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 Poincare who had already reached a similar conclusion. In this paper, we flesh out the historiographical tensions arising from these confrontations: longue-duree history and revolution; abstract mathematics and the use of mathematical techniques in various other domains. After reviewing the historiography of dynamical systems theory from Poincare 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. © 2002 Elsevier Science (USA). Entre la fin des annees 1960 et le debut des annees 1980, la reconnaissance du fait que des lois dynamiques simples peuvent donner naissance a des comportements tres compliques a ete souvent ressentie comme une vraie revolution concernant plusieurs disciplines en train de former une nouvelle science, la “science du chaos.” Rapidement, les mathematiciens ont reagi en soulignant l'anciennete de la theorie des systemes dynamiques fondee a la fin du XIXeme siecle par Henri Poincare qui avait deja obtenu ce resultat precis. Dans cet article, nous mettons en evidence les tensions historiographiques issues de diverses confrontations: l'histoire de longue duree versus la notion de revolution, les mathematiques pures versus l'utilisation des techniques mathematiques dans d'autres domaines. Apres avoir passe en revue l'historiographie de la theorie des systemes dynamiques de Poincare jusqu'aux annees 1960, nous soulignons les travaux pionniers d'un petit nombre d'individus: Steve Smale, Edward Lorenz et David Ruelle. Nous poursuivons en discutant la nature du phenomene du chaos qui constitue, selon notre analyse, tant une reconfiguration conceptuelle qu'une convergence sociale et disciplinaire. © 2002 Elsevier Science (USA). MSC subject classifications : 01A60, 01A85, 37-03, 76-03, 82-03, 86-03.

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