Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures

Abstract

Between the late 1960s and the beginning of the 1980s, the wide recognition that simple dynamical laws could give rise to complex behaviors was sometimes hailed as a true scientific revolution impacting several disciplines, for which a striking label was coined-"chaos." Mathematicians quickly pointed out that the purported revolution was relying on the abstract theory of dynamical systems founded in the late 19th century by Henri Poincaré who had already reached a similar conclusion. In this paper, we flesh out the historiographical tensions arising from these confrontations: longue-durée history and revolution; abstract mathematics and the use of mathematical techniques in various other domains. After reviewing the historiography of dynamical systems theory from Poincaré to the 1960s, we highlight the pioneering work of a few individuals (Steve Smale, Edward Lorenz, David Ruelle). We then go on to discuss the nature of the chaos phenomenon, which, we argue, was a conceptual reconfiguration as much as a sociodisciplinary convergence. C 2002 Elsevier Science (USA) Entre la fin des années 1960 et le début des années 1980, la reconnaissance du fait que des lois dynamiques simples peuvent donner naissanceà des comportements très compliqués aété souvent ressentie comme une vraie révolution concernant plusieurs disciplines en train de former une nouvelle science, la "science du chaos." Rapidement, les mathématiciens ont réagi en soulignant l'ancienneté de la théorie des systèmes dynamiques fondéeà la fin du XIXème siècle par Henri Poincaré qui avait déjà obtenu ce résultat précis. Dans cet article, nous mettons enévidence les tensions historiographiques issues de diverses confrontations: l'histoire de longue durée versus la notion de révolution, les mathématiques pures versus l'utilisation des techniques mathématiques dans d'autres domaines.1 A first version of this paper was delivered at the workshop "Epistémologie des Systèmes dynamiques," Paris, November 25-26, 1999. We thank the organizers and our colleagues from the sciences (and especially Yves Pomeau) for their useful comments. In the course of our research, interviews have been conducted and letters exchanged with various people; we thank in particular Vladimir Arnol'd, Alain Chenciner, Pedrag Cvitanovic, Monique Dubois, Marie Farge, Mitchell Feigenbaum, Micheal Hermann, Igor Gumowski, Edward Lorenz, Jacques Laskar, Paul Manneville, Paul C. Martin, Christian Mira, Mauricio Peixoto, David Ruelle, René Thom, and JeanChristophe Yoccoz. For their comments on parts of this paper, we thank Umberto Bottazzini, Philip J.

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