Why are we so complacent until it’s a crisis?

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:

https://www.youtube.com/watch?v=byk3pA1GPgU

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:

Covid-19 cases with an outcome (death or recovery), figures for 16 April 2020 from Worldometer

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:

Source as for previous graph

(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.

6 thoughts on “Why are we so complacent until it’s a crisis?

  1. Well, I admit to have certainly been taken by surprise! One day I was going merrily about my life, thinking that perhaps people were being a little over-reactive. The next day this exponential thing hit me in the face! And then I abruptly stopped merrily going about my life.

    This is a very astutely delivered explanation. Thank you, Lara. You’ve explained exponentiality much better than did Mrs Gaunt, my maths teacher at Churchill Boys High.

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  2. No, that wasn’t a mistake. It WAS at Churchill Boys High that I did A-level maths.

    And the Churchill boys in turn ambled down the road (turned out, for the amble, in blazers and purple caps) to do their A-level chemistry with us in Miss Lambert’s class.

    Prior to launching her career as a chemistry teacher, Miss Lambert had been my mother’s lab technician in the Department of Agriculture at the University of Rhodesia.

    Not that this has much to do with exponentiality and corona virus. But I think the fact that Churchill boys were not allowed off their premises without being properly attired is worth being recorded.

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      1. I’ve no way of knowing whether I did, Ashley. But what I do know, is that I had frequent sight of your grandfather (with an avocado in one hand) – albeit not during perambulations between Churchill Boys High and Roosevelt Girls high, but in Rezende Street in the cows’ guts of Harare, where he and my uncle each had a factory, directly opposite each other. I used to work for my uncle during school holidays.

        Your grandfather and my uncle were the sworn enemies of each, for some reason which was never revealed to me.

        And the reason your grandfather had the avo in his hand was because at lunchtime each day my uncle would saunter out onto the pavement (with an avo in one hand) bellowing “Come out BDiii’s … I’m waiting for you!” And these two grown men would then hurl avos at each other across the street until Ticky Tyschen, my uncle’s secretary, came to the door to chastise them and tell them that when they’d cleaned up the avo mess (which was usually on the windscreens of their respective cars), coffee was ready. They’d go in, laugh and tell jokes over coffee, and then resume their war at lunchtime the next day (but only after having collected a fresh supply of avos from their respective back gardens).

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      2. I’ve no way of knowing whether I did, Ashley. But what I do know, is that I had frequent sight of your grandfather (with an avocado in one hand) – albeit not during perambulations between Churchill Boys High and Roosevelt Girls high, but in Rezende Street in the cows’ guts of Harare, where he and my uncle each had a factory, directly opposite each other. I used to work for my uncle during school holidays.

        Your grandfather and my uncle were the sworn enemies of each, for some reason which was never revealed to me.

        And the reason your grandfather had the avo in his hand was because at lunchtime each day my uncle would saunter out onto the pavement (with an avo in one hand) bellowing “Come out BDiii … I’m waiting for you!” And these two grown men would then hurl avos at each other across the street until Ticky Tyschen, my uncle’s secretary, came to the door to chastise them and tell them that when they’d cleaned up the avo mess (which was usually on the windscreens of their respective cars), coffee was ready. They’d go in, laugh and tell jokes over coffee, and then resume their war at lunchtime the next day (but only after having collected a fresh supply of avos from their respective back gardens).

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  3. Thank you for this Lara! This was such an interesting read! I must admit that I don’t know if I understand all of it (you lost me at exponential growth 🙂 — I have zero math skills ), but what you said about getting that number below 1 is something that I’ve heard thrown about quite a bit. I don’t know where we are at this stage right now, at least here in Italy. Antonello said that today the total numbers in Italy had dropped to around 760 new cases, but that’s deceiving because I think most of those cases are in a specific area in Italy (perhaps Lombardy). I feel like the one thing I’ve learned during this virus is how misleading statistics can be, even when they don’t mean to be.

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