Connect

Exponential Growth and Doubling Time:
Comments by Don Mann, NPG President

An article in The New York Times on July 19, 2006 with the headline "China's Surge Raises Fears of Runaway Economy", reported that China's economy grew last quarter at an annual rate of 11.2 percent. No material growth can continue for very long in a finite world, but growth at such a pace must lead in a very short while to both environmental and economic disaster.

An understanding of a simple but vitally important concept reveals why that is so. The concept involves exponential growth and doubling times. When a quantity or rate is growing at a fixed percent per year the growth is said to be exponential. Interest on a bank account is a good example.

The important property of such growth is that, at a given rate of growth, the time it would take anything (population, the economy, etc.) growing at that rate to double in size can be calculated by dividing the growth rate into seventy. Thus, we find that 70 divided by the annual growth rate of China's economy, 11 percent, would result in a doubling time of slightly over six years!

At the current rate of growth, therefore, in a mere six years China's already huge economy would be twice as large as it is today. Other things being equal, its consumption of non-renewable raw materials, and the quantity of pollution emitted by its industrial processes, already far too large to be sustainable for the long term, could also be twice as large as they are today.

One of the most interesting – and alarming -- features of exponential growth is the almost unbelievable size of the numbers that result from a very few doublings. For example, if it were at all possible (which it is not) for China's economy to keep growing very long at an annual rate of 11 percent, after the first doubling at the end of six years its economy would be twice as large as today's. After the second doubling, in a mere 12 years, it would be four times larger than it is today! After the third doubling at the end of 18 years, it would be eight times larger than it is today.

After only four doublings, at the end of 24 years, China's economy would be 16 times larger than it is today, and so on. With a few more doublings it would be hundreds of times larger than it is today! Does anyone believe that such growth would be remotely possible? Of course not.

The truth is that no matter how vast, no material resource can possibly withstand more than a very few doublings. As the late eminent economist Kenneth Boulding said, "Anyone who believes exponential growth can go on forever in a finite world is either a madman or an economist."

Is it possible to create an economy that would be sustainable indefinitely in a sound and healthy environment, and still afford an adequate standard of living for all? It is but only if demand for energy and materials are stabilized and become non-growing at a sustainable level, far lower than today's. That could only be achieved with a far smaller world population than the over six billion we have today.

What is urgently needed is a negative rate of population growth for an interim period of population decrease until world population can be stabilized at a sustainable level, which we, and many scientists, believe would be in the range of one to two billion.

---

Click on the below links to see the following NPG Forum papers on exponential growth and a sustainable population size:

Confronting the Twenty-First Century's Hidden Crisis: Reducing Human Numbers by 80 Percent, by J. Kenneth Smail.

Forgotten Fundamentals of the Energy Crisis, by Professor Albert A. Bartlett, professor emeritus in the Department of Physics at the University of Colorado in Boulder.

An Essay on a Sustainable Economy, by Donald Mann.

A No-Growth, Steady-State Economy Must Be Our Goal, by Donald Mann.

The Steady-State Economy: What It Is, Why We Need It, by John Attarian.

Also a book by Herman E. Daly that we consider indispensable reading:

Beyond Growth. Beacon Press, Boston Massachusetts.