Seeing Structure, Structuring Sight: Bénard’s Cells and the Visualization of Self-Organization

Seeing Structure, Structuring Sight: Bénard’s Cells and the Visualization of Self-Organization

David Aubin

Other involved Scholars: 

Otto Sibum

Cooperation Partners: 

Université Paris VI

Henri Bénard was a French physicist who performed experiments on fluids for a Collège de France physics course given by Marcel Brillouin at the turn of the century. Bénard was among the first to study the behavior of a thin layer of liquid, about a millimeter in depth, when heated from below, the upper surface being in contact with air at a lower temperature. Experimenting with liquids of different viscosity, he observed in all cases the formation of a striking pattern of hexagonal cells. In 1916, Lord Rayleigh provided a mathematical explanation for the onset of instability in such a convective system.

In his 1900 article, Bénard used a variety of means to visualize the structures he wanted to exhibit. They ranged from material substances he added to the liquid to optical contrivances such as lighting and the design of special photographic setups. His papers were abundantly illustrated with sketches and photographic clichés. Starting in 1904, he produced a series of films, which he used to analyze the phenomenon and showed at the Easter, 1914, meeting of the French Physical Society. An expert in optical devices, he developed new types of binoculars fro the French navy during World War I and later became a professor at the Fluid Mechanics Institute in Paris.

This appearance of order in the Rayleigh-Bénard system was a phenomenon that never failed to captivate those who tackled the system for the first time. The observation of self-organization in physical systems provided a formidable boost to those who wished to explain the phenomena of life in mechanical terms (D’Arcy Thomson). Bénard himself thought that physicists ought to be more ambitious in their pretension to understand nature, and this spontaneous emergence of organization struck him as having potentially important applications for the life sciences.

"I think it is impossible not to concern oneself with what the consequences [of this phenomenon] might entail from the point of view of biological theories. . . . Purely physical research, such as this, might perhaps have some interest in the eyes of scientists who do not despair of reducing the complex phenomena of life to the general laws of inorganic nature (Bénard 1900, 144)."

How to make self-organization visible? What does it mean to observe a system and say that it is “self-organizing”? How does one represent it? What is the relation between an observation, its representations, and the way it is understood theoretically? What is the relationship between understanding and mathematization? What role does analogy play in trying to explain the emergence of forms in nature? These were some of the questions that formed the basis of this research project, which emerged from David Aubin's work on the history of fluid mechanics, catastrophe theory, and chaos theory.

  • “Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures,” co-authored with Amy Dahan Dalmedico. Historia Mathematica 29 (2002), 273-339.