Modern economies are structured so that they must grow.  Economic growth is a year-by-year increase by the same proportion, rather than by the same amount, and is, therefore, exponential growth.  Most modern economies are tuned carefully by banks, businesses, and governments to grow at 2-3% every year, and they will grow in a fairly accurate exponential growth curve.  An exponential growth curve looks like this:

An exponential growth curve gets steeper and steeper at an ever increasing rate, has no limit, and approaches, but never reaches, infinity.

As we use technology to try to reduce the use of resources in our economic activity we will do relatively easy and effective things first, and then we will do progressively more difficult and less effective thing afterwards. As time goes by we will be able to achieve less and less only with more and more effort.

Although it's not certain, it is likely that, as we use technology to reduce the use of resources, we will typically do the things that make big differences first, because these thing will have the greatest effect and will be the most worthwhile to make the effort to do. After that, we will do things that make progressively less and less difference as our options are reduced.

It's possible that important new technology that makes a big difference may be invented later, bringing about a sudden reduction in the use of a particular resource. Nevertheless, over the vast range of resources that an economy uses, the vast range of products that an economy produces, and the vast size of the economy, this variability will even out and will result in a similar proportion of reduction for each ongoing year. The same proportion of reduction each period of time means that the reduction is occurring exponentially; exponential reduction is called exponential decay. The ability of technology to reduce the amount of resources used in economic activity is likely to decrease in a fairly accurate exponential decay curve. An exponential decay curve looks like this:

An exponential decay curve gets flatter and flatter, and approaches, but never reaches, zero at an ever reducing rate.

To keep our rate of use of resources steady, technology must be able to reduce the amount of resources that are needed for a given amount of economic activity at rate equal to and opposite to the rate that the economy is growing. However, economic growth is on a curve that gets progressively steeper and steeper as the size of the economy increases more and more quickly, while the reduction of resource use brought about by technology is on a slope that gets flatter and flatter as the ability of technology to reduce resource use gets less and less.

This means that it is impossible for technology to reduce the use of resources by our economic activity at a rate that can balance out the exponential growth of the economy. Because the economy grows, technology will not enable us to reduce our rate of use of resources to a sustainable level, or even enable us to keep our use of resources at a steady, but unsustainable, rate.

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decoupling using technology

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