World by oppressive societies inhabited by robots or beings with no memory, manipulated by pseudo-Prometheuses promising happiness at the expense of freedom. While novels and the cinema soon began to be wary of science, and advised caution against the Faustian myth, throughout this century public opinion on science and technology has kept a basically ambivalent attitude where, in the words of Marcel LaFollette: "The message appears clear: science gives, and science takes away".111 Without a shadow of doubt the most wide-spread stereotype in popular culture is the mad scientist, the evil being who —for the most varied of reasons— wants to dominate the world or, failing that, to destroy it with the amazing powers that his knowledge bestows upon him.112 Innumerable versions of this Faustian figure fill the pages of as many comics and popular novels, as well as the pictures of countless films and TV series. In all of these media the scientist's only role seems to be that of an opponent to the hero, and his intrinsic wickedness (or in other variations, his access to special powers which finally get out of control) separate him from the popular image of the typical man in the street with which one could perhaps identify. But, even without taking into account this extreme case —albeit the most typical in popular culture— other more neutral or even positive depictions of scientists also underline this difference from what is implicitly considered normal. Who could forget Sinclair Lewis' magnificent and idealised description in his famous Doctor Arrowsmith, one of the masterpieces of the genre in question? "h-le had never lunched with a duchess, never received an award, he had never been interviewed, never done anything the public could understand nor, since his school-boy crushes, had he ever had any experience which people might consider romantic. He was, indeed, a true scientist". A description which recreates and updates the image par excellence of the isolation of the scientist from his social environment, a legend which winds throughout all the historiography based on the Big Picture. Between the case of Lavoisier and the others we have mentioned, there is one major difference. In the nineteenth century mistrust grew up like the myth of Faust. And although Jonathan Swift, too, in Gulliver's Travels distances himself from scientific fashion, his criticism is no more than irony towards certain types of pedantry. Swift is irritated by the petulance of the scholar, but he still does not 111 Marcel C. LaFollette, Making Science Our Own. Public Images of Science, 1910-1955 (Chicago, 1990), p. 175. 112 Concerning this, see Spencer Weart, "The Physicist as Mad Scientist" (Physics Today [June 1988]), pp. 28-37, and Andrew Tudor, Monsters and Mad Scientists. A Cultural History of the Horror Movie (Oxford, 1 989), specially pp. 133-157. AIso Joan Bassa & Ramón Freixas, El cine de ciencia ficción. Una aproximación, Paidos, Barcelona, 1993.

accuse him of arrogance. Which is exactly what Dumas, the judge who sentenced Lavoisier, was to do later. And so the conflict between science and politics now takes the form of a certain tension between scientists and humanists, which disguises what the public sees and remembers: that is, the split between elite and popular culture.113 The misanthropy of the scholar It was not always so. In earlier times, when there was still no clear distinction between a philosopher, a politician, an engineer or an astronomer, there was no tension between people of the Arts and those of Science. The roles alternated, since a good intellectual had to be a jack of many trades, unless he was prepared to renounce the idea that every-thing was the expression of one unique principle, that every part of the Universe could only be understood as a microcosm; that is, that each individual thing contained everything within it, being no more than a specific reflection of one great universal harmony. In the centuries to which we refer the essential tension was between learned and laymen, between the refinement of the elitist culture and the barbarism rife among servants and peasants, and which also affected practically all public officials, soldiers and clergy. And we have three stories to tell in order to illustrate this change. We cannot reconstruct them documentally, be-cause, as in Lavoisier's case, they deal with things which everyone knows but which never actually happened. They are historic, but there were no witnesses. And, of course, we know so much about them that they are more real and more relevant than most of what we find in history books. They are real myths and give off the rosy glow of dawn: they are founding myths. And here they are. First we shall talk of Galileo's EPPUR si MUOVE, then of Archimedes' EUREKA and, finally, of the laughter of the Thracian woman, the story of the well of Thales of Miletus. The bare facts of the legend about the difficulties of Copernicanism can be quickly told.114 Galileo has just renounced his Copernican beliefs before the Inquisitional court. He is more angry than frightened, and between his teeth he mutters Eppur si muove, And yet it moves. What has happened? The greatest courtier, the most outstanding scientist, the greatest prose-writer in the Italian language has misjudged his strength, and against the advice of friends and enemies he has not recanted in time. He knows that the Earth moves round the Sun and declares that he has proved it. He fights to the end, but finally realises that torture and maybe even death at the stake await him. His judges are not prepared to negotiate, and obstinately they all turn up for this fascinating appointment with fate. They are 113 See Roger Cooter and Stephen Pumfrey, "Separate Spheres and Public Places: Reflections on the History of Science Popularization and Science in Popular Culture", History of Science, 32, 1994, pp. 237-267. 114 Mario Biagioli, Galileo, courtier: the practice of Science in the culture of Absolutism, University of Chicago Press, Chicago: 1 993. Dava Sobel, La hija de Catiteo: una nueva visión de la vida y obra de Galileo, Debate, Barcelona: 1999.

making history, they are going to humiliate Galileo and the astronomer, former friend of the powerful, shining star of the Florentine court of the Medicis, confidant of popes and cardinals, is on his knees reading a text which they have prepared for him.:

I, Galileo Galilei, [...] seventy years of age [...] and kneeling before you [...] swear that I have always believed and now believe, and with the help of God shall always believe in all that which the Holy Catholic Apostolic Roman Church holds to be true, preaches and teaches [...] Insofar as I have written and caused to be printed a book in which I expound this condemned doctrine [...] With sincere spirit and true faith I abjure all my errors, and reject and abominate them...

And this is what the documents show. But the story does not end there because somebody at some time explained that Galileo, as proud as ever, muttered between his teeth the phrase which fits in so well with our need for myths. "Yet it moves" resounds in our collective imagination like a rebel cry against Church's authoritarianism, as a gesture meant to remind us of superiority of scientific reason over the reasons of state, a sublime affirmation of individual freedom against social conventions. How could we fail to identify these words of rage as ours, still bursting with emotion? These are "facts" which we manufacture through necessity and which give dignity to our ever-threatened human condition. But let us go back a little. The extensive historiography about Galileo available —some 5 000 titles—, seems to confirm the theory that his misfortune was due to his Copernican convictions, but that the basic motive was something else. His enemies, the Jesuits, managed to persuade the Supreme Pontiff that the character Simplicio who appeared in the Dialogues was a caricature of the Pope of Rome. The evidence was elusive, as indirect and shaky as that adduced by Galileo in defence of the movement of the Earth, but the tense atmosphere made it credible. And from that moment, the die was cast. For the argument ceased to be about astronomy or theology, to become instead a crude exercise of power aimed at discouraging anyone who imagined that political power should be subject to scientific authority. Furthermore, since Simplicio spoke like an ordinary man, putting forward all the common sense arguments, the trial in a sense dramatises a revolt of laymen against scholars. It is not clear who was the first to tell this story, but there is a version which adds a surprising new character: it was to his dog that he addressed his Eppur si muove.115 This may seem absurd, and indeed it is. But, as we have said, it is not a matter of justifying one version or an-other, but of extracting the cultural consequences. It seems that in this context we are being told that even dogs, unprejudiced brutes creatures, could understand him better. Galileo's conviction, like Lavoisier's later, meant his immediate promotion to divine

115 Galileo Galilei, Consideraciones y demostraciones matemáticas sobre dos nuevas ciencias, by Carlos Solis and Javier Sádaba (eds.), Editora nacional, Madrid: 1976, see reference in introduction, p. 32.

status. His disciples fabricated his biography, insofar as it includes other inventions which are no less significant and widely-known.116 For example, his birth certificate was forged to show that he carne into the world on the day after the death of the great Michelangelo. It was also considered a fact that he had climbed to the top of the Tower of Pisa to drop two spheres of different weight which reached the bottom at the same time, thus destroying Aristotelian physics. But nobody has ever found a document proving the existence of this farnous and crucial experiment. And we could go on, because the greater the myths, the better embroidered are the narratives describing them. The jump we now make takes us to Sicily, nineteen centuries before. We are in the third century BC to talk about Archimedes.117 We know very little of his biography, and almost all of it would fit into a few lines. Born in 287 BC, son of a rich patrician astronomer, he lived for 75 years until 212 BC His fame, like Galileo's, is legendary and also like the Pisan he maintained close relationships with those in power. Archimedes was a sort of palace counsellor of the tyrant Hieron II of Syracuse. His death was a martyrdom, although he was killed by human stupidity rather than hate. Liceus, Plutarch, Valerius and Maximus, among others, tell that at the end of the lengthy siege of Syracuse ordered by the Roman Consul Marcellus our sage was in the garden of his house (others say he was on the beach) resolving an intricate geometrical problem whose lines he had drawn in the sand. Then a Roman soldier trod on his "manuscript", enraging the scientist. And that was that: at one blow the vulgar soldier ended the man's life and turned him into a myth. Once again we have the struggle between the scholar and the layman, and once again ignorance prevails by brute force over genius. And everyone was deeply sorry, because the Consul had ordered his troops to respect the scholar. This is no mere detail, because the chronicles tell that Archimedes invented some engineering devices which delayed the end of the siege and seriously annoyed the invading troops. They talk of marvels such as colossal catapults or a system of mirrors capable of concentrating light on the sails of ships and setting them alight. Much has been written of these marvels, but we have no choice, we have to say that they are fictional. Seven centuries later Procius finds another gem to delight the believers. We do not know where he found it, but who would dare to say ¡t was false? The Archimedes he shows us is the greatest of magicians, and he addresses the king: "Give me but one firm spot on which to stand, and I will move the earth". Fantastic! So they ask him to demonstrate this stroke of genius. Then after many calculations and much hard work he builds a gigantic system of pulleys and out of the water he drags the 5/racuse, a three-masted ship of some fifty feet in length, full of cargo. What more could they ask for? All the crowd stood open-mouthed as they watched the amazing spectacle: science could dominate nature or, in other words, the control of science gave great power.

116 Michael Segre, Nel segno di Galileo. La scuola galileiana tra storia e mito, il Mulino, Bologna: 1993. 117 Michel Authier, "Arquímedes o el canon del sabio", in Elementos para una historia de las ciencias, Michel Serres (ed.), Cátedra, Madrid: 1991.

And the best is yet to come. Once again we have Hieron II —power is still at centre stage— and our man. This time the problem is nothing to do with matters of war, but with the court. The King —recounts the great Vitruvius— has received a crown and suspects that all that glisters is not gold. What is more, he is convinced that he has been cheated with an alloy which is an offence to his dignity. He goes to Archimedes for help, who racks his brain to find a way of solving the enigma without destroying the symbol. In the next scene we see him in a bath full of water which overflows as he gets ¡n. What could be more normal? Perhaps, but it is all Archimedes needs. Eureka! I've got it! he is said to have shouted, running naked down the street. He had discovered the famous Archimedes' principle, where a body submerged in water experiences a vertical upwards force equal to the weight of water displaced. It would then be possible to construct a hydrostatic scale and check whether the crown displaced the same amount of water as if it was of pure gold. He built ¡t and confirmed the suspicions. While there was much merit in doing so, it is only fair to say that it is always easier to prove what "is already known" than the opposite. This is where Galileo went wrong before a court which "already knew" what was true, however much some-of the evidence might point in another direction.. The Simplicio of this story is no longer in disguise, nor is he a parody of anybody. This time it is the people who witness the scholar's eccentric behaviour, the unsettling evidence of genius. The nudity in which the discovery ¡s clothed is important, and the subliminal message is clear: a scientist only needs his brain, all the rest is incidental. And there is another exciting thing about this story: the overwhelming joy, the unbounded satisfaction. And as nothing is comparable to the pleasure of discovery, we get the explosion of glee with which he runs through streets before the once more astonished citizens of Syracuse. A bathtub is all that it needed. War, ships, these are overcomplicated affairs. But science is simple. It is very difficult, it is the province of the chosen few, but a great discovery only needs great curiosity. It ¡s the same as the story of Newton's apple, another doubtful fact which has been handed down to us by tradition and which we cannot prove.118 It was his niece who claimed to have been a witness, and she

118 The history of the novel, of poetry, painting or music is full of references to muses responsible for the miracle of creation. And nobody ¡s surprised to see how many artists become tongue-tied when asked where this brilliant idea carne from, or what produced that particular feeling. And muses are like witches: they don't exist, of course, but they are about somewhere. The history of science is in every way as good as that of art. Hefty volumes are dedicated to collections of all sorts of discoveries, often trifling, which have been made by chance. There are al] types, including some made by ordinary folk who did not expect to make any contribution to knowledge. It is said, for example, that there was a Peruvian Indian who, burning with the fever of malaria, dived into a river very close to a forest of cinchona trees. He drank and drank, believing his death was imminent, but he survived. Nobody was safe, and when he told the story in his village, the remedy be-came popular. Then, much later, the Countess of Chinchón, wife of the Viceroy of Peru, also fell ill with malaria, an illness which European medicine was powerless to treat, but which was cured by traditional Inca herbalists. Legend saids it that it was she who sent back samples of the tree-bark to Europe, bringing the first proven anti-fever drug in history. A century later the news reached Linnaeus, who in classifying it as Cinchona committed two errors at once. The first was not calling it "Chinchona" if, as it seems, he wished to give credit for the initial discovery, and the

went around telling the story until it finally reached the ears of Voltaire, who was able to play "Vitruvius" and to make up a good story. What both cases have in common is that a genius converts a vulgar and commonplace event into a far-reaching scientific fact. These two myths are telling us that a scholar is someone very special who can put everything to use, whose sight and sensitivity are very far from ordinary. He is different; he lives among us but he sees other things. His world and ours are the same only in outward appearance. Let us get back into our time-machine and call at Miletus. It is the end of the sixth century BC and Thales, for the Greeks one of the seven great sages of antiquity, founder of Philosophy and astronomy, goes out of his house to look at the sky. Absorbed in his thoughts he doesn't see the well which is in his way, and he plunges to the bottom. Plato tells us the story through the mouth of Socrates; the only witness is his Thracian servant, an ignorant woman and, like all Thracians, obsessed by the worship of her many gods. And Thales had just the opposite obsession because in his opinion there were too many gods in the minds of his contemporaries. It was enough for him to open his eyes in that harbour town to be convinced that everything carne from water, that water was the primordial element at the origin of everything that exists. And so was born philosophy, for it was Thales who had the distinction of first looking for the reason of things in nature and not in the capricious world of the gods. And again, as in the case of Newton and Archimedes, his discovery was a response to the simplicity of the formulas which

second attributing it to a woman who never returned to Europe and who had done no more than to admit that the natives might possess more effective medicines than the palace doctors. So who made the discovery? The legendary Inca, the Countess in the fable or the historical botanist who transformed a series of mistakes into a famous breakthrough? No mistake had greater consequences than the discovery, accidental finding, or invention of America, which at all events has been called the Columbian breakthrough. Columbus was looking for the Indies and found America and, as such, deserved to be included as yet another character in Walpole's tale "The Three Princes of Serendip". Archimedes and Newton were enjoying a rest when something pulled them out of the everyday run of things and raised them to the status of discoverers. We remember jenner for discovering smallpox inoculation and he relates the story that a simple milkmaid told him that she would never catch such a virulent disease because she has had already the cowpox —vaccinia. The story was remembered years later and became the origin of the methodical research programme which the scientist carried out until the discovery was made. Once again we have a day-to-day fact becoming a scientific breakthrough. In the same way, many stories have circulated about the discovery of penicillin by Fleming, rubber vulcanisation by Goodyear, the Rosetta stone by Champollion, radioactivity by Becquerel, or the positron by Anderson. Chance is a common factor in all these cases, although it is highly debatable whether they may rightly be attributed to common or garden luck or to prestigious serendipity. Certainly, to say that luck was important gives a certain aura to the scientist, as shown in the case of the discovery of benzene, a molecule which chemists could not understand. The story that Kekulé told thirty years later turned out to be a fraudulent lie, since he said that he dreamt that a snake coiled round itself, which enabled him to devise the hexagonal form. But it was not true, since it was then shown that he had not been inspired by dreams but by reading the work of his predecessors. For more tales, see Sven Ortoli and Nicolás Witkowski, La baignoire d'Arquiméde, Seuil, Paris: 1996, and aiso Federico di Trocchio, Las mentiras de la ciencia. ¿Por qué y cómo engañan los científicos?, Alianza Editorial, Madrid: 1995.

led to success, and also has its origins in his curiosity about things which could happen, about his surroundings, about everyday things. But what part does this woman play in the story? She is there to laugh; the servant mocks the fact that someone looking so far above him fails to notice what is at his feet: if you look at the sky, you are unaware of the ground. The Thracian woman not only evokes the intellectuals' loss of a sense of reality, but she reproaches them for their lack of concern for worldly things —perhaps even their disdain for popular religious beliefs— and for the concerns of ordinary folk. Plato tells us a fable, probably borrowed from Aesop, which is far from innocent, since Thales' action anticipated what was to become normal in Socrates, and which finally became intolerable to the Greek polis. Scholars interfered in their affairs, questioning everything, rummaging around their refined traditions, and rather than the solution they were the real problem faced by the fragile social structure. If Thales was a victim, Socrates ended as a martyr. The myth has been told a thousand times and changed as often. Its shadow stretches as far as our own time, because the accusation that the philosopher is a waste of time and a social parasite is a platitude which is far from exhausted, even though he was born at the same time as astronomy. And there are versions for all tastes: Montaigne brands the Thracian woman as the enemy of knowledge because she did nothing to prevent his fall, Serres angrily asserts that the well was none other than an astronomical observatory and that the scientist was working down there, something which the coarse servant was unable to understand.119 But there is another story worth recalling. Aristotle recounts that Thales was very angry because people laughed at him for being so poor, even though he was so wise. More laughter. And in order to disabuse his fellow-citizens he offered them proof that his situation was voluntary and not imposed. His knowledge of astronomy enabled him to forecast a splendid olive harvest, and he then rented all the mills in order to organise a monopoly from which he could speculate and make fat profits. He did so and then got rid of all the wealth he had made. Scholars have no time for trivia, and if they seem shabby or idle, it is not because they hate the world or cannot enjoy life, but because no passion is the equal of passion for knowledge, and no success so great as that of discovery. Who has the last laugh? In other words, who can afford to laugh at whom? Scholars or laymen? Let us leave the answer for a moment, and not fall into the trap lurking behind such apparently innocent questions. The problem we pose is an old one, but what our wise guests are talking about is right up-to-date, problems yet to be solved. Thales and Archimedes are still alive, but we have to resume our journey. And from most ancient to most modern times. Barely a second passes and we are back with Snow, who in 1959 wrote a book whose success is still a mystery to many of us. Snow says that the West is rushing headlong towards a terrible crisis. The problem is the communication gap between the two cultures —traditional or literary and liberal or positivist— a tragedy which threatens the very 119 Hans Blumenberg, La risa de la muchacha tracia. Una protohistoria de la teoría, Pre-Textos, Valencia: 2000.

idea of democracy and which, if true, would be bemoaned by all the Tocquevilles travelling round America. The solution he proposes is simple, and consists in fusing into a single, third, culture knowledge of nature and knowledge of conscience, common speech with learned language. Snow, like Frank Oppenheimer before him with his paradigmatic popularising project in the San Francisco Exploratorium, disappointed like his brother Robert by the circum-stances surrounding the bombing of Hiroshima and Nagasaki, wants better republicans, citizens involved in culture and science. And for this he seeks an army of intermediaries to build a bridge between the two shores. At the end of the Second World War Vannevar Bush, Director of the Federal Office for Science and Technology, president of the Carnegie Foundation and former architect of the Manhattan project, published a text entitled Science: the Endless Frontier to remind politicians and citizens that America's strength lay in its capacity for scientific and technical innovation.120 And this enthusiasm continued unabated until the Soviets overtook them in the space race. Then began the drama and the Americans suffered an identity crisis: they could not believe, ¡t was absurd, that the Communists, in the typical language of the cold war, could go forward more quickly in the march to progress. And among the many diagnoses of this supposed decadence that of Snow, pointing out the tragedy of the two cultures, gained credibility. And thus arose the myth. However, our opinion differs, for the problem continues to be the gulf between scholars and laymen, or between the elite and the people. Popular Scientists We have already quoted Voltaire who, for Snow, would have personified the paradigm of the intellectual bridge and who, as is well-known, played an important part in the introduction of Newtonianism into France. The publication of his Elements de Philosophie de Newton was praised unreservedly by the Jesuits themselves, his old teachers : "Behold, all that which seemed difficult or impenetrable in Newton is here, how-ever, within our grasp... Everyone wishes to read at least a chapter, to glance at the titles, to feast their eyes upon the book [...] /e tout Paris is buzzing with the name of Newton, is prattling about Newton, is studying and understanding Newton".121 Lo and behold, the dilemma of the two cultures is apparently resolved. A man of letters, the Poet of France, explains science to all, and nobody who aspires to be enlightened can be unfamiliar with Newton. Sir Peter Medawar, winner of the Nobel Prize for medicine, protested two centuries later that not reading Shakespeare was

120 Roy MacLeod, "A Ciência e a Democracia: Reflexôes Históricas sobre Descontentamentos Actuais", in María Eduarda Goncalves, Ciência e democracia, Venda Nova: Bertrand Editora, 1996, pp. 31-61 121 Antonio Lafuente, "Newton a la carta", introduction to the edition of the Elementos de la filosofía de Newton, by Voltaire, Círculo de lectores, Barcelona: 1996.

tantamount to being an ignoramus, whereas total ignorance of the theory of relativity was still forgiven. In the eighteenth century, however, to talk of the theory of gravity or the refraction of light through prisms was the frontier which had to be passed before entering the salons of Madame de Pompadour or Madame de Châtelet.122 The dream of science within everyone's reach seemed to have come true, and was the precursor of such astounding facts as the Great Exhibitions or the Cité des Sciences et de 1'lndustrie de la Villette in Paris. And so runs the well-established propaganda, concealing a reality which is not quite so obvious. How did the grim Mr. Newton reach the hearts of all these wise ladies? Voltaire had to invent the genre of popularisation. The facts articulating his tale of mathematical laws and principles of physics are no more than a collection of anecdotes which, by being entangled with everyday events, mean a new way of expressing collective experience and thus common sense. And when he could not find the right metaphor he did what has always been done: he re-sorted to the authority of the divine Newton and asked his reader for an act of faith... When he does not know what to say he attacks Descartes and rather than prove the dictum of the new science he ridicules the principles of the old. He contrasts the absurdity of the Cartesian ether with the simplicity of the vacuum, and always with a rhetoric which creates the illusion that Descartes was cunning and Newton straightforward. It is absurd to admit the concept of action-at-a-distance, but his rhetoric was successful. Voltaire knew that it was impossible to become Newtonian without an act of faith and so he asked help from his friend Maupertuis in the following forceful and revealing terms: "I await your reply to know whether or not I should believe in attraction [...] My faith will depend on you". And a few days later, after receiving the reply, he writes back enthusiastically: "You have banished my doubts... Behold, I am a Newtonian like yourself. I am your disciple and I put my profession of faith in your hands".123 There is no doubt. Voltaire, who knew little of science, needed to be converted. This is the trap into which anyone trying to enlighten the ignorant will fall. Science, intended as an activity for privileged brains, is spread to the ignorant using a style which needs the literary wiles of a great seducer. Voltaire was great, but Georges-Louis Leclerc, Conde de Buffon, was in no way inferior. Author of the monumental 90-volume Natural History and a sworn enemy of Voltaire, he proposes other ways to understand the relation between science and public.124 The change, however, demands a new approach. And again we have the same rhetoric which always tries to ally itself with common sense. Is it not absurd, says Buffon, that the dog, which "...customarily follows the horse in real life", should appear, according to Linnaeus, immediately before the horse in his 122 Georges Rousseau, "Los libros científicos y sus lectores en el siglo XVIII", in Javier Ordoñez and Alberto Elena (eds.), La ciencia y su público: perspectivas históricas, CSIC, Madrid: 1990, pp. 147-224. 123 See Antonio Lafuente, "Newton a la carta.... Op. c;t. 124 Our comments on the case of Buffon are based on our own work, Antonio Lafuente and Javier Moscoso, "El sensire aude de Buffon. Escritura y público de la ciencia popular de la Ilustración", introduction to the edition of texts Georges-Louis Leclerc, conde de Buffon (1707-1788), CSIC, Madrid: 1999.

system of zoological classification? The Creator cannot be a Great Geometrician, as Voltaire had it, but a Sublime Gardener who has ordered nature in accordance with what we are and, of course, what we could be. But this "we" to whom Buffon addresses his words is not the thinking logos of Descartes and Newton, but the collective subject which emerges as spokesman of public opinion. Buffon's Natural History re-quires a radical expansion of the sensory universe, capable of "follow-ing... the order of relationships which things seem to have to have with us". Rather than create complicated systems of classification it is more important to "look and look again". Not such an easy task, unless we can open our eyes to look as if for the first time. In order to know nature, we have to shake off a heavy inheritance: we have to be re-born, or invent a new res publica to restore our atrophied sensitivity. And the battle must be fought in the field of public opinion, without whose expansion there can be neither civil history nor natural history. Buffon then appears as the awaited prophet, he comes to fulfill a long-deferred promise: the creation of popular science. Not elitist and then popularised, but totally woven into the warp of society and, nevertheless, endorsed by Royal Privilege or authorised by the Academy of Sciences of Paris. Buffon represents the possibility that the knowledge of nature, of its order and distribution, its culture as is generation, may be ours by right. And the French love him. His books were bought with great delight, until they became the greatest publishing success of all time. Yes, they love him because his rejection of a mechanical-geometric concept of nature opens the way to new ways of understanding within the grasp of the ordinary intellect. There is a direct contact between the scientist and the public which does not need the intervention of the intellectual. The strength of his Natural History lies precisely in his ability to address the reader directly, without a need for go-betweens, and to teach him that there is no more order in nature than we our-selves want to find in it. Thus the reader takes a decisive role. The knowledge described by Buffon avoids the simplifications introduced by all the other systems and, without scorching biological diversity with abstract laws, takes as much pleasure in feeling it as in reading about it. The history of Nature cannot be excluded from the history of the ways in which we feel it and therefore write about it. If Voltaire and his scheme of popularisation can be seen as the realisation of the dreams of Snow, Oppenheimer or Medawar, Buffon seems to embody Brockman's aspirations. In what may be considered the manifesto of "The emerging third culture", John Brockman declares that the scientists of the third culture communicate directly with the public, without need of philosophers or popularisers, and so acquire their status as the new public intellectuals.125 They call Daniel Dennett the new Bertrand Russell, Tom Wolfe describes Edward O. Wilson as the new Darwin, and Richard Dawkins is now one of the most sought-after writers in Great Britain. Science is posing challenges which affect the fundamental values of our social order and which involve the very survival of the species. People have been seduced by this message and now they demand that these tensions should 125 John Brockman, La tercera cultura, Tusquets, Barcelona: 1996.

be brought into the open. And Brockman, who has read the signs of the times, confirms that "his" authors, converted into sexy scientists, have at least a tenth as many readers as those who follow the writings of the Pope. So, as well as being a great propaganda exercise, the third culture is also a big business which nobody is quite sure how to interpret.126 What characterises the science produced by this third culture is its ability to create objects which were previously unthinkable within the traditional scientific world. It is not just that we are talking of problems of an interdisciplinary nature made up of a greater number of variables, nor that they need any greater understanding of chance as a motor for change, nor even that they include theories relating to human consciousness or behaviour: but it is the combination of all these difficulties which make them unmanageable. Not all problems are automatically accessible. Each discipline has its traditions, and its own way of reducing phenomena to observable and quantifiable parameters. So to pin down an object in a laboratory requires a scale more suited to the mathematical and experimental styles of a "fact factory" which is used to theoretical and technical simplifications. These have split nature up into disciplines and, above all, have kept her isolated from the contagion of the realm of the so-called social sciences. What the new historiography has taught us about the Scientific revolution now echoes what the scientists of the third culture are demanding: to be in possession of tools in order to work with objects which cannot be created artificially, ¡n order later to manipulate them in the laboratory. So that in order to isolate them they have to operate as Galileo, Newton, Linnaeus or Lavoisier did: first, to imagine them as a synthesis of different traditions; second, to fix them by ad hoc experimental means developed in the laboratory; and third, to disseminate them by means of propaganda aimed at increasing their presence in the public awareness.127 It is far from easy, as science studies show, but the iconoclasts are in luck. Literature abounds, but few have shown such mastery as Steven Shapin,128 expert in the great superproductions of Hollywood's Golden Age, but who shows us a view of science and scientists which does not follow in the wake of Cecil B. de Mille but rather the models of Woody Alien or Robert Guediguian. And the change is as great as that which took place in the cinema, all that we lose in spectacle and glitz we gain in truthfulness and freshness. The actors are ordinary people who cook ordinary food, although they still hesitate about what spice to use for seasoning and sometimes they venture on vague projects. So are scientists also like us? Yes, and in two senses. First, because they are human beings; they live in society, they feel passions and they make lots of mistakes. But Shapin also draws a picture which, without detriment to 126 Marek Kohn, "Laboratories against the literati", article on Brockman in The In-dependent, 24th March 2000. 127 See Larry Stewart, The Rise of Public Science. Rethoric, Technology and Natural Philosophy in Newtonian Britain, 1660-1750, Cambridge University Press, Cambridge: 1992. And also Christian Licoppe, La formación de la pratique scientifique. Le discours de l'expérience en France et en Angleterre (1630-1820), La Découverte, Paris: 1996. 128 See Steven Shapin, La Revolución Científica. Una interpretación alternativa, Paidós, Barcelona: 2000.

historical accuracy, is relevant to the reader who is trying to understand the world of today. The scientists of the 16th and 17th century are invited to join in as our contemporaries in this feast of words and gestures which we call culture.129 To be sure, they speak about their affairs, their world, their dreams, their favourite books and their contacts; but they speak our language, they know about our interests, they are not autistic. And they do indeed need the conversation we offer them. The image they have been landed with is uncomfortable, they wear grandioso clothes, they look like brains stuck onto a sphinx, and they don't want to waste any more of the life they have left in feeding our insatiable hunger for myths and legends. And they are quite right. This strategy was always plagued with controversy and theoretical or experimental difficulties. Looking for the protagonists of these procedures with Nanni Moretti's hand-held camera teaches us to see them smuggling instruments designed for other purposes, acting without a script, with histrionic gestures and with dynastic ambitions. What is new about the aims which are behind the third culture is that they are fusing together problems whose scientific and humanistic nature is no longer dual, as Snow describes the drama of our culture, but unique and indistinguishable. Systems as complex as the brain and the consciousness, matter and life, the biosphere and culture, are not pairs of independent problems, but are all subject to a common evolutionary process. And to think of them as interdependent we need a whole arsenal of new metaphors which will transform our culture into something hitherto unimaginable, and of course as revolutionary as the change which took place in the Renaissance.130 And we are not only talking of books. Another of the characteristics of the third culture is that the frontiers between scientists and amateurs are breaking down more and more. The very notion of science and academia has become something too abstract or else too political and worldly. The reasonable thing is to talk of research, a term which simply describes a single activity which is not encumbered with dense clinging utopian or ideological values. To accentuate the contrasts, it seems that the commitment is no longer so much with truth as with the wish to make things work. Old-style scientists would measure and test the mind or the intelligence, while those of the third culture would try to make something that worked well, or seemed to. In order to answer the question of how the mind works, the solution which would meet with most approval would be to build something which tried to replicate it. And we could generalise this change of direction into all topics characteristic of the third culture, for the answers always take the form of new technologies. What is reality? What is life? What is consciousness? The third culture makes use of supercomputing and replies with artificial reality, artificial life and artificial consciousness.

129 See Andrew Cunningham and Perry Williams, "De-centring the 'big picture': The Origins of Modern Science and the modern origins of science", British journal for the History of Science, 26, 1 993, pp. 407-32. 130 Boaventura de Sousa Santos, A Crítica da razâo indolente. Contra o desperdicio da esperiência, Ed. Afrontamento, Oporto: 2000.

For Popper science transcends culture. Something which Polanyi expressed more radically when he considered it the epitome of transculturalism, a production capable of overcoming the multiplicity of races and cultures. But what happens when tension arises between people of different levels of access to education, between rich and poor, between centre and fringe? Here Snow, fascinated like other armchair leftists by the Soviet education system, hesitates between sending an army of engineers to impose modernisation in all corners of the planet, and recruiting battalions of scientific teachers to banish the local culture. But all these points now seem archaic. Today the culture which transcends all others is technology. We are talking not of the missionary experts that Snow visualised in mid-century, but of the masses of Internet users. The PC is the greatest symbol of the third culture. More than a tool it is a destiny: its millennium lies in the promises of nanotechnology, and its acolytes keep swelling the ranks of the technopagans.131 Computers, said MacLuhan, are LSD for the leaders of the New Economy. Their heaven ¡s in Silicon Valley and in innovation-oriented capital-intensive industries. Their spokespersons have no great respect for scientific credentials and rather favour free initiative and amateur-ism. Understanding is less important to them than innovation. Many of the protagonists make up a sort of pop science, full of people whose culture is their technology. It is the generation of the Nintendo or Tamagoshi kids: it is the generation of the nerd, a popular term to describe those eternal adolescents who dress without style, who can't get a girl and who are obsessed by computers, the noisiest electric guitars, and science - fiction B-movies. Any teenager can get hold of a powerful PC and keep a virtual farm and develop software until he produces something never seen before. It was nerds who created the dinosaurs in Jurassic Park, inventing a whole virtual structure of bones and muscles under a simulated skin, which showed aspects of the movement of di-nosaurs which no palaeontologist could ever have imagined. The nerd is an explosive hybrid born of the convergence between ease of access to Internet and the proliferation of unqualified experts who roam the net. And this is not a Hollywood scenario, and it is not just for "gringos" -for nerds are everywhere, they are an international phenomenon.132 Their heroes are hackers, those computer pirates who, after a spectacular attack, are hired by some multinational for astronomical sums. The hackers respect nothing and nobody, they break into the Pentagon and shop with Bill Gates' credit card. With their home computers they laugh at official experts. Once again, laughter, only this time those who laugh are fans of Internet II, unclassifiable people with great influence. Even if history meant anything to them, they would admire neither New-ton nor Einstein. Perhaps their mythological hero would be

131 See "Technoculture: Ghost in the Machine", interview with Erik Davis (March, 1999), author de TechGnosis: Myth, magic and Mysticism in the Age of Information, published on the Web: www.redindustries.conri/portfolio/spicer/dtf/l999/11/feature1_a.html. 132 Kevin Kelly, "The Third Culture", Science, 279 (5353), February 13, 1998, pp. 992-993. Can be found on http://www.sciencemag.org/feature/data/150essay.shl.

Edison, some-one without university degrees who improvised tools as he needed them and who, like a good nerd, had certain business ambitions. Edison did not stop to think of the possible perverse or wicked uses of his inventions. What concerned him was whether the gadgets worked, and incidentally to increase his income. Essential tension The sect of the Edisonians is forceful, but they would never manage to win the contest to nomínate the person of the century with which Time magazine welcomed the year 2000: the winner was Einstein. Fifty years before the Americans who took part in the same competition choose Roosevelt. A significant fact which emphasises the idea that scientists are special people and that even today they have greater credibility than politicians. Talking about science is not a recent fashion and rarely has a theory aroused such media enthusiasm as that of relativity. Its conclusions were as amazing and incomprehensible as those proposed by Newton. Is it acceptable for the same phenomenon to be described in a different way by two observers? We know that this is normal in human sciences and in café conversations, but the positivists led us to believe that science was different. Well yes, it happens, it is against common sense, but eppur si muove. For one you only need to stretch time and for the other to shrink longitudes. Many physicists hesitated, and it was some time before scientists admitted it to their canon. But where scientists feared to tread, artists rushed in. The former talked cautiously of space and time as mathematical variables included in equations explaining incomprehensible phenomena at the hand of Newton or MaxweII; the latter wanted relativity to be the exaltation of subjectivism, the final assault on the academic spirit, and the greatest Impetus to abstraction in painting, atonality in music, free verse in poetry and moral vagueness in politics. "A silo full of concentrated sin" was the verdict of one of the commentators worried at the end of civilisation portended by Einstein's ideas. Everyone had his say and few of them appeared to listen to what the wise man actually said. In a famous play by Tom Stoppard, a philosopher wonders "If you can no longer believe that a twelve-inch ruler is always a foot long, how can you be sure of things which are relatively less certain?". Einstein pro-tested at this polyphonic flood of banalities, but to no avail. The theory of relativity was a universal potion, to cure all ills, because now every-thing was relative. The image of the person carne before that of the scientist, and the more irony he heaped into his comments against so many charlatans and so many pedantic opportunists, the more brilliant he seemed. And relativity? Nothing, for it soon became clear that few were to be able to understand it. Further, such

difficulty only served to make the myth more powerful, because the more inaccessible his ideas, the more undeniable was his brilliance.133 Einstein got tired of correcting those who looked for the myth rather than his theories. And here we find another great joke. Einstein laughed at himself. There are few images more widely-known than that offered to the cameras on his 72nd birthday, with his tongue out and the look of a naughty schoolboy, framed by a great mass of unruly hair. He is making fun of himself. There is no hint of animosity between the actor and his audience. The fascination is mutual, but the script is well-known. The press still wants to overwork an image which wavers between distant sphinx and popular hero. Nobody wants to look for another piece of news, for Einstein is not a fashion: he is a necessary myth. No matter what he does, the reporters will not interpret his pose as a gesture of arrogant rejection but as further proof of his incomparable genius.134 And before we end, we have another great burst of laughter, whose echoes can still be heard. Now, many centuries earlier, it is Democritus who is laughing. What is the matter with the venerable sage? Some apocryphal letters between the citizens of Abdera (Thrace), his native town and the great Hippocrates tell the story. They are very worried because their Democritus, their much-admired sage, laughs at every-thing, doesn't sleep, sings to himself at midnight, listens to the birds' song, wants to travel to the outer limits, declares that the air is full of shadowy figures. A misfortune which calls for a doctor's opinion, since it threatens to spread to other citizens. Hippocrates, continues the legend discovered by Littré, goes to the town and gives his diagnosis: "I do not think this is an illness: he has just had a surfeit of science, which is really only an excess in the eyes of ordinary 133 The cult of the genius extended to his grey matter. On the 18th April 1955 Thomas Harvey, in charge of the autopsy, left the operating theatre with the genius' brain under his arm. Now the problems began, because the son protested, fearing that such an object might become the focus of popular cults. On the 25th April there was announced a conference of specialists which, after meeting, ended in disarray. Then the army claimed its right to study such a unique specimen, but Harvey refused to hand it over. Pressure mounted. It was a serious matter, and it was to cost him his careen first he was expelled from the hospital and later lost his medical certificate. Harvey disappeared for twenty years, until in 1978 he was found by a journalist. And yes, as well as photo-graphs, he showed him the brain cut into some two hundred and forty cubes. The news caused a media storm. Dozens of scientists ask for a piece to experiment with, and some were successful. But the results were poor and inconclusive: and so Harvey and his prize went back to their game of hide and seek. In 1 990 the brain was donated to a pathologist at Princeton hospital. And that brings us up to date. Because in June 1999 the influential magazine The Lancet published an article which claimed to be a definitive study of this priceless relic. There was controversy. Many though it incredible that efforts could again be made to find a relationship between morphology and intelligence. Of course, the most modern techniques have been used and there are a couple of very notable anomalies in the parietal lobes. S. Pinker was delighted and has announced his happiness to the four corners of the Earth with ringing phrases: "It is a strange coincidence that this brain which brought together the fundamental categories of existence, space and time, matter and energy, gravity and movement, should be helping us to unify the last great dichotomy of the conceptual universe, mind and matter". See Mundo científico, 209, special issue, "El cerebro de Einstein" (february, 2000). 134 Antonio Lafuente, "Albert Einstein, el genio del siglo", Muy Extra. Biografías, Summer 2000, pp. 122-129

citizens". Splendid. If it were not for Einstein's clowning, this would be the antimodel. Now it is the scholar who laughs. He scorns human stupidity and, if he has with-drawn from what the people call the world, or life, it is to inhabit another more forceful and attractive. Here we have one of the scientist’s favourite images: the priesthood of truth, reclusion in the exclusive space of the laboratory.135 Galileo did the same after his conviction: he with-drew in order to write his finest works. And Cicero says that this was a characteristic of Archimedes' life: far from the image of an engineer concerned with practical matters, he shows us a timid watcher of the world and its secrets who was not even able to sense the danger he was in when the Romans overran his city. A mistake which cost him his life, but which elevated him to Parnassus. We began with a martyr and end with a madman. But we have also redeemed a good deal of laughter. What makes them laugh, what makes them die? Sometimes an excess of wisdom and always what they do not understand. Lavoisier, Galileo, Archimedes and Thales died in a reverie. Einstein, Voltaire and Democritus drifted towards disillusionment. Buffon and Brockman have an overdose of academia and, finally Mary Shelley and the woman of Thrace tremble with anxiety. Science is certainly special and all too often creates insuperable distances. The image of the two cultures is a recent illusion which hides a harsher reality: the schism between scholars and laymen.

135 Bernardette Bensaude-Vincent, L’opinion publique et la science. A Chacun son ignorance, Sanofi-Synthélabo, Paris: 2000.

Western and non-western science:

history and perspectives*

JUAN JOSÉ SALDAÑA** Has a non-western science ever existed? This seemed to be the first question that the title of this communication suggested. But, as we will see, ethnocentrism has been a limitation for the historical study of world science as well as to formulate appropriately and give an answer to such a question. At present we know of historical evidences to respond affirmatively to that question. The history of science has been able to sustain, for example, that in the Chinese, Hindu and Amerindian civilizations original scientific knowledge that arose totally independent from the West took place.136 It has also been established that science, as much Western as non-Western has made a place for transhistorical and transcultural processes of appropriation of scientific knowledge, and for diverse forms of scientific activity in different societies. Thanks to that today we know, for example, that Classical Greece was not the only/sole source of rational thought and scientific knowledge. The relationship of Classical science to cultures of the Near and Far East are expressed by the type of influences that were exercised on it by previous cultures (Egypt, Babylon and China) or contemporary (India and China). It is cross-cultural processes that have taken place throughout history, and which have ended up constituting one of the main areas or characteristics of science| ecumenism, as Joseph Needham calls it. For the topic of this intervention, it is necessary to establish the fact that in all societies of any time and place, one or several systems of knowledge about natural phenomena such as material and energy processes, the celestial and climatic changes, soil and minerals, plants and animals, human organisms and their illnesses, etc. have been present as one of the central elements of each culture. The second question is if non-Western science has been reducible to the Westerner, that is to say if both are not but portions of their our scientific knowledge. It has been equally affirmed that non-Western science ended up

* Paper presented at the World Conference on Science, ICSU-UNESCO, Budapest, 1999. ** Professor of History and Philosophy of Science at National Autonomous University of Mexico. E-mail : saldana@servidor.unam.mx 136 The bibliography on ancient science is abundant. Classical studies on Chinese science and cross-cultural diffusion are those of Joseph Needdham 1954, 1972, 1975, 1977, 1978, 1985 ; some recent studies on Greek science are : Bernal, 1992; Pingree 1992, Rochberg 1992, Von Staden 1992 ; on Indian science Biot 1969 and Subbarayappa 1971 ; on Islamic science : Rashed 1980, Vernet 1978; Sabra, 1996; on pre-Columbian science see Garces, 1982.

integrated into the Western scientific tradition in large or small measure and at different moments of its evolution. This was the case, for example, in the Greek and Hellenistic times with Mesopotamian algebra, arithmetic and mathematical astronomy;137 in the high Middle?! Ages with Islamic mathematics, astronomy, physical optics, natural history and medicine;138 or as a consequence of the Discovery of America^ with botany, zoology and pharmacology among others.139 On the other hand, in some other cases like that of Amerindia, China, or India an abortion of non-Western cognitive traditions took place as a result the imposition of Western science, which didn't integrate those traditions into Western science mainstream because of that abortion.140 It is true that areas of knowledge that were developed outside of the west, although they have arrived recently, still have not been integrated in to Western science, as in the very well-known cases of the Chinese acupuncture or traditional medicine of several regions.141 On the other hand, in terms of Western modern science, one of the main characteristics is the one that refers to the geographical expansionism in regions outside Europe, and in certain cases that have been documented in Europe itself in regions far from main scientific centers. This is another transculturation which is historically recent but which is the one that has reached the widest span, to the point of becoming a world phenomenon at present time. The diffusion of science that took place during the last 500 years led to a "westernization" of the societies where it was implanted. However, it didn't mean that a resulting homogeneity of the simple adoption of the scientific practice that was typical in Europe took place. In the European case this was because of the social, economic and cultural conditions. Neither gave way to the surrendering of traditional knowledge and traditional culture. What the most recent historiography on the topic presents us is an interaction of modem science and of its institutions with local cultures, making room for multiple developments of science in other regional civilizations and in other historical processes. This fact led to the formation of new and different peculiar scientific practices in each case, the resulting processes of local domestication to which science was subjected. In general, at present it is accepted that the institutionalization of science in diverse societies has been the result of a complex social process and not the simple transfer of knowledge between centers and peripheries. This is a conclusion that will surely enlighten science policies carried out by governments of numerous non-Western countries, and also for international public and private organisms whose actions have been guided by the idea that what is needed to modernize is a kind of a hypodermic injection to get a quick inoculation of foreign science and its institutions in non modern societies. We will return to this point later.

137 Bernal, 1992. 138 B.Sabra, 1996. 139 Fresquet, 1995. 140 Goonatilake, 1984. 141 Needham, 1978, Estrella, 1996, Valdivia 1996 and Rojas 1996.

Then, we intend, shortly, to identify in the evolution of the historiography of science some of the factors that it used: first, to give up the point of view that sustained the European-western nature of science; second, to supersede in a recent time this vision of things and to sustain that every historical period and each locality should be seen as valuable in themselves; and, third, to extract from this new historiography some viable strategies to achieve the domicile of science in all societies, since by such strategies the existing cultural diversity in the planet takes its place. The formation and the development of science in different localities only recently has begun to occupy the attention of historians. The history of traditional science didn't grant greater interest to this topic and it stops its understanding at only simple and general ideas, leaving to the margin of the analysis the complexity of the situations and its geographical and cultural diversity. In 1938, George Sarton, the influential promoter of the history of science in the first half of this century, in "The Scientific Basis of the History of Science"142 established that the object of study of this discipline was constituted by the discovery of objective truth and its diffusion. The geographical expansion of science consequently was considered a result of a diffusion process. That is to say, modern science was transplanted from European scientific centers to diverse regions, and it; ended up, after a gradual process, tossing roots to the peripheries. Simultaneously, following a point of view characteristic of the Enlightened tradition, it was sustained that the diffusion of science led to modernity and the westernization of societies in which it was implanted. The ignorance, the superstition and the cultural, (and sometimes material) backwardness characteristic of the traditional societies was overcome thanks to the penetration of science in such societies. The same Sarton in The Quest of Truth affirmed: "science is at the root of social change",143 because it introduces not only a new way seeing but a new being. Their diffusion was not able to, therefore, constitute but one factor of the progress of nations. The diffusionist point of view was generalized to all type of situations, in such a way that the installation of science inside European countries themselves, for example in Scotland or in Ireland, in the British case, had also followed a diffusion process.144 In the same way the cases of scientifically backward European countries were understood in the XVIII century as, for example, Russia or Spain.145 The process of globalization of science that took place from 1492 on with the Discovery of America was conceived, of course, in a similar way. Wide geographical and cultural areas such as, for example, Spanish America from the XVI century, English America from XVII , French and British India as well as the region of the Pacific from XVIII, and the African region to the north of the Sahara

142 Sarton, 1938. 143 Sarton, 1953. 144 Shapin, 1983 and Jarrel, 1987. 145 Boss, 1972 and Sarrailh, 1957.

from XIX , were for Europe examples that civilization had achieved advances in other regions thanks to the diffusion of science.146 The idea of the diffusion of science was born with the philosophy of Enlightenment and consolidated in the time of the world empires. On the other hand it formed part of the optimism from the XVIII century of the trust in the power of the reason, and it was expressed in the controversial notion of progress. The diffusionist position assumed the superiority of the culture and of the Western social organization and, as a result, a missionary purpose, the advance of science, served as encour-agement. Although, it is necessary to mention it, this noble purpose was also used as a justification of the imperial ambitions of dominance and exploitation of countries and their natural resources. With the independent advance that indeed conceived science as a consequence of the discovery of new worlds for the investigation,147 and of what Europe learned of its contact and of its conflicts with other cultures,148 we believe that the fundamental fact remains that science and the European technique were also instruments on the dominance that Europe imposed to the rest of the planet starting from 1492. This left their mark on the scientific activity that took place in the colonized regions and it characterized their historical periods. Alexander von Humboldt inaugurated the genre that some have called "history of colonial science", with the observations that he made about the progress of science in the countries that he visited during his American periplus that had begun exactly two hundred years ago(1799-1804).149 These observations reflect the diffusionist conception already sharply present in the XVIII century. In the correspondence of this celebrated traveling Prussian as well as in his journals150 and scientific works written on American topics one can notice the enthusiasm that, as a good Enlightened man, was always produced at his encounter with pre-Columbian science, American scientists, or with the works of those to whom he could not know.151 In his Political Essay on the Kingdom of the New Spain (1822) 146 Ziadat, 1986; Reingold and Rothenberg, 1987; MacLeod and Rehbock, 1988; Polanco, 1990; Petitjean, 1992; Lafuente and Sala, 1992; Saldana, 1993. 147 Cohen, 1960. 148 Bitterli, 1989. 149 Regarding the existent institutions in America, those of the city of Mexico like the Botanical Garden, the Academy of Arts and the Seminar of Mining deserved Humboldt the following concepts: "Any city of the new continent, without excepting those of the United States ones, presents scientific establishments so big and solids as the capital of Mégico." (Humboldt, 1822; p. 227). He recognized the bring up to date of the scientific knowledge that there were teached as the chemistry of Lavoisier, the system of geologic classification of Werner, the orictognosia or mineralogy of the school of Freiberg, as well as in the courses of mathematics the teaching of the analysis and the integral and differential calculation. Of the Botanical Garden he highlighted their courses based on the system of Linneus, their herbarium and the rich collection of minerals that it possessed. 150 Humboldt, 1980. 151 Among the scientists with whom he entered in contact were Mutis and Caldas in Bogota; Unanue and Urquizo in Lima; Tafalla in Guayaquil; Olmedo in Loja; Del Rio, Cervantes y Constanzo in Mexico. Among those Mexicans that he didn't know but for their works are Velazquez de Leon, Leon y Gama and Alazte. Also made mention of scientific knowledge that the natives possessed previous to the Spanish conquest and he praised them (Humboldt, 1822).

he related the magnificent impression that scientific institutions that existed in Mexico city caused him and he made some general judgments on the state of the sciences in America, affirming: "There is certainly very remarkable progresses [of the science] in Megico, Havana, Lima, Popayan and Caracas. ...Everywhere a big impulse may observed nowadays toward the Enlightenment..." (p. 226). But, for a Enlightened liberal like Humboldt, his enthusiasm for the diffusion that reached science in Spanish America didn't prevent him from also observing that these advances took place in an incoherent context (the colonial mark) for what he called the progress of the civilization. "The civil and religious despotism" the Spaniards maintained for so long are among the obstacles pointed out by Humboldt (p. 179); a great inequality of fortune, of enjoyments and individual prosperity, [these places] ...a part of the nation under the guides and dependence of the other one" (p. 189); the isolation in which Spain maintained its colonies and the lack of good social institutions for the development of science and the progress of society (p. 239); and the fact, unacceptable for him, that the breed of the whites is the one which reaches the progresses of understanding almost exclusively [and] ...which possesses great wealth" (p. 239). For Humboldt all this was the logical consequence of the true character of the colonial regime under which one lived in Spanish America. These observations of Humboldt on the social conditions of science that he found in America, light up the complexity of the phenomenon of diffusion, but regrettably they were disregarded. The professional historians of colonial science built Ethnocentric models, simplistic and were ignorant of the social context in which science acts in non-Western societies. In the contemporary historiography the topic of science in the periphery was developed by George Bassalla using an evolutionary model of three phases or stages to explain the scientific diffusion.152 For Basalla the expansion of Western science toward non western societies initially took place as a result of the scientific investigation carried out in the regions by European scientists. From this phase continued that of colonial science, in which scientific activity that is developed in the recipient society is carried out by scientific "settlers" and it depends on the institutions and the European traditions. In the third phase the society arrives finally to the establishment of an independent scientific culture. This model has been broadly questioned and considered by several investigators as inadequate to understand the variety on ways that the geographical expansion of science and the contextual complexity adopted.153 Indeed, it has been criticized that the model ignores the local context in that science acts and considers colonial science on the margin of important elements like colonization, economic exploitation, homogeneity and cultural clash that its native societies experienced. It has also been pointed out that Bassalla's model doesn't take into account the

152 Basalla, 1967. 153 See the works gathered in: Reingold and Rothenberg, 1987; MacLeod and Rehbock, 1988; Petitjean, 1992.

internal social dynamics that are the responsible for the forms that adopt the social and cultural organization of the colonial world, and that are different certainly to those of Europeans. Consequently, with this model the influence which exercises the context and the local culture in the motivations of the scientists is devaluated; the establishment of the objectives of the investigation programs and in the means used for its development; the formation of the local communities dedicated to science and its professionalization; among other important aspects.154 It was in the last three decades when the study of globalization of science began to take into account the diversity of situations and their complexities. In the bibliography that today exists on the matter there are studies on geographical areas that were occupied by the old European empires or the new ones as the U. S.155 In them the diversity of situations are analyzed and has given up the idea of a singular model for the understanding of the globalization of science. As for their methodological tendencies we can distinguish grosso modo two types of studies. The first one has been in charge of colonial science and it analyzes the scientific activity developed in the non-European regions under the influence of European institutions. The second has arisen more recently and is interested in "national science" (still when chronologically it can correspond to the scientific activity carried out previously to the rupture of the colonial bond with the metropolis), going to a perspective that puts the emphasis on the local context and attributes it an explanatory or causal value. The first one sees the periphery science from Europe, the second from their own "ecology". Now, we will refer to such conceptualizations. The colonial science The analytical perspective that we have called colonial science directs its attention toward the applied sciences promoted by the metropolis in its colonies or in its influence areas. The topics that have been studied are the following ones: the conformation of imperialistic strategies with participation of science; the optimization of the economic exploitation of the colonies by means of the employment of science; the metropolitan projects for the accumulation of data and scientific materials with investigation ends,156 or of clear economic, political or military purpose;157 the careers of metropolitan scientists in the colonies among others.158 The studies carried out inside this perspective have thrown abundant data and interesting results about the scientific colonialism and their modalities. These have 154 Grove, 1990; Krishna, 1992; Saldana, 1990 and 1993'. 155 On the case of Latin America they are representative the studies that have appeared in Quipu, Latin American journal of History of Science and Technology, quarterly published in Mexico from 1984. For other regions see the works mentioned in the bibliography. 156 Latour.1987, Polanco, 1990a. 157 Frost, 1988; Puerto, 1988; Gonzalez, 1988. 158 Lafuente and Mazuecos, 1987; Peset, 1987; Pyenson, 1984, 1985 and1987.

depended on the different economic and political structures, as well as of the cultural and ethnic variants that characterized European empires as Spanish, English and French. In the same way, these studies also point out differences that respond to the particular "architecture" that the scientific system had along with the pattern of scientific expansion of each empire, which was dictated by the peculiarities of their political and administrative regime, because of the ambition and strength of their bourgeoisie, because the necessities of their foreign policy and of their military, and other more.159 Finally, the unequal participation of these modalities of empires has also been invoked in the conformation of the modern science corpus.160 These studies, in spite of their thematic diversity, possess some notes that are common and significant from of historiographic point of view. We consider that these notes are susceptible to be generalized to most of the historiography of the colonial science. We refer to the fact that in these studies a prevalence of documentation of European sources has existed, as well as an interest to give pursuit to the careers of European scientists that went on outside of Europe. To say it this way, for this historiography the argument and the characters of the drama that it describes are European, and the peripheries only contribute to the scenario. In the historiography of colonial science according to our point of view, the existence of a statement and of two omissions or important absences is also perceived. The statement that we refer to has emphasized a fundamental question: for the understanding of European science itself it is indispensable to know the luck that it had in the "land of the unfaithful", as well as the metropolitan politics in this respect. This statement has allowed the simplified version of other times to be overcome. Also, this new focus has begun indeed, to toss light on enough important aspects of European science before unknown or suspected. They are, among others, the nature of the process of accumulation of data and of scientific materials in the calls "calculation centers";161 their form of operation through international networks whose knots are in the metropolitan centers;162 the decisive paper that has resulted in popularization, the teaching and the normalization of science through the canonical texts for the consolidation of European science inside and outside Europe;163 the importance that scientific careers developed Outre-Mer had for the internationalization of science;164 etc. In synthesis, the emergence of this way of studying colonial or peripheral science has meant the recognition of the inadequacy of a self-centered focus like the traditional one that idealized the geographical expansion of science, and the

159 MacLeod, 1987; Numbers, 1987; Puerto, 1988; Lafuente, 1992; McLellan, 1992. 160 De Gortari, 1963; Ch. 8; Inkster, 1983; Numbers, 1987; Chartrand, 1989. 161 Latour, 1987. 162 Lafuente, 1992. 163 Grove, 1981; Grove 1987. 164 Pyenson, 1987.

science itself, when considering them outside of the social and international means where they were carried out.165 Regarding the omissions that we find in the historiography of colonial science, the first one is of a methodological character. It is the absence of the social local context as explanatory element of the peripheral scientific activity. Notice from now on the difficulty that it outlines for us by the use of the term "peripheral science", because appealing to the local context would demand that it is considered the scientific activity carried out in Beijing, Baghdad or Rio de Janeiro, for example, as scientific in it's own right and not for their relationship to a "center" which is outlying. In other terms, this historiography doesn't establish a nexus or causal bond between the scientific activity and the social context in which it takes place. As a consequence, the scientific aspect of the activities carried out by the scientists that reside in the periphery has been defined by the articulations of these and of their institutions with the metropolitan scientific centers, such as organic linking, publications, prizes, etc. The second omission is of a highly ideological nature. We refer to the "forgetfulness" of which has been part the historiography of colonial science as what constitutes the fundamental fact of the colonialism: i. e. the metropolitan exploitation. It is, nevertheless, a reality impossible to evade for the historian since he settled down in the scientific and technical medium, like in other, a relationship of the dominance of the metropolis over the colonies. This relationship put the colonies in the position of being only observational and experimentation fields, or for obtaining scientific materials, and to the metropolis, in an asymmetric relationship, in a center of accumulation of information, of calculation, scientific theorizing and systematizing of data. In the historiography this omission has led to frankly ideological notions as that of a missionary disinterest of Europe in the propagation of science. All form of political, economic or cultural relationship that imply subordination or dependence of a nation or society regarding another, necessarily makes science acquire a function of dominance from the perspective of the rulers. As for those dominated, the science can end up playing a liberating role when it responds to local motivations. The Colonial science was, therefore, determined by the authoritarian imposition of the metropolitan interests in the colonies. The preeminence of these interests pointed out limits and essential modalities such as, for example, the asymmetry among the center and the periphery, the practicality of the goals or "localism", the discipular character of the scientific local practice, and even, the authoritarian imposition of concepts and theories, and a negative valuation of the autochthonous scientific culture. The National science in the non-western societies should have taken steps opened up dragging the shackle that colonial dependence imposes on

165 Nathan Reingold and Marc Rothenberg has interpreted this process as an European cultural hegemony (to the margin to a certain extent of the political hegemony and the economic exploitation). These authors propose as heuristic solution considering science as a polycentric and part of a international process. (Reingold and Rothenberg, 1987: Introduction).

them with leaning on in the patriotic purposes of scientists. Neither the "progress of knowledge", nor the "advance of civilization", nor any other of the formulas that have been coined to conceptualize the so called "missionary" science, can hide the fact of metropolitan exploitation as the motive of colonial scientific activities. Now then, both omissions are serious because they have biased the analysis and limited the historian's perspective and that of the planners of the scientific development. Indeed, the analytical and explanatory capacity of history becomes poor when it loses sight that scientific activity carried out in colonies took place in a defined social, cultural and geographical context, under the influence of diverse instances certainly, but local ones being decisive. And when it is ignored that the colonial or dependent science was framed by the metropolitan authoritarianism and for his policies of economic spoilage, then the historical analysis becomes false and apologetic for a supposed disinterested and edifying action of the metropolis. The national science The formulation of the analytical perspective that studies national science is more recent than the one that is interested in colonial science. It is the result of its conceptual evolution that followed the historiography of science during the last decades.166 And it is, also, a consequence of the expansion that did, in last decade, the historical studies on science in old colonial regions like Australia, India, Islamic countries, Latin America and the Pacific Rim where important investigations are taking place on the science that was developed there. In spite of it, the topic of the national science is still in a stage that we can describe as initial from the historiographic point of view. Although it is also certain that at the present time it is already has a certain number of significant empirical studies, which justifies our intent of making a first reflection on them. The formation of science and of the national scientific community although is a typical problem of the countries that arose from an old colonial relationship, it is not exclusive of them. As a matter of fact it also concerns the modernization of countries and the historical fact of globalization of modern science. Traditional countries like Japan, although non-subjected to colonial bonds, are also now object of the attention of historians of the national science.167 Plus still, we think that science of other regions like central Europe and Scandinavia, and that of the prov-inces of the European states monopolists themselves of the knowledge in their capital cities, is susceptible to being analyzed from a nationalistic perspective.168 It 166 Saldaña, 1989b. 167 Satofuka, 1990. 168 Studies of this nature have been carried out although they have been directed mainly to technology. The definitive distinction between science and technology is doubtful and what is it more it stops through time. See, for example, the studies begun on the national history by the Rumanian magazine Noesis starting from 1973 and book of C. Giurescu, Contributions to the history of Romanian science and Technique from the 15th to the early 19th century, Bucharest, Historical Bibliotheca Romaniae, 1974; other examples: Technology & Industry. To Nordic Heritage,

is surprising that it is not venturous to advance that studies that today are being generated in old peripheries on their science will illuminate a historical process that affected all the nations equally. Between science and nation or, as we have said before, between science and their context there are resulting nexuses that are significant for the historian. When taking them into account, the notion of "scientific heritage" that makes relative the meaning that has the local dimension is abandoned, to another, that of national science which rescues the diversity of relationships when science and scientists settled down with their environments and received local culture. In reference to the old colonial regions, science and the national scientific community are matters intimately related with the gestation and formation of their own modern national state. On occasion, like in the cases of Colombia and Mexico, for example, the scientific community and an effective nationalist scientific practice have preceded, and like their precedent, to the independent state.169 In other cases, as those of Argentina, India or Japan, the formation of a national science has been the task of the new state (or of the state renovated as in the example of the restoration Meiji in Japan).170 This situation forces us, therefore, to distinguish two moments in the evolution of scientific nationalism. The first of them predates colonial emancipation and the constitution of the national state, and has individually considered scientist's motivated liberal aspirations. The second is the one that is developed once the national state exits and it is characterized by its republicanism (res publica). In that, the national science takes a step through the interstices of the colonial society to complete a patriotic mission; in this, the state and the national society incorporate science like a matter of public interest. Above all it is necessary to recapture here what I called ideological and methodological omissions before. Indeed, their repair has come to constitute the same nucleus which we have called history of national science. When being extracted the consequences that are imposed (and that they are properly documented) of the inclusion of the colonialism and of the local context in the history of science of the excolonial societies, an unexpected perspective opened up for the historians and I will sustain that for science policy also. Their emergence came to enrich the historical analysis when important questions are even still needy of ulterior investigations. In spite of that, concepts and an appropriate vocabulary have already been forged to the realities that historians of the national science study. They are, for example, the notions of domestication, intellectual negotiation, locality, and others applied to the national science. At the same time it was and it continues to be necessary to make a critique of inherited notions of historiography of colonial science, of the diffusionist theories and of other adopted

j. Hult and B. Nystrom (eds.). Science History Publications, 1992; the works gathered in Metropolis and province, Op. eft.; La fisica a Pavia nell'800 e'900. Scritti di Ciuseppe Belli, G. Bruni (ed.), Universita degli Studi di Pavia, 1988. 169 Luque, 1988; Saldaña, 1996; Saladino, 1988; Grove, 1990; Campos, 1991. 170 Babini, 1954; kumar, 1997; Satofuka, 1990.

mimecry of economic history and politics (as those of dependence, center-periphery, etc.). An example of the notions that we have inherited, seemingly innocuous, it is the one that made the scientific life in the colonies depend on the "generosity" of the metropolitan governments. Was the establishment of a botanical garden in Calcutta or a school of Mines in Mexico in the XV111 century the result of political sense of London or of Madrid? Were such decisions the spontaneous answer to the requirements of the colonial societies? Is the modern science benevolent, apo-litical and value-neutral? Can imperialistic motivations exist in the very heart of natural knowledge? As we have seen we met enough historical evidence that the answer to those questions is negative. Now, lets us take a look at the future. During the last years many futurologists appeared and their visions about what we should expect in the next century is more or less imaginary and catastrophist.171 By opposition a serious and thoughtful book was recently published by UNESCO: Our Creative Diversity (1996),172 containing a report of the World Commission on Culture and Development. The president of that commission Mr. Javier Perez de Cuellar, the former General Secretary of the United Nations and President of the Commission, observed that "the initiatives for development had failed with frequency because 'in many of the development projects the importance of the human factor was underestimated, the complex fabric of relationship and beliefs, values and motives is the heart of a culture", (p. 11) This statement makes us rethink the very process of development, and has corresponded to the previously mentioned UNESCO commission which was created for that task.'" The development—as affirmed in another place in the report— can no longer be conceived as a singular path, uniform and linear, because that would eliminate the inevitable diversity and cultural experimentation and would gravely limit the creative capacity of humanity with its valuable path and unpredictable future." This affirmation by the commission, in itself, converts the subject of cultural diversity into a true means to achieve the strategies required for construction of greater opportunities in the future for all humanity. In the face of the change in focus that such a declaration suggests, a change in perspective should also take place and as a consequence we should stop assigning a "purely instrumental role to culture in order to attribute it, instead, a constructive, constitutive, and creative role." This implies beginning the conception of development in a different way. Particularly, by abandoning some of the most influential economic and political theories at the end of this century, which as far as science and technology are concerned, considers them only as merchandise to be bought and sold. As we have seen, contemporary history of science offers us a renewed vision of what has been the scientific experience of humanity. Beginning with an interpretation that has a solid conceptual and factual basis and is already far from Ethnocentric ideas and linear development of science, an existing cultural diversity 171 Kennedy, 1993, Drucker 1998 and Huntington 1988. 172 Perez, 1996.

in scientific material is brought into evidence. It is, then, from this point of view that conceivable perspectives and alternatives result for the development of science, as much Western as non-Western. I hope that it will become evident to everyone that although the initial step has been taken by the historiography of science, the restoration of cultural diversity as an essential part of scientific practice and its development has not yet taken place. Let me illustrate my point. Some years ago, in an interview I had with Professor René Taton at his apartment on Rue Gay Lussac, in Paris, he told me that in the sixties, during the time in which he was preparing for the publication of his Histoire Generale de Sciences, he could not find a person to write some chapters on the development of science outside of Europe in regions such as Latin America, because of the lack of researchers working on that subject. As a result, it was his own wife who collected data about Spanish America and Portuguese Brazil, with the intention of filling those gaps. Other regions of the planet such as Africa and Australia, for example, were not able to be represented in that work for that same reason. In any case, I must say that Professor Taton was, from this and other points of view a real pioneer, since he regularly included information on the scientific life developed in other regions and thanks to that, many of us were able to become conscious of the existence of other non-western scientific traditions. Approximately twenty years later The Cambridge Illustrated History of World's Science by Colin Ronan,173 was published. In this work, such themes as the origins of science including some pages dedicated to Egyptian, Mesopotamian and Precolumbian science; ancient Greek, Chinese, Indian and Arabian science were discussed. Of these, he affirms that in spite of their original contributions prior to the Renaissance, at not having had a scientific revolution, they never developed into "fully-fledged science". By the same token, in the case of India for example, he sustains that in the past 200 years science has had a "Western flavour", and that is the reason that only six lines are dedicated to what the author calls "some important contributions to science" made in India in the XX century (p. 196). In the case of Islam, because of the connection between science and religion, he simply affirms that "the torch of science had to be carried on by others" (p. 240); and in China without overlooking that "many of its ideas and methods are being used vigorously", he states "still, the breakthrough into the era of powerful modern science occurred in Europe not in the East" (p. 186). It is clear that in the world history of science what was lacking for it to really be so is, exactly, world scientific experience, deeper than what the written history of the conqueror might claim. Twenty years later, in 1996, Science in the Twentieth Century174 was published. Edited by John Krige and Dominique Pestre, a work in which there is a chapter dedicated to "Regional and National Institutions". The case studies are of the United Kingdom, Russia, Germany, the United States, the European Community, Japan, India and Latin America. Note that now even a certain European diversity

173 Ronan, 1983. 174 Krige and Pestre, 1996.

has been included and Non-European regions are studied as well. Still, treatment of many other regions that are important to know about is lacking. Also in 1996, the book Mathematical Europe. History, Myth, Identity175 edited by Goldstein, Gray and Ritter was published. Here, the works presented at the European Mathematical Society Congress of 1992 are collected. Before telling the content of this book, I would like to point out that, just as was the case old in cinema, we go from passing through large panoramas to more and more detailed subjects in which the objects and characters occupy a larger scope. So, we see that in this book the authors reject the idealized vision of science that history of science produced because it is "fallacious from several points of view", and they point out that "it ignores the crucial and autonomous contributions from civilizations which have arisen outside the European continent"; at the same time that they sustain "mathematicians from these societies are presented as mere passive receivers and transmitters —even corrupters— of a European-originated knowledge". But, equally grave, it is pointed out that this way of seeing history of science "impoverished European mathematics themselves". And, they add,

Descartes and his contemporaries profited form a rich heritage which is not simply reducible to sources from classical Antiquity. Important and complex relationships bound mathematics to contemporary economic life, even before the sophisticated dynamic simulations, econometrics, and medical statistics of today; commerce, architecture, demographics and fortifications were among the many fields which justified or favored the development of mathematics in the period prior to the eighteenth century (p. 7).

In addition, in the book the origins of European mathematics are studied in the Greek, Indian, Arabian, Jewish and Europe's own traditions. In another part of the book the happenings are analyzed at the "frontiers" of European mathematics in China, Japan, modern Greece, Iberoamerica and Central Europe. At the same time, the diversity of schools of mathematical thought, institutions, etc. are studied, which inside Europe itself have existed in different countries and eras, by means of which the dissolution of the homogenous and immobile image of science and its institutions is targeted. As one can see, this is a book that, jointly with material making up the literature on national and local science being produced in various regions, shows us merely the tip of the iceberg whose real volume, although we may imagine, we do not know. Before the impossibility of referring to the entirety of this movement to study local science, I will briefly mention that in July of 2001 the XXIst International Congress of History of Science will take place, and the general theme will be "Science and Cultural Diversity". At this conference we hope to have the opportunity to see in more detail and with a wider scope, what has been the scientific experience of humanity. Like what is happening in other fields, at this turn of the century we are witnessing a review of our ideas about the nature of science. We are doing that by means of 175 Goldstein, Gray and Ritter, 1996.

incorporating social and historical processes that we know have acted on their evolution. From a more or less static vision of science in place for too long, we are moving toward another vision of a dynamic nature. That is one step forward which will have great importance since it is a call to modify our current conceptions and attitudes in subjects such as general education and the teaching of the sciences in particular; the scientific policy of the state and private enterprise; public communication of science; the relationship of science to society, culture and history; the self-value of societies; and programs for cultural, economic, and social development. In consequence, it seems that two tasks are a priority in the immediate future. The first, is to develop in a preferably international frame like UNESCO, advanced investigations on the history of national science in all countries, as well as international science that has been developed in this century, so that such histories are capable of giving us the diversified image needed. This may contribute to the writing of a true world history of science. The second, with the valuable empirical information that historical and social studies of local science provide us, is to fuel our national and international projects for development with the purpose of giving ourselves the realism that has normally been lacking at the point of creating prospects for the future that we aspire to and in the definition of that future. It is also true that in order to transform the present situations we must learn about them and learn about them in their evolutionary and interactive movement. Having wanted to present to you the history and perspectives of western and non-western science, I must finally recognize that like a painter in the first stage of a painting, I have barely outlined the profile that will later have precise forms and color. So, this forces me to leave the canvas unfinished and the complete development of the landscape for another occasion. Bibliography Babini, J., La evolución del pensamiento científico en la Argentina, Ediciones La

Fragua, Buenos Aires, 1954. Bargalló, M., La minería y la metalurgia en la América española durante la época

colonial, Fondo de Cultura Económica, México, 1955. Barnadas, J. M., Álvaro Alonso Barba (1569-1662). Investigaciones sobre su vida

y su obra, Biblioteca Minera Boliviana, La Paz, 1986. Basalla, G., "The Spread of Western Science", Science, núm. 156, 1967, pp. 611-

622. Bernal, Martin, "Animadversions on the Origins of Western Science", ISIS. An

International Review Devoted to the History of Science and its Cultural Influences, vol. 83, núm. 4. 1992, pp. 596-607.

Biot, J. B., Études sur L' Astronomic Indienne et sur L' Astronomic Chinoise, Librairie Scientifique et Techique Albert Blanchard, Paris, 1969.

Bitterli, U., Cultures in Conflict. Encounters Between European and Non European Cultures, 1492-1800, Stanford University Press, Stanford, Calif., 1989.

Boss, V., Newton & Russia. The Early Influence, 1698-1796, Cambridge, Harvard University Press, Mass., 1972.

Cohen, I. B., "The New World as a Source of Science for Europe", Actes du IXe Congrès International d'Histoire des Sciences, Barcelona, 1960.

Chartrand, L. et al., Histoire des Sciences au Québec, Les Editions du Boréal, Montréal, 1987.

Drucker, Peter F., La Sociedad Post Capitalista, Editorial Norma, México, 1998 (Original English version: Post-capitalist Society, Butterworth-Heinemann, Oxford, 1993).

Estrella, Eduardo, "Medicina Autóctona Precolombina" en Historia Social de las Ciencias en América Latina", Editorial Miguel Angel Porrúa, México, 1996, pp. 43-68.

El mestizaje cultural y la medicina novohispana del siglo XVI, Fresquet Febrer, J. L., j. M. López Pinero (eds.), Instituto de Estudios Documentales e Históricos sobre la Ciencia, Universidad de Valencia, Valencia, 1995, (Cuadernos Valencianos de Historia de la Medicina y de la Ciencia).

Garcés Contreras, Guillermo, Pensamiento Matemático y Astronómico en el México Precolombino, IPN, 2ª ed., México, 1990.

Mathematical Europe. History, Myth, Identy, Goldstein, Catherine, Jeremy Gray and Jim Ritter (eds.). Foundation Maison des de I'homme, Paris, 1996.

González C., V., La expedición científica de Malaspina en Nueva España. 1787-1794, El Colegio de México, México, 1988.

Goonatilake, Susantha, Aborted Discovery. Science & Creativity in the Third World, Zed Books (third world studies), London, 1984.

Gortari de, E., La ciencia en la historia de México, Fondo de Cultura Económica, 1963.

Humboldt. A., ensayo político sobre el reino de la Nueva España, ed. facsimilar, 1822, editorial Porrúa, tomo I, México, 1985.

Lettres Americaines d'Alexandre de Humboldt 1798-1807, introduction et des notes E. T., Hanny, E. Guilmoto (ed.), Librairie Orientale & Americaine, Paris, 1905.

Huntington, Samuel P., El choque de las civilizaciones y la reconfiguración del orden mundial, Editorial Paidós, México, 1988.

Metropolis and Province. Science in British Culture, 1750-1850, Inkster I. and J. Morrel (eds.), Hutchinson, London, 1983.

Jarrell, R. A., "Differential National Development and Science in the Nineteenth Century: The Problems of Quebec and Ireland", Scientific Colonialism, N. Reingold and M. Rothenberg (eds.), Op. c/t., 1987.

Kennedy, Paul, Hacia el siglo XXI, Plaza & Janes Editores (Original English version: Preparing for the Twenty-First Century, 1993), Barcelona, 1993.

Science in the Twentieth Century, Krige, John and Pestre Dominique (eds.), Harwood Academic Publishers, Paris, 1997.

Krishna, V., "The Colonial 'model' and the Emergence of National Science in India: 1876-1920", en Science and Empires..., Petitjean et a/, (eds.), Op. cit., 1992.

Kumar, Deepak, Science and Raj. 1857-1905, Oxford, India Paperbacks, New Delhi, 1997.

Lafuente A. and J. Sala, "Ciencia colonial y roles profesionales en la América española", en Quipu, Revista Latinoamericana de Historia de las Ciencias y la Tecnología, México, 1989, Vol. 6, num. 3, pp. 387-403.

—————— (eds.), Ciencia colonial en América, Alianza Universidad, Madrid, 1992.

Lafuente, A., "Institucionalización metropolitana de la ciencia española en el siglo XVIII", Ciencia colonial en América, A. Lafuente y J. Sala (eds.), Op. cit., 1992.

Lafuente, A. and A. Mazuecos, Los caballeros del punto fijo. Ciencia política y aventura en la expedición geodesica hispanofrancesa al virreinato del Perú en el siglo XVIII, Serbal/CSIC, Madrid, 1987.

Latour, B., Science in Action, Harvard University Press, Cambridge, Mass., 1987. Luque, L. M., Presencia de las ideas ilustradas acerca de las ciencias en el

pensamiento neogranadino de fines del siglo XVIII: el caso de Francisco lose de Caldas, Thesis M. A. (Philosophy) supervisor J. J. Saldaña, Facultad de Filosofía y Letras, UNAM, 1988.

Lloyd, G. E. R., "Methods and Problems in the History of Ancient Science: The Creek Case" en ISIS, vol. 83, num. 4, 1992, pp. 564-577.

Nature in its Greatest Extent Western Science in the Pacific, MacLeod R. and Ph. F. Rehbock (eds.). University of Hawaii Press, Honolulu, 1988.

MacLeod, R., "De visita a las 'moving metropolis': reflexiones sobre la arquitectura de la ciencia imperial", Nuevas tendencias en la historia de las ciencias, A. Lafuente y J. J. Saldaña (coords.), Op. cit., 1987.

McClellan, J. E., Colonialism and Science. Saint Domingue in the Old Regime, The Johns Hopkins University Press, Baltimore, 1992.

Needham, Joseph, Science and Civilisation in China, Cambridge University Press, Cambridge, 1954, 5 volumes.

———, The Grand Titulation, Science and Society in East and West, London, Alien, 1972.

———, Dentro de tos cuatro mares; el dialogo entre Oriente y Occidente, Siglo XXI Editores México, 1975 (Original English version Within the four seas. The Dialogue of East and West, George Alien & Unwin Ltd.).

———, La gran titulación, ciencia y sociedad en Oriente y Occidente, Alianza Editorial, Madrid, 1977.

———, De la ciencia y la tecnología chinas, Siglo XXI Editores, México, 1978. ———, The Shorter Science and Civilisation in China, Cambridge, 1978. ———, Trans-Pacific Echoes and Resonances Listening Once Again, World

Scientific Publishing Co, Singapore, 1985. ———, "History and Human Values; a Chinese Perspective for World Science and

Technology", in Philosophy and Social Action.

Medicine in the New World. New Spain, New France, and New England, Numbers, R. (ed.), The University of Tennessee Press, Knoxville, 1987.

Nuestra diversidad creativa. Informe de la Comisión Mundial de Cultura y Desarrollo, Pérez de Cuellar, Javier (coord.), Ediciones UNESCO, México, 1996.

Peset, J. L, Ciencia y Libertad. El papel del científico ante la independencia americana, Consejo Superior de Investigaciones Científicas, Madrid, 1987.

Science and Empires. Historical Studies about Scientific Development and European Expansion, Petitjean, P. et al, (eds.), Kluwer Academic Publishers, Dordrecht, 1992.

Pingree, David, "Hellenophilia versus the History of Science", in ISIS, vol. 83, núm. 4, 1992, pp. 554-563.

Naissance et developpement de la science-monde. Production et reproduction des communautes scientifiques en Europe et Amerique latine, Polanco, X. (ed.), Editions de la Decouverte/Conseil de I'Europe/UNESCO, Paris, 1990.

_____, "Une science-monde: la mondialisation de la science europeenne et la creation de traditions scientifiques locales", Naissance et developpement de la science-monde..., X. Polanco (ed.), Op. cit., 1990a.

Puerto, F. J., La ilusión quebrada. Botánica, sanidad y política científica en la España ilustrada, Serbal CSIC, Madrid, 1988.

Pyenson, L, "In Partibus Infidelium: Imperialist Rivalries and Exact Sciences in early Twentieth-Century Argentina" in Quipu, Revists Latinoamericana de Historia de las Ciencias y la Tecnología, México, 1984, vol. 1, num. 2, pp. 253-303.

_____, "Functionaries and Seekers in Latin America: Missionary Difussion of the Exact Sciences, 1850-1930" in Quipu, Revista Latinoamericana de Historia de las Ciencias y la Tecnologia, Mexico, 1985, vol. 2, núm. 3, pp. 387-420.

———, "Ciencia pura y hegemonía política: investigadores franceses y alemanes en Latinoamérica", Nuevas tendencias en la historia de las ciencias, A. Lafuente and J. J. Saldaña (coords.), Consejo Superior de Investigaciones Científicas, Madrid, 1987.

Rashed, R., "Science as a Western Phenomenon" in Fundamenta Scientiae, vol. 1, 1980, pp. 7-21.

Reingold, N. and M. Rothenberg, Scientific Colonialism. A Cross-Cultural Comparison, Smithsonian Institution Press, Washington, 1987.

Rochberg, F., "Introducción" in ISIS, vol. 83, núm. 4, 1992, pp. 547-553. Rojas Rabiela, Teresa, "Tecnología Agrícola Precolombina" in Historia de las

Ciencias en América Latina, Op. cit., 1996, pp. 71-90. Ronan, Colin A., The Cambridge Illustrated History of the World's Science,

Cambridge University Press, Cambridge, 1983. Sabra, A. I., "Situating Arabic Science: Locality versus Essence", en ISIS, vol. 87,

núm. 4, 1996, pp. 654-670. Saladino, A., La ciencia entre los ilustrados del Nuevo Mundo, Ph. D., Dissertation

in Latín American Studies, supervisor, j. Saldaña, Facultad de Filosofía y Letras, UNAM, 1988.

Saldaña, Juan José, "La historia de la organización de la ciencia y la tecnología en México: una aproximación a sus criterios de organización", Memoria del Seminario Internacional "Derek de Solla Price" sobre la Dinámica de las Disciplinas Científicas en la Periferia. San José, CONICYT, 1987, t. II, pp. 441-457.

———, "25 años de historiográfica de la ciencia en América Latina", Memorias del Primer Congreso Mexicano de Historia de la Ciencia y de la Tecnología, Sociedad Mexicana de Historia de la Ciencia y de la Tecnología, México, 1989, tomo I.

———, "Nacionalismo y Ciencia Ilustrada en América", Ciencia, Técnica y Estado en la España Ilustrada, J. Fernández and I. Tascón (eds.), Ministerio de Educación y Ciencia, Madrid, 1990.

———, "Science et pouvoir au XIXe siècle. La France et Ie Mexique en perspective", Science et Empires, Petitjean et al. (eds.,) Op. c/t., 1992.

———, (ed.), Historia social de la ciencia en América Latina, Consejo Nacional para la Cultura y las Artes/ Fondo de Cultura Económica, México, 1993.

———, "El sector externo y la Ciencia Nacional: el conservacionismo en México (1934-1952)" in Quipu, México, 1 994, vol. 11, núm. 2, pp. 195-218.

———, "La ilustración científica en América Latina" in Historia social de la ciencia en América Latina, J. J. Saldaña (ed.), Op. cit., 1996.

Sansom, G. B., The Western World and Japan. A Study in the Interaction of European and Asiatic Cultures, Charles E. Turtle Company, Tokyo, 1984.

Sarrailh, J., La España Ilustrada de la segunda mitad del siglo XVIII, Fondo de Cultura Económica, México, 1957.

Sarton, G., "The Scientific Basis of the History of Science", in Sarton on the History of Science. Essays by George Sarton, D. Stimson (ed.). Harvard University Press, 1962.

———, "The Quest of Truth: A Brief Account of Scientific Progress During The Renaissance", in Sarton on the History of Science, Op. cit., 1953.

Satofuka, F., "Some Aspects to the Debate on Scientific Tradition in Japan", Historia Scientiarum, 41; 44 y 46, 1992.

Shapin, S., "Nibbling at the Teats of Science": Edimburgh and the Diffusion of Science in the 1830s", in Metropolis and Province. Science in British Culture, 1780-1850, Inkster I. and J. Morrel (eds.), Op. cit., 1983.

Subbarayappa, B. V., A Concise Histotory of Science in Indian National Science Academy, New Delhi, 1971.

Cultura Clásica y Cultura Mexicana. Conferencias, Tapia Zúñiga, José (comp.), UNAM (Cuadernos del Centre de Estudios Clásicos 17), México, 1983.

Valdivia Gutiérrez, Oscar, "Matemáticas y Astronomía Precolombina" in Historia Social de las Ciencias en América Latina, Op. cit., pp. 91-118.

Vernet, Juan, La cultura hispanoárabe en Oriente y Occidente, Editorial Ariel, Barcelona, 1978.

Von Staden, Heinrich, "Affinities and Elisions: Helen and Hellenocentrism", in ISIS, vol. 83, núm. 4, 1992, pp. 578-595.

Wade Chambers, D., "Period and Process in Colonial and National Science", Scientific Colonialism..., Reingold, N. y M. Rothenberg (eds.), Op. cit, 1987.

Xiaoli, Sun, "A Wrong Statement about Leibniz and his Interpretation of Chinese I Ching Figure", in Historia Scientiarum, vol. 8, núm. 3, 1 999, pp. 239-247.

Ziadat, A. A., Western Science in the Arab World, St. Martin's Press, New York, 1986.

Science and cultural diversity in a post-colonial context

S. IRFAN HAB1B

"Cultural Diversity is to human species what biological diversity is to the genetic wealth of the world"

Rodolfo Stavenhagen Science and cultural diversity has a little different meaning in post-colonial societies, different from the currently widespread understanding in Euro-American world. I do not wish to enter into the diverse meanings of post-colonialism, but in the South Asian context it means the era, which began with the end of British colonial rule. Thus most of the reactions to science in India as well as in other postcolonial societies are premised on a wide range of colonial experiences as the project of modern science itself unfolded here with imperialism. Another contribu-tory factor to the current understanding of science in postcolonial societies is the characteristic bluntness of some of the leading lights in the Euro-American world when they talk of the mission of spreading science to Third World countries. As an example, we can look at the following lines:

With European industrial civilization comes European science. It is a package deal. The question whether a culture thus superseded or repressed had its own form of science has become purely academic....In the present discussion, it is taken for granted that European science should become a dominant cultural force throughout the world.176

Such Eurocentric constructions are not only nasty, to say the least, but also hurt the self-esteem of the postcolonial societies. They are akin to the missionaries of old, who so fervently believed in Christian salvation. For them the so-called 'superseded or repressed' societies are worthy of the trash bin. But what happens to the vast corpus of knowledge that the Chinese, Mayan, Islamic and Hindu civilizations claim they have exchanged with each other and with Europe since ages? Keeping the above in mind, I want to raise few points on science and cultural diversity in a postcolonial context.

176 Michael Moravcsik and John Ziman in 'Problems of Science Development', World Scientific, Singapore, cited in Pervez Hoodbhoy, Islam and Science, Zed Books, London, 1991, pp. 18-19.

• Most of the postcolonial societies feel that science is taught at the expense of indigenous knowledge and this precipitates charges of epistemological hegemony and cultural imperialism. The nature of colonial rule itself is seen as a concerted 'history of the cultural hegemony of the imperial powers established over the dominated societies'.177 Thus what follows is the conclusion that modern "western" science is hegemonic and oppressive and invoking cultural diversity, the indigenists propose an alternative called indigenous science, which will be traditional, kinder, and will have gentler ways to relate to each other and to nature and thus will not be as arrogant as western science.

• What follows from above is that the third world witnesses the shadow of revivalism lingering in the background. The space created for the critical evaluation of indigenous knowledge systems has inadvertently' reinforced the claims made by a new community of religious essentialists in South Asian sub-continent, and by these I mean the Hindu and Islamic-centrists. This is a menacing development for it threatens existing pedagogy of science and posits social schisms that were not as antagonistic in the past as they are now, thanks to the media. The need for working towards a more cognitively just framework for the history of science becomes all the more urgent.

The challenge then exists at least at two levels:

1. The pedagogy of science teaching. Multiculturalism was an offshoot of postcolonialism and the phenomenon of failed states in the postcolonial world, seen socially in the migration of people from the former colonies to the developed world. In way multiculturalism as pedagogic movement in the Euro-American world embodies a modality of coping with the changing character of Western societies over the last few decades. We can see the most radical changes taking place in the USA, where courses are being redone in the light of multicultural pressures, particularly the diversity in the classroom. The students from diverse cultural backgrounds demand their share of civilizational contribution to the corpus of modern science. This has thrown up new research concerns for the history of sciences-concerns that feed into the pedagogy of science education, but mediated through developments in the cognitive sciences, and cognitive learning.178

2. The political legitimization of a totalitarianism when it speaks in the name of indigenous knowledge, but in fact foregrounds one dominant tradition and destroys cultural diversity. For example, the Islamic past is being seen by the interpreters today as something pure and unadulterated, much different from what it has become now a mix of varied cultures and languages. They

177 Amartya Sen, On Interpreting India's Past, Calcutta, 1996, p. 27. 178 Dhruv Raina, "The Present in the Past: Trajectories for the Social History of Science", in Romila Thapar (ed.), India Another Millennium, Viking, New Delhi, 2000, p. 24.

fail to realize that Islam had been a culturally diversified project from its very inception, which should be projected as its strength and not weakness. In this era of exclusivism, identity consciousness has taken a heavy toll of cross-cultural contributions in different civilizations and science is one of its major victims. Historian of science Roshdi Rashed points out in extensive researches that the first international science emerged in the Arab world during the early five centuries of Islam.179

However, the opposition to Eurocentrism and the inability to effectively engage with Western hegemony in the domain of international affairs, or the poor performance of former colonial governments back home has provoked reverse commentaries that mirror the chauvinism of Eurocentrism in the history of science. The main feature of this sort of history is that it seeks to claim priority of discovery for every scientific theory or any significant invention. Despite these developments there are historians of science committed to understanding the process of evolution of scientific ideas rather than getting bogged down by question of priority. But it seems that the pressures of globalization on the developing countries is likely to exacerbate the politics of identity, the parochial genre of the history of science will continue to prosper for some time to come.180 The Universality of science in a post-colonial context Most of the multi-cultural literature on science seems to say that the problem with the Standard Account is that it is taken to be the only account of science. It is an exclusive and universally appropriate account. But is it really the bone of contention among those who talk of diversity? Is it the alleged universality of science or is it the intellectual exclusiveness of science according to the Standard Account or the universalist perspective of science. We raise this because the post-colonialist arguments rejecting the universality of science seem to be arguments more about the exclusivity of science. It seems that even if the definition of science were broadened to include what is now excluded, one would still have a universal science. That means modern science can be really culturally diversified only when it allows itself to be more inclusive. I mean all the indigenous knowledges find a place in the redefined and broadened definition of science. Unfortunately even this is not going to solve the problem. The above solution comes from within science, with empathy for other knowledge systems. But a large number of post-colonial critics seek an epistemologically different science, different from modern science. They have a lot in agreement with the feminist critics of Sandra Harding variety, who talk in terms of ethnosciences and modern science thus for them is just a Western ethnoscience. In that case they have no problem

179 Roshdi Rashed, "Appendice: La notion de science occidentale", in Entre Arithmetique et algebra, Les Belles Lettres, Paris, 1984. 180 Ibid., pp. 25-26.

with the categories like Hindu science or Islamic science and some have gone to the extent of calling modern science just a Christian science, which is of course necessary for the justification of their own existence. In such a situation what exactly one has to do, keeping in mind one's respect for the universality of science and also the cultural diversity, which I believe is one of the strongest weapons to defend science. For me Needhamian ecumenism and his river metaphor is one valid recourse. He proposed an ecumenical history of science that would recognize the different contributions of civilizations and cultures to the growth of modern sci-ence. While this has enabled non-Western civilizations to look upon themselves with a greater degree of self-confidence, and depart from colonial constructions of the East, at the epistemological level, critical scholars in the area would not entirely like to abandon the enlightenment ideal. What is considered problematic is the privileging of a European version of universality over other definitions of universality a paradox in terms. Rather one must now ask whether it is possible to speak in terms of a critical enlightenment that would reinstate the dialogue across civilizations in more egalitarian terms.

Diversidad cultural en la memoria histórica y gráfica de México*

TERESA ROJAS RABIELA México, como muchos otros de los países del mundo, es una entidad política artificial que encierra una gran diversidad. Imaginemos por un momento que las fronteras políticas estuvieran en las fronteras culturales reales. México sería al menos dos países: el del sur, correspondiente al sucedáneo de Mesoamérica, la superárea de civilización, de pueblos agricultores y sedentarios anterior a la llegada de los europeos, que se prolongaría hasta más allá de sus fronteras actuales, hasta Nicaragua y Honduras. El del norte, sería el sucedáneo del país de los pueblos nómadas, cazadores, pescadores y recolectores, que se extendería por las áridas regiones septentrionales de México y el sur de los Estados Unidos, por los actuales estados de California, Arizona, Nuevo México y Texas, territorios que formaron parte de México hasta el despojo por los norteamericanos culminado en 1848. Esta alegoría sirve como entrada para plantear que estos "dos países en un solo país" albergaron, en los aproximadamente 500 años transcurridos desde el arribo de los europeos, dos realidades bastante contrastantes desde la óptica de sus pueblos originarios, tanto como de los patrones de colonización desarrollados por los españoles en el curso del proceso de guerra, dominación, cristianización y explotación de poblaciones y territorios. En última instancia, dichos patrones de colonización tuvieron su origen precisamente en las diferencias existentes entre los pueblos prehispánicos del norte y del sur, unos errantes, otros sedentarios; unos con formaciones políticas estatales y alta civilización, otros con organizaciones políticas y culturales más sencillas, si bien no exentas de complejidad por su alto grado de adaptación a medios difíciles, de extrema aridez. Ya en el Virreinato, un mismo fenómeno biológico hermanó, trágicamente, a los mesoamericanos y a los norteños: la debacle demográfica, sin duda una de las más grandes y dramáticas crisis poblacionales de la historia de la humanidad. El resultado fue la pérdida de entre el 80 y 90% de la población nativa al cabo de un siglo de presencia europea. Imaginemos los efectos de este hecho en la vida cotidiana de estas gentes, en todos los aspectos de su existencia.

* Conferencia, Vil Congreso de Historia de la Ciencia y la Tecnología, Tema general: Ciencia y diversidad cultural en México; Universidad Autónoma de Hidalgo, Pachuca, Hidalgo, 28 de noviembre de 2000.

México independiente: país diverso, pluralidad negada En 1810 la población denominada "india" era de 3 676 282 personas, cantidad que representaba aproximadamente el 60% de la población total de México. Un siglo después, en 1910, había 4 900 000 indígenas, que ya sólo constituían el 25% de la población total.181 México cuenta hoy con 100 millones de habitantes. La población hablante de alguna lengua indígena en las estimaciones más altas es de entre 8 y 10% del total (incluyendo a los niños menores de 5 años).182 Ésta pudo ser la cantidad total de habitantes que poblaba Mesoamérica en el momento de la llegada de los europeos. De acuerdo con un estudio reciente de Arnulfo Embriz sobre los estados de la República con mayor cantidad de hablantes de lenguas indígenas en 1995, Oaxaca es el que más los concentra, con 19% del total de la población, seguido por Chiapas con 14%, Veracruz con 10.8%, Yucatán con 10% y Puebla con 9.6%.183 Pero si tomamos la proporción de hablantes de alguna lengua indígena por entidad federativa, Yucatán tiene alrededor del 40%, Oaxaca el 37%, Quintana Roo el 26% y Chiapas el 25%.184 Aparte de la fuerte presencia indígena, la gran diversidad de lenguas es, sin duda, otro de los rasgos distintivos de México, antes y ahora. Esta característica lo marca y lo distingue de otros países americanos de raigambre indígena como los andinos (Perú, Bolivia, Ecuador, sur de Colombia, norte de Chile y norte de Argentina), que presentan una mayor uniformidad lingüística. Para la época del contacto (es decir los siglos XVI y XVII), en el que hoy es su territorio, existían 182 "hablas" (entre lenguas y dialectos),185 se redujeron a unas 80 durante la Colonia y el siglo XIX, al extinguirse la población que las hablaba. Actualmente el número de lenguas indígenas en México es de 66,186 agrupadas en 14 familias lingüísticas.187 La negación de la multiculturalidad Pese a la abrumadora presencia de la población indígena durante los casi 300 años del virreinato y a su existencia mayoritaria en los siglos XIX y XX, México

181 Carlos Zoila, "Análisis y reelaboración de los contenidos relativos a la presencia indígena en los libros de texto gratuito", mecanuscrito inédito, INI, 1995, p. 46. 182 6 411 972 personas según cifras del INEGI; 8 701 688 personas de acuerdo con los cálculos del Instituto Nacional Indigenista. En: Arnulfo Embriz, "Quiénes son los indios y cómo reconocerlos en las estadísticas", mecanuscrito inédito. 183 Ibídem, p. 5. 184 ídem. 185 Según M. Orozco y Berra, en Bárbara Cifuentes, Letras sobre voces. Multilingüismo en la historia, México, CIESAS/INI, 1998 (Historia de los Pueblos Indígenas de México), p.37. 186 El censo oficial de 1990 distingue 92. 187 Según L. Manrique, en B. Cifuentes, Op. cit., pp. 41-42.

como nación y como Estado ha negado su condición multicultural, en su tenaz lucha por lograr un modelo ideal de país, mestizo racialmente y occidental culturalmente. No fue sino hasta 1992 que el Estado mexicano realizó una reforma al artículo 4° de su Constitución política para dar cabida al reconocimiento de la pluralidad. El texto dice lo siguiente:

La Nación mexicana tiene una composición pluricultural sustentada originalmente en sus pueblos indígenas. La Ley protegerá y promoverá el desarrollo de sus lenguas, culturas, usos, costumbres, recursos y formas específicas de organización social, y garantizarán a sus integrantes el efectivo acceso a la jurisdicción del Estado. En los juicios y procedimientos agrarios en que aquellos sean parte, se tomarán en cuenta sus prácticas y costumbres jurídicas en los términos que establezca la ley.

Sin embargo, es evidente que en el imaginario colectivo, México aparece como un país occidental, mestizo, que comparte un proyecto histórico común y con orígenes más o menos antiguos, según se reconozca la historicidad del largo periodo prehispánico. En este imaginario el indio y lo indio está presente, pero en la figura del indio muerto, del mesoamericano civilizado que hemos idealizado y de cuyo legado nos orgullecemos; esta rígido y estático en las vitrinas del museo. En este cuadro rara vez tiene cabida el indio conquistado y explotado del periodo colonial y del siglo XIX; el indio "bárbaro" cazador-recolector del norte, o el indio empobrecido que es nuestro contemporáneo.188 La historia indígena, esa desconocida La historia de los pueblos indígenas casi no figura en el imaginario de la nación mexicana. Esta afirmación puede sustentarse en muchas pruebas. Por ahora hablaré de la que ofrecen los libros de texto gratuito preparados por la Secretaría de Educación Pública para la instrucción elemental, donde la presencia indígena aparece desdibujada, en especial aquella correspondiente a los últimos 500 años.189 Según un esclarecedor análisis hecho por el Instituto Nacional Indigenista del contenido de esos libros oficiales, los indígenas que más se resaltan en sus páginas son los del periodo prehispánico (con 306 citas), mientras que los del Virreinato y el siglo XIX aparecen desdibujados (con sólo 44 citas). Los indígenas actuales figuran en sus páginas, pero disminuidos (con 121 citas).190 188 El nómada ni siquiera forma parte de la idealización del indio muerto que se dio en el siglo XIX y persiste hasta hoy, como acertadamente lo ha señalado Carlos Manuel Valdés, La gente de/ mezquite. Los nómadas del noreste en la Colonia. México, CIESAS/ INI, 1995 (Historia de los Pueblos Indígenas de México), p. 20. 189 Otra prueba de esta invisibilidad la podemos apreciar en los museos, donde a las imágenes se les relega a los museos de antropología y de arte de cultura popular. 190 C. Zoila, Op. cit.

De todos los grupos de la época prehispánica, los más nombrados son los aztecas-nahua-mexicas, con lo que, dicho sea de paso, se acentúa el "aztecacentrismo" imperante desde hace mucho en el imaginario nacional. Así, del total de 299 citas, 128 (el 42.8%) les corresponde a los aztecas, seguidos por los mayas con 62 citas (20.7%) y muy lejos por otros como los toltecas con 19 (6.3%), los zapotecos con 17 (5.6%), los olmecas con 14 (4.6%), los mixtecos con 13 (4.3%), etcétera.191 En lo que respecta a los grupos indígenas de la época virreinal y hasta 1910, el de los mexica-azteca-nahua es nuevamente el más nombrado, con 12 citas (27.3%), seguido por los genéricos "indios" con 5 (11.4%), maya con 4 (9.1%), zacapoaxtla, chichimeca y "naturales", cada uno con 3 citas (y el 6.8% cada uno). El resto son: zapoteco, tzeltal y tzotzil, con 2 a 1 cita cada uno.192 Estas y muchas otras evidencias, nos revelan que la historia del "indio" conquistado, pobre, dominado y en gran parte asimilado y deculturado, aquel que tuvo que cambiar y occidentalizarse para sobrevivir, tampoco ha sido visto con demasiado interés por los estudiosos, ni por la nación. Desconocida por éstos e ignorada por la mayoría, su historia ha carecido del suficiente interés, y no ha sido incorporada ni deseada en los episodios de la "historia de bronce" nacional (salvo, si acaso, lo indispensable para resaltar ciertos episodios o valores "positivos"). ¿Cuál es el origen de esta situación? El origen de este olvido, de esta desmemoria, lo podemos encontrar en los proyectos políticos elaborados en el siglo XIX para el naciente Estado-nación, que no admitieron a los indios como parte de la cultura y el patrimonio nacionales; no los reconocieron como pueblos con tradiciones específicas y distintas a la de criollos y mestizos. Ajenos al proyecto de Estado-nación, se olvidó su historia, se omitió su participación en las luchas y la construcción nacional, se atacaron las bases corporativas que les habían permitido sobrevivir en los siglos coloniales, se combatió a todos los que se rebelaron, se omitió dictar legislación social a su favor, al declarar la igualdad de derechos y obligaciones de todos los ciudadanos... Pero lo peor: se perpetuó la imagen negativa de la población indígena, imagen implantada profundamente en la conciencia nacional desde la conquista.

Los retos y los remedios Pasaré ahora a exponer algunos de los retos que enfrenta el estudioso que se propone documentar y analizar la historia de los pueblos indígenas. Los retos son muchos, complejos y de índole muy diversa. Unos son de carácter ideológico- 191 C. Zoila, Ibídem, gráfica 4. 192 Ibídem, gráfica 5.

político (ya señalé algunos), otros más de tipo técnico, si bien los límites entre unos y otros no son del todo nítidos. Los enumeraré más como una forma de verlos en una panorámica, que con el afán de agotar el tema. Los 5 retos de tipo ideológico-político:

• El primer reto: vencer la desmemoria. • El segundo: luchar contra el desinterés. • El tercero: combatir la idea de la no historicidad del acontecer indígena. • El cuarto: luchar contra la invisibilidad del indio y de su papel en la historia. • El quinto: lograr que esa historia sea plenamente incorporada a la Historia

Nacional (esa escrita con mayúsculas) y al proyecto de Estado-nación. Los 5 retos y problemas de carácter técnico:

• El primero: el desbalance informativo existente en la historiografía, derivado de la poca atención y preocupación de los que han producido tanto las fuentes de conocimiento como las investigaciones sistemáticas sobre la historia indígena. La poca producción consagrada a su estudio es un reto mayúsculo, especialmente la de ciertas regiones y épocas.

• El segundo: la dificultad para disponer de las fuentes para realizar la historia indígena, tanto por su escasez como porque en la gran mayoría de las crónicas y registros que se conservan, los indios no aparecen como actores sino como mero "telón de fondo" del acontecer y de los hechos de los europeos y sus descendientes.

• El tercero: la escasez de las fuentes que pueden servir para documentar la historia indígena, su dispersión y su poca disponibilidad pues a menudo son de difícil consulta. Los documentos en lenguas indígenas o en pictografías, en su mayoría no han sido estudiadas ni publicadas en ediciones críticas y accesibles.

• El cuarto: existen pocos especialistas capaces de traducirlas, descifrarlas y editarlas.

• El quinto: las voces indígenas rara vez son audibles. Los documentos donde las escuchamos en forma directa son raras, la mayoría de las veces mediadas por formatos o machotes preestablecidos, de rígidas formas, o bien por los intermediarios (llámense éstos eclesiásticos, abogados, funcionarios o traductores de antaño).

Las fuentes Pese a la existencia de todos estos problemas, es también un hecho que desde el siglo XVI muchos frailes y estudiosos han dedicado su vida y sus esfuerzos tanto a recoger el conocimiento y la memoria indígenas, como a ordenar, estudiar y dar a

conocer las fuentes para elaborar la historia y la etnohistoria de los grupos indígenas de México. Investigadores mexicanos y de otras nacionalidades han venido trabajando consistente y seriamente en la tarea de ordenar archivos, localizar documentos, por varios rumbos del mundo; paleografiar, traducir, descifrar y publicar crónicas históricas, manuscritos diversos y códices pictográficos; sistematizar y analizar la información que éstos contienen; producir series y catálogos documentales, que han servido como base para elaborar numerosos estudios que permiten vislumbrar mejor la historia indígena durante los casi cinco siglos que corren desde la conquista hasta nuestros días; recopilar fuentes hemerográficas que contienen noticias y opiniones sobre la población indígena; formar bancos de imágenes con los testimonios gráficos que recogen diversos aspectos de su existencia. El proyecto "El mundo indígena y su iconografía: 1826-1947" La idea de realizar un proyecto específico sobre la iconografía indígena de los siglos XIX y XX y su análisis como fuente histórica, se pudo concretar gracias al interés y buena disposición del etnohistoriador Ignacio Gutiérrez Ruvalcaba, especialista en el tema y con una gran experiencia acumulada al respecto. Uno de los resultados de su colaboración será, la redacción de un libro temático para la colección Historia de los Pueblos Indígenas de México, que versará sobre la representación del mundo indígena en el siglo XIX y el Porfiriato (que publican el INI y el CIESÁS). La memoria gráfica sobre lo indígena Pese a que la litografía y la fotografía sobre lo indígena tiene ya una larga tradición en México y constituye un corpus de gran importancia y riqueza excepcional, no existe un solo trabajo global de recopilación e investigación que de cuenta de las formas de representación de lo indio a lo largo de la historia y en sus diversas dimensiones (física, material, social y cultural). Por lo general, los libros de fotografía publicados sobre el tema indígena, están inscritos en la valoración estética de la imagen,193 más que en un análisis iconográfico que ofrezca una explicación sobre el porqué determinadas imágenes se produjeron en un contexto específico. Nuestro objetivo es mostrar las diferentes formas en que la cultura occidental representó a lo indio a través de imágenes, y de entenderlas en el contexto histórico en que se elaboraron. Se intenta establecer, cuando esto sea posible, la relación histórica de la imagen con los cambios que la política nacional y regional produjo en el mundo rural indígena, a

193 Olivie Debroise, Fuga mexicana, México, Consejo Nacional para la Cultura y las Artes/Grijalbo, 1996; Guillermo Aldana, et al., México indio, México, InverMéxico, 1993; El ojo de vidrio, México, Bancomext, 1993.

partir no sólo del imaginario que construyeron los estudiosos de la época, sino también de la captura de lo exótico. Todo lo anterior tiene, en última instancia, la finalidad de hacer de la imagen una "fuente para el estudio histórico y antropológico del mundo indígena" durante 120 años, a partir de la introducción de la litografía por Claudio Linnati, hasta la conclusión del proyecto "Etnografía de México", realizado en la UNAM bajo la dirección del sociólogo Lucio Mendieta y Núñez, de 1939 a 1949.194 Pasando por la introducción y popularización de la fotografía en México. La aparición en el mundo y en México en el siglo XIX de la daguerrotipia y de sus sucedáneas hasta la fotografía, inventos y tecnología que permitieron la reproducción de imágenes, tuvieron y tienen un impacto y efectos sorprendentes en el imaginario y en la ideología en torno a lo indio. Revisión, selección, documentación y digitalizaciones de las fotografías (y negativos)

1. El proyecto ha trabajado (o planea trabajar) los siguientes acervos: Fototeca del Archivo General de la Nación, fondos Enrique Díaz, Propiedad Artística y Literaria, C.B. Waite y Presidentes.

2. Fototeca Nacho López del Instituto Nacional Indigenista, fondos Cari Lumholtz, Julio de la Fuente, Alfonso Fabila y otros no identificados con nombres.

3. Archivo Histórico de la ciudad de Oaxaca. 4. Fundación Bustamente Vasconcelos (Oaxaca, Oaxaca). 5. Fotetoca privada de Walter Reuter. 6. Fototeca del Instituto de Investigaciones Sociales de la UNAM (proyecto

Etnografía de México, de Lucio Mendieta y Núñez). 7. Fototeca del Instituto Nacional de Antropología e Historia, fondos Étnicos,

Felipe Teixidor y Cásasela. 8. Biblioteca del Palacio Postal (México, D.F.). 9. Biblioteca Pública del Estado de Jalisco (Guadalajara). 10. Archivo Municipal de Guadalajara. 11. Fototeca del Archivo General del Estado de Veracruz (Jalapa).

194 En ese proyecto participaron Francisco Rojas González, Rene Barragán Ávila y Roberto de la Cerda Silva. Las fotografías fueron tomadas por Raúl Estrada Discua y Enrique Hernández, Etnografía de México. Síntesis monográficas, México, Universidad Nacional Autónoma de México, 1957.

Part II Remarks to stimulate discussions

on Science and cultural diversity

A Letter from Madrid

ANTONIO LAFUENTE The XXI Congress of the International Union of History and Philosophy of Science/Division History of Science (1UHPS/DHS) will be held in Mexico City from 8-14 July 2001 with the general theme, "SCIENCE AND CULTURAL DIVERSITY." The majority of the sessions will be developed within the framework of symposia. Their objective should be to explore some of the many ways that the relationship between science and other cultures can be understood, whether they be local, regional or national or popular, ethnic or professional. Science and cultural di-versity is a train made up of many cars; some of those cars being studies on science and public opinion, colonial and imperial expansion of science and scientific acculturation. Other subject-matter should also be touched upon such as that which explores the relationship between among scientific disciplines (interdisciplinary or trans- disciplinary) or those that analyze the emergence of pseudo-sciences and near-sciences as well as the presence of science in the cinema, television, museums, the press, art, novels, comics, videogames, or the Internet. Of course, there should be considerations of gender, race, ideology, religion as attempts to segregate have always existed or there should be a dialogue among the many delicate issues in an evermore complicated society. The concept of cultural diversity is an archipelago, with some islands more pronounced than others. Considering those islands inhabited with anthropologists, sociologists, experts in politics, historians, and those with a background in media, art and literature, it is still necessary to incorporate some Atolls of archeologists, promoters or conservatives. Certainly, we are referring to well-established professional roles which do not always communicate well among themselves. Very often, they fight for hegemony and control of public opinion. These are debates to which we are accustomed and in which it appears unlikely that any surprising or innovative ideas will arise. Furthermore, the literature related to the concepts of science and cultural diversity is very scarce and what is more, has not had an important role in the make-up of our image of science. There seems to be two reasons which explain this type of reciprocal indifference of both concepts. In one way, it is because for centuries, science has succeeded in showing itself as an entity independent from time and production: subject-matter of and for scientists whose autonomy, in respect to the ordinary culture, was increasing. The Utopias most committed to social well-being were abandoning the motto "science for science" and beginning to embrace the motto, "science for the people, but without the people." In another way, the very concept of diversity was held to be improper when referred to a professional discursive practice, which attempted to align the universe over a foundation of a convergence of languages, practices and appear-ances in new and universal type of languages, methods and (scientific) icons.

However, it was some time ago that numerous studies were presented which attested to the need for this dialogue and risked to obtain a more cultural image of the natural sciences. Such a tangent, impossible to imagine only a couple of decades ago, has converted science into another one of the islands in the mentioned archipelago. In contrary to that which drew up our cartography tradition, it no longer has been mare nostrum, which has fused and strengthened this group of islands. Many fear that the new map that is being drawn up reflects a world with a lack of ethical values and one that is dangerously relativist. Yet, the new geographers do not agree and refute the need to search for new equilibriums that do not compromise the notion of truth in benefit of new projects that guarantee equality. The new Mediterranean is splashed with islands that withstand different ways of understanding culture. Science is affected by constant movements of adaptation within this group of islands that generically are of movement (between territories), rarefaction (between social segments) and bifurcation (between disciplines). TYPE

MOVEMENTS

FORMS

THEME

Movement. Horizontal Displacement between locals

1 Science & Empires 2 Exile and Migration

• Science as an instrument • Science as a symbol

Historiographic Perspective

3 Universal Expositions 4 Scientific-Technical Espionage

• Technology Transfers • Technology and the Public • Machines and the Public

Globalization. Science expands its presence throughout the world

5 Scientific Expeditions

• Expeditions as a Mobil Institution • Expeditions as Patrimony

1 Science and Public Opinion

• Science in the Media and Novels: Popular perceptions of Scientific Value Added Objects • The City as a Mirror of Science and Technology

TIPE

MOVEMENTS

FORMS

THEME

2 Science and Public Participation

• Popular Reactions to Science: Threats, Enthusiasm • Laymen Movements and Science: The Environment

3 Elite and Laymen 4 4 Museums and Cabinets

• The Two Cultures: Ideology and Business • Pedagogical Movements • Collectionism and Museography

5 Science and Gender

• Gender and Science • Women in Science

6 Science and Nation

• Science, the State, the Nation; War. Territory, Prisons • The Civil Republic and Letters; Internationalism • Scientific Nationalism; Nazis, Soviets, Islam... • Natural, Civil, Sacred History

Rarefaction. Vertical displacement among social-cultural segments Sociological perspective Globalization. Science expands its presence throughout all its levels, groups, classes or social segments

7 Science and Faith

• Orders, Sects and Religious Movements in

Light of Science • Religion as Science and Science as Religion • Positivism, Romanticism and Science

8 Science and Race 9 Science and Pseudoscience 10 Science and Near- science 11 Science and Ethno- science

• History of the Body; Psychology, Anthropometry, IQ, Monsters, Pain, Physiology, Body of the King... • Alternative Science and Particular Science • Scientific Knowledge and Local Knowledge: Biodiversity, Drugs, Alimentation, Sicknesses

1 Science and Canon 2 Spaces in Science 3 Consensus in Local Science 4 Scientific Polemics 5 Fiscals, Biologics...

• Method and Culture: Big Picture and Big Science • Architecture of Laboratories, Gardens... • Scientific Polemics: Types and History • Facts and Proof: Hands and Words

6 Pure and Applied Science

• Engineers and Scientists: Two Cultures?

7 Science and Iconographic Science

• Iconographic Program of Science

Bifurcation. Internal displacements among disciplines Philosophic perspective Institutionalization. Science expands its presence throughout all forms of knowledge

8 Experimentation and Rhetoric

• Metaphors, Styles, Narrative

A Letter from Australia

ROY MACLEOD Dear Colleagues, As I may be unable to attend your forthcoming meeting in Mexico City, I hope you will let me share with you some preliminary thoughts by internet. Both now and next year, I believe our Commission has a powerful role to play, both in relation to the developing world, and in relation to the development of our profession. Despite its youth, its actions could turn out to be among the most (if not, the most) exciting features of the IUHPS in the coming decade. Let me refer at the outset to the two messages we have received from our good friends Antonio Lafuente and Michel Paty. I am excited, as always, by Antonio's vigorous mental leaps, and in this case, by his innovative metaphors. Whether I am on a train, somewhere on a map, or at sea, remains to be seen. But it is clear that there is something in his plan for everyone, whether they prefer to stand, sit, or remain horizontal. I am also impressed, as always, by Michel's distillation of the problematique into (at least some of) its most interesting philosophical fractions. We see before us — as always — different approaches, reflecting our different scholarly backgrounds and traditions — and also, sometimes (but less frequently, I suspect) differences in interpretation. At the outset, I would suggest that the idea of 'cultural diversity' carries considerable political baggage, of a kind that until recently would not be considered especially appropriate for a 'scientific' body such as ours; and that almost anything one says on the subject will have a political bearing (especially if not 'politically correct'). I also respect the fact that two of my respected colleagues have generously chosen to write in English. Our language has developed to reflect and absorb cultural differences, and in some measure contributes to them; and no doubt we shall be open to conceptual contributions from other tongues as well. Assuming that we as a group have enough in common; and are moreover sufficiently like-minded to work together, then (if you will forgive my being 'Anglo-Celtic'), the practical question becomes, what is our Commission actually to do? For the sake of simplicity, let us agree:

1) that the phrase 'Science and Cultural Diversity' is more a useful collection of categories than a coherent programme; 2) that the tendencies of 'universalism' and 'relativism' have pulled us all in

opposite directions; and that we all can find many 'diverse experiences' in between;

3) that otherwise welcome tendencies to 'specify' and retrieve the histories of non-Western knowledges — whether, for example, 'colonial' or 'indigeneous' — have in fact not resolved key intellectual debates; but rather have created new 'islands' (in Antonio's happy phrase), without improving communications between them and the 'mainland';

3) that contemporary tendencies incline us towards a greater measure of interpretative flexibility, and greater class and gender consciousness, in relation to scientific practice (historically, and at present); towards a much greater recognition (and closer criticism) of interests that 'own' and 'control' knowledge; and towards a greater respect for 'diversities' in culture, art and innovation;

4) that the activity of Western 'science', as generally understood, as the dominant tendency, or the conventional model, remains after all, a highly effective way of understanding and using what is known of the natural world;

5) that the cultivation, ownership and distribution of Western (for which read, global) knowledge remains partial and incomplete;

6) that the significance of 'other' knowledges, however widespread among the world's peoples, remains less appreciated (if not actually rejected) by Western systems;

7) and that in the interests of all, we should try to make clear precisely what we are doing, to encourage scholars in our community, and in other communities, to recognise what we might call, the 'validity of diversity'; which does not at the same time threaten, much less, undermine the value system of Western science. In working out what we might actually 'do' as a Commission, we are — as always, in my experience — handicapped by linguistic conventions. The word 'science' itself is not above confusion, as by definition it can include so many overlapping categories (methods and mentalities, theory and practice, institutions and governance, ideas and ideologies). However, we have little alternative, and must work with the 'mot', insofar as it helps throw light on the 'chose'. But what is this 'thing' that we wish to do? Do we wish to launch a series of studies along the lines Antonio suggests? If so, we will have at least one huge book, a unesco-of-sorts? Do we wish to publish a series of 'thinner', discursive papers, written by and from different traditions (different Western, Eastern, Pacific, etc traditions); on the 'nature of knowledge'? This would make an interesting library (and perhaps a development of Selin"s encyclopedia of non-western science?), and so, readable works for students. Do we wish to 'recognise' (that is, give a degree of, perhaps rather ineffective, but well-intentioned 'diplomatic recognition' to) 'indigenous' knowledge and belief systems (regardless of what our conservative philosophers might say against us), and so, welcome the presence of indigenous knowledge (and other diverse knowledges) within the ambit of the IUHPS? Do we wish to create new societies and institutions? If so, with what purpose? Each of these (and doubtless other) alternatives has important implications. Diversity, by definition, has no end; are we to create boundaries, either for

ourselves or others? Studies are useful, but of course will vary in quality and appeal. Will institutions (based on Western models) not almost inevitably tend towards universal norms, denying the different ecologies that give 'diversities' self-definition? My sense is that the themes Antonio suggests are, in themselves, interesting and important (of course!), but that they do not set our Commission apart, from any other, in its particular mandate. Of course, they could do so, if the Commission chose to respond in this way; and 1 agree that, however it responds, it should do so in reference to 'historical' processes and voices. On the other hand, the philosophical agenda that Michel outlines (in part 3 of his message) is valuable. However, it seems to me that most of these themes are already 'current' in the literature; and his topics would have to be carefully archetraved so as to be distinctive of our particular Commission. To make my point, let me play slightly with words. The Commission is self-entitled 'Science and Cultural Diversity,' as if to suggest that 'science' by definition is something separate and apart from cultural diversity. This is an established intellectual position. Both Antonio and Michel (and many others) have problems with it. But it is not, I think, a target on which we would automatically set our sights. On the contrary, are we not looking instead, in this Commission, for new inter-relationships — new 'conjunctions', so to speak? If so, perhaps we should vary our language, and consider, for example, the following alternatives — as the basis of a unique mandate and research and publications strategy:

I) Science in Cultural Diversity — eg, the role that Western science has played in establishing relationships

between cultures, across cultures, through time. II) Science for Cultural Diversity — eg, the role that the sciences might play in stressing cognitive and

cultural linkages, in which natural knowledge is shared as the common heritage of mankind.

III) Science as Cultural Diversity — eg, the equivalent roles that different civilisations (and cultures) have

played in articulating elements of our knowledge of nature. Of course, others will have different ideas. My point is, in fact, not to play with words, but to suggest that, as a Commission, we should develop a strategic outlook that — and why not! — includes elements of Antonio and elements of Michel, and of course others — but which also looks for relevant relationships that are not the existing 'job' of any other part of IUHPS — but which are unique to us. In this context, we could discuss the establishment of 'special relationships' with particular journals (there are precedents, in the long history of IUHPS), and with particular book series. We could even develop our own website. Above all, we

could develop teaching materials, which can use the new technology to reach a much wider audience, well beyond the confines of 1UHPS itself. Such 'visions' are by now commonplace, but I hope you agree that we should not exclude them, for which reason, I hope they may be included on your agenda. Roy MacLeod

A Letter from Paris

MICHEL PATY

Incidences on the philosophy of science of the historiographical thema "Science and cultural diversity"

Equipe REHSEIS (UMR 7596), CNRS et Université Paris 7 Denis Diderot, Paris

e-mail : paty@paris7.jussieu.fr

Some remarks for the Symposium of the International Association on Science and Cultural Diversity to be held at Pachuca, Mexico,

november 28th, 2000.

1. Philosophical problems

in the field of the history of science History of science and philosophy of science are interrelated despite the separation that predominantly occurred in XX th century, at least in cultural contexts influenced by the "anglo-saxon" philosophy. But, actually, history of science provides a rich field of philosophical problems, and this consideration may powerfully help renewing many "standard" considerations of the philosophy of science, such as, for instance, the changes and evolutions of scientific theories and representations, to take only one example, but which has been significantly related with the structural or systemic character of these theories or representation, with known consequences from the "impossibility solutions" (claimed for rationality) on the debates about the social aspects of science. If, instead, history and rational concerns are to be taken together in considering, both philosophically and historically, the problem of scientific changes, then the a priori impossibility shows no more relevant, as the existence of changes is taken as factual, and we have to think deeper to understand how they occur. Also, the question of the relation between rationality (preferably to a pure logical concern) and invention or discovery in science could be more adequately considered by taking true historicized science, which is that on which scientists do work, than his "rational reconstructions" (see, for instance, what a "problem", or a "difficulty" is, for a scientist at work, in a given case study). In particular, the

epistemologico-historical concepts of "scientific style", of "scientific programme", of "scientific tradition" ([1990]),195 that express a diversity of possible (legitimate) ap-proaches for a same kind of object or of problem in a given time, are useful to understand how science is always in the making and is never already given (be it potentially) or "natural", as if there were a unique standard response or statement to a only one-way formulable question. Clearly, such a concept as "objectivity" is doomed to be reconsidered in these circumstances, and other fundamental concepts and categories as well. But this does not mean that they would have to be left out, and that one would have to adopt a purely historicist conception of knowledge and adhere to a "strong relativist" conception with social reductionism, or to a philosophically nominalist position rejecting rational abstraction and generalization. For this would be too cheap a position, and would lead to absurd conclusions about science and rational-ity, when, on the contrary, the confrontation of both requirements of real or effective science, i.e. its dimensions of knowledge (meaning contents) on the one hand and of human practice of knowledge (which includes sociality and context-dependence, most often casual), on the other hand, is a worthwhile challenge for thought. It is worthwhile, because only from it can we expect to get at some sound, exact and balanced signification about science, scientific activity and rational con-tents. We could make an inventory of such items of the kind. The question of the "interpretation" itself can be differently seen when it is shifted from a purely logical point of view (as if there was one given compelling interpretation, in the philosophical sense), up to a circumstancial, i.e. rational-and-contingent one (see, for example, the importance of the historically situated cultural context for the acceptation of the so-called "Copenhagen interpretation" of quantum mechanics).196 For all this, and furthermore, history of science, by making know historical facts about science, i.e. the actual reality of science, as a human, intellectual and social activity considered in the historical time, appears as being essential in knowing better what science is. Philosophy of science can no more ignore this knowledge and stand within an abstract idealization of science (after all, such an idealization has been historically coined and its knowledge is history dependent). We must admit, symmetrically, as accepted (even if not by everybody) that history of science (as history itself) is not merely description of events, nor with purely social concern, and that it has to do with meanings that have to be searched for (they, too, are not immediately given), which implies the use of reasoning, including epistemological analysis, and at least some philosophical reflections on what all this is about.

195 I quote in braquest references to some previous works of mine that are correlated with these remarks. 196 The question of the relation between changes in interpretation and scientific contents will be the subject of a thematic session proposed at the XXIst International Congress of History of Science to be held at Mexico, 8-14 July 2001.

2.

The Anthropological Approach of Science considered through a variety of historical conditions and cultural diversity

The taking into account by history of science, since a few decades, of the variety of the historical conditions (in space and time) under which science has emerged, has developed or has transformed, corresponds to one of the major aspects of the thema "Science and cultural diversity". This "œcumenical" widening of history of science entails new perspectives for the philosophical approach of problems related with science - in an enlarged, dynamical and diverse conception of science. To reflect on science and cultural diversity means :

1. To consider many possible interrelations between science and cultural aspects, some of which are mentioned in Lafuente's document, essentially from a contemporaneous point of view. Clearly, our views on these problems are affected by the fact that we situate ourselves in the context of modern science in the present world, even if from some diversity of origins. Most of our categories are rooted in this context. Internationalism and mundialization are our present. But we can always inquire their modalities and their roots, now and in history, and we can reflect also on the lessons of other cultural systems in the history of civilizations, that include forms of knowledge that can be seen as corresponding to what we call science. And we are thus led to point 2.

2. To see science as an aspect of the various cultures considered according to their diversity in time and space. The problem is to identify what "science" is in each culture, and to analyse its relations with the other culturals components. In such an inquiry, we cannot start from "science" in general, for it would mean to impose an external philosophical scheme onto a given cultural representation ; but we should try to identify which activities (and objects and methods) are to be pertinently compared to what we consider as "scientific" (from our own questioning), so as to be qualified as such, though knowing however that there are different systemic meanings for knowledge in different cultures. In doing that, we should assume that some communication is somewhat possible and meaningful between different "cul-tural systems". It entails some changes in the possible definitions of science.

Note that there would be similar problems to define art as aethetics from the produced objects and forms that we appreciate as such, and for other cultural components as well. Anyhow, if we want to go further than describing mere facts or local situations, and try some deep understanding of them, and of their meaning, culturally speaking, be it from a simple anthropological point of view, we need to use some categories such as science, technique, religion, art, aesthetics,

philosophy, reasoning, meaning, etc., even if we must be ready to find that they are not uniquely and rigidly defined since the start. We could therefore even consider that they are our creations (as well as the notion of history is our creation, I mean the creation of a given culture), but they are useful to enlighten what cultural forms are, and we can even ask ourselves from which more complex cultural forms they have been constituted (and separated by our minds). We should consider in this respect the eventual status of general and abstract knowledges and of general and abstract categories, as well as the reflex-ive thought about these, in various situations of cultural diversity (through comparative studies). And inquire about the communication (as possibility and as modalities) respectively of concrete elements of knowledge and of abstract ones.

3. Philosophical problems of science

and cultural diversity On this background, let me formulate some questions of a philosophical nature that would come out afresh from the study of such historical situations. We may consider that they concern the intellectual conditions of possibility of science and cultural diversity or, in other words, that they point at philosophical problems emerging from the field of historical facts about science and culture. The following evocation is far from being exhaustive and serve merely as indications and suggestions for further inquiry.

1. Are there general categories (from our historical and epistemological analyse) compatible with diversity ? In particular, what is the status of universality, of rationality, of reason, and even of common sense ? At least some common intelligibility within cultural diversity has always been the basis of interethnical communication, as testified by many reports by travellers through centuries ; this having to be tempered by the frequent occurrence of misunderstandings, of only partial understandings, and of lack of communication as well... Also, reasoning, despite differences in the definitions or premisses, is a common faculty of human beings, as wordly testified. Universality, which is at odds with uniformity and uniqueness, shows to be an adequate category when one looks at anthropological and historical facts such as ability to language, to symbolic representation, to social life, to technical realizations, to the invention of forms, ideas and organizations (social one, in particular), to knowledge in general : see the "neolithic revolution", the invention and dissemination of writing, the industrial revolution, not to speak of science, for our ultimate question is : how (in which sense) can we speak of the universality of science ? (See Paty [1997, 1999]).

2. What are the modalities of the transmissions of knowledges, either inside a cultural tradition or through different ones, and are there useful epistemological concepts or categories able to give account of them? In this respect, I would oppose to the kuhnian notion of "paradigm" another one that seems much more appropriate from the point of view of history of science that includes the consideration of cultural diversity, and less philosophically biased, such as that of inheritance (of Styles or traditions or programmes about knowledge197), that leaves all space for creative activity. A "normative conception" would admit creative activity only as an accident or through a revolution, although scientific creativity appears to be not extraordinary or "a-normal", but inherent to science as formation of new knowledge, with or without scientific revolutions, the latter being by definition exceptional.

3. Is the notion of structural incommensurability (of the conceptual representations) of some relevance when we must consider that, communication being historically evidenced, communicability is possible and factual ? On the other hand, historical understanding needs to respect the systems of meanings of the "cultures" considered, which are, at a given state in time, governed by their structurations. This means that we have to relativize the concept of incommensurability for structures in order to let space for communicability. Actually, it is absolute only in an axiomatic acception, when one considers conceptual meanings as fully closed inside theories or representations, but it is not really adequate with respect to the historical point of view on conceptual elaborations. The idea of "systemic character" is for sure an interesting one from the historical point of view, when one considers the questions of meaning in knowledge transmissions, but it cannot be identified to incommensurability in the strict sense. This should be developed and enriched with epistemological analysis of exemples taken in the history of science, particularly of transmissions through cultural diversity.

4. What is the interplay between intelligibility and historicity ? This question leads inevitably to that of the transformations (and widenings) of rationality, and to that of the nature of such transformations [forthcoming, a].198

5. What can be said about such notions as problematization, demonstration, proof, etc., when confronted to the various conceptions of science ? (There are investigations on some of these problems that are already published or in the course of publication).

6. The problem of knowledge's communication and of translation, that often entails inadequacies ("traduttore, tradittore"), leads also to that of invention as a possible consequence (although it is not the only way to invention,

197 See, for example, the case of d'Alembert, who made his own views and ways of investigation by borrowing or inheriting from three "traditions" : the newtonian, leibnizian and cartesian ones (Paty [in press, b]). 198 Paty [in press, a].

according to what we have stated above on creativity : through the translation and assimilation process alone it would be more accidental and casual). How does this happen in relation with the insertion of science in cultural contexts ? (this question joins again that one considered above about the relations between changes of interpretations and contents).

There are, of course, many other possible items... Note that philososophical questions of this kind may lead to historical investigations in the form of case studies or of comparative researches, as historical facts are essential, in our perspective, to situate these questions and to test their possible answers (as we have experienced elsewhere with the problem of universality of science [1997, 1999]). References to Correlated works by the author Remark. This being more a working note than an achieved paper, I omit

bibliography, and only include my own papers that are related with this research.

Paty, Michel [1990]. L'analyse critique des sciences, ou Ie tetraedre epistemologique (sciences, philosophic, epistemologie, histoire des sciences), L'Harmattan, Paris, 1990.

——— [1997]. L'idee d'universalite de la science et sa critique philosophique et historique, in Arboleda, Luis Carlos y Osorio, Carlos (eds.), Nacionalismo e internacionalismo en la historia de las ciencias y la tecnología en America latina, memorias del IV Congresso Latino-Americano de Historia de las Ciencias y la Tecnología, Universidad del Valle, Cali (Colombia), 1997, p. 57-89. Egalement, Asclepio (Madrid), 49 (2), 1997, 5-43. Trad. portug. (Brasil) por Pablo Ruben Mariconda, A ideia de universalidade da ciencia e sua crítica filosófica e histórica, Discurso (USP, Sao Paulo), n° 28, 1997, 7-60.

——— [1999a]. L'universalite de la science. Une idee philosophique a I'epreuve de I'histoire, Mâat. Revue Africaine de Philosophic, 1ère année, n° 1, avril 1999, 1-26. English transl. by the author: Universality of Science : Historical Validation of a Philosophical Idea, as Chapter 12, in Habib, S. Irfan and Raina, Dhruv (eds.), Situating the history of science : Dialogues with Joseph Needham, Oxford University Press (New Delhi), 1999, p. 303-324.

——— [1999b]. Comparative history of modern science and the context of depen-dency, Science, Technology and Society. An International Journal Devoted to the Developping World (New Delhi, Sage Publications), vol. 4, 2 (July-dec.) 1999, 1 71-204.

——— [forthcoming, a]. Intelligibilite et historicite (Science, rationalité, histoire), Expose invite au Colloque Les grandes rencontres de la science et de I'histoire, Palais de la Decouverte et UNESCO, Paris, 20-24 mars 2000, Quipu, this issue (eventually). Engl. transl. by the author: Intelligibility and

historicity (Science, rationality, history), in Margolis, Joseph and Rockmore, Thomas (eds.), to be published.

——— [forthcoming, b]. D'Alembert, la science newtonienne et l'heritage cartesien, Corpus (Paris), forthcoming.

A Letter from Sweden

FERNANDO FLORES Unfortunately it is impossible for me to personally attend the meeting of the International Association for the Study of Science and Cultural Diversity next November in Mexico. My contribution will be instead virtual - as it is the habit to say today - with some comments to the interesting ideas presented by Professors Lafuente, MacLeod and Paty, and thus contribute in some way to a successful meeting in the beautiful scenery of Pachuca. We have to recall that the term "science" is already the consequence of cultural bias. If we use the term "science" without any further specification, it means more or less the "systematic knowledge as the kind developed first in Europe, from the 17th century until our days, including its developments outside that continent". This kind of systematic knowledge is characterised by its mechanical relation to the natural word, connecting facts and terms in a step by step methodology that makes possible the use of the achieved knowledge in technological applications of different sorts, even when those mechanical applications are not known and therefore are only hypothetical. It is obvious that this was not the case of any development of systematic knowledge before the 17th century in Europe. It is also an open question whether some of the current developments within "science", can be counted into this tradition. (I mean e.g. Catastrophe theory, Chaos theory, Fractal geometry, Fuzzy logic, etc.) The use of this biased term leads later to the necessity of using other related terms that also are biased, terms used to depict other kinds of systematic knowledge, terms which are sometimes tightly related to "science". Examples are - using professor Lafuente's terminology - the terms "pseudo-sciences" and "pre-sciences". As an immediate consequence of this, all the produced systematic knowledge of the world - except some specific kind of European systematic knowledge and its further developments - became the object of study of history. But they could not by itself reach the high plateau of a "History of". They became "an issue in history" as when instead of a "History of Occultism", we have "Occultism in Renaissance" or instead of a "History of the Hermetic Thought", we have "Hermetic thought in Sweden", or instead of a "History of Sorcery" we have "Sorcery during the 1 7th century in Spain". This devaluation of some of the products of rationality, reduce our possibilities to understand all the mechanisms which leads to a full picture of the development of the rational mind, or in other words, to a proper History of Rationality. I think that Professor MacLeod is right when he says: "The phrase 'Science and Cultural Diversity' is more a useful collection of categories than a coherent programme". I do not know if any program of this kind is possible in our days, and if

it is possible for us to present anything so ambitious. Any possible program would however have to start from a generic point of view, some kind of global history of rationality, which either incorporates "science" as a subset of "systematic knowledge" or redefines "science" as "systematic knowledge of any kind". I also agree with Professor MacLeod when he says that the idea of "cultural diversity" has strong political associations. In the world of today, we know by certainty that the development of "science" has been possible in connection with the development of a complex of political and economical ideologies. In this sense, any attempt to change the basis of this ideological complex could be understood as a menace to the establishment. The connection between a History of Science and a History of Rationality becomes more transparent when we - following Professor Paty's interesting remarks - ask ourselves about the actual differences between rival theories or rival methodologies, and especially between rival interpretations of the same dignity and the same range of public acceptance, as e. g. the different worldviews connected with Relativity and Quantum mechanics. Philosophy of science shows during the last fifty years that ideas as "proof", "empirical evidence" etc., are highly problematical, and that the naive era of Positivism is definitively over. Those times of crude "science-ideology", are now followed by a new form of ideology which Professor Lafuente expresses as "science for the people without the people". It could be shown that this new mechanical development follows pure 17th traditions, and it is almost transparent in a new and powerful front of expansion: genetics. Is obvious to me that many "older" ways to confront these problems are not longer valid. This can be illustrated by two of MacLeod's chosen terms: "colonial" and "indigenous". If they were important in the past, they are no longer of use. But how could those terms be substituted? Many of them belong to a corpus of systematic knowledge that is very important to the historian. We have to remember that in our discipline, there are truths of an almost indisputable nature, truths that are as rooted in our minds as e.g. the idea of a heliocentric planet system. The historian of today is imbedded in a world of "sciences" and he has his own "Science of History". To illustrate this last point shall I call your attention to terms as "capitalism". The history of "capitalism" is associated to the history of "science". The history of "capitalism" is also associated to the history of "private property". So if we want to see the history of science in a new light we have to revise a lot of other concepts that are at least as firmly established as the concept of science. Now, how open are we to question these truths and their relations? Could it be possible for the historian of today to question the status quo of theories concerning the de-velopment of capitalism? Could it be possible that the process that we usually call "capitalism" is in fact the combination of many other processes that have been present in history even in other periods? If this intellectual liberation is possible, the connection between "modern systematic knowledge" - as the kind we describe by the term "science" - and some "archaic systematic knowledge" - as the kind we describe as "pre-science" or "pseudo-

science" - will be liberated from the obligatory reference to a corpus of ideas that eclipse new insights. Cultural diversity - as I see it - means more than ethnological relativity, it means moving into the field of history as well as the most recent results from the field of science and the philosophy of science, results that show the limits of our capabilities to reach definite answers. To sum up: as I see it, "cultural diversity" implies the acceptance of the contingency of any form of systematic knowledge. Lund, 24 October 2000 Fernando Flores

Part III Statutes and By-Laws

Of the international Association For Science and Cultural Diversity

Statutes

International Association for Science and Cultural Diversity

A Scientific Section of the Division of History of Science International Union for History and Philosophy of Science

Section A The aim of the International Association for Science Cultural Diversity is to promote the History of Science by establishing and extending the scholarly bases for the study of Science and Cultural Diversity. Section B The Association is a non-profit organisation composed of Ordinary Members, Honorary Members, and Benefactor Members. Ordinary Members and Benefactor Members become active by conditions determined from time to time by the Assembly. Section C Members of the Association will meet in Assembly at call of the President, Council, Executive Committee, or petition by ten per cent (10%) of active Ordinary Members.

(a) The Assembly is responsible for policies, programmes, budget, election of officers, and other business of the Association.

(b) During the interval between Assemblies, the Association will function through its Council, Executive Committee, and Executive Officers.

Section D Executive Officers of the Association are President, Secretary-general, and Treasurer.

(a) The President of the Association is elected by the General Assembly of the Division of History of Science of the International Union of History and Philosophy of Science, in accord with the constitution of the Division.

(b) Other Officers and Assessors may be determined and elected by the Assembly. Section E The Association acknowledges religious, philosophical, cultural, and political characteristics of diverse cultures and societies throughout the History of Science which scholars should take into account. Nevertheless, no motion or resolution concerning such questions will be recognised and no actions may be taken about

those characteristics in meeting of the Assembly, Council, or Executive Committee of the Association. Section F The International Association for Science and Cultural Diversity is governed by these present Statutes and the attached By-laws whose English and Spanish texts provide the definitive interpretation, as well as by the laws relative to non-profit associations in those countries where its headquarters is located and where its activities take place. The Statutes and By-laws are deposited with the Division of History of Science/I UHPS. Amended Statutes and By-laws shall be so deposited promptly. Section G If recommended by Council of the International Association for Science and Cultural Diversity, any Statute may be changed by the quadrenniel Assembly of the Association, provided that.

(a) at least six months before the Assembly is convened for that purpose, the Council's recommendation is submitted to active members individually by the Secretary-general;

(b) at the Assembly, a quorum for this purpose is constituted by one-half the number of active Ordinary Members of the Association;

(c) a Motion for change of any Statute receives the vote of two-thirds majority of active Ordinary Members present;

(d) as amended, the Statutes are deposited with the Division of History of Science/IUHPS.

Section H The International Association for Science and Cultural Diversity is also governed by the By-laws herewith attached to the Statutes and deposited with the Division of History of Science/IUHPS. If recommended by Council, By-laws of the Association may be changed

(a) during a quadrenniel Assembly, by a simple majority vote of those active Ordinary Members present;

(b) during an extraordinary Assembly, by the process and order for change of Statutes;

(c) as amended, the By-laws are deposited with the Division of History of Science/IUHPS.

Section I

The Assembly is empowered to dissolve the International Association for Science and Cultural Diversity, provided that

(a) an extraordinary Assembly is convoked by call of the President or the Council for purpose of dissolution and, twelve months prior to the Motion to Dissolve, the Notice of Motion is sent to active members: Ordinary, Honorary, and Benefactor;

(b) at the Assembly for this purpose, a quorum consists of one-half (1/2) the number of active Ordinary Members of the Association; members may be present in person or by proxy registered with the Secretary-general one-day prior to the calling the Motion;

(c) a Motion to Dissolve the Association receives a majority vote of two-thirds (2/3 s) the number of active Ordinary Members present in person or by proxy registered with the Secretary-general on the day prior to calling the Motion.

By-Laws

in addition to Statutes,

enacted by the Assembly for governance of the Association

TITLE 1-AIMS and MEANS

Article 1. The aims of the International Association for Science and Cultural Diversity are:

(1) to promote the History of Science by establishing and extending the scholarly bases for the study of Science and Cultural Diversity; (2) to foster historical study of the relationship between the sciences, technology,

medicine, and the cultures in which they arose throughout the world from ancient times to the present; (3) to encourage international cooperation and maintain close working

relationships among specialists of different disciplines; (4) to facilitate research documentation in the History of Science and

Cultural Diversity for scholars in all countries through exchange of information and by enlarging the material means necessary for this objective. Article 2. In order to attain those aims, the International Association for Science and Cultural Diversity will:

(1) establish itself in the greatest possible number of countries and recruit the greatest possible number of qualified members therein;

(2) create committees and working groups charged with conducting studies focussed on particular aspects of the History of Science and Cultural Diversity;

(3) seek financial means which may become available to assist the work of these groups;

(4) organise colloquia, seminars, and other meetings in order to make possible the direct cooperation of its membes;

(5) establish and maintain at the disposition of its members indispensable information, documents, and scientific exchanges;

(6) publish reports and results of works of the Association and give them the widest possible disseminations;

(7) cooperate with other national and international scientific organisations which pursue similar goals concerned with History of Science and Cultural Diversity.

TITLE 11-MEMBERS

Article 3. Forms of memberships:

(1) Ordinary Members are individuals who are active in their own names. They are expected to contribute advice to their colleagues and to the Assocation, publish their research findings, participate in meetings of the Association, and support the Association by payment of annual dues.

(2) Honorary Members are those individuals who have rendered exceptional services to the Association for SCD. Such persons may be recommended by two or more active Ordinary Members. Evaluation and nomination may be made by the Council. Election as Honorary Member is by vote of the quadrenniel Assembly.

(3) Benefactor Member is a scientific or cultural institution, corporation, or university which supports the aims of the Association. Recommendations may be submitted by two or more active Ordinary Members. Evaluation and nomination may be made by the Council. Election as Benefactor Member is by vote of the quadrenniel Assembly. Article 4. Annual dues of Ordinary Members will be recommended by the Executive Committee and determined from time to time by the Assembly. Dues of Benefactor Members will be assessed at then times those of Ordinary Members. Honorary Members are not be required to pay dues. Honorary Members and those who pay their annual dues are considered to be "active members." Article 5. Active Ordinary Members may participate in meetings of the Assembly in person or by proxy. Officers and Assessors participate also in meetings of Council or Executive Committee, to which they have been elected, either in person or by proxy.

(1) A Proxy may be in writing (by post of fax) or by e-mail and must be received and registered by the Secretary-general on the day prior to the Chair's call for vote on a motion or for an election.

(2) If challenged, the registration of a Proxy may be appealed to Council and authorised by vote of the Council prior to the Chairs's call for a vote. Article 6. Loss of Membership. The membership of Ordinary Members or Benefactor Members may be terminated by resignation, non-participation, non-payment of dues, or by action of the Executive committee for cause. If termination seems unfair, the active Member may explain the circumstances and request reinstatement to the Executive Committee. If reinstatement is not granted , the active Member may appeal to Council.

TITLE ///. OFFICERS and ASSESSORS

Article 7. Officers of the International Association will be President, First Vice-president, Second Vice-president, Secretary-general, Assistant-secretary, Treasurer, two or more Assessors.

Article 8. Election of Officers. (1) Except for the office of President, the Officers and Assessors of the

Association are elected by active Ordinary Members, voting in the quadrenniel Assembly.

(2) Those eligible for nomination and election as Officer or Assessor must be active Ordinary Members of the Association when nominated, as determined by Council.

(3) Each Officer and Assessor is elected by the Assembly for a term of four years, begining with the conclusion of the quadrenniel Assembly.

(4) Anyone may be re-elected to the same office for a second term only once; for this purpose, a partial term filled because of vacancy is counted as a full term. No person may hold the same office for more than eight consecutive years.

(5) Following service in one office, anyone may be eligible for election to a different office.

(6) Anyone elected to office who becomes inactive during the term has vacated the office, as determined by Council. Article 9. President. The President is responsible for all matters of policy, as determined by the Assembly of the Association or by the General Assembly of the Division of History of Science/IUHPS.

(1) He will represent the Association on occasions appropriate for the programme and activities on History of Science and Cultural Diversity.

(2) The President will preside and conduct the business of the Assembly, Council, and Executive Committee of the Association. In his absence, business will be conducted by the First Vice-president or next senior officer of the Association.

(3) As policy and business of the Association require, he will advise the Secretary-general throughout each year. He will consult the Executive Committee and the Council about policies and current affairs of the Association at least once a year. (4) In the event the President becomes unable to exercise the functions of office,

the First Vice-president succeeds to the office after obtaining consent of the Division of History of Science/IUHPS.

Article 10. Secretary-general.

The Secretary-general is responsible for the current affairs of the Association during the interval between Assemblies in accord with policies determined by the Assembly and the President. The Secretary-general will

(1) maintan close relations with programme committees and working groups of the Association and encourage their activities in History of Science and Cultural Diversity;

(2) keep the annual and quadrenniel budgets of the Association in balance; (3) report to the President on all important matters as they occur, report to

the Executive Committee and to Council about important affairs of the Association at least once a year, and communicate with Members on appropriate occasions;

(4) organise meetings of the Assembly, Council, and Executive Committee; (5) register each Proxy to a meeting of Assembly, Council, or Executive

Committee, at least one day prior to the call for a vote, and refer the challenge or appeal of a Proxy to Council for decision. Article 11. If the President is unavailable for a meeting of DHS/IUHPS in person, the Association for Science and Cultural Diversity will be represented by the Secretary-general in person. If neither is available, another Officer or Assessor may be designated by the President for this purpose. Article 12. Treasurer. The Treasurer is responsible for financial accounts of the Association. Those accounts shall be comprehensive of all revenues and expenditures of the Association, its committees, working groups, meetings, and professional contracts. (1) Receipts of the Association consist of dues of its members and all other grants,

donations, or subventions to the Association by individuals, private organisations, or public institutions with which the Association is involved nationally or internationally. Receipts may also include the positive balance resulting from contracted professional work. (2) Expenditures of the Association consist of the expenses incurred by the

President, Secretary-general, and Treasurer required for business of the Association and approved by the Executive Committee, including communications and publications; meetings of its own Assembly, Council, and Executive Committee; travel to those meetings and to meetings of the Division of History of Science/IUHPS.

(3) Such other expense deemed necessary by an executive officer may be allowed in each case on condition that

(a) specific prior approval has been given by the Executive Committee, and (b) it is subsequently ratified by Council.

(4) In any case wherein an expenditure has been incurred by an officer or by any member and reimbursed by the Association, all such reimbursed funds shall be returned to the Association

(a) if it did not receive specific prior approval by the Executive Committee, and (b) if it is not subsequently ratified by Council.

(5) The Association will not reimburse the negative balance of an Association committee or working group or financial loss from contracted professional work, unless specific prior approval has been given by act of Council. Article 13. The Treasurer will report annually to the Executive Committee the state of the budget for the Association, its committees, working groups, meetings, and professional contracts.

(1) All financial accounts of the Association will be reviewed annually by Council and each quadrennium by the Assembly, or reviewed at any time by decision of the Council or of the Assembly.

(2) At the conclusion of each four-year period, in consultation with the Executive Committee and the Council, the Treasurer will report to the Assembly on the budget which it had voted.

(3) An audited financial report will be prepared in accordance with commonly accepted accounting practices and presented to each quadrenniel Assembly. Approval of the audited financial report by the Assembly discharges the Treasurer of responsibility for receipts and expenditures reported in the budget of the past quadrennium.

(4) In consultation with the Executive Committee and the Council, the Treasurer will propose and ask for approval by the Assembly of a new budget for the subsequent four-year period. Article 14. If the Treasurer becomes unable to exercise the functions of office, the President will nominate someone to replace him temporarily until the next Assembly. Such succession to a vacant office may occur only by consent the Council. Article 15. The Association may enter into contracts with other organisations, universities, or corporations to perform work or provide consultation in matters of its professional competence, provided that such contracts

(1) are recommended by the Executive Committee, (2) approved by act of Council, and (3) subsequently reviewed and ratified by the Assembly. If the Assembly

does not ratify it, a contractual agreement will be concluded expeditiously and, with recommendation of the Executive Committee and by act of Council, as beneficially to the Association as possible.

TITLE IV. ORGANISATION Article 16. Assembly. The Assembly of active members is responsible for policies, programmes, budget, elections, and other business of the Association for Science and Cultural Diversity. Article 17. The Assembly will meet at call of the President ordinarily once every four years in comjunction with the Division of History of Science/IUHPS and the International Congress of History of Science organised by that Division. There may also be extraordinary assemblies called by the President, by a majority of Executive Committee members, by a majority of Council members, or by ten per cent (10%) of the number of active Ordinary Members. An Assembly, either ordinary or extraordinary, will occur

(1) on the date and in the place determined by the Executive Committee of the Association; and

(2) by notice to every member from the Secretary-general no later than three months before that date and preferably earlier. Article 18. The Assembly will receive and hear Minutes of the previous quadrenniel meeting and of any extraordinary meeting; such Minutes may be approved or corrected, as deemed appropriate. It will receive Reports from the executive officers:

(1) the President, on the policies of the Association; (2) the Secretary-general, on activities of the Association; (3) the Treasurer, on financial accounts during the past quadrennium and

accounts of any other financial activities of the Association. Article 19. The Assembly will receive and review reports of their activities from the Executive Committee, the Council, and each committee or working group formed under its authority. It will hear and decide appeals from decisions of the Executive Committee and from decisions of the Council, except those for which decision of Council is final. Article 20. The Assembly will hear and dispose of all old and new business according to its own agenda. It will evaluate the work of its committees and working groups and, on recommendation of Council, it will determine whatever is required for the programme of the Association. Article 21. Upon recommendation of the Treasurer and advice by Council, the Assembly will prepare a new budget for the next quadrennium of activities of the Association. Article 22. Decisions of the Assembly shall be taken by vote of active Ordinary Members present in person or by proxy. For motions and elections, a quorum is a simple majority of those present, except for change of Statutes, change of By-laws, or Dissolution, as defined in Statutes of the Association. Article 23. Executive Committee. The Executive Committee of the Association is composed of the President, Secretary-general, Treasurer, and the immediate past-Secretary-general ex officio. Article 24. During the interval between Assemblies of the Association, the Executive Committee will act in behalf of the Assembly to fulfil the policies and programmes of the Association. It is responsible to Council and to the Assembly. Thus, it will

(1) receive and review reports from committees and working groups, and offer recommendations to the chairs concerning their activities;

(2) nominate to the quadrenniel Assembly active Ordinary Members as chairs of programme committees and working groups. (3) refer business and recommend actions to the Council and to the Assembly.

(4) in consultation with the Treasurer, review the budget annually and make recommendations to Council or to the Assembly. Article 25. The Executive Committee will meet immediately following the Assembly at which it was elected, and it will meet again in preparation for the next Assembly. It should also meet once in each intervening year, insofar as the budget of the Association permits.

(1) Meetings of the Executive Committee are by call of either the President or the General-secretary. A quorum consists of three members present in person or by proxy; decisions may be taken by a majority of those present.

(2) Decisions and activities of the Executive Committee will be submitted annually to Council and each quadrennium to the Assembly for review, approval, or modification. Article 26. Council. The Council of the Association consists of the Officers and two or more Assessors elected by the quadrenniel Assembly, and the past-Secretary-general ex officio. Nomination and election of active Ordinary Members as Assessors is intended to maintain a balance of geographical regions and of professional disciplines on Council. Article 27. The Council is responsible for

(1) programme and budget of the Association during the interval between meetings of the Assembly; therefore it will receive annual reports from the Secretary-general and the Treasurer;

(2) the status of members of the Association, including nomination of Honorary Members and Benefactor Members; for these purposes, Council will receive recommendations by the First Vice-president. (3) Continued functions of all offices, recognising that vacancy may occur by

absence, negligence, resignation, or death. In case of a vacancy is determined by Council, the First Vice-president will nominate an active Ordinary Member of the Association to complete the term of office; Council will decide whether to accept such nomination.

Article 28. The Council will.

(1) review the Treasurer's quadrenniel report on the curent budget and the proposed next quadrenniel budget, and it will make recomendations to the Assembly;

(2) review expenses of Executive Officers annually or as appropriate;

(3) name auditors of the financial accounts of the Association for each quadrennium, receive and review the auditors' report, and recommend to the Assembly whether it should be accepted;

(4) recommend to the Assembly whether the Treasurer should be discharged of responsibility for receipts and expenditures in the audited financial report for the closing quadrenniel budget. Article 29. Council decision is final and may not be appealed concerning

(1) the status membership for any individual or benefactor; (2) the status of a Proxy for any meeting of Assembly, Council, or Executive

Committee. Article 30. The Council is responsible for maintaining the Statutes and By-laws of the Association. By simple majority vote, it may recommend to the Assembly a change in the By-laws. By two-thirds majority vote, it may recommend to the Assembly a change in the Statutes or Dissolution of the Association. TITLE V. LOCATION Article 31. The headquarters of the Association will be the seat of the Secretary-general, unless otherwise determined from time to time by decision of the Executive Committee.

Science and Cultural Diversity de la serie Cuadernos de Quipu, núm. 5

publicado por la Sociedad Latinoamericana de Historia de las Ciencias y la Tecnología,

se termino de imprimir en junio de 2001. Composición tipográfica, formación e impresión:

Grupo Edición, S.A. de C.V., Xochicalco 619, Col. Vértiz-Narvarte, 03600 México, D.F.

Se tiraron 1 500 ejemplares. La edición estuvo al cuidado de Rodrigo Bache Saborío.