PREDICTIONS – 10 Years Later - Santa Fe Institute

3. INANIMATE PRODUCTION LIKE ANIMATE REPRODUCTION
professor of physics at Johns Hopkins University, would not hesitate to
involve statistics, biology, mechanics, and the understanding of consciousness
all in the same work. Volterra, an Italian mathematician and
professor at the Universities of Pisa and Rome, contributed to the advancement
of mathematics, physics, biology, politics, and Italian
aviation during World War I. In the 1920s Volterra and Lotka cast the
predator-prey relationship into a set of equations. 2 The work, now
known as the Volterra-Lotka system of differential equations, draws on
Verhulst’s original description of natural growth for a species population.
There have been numerous observations that species populations do
indeed grow along S-curves. It was reported early in the twentieth century
that under controlled experimental conditions populations of fruit
flies grew along S-shaped curves. 3 The fly population followed the
smooth theoretical curve quite closely all the way to the end (Appendix
C, Figure 3.1). The intriguing question, which Lotka was the first to ask,
is whether this theory can also describe the growth of inanimate populations.
There are, in fact, similarities between the growth of rabbits in a
grass field and automobiles in society. In both cases growth is capped by
a limited resource that becomes scarce as the population competes for it.
For rabbits it is grass, for cars it may be space, which is becoming increasingly
precious in city centers and on highways.
During the early phases of a rabbit population, the growth is rapid—
exponential in mathematical terms. If each couple has two offspring, the
population doubles every mating cycle. The element of rapid, exponential-like
growth during the early stages is also observable in car
populations. In an affluent society one car brings another. In a household
in which both parents have a car, the daughter asks for hers as soon as
the son gets his. The number of cars owned by the neighbors may play a
role, and it is not rare to find individuals owning several types of cars to
match a variety of personal uses. The more we become accustomed to
cars, the more we need them—at least it seemed that way some time
ago.
The conceptual similarity between the way rabbits colonize a grass
field and automobiles “colonize” society points to a common underlying
law. The difference lies with the time scales. It may take rabbits months
or years to fill up their ecological niche, while it takes cars decades to
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