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Whether it’s the climate crisis, a pandemic or a nuclear war, some doomsday scenarios seem more plausible than they did a few years ago. Mathematicians who make predictions about the end of humanity, basing their arguments solely on statistical considerations, have come up with multiple conclusions about when human beings will go extinct. One estimate, which I will break down in detail, concludes with 95 percent certainty that we humans will inhabit the planet for, at most, another 17,100 years.

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The “doomsday argument,” developed from work put forward by astrophysicist Brandon Carter in 1983, makes predictions about the total number of humans who will ever live. It is based on the fundamental idea that we, as observers, do not occupy a privileged position in the universe—but rather a completely random one. This is known as the Copernican principle, named after astronomer Nicolaus Copernicus, who, in the 16th century, realized that the Earth is not the center of the universe. This idea is frequently used in cosmology, for example, to argue that our surroundings (such as our solar system) are nothing special and are rather quite common in the universe.

The idea can be taken further. Imagine plotting the total number of people who have ever lived on a timeline that encompasses both the past and the future. That’s a tricky thing to reckon with, as I’ve written about for Scientific American. But we can say that the world’s population continues to grow with every passing year. We can also say that eventually humanity will perish, either because we destroy ourselves (which currently seems possible) or because the sun has exhausted its fuel and engulfed Earth. But perhaps by then we will have managed to colonize other planets and galaxies. In the most extreme case, we could survive until the end of the universe.

If we believe that humanity will conquer the universe—that is, that we will spread across vast distances and survive for extremely long periods—then the total number of people who have ever existed will be extremely high. If, on the other hand, we destroy ourselves in a few thousand years, the number of people who have ever lived might double or quintuple but will be significantly smaller than in the first scenario. But how can this information lead to a prediction of when humanity will perish?

We Are Nothing Special

Suppose you are the xth person ever born. It seems only logical that the probability of having been born before or after a particular person is equally distributed. According to current estimates, approximately 117 billion people have lived on Earth so far. This knowledge can now be used to estimate the total number N of people who will have existed at some point.

Imagine drawing an extremely long straight line from 0 to N, marking the locations of all people who will ever have been born. Each point on the line represents one person. The probability of someone (like you or me) being in the first half of the line is 50 percent. The probability of being born somewhere in the second half is the same. You can increase the interval under consideration to also increase the probability of being in that range: for example, we are 95 percent certain to be in the region extending from 0.05N to N.

And now comes the incredible argument: If our position x on the number line lies between 0.05N and N with a 95 percent probability, and we know the value of x (approximately 117 billion), then we can deduce the total number of people N who will have ever lived: x > 0.05N, and therefore, 20x > N—at least with a 95 percent probability. In this case, the highest possible total number of people who will ever have lived is 20 × 117 billion, or 2.34 trillion.

Juggling Probabilities

This estimate probably seems a bit audacious. A simple thought experiment can help illustrate the idea. Imagine two identical boxes, each with a small opening at the bottom. One box contains 10 ping-pong balls numbered 1 through 10. The other contains 100,000 balls, also labeled with ascending numbers. You don’t know how many balls each box contains. Now a ball numbered 4 is taken from the opening of a randomly chosen box. Which box do you think it came from?

Most people would probably choose the almost-empty box: after all, the probability of drawing a 4 from this box is 1 in 10. In the other box, it’s 1 in 100,000. The same applies to the number of people. Every person who has ever lived can be seen as a ping-pong ball in a box. The nearly empty box corresponds to the scenario in which there won’t be too many total people because humanity will destroy itself in the near future, while the full box corresponds to the scenario in which humanity conquers the galaxy. If 117 billion people have already lived before us, it seems more likely that a few hundred billion more will be born in the future and humanity will destroy itself for some reason than it is that trillions and trillions more people will follow.

If the maximum number of people who have ever lived is 2.34 trillion with a 95 percent probability, we can estimate when our end is approaching based on annual birth rates. For the past 40 years, approximately 130 million children have been born each year. Although the birth rate is declining, the population is increasing. Therefore, assuming that the 130 million births remain constant, it would take another 17,100 years for the total population to reach 2.34 trillion. Of course, this number can vary depending on whether the birth rate rises or falls, but the general order of magnitude remains the same.

Of course, the doomsday argument is highly controversial and rejected by many scientists. For example, one might think beyond our own species when evaluating end-of-the-world scenarios, which would significantly increase the numbers to encompass all of the organisms that have ever existed, pushing the apocalypse into the distant future. Similarly, you could argue that the idea of a doomsday argument emerged quite early in human history—namely, as soon as we crossed a certain threshold of knowledge. This increases the probability that we are only at the beginning of evolutionary history: our position on the number line is therefore not as uniformly distributed as assumed in the Copernican principle.

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.