Listening to the endless chatter about coronavirus, COVID19, I was struck by the number of commentators who have been talking about the growth of the virus in the community as being exponential.
One, less than helpful, definition of exponential is this :
“Exponential growth is a specific way that a quantity may increase over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself.”
Perhaps a more useful illustration of exponential growth is the rice on the chessboard equation.
The myth tells us that an ancient sage (picture Rupert Murdoch if you will) invented the chessboard and the game of chess and presented it to the Emperor (picture Donald Trump – with or without clothes – if you must ) and the Emperor was so taken by this invention that he offered the ancient sage anything he wanted as a reward for his ingenuity.
Rupert, the ancient sage, never being one to miss an opportunity, asked the Emperor only for one grain of rice, placed on the first square of the chessboard, two grains on the next, four on the next ; doubling until all sixty-four squares were covered. The Emperor who was not necessarily the sharpest knife in the drawer eagerly agreed to this request thinking what a great deal he had done – after all he was the greatest deal-maker in the world !
So the Palace (White House) servants started to apply the grains of rice, doubling square by square on the chessboard as instructed by the Emperor, who had gone off to play a round golf as was his custom.
Around the eleventh hole – his card prepared the night before showed that he had scored a hole-in-one on the 3rd and 5th – the Emperor received a tweet telling him that a problem had arisen and that the the West Wing of the Palace had collapsed under the weight of rice exuding from the Oval Office.
The Emperor was the victim of exponential growth and the remorseless application of compounding maths : as explained by this YouTube video.
This application of exponential growth had led to the sixty-fourth and final square of the chessboard having some eighteen quintillion grains of rice stacked on it : or the equivalent of 210 billion tonnes of rice which is quite a lot when you consider that global rice production for 2019 was around 500 million tonnes.
So the moral of this story resides in what happened next and, as with all fables there was a happy ending, depending on your point of view.
The ancient sage who we are calling ‘Rupert’ contracted the virus as did the Emperor who we are calling ‘Donald’. When they presented at the Center for Disease Control (CDC) in Atlanta Georgia they were subjected to triaging along with the rest of the population and as they were both over sixty-five they were turned away in favour of younger patients : so they both died !
Don’t forget to wash your hands, folks.
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