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Monday, March 23, 2020

Exponential growth and the spread of COVID-19

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Why is it so difficult for us to appreciate the scale of what an unchecked global pandemic could do? The answer may have something to do with how difficult it is to intuitively understand abstract concepts like exponential growth.

This difficulty has been appreciated since at least 1256, when an Islamic scholar recorded what is known as the wheat and chessboard problem. The problem appears in a parable about the inventor of chess, whose king demands to purchase the new game. The inventor names his price, to be paid in wheat. He suggested that one grain of wheat should be placed on the first square of the chessboard, two grains on the second, and so on, with the sum doubling in this way over 64 squares. The king thinks this a great bargain, and is stunned when his treasurer informs him that the sum would bankrupt the kingdom. The total number of grains comes to 18,446,744,073,709,551,615.

Here’s another example. If you took 30 steps from your front door, with each step twice as large as the last, how far could you get? The answer might surprise you – it’s 26 times the Earth’s circumference. Our inability to appreciate how extraordinarily powerful exponential growth can be has concrete consequences. It’s a major reason why people don’t take their retirement accounts seriously enough, for one. It’s also why people seem to be struggling to understand why every single day matters enormously in limiting the spread of the coronavirus, which follows an exponential growth pattern.



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