PREDICTIONS – 10 Years Later - Santa Fe Institute

10. IF I CAN, I WANT
producing chaos. Figure 10.1 is taken from their book. It shows three
possible ways to reach the ceiling. The simplest one is oscillations of
decaying amplitude converging in a steady state. The second case produces
regular oscillations that do not diminish with time. The last case
shows chaos—oscillations of no regularity whatsoever.
Well before chaos studies, ecologists had become aware of some erratic
behavior in species’ populations. James Gleick argues that they simply
did not want to admit the possibility that the oscillations would not
eventually converge to a steady state level. The equilibrium was for
them the important thing:
J. Maynard Smith, in the classic 1968 Mathematical Ideas in Biology,
gave a standard sense of the possibilities: Populations often
remain approximately constant or else fluctuate “with a rather regular
periodicity” around a presumed equilibrium point. It wasn’t that he
was so naive as to imagine that real populations could never behave
erratically. He simply assumed that erratic behavior had nothing to do
with the sort of models he was describing. 8
Outside biology there have been many observations of data deviating
from the idealized growth pattern once the 90 percent level of the
ceiling has been reached. Elliot Montroll gives examples from the
United States mining industry in which the annual production of copper
and zinc are known to fluctuate widely over the years.9 These
instabilities can be interpreted as a random search for the equilibrium
position. The system explores upwards and downwards while “hunting”
for the ceiling value. If the optimal level is found, an oscillation
may persist as a telltale signal of the regulating mechanism. If such a
level cannot be found, erratic fluctuations may ensue, resembling
chaos.
A characteristic chaotic pattern emerges in the annual rate of plywood
sales. In an article published by Henry Montrey and James
Utterback there is a graph showing the evolution of plywood sales in the
United States, shown here updated in Figure 10.2.
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