Apocalypse Now (Or Maybe Later)

As the year draws to a close, it appears to be common practice in informed communities to point out, with reliable regularity, that the world is actually not as terrible as it often seems and with the apocalypse having to wait a little longer. This is often illustrated by the positive achievements of recent years and the prophecies of doom which never came true. No population explosion, no shortage of natural resources, less pollution, no extinction of species, and climate change is not too problematic either (at least the last two points are questionable). Despite all past warnings, the world is not on the brink of the abyss, and thus will not be in the future. But this conclusion is not logically compelling.


World of Numbers

The desire to convey an unagitated view of the world is always commendable. Fear and panic lead to quick, rash and often bad decisions. Only those who have a solid data basis at their disposal can develop meaningful strategies to deal effectively with problems that arise. In enlightened groups, works such as Steven Pinker’s The Better Angels of Our Nature The Better Angels of Our Nature: Why Violence Has Declined or Hans Rosling’s Factfulness enjoy a high status, because they demonstrate how the state of the world is not as dystopian as is often conveyed by the media, which crave for constant sensation. Reports on plane crashes, epidemics or terrorist attacks are rewarded with high prominence in almost all relevant media products – not despite their rarity, but because of it. For many readers it would be very boring to learn that today was another day when all passenger planes took off and landed safely; meanwhile about 89% of all one-year-old children are vaccinated against tuberculosis and 86% against measles – world-wide. Or articles about the fact that between 1991 and 2015 the number of people suffering from malnutrition fell from over a billion to about 781 million and only increased again by about 40 million from 2015-2017 onwards, probably largely as a result of the increase in local conflicts.
In Factfulness, Rosling describes very impressively the lack of knowledge in high income countries about the actual state of the world  and the fact that people have a much more negative view of reality than it often is.
A factual view of what is really happening is more necessary today than ever before. But at least as important is an understanding of how statistics should be read and what limitations they are subject to.

Statistical considerations

Many of the prophecies which never occurred suffer from the exact same problem: they attempt fortune-telling.
This accusation may sound a bit brusque at first reading, but it is based on an assessment that, among others, the mathematician Benoit Mandelbrot formulated as follows in his book The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward:

“We cannot know everything. Physicists abandoned that pipedream during the twentieth century after quantum theory and, in a different way, after chaos theory. Instead, they learned to think of the world in the second way, as a black box. We can see what goes into the box and what comes out of it, but not what happens inside; we can only draw inferences about the odds of input A producing output Z.”

Two statements of this quotation are fundamentally important. Namely the insight that we do not know everything, but can still draw conclusions about probabilities. Intuitively, such assertions sound terribly trivial. Of course we know that there are limits to our knowledge and we have also heard of probabilities at some point.
However, this does not prevent us from chasing after every media report suggesting a scientifically proven finding for a certain event. Many of the horror scenarios therefore do not originate from research itself, but from the media reports following on from it. But anyone who has read academic literature will know how rarely such certainty is conveyed. It is part of the good standard of scientific work within a study to also indicate possible sources of error, limitations and alternative explanations. However, experience has shown that these aspects often fall by the wayside in media reproduction.
The first reason why people often misjudge the world they live in is thus to be found in the way the media deals with scientific research.

The second reason is of a more technical nature, as it deals with the question of which statistical models are suitable for investigating certain events. For this purpose it is necessary to explain some basic concepts of probability theory. Most people will have come into contact with the concept of normal distribution and the associated Gaussian bell curve at some point during their school education. We remember obvious examples such as height, weight, blood pressure or IQ tests. All these aspects move with decreasing probability around a central expectation value. This means that in Germany about 94.3% of all people over the age of 18 years have an average height of 175.4cm (men) or 162.8cm (women). Deviations from these values are possible, but with increasing extremes they become increasingly unlikely or almost impossible. There are people who grow to be over 250cm tall (the tallest to date was Robert Wadlow at 272cm), but it is almost impossible that we will ever encounter a five-meter giant on earth.

Normal distributions are intuitive. We encounter them in everyday life and thus build up a familiar relationship. We have certain expectations about how our weight or height will develop and often this assumption comes true with minor deviations. Due to these expectations and the associated underestimation of how likely extreme events can be, it is all the more understandable why it is difficult for us to adequately imagine the complexity of the world.
At this point, other probability distributions and their conceptual worlds enter the stage. For the sake of better understanding, we shall stick to a Pareto distribution.
This form of probability distribution, which goes back to the economist of the same name, was originally used to study the distribution of wealth within a society. One of its basic propositions states that a small percentage of people own the majority of wealth. A finding now common knowledge for many people. Closely related to this form of probability is the concept of “fat tails”.
Normal distributions are also described as “thin tails”, which only expresses that in a normally distributed world, extreme events are highly unlikely. In contrast, fat tail distributions, which include the Pareto distribution, attribute a much higher probability to extreme events.

Understanding risk

This technical introduction was necessary in order to give an idea of how predictions and possible risks can be better classified.
Most people are quite miserable when it comes to correctly predicting events. Significantly, many amateurs are even better than selected experts, as Philip Tetlock and Dan Gardner impressively demonstrated in their book Superforecasting: The Art and Science of Prediction, published in 2015.
Considering this, it is even more likely that scientists whose job is making predictions are more likely to be wrong. We can only speculate about the reasons behind this, but it clearly shows that more available information does not automatically lead to more precise predictions. The black box described by Mandelbrot comes into play exactly here.
But does it automatically imply that we will also be wrong with current predictions?
Not at all. This form of proof is also known as inductive logic. Based on a number of past experiences, a general rule is deduced. The best known example is the Black Swan: If you see only white swans, you can quickly conclude that all swans are white – but a single Black Swan will prove this hypothesis to be wrong. I have already made a more comprehensive consideration of this argument in another article.
Let us therefore (once again) take a closer look at the point of the apocalyptic scenarios which did not occur, and are often used as proof that everything is completely at ease – climate change.

At this point it is important to make a significant distinction: it is often above all the media, politicians and activists who are the originators of horror scenarios now firmly established in many people’s minds. A criticism which finds approval here as well.
In scientific research, as is so often the case, the situation is much more differentiated. There is widespread agreement that humanity has an influence on the climate, but there are different assumptions about how strong this influence actually is.
Based on the available data and models, various emission levels and their actual or potential effects are calculated. If a model can accurately predict historical data, it can be deduced that it also predicts future developments fairly reliably (of course, I have discussed it in this piece that there is by no means a guarantee). Business as usual.
In a normal distributed world, we could now sit back and relax and say that the probability of climate change causing extreme changes in global climate conditions is so small that we can safely ignore it. Harvard economist Martin Weitzman illustrated this idea very vividly in a study published in 2011. The predictions then made of probable global warming, which could occur as a result of a doubling of the CO2 concentration, ranged between 2 and 4.5°C. It becomes interesting as soon as the clustered probabilities are presented both as normal and Pareto distributions. Two very different probabilities can be calculated for the two upper extreme values. In a normal distributed world, the probabilities that the Earth will warm up by 10°C and 12°C are 0.00007% and 0.00000003% respectively. So we are quite close to the “will almost certainly not happen” range. But if you look at the values of a Pareto distribution in comparison, you might get a clue. There are probabilities of 1.4% and 0.8%. Both are still very small, but whole orders of magnitude closer to the realm of possibility than we would expect on the basis of a normal distribution.
Which reveals the real crux of the matter: We are misjudging risk.

Although I do not claim that the probabilities of Pareto distributions are accurate, there are good reasons to consider them as more realistic options than their normally distributed sisters. After all, not only Gaussian bell-shaped curves are part of our everyday experience, but occasionally also seemingly completely unexpected events. The Black Monday of 1987, the dotcom bubble of 2001, the terrorist attacks in September of the same year, the financial crisis of 2007, the accident in Fukushima in 2011, the presidential victory of a Donald Trump in 2016 – the list is long.
The solution is not to rest on minimal probabilities of occurrence, but to find ways to minimize the effects of a worst-case scenario.
To put it bluntly: Nuclear power plants should not be built with the idea in mind that everything is going to be fine, but that everything catastrophic will happen on the same day – and still not result in absolute disaster for the surrounding area.

For climate change and its potential effects, at least the same conditions should apply as for nuclear power plants. Perhaps the probability of a total disaster occurring is indeed negligible, but does this justify inaction? What is the ultimate benefit if the 1:1 billion event of a normal distribution occurs, when we were so sure that it would not happen?
The good thing about the current situation, though, is that we have very reliable data suggesting even temperature changes outside such extreme ranges can already lead to serious changes – and here the probabilities are many times higher.
We should not panic, but neither should we look to the future in a glorifying way just because we have been wrong many times in the past. A factual risk assessment of the possible effects seems much more purposeful. In the case of climate change, a worst-case scenario would be the global collapse of human civilisation and its imminent extinction. In view of such an astronomically high profit-loss calculation, fact-based risk management suddenly seems very reasonable.

You are a decent human being. Behave accordingly.

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