COVID-19 and the ‘Wheat and Chess Board Problem’
I’m seeing so many people struggling with understanding why our nation (and other nations) are essentially in lockdown, especially when “more people die of flu” and “just a tiny few have been identified so far“.
Do you understand how quickly the growth of a virus can move throughout humans? The wheat and chess board problem below is a great illustration of how exponential growth works — similar to how a virus spreads in a human population — and why the governmental reaction is happening to restrict our movements at this point in time.
THE CALIFORNIA EXAMPLE
As of yesterday, all non-essential services in my current State of California are shut down and people are mandated to “shelter in place” so as not to communicate the novel coronavirus to others. But why is this happening now?
According to How overwhelmed is California’s health care system about to be? California may not even be able to handle the surge of COVID-19 cases with the current hospital beds:
“Projections by state health officials have indicated that California hospitals could handle a surge — right now, statewide — of about 10,000 patients. But given the potential for the virus to spread so far and so fast, some models project the state could need twice that, closer to 20,000 extra hospital beds.”
A few facts about the State of California and the death rate and the state’s ventilator need is in order:
- As of the end of 2018, the population of California is 39.56 million people.
- Approximately 3.4% of people 60+ years of age are dying from the virus. Others in multiple younger age ranges are ending up with lung damage and both require ventilators to survive or minimize that lung damage.
Yesterday California Governor Newsom made announcements and sent a letter to the Trump administration stating that 56 percent of the state’s population — 25.5 million people — is projected to be infected with the coronavirus over an eight-week period.
With California’s citizenry being left to move about as before the virus emerged, the projection is that within two months a whopping 25.5 million people would have COVID-19 and therefore 3.4% of 25.5 million = 850,000 dead (and an unknown number of younger people with lung damage).
THE WHEAT AND CHESS BOARD – A LINEAR VS. EXPONENTIAL GROWTH EXPLANATION
The reason for the lockdowns is that the deaths are caused by acute respiratory failure requiring ventilators for those afflicted. If there aren’t enough ventilators the death rate goes way up.
The spread of a virus, especially one as communicable as this novel coronavirus, is exponential…and that’s the problem. Left unchecked (i.e., we were NOT locked down) the virus would spread exponentially.
You maybe saying, “Steve…I still don’t get how or why it would grow so fast and why the government’s numbers of people infected are so high.” It’s not your fault if you don’t understand since your brain understands linear growth easily, but your brain is NOT good at understanding exponential growth.
Linear growth is always at the same rate, whereas exponential growth increases in speed over time. If the coronavirus spread at a linear growth rate the numbers are larger than most people can understand since they are so enormous.
To understand both types of growth, let’s look at a chess board which has 64 squares on it and is one where you place grains of wheat on each square.
1) Linear growth is always at the same rate, so this is easy when you put one grain of wheat each day for 64 days. At the end of 64 days you have 64 grains of wheat.
2) How many grains of wheat would be on the chessboard when you finish with exponential growth? Since exponential growth increases in speed over time — just like a virus would spread — let’s see what happens when you double the number of grains each day for 64 days like you would if you were at the mall, in a restaurant, and moving about as you did normally before the virus hit:
- FIRST DAY: You place one grain of wheat on the first square on the chess board
- SECOND DAY: You double the grains of wheat on the second chess board square … so now there are two grains on that second square
- THIRD DAY: You double the grains again and now you have four grains on the third chess board square
- FOURTH DAY: You double the grains again and now you have eight grains on the fourth chess board square
- FOURTH THROUGH 64TH DAY: For the next two months continue to double the grains each day and place them on each subsequent square.
At the end of 64 days you would have 18,446,744,073,709,551,615 quadrillion grains of wheat! (NOTE: A quadrillion is a thousand trillion).
THAT is why we are in lockdown and trying hard to flatten the curve, performing social distancing, and trying to stop the exponential spread of this virus until a vaccine (and other mitigation strategies) can be found.
Here’s an interesting video to give you an idea on how quickly exponential growth occurs: