Rice on a Chess Board
What exponential growth can teach us about viruses, startups and software
"Chess Board in Mell Square, Solihull" by ell brown is licensed under CC BY 2.0
The history of chess stretches back around 1,500 years to India, although the modern version of the game only evolved around the 15th Century. An ancient legend suggests that a great king was so pleased with the game that he offered its inventor whatever he wanted. The inventor asked for a single grain of rice on the first square of the board, two grains on the second square, four on the third and so on. The king agreed. His treasurer had to explain to him that by the time they got halfway round the board, the king would owe more rice than existed in the whole kingdom. Outraged, the king had the inventor killed.
The story might or might not be true, but it reveals a great truth to us. Our brains didn’t evolve to understand multiplication, very large numbers or exponential growth (defined below*) without training. If you struggled to learn your times tables as a child, now you know why. The maths of extreme multiplication gets very scary very fast. In the example of the chess board, by the time you get to the 64th square, there would be 18 quintillion grains of rice on the board - that is 18 followed by 18 zeros. It is almost impossible for most people to imagine such a large number.
With training, though, it is perfectly possible to get to grips with some of the implications of exponential numbers. Two groups of people who have thought about this more than most are virologists, who study how viruses spread and grow; and people who are involved with startups. If you look at any list of billionaires, you will see that most of them are first-generation entrepreneurs; most of their wealth is tied up in the capital of the companies they founded; and at some point of their career they benefited from exponential growth.
Software entrepreneurs are particularly notable in lists of billionaires. Software is well placed for exponential growth - once you have created a piece of code, it is in theory just as easy for a million people to download it as it is for one person. In practice, you’ll need to think about sales, marketing, distribution platforms and so on, but the principle is basically sound - software can be scaled in a way that physical products can’t.
It was very interesting to see the startup world using its knowledge of exponential growth to get to grips with the beginning of the COVID-19 crisis. The GSMA cancelled the Mobile World Congress in Barcelona on 12th February 2020. This was a full month before the World Health Organization declared the emergency was a pandemic. I remember many people in Barcelona were confused by the decision, but it suggested to me that some of the top people in software had crunched the numbers and come up with some very scary conclusions.
We have seen in recent weeks that the crypto world is vulnerable to fraud by con artists; but that starting to save and invest money while young can lead to tremendous results. A basic understanding of exponential growth shows why joining a startup and getting stock options can be such an exciting career choice, particularly when you are young and tolerant of risk: A very small slice of an enormous cake is much more valuable than owning all of a tiny cake. Be warned, though, that the failure rate among startups is also very high. See you next week!
*Exponential growth is defined as growth whose rate becomes faster as the total number grows.
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[Updated on 10 March 2022] Opinions expressed on Substack and Twitter are those of Rupert Cocke as an individual and do not reflect the opinions or views of the organization where he works or its subsidiaries.