Which would you rather have?
1. A million dollars
2. The amount of money earned in a month by getting a penny the first day, 2 pennies the second, 4 the third and so on
There’s something called the wheat and the chessboard problem. You place a single grain of wheat (or rice) on the first square, two on the second, four on the third and so on. How many grains of rice will be on the final square? Will it be more than the board can hold? More than you can count?
The chessboard problem illustrates the concept of exponential growth. Linear growth is what most of us are familiar with. Our height and weight follow a linear path. You gain a little at a time. More or less in a straight line. Hence the name “linear.”
Exponential growth is different. It starts low and goes up very, very, VERY fast.
Epidemics experience exponential growth as opposed to linear growth. I saw someone say that “Only 1000 people have died in the United States from the virus.” They questioned the draconian measures that governments are taking to stop the spread of the virus.
Of course there are more than 1000 dead now. In fact, it’s been less than a week since the USA passed 1000 deaths. Today? There are 3,167 deaths. In 5 days, the number of death has increased 200%. And it’s going to continue going up.
I don’t know if the United States will end up with 100,000 dead, which is the low end estimate, or 1,200,000 which is the high end. And if the numbers follow their graph, we’ll see all those deaths in the next month. It’s unlike anything we’ve seen in America since the Spanish Flu epidemic of 1918 when 675,000 died in the United States and 50 million worldwide.
Don’t let the low numbers fool you. Math works. And the math, the horrible, relentless, deadly math is following an exponential curve.
Oh, the answer to the two riddles?
You would absolutely want the the doubling pennies rather than the million dollars. After a month (call it February with it’s 28 days) you have:
2^27 + 1 penny for the first day = 134,217,729 pennies, or over $13,000,000
and that would just be awarded on the last day. The totals for the other days added together would be close to another $13 million.
And the wheat and the chessboard? That is even more outrageous.
2^63 + 2^62 + 2^61. . . + 2^3 + 2^2 + 2 +1 = 18,446,744,073,709,551,615
That’s 18 quintillion and change. Just to give you some perspective. If you wanted to travel 18 quintillion miles you could rack that up by travelling the 93 million miles from the earth to the sun. You’d have to make multiple trips, of course. 200 million of them, or 100 million round trips.
The virus won’t reach that many, of course. And not just because we have less than 8 million people on earth. Governments are attempting to “flatten the curve.” To prevent the virus from spreading as rapidly as it might have.
But, if anyone tries to convince you that it’s “only 1000” or “only 3,167” deaths, ask them for some pennies and a calendar, or wheat and a chessboard.
Stay safe.
Rodney M Bliss is an author, columnist and IT Consultant. His blog updates every weekday. He lives in Pleasant Grove, UT with his lovely wife, thirteen children and grandchildren.
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