Chaos - James Gleick [131]
Out on the floor, another biologist took the microphone, still frustrated by the stick-figure simplicity of Huberman’s model. In real eyes, he pointed out, four muscle–control systems operate simultaneously. He began a highly technical description of what he considered realistic modeling, explaining how, for example, the mass term is thrown away because the eye is heavily over-damped. “And there’s one additional complication, which is that the amount of mass present depends on the velocity of rotation, because part of the mass lags behind when the eye accelerates very rapidly. The jelly inside the eye lags behind when the outer casing rotates very fast.”
Pause. Huberman was stymied. Finally one of the conference organizers, Arnold Mandell, a psychiatrist with a long interest in chaos, took the microphone from him.
“Look, as a shrink I want to make an interpretation. What you’ve just seen is what happens when a nonlinear dynamicist working with low-dimensional global systems comes to talk to a biologist who’s been using mathematical tools. The idea that in fact there are universal properties of systems, built into the simplest representations, alienates all of us. So the question is ‘What is the subtype of the schizophrenia,’ ‘There are four ocular motor systems,’ and ‘What is the modeling from the standpoint of the actual physical structure,’ and it begins to decompose.
“What’s actually the case is that, as physicians or scientists learning all 50,000 parts of everything, we resent the possibility that there are in fact universal elements of motion. And Bernardo comes up with one and look what happens.”
Huberman said, “It happened in physics five years ago, but by now they’re convinced.”
THE CHOICE IS ALWAYS the same. You can make your model more complex and more faithful to reality, or you can make it simpler and easier to handle. Only the most naïve scientist believes that the perfect model is the one that perfectly represents reality. Such a model would have the same drawbacks as a map as large and detailed as the city it represents, a map depicting every park, every street, every building, every tree, every pothole, every inhabitant, and every map. Were such a map possible, its specificity would defeat its purpose: to generalize and abstract. Mapmakers highlight such features as their clients choose. Whatever their purpose, maps and models must simplify as much as they mimic the world.
For Ralph Abraham, the Santa Cruz mathematician, a good model is the “daisy world” of James E. Lovelock and Lynn Margulis, proponents of the so-called Gaia hypothesis, in which the conditions necessary for life are created and maintained by life itself in a self-sustaining process of dynamical feedback. The daisy world is perhaps the simplest imaginable version of Gaia, so simple as to seem idiotic. “Three things happen,” as Abraham put it, “white daisies, black daisies, and unplanted desert. Three colors: white, black, and red. How can this teach us anything about our planet? It explains how temperature regulation emerges. It explains why this planet is a good temperature for life. The daisy world model is a terrible model, but it teaches how biological homeostasis was created on earth.”
White daisies reflect light, making the planet cooler. Black daisies absorb light, lowering the albedo, or reflectivity, and thus making the planet warmer. But white daisies “want” warm weather, meaning that they thrive preferentially as temperatures rise. Black daisies want cool weather. These qualities can be expressed in a set of differential equations and the daisy world can be set in motion on a computer. A wide range of initial conditions will lead to an equilibrium attractor—and not necessarily a static equilibrium.
“It’s just a mathematical model of a conceptual model, and that’s what you want—you don’t want high-fidelity models of biological or social systems,” Abraham said.