Chaos - James Gleick [27]
The spot is a self-organizing system, created and regulated by the same nonlinear twists that create the unpredictable turmoil around it. It is stable chaos.
As a graduate student, Marcus had learned standard physics, solving linear equations, performing experiments designed to match linear analysis. It was a sheltered existence, but after all, nonlinear equations defy solution, so why waste a graduate student’s time? Gratification was programmed into his training. As long as he kept the experiments within certain bounds, the linear approximations would suffice and he would be rewarded with the expected answer. Once in a while, inevitably, the real world would intrude, and Marcus would see what he realized years later had been the signs of chaos. He would stop and say, “Gee, what about this little fluff here.” And he would be told, “Oh, it’s experimental error, don’t worry about it.”
But unlike most physicists, Marcus eventually learned Lorenz’s lesson, that a deterministic system can produce much more than just periodic behavior. He knew to look for wild disorder, and he knew that islands of structure could appear within the disorder. So he brought to the problem of the Great Red Spot an understanding that a complex system can give rise to turbulence and coherence at the same time. He could work within an emerging discipline that was creating its own tradition of using the computer as an experimental tool. And he was willing to think of himself as a new kind of scientist: not primarily an astronomer, not a fluid dynamicist, not an applied mathematician, but a specialist in chaos.
Life’s Ups
and Downs
The result of a mathematical development should be continuously checked against one’s own intuition about what constitutes reasonable biological behavior. When such a check reveals disagreement, then the following possibilities must be considered:
A mistake has been made in the formal mathematical development;
The starting assumptions are incorrect and/or constitute a too drastic oversimplification;
One’s own intuition about the biological field is inadequately developed;
A penetrating new principle has been discovered.
—HARVEY J. GOLD,
Mathematical Modeling
of Biological Systems
RAVENOUS FISH AND TASTY plankton. Rain forests dripping with nameless reptiles, birds gliding under canopies of leaves, insects buzzing like electrons in an accelerator. Frost belts where voles and lemmings flourish and diminish with tidy four-year periodicity in the face of nature’s bloody combat. The world makes a messy laboratory for ecologists, a cauldron of five million interacting species. Or is it fifty million? Ecologists do not actually know.
Mathematically inclined biologists of the twentieth century built a discipline, ecology, that stripped away the noise and color of real life and treated populations as dynamical systems. Ecologists used the elementary tools of mathematical physics to describe life’s ebbs and flows. Single species multiplying in a place where food is limited, several species competing for existence, epidemics spreading through host populations—all could be isolated, if not in laboratories then certainly in the minds of biological theorists.
In the emergence of chaos as a new science in the 1970s, ecologists were destined to play a special role. They used mathematical models, but they always knew that the models were thin approximations of the seething real world. In a perverse way, their awareness of the limitations allowed them to see the importance of some ideas that mathematicians had considered interesting