Exponential Growth, Time-Delayed Reactions, and other problems of human cognition

«Once upon a time a Chinese sage was asked by a friend to bless his newly born son. His benediction was, ‹Let’s pray he lives in interesting times.›»
Noble House

Hindsight is twenty-twenty, but the current development of the Corona crisis is not that surprising. When the cases started to grow exponentially in Germany about two weeks ago, it was pretty clear that the virus was already spreading in the general population and could not be contained. There were too many cases in different parts of Germany, and given that only a small percentage are severe enough to get diagnosed, the estimated number of undetected cases had to be at least an order of magnitude higher. While early reporting did show a lack of understanding of this fact (it’s the «number of diagnosed cases», not the «number of cases»), there are two other aspects of the pandemic that show the limits of human cognition.

1. Exponential Growth

As humans, we are unable to make accurate intuitive predictions when it comes to exponential growth. If the number of cases double a couple of times, the resulting number of cases is much higher than we intuitively expect them to be. Sure, you can memorize tables and use them as a guide, but even that has its limits.

A nice example (IIRC) is to take a sheet of paper and fold it in the middle. Then fold it in the middle again, and again, so that the thickness doubles each time. If it were possible, after folding it about 51 times, how thick would the paper be? Well, you couldn’t put it between the Earth and the Moon. A couple of times more and …

So, whenever we are dealing with exponential growth, we need visualizations. Those help to understand the development. And then you’d better annotate the axes with reference numbers, e.g., the number of people in Germany, in Europe, in the World.

In this sense, the development of the number of cases in Germany, without any counter-measures, was not that surprising. But looking at the capacity of the health care system — it also means there is very little warning when it will break. If it does break. It’s a case of a development that is «Gradually, then suddenly.», to quote Hemingway.

2. Time-Delayed Reactions & Inertia

Humans are bad in steering anything with a large lag, not only since we are living in a world of instant feedback and gratification (though that probably did not help). And it’s not only that the reaction comes later, the inertia of the system leads to slower (or quicker) reactions depending on its current state.

A nice example is a study by Dörner (described in «Die Logik des Misslingens», German book) in which participants were responsible for the goods in the cold-storage warehouse with a broken automatic cooling unit. So they had to manually control the temperature in the refrigerated warehouse and had limited time to save the goods by reducing the temperature to a specific value. They only had a controller with numbers between 1 and 200 and information about the current temperature. But there was a time-delayed reaction from setting the controller to the reaction of the cooling unit and thus the temperature in the warehouse. The result: Many participants did change the settings too quickly and created a roller-coaster ride of the temperature inside the warehouse. They even used magical thinking («120 is a good number»), did focus on sequences («alternate between 0, 1, 2, and 3»), or developed meta-hypotheses («controller does not work», «situation cannot be solved, they are measuring stress»).

It is very hard to wait under time pressure and monitor the effects of the action over time when the costs of waiting are high. To wait, then make smaller and smaller adjustments. But that’s necessary to deal with these kinds of situations. You have to stop managing the current state and focus on managing the process.

This effect is relevant when it comes to the proposed counter-measures. Especially with the urgent need to flatten the curve to avoid overwhelming the health care system, the increasing media scrutiny, and changing public reaction (Germany has a deep, submissive-paternalistic streak). Personally, I am skeptical whether the government will give these measures the required amount of time to determine the effects. With an incubation time of between 1 and 14 days (and in some cases, even longer), the consequences of anything that is done will only become clear a week or two later.

And yeah, the time pressure is an argument for strong measures. However, there is a sweet spot, as extreme measures will likely backfire. They just create too much fear and outright resistance. Plus they are very hard to implement, unless there is a way to protect the police (later: the military) from the virus (loyalty is another issue).

Concluding Remarks

The current pandemic shows the limitations of human cognition — and makes dealing with this crisis very hard. At the moment, the situation is not that grave. But the virus will spread, and there are a few developments that are possible:

  1. The virus mutates into a more dangerous form. It already spreads easily, but so far, the number of deaths is rather low (and I’m writing this with having people I love in the vulnerable age range). IIRC, the Spanish flu was not that deadly when it first spread across the globe, but with all that biomass to grow in, it evolved into a more dangerous strain and killed much more people than usual in the lower age ranges. The ray of hope here is the research going on to develop a vaccine, which we did not have in 1918-1920.
  2. The government gets drunk on power. I do not have the best impression of politicians, and with a crisis and a law that might allow draconian measures, politicians might get drunk on power and curtail our freedoms for a long time. After all, if we flatten the curve, the pandemic will be drawn out for months to years. And yeah, power corrupts, especially with a government that is itching to go for undemocratic measures when it comes to — what it sees as — serious problems, e.g., climate change or the threat of right-wing parties. It’s just quicker and easier to just decide paternalistically. After all, they know they are right (as do almost everybody else about what they themselves think). And yeah, the building blocks are there — including ways to censor the net (to stop, so-called «fake news»), all under the guise of protecting the population.
  3. We don’t learn anything from it when the next pandemic comes. There is a risk that we see this as a one in a hundred years event and forget about it as soon as it is over. Especially if the health system does not get overwhelmed. But viruses won’t go anywhere, and new strains will develop. With Covid-19, if it stays the same, we did get a serious warning. It made the number of people who die from a virus highly visible, but it could have been much, much worse. Just imagine a virus that spreads like Measles with the mortality rate of Ebola. Highly unlikely, but we would be screwed if a virus would evolve this way (or: if a lab decides to create such a virus). IIRC, some Asian countries were better prepared for such an outbreak, both with equipment and with societal attitude to dealing with such a crises. Perhaps the same will happen here — instead of only having some risk analyses (e.g., Bericht zur Risikoanalyse im Bevölkerungsschutz 2012, German report, describes an outbreak of a corona virus eerily similar to the one we have today but with the — apparently — worst case scenario, i.e., the researchers did a good job), we might get better prepared for future pandemics.

Personally, I’m became seriously concerned about 1 to 2 weeks ago. And at the moment, I am still concerned, but not that worried. I’m not in the age bracket that is currently at risk and I did take a couple of precautions weeks ago, or did I? But the pandemic is serious, volatile, and its characteristics — when dealt with it by people who do not grok exponential growth and time-delayed reactions/inertia — might pose a serious problem. Overall, I think this will pass. And even if it gets worse, much, much worse, it will be a test for the government how to deal with crises — and whether we have the necessary checks and balances in place. Or whether we need to put it some more controls to avoid overreactions.


Update: Small changes to improve readability.

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