We all know the ancient story of King Canute…
…who was so displeased by his courtiers excessive praise, likening him to a powerful god, that he brought them all to the seashore where he had a throne placed at the water’s edge. There he sat and commanded the tide to stop. It, of course, did not. He wanted to show his sycophants that there were regularities of nature that were beyond any king’s command.
Toward the end of the classic 1987 book Chaos, Making a New Science, James Gleick wrote…
“…University of Arizona Professor of Ecology William M.] Schaffer is using strange attractors to explore the epidemiology of childhood diseases such as measles and chicken pox. He has collected data, first from New York City and Baltimore, then from Aberdeen, Scotland, and all England and Wales. He has made a dynamical model, resembling a damped,driven pendulum.
The diseases are driven each year by the infectious spread among children returning to school, and damped by natural resistance. Schaffer’s model predicts strikingly different behavior for theses diseases. Chicken pox should vary periodically. Measles should vary chaotically. As it happens, the data show exactly what Schaffer predicts. To a traditional epidemiologist the yearly variations in measles seemed inexplicable — random and noisy.
Schaffer, using the techniques of phase-space reconstruction, shows that measles follow a strange attractor, with a fractal dimension of about 2.5… Although the attractor is chaotic, some predictability becomes possible… A year of high measles infection will be followed by a crash. After a year of medium infection, the level will change only slightly. A year of low infection produces the greatest unpredictability…” (pages 315-316)”
Recent statistics validate Professor Schaffer’s analysis.
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