Chaos - James Gleick [93]
“There has been since the eighteenth century some kind of dream that science was missing the evolution of shape in space and the evolution of shape in time. If you think of a flow, you can think of a flow in many ways, flow in economics or a flow in history. First it may be laminar, then bifurcating to a more complicated state, perhaps with oscillations. Then it may be chaotic.”
The universality of shapes, the similarities across scales, the recursive power of flows within flows—all sat just beyond reach of the standard differential-calculus approach to equations of change. But that was not easy to see. Scientific problems are expressed in the available scientific language. So far, the twentieth century’s best expression of Libchaber’s intuition about flow needed the language of poetry. Wallace Stevens, for example, asserted a feeling about the world that stepped ahead of the knowledge available to physicists. He had an uncanny suspicion about flow, how it repeated itself while changing:
“The flecked river
Which kept flowing and never the same way twice, flowing
Through many places, as if it stood still in one.”
Stevens’s poetry often imparts a vision of tumult in atmosphere and water. It also conveys a faith about the invisible forms that order takes in nature, a belief
“that, in the shadowless atmosphere,
The knowledge of things lay round but unperceived.”
When Libchaber and some other experimenters in the 1970s began looking into the motion of fluids, they did so with something approaching this subversive poetic intent. They suspected a connection between motion and universal form. They accumulated data in the only way possible, writing down numbers or recording them in a digital computer. But then they looked for ways to organize the data in ways that would reveal shapes. They hoped to express shapes in terms of motion. They were convinced that dynamical shapes like flames and organic shapes like leaves borrowed their form from some not-yet-understood weaving of forces. These experimenters, the ones who pursued chaos most relentlessly, succeeded by refusing to accept any reality that could be frozen motionless. Even Libchaber would not have gone so far as to express it in such terms, but their conception came close to what Stevens felt as an “insolid billowing of the solid”:
“The vigor of glory, a glittering in the veins,
As things emerged and moved and were dissolved,
Either in distance, change or nothingness,
The visible transformations of summer night,
An argentine abstraction approaching form
And suddenly denying itself away.”
FOR LIBCHABER, GOETHE, NOT STEVENS, supplied mystical inspiration. While Feigenbaum was looking through Harvard’s library for Goethe’s Theory of Colors, Libchaber had already managed to add to his collection an original edition of the even more obscure monograph On the Transformation of Plants. This was Goethe’s sidelong assault on physicists who, he believed, worried exclusively about static phenomena rather than the vital forces and flows that produce the shapes we see from instant to instant. Part of Goethe’s legacy—a negligible part, as far as literary historians were concerned—was a pseudoscientific following in Germany and Switzerland, kept alive by such philosophers as Rudolf Steiner and Theodor Schwenk. These men, too, Libchaber admired as much as a physicist could.
“Sensitive chaos”—Das sensible Chaos—was Schwenk’s phrase for the relation between force and form. He used it for the title of a strange little book first published in 1965 and falling sporadically in and out of print thereafter. It was a book first about water. The English edition carried an admiring preface from Commandant Jacques Y. Cousteau and testimonials from the Water Resources Bulletin and the Journal of the institute