###### By José Alberto Cuesta Martínez

**Linear and exponential growth**

Mathematics distinguishes between two types of growth: linear and exponential. The nature of the first is addition, while that of the second is multiplication. At first, the difference between the two is small, but as time passes it becomes vast. We see the difference in their first ten terms:

Linear growth: 1, 2, 3, 4, 5 ,6, 7, 8, 9, 10…

Exponential growth: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512…

Linear growth is constant (it’s represented on a graph by a straight line that always has the same slope) while exponential growth is accelerated, it grows on the previous growth (it’s represented on a graph by a curve with a constantly increasing slope). We can see the difference through a simple example:

A piece of paper has an approximate width of 0.125mm (an eighth of a millimeter). Stacking pieces of paper on top of each other is an example of linear growth, 50 pieces of paper stacked up would have a width of 6.25mm. An example of exponential growth would be not to stack 50 pieces of paper one on top of the other but rather to fold a piece of paper in half 50 times. If that were possible (which it’s not), the width of the piece of paper would reach 140 million kilometers, almost the distance from the Earth to the Sun.

**Exponential economic growth:**

The above example supposes an exponential growth of 100% (every time we fold the piece of paper in half its width doubles), but growth that is this extreme and continuous is rarely found in our daily lives.

For the “normal” functioning of the industrial capitalist system, an annual GDP growth of 3% is necessary, and this economic growth demands an increase in the consumption of materials and energy. There is a mathematical formula to calculate how much time it takes to double an amount (for example the size of a population, or the size of a debt or a mortgage) to a determined annual percentage. The formula consists of dividing 70 by this percentage.

Let’s give an example not of the 3% growth that the economy aspires to but rather of 2% growth. Let’s imagine that a man or a woman in year one of our human era uses 1 square meter of land and that every year they increase their expanse of land by 2%. What expanse of land would their descendants be using today? If the growth were linear (growing 200 square centimeters every year) the area would be 41 square meters. But if the growth were exponential, the area would double every 35 years (70 divided by 2) and it would surpass the surface area of the planet in the eighteenth-century, and would surpass the use of 400 planet Earths today.

So the question is, if a sole person growing at an annual rate of 2% would surpass the planet’s carrying-capacity, how much time would it take the 7.5 billion people who live in the world currently? Today, thanks to the concept of the “environmental footprint,” we know that we surpassed the carrying-capacity of the earth before 1980, and that today we’d need 1.7 planets to maintain our current level of consumption of resources and the current level of waste emission.

Economic growth has been very slow throughout human history, with advances and retreats. Exponential economic growth is a very recent historical phenomenon, and it’s made possible by the use of an enormous treasure wrought for millions of years below the Earth’s crust: fossil fuels (coal, oil, and natural gas) that have made the twentieth-century (and above all the second half of the century, with the extraction of oil) a unique and irreproducible century. To give a few facts, in the twentieth-century the world population multiplied by 4, the urban population by 13, the world GDP by 14, the consumption of energy by 16, and the consumption of water by 9.

The above facts show that there will not be a twenty-first-century like the twentieth-century. The decline of fossil fuel resources, especially oil, which made this exponential growth possible, will demand a reduction of the consumption of resources. We could do it voluntarily and in an organized manner (as degrowth defends) or by a matter of course through an all out war for these resources. We need to live in a sustainable society with a ceiling within the environmental footprint of one planet, and a social grounding that guarantees the fulfillment of the Declaration of Human Rights for all of humanity. By prolonging growth, which exhausts resources and deepens inequality, the window of opportunity for this is getting smaller each year. It’s degrowth or mayhem. As Jorge Riechmann affirms, the twenty-first-century is the century of the “Great Test” in the history of humanity.