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The confusion about numbers

For many people, mathematical tasks sound like this: "A red camel stands in the moonlight in the desert. How heavy is the trout when it sings?" unizeit discussed what you can do to better grasp numbers with statistics Professor Sören Christensen.

Dices with numbers
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unizeit: Professor Christensen, many people have a problem with numbers. Why is this, and how can they be helped?

Sören Christensen: There are many reasons for this. One of them is that we investigate abstract structures in mathematics that we can use in very many areas. However, when doing so the language must be kept rather general, so that everyone is talking about the same thing. It is therefore necessarily decoupled from the reality of life. There are a few nice experiments on this topic. In one of them, people are assigned logical tasks. If these have an abstract mathematical formulation, then experience shows that 90 percent of people will fail. But if exactly the same task is translated into a real-world scenario, 90 percent achieve correct answers. The abstract language leads to many other problems. For example, I have experienced that when a number is quoted, critical thinking often ceases.

Can you explain this in more detail?

Numbers are also used as a rhetorical means, in order to end a discussion. As soon as numbers or mathematics come into play, people switch off, and this is also true in areas that are not really abstract. For example, in an interview the then president of the German Environment Agency (Umweltbundesamt, UBA), Jochen Flasbarth, said that the rubbish in the North Sea was equivalent in volume to a cube of 80 kilometres in length. The next day this number was a headline, which the media simply used without question. But if you translated this into real life, it means that the rubbish would form a giant pile 500 metres high, over the entire surface of the North Sea. What had happened? Jochen Flasbarth had misspoken. He meant to say a cube of 80 metres in length. Therefore, whenever numbers play a role, we should ask questions.

Based on the example of the coronavirus infections, it became especially clear that the concept of exponential growth is not familiar to everyone. Is this also a translation problem?

The difficulty also lies in the fact that "exponential growth" used colloquially means that something is growing very fast. However, in mathematics, with exponential growth often next to nothing happens for a long time. Let’s take the example of a sheet of newspaper, to serve as a prototype for exponential growth. Let's assume that it’s a tenth of a millimetre thick. I fold it repeatedly in the middle. Then, after I have folded it six times, it’s still only half a centimetre thick. If you were able to continue, despite the thick folding edge, then after folding ten times it would already be ten centimetres, and after fifteen times it would be more than three metres. After folding 40 times, it would reach to the moon. It starts very slowly, and almost nothing happens, so you think you could continue folding forever, but at the end the height increases dramatically.

Do you have another example linking mathematics with real life?

Imagine that you live at the end of a long one-way street, and are looking for a parking space in the rain. You turn into the street, and there is a free parking space right at the beginning. You now have two options: you can take this parking space, must walk a long way and will get wet. Or you can drive a bit further, in the hope of a potentially better parking space closer to your home. But in doing so, you risk ultimately not finding one. Now if I were to approach this mathematically, I would observe beforehand how high the probability is of getting the best parking space. If on average every tenth parking space is free in front of the house, then you should take the ninth at the latest.

Is it also possible to help adults lose their fear of mathematics?

Yes, I think so. I have conducted quite a few one-day seminars with journalists. If you explain a few basic concepts, and link them to examples from the journalists’ field of expertise, then it helps their understanding of numbers considerably. For most people, this actually works if the concepts are linked to their real lives.

This interview was conducted by Christin Beeck.