This year will go down in history as the year a person became a trillionaire for the first time—on paper, at least. Elon Musk’s net worth catapulted to this unprecedented height thanks to the spectacular initial public offering of his company SpaceX. Putting the moral, social and economic consequences of a single person amassing so much capital aside, how we conceptualize Musk’s wealth reveals humans’ flawed sense of numbers.
Very few people have an immediate grasp of the immense size of a trillion—or even a million, for that matter. Knowing a million is a 1 followed by six 0’s is a start, but most of us don’t have such sums in our bank accounts, and most of us will never see a million of anything. Similarly, you would have a tough time standing in the middle of a desert and estimating whether there are a million or 100 million—or more—grains of sand around you.
If a million is tricky, what does that make a billion—that is, a 1 followed by nine 0’s? And what about Musk’s fortune, which is a 1 followed by 12 0’s? It seems downright impossible to comprehend such magnitudes.
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Worse still, purely intuitively but entirely incorrectly, many people estimate the leap from a million to a billion to be just as big as the leap from a billion to a trillion. This mistake has to do with the pattern that the numbers follow: to get from a million to a billion, we add three 0’s; to get from a billion to a trillion, we need three more 0’s. The leaps seem equivalent.
Counting 0’s is useful for representing large numbers concisely and performing calculations. But they don’t help our subconscious mind grasp these large quantities. On the contrary, the “counting 0’s” method tends to cause confusion. Adding a 0 means nothing more than multiplying the initial number by 10. Following that rule, however, means that the jumps from one million to one billion to one trillion are exponential: if you are a millionaire, you have to earn another 999 million to become a billionaire. But once you’re a billionaire, you need to amass another 999,999 million to become a trillionaire.
To get a clearer sense of gigantic numbers, it’s helpful to convert them into units of time. Let’s assume that $1 equals one second. A modest sum of $3,600 would thus equal one hour. Meanwhile $1 million dollars is roughly 11.5 days. On the other hand, $1 billion represents more than 31.5 years. And $1 trillion—the wealth that Elon Musk now has on paper—equals roughly 31,709 years! Now, be honest: Did you expect that?
There is a reason why we have such trouble with gigantic numbers. Our brains process numbers completely differently than the way we learn to count in school. If I were to ask you to arrange numbers between 1 and 10 in order of size on a line, you would probably choose equal distances between consecutive numbers, just like on a ruler. But, theoretically, nothing is stopping you from choosing different distances between the numbers.
And in fact, the human brain seems to prefer a different arrangement. Cognitive neuroscientist Stanislas Dehaene and his colleagues discovered this number-space mapping when they presented the same task to Indigenous children and adults in the Amazon who had not had any contact with Western educational systems. The participants were given numbers to place on a line segment in various forms: sets of dots, spoken words and tone sequences. The results showed they tended to place larger numbers closer together at one end of the line and smaller numbers farther apart at the other.
The findings, detailed in 2008 in Science, suggested participants intuitively placed more value on the relationship between the numbers than on the absolute difference between them. For instance, because the number 2 is twice as large as the number 1, the participants placed them farther 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 whole numbers are always the same distance apart. But as soon as we are confronted with values we can no longer visualize, we fall back on more intuitive pattern recognition. We perceive much smaller differences between large numbers than smaller ones because we focus on their ratio to each other rather than their absolute difference.
So it’s not our fault that we underestimate the wealth of the world’s superrich—it’s just how our brains work.
This article originally appeared in Spektrum der Wissenschaft and was reproduced with permission. It was translated from the original German version with the assistance of artificial intelligence and reviewed by our editors.
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