“The greatest shortcoming of the human race is our inability to understand the exponential function.”
― Albert A. Bartlett
The exponential function is a crucial mathematical function which has its own form: f(x)=a^x. The graph with this type of function represents a curve with an increasing gradient as the independent variable x becomes larger. Exponential growth is a specific way in which a quantity may increase over time. History has shown how human beings have difficulty understanding exponential growth. Exponential growth bias is the tendency to underestimate compound growth processes. Human minds normally perceive growth as a linear or arithmetic fashion, not as an exponential trend, which is why we underestimate epidemic growth
A famous historical anecdote that conveys how exponential growth is immense and unsustainable is the ‘Rice on a Chessboard' story. The wise man who created chess was brought to the Emperor of India in the 6th century. The Emperor was so pleased with this game that he decided to offer the wise man a reward of his choice. He only asked for one grain of rice for the first square on the chessboard, two grains on the next square, four on the following and so on for all sixty-four squares, with each square having double the number of grains as the square before. The Emperor, astonished by such a small price for a wonderful creation, immediately agreed, and ordered the treasurer to pay the agreed upon sum. A week later, the wise man went back and asked the Emperor why his modest reward had not been paid. The Emperor outraged and immediately asked his treasurer why he had disobeyed him, and had not yet paid the wise man. The treasurer tried to explain the Emperor that it was impossible to pay the wise man such a gigantic amount of rice. He explained that by the time you got half way of the squares (number 32) there wasn’t enough rice in the entire Empire to meet the demands made by the wise man.
Nowadays, we are living a situation that perfectly provides evidence for the incomprehension of the exponential concept. I refer to the terrible damage that the Coronavirus is causing. This chaos could have been predicted from a mathematical point of view. Whenever you have exponential growth, whatever it is that is growing will double its population in a given amount of time. Without introducing a factor to suppress it, exponential growth is an infectious disease that increases with time. There are a number of actions we can take which will have different effects and impacts how rapidly and extensively this disease will spread. If we have a population that starts with one infected person and doubles every three days, after 11 weeks, 67 million people will be infected, and only three days after, a total of 134 million will be infected. Covid-19 is even worse, it triples the number of infections instead of doubling. Even though it is hard to wrap our minds around it, that is what exponential growth does if we don’t intervene at an early stage.
Why do we encounter difficulties in visualising exponential growth? The answer is simple: it is just not in our genes. We are not made to visually comprehend it. We are all like the Emperor in some way. We find it hard to grasp how fast functions like doubling make numbers grow. These are exponential functions and are actually found everywhere around us, from finance to the spread of a virus. It was hard to predict the impact that Covid-19 was going to have upon us because human beings can’t entirely visualise how fast a pandemic can spread in a short period of time.
Jaime T, Year 12