Sunday, May 25, 2008

Our Greatest Shortcoming

"The greatest shortcoming of the human race is our inability to understand the exponential function" Albert A. Bartlett

Modern economies and societies are often based on the idea of continuous growth. Unfortunately there is a fundamental flaw in any such design. Any given resource, while potentially having vast reserves will always have some eventual limit. The question then is when do you reach that limit.

Any system with a constant growth rate will experience exponential growth. Whether we are discussing a national economy that experiences 2% growth every year for decades, or bacteria growing in a petri dish dividing at a constant rate.

The hazard of an exponential system is that by the time you realize that you are approaching a limiting factor, it may be to late to react. Observe the example chart below:

This chart shows series1 and series2. These are plots of US coal consumption at a constant growth rate of 2% per year but at different starting annual consumption. Series1 has a total reserve lifetime of 260 years and series2 has a total reserve lifetime of 120 years. Notice that in both cases after 50% of the available reserves have been consumed, only 30 years worth of reserves remains (this is because both series have the same growth rate).

How many people would become concerned about the amount of a vital resource available when you still have 50% of your initial supply available? Many people would consider becoming concerned when 75% or perhaps 80% have been used. The point to be taken from this graph is that by the time most people become concerned about the state of a vital resource, it may very well be too late to react. In series 2 it takes 90 years to consume the initial 50%, but only 30 years to consume the final 50%. if you wait until you have used 75% of your reserves in series2 then you would only have about 15 years to react. How long would it take for a society to recognize that a resource is becoming depleted and then make the required infrastructure changes to shift to a new resource? Historically it takes decades. This means that in a society experience constant growth, if you have not begun to shift to an alternative resource once you have used 50% of a resource, it is highly unlikely that you will be able to transition without the potential for significant disruption.

Constant growth in the context of this description does not mean or require that a system grow at exactly X%. It simply means that if the average (mean) growth rate for a given time span is greater then zero, then the system has experienced exponential growth (this sort of growth is also referred to as geometric growth/geometric progression). Therefore a system can experience negative growth, zero growth and positive growth all within the same time period and as long as the average growth rate is positive then rates of consumption are exponential.

Next time you hear an economy, a budget, or any other system is experiencing continuous growth, consider what the actual implications are. But also consider that this is not always a bad thing. Exponential growth is the power behind saving for retirement. By investing early at a continuous rate you can achieve substantial gains in the long term.

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