Forty years ago, Roger Caillois approached the International Council for Philosophy and Humanistic Sciences and proposed that the Council establish a most unusual journal. At the request of UNESCO, the council had brought together a number of learned organizations in the realm of the humanities; Jacques Rueff had just assumed the presidency. In Caillois's mind, the objective was to put an end to the isolation enjoyed by most disciplines, which jealously guarded their prestige and authority and cared little to have their neighbors meddle in their affairs. For Caillois, the musicologist needed the classicist, the prehistorian the philosopher and, of course, the religious historian the linguist and the economist. The interdisciplinarian, at that time, attracted a fair amount of attention. But Caillois was not satisfied. Too often, it seemed to him, the interdisciplinarian was content with arbitrary and superficial juxtapositions. Caillois wanted to raise the transdisciplinary to the level of a methodology, and he wanted to try to draw together the different scholarly sectors reluctant to step beyond historical boundaries all too often frozen by time. Haunted by the theme of the chess board at least as much as by the medusa or by fulgora lantern flies, he coined a term of his own for all this, a term destined to a brilliant future: the lateral sciences.

We are approaching two dates in our personal and collective calendars that oblige us to pause and reflect on our place in time and on our task in history.

We share the first date with all of humanity. We are coming closer to a new century and a new millenium, leaving behind the epoch of grandeur and servitude that we call “the twentieth century,” even though we live our time, like all times, accompanied by its multiple pasts.

The longing for aerial flight has been one of mankind's most consuming preoccupations. A burning desire for lightness, verticality, and flight is opposed to the fatality of universal gravity. Jules Michelet, in his study of the subject, entitled L'Oiseau (The Bird), which he wrote toward the end of his life, deems this aspiration for upward motion to be characteristic of all nature. He writes: “It is the cry of all the earth, of the world and of all life… : ‘Wings! We want wings, we want flight and movement.’” From ancient times, this basic element of physical experience has nourished human imagination and been a source of motivation for the pursuit of scientific knowledge. Mesopotamian civilization had its winged divinities and spirits; indeed the Western tradition of depicting winged persons has been linked to the influence of Mesopotamian art. As Jules Duhem has pointed out, four centuries before Jesus Christ, Aristotle himself was already exploring certain notions that have become part of the history of ideas of aeronautics and astronomy. Among these are the ideas of void, weight, the resistance of air, and the movement of birds and other flying creatures. Duhem has also demonstrated that Aristotle proposed an explanation, as imperfect as it was, for what causes projectiles to fall from the sky. Throughout the ages, humanity has continually expressed its desire to fly: “Man is proud of being free and of leaning on nothing,” Elias Canetti has written in regard to man's upright position. Striking examples of the impulse to fly are to be found not only in scientific discourse but in myths, literature, and works of art.

When the world reveals a part of its beauty, what should our reaction be? How can we respond adequately? Is not our initial reaction one of a “discrepancy between our impressions and their habitual expression?” It is this question that Proust poses in one of the crucial passages early on in his masterpiece. Describing his walks along Méséglise's Way, and “the humble discoveries” he made there, the narrator details for us the overwhelming, decisive impression made on him by a shaft of sunlight:

The existence of a partnership between knowledge and armies - and, connected with it, between knowledge and wars, conquests, and the entire apparatus of empires - has been affirmed since the time of Xenophon. The troops clear a path that the scholars follow, and an increase of knowledge is a side effect of the incursion. The great linguistic discoveries of the eighteenth century - that is, the Zend and Sanskrit languages - would have been impossible without the expansion of the French and British empires into Asia; and Bonaparte, in his foray into Egypt, was accompanied by a large contingent of scholars. After the uniformed troops march in, official scholarly missions follow. For example, in 1849, Italian archives were opened to French scholars as a result of the French occupation of Rome. Renan's access to Italian libraries, monasteries, and manuscript collections was a result of the presence of French troops in Italy. This was a period of preliminary analyses, of the publication of catalogues, and of amazement at the wealth of available documents. In brief, it was a period of successful compilation, of rapid and exhilarating erudition. It was a time when everything rang true. In 1860, it was once more Renan who set off, on the margins of the French intervention in Syria and Lebanon, in search of epigraphical materials. In fact, all of nineteenth-century French, German, and English archaeology follows in the wake of the colonial expansion of the various empires.

Nothing that can be called thinking is formalized or formalizable; nor can it be likened to a mechanical process (Church's hypothesis). Rather, thinking sets into motion human imagination and passion.

Having already written extensively on the imagination,' I will limit myself here to outlining its basic structure. At the two opposite poles of knowledge, as well as in its center, lies the creative power of the human being, that is, radical imagination. It is thanks to the imagination that the world is presented in this form and not in some other: it is imagination that creates axioms, postulates, and the fundamental patterns that subtend the structures of knowledge; finally, it is imagination that both furnishes the hypothetical models and idea-images of knowledge, and makes possible their potential development and/or insight into them. This imagination, however, both in itself and in its essential operations – which include its social forms, experienced on this level as the creation of an anonymous collective force – is neither formalized nor formalizable. Obviously, the imagination contains – just as does everything else that exists – a totalizing, identity-bearing dimension (which for brevity's sake we have elsewhere called ensidiqt,ce)2; but this dimension of the imagination is not the essential one, neither in its operations nor its results, no more than the arithmetic relations between tones are the essential element of a Bach fugue.

A multiplicity of circumstances - including geographic and political isolation, and differences of social organization and customs - has led different groups of people to develop mathematical knowledge independently of each other. Yet history has shown us again and again that by some necessity these separate groups often encounter the same problems. The solutions they propose, however, are often different. This suggests a series of questions. First of all: what is the relationship between the solutions? Is one solution an alternative to the other, and if so, how to account for their differences? Or, on the contrary, are the solutions complementary? Both of these configurations can be found in the history of mathematics: in the following article we will investigate two elementary examples of these phenomena and trace the historical circumstances under which different solutions have come into contact.

To commemorate the fortieth anniversary of Diogenes is, above all, to honor Roger Caillois. From 1952 until his death in 1978, this periodical was the heart of his working life. In July 1948 Caillois had become an international public servant, working for a brand new institution, UNESCO, as a member of its “ideas office” responsible for program planning. UNESCO and the nongovernmental organizations clustered around it adopted a grand and magnificent objective: to promote peace through education and culture. One avenue to pursue this goal was the publication of books and periodicals. Diogenes was therefore the fruit of the interaction between the plans of UNESCO and the International Council for Philosophy and Humanistic Studies and the life experience of Roger Caillois.

This article is the result of collaboration between a linguist and an anthropologist. In La Troisième planète. Structures familiales et systèmes idéologiques (The Third Planet: Family Structures and Ideologies) (Todd, 1983), anthropologist Emmanuel Todd provided a world map of family types, which he used to explain the distribution of major political philosophies around the world. However, this did not explain the distribution of the family types themselves. Indeed, a concluding chapter entitled “Le Hazard” (The Effects of Chance) stated that the distribution of family types did not seem to be the result of any particular economic or ecological factor and was therefore a prime example of the uncertainty principle at work. However, Laurent Sagart, a linguist specializing in Chinese dialects, noticed that this map of family types exhibited a structure well known to experts in historical linguistics and dialectology, contrasting a large, continuous zone in the center with a number of small, independent zones located around the periphery of the central zone or in isolated enclaves within it. When such maps appear in linguistic atlases, dialectologists usually conclude that the central zone was the innovative area while the peripheral and isolated zones conserved the original features. The same analysis, if applied to the map of family types, would lead to the conclusion that the communal family system in the center of the map represented a more recent innovation than the systems around the periphery.