India under lockdown: what's chess got to do with it?

Source : SIFY
Last Updated: Wed, Mar 25th, 2020, 14:06:55hrs

Emperor Akbar was faced with a peculiar problem. The ruler of a neighboring kingdom had felt slighted by the emperor’s actions and wanted war at any cost. Akbar, a warrior-king who had fought enough battles to know its price, wanted to avoid one at any cost. So, he turned to his most trusted minister, Birbal. Wise Birbal said he might have a bloodless solution.

Birbal paid the adamant king a visit and was welcomed with courtesy. Birbal said he had not come as Akbar’s minister but as a civilian accepting the king’s famous chess challenge: anyone who defeated the king 2 out of three times would become the landholder of 20 villages.

Birbal – a chess expert – defeated the king easily in the first game. The second he deliberately lost as he did not want the king to lose face before his ministers. He made the third game look like a close contest that he barely won. The king, pleased at having stretched the smart Birbal so far, asked where he wanted his 20 villages.  

Birbal said he didn’t want 20 villages but something much smaller. He wanted enough rice to fill a chessboard when one grain is placed on the first square, two on the second, four on the third, and so on i.e. double the number of grains on each subsequent square.

The king and his ministers laughed but agreed. Birbal retreated to his guest quarters and made himself at home, aware that it would be days before the king asked to see him. Instead, a week later, an anxious-looking king came to see Birbal himself. Could I interest you in something other than a board full of rice, he asked Birbal.

Birbal smiled and said: ‘Of course o gracious king.’

You already know what Birbal asked. He asked that the magnanimous king consider a private apology and a treaty with Emperor Akbar instead of war. The king readily agreed.

The two questions that might arise in your mind are: what spooked the king and what has this story got to do with the total national lockdown called for by the Government of India to fight COVID-19.

Let’s replace Birbal’s grain in square one of the chessboard with a single novel coronavirus infected person. The R0 i.e. R-naught of the virus is 2.2 which means every patient transmits it to 2.2 persons.

Now let’s say each square on the chessboard is equal to one day and that every infected person infects not 2.2 but one more person every day. Considering that India’s population is 1.3 billion, how many days do you think the virus, if allowed to run unchecked, would take to infect every single Indian?

On the 31st day, 1,07,37,41,824 or 1.07 billion people would be infected. On Day 32 we would have surpassed our population with 2.14 billion infections. And you know how many days it would take to infect every single person on Earth: just 2 more days i.e. 34 days when 8,58,99,34,592 i.e. 8.5 billion people would be infected. Earth’s current population is 7.8 billion.  

Don’t believe me? Do a simple, 2-minute calculation on an Excel sheet.

This analogy, taken from what in mathematics is called the ‘wheat and chessboard problem’ is a good way to understand how a virus like COVID-19 can spread to a large population extremely rapidly.

Of course, the simplistic analogy ignores innumerable factors, one being that having an incubation period of 14 days, the person on square one would either recover or die on day 15 and thus not infect more people. The second person would reach the same fate on day 16 and so on.

Yet, this is a good analogy to understand the power of exponent i.e. how exponentially something can grow. This is the same principle used in calculating compounding interest as well.

This also helps us understand why the Government of India took the extreme, unprecedented decision of putting the entire nation under lockdown. Considering how insufficient and at times inefficient India’s healthcare system is, there is no way to control COVID-19 if it grows exponentially for a long period of time. The sudden spike in cases would not only overwhelm medical infrastructure, but also has the potential to unleash economic, social and political anarchy in the country.

It is with the intention of preventing even the possibility of all these, that the government has taken this tough decision – something which we at Sify were perhaps the first to suggest on March 11. Though it would affect a lot of people adversely, what we as citizens must do, is take efforts to mitigate the negative impact of this on the poor and marginalized, while at the same time following lockdown protocol. This is not just in the interest of the nation or of the world at large, but also in the interest of our own individual survival and the survival of everyone we love.

In the fictional story of Birbal and the king, do you now know why the king readily agreed to Birbal’s proposal? Because the number that comes on square number 64 is a 9,223,372,036,854,775,808. Thus if you add all the grains from square one to square 64, it adds up to 18,446,744,073,709,551,615. Forget the king having that many grains, the entire universe cannot have that many atoms, even if it stretches to infinity.

(Satyen K Bordoloi is a scriptwriter, journalist based in Mumbai. His written words have appeared in many Indian and foreign publications.)

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