The “Exponential Growth Problem”

“At this moment there are only 546 confirmed cases of Coronavirus, with 22 deaths. Think about that!”
POTUS

To understand how fast an epidemic can spread, think about the following mathematical problem:

  • If a chessboard was to have wheat placed upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent square), how many grains of wheat would be on the chessboard at the finish?

This is known as the wheat and chessboard problem. There are different stories as to how and when it originated. One of these, has the inventor of chess making the king promise to give him payment equal to the number of grains on the board. The king, thinking it as a peasantry price for the invention of a game, laughs it off and agrees to pay the man by this method. As the ancient legend goes, sometime later, the ruler treasurer walks into the castle and informs the king that the amount would outstrip all of his resources.

Versions of the story differ as to whether the inventor becomes a high-ranking advisor or is executed on the spot. As you’re probably already imagining by now, the hypothetical number of grains on the chessboard is widely counterintuitive. The sum total, would equate to approximately 600 times the global production of wheat. Precisely: 18,446,744,073,709,551,615 (I believe we call those ‘quintillions’).

We don’t understand the visceral power of exponential growth. Humans are not used to dealing with big figures. Most of the numbers we use in our daily lives are small. Between one and a hundred, one and a thousand. The bigger they become, the less we understand them. It’s not in our nature to. Less than three weeks ago, in Italy, there were only two deaths confirmed from COVID-19. Today, they amount to almost 600. Twice that of Friday’s, four times that of last week, a lot more than most of us would have guessed before the early alarms rang, and the street and squares started emptying.

It’s not irrational to worry about the potential ramification of the Coronavirus outbreak, no matter how early it might seem. Amid the crisis we as a country are facing, and as most countries soon will, the next time one of our leaders tells us that, so far, there are only a handful of cases detected, it would be better keep the ‘exponential growth problem’ in mind. He might be a good player, but chances are, he probably isn’t as smart as the man who invented the game.

by: Mark Granza

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