The crisis came, as Hemingway would have put it, gradually then suddenly. Why did so many of us see coronavirus on the horizon and sit there calmly waiting for it to arrive, only to go into a flat panic once it was already on top of us, in the manner of one who wakes up five minutes before it’s time to leave the house, having forgotten to set an alarm?
One interesting reason is the non-intuitive nature of exponential growth (when numbers grow by multiplying rather than by adding). The power of exponential growth is illustrated in the story of the man who invented chess. There are multiple versions of the story, but the basic idea is as follows.
The inventor of chess presented his invention to the king, who was very pleased with it asked what the man would like as a reward.
“I am a humble man,” said the inventor (although he wasn’t humble at all; he was devious in the extreme). “All I ask is one grain of rice for the first square on the chessboard, two for the second square, four for the next, and so on, doubling the number of grains for each subsequent square.”
The king, surprised at such a modest request, sent his assistant to go and count out the grains of rice. The assistant came back, having done the calculations, and reported that there wasn’t enough rice in the kingdom. In fact, there wasn’t enough rice in the world. As Ray Kurzweil (who coined the term “the second half of the chessboard” to refer to the point at which technological progress slips its leash and goes stratospheric) puts it: “At ten grains of rice per square inch, this requires rice fields covering twice the surface area of the Earth, oceans included.“
Here’s an arresting visualisation made by a very patient Swiss person:
The sneaky thing about exponential growth is that it starts off looking quite benign. In the case of doubling, it goes: 1, 2, 4, 8, 16, 32, 64, 128… So far, so manageable, so complacency-inducing.
And then at some point it dawns on you that the numbers have morphed into monsters. (You have entered the “second half of the chessboard”.) And if those numbers are instances of a contagious disease, by the time it becomes apparent that it’s going to start turning into a problem, it’s already a problem.
Incidentally, don’t be fooled by graphs that look like this:
The growth doesn’t look particularly dramatic. But look at the numbers on the y axis. They don’t increase arithmetically (adding the same amount from one number to the next). They increase exponentially, multiplying by 10 from one number to the next. That artificially dampens the precipitous climb of the blue line.
This is what that blue line looks like without being thus compressed:
(See where the “second half of the chessboard” sets in shortly after mid-March?)
Exponential growth will happen if you multiply the original number by anything more than 1, even a tiny bit more. In the case of a disease, transmission will be exponential if each infected person transmits it, on average, to more than one person.
That’s why there’s been so much talk of bringing the “R0 value” of coronavirus – the average number of people that each infected person transmits the virus to – to below 1. If it is anything above 1, the virus will keep spreading, ever faster. If it is brought below 1, the pandemic will die out.
The R0 value of coronavirus is not yet known, although preliminary estimates from the London School of Hygiene and Tropical Medicine put it at a chessboardesque 2.6 in the UK before the lockdown but a very reassuring 0.62 during the lockdown.
Exponential growth is why a few of cases of covid-19 can lead an entire country to seize up – and not in weeks or in months, but in days. The emergence of such big numbers from such small ones is not something we tend to grasp intuitively, which is why so many of us were taken by surprise.