Friday, April 6, 2012

Exponential Growth Forever - NOT!

The greatest failing of the Australian people is the failure to understand the basic implications of exponential growth. (paraphrasing/adapting Alfred Bartlett of university of Colorado).

The greatest failure of our leaders is to adequately prepare our children for the Limits to Growth.

There are a couple of basic things we should all know about growth, compounding and the exponential function..

1. The rule of 72 lets you estimate doubling times for any rate of exponential growth by mental arithmetic. Just divide 72 by the rate of growth.
2. During the next doubling period (at whatever rate is used) of resource usage we will use more of a resource than has been used in all recorded history.
3. Estimates of resource life at current rates of usage are highly misleading in the face of annual growth in the rate of extraction.

Let's look at a few simple examples, using assumed numbers.

Assume we have 300 years of coal at current rates of extraction, but extraction is growing at 7% pa. (it has averaged over 10% growth pa over the last decade). The doubling time for the rate of extraction is just over 10 years (72 (from the Rule of 72) divided by 7% is 10.something times).

That means that over the next 10 years we will mine more coal in Australia than has ever been mined in the whole of Australian recorded history.

In very simple terms which significantly underestimate the shortening of resource life in 10 year time the resource life will have halved to 150 years from now. In a further 10 years of the same 7% rate of growth it will have more than halved again to only 75 years, but there are only 55 of those 75 years left.

Add a further 10 years of 7% growth in extraction and we can see that again the extraction rate doubles (its just simple mental arithmetic), we use more than has ever been used before in that decade (for the third decade in a row), the resource life halves again to only 37.5 years but 30 of those years are already gone.

300 years of resource at current rates of extraction are gone in 40 years at 7% compound growth per annum. (if you do this with Excel the exact answer is it runs out in the 45th year.)

If you do this exercise with Excel you will find that at 7% compound per annum the resource runs out in the 45th year, but the importance of this exercise above is to show how simple it is to work out the doubling time of the current rate of extraction and a reasonable estimate of the time of depletion of current resources using mental arithmetic.

You can convert this story to oil, iron ore, copper, brick making clay, concrete components, whatever you like. You can do it for population size, the cost of a loaf of bread. How long will it take your city to double in population at x% growth per annum.

Please don't just take my word for this. Open an Excel spreadsheet and do the numbers yourself.

Now many will say more resources will be found, human ingenuity will overcome etc.  If so, what is the cost of extracting those additional resources going to be? And transporting them if oil is also growing in scarcity or cost of extraction?

Prof Albert Bartlett of the University of Colorado has an excellent video (in 8 parts on Youtube) and a transcript of the lecture available on his website. I commend it to you.

 111. Exponential Function transcript - Arithmetic, Population and Energy - a talk by Al Bartlett on the impossibility of exponential growth on a finite planet

111. Exponential Function - Video parts 1 through 4 of Arithmetic, Population and Energy - a talk by Al Bartlett on the impossibility of exponential growth on a finite planet

Limits of Growth
All this leads to consideration of  "The Limits to Growth", both the book and its principles.

This book forecasts the collapse of life as we enjoy it in about 2050 based on increasing resource scarcity.

While it has had many detractors, many of them have not read or understood the book.

In 2008 Graham Turner at the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Australia published a paper called "A Comparison of `The Limits to Growth` with Thirty Years of Reality".

It examined the past thirty years of reality with the predictions made in 1972 and found that changes in industrial production, food production and pollution are all in line with the book's predictions of economic and societal collapse in the 21st century.

 In 2010, Peet, Nørgård, and Ragnarsdóttir called the book a "pioneering report". They said that, "its approach remains useful and that its conclusions are still surprisingly valid... unfortunately the report has been largely dismissed by critics as a doomsday prophecy that has not held up to scrutiny."

The implications for poor populations (even in developed countries) and poor countries of increasing resource scarcity are profound. Resource wars and colonial subjugation to control resources are clearly possible and probably likely within 50 years. Some would say the Iraq war, East Timor and the Spratley Island tensions are all at least partly about oil.


  1. Hi Explorer

    Of course you can't expect Australian coal production to continue growing at 7% p.a. and then one day in the year 2060 the men go to the pit to find there is nothing left!

    The other side of the exponential increase story is of course once the peak level of resource extraction is reached, exponential decline then follows. So the rate of extraction (and particularly the peak rate of extraction) are key considerations.

    I would highly recommend "A global coal production forecast with multi-Hubbert cycle analysis" by Tadeus Patzek and Gregory Croft.

    His findings are essentially that coal production will peak in the near future, that production from existing mines will be half what it is today in 2047, and that Australia is one of the few regions that have not reached peak coal production (this would be reached in 2042).

    David Rutledge has made similar predictions, with 90% of coal being consumed by 2088 (at which time the coal extraction rate will be about 40% of the peak value reached sometime this decade).

    1. Thanks David,

      You are correct of course, and thanks for the references.

      It does however highlight the nonsense of growth forever and the resource lives ascribed by proponents of projects.