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Computation and the Human Predicament

The Limits to Growth and the limits to computer modeling

Brian Hayes

Vats and Valves

A diagram of a system dynamics model could well be mistaken for the schematic layout of an oil refinery. Various tanks or vats are connected by pipes; flows through the pipes are regulated by valves; the valves are controlled by signals that derive from the state of reservoirs or flows elsewhere in the model.

The World3 model has five main sectors: population, agriculture, industry, resources and pollution. In the population sector, the quantities held in the vats and flowing through the pipes are people; the valves controlling the flows represent birth rates, death rates and the process of maturation that carries people from one age category to the next. The agricultural sector has stocks of arable land, which are augmented when new land is cultivated and diminished when farmland is lost to erosion or urban development. The main stock for industry is capital, which is measured in dollars but really represents factories or other productive facilities. The level of capital is determined by the balance of inflow from investment and outflow to depreciation.

2012-05HayesFB.jpgClick to Enlarge ImageIf you examine a small region of the plumbing diagram in isolation, you can often figure out how that subsystem will behave. For example, the resources sector of the model includes only nonrenewable resources such as ores and fossil fuels, and so the level of this stock can never rise. The rate of resource outflow is governed by the total population and the per capita level of resource consumption.

Looking at the entire Rube Goldberg diagram—which won’t fit comfortably on a page smaller than a newspaper broadsheet—there’s no hope of understanding all the interactions at a glance. This is the reason for turning the conceptual model into a computer simulation: The computer can keep track of the levels and flows as the system evolves.

2012-05HayesFC.jpgClick to Enlarge ImageThe World3 simulation covers the period from 1900 to 2100. In the standard run, using default values for all parameters, nonrenewable resources are exhausted by the middle of the 21st century, causing steep declines in industry, food and population. Adjusting the initial conditions to double the available resources alters the outcome, but not for the better: Higher industrial output leads to runaway pollution, which chokes off growth—and even life—a few decades later. The persistent shape of the model’s trajectory is overshoot followed by collapse.

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