Chaos - James Gleick [96]
The mathematics available to D’Arcy Thompson could not prove what he wanted to prove. The best he could do was draw, for example, skulls of related species with a crosshatching of coordinates, demonstrating that a simple geometric transformation turned one into the other. For simple organisms—with shapes so tantalizingly reminiscent of liquid jets, droplet splashes, and other manifestations of flow—he suspected physical causes, such as gravity and surface tension, that just could not do the formative work he asked of them. Why then, was Albert Libchaber thinking about On Growth and Form when he began his fluid experiments?
D’Arcy Thompson’s intuition about the forces that shape life came closer than anything in the mainstream of biology to the perspective of dynamical systems. He thought of life as life, always in motion, always responding to rhythms—the “deep-seated rhythms of growth” which he believed created universal forms. He considered his proper study not just the material forms of things but their dynamics—“the interpretation, in terms of force, of the operations of Energy.” He was enough of a mathematician to know that cataloguing shapes proved nothing. But he was enough of a poet to trust that neither accident nor purpose could explain the striking universality of forms he had assembled in his long years of gazing at nature. Physical laws must explain it, governing force and growth in ways that were just out of understanding’s reach. Plato again. Behind the particular, visible shapes of matter must lie ghostly forms serving as invisible templates. Forms in motion.
LIBCHABER CHOSE LIQUID HELIUM for his experiment. Liquid helium has exceedingly low viscosity, so it will roll at the slightest push. The equivalent experiment in a medium-viscosity fluid like water or air would have taken a much larger box. With low viscosity, Libchaber made his experiment that much more sensitive to heating. To cause convection in his millimeter-wide cell, he had only to create a temperature difference of a thousandth of a degree between the top and bottom surfaces. That was why the cell had to be so tiny. In a larger box, where the liquid helium would have more room to roll, the equivalent motion would require even less heating, much less. In a box ten times larger in each direction, the size of a grape—a thousand times greater in volume—convection would begin with a heat differential of a millionth of a degree. Such minute temperature variations could not be controlled.
In the planning, in the design, in the construction, Libchaber and his engineer devoted themselves to eliminating any hint of messiness. In fact, they did all they could to eliminate the motion they were trying to study. Fluid motion, from smooth flow to turbulence, is thought of as motion through space. Its complexity appears as a spatial complexity, its disturbances and vortices as a spatial chaos. But Libchaber was looking for rhythms that would expose themselves as change over time. Time was the playing field and the yardstick. He squeezed space down nearly to a one-dimensional point. He was bringing to an extreme a technique that his predecessors in fluid experimentation had used, too. Everyone knew that an enclosed flow—Rayleigh-Bénard convection in a box or Couette-Taylor rotation in a cylinder—behaved measurably better than an open flow, like waves in the ocean or the air. In open flow, the boundary surface remains free, and the complexity multiplies.
Since convection in a rectilinear box produces rolls of fluid like hot dogs—or in this case like sesame seeds—he chose the dimensions of his cell carefully to allow precisely