Professor Al Bartlett of Colorado University is well-known in sustainability circles for his contributions to the population debate and especially for his famous lecture, “Arithmetic, Population and Energy” which he has personally delivered over 1600 times (on average, about once a week for the last 30 years!). His message remains absolutely relevant today.

In a recent paper, published in the journal of Natural Resources Research, Bartlett criticises the Australian Government’s approach to energy resources management (namely, claiming to embrace a sustainable and secure energy policy for the future whilst simultaneously ramping up the exports of Australian fossil fuels). In his classic style, Bartlett uses simple mathematics to demonstrate that our leaders are totally innumerate in thinking that growth in consumption of non-renewable resources can be considered to be a sustainable plan for any useful timeframe.

In this paper, Bartlett draws on the work of M. King Hubbert, who developed a concept for forecasting the nationwide or worldwide production of non-renewable fossil fuel resources: in short, that they can be expected to follow a bell-shaped curve. There are economic forces acting on real-world production so this curve will never be perfectly symmetric, but it is true that cumulative production of any non-renewable resource will follow some sort of curve with a peak and decline.

As an analogy, consider a large rowing boat. Suppose the rowers decide they want to see how fast they can make the boat go – they all put their muscles into the task and the boat speeds up. It gains speed as they row faster and faster. But gradually, because not all rowers are built exactly the same, and because none of them is Superman, one-by-one they start to tire. First one starts to slow down, and then others, each time requiring yet more effort from the rest of the team. Eventually the slower rowers outweigh the faster ones and the whole boat begins to slow down. So naturally if you recorded the speed of the boat over time, it would go up, then peak, and then decline. That, in essence, is Hubbert’s peak.

With fossil fuel production across a large area (such as a country, a continent, or even the whole world), because different fuel deposits are different sizes, and they are mined at different rates, the cumulative result of all this extraction is that total production goes up as more and more mines get going, then cumulative production reaches a peak before declining as more and more mines exhaust their reserves and close down. This phenomenon has been observed in nationwide oil production in many countries (including Australia) and is known broadly as “peak oil”.

Because we don’t know exactly what form these curves will follow, Bartlett suggests that we consider a “family” of curves. These range from curves with high peaks and steep declines to curves with low peaks and gentle declines. The thing that connects the family of curves is the fact that the area under each curve is the same. The area under the curve is the total recoverable resource. In other words, if you have a given amount of a resource (say, the known economic reserve), then you may be able to have fast growth (leading to a high peak followed by steep decline) or slow growth (low peak followed by gentle decline). It’s a bit like your car: either drive it very fast and use your fuel up after a short distance, or drive it sedately and get further. Bartlett then draws a line that envelopes the whole family of curves: whatever the actual production curve is in real life, it should basically sit somewhere inside the envelope curve.

In fact there are more accurate ways to predict future production than the generic Hubbert curves, such that it may be possible to have brief excursions “beyond the envelope”, but the basic logic of peaking production is sound and therefore the envelope-curve concept is also valid. One notes that the envelope is a continually declining curve. This fact should be truly shocking to governments and economists, and in fact anyone who likes growth – it demonstrates that there is no way to grow infinitely into the future, because sooner or later the growth curve will intersect the envelope curve and after that the only way is down. The point that growth itself is unsustainable is a fundamental principle that remarkably often evades discussion. In the future, humans (quite possibly today’s young people) will be forced to accept this reality and will not be grateful for the preceding decades of denial.

So if growth can’t be sustainable, then what can? Well, in short, decay. If a nation mines its fossil fuels at an ever-decreasing rate, it is possible to ensure that there will always be some resources available to future generations, except that every generation will have fewer resources left to them than the previous one (such is the nature of mining, oil production and resource depletion in general).

Here’s how it works. Imagine you have $1000 of savings, and you use $100 of this each week. At that rate of consumption, you have 10 weeks left – in other words, if you continue to use $100 a week, you will be broke in 10 weeks. But if after the first week you can drop your weekly spendings to $90 a week, then you will still essentially have 10 weeks left. And if after the second week (when you’re down to $810), you drop to $81 a week, you will still have 10 weeks left. If this trend continues, you can ensure that you always have 10 weeks left, and you can claim to be spending your savings at a “sustainable” rate. This is the same approach as a nation that opts for ever-decreasing consumption of a non-renewable resource and it is called a “depletion protocol”. Obviously, because nobody can get by on zero spendings, it makes infinitely more sense to seek to base one’s lifestyle on regular income rather than eating into finite savings!

Bartlett’s concept of ever-decreasing consumption of oil or coal may be an utterly undesirable result, but desirable or not it is the only way to sustainably consume a non-renewable resource (whether it’s oil, gas, coal or uranium). New discoveries and enhanced recovery techniques might mean we can raise the curve a bit, but nothing will change its general trend: downwards. The mathematics dictate that economic, business, and government policies must be radically reformed to match the “exponential decay” scenario if humans are to continue to base our existence on the consumption of non-renewable fuels and claim that it is sustainable. Bartlett’s work (in this paper and others) is quite profound in that it highlights the deception of terms like “sustainable growth”.

As far as our energy goes, a more desirable approach would be to consume our regular “income” (i.e. from renewable sources) rather than eat into nature’s “savings” (i.e. non-renewable fuel deposits). By definition, renewable energy sources do not deplete and hence a “depletion protocol” is irrelevant. However, one thing is certain: like a badly managed household budget, basing a national and global economy (and worse, basing the very notion of “progress”) on ever-increasing consumption of non-renewable fuels is a recipe for ruin.


Bartlett, Albert A. (2006), A Depletion Protocol for Non-Renewable Natural Resources: Australia as an Example, Natural Resources Research (IN PRESS)