New technologies are transforming our daily lives at an accelerating pace. Protecting the environment with a view to sustainable development requires anticipating the medium- and long-term impact of the actions being taken. The future is shaped by a host of political, economic and social factors.
For any company, the ability to anticipate change is becoming a matter of survival. Numerical models can now describe the evolution of complex systems that depend on many parameters. Yet these models have limitations, making foresight as much an art as a science.
Forecasting how a system will evolve
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Extrapolating data along the observed trend remains a widely used way of forecasting future developments. Since energy consumption is currently growing by 2% a year, forecasts of energy or other resource consumption are most often based on an exponential law. In practice, resources are finite and their consumption cannot grow indefinitely.
For oil, extrapolating the current growth rate of consumption would lead to an almost twofold increase by 2050, although many experts believe that production has already reached a plateau at around 95 million barrels per day. Such a production ceiling can be represented by a sigmoid curve Y, whose dependence on time t is given by Y(t) = K / (1 + a exp(–rt)), where a and r are suitable positive constants. This function solves the differential equation in Verhulst's model; he called it the logistic function:
