Chaos - James Gleick [130]
Physiologists accumulated vast amounts of data over the years, making tables and graphs to show the patterns of erratic eye motion. They generally assumed that the fluctuations came from fluctuations in the signal from the central nervous system controlling the eye’s muscles. Noisy output implied noisy input, and perhaps some random disturbances afflicting the brains of schizophrenics were showing up in the eyes. Huberman, a physicist, assumed otherwise and made a modest model.
He thought in the crudest possible way about the mechanics of the eye and wrote down an equation. There was a term for the amplitude of the swinging pendulum and a term for its frequency. There was a term for the eye’s inertia. There was a term for damping, or friction. And there were terms for error correction, to give the eye a way of locking in on the target.
As Huberman explained to his audience, the resulting equation happens to describe an analogous mechanical system: a ball rolling in a curved trough while the trough swings from side to side. The side-to–side motion corresponds to the motion of the pendulum, and the walls of the trough correspond to the error-correcting feature, tending to push the ball back toward the center. In the now-standard style of exploring such equations, Huberman had run his model for hours on a computer, changing the various parameters and making graphs of the resulting behaviors. He found both order and chaos. In some regimes, the eye would track smoothly; then, as the degree of nonlinearity was increased, the system would go through a fast period-doubling sequence and produce a kind of disorder that was indistinguishable from the disorder reported in the medical literature.
In the model, the erratic behavior had nothing to do with any outside signal. It was an inevitable consequence of too much non-linearity in the system. To some of the doctors listening, Huberman’s model seemed to match a plausible genetic model for schizophrenia. A nonlinearity that could either stabilize the system or disrupt it, depending on whether the nonlinearity was weak or strong, might correspond to a single genetic trait. One psychiatrist compared the concept to the genetics of gout, in which too high a level of uric acid creates pathological symptoms. Others, more familiar than Huberman with the clinical literature, pointed out that schizophrenics were not alone; a whole range of eye movement problems could be found in different kinds of neurological patients. Periodic oscillations, aperiodic oscillations, all sorts of dynamical behavior could be found in the data by anyone who cared to go back and apply the tools of chaos.
But for every scientist present who saw new lines of research opening up, there was another who suspected Huberman of grossly oversimplifying his model. When it came time for questions, their annoyance and frustration spilled out. “My problem is, what guides you in the modeling?” one of these scientists said. “Why look for these specific elements of nonlinear dynamics, namely these bifurcations and chaotic solutions?”
Huberman paused. “Oh, okay. Then I truly failed at stating the purpose of this. The model is simple. Someone comes to me and says, we see this, so what do you think happens. So I say, well, what is the possible explanation. So they say, well, the only thing we can come up with is something that is fluctuating over such a short time in your head. So then I say, well look, I’m a chaotician of sorts, and I know that the simplest nonlinear tracking model you can write down, the simplest, has these generic features, regardless of the details of what these things are like. So I do that and people say, oh, that’s very interesting, we never thought that perhaps this was intrinsic chaos in the system.
“The model does not have any neurophysiological data that I can even defend. All I’m saying is that the simplest tracking is something that