Chaos: Making a New Science

by James Gleick

As May looked at more and more biological systems through the prism of simple chaotic models, he continued to see results that violated the standard intuition of practitioners. In epidemiology, for example, it was well known that epidemics tend to come in cycles, regular or irregular. Measles, polio, rubella—all rise and fall in frequency. May realized that the oscillations could be reproduced by a nonlinear model and he wondered what would happen if such a system received a sudden kick—a perturbation of the kind that might correspond to a program of inoculation. Naïve intuition suggests that the system will change smoothly in the desired direction. But actually, May found, huge oscillations are likely to begin. Even if the long-term trend was turned solidly downward, the path to a new equilibrium would be interrupted by surprising peaks. In fact, in data from real programs, such as a campaign to wipe out rubella in Britain, doctors had seen oscillations just like those predicted by May’s model. Yet any health official, seeing a sharp short-term rise in rubella or gonorrhea, would assume that the inoculation program had failed.

On nonlinear reactions to vaccines

As the Nobel laureate Wassily Leontief put it, “In no field of empirical inquiry has so massive and sophisticated a statistical machinery been used with such indifferent results.”

On use of gauss curve in economics

The question, at first sight foolish, improves on acquaintance,”

Glib

From sperm to man

Climatologists who use global computer models to simulate the long-term behavior of the earth’s atmosphere and oceans have known for several years that their models allow at least one dramatically different equilibrium. During the entire geological past, this alternative climate has never existed, but it could be an equally valid solution to the system of equations governing the earth. It is what some climatologists call the White Earth climate: an earth whose continents are covered by snow and whose oceans are covered by ice. A glaciated earth would reflect seventy percent of the incoming solar radiation and so would stay extremely cold. The lowest layer of the atmosphere, the troposphere, would be much thinner. The storms that would blow across the frozen surface would be much smaller than the storms we know. In general, the climate would be less hospitable to life as we know it. Computer models have such a strong tendency to fall into the White Earth equilibrium that climatologists find themselves wondering why it has never come about. It may simply be a matter of chance.

White earth climate

Little pretense at science marred Schwenk’s exposition, and none at mathematics.

You would begin with a drawing of the shape you wanted to reproduce. Barnsley chose a black spleenwort fern for one of his first experiments, having long been a fern buff.

..a what?

Leon Glass of McGill University in Montreal was trained in physics and chemistry, where he indulged an interest in numbers and in irregularity, too, completing his doctoral thesis on atomic motion in liquids before turning to the problem of irregular heartbeats. Typically, he said, specialists diagnose many different arrhythmias by looking at short strips of electrocardiograms. “It’s treated by physicians as a pattern recognition problem, a matter of identifying patterns they have seen before in practice and in textbooks. They really don’t analyze in detail the dynamics of these rhythms. The dynamics are much richer than anybody would guess from reading the textbooks.”

Arrhythmias, complexity

biological clocks—circadian rhythms.

Circadian rhytms

mother lode.”