Whether climate crisis, pandemic or nuclear war of annihilation: Unfortunately, some doomsday scenarios seem more conceivable than they were a few years ago. In addition to epidemiologists and climate activists, some mathematicians also provide forecasts for the end of mankind. However, they do this without analyzing the threatening scenarios, instead basing their arguments solely on statistical considerations. In doing so, they conclude that we humans have a 95% certainty that we’ll only be on the planet for another 17,100 years, at most, before we disappear altogether—in any way whatsoever.

The “doomsday argument” that makes such predictions, first put forward by Brandon Carter in 1983, is based on the fundamental notion that we as observers do not occupy a distinguished position – but a completely fortuitous place. This is known as the Copernican principle, named after the 16th-century astronomer Nicholas Copernicus, who realized that the Earth is not the center of the universe. Among other things, this idea is often used in cosmology, for example to argue that our environment (such as our solar system) is nothing special, but occurs more frequently in space.

The idea, which sounds quite reasonable, can be developed further: Suppose you were to record the number of all people ever living on a timeline (which includes both the past and the future). As we know, far fewer people lived in the past than today, and the population is – at least currently – constantly growing. Eventually, however, humanity will perish; be it because we are destroying ourselves (which currently seems quite likely) or because the sun has run out of fuel and is swallowing the earth. But maybe we’ll have managed to populate foreign planets and galaxies by then. In the most extreme case, we could survive to the end of the universe.

If we trust humanity to conquer the universe – that is, to spread over vast distances and last extremely long, then the total number of people who have ever existed will be extremely high. On the other hand, if we annihilate in a few thousand years, the number of people who have ever lived may double or quintuple, but it will be far smaller than in the first scenario. But how can this information lead to a prediction of when humanity will perish?

Suppose you are the umpteenth person ever born. It seems only logical that the probability of having seen the light of day before or after a certain person should be equally distributed. According to current estimates, around 117 billion people have lived on earth to date. This knowledge can now be used to estimate the total number N of people that will ever have existed.

Imagine drawing an extremely long straight line, going from 0 to N, listing all the people that have been born. A point on the straight line corresponds to a person. There is a 50 percent chance that someone (like you or me) is in the first half of the line. The chance of being born somewhere in the second half is just as high. You can increase the interval you’re looking at to increase the probability of being in this area: we’re about 95% certain that we’re in the area that goes from 0.05·N to N.

And now comes the crazy reasoning: if our position x on the number line is between 0.05 N and N with a 95% probability, and we know the value of x (about 117 billion), then we can use this to calculate the total number of ever living people N close. Because: x > 0.05 N and from this follows 20 x > N – at least with a probability of 95 percent. In this case, the highest possible total number of people who will ever have lived is 20 117 billion, or 2340 billion.

This estimate probably seems a bit daring. The idea can be better understood with a fairly simple thought experiment. Imagine two identical boxes, with a small opening at the bottom. One box contains ten table tennis balls, numbered from one to ten. In the other, on the other hand, there are 100,000 balls, which are also labeled with increasing numbers. However, you do not know which box contains how many balls. A ball bearing the number 4 is now removed from the opening of a randomly selected box. What box do you think it came from?

Most would probably bet on the almost empty box: Because for this the probability of drawing the 4 is at least one in ten. In the other, however, it is one in 100,000. The same is true of the number of people: every person who has ever lived can be seen as a ping-pong ball in a box. The almost empty box corresponds to the scenario that there will not be too many people and humanity will destroy itself in a timely manner, while the full box corresponds to the galaxy-conquering scenario. If 117 billion people have already lived before us, it seems more likely that a few more hundred billion will be born in the future and humanity will annihilate for some reason than that trillions and trillions will follow.

If the maximum number of people who ever lived is 2340 billion with a 95 percent probability, annual births can be used to estimate when our end is near. About 130 million children have been born each year for the past 40 years. The birth rate is declining, but at the same time the population is increasing. So, assuming that the 130 million births will not change, it would take another 17,100 years for a total of 2,340 billion people to live. Of course, this number may vary assuming birthrates go up or down, but the order of magnitude remains the same.

Of course, the doomsday argument is highly controversial and rejected by many scholars. For example, for the end-of-the-world scenario, one could include not only humans in the consideration, but living beings in general. As a result, the number of all organisms that have already lived is significantly larger – which moves the possible apocalypse into the distant future. Likewise, it can be argued that the thought of a doomsday argument appears quite early in human genesis, once we have crossed a certain threshold of knowledge. This makes it more likely that we are only at the beginning of the history of development: our position in the number line is not as evenly distributed as assumed in the Copernican principle.

There are countless other reasons why the doomsday argument is probably incorrect. Still, it is interesting to see how such logic has led to correct conclusions in the past. The theoretical physicist John Richard Gott III used the argument to infer the duration of the Berlin Wall. During a chance visit to the then-divided city in 1969, when the wall was already eight years old, he made the following reflection: if the wall lasts for a period of time, then there is a 50 percent chance that he will have the monument in a period of length 1/2 visited. The eight years of existence, for example, could be as little as a quarter of the lifespan of the Wall, or even three-quarters of it. In this way, such a time interval from 1/4 to 31/4 has been marked out. Since the time of God’s visit falls within this interval with a 50 percent probability, the wall would still stand between 8 ⅓ ≈ 2.7 and 8 3=24 years. And he was right about that: 20 years after his visit, the Wall fell.

What is your favorite math theorem? Feel free to write it in the comments – and maybe it will soon be the topic of this column!

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The original of this article “Mathematicians calculate: The world will end in 17,000 years at the latest” comes from Spektrum.de.