PREDICTIONS – 10 Years Later - Santa Fe Institute

PROLOGUE
survivors a chance to renew their numbers. Could this phenomenon be
described mathematically?
Volterra succeeded in building a mathematical formulation that described
well the fisherman’s observations. A model for the growth of
populations, it states that the rate of growth is limited by competition
and that the overall size of the population (for example, the number of
rabbits in a fenced-off grass field) slowly approaches a ceiling, the
height of which reflects the capacity of the ecological niche. The model
would serve as a foundation for modern biological studies of the competitive
struggle for life. Alfred J. Lotka also studied such problems to
some extent. Today, there are applications bearing both men’s names.
Half a century later, Cesare Marchetti, a physicist at the International
Institute of Applied Systems Analysis (IIASA) near Vienna, Austria,
was given the task by the energy-project leader to forecast energy demands.
Another kind of war had been shaking the West recently: the
fierce competition for oil. The need for increased understanding of the
future energy picture was becoming imperative. Marchetti approached
the problem as a physicist, who sought answers through the use of the
scientific method: observation, prediction, verification. In this approach
predictions must be related to observations through a theory resting on
hypotheses. When the predictions are verified, the hypotheses become
laws. The simpler a law, the more fundamental it is and the wider its
range of applications.
Marchetti had long been concerned with the “science” of predictions.
In his work, he first started searching for what physicists call invariants.
These are constants universally valid and manifested through indicators
that do not change over time. He believed that such indicators represent
some kind of equilibrium even if one is not dealing with physics but
with human activities instead. He then suspected that the fundamental
laws which govern growth and competition among species may also
describe human activities. Competition in the market place can be as
fierce as in the jungle, and the law of the survival of the fittest becomes
indisputable. Marchetti noted that growth curves for animal populations
follow patterns similar to those for product sales. Could it be that the
mathematics developed by Volterra for the growth of a rabbit population
describe equally well the growth of cars and computers? Marchetti
went on to make a dazzling array of predictions, including forecasts of
future energy demands, using Volterra’s equations. But how far can the
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