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Text by Christian Stöcker. Born in 1973, he is a cognitive psychologist and, since autumn 2016, has been a professor at the Hamburg University of Applied Sciences (HAW). There, he heads the degree programme “Digital Communication”. Before that, he ran the Netzwelt section at SPIEGEL ONLINE.
This week, Angela Merkel explained what exponential growth means: a dramatic acceleration. She was talking about Covid-19 — but there are other exponential curves that are far more threatening.
Corona pandemic: Unfortunately, neither the Chancellor nor other politicians like to talk about the many other exponential functions.
Recently, the physicist and Federal Chancellor Angela Merkel once again explained the exponential function at a press conference. Because, as she put it months ago, “not everyone is familiar with it every day”. Over the past three months, Merkel said this week, the number of new coronavirus infections in Germany had tripled twice over; and if that continued, the country would be looking at 19,200 new infections in December. Action was needed, she said, “if we see growth heading back into the exponential”.
I was genuinely pleased by this little detour. Not only because this basic, crucial truth about corona seems to have been forgotten all over again, but also because I wrote an entire book about the exponential functions shaping our world. There are, after all, many more of them. They determine our lives and our future. It is high time humanity finally grasped that — before it’s too late. Humans are, unfortunately, astonishingly bad at understanding exponential functions. In psychology, this blind spot is even considered a classic example of the limits of a mode of information processing that the psychologist and Nobel laureate Daniel Kahneman simply called “System 1”.
“System 1” is something like the empirically grounded, and less sex-obsessed, cousin of Sigmund Freud’s “Id”: System 1 processes run automatically and largely — or entirely — without conscious control, and they feel effortless. They suit what psychologists call the “cognitive miser”. We’re quite lazy thinkers, after all. You can test this on yourself. If I suggest, for instance, that you quickly work out 17 × 23.8 in your head just for fun, you don’t feel like it, do you? Too much effort.
Doing sums, whistling, riding a bike
17 × 23.8 — System 1 can’t do that, but four plus four it can. The first requires mental effort, executive control, as psychologists call it. The second is simply retrieved from memory. You can also “work out” four plus four while riding a bike and whistling a tune. With 17 × 23.8, that quickly becomes very difficult. For that, you need System 2: rule-based, controlled, logical, guided by prior knowledge and convictions. Effortful. Not something you can freely combine with other activities.
System 1 processes, conversely, are often hard to explain in words: try telling a child, using only language, how to ride a bike while whistling.
System 1 processes are absolutely vital to life (without System 1 processing, you couldn’t sit or stand upright while reading this text), but in a complex world like ours they are also highly prone to error. Most of the biases and mistakes our thinking and reasoning fall prey to are System 1 processes. One example is the availability heuristic, which makes us believe something is likely simply because we can recall it easily. Whatever appears frequently in the news feels more dangerous. Many people are more afraid of terrorists or “migrants” than of cancer, even though cancer kills far more than 200,000 people a year. Cancer, however, rarely makes the news.
Our enormous difficulties in dealing with exponential functions are also a consequence of System 1’s shortcomings.
There is a very short test that demonstrates this. It comes from Shane Frederick, who worked closely with Daniel Kahneman for a long time. The test consists of only three questions; the third one is this:
The water lilies in a pond double the area they cover every day. If the pond is completely covered with lilies after 48 days, how long did it take for it to be half covered?
Think about it — but only very briefly — and then answer in your head.
A great many people answer this question with: “24 days.” That’s the System 1 answer. At first glance it feels intuitively convincing: half the pond covered, half the days. But it’s wrong. The correct answer is this: the pond is half covered after 47 days. The final doubling takes only one day — just like every doubling before it.
Many other exponential curves on the road to the abyss
In a wide range of studies involving more than 44,000 participants in total, around half of all respondents gave the wrong answer to this question. That’s the nature of an exponential function: our minds resist accepting these crazy leaps as reality. But they are real. And not only during a pandemic.
So it was good and right that Merkel once again explained the principle of exponential growth to the assembled journalists. Unfortunately, neither the Chancellor nor other politicians like to talk about the many other exponential functions that are, right now, relentlessly carrying us towards a catastrophic cliff edge. But they urgently should.
Doubles in around 250 years
The most important one at the moment is the amount of CO2 we are pumping into the atmosphere. It is still growing exponentially. Despite all the climate agreements. Before the beginning of industrialisation — and for about a million years before that — the share of CO2 in the atmosphere was around 280 ppm (parts per million). Sometimes a little more, usually less, but always in that range. Then industrialisation arrived, and exponential growth began.
In 2019, 415 ppm of CO2 in the atmosphere was measured for the first time. The concentration had never been that high in the entire history of humanity. That is why permafrost in Arctic regions is now thawing. That is why the Greenland ice sheet is melting. That is why coral reefs are dying.
The only good news in this context is that, at the moment, the global average temperature is not rising exponentially, but linearly. That doesn’t have to remain the case.
If we carry on as we are now, we will reach 560 ppm around the year 2060. That would mean we humans will have doubled the amount of CO2 in the atmosphere within roughly two and a half centuries.
We are the experiment. Our world is changing at such a breathtaking pace that we lurch from one crisis to the next. We have to learn to steer this immense acceleration.
Many other measurements and indicators in our world are growing exponentially as well. Global GDP, for instance. The population of major cities. Plastic waste — and other kinds of rubbish. The concentration of nitrogen in coastal waters (driven by fertiliser).
Many people don’t realise that constant percentage growth ultimately produces an exponential function — a curve that becomes ever steeper as it moves to the right, until it looks almost vertical. But that’s exactly how it works. A steady economic growth rate of two per cent per year, for example, means an economy roughly doubles in size in about 35 years. We do this deliberately. In fact, we actively aim for it.
It’s like corona
And of course there’s a grim connection: our constant exponential economic growth consumes exponentially more resources, produces exponentially more waste and toxins, and pumps exponentially more CO2 into the atmosphere. Everything keeps speeding up. That is the Great Acceleration.
It would be nice if, one day, Angela Merkel were to explain this in a press conference as well. Again with the add-on that action is needed “if we see this kind of growth heading into the exponential”.
Because when it comes to the climate and environmental destruction, it’s like corona: if you wait too long, it’s simply too late. Then the catastrophe is already here.
