Why we can

This year will go down in history as the year someone became a billionaire for the first time – at least on paper. Elon Musk’s net worth catapulted to this unprecedented level thanks to the spectacular IPO of his company SpaceX. Setting aside the moral, social, and economic consequences of a single person accumulating so much capital, the way we conceptualize Musk’s wealth reveals the flaws of humans. sense of numbers.

Very few people have any immediate idea of ​​the immense size of a trillion, or even a million, for that matter. Knowing that a million is a 1 followed by six 0s is a start, but most of us don’t have such amounts in our bank accounts, and most of us will never see a million of anything. Likewise, you would have difficulty standing in the middle of a desert and estimating whether there are a million or 100 million, or even more, grains of sand around you.

If a million is tricky, what is a billion, that is, one 1 followed by nine 0s? And what about Musk’s net worth, which is a 1 followed by 12 0s? It seems downright impossible to comprehend such magnitudes.

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Worse still, purely intuitively but completely wrongly, many people believe that going from a million to a billion is just as important as going from a billion to a trillion. This error is linked to the pattern that the numbers follow: to go from a million to a billion, we add three 0s; To go from a billion to a trillion, we need three more 0s. The jumps seem equivalent.

Counting 0s is useful to represent large numbers in a concise and efficient manner. But they don’t help our subconscious grasp these large quantities. On the contrary, the “counting 0” method tends to lead to confusion. Adding a 0 means nothing more than multiplying the initial number by 10. However, following this rule means that the jumps from a million to a billion to a trillion are exponential: if you are a millionaire, you need to earn an additional 999 million to become a billionaire. But once you are a billionaire, you need to raise another 999.999 million to become a billionaire.

To get a clearer idea of gigantic numbersit is useful to convert them to units of time. Let’s say $1 equals one second. A modest sum of $3,600 would therefore be equivalent to one hour. Meanwhile, $1 million is about 11.5 days. On the other hand, $1 billion is over 31.5 years. And $1 trillion – the wealth Elon Musk now has on paper – is about 31,709 years old! Now be honest: did you expect this?

There’s a reason we struggle so much with gigantic numbers. Our brains process numbers completely differently from how we learn to count in school. If I asked you to arrange the numbers between 1 and 10 in order of size on a line, you would probably choose equal distances between consecutive numbers, like on a ruler. But, in theory, nothing stops you from choosing different distances between numbers.

And in fact, the human brain seems to prefer a different layout. Cognitive neuroscientist Stanislas Dehaene and his colleagues discovered this mapping of digital space when they presented the same task to indigenous children and adults from the Amazon who had had no contact with Western education systems. Participants were given numbers to place on a line segment in various forms: sets of dots, spoken words, and tone sequences. The results showed that they tended to place larger numbers closer together at one end of the line and smaller numbers further apart at the other.

The results, detailed in 2008 in Sciencesuggested that participants intuitively placed more value on the relationship between numbers than on the absolute difference between them. For example, because the number 2 is twice as large as the number 1, participants placed them further apart than 8 and 9, which they placed closer together on the number line.

Through formal education, students learn to work with a number line where consecutive integers are always the same distance apart. But as soon as we are confronted with values ​​that we can no longer visualize, we resort to more intuitive pattern recognition. We perceive much smaller differences between large numbers than between smaller ones, because we focus on their relationship to each other rather than their absolute difference.

So it’s not our fault if we underestimate the wealth of the world’s super-rich: it’s just the way our brains work.

This article was originally published in spectrum of science and has been reproduced with permission. It was translated from the original German version with the help of artificial intelligence and reviewed by our editors.