PREDICTIONS – 10 Years Later - Santa Fe Institute

10. IF I CAN, I WANT
In addition to observations of chaos when approaching the ceiling
value, deviations between data and S-curves are also seen in the early
phases of the growth pattern. In an anthropomorphic interpretation we
attributed them earlier to “infant mortality” or “catching up.” In growth
in competition, the times before reaching 10 percent of the maximum
can be seen as a trial period during which survival is at stake and major
readjustments may be undertaken. In industry, for example, products are
often repositioned by price changes shortly after launching. Other deviations
observed in the early phases of growth are due to the release of
pent-up energy following delays usually attributed to “technical” reasons.
Many of the life curves of the creative careers shown in Chapter
Four feature such an early accelerated growth, which was interpreted as
an attempt to make up for time lost.
This is a behavioral explanation of the irregular patterns often encountered
at the extremities of S-curves. Chaotic behavior dictated by
the discrete nature of populations can account for half of these irregularities,
the erratic behavior at the ceiling. It does not account for the
early deviations. Alain Debecker and I obtained a mathematical understanding
of this phenomenon by linking S-curves to chaos in a way
different from the classical approach described above. It happened
while we were looking into the chaotic behavior in the annual production
of coal in the United States as shown in Figure 10.3.
Production of bituminous coal increased naturally during the better
part of a hundred years. After 1920 production reached a plateau and
the familiar erratic oscillations appeared, but the last part of the graph
revealed a “disturbing” systematic increase since 1950. Was it an exceptionally
large chaotic fluctuation, or was there a new niche opening up?
Ten Years Later
The small circles in Figures 10.3 give the answer. During
the last dozen years coal production followed closely the trajectory
that had been predicted which outlined the opening up
of another niche. As with annual car registrations in Japan, a
new growth cycle emerged from a state of chaos.
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