The Awesome Power of Exponential Growth

Exponential growth is the steady growth of anything by a fixed percentage over a period of time.  Compound interest on a savings account is a good example of exponential growth.  The late Professor Albert A. Bartlett said “The greatest shortcoming of the human race is our inability to understand the exponential function.”  We fully agree.

I often wonder if the proponents of perpetual economic growth understand the awesome power of exponential growth, or if they are even familiar with the concept.

 Doubling Time

One of the most fascinating things about exponential growth is that any given quantity growing exponentially will double in size periodically – with this “doubling time” depending on the annual rate of growth.  Doubling time can be determined by dividing the number 70 by the annual growth rate.

For example, if the annual growth rate were 5% the doubling time would be 70 divided by 5, or 14 years.  If the annual growth rate were 4%, the doubling time would be 17.5 years.  If it were 3%, the doubling time would be 23.3 years.

After a very few doublings, the initial quantity of anything growing exponentially will reach absolutely astonishing proportions.  Professor Bartlett taught that no resource, regardless of how great, could possibly withstand more than a very few doublings of demand.  Fossil fuels are no exception to that rule.

Here is an example from John F. Rohe’s excellent book A Bicentennial Malthusian Essay (p. 35):  a single sheet of paper doubled only forty times would create a pile of paper 241,000 miles high – reaching from the earth to the moon.  Only nine more doublings would reach the sun!  There is another example on page 46.  Suppose that our Gross National Product (GNP) grew at the rate of 5% a year, giving a doubling time of 14 years.  In 98 years there would be seven doublings, and our economy would grow to an unthinkable size – 128 times larger than it was in the beginning!

This simple arithmetic (2, 4, 8, 16, 32, 64, 128) means dire consequences for our world.  Does any sane person imagine that our small planet could possibly supply enough resources to support an economy of such a monstrous size?  The concept of doubling times is proof positive that exponential growth cannot long continue in a world of limited resources.

But 98 years from now is quite far in the future.  Let’s take a look at the effect of only one doubling of our GNP over 23 years (if the annual growth rate were 3% rather than 5%).  That would take us to the year 2037.  With the end of the fossil fuel era now in sight, what is the likelihood that our earth could provide resources for an economy twice its present size, and maintain them for a very long period of time?  We are convinced that such a likelihood is very close to nil, and we also believe that a vast majority of scientists would agree with that judgment.

Economic Growth Is Not Sustainable

Here is a quote from Chapter Three, titled “Economic Growth,” from an excellent book by Lindsey Grant:  Too Many People, The Case for Reversing Growth (2000, Seven Locks Press).

“The pursuit of GNP growth is a curiously misdirected focus.  The economic benefits (such as they are) result from rising per capita income, not the GNP.  But the pursuit of higher per capita income is limited in turn by a mighty reality that economists usually ignore:  the economy operates only within the environment, even as it transforms the environment.  The entire economic enterprise, if it is to survive, must operate within the constraints of environmental sustainability.

“The only way to reconcile the economic objective with the environmental constraint is to keep total economic activity within tolerable environmental limits.  That is, decide first how large a pie the environment can tolerate.  Then decide how big the individual slices (the standard of living) should be.  Then divide the pie by the size of each slice.  The result is the number of slices (the population) the system can support.”  (Emphasis added by NPG.)

There you have it in a nutshell:  Total economic activity must be kept within tolerable environmental limits, if it is to be sustainable.  End of story.

To summarize:  At present, the size of our economy is far too large to be sustainable. We urgently need to reduce the scale of our economy – by gradually reducing the size of our population – so that our economy will be sustainable for the very long term, while affording an adequate standard of living for all in a sound and healthy environment.                                                       

Only a non-growing, steady-state economy could possibly maximize per capita income in a way that would make it sustainable for the very long term. 

The following quote is from the late Professor Albert A. Bartlett, whose life work on the Arithmetic of Sustainability has been instrumental to the NPG mission:

“Sustainability” has to mean “for a long time,” where “long” means compared to a human lifetime.  The basic exponential arithmetic shows that growth of numbers of real things can’t continue for long times.  This simple observation leads to the First Law of Sustainability.  “Growth of populations and/or growth in rates of consumptions of resources, cannot be sustained.”  It follows that the term “sustainable growth” is an oxymoron.  It remains a mystery as to why all the ardent advocates of sustainability talk about everything except the First Law of Sustainability.

The Essential Exponential!  For the Future of Our Planet (p. 10)

For more information on Professor Bartlett, visit his website (  His publications for NPG are available within our online library.

Donald Mann

President of Negative Population Growth, a national non-profit membership organization dedicated to educating Americans about the devastating effects of overpopulation on our environment and quality of life.
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