‘Going Viral’: The Power of Exponential Growth

‘Exponential growth’ should have been the expression of the year 2020. In the mathematics courses of coming decades, the coronavirus is sure to serve as a prime example of exponential growth. Yet the virus is not the only factor in our lives that exhibits an exponential growth function.

The lockdown measures, which massively affect our daily lives, are ultimately founded on a fear of runaway growth in infection rates. Chancellor Merkel provided a vivid illustration of exponential growth in September 2020, when she observed that daily infection rates had doubled each month over the past three months, and that, were this rate of doubling to continue, “October, November and December would see a rise of infection rates from 2,400 to 4,800, 9,600 and 19,200 per day.” And so it came to pass: Germany hit a daily infection rate of 20,000 by mid-November.

The coronavirus is just one example of an exponential growth function. The level of digitalisation we see today would not have been possible without an exponential increase in processing capacity. Indeed, the number of transistors on a computer chip has doubled approximately every two years since the 1970s – a trend known as Moore’s law. Big data and artificial intelligence on a large scale would be unthinkable without this tremendous explosion in computing power, which is many millions of times greater today than it was in 1970.

Any quantity that has a rate of increase proportional to itself grows exponentially. The economy provides another demonstration of the power of exponential growth. China, for example, has registered annual GDP growth of ten per cent in recent decades. Accordingly, the Chinese economy has doubled in size every seven years. While China’s GDP was 1/18 the size of Europe’s in 1990, this ratio stood at 1/6 in 2000, at 1/3 in 2010, and at nearly 1/1 in 2020. Chinese GDP growth has slowed in recent years, and now stands at five to six per cent annually, such that a further doubling can be expected every 12 to 15 years. As a result, there has been a tectonic shift in economic power. The US would not be taking such powerful measures against China if the country were still at its 1990 level and therefore not a serious competitor.

Historically, there has been a tight correlation between economic growth and man-made climate-damaging emissions. The climate crisis is thus also a consequence of exponential growth. Carbon emissions have experienced growth at an annual rate of three per cent since 1950, doubling every 25 years. Over the past ten years, however, emissions growth has slowed to approximately one per cent per year. Yet as long as energy is mainly produced with coal, oil and gas, and more economic output is linked with more energy, the correlation between economic growth and emissions growth is inevitable.

There are three ways to deal with the negative consequences of exponential growth, whether human health or the health of the climate is at issue. The first option is to directly interrupt the growth process, whether by social distancing or slowing economic activity. The second option is to deny inputs for further growth, whether through immunisation, or by decoupling emissions from economic growth. The third option is to focus on reducing impacts, whether by treating virus patients, or by adapting to climate change.

The second option leads to the least welfare losses, provided it is technically feasible – that is, a vaccine or suitable renewable technologies must be available. The vaccine was developed with impressive speed. Similarly, decoupling emissions from economic growth is also possible: Electricity from renewables has become increasingly less expensive over the past few decades, and now covers almost half of electricity demand in Germany. Indeed, over the last 30 years, Europe has managed to increase GDP by 60 per cent while simultaneously reducing carbon emissions by more than 20 per cent. However, to accelerate this development and ensure it spreads worldwide, no single ‘vaccine’ is available – rather, we must deploy a range of green innovations. Further success in the battle against climate change will depend on additional cost declines in the price of renewables, the adoption of new production processes in industry and agriculture, and the development of inexpensive energy storage technologies, to ensure continued power grid reliability.

Processes involving exponential growth have changed our world and are changing it every day. Understanding the exponential growth function is hugely important – not only for students of mathematics, but also for political scientists, social scientists and economists seeking to comprehend our world.