What do airplane engines, nuclear power stations and the Paris attacks have in common?

-An approach to business as usual under the certainty of death

By Jan Eggers, stud.ha(fil.)


Can we trust an airplane engine?

A good friend of mine develops airplane engines at Rolls-Royce. Questioning him about the security of these engines he used to tell the following story. If one of the engines should stop working during the flight, which is very, very unlikely, the power of the remaining one is still strong enough to bring the plane to the next airport. In the even more unlikely case, that also the second engine stops functioning, chances increase drastically, that the first engine just decide to work again.

But why are circa 20% of passengers still worried about falling down from the sky? Following physician Ranga Yogeshwar an engine defect occurs with about every 8.000th flight hour. Even if the error occurs during the take-off process, the remaining engine is strong enough to bring the aircraft up. Pilots are training these scenarios regularly. Due to the engines independence from each other, the dysfunction of both engines at the same point of time is from a statistical point of view nearly impossible. But even if that will happen, a modern Airbus airplane is able to glide a distance of 200 km, which is enough to come down to earth from 10.000m of altitude (Wissen vor acht, episode 265). So, to sit in a plane and fly, is absolutely safe from a technical point of view.

But what do we learn from the statistics of airplane crashes? In 2014 the top 100 flight companies transported about 2.6 billion passengers (statista.com). 2014 had been a bad year for flight-safety, we remember the two crashes of Malaysian Airlines and one of a German Wings machine. In total, 970 people died (Jacdec).

These numbers lead to an average change of 1:2.68 million to die in an airplane crash in 2014. To get a feeling for this numbers meaning, it should be compared with data material of the Deutsche Bahn and German traffic participants. Concerning the first, 2.2 billion travel actions matches 172 deaths in 2014. The chance to be lethally involved in a train accident is approximately 1:12.8 million. Concerning traffic 3338 deaths relate to traffic accidents in Germany in 2014. We assume, that the average German has two traffic actions a day (car, bike, pederast) on five days a week. That means 82.000.000 inhabitants multiplied with two daily actions on about 250 days in 2014, which results in 42 billion yearly actions. Compared with the 3338 deaths, the chance to die in a traffic accident in Germany was about 1:12.2 million, so circa the same chance as dying in a train accident. What are these numbers about? Obviously it is much safer to use the train or to participate in ordinary traffic, than to use an airplane. But does not every article about airplane security point out, that an airplane is the safest way to travel? Indeed, and maybe the mistake can be found within the numbers. First, we compare one global statistic with national statistics. Due to lower train and traffic security in less developed countries than Germany, the thesis of the airplane as safest transport medium maybe could be validated if we concern the world’s average train safety. As well we have to question the numbers of train deaths in Germany. Where do these 172 people come from? Are these passengers? Are these car drivers, who collide with a train? Are suicides included? But despite this critical approach towards our own numbers, we have to figure out a conclusion from our number game. So let us accept that taking a train in Germany is five times safer than to fly with one of the top-100 airlines in the world. But is that statistical evidence a rational explanation, why people feel uncomfortable while sitting in a plane, although the chances to die are nearly to neglect? From a statistical point of view, we can point out, that in 2014, two Danes died in an airplane crash. Even if a person has a tendency to risk-aversion, that game will be considered as acceptable.

That first case proves once again how different fears can influence our ability to think statistically. Professor Walter Krämer analysed exactly that question on the 6th World Sceptic Congress in 2012. Although we know about statistical data, we feel fear, contradictory to the statistical evidence. “We are feared of things, which we cannot control, but not, if we have the (apparent) feeling that we have control, for example if we drive a car. We are more feared of ‘new’ dangers, than of ‘old’ ones.”


So we can define the fear of losing control as a first main influence on our acceptance of statistical evidence. But how does our statistical brain work, if we are not directly feared? Let us consider the following example from Nobel-prize winner Daniel Kahneman:

An individual has been described by a neighbor as follows: “Steve is very shy and withdrawn, invariably helpful but with little interest in people or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail.” Is Steven more likely to be a librarian or a farmer? (Kahneman, 2011)

Feel free to answer the question before you go on reading. Kahneman explains, “that participants in our experiments ignored the relevant statistical fact and relied exclusively on resemblance.” The statistical fact Kahneman is referring to, simply says, that there exist much more farmers than librarians. Regarding that fact, chances are pretty high, “that more ‘meek and tidy’ souls will be found on tractors than at a library information desk.” (Kahneman, 2011).

Let us consider another example to confuse our brain. In 2013 an overall amount of about 100.000 Germans died. Relating to a population of about 82 million, what can be said about a specific Germans chances to die in 2014? Of course there comes an intuitive answer to mind and it tries to tell, that the chance is about 1:820. If we consider a general estimation, that a person knows about 1.000 people, we will appreciate, that an average of 1.2 deaths per year under this group of people could be a realistic amount, but that there will be years with more or less deaths. We are confronted with an example, where the law of big numbers is influencing our rational analysis competences. 1:820 expresses the average mortality of Germans in 2014. It transmits no concrete information about a single Germans chance to die. It sums up the dying-chances of a 95-year old grandmother, 45-year old businessman, who drives 60.000km on highways within the year or a 25-year old who decides to fight for the IS. They all have a specific, individual chance to die or not to die in 2014. Again the mind is confused, but not as in Kahneman’s example by misleading information (“shy and withdrawn”, “meek and tidy soul”, but by an active misinterpretation of obvious facts.

The both examples illustrate that we are neither good in using our statistical intuition nor to work with given statistics in an adequate way. Our intuition tries to make us believing the first answer in mind as truth. Kahneman defines that intuition as “system I” and compares it with a so called “system II”, which in Kahneman’s perspective is in much better shape to solve complex problems, including statistical ones. If you now concern yourself to be stupid, because the right answers seem to be so logically, be assured, that Kahneman also tried these kind of experiments with students from Harvard university. As you will maybe not guess, they showed an astonishing tendency to fail on their intuitive statistical thinking.

So, a second conclusion remarks, that we are not only failing in statistical matters, if we are feared, but as well, if we should evaluate a statistical chance based on given data.


Will we die because of a maximum credible accident?

It has already been shown that we are feared of events, which source is outside our range of control. As well we seem to have a bad intuition about statistical evidence and evaluation of the possibility of outcomes. A third example should add a more metaphysical dimension to the given problem. Let us consider the risk of a maximum credible accident in a nuclear power station. What is your first intuitive thought?

Following an analysis of the European Union, only 20% of Europeans have been feared in 2011 of a maximum credible accident, although it has been the year of Fukushima (Eurobarometer, 2011). That astonishing low number is giving an impression, how people consider abstract risks. The Deutsche Risikostudie Kernkraftwerke defined already in 1989, that the chance of a maximum credible accident within the EU is 1 at every 17th year. (Deutsche Gesellschaft für Reaktorsicherheit, 1989) They estimate furthermore, that such an accident will kill 10.000 people immediately and 200.000 in long-term perspective. Using these numbers, the average probability to die because of a nuclear accident in the EU within a 17-year period (350 million inhabitants) is 1:1666. That means a personal risk of 1:333 in a lifetime period of 85 years. This example does also illustrate the work of Kahneman’s “system I”. The typical reaction of these numbers will be refusal. The risk to die because of a nuclear accident cannot be higher than the risk to die in an airplane crash, in a train or in traffic. What is a possible explanation for that refusal and the misleading of our intuition?

We can imagine a kind of moral explanation. The driving of a nuclear plant and the connected physical theories are hardly understandable for normal people. In the case of airplanes for example, the situation is different. People are maybe not able to design and build an airplane, but they have a much better understanding of it. In general we can talk about an airplane as we talk about a bus: we get in, take a seat, there are technical routines we are maybe able to understand, and there is a driver who is responsible to control these routines and to master unexpected situations. The driver is also welcoming us, if we enter the plane, which gives a personal feeling of connection to the situation. We have a face. Even if we could figure out a theoretic line like that one for a nuclear power station, we will still have one question: What is actually happening in there and who is responsible for it? So the question of trust in nuclear plants is much more a question of trust in the society, especially politicians, involved physicians and energy companies. This reliability bases on moral expectations and one of the best concepts to underline it, is still Kant’s categorical imperative:

”act only according to that maxim whereby you can at the same time will that it should become a universal law without contradiction” (Kant, 1993).

Therefore we assume, that processes in a nuclear power station should be designed in a way, which could hardly be influenced by outside interruptions or humans. We accept of course that an airplane crash can be the result of a human mistake, but comparing an amount of about 220 possible deaths with the amount of about 210.000 possible deaths we can hardly accept, that the processes within a nuclear plant can be influenced my human failures. The general reader will agree with this thesis, even it must be stated that every life is from equal value. But our moral intuition will agree in a certain way. 220 deaths due to human mistake, possible. 210.000 deaths due to human mistake, in no way.


But the terrorist threat…!

A good current example about the misleading of our statistical intuition is the feeling of terrorist threat. Of course we can easily consider numbers, which stand for the high security standard we still enjoy in Europe. The Economists currently counts the number of victims of global terrorism in 2014 at 32.700 people. (The Economist, daily chart Nov 18th 2015) The analysis has not to go into detail to guarantee, that concerning about 400 terroristic victims in Europe within the past 13 years, chances are pretty low to die there because of a terrorist attack. But, despite this certainty, why are one third of Europeans still feared of terrorism (Eurobarometer 2011)?

In terms of a terrorist attack, we are confronted with all three conclusions described above. First, we imagine our involvement in a terrorist act, as a situation out of our control. Therefore our fear of it, makes it difficult for us to rely on statistical evidence. Second, the given statistical evidence is often presented in a form, difficult to understand the real individual thread. This could considered at one reason, why people from the countryside are more feared of refugees, than people in cities are, even if refugees hardly will chose to live in the countryside. Third, we are confronted with a metaphysical paradox, that most people will hardly ever consider to kill other people, especially not innocents, out of political or religious believes. But at the same time, our moral expectations are challenged to understand, that our moral expectations maybe do not have a value to terrorists.

What can we use these considerations for? As Kahneman suggests we can train our statistical attention. We can try to identify, why we are unable to accept certain statistical facts and instead are influenced by our intuitive thinking. Thereby it will be possible to question and develop our thinking as usual, often led by our intuition. Of course that sounds much easier than it in reality is. But we can begin with a simple question with a last comparative answer. How many people have terrorists to kill in Europe, until the average chance to get killed by them will be as high as the chance to die as result of a maximum credible accident? Even if you do not like to figure out the exact number on your own you will already have the feeling that the number will be pretty high. The answer is 1.050.000 within the next 60 years. Now it is your task to figure out your individual risk from the average risk and to validate its potential of frightening you.


Kant, Immanuel (1993) [1785]. Grounding for the Metaphysics of Morals. Translated by Ellington, James W. (3rd ed.). Hackett. p. 30.

The Economist: Daily chart; Terror attacks; Jan 15th 2015

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