My sincere thanks to the participants in my seminar “Le temps des populations” at the École des hautes études en sciences sociales for their enthusiasm in discussing this article: Anne-Sophie Bruno, Paul Costey, Christelle Rabier, Frédéric Sally, Charlotte Vorms, and to Maya and Vladimir Kostov.
THE MATHEMATICS OF TIME IN HISTORY1
Article first published online: 8 DEC 2010
© Wesleyan University 2010
History and Theory
Special Issue: THEME ISSUE 49: History and Theory: The Next Fifty Years
Volume 49, Issue 4, pages 28–46, December 2010
How to Cite
BONNEUIL, N. (2010), THE MATHEMATICS OF TIME IN HISTORY. History and Theory, 49: 28–46. doi: 10.1111/j.1468-2303.2010.00558.x
- Issue published online: 8 DEC 2010
- Article first published online: 8 DEC 2010
- human agency;
The themes of connectedness and continuity, which are also mathematical properties, have run like a red thread through the last fifty years of History and Theory, notably in the theory of the narration of action in history. In this essay I review various answers to the question of the driving force that motivates action and that propels a sequence, continuous or discontinuous. These answers underpin narrative strategies intended to solve the problem of human agency and thereby to provide the basis for historical narratives. I argue that both continuous and discontinuous conceptions of history have to do with the restrictive concept of trajectory. Most of our familiar concepts such as trajectory, equilibrium, optimum, probability, and sensitivity to initial conditions are taken from mathematics and physics, but how well adapted are they to dealing with the time of actors, whose actions are intermingled with uncertainty? I shall present alternative concepts of dynamics, ones that no longer lead toward just one particular future or that reflect a single past. On this basis I suggest reorganizing our view of historical time along the principles of maintenance, acquisition, and victory. Historical sources trace back not to one story or one process that is plausible or that appeals to common sense, but to a whole family of processes. From the past, we can obtain sets of constraints that circumscribe sets of stories rather than a single scenario. I shall then propose a topology of the time of action based on my alternative conception of dynamics, a topology made of what I call viability kernels, capture basins, and victory domains.