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Chaos, Disorder, and Mixing

9 October 2012, 06:00

Chaos and the sciences of disorder or mixing concern particular disciplinary sectors (e.g., mathematics, fluid mechanics, physics, engineering science, etc.) but they also form disciplinary crossroads, which symbolize a new mode of conceiving and practicing science. Moreover, they go hand in hand with a discourse proclaiming a new episteme or a new paradigm—the idea of a third scientific revolution has even been mentioned. To characterize this new area of science is a delicate matter since it involves both specific scientific practices and theories and also diffuse representations of them among audiences more remote from practice. Such a representation of science is always partial; even when it has a hegemonic ambition, it competes with other representations, built by other scientific subgroups, who regard it as partly ideological. But since my aim is to reflect on a certain “air du temps” in contemporary science rather than to establish a Kuhnian paradigm or a Foucaldian episteme, I will deliberately use somewhat vague terms such as images and representations of science.
A few historical remarks on representations seen as characteristic of an “air du temps” may be useful. Our historiographical tradition has constructed an image of 17th C. science as being about a world ruled by clockwork, whose harmony was mathematical. Nature was an automaton exhibiting repetitive phenomena ordained by a God who was likened to an architect (or a clockmaker). Several recent historical studies, however, have shown that this representation did not exclude others coexisting with it, even within one individual (Newton for example). Moreover, this representation differed significantly between different individuals and groups, for example, between continental mechanical philosophers (Descartes, Pascal, or Huygens) and English natural philosophers (Boyle and Newton). Perforce, it varied considerably among groups with more remote interests and practices: there was little in common between, on the one hand, the astronomers of the Academy of Sciences in Paris and the Royal Society in London, and, on the other, Baconian naturalists or the practitioners who experimented with thermometers and barometers, or tested the stiffness of wood and glass. In spite of this heterogeneous variety, however, the mechanical image retains some validity; it no doubt conveys something essential about the 17th century.
As a second example, consider the common representation of Laplacian science at the end of the 18th century. In a recent study, I have shown how Laplace’s vision has been demonized, and turned into a Manichean opposition between a Laplacian totalitarian universe and the freedom authorized by contemporary theories of chaos. In fact, Laplace merely presupposed in principle the possibility of total prescience and complete predictability, but he was perfectly conscious that their practical possibility was out of reach. For this precise reason, he judged it necessary to forge the tools of probability theory, allowing for a statistical description of some processes. We can, nevertheless, claim once again that Laplacian determinism expressed a “general conviction of the time,” i.e. a belief in the causal structure of the world, a faith in the mathematical intelligibility of laws which the scientist has to discover or to approach as nearly as possible.
In both of these cases, we meet constructed, but incomplete, images expressing some important part of the air du temps. Let me now summarize some key elements that characterize the representation of contemporary science:
1 the logic of scientific reasoning, i.e. the relation between causes and effects, has changed: in brief, "the world is nonlinear," and a small detail can bring forth a catastrophe;
2 complexity was formerly believed to be decomposable into elementary units, yet only a global approach is pertinent;
3 sand heaps and water droplets reveal the profound physical nature of matter’s behavior, which cannot be revealed by atomic physics;
4 reductionism has reached its limits and its end has been announced for the near future;
5 the scientific method associated with the names of Galileo and Newton and once believed immutable has now been supplanted by an historical point of view which has become dominant in the geosciences, and in the life and social sciences.
Finally, in the representation following from the above theses, the hierarchy of the disciplines has been upset. In particular, mathematics and theoretical physics have lost their dominent position, and the biological and earth sciences have been promoted into the new Pantheon of science.
Within the confines of this article, it will not be possible to discuss in detail either the many texts that have adopted these theses (and sometimes loosely extended them to economic, political, or social domains) nor the history of their development over the past 20 or 30 years (even 50 years in the case of cybernetics). Instead, I will review a few recurrent themes constituting this new representation of science and, for each, to examine what is at stake—in general, to show that everything is more complicated and subtle than is often supposed. Since the themes are intimately linked, to separate them as if their evolution were independent from one another is rather artificial, but it will enhance the intelligibility of the text. Finally, concerning intelligibility, we should recognize that the subtlety of the themes lies in the fact that most of the expressions involved, such as determinism, predictability, randomness, and order, assume a precise meaning only in the framework of a mathematical formalism. But in this remark, far from aiming at discouraging unavoidable, and probably desirable, non-formal discussions, I intend to underscore the difficulties of conducting a wide debate on the issues without exhibiting an excessive scientistic authoritarianism.

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