How the World’s Population Grew

In November 1960, the journal Science published a paper with an alarming title: Doomsday, Friday, the thirteenth of November, A.D. 2026. The date it named was this autumn.

Its three authors, led by the physicist Heinz von Foerster, had not predicted an asteroid or a war. They had fitted a curve to two thousand years of world population, and the curve shot to infinity.

We are still here, more than eight billion of us. So what did the curve get right, what did it miss, and how does a population really grow?

Their formula is short. World population, N, equals a constant divided by the number of years left until one particular date. Halve the years left, and the population doubles.

As the calendar approaches that year, the gap on the bottom shrinks toward zero, and the number on top grows without limit. The best fit put that date at 2026 point eight seven, give or take five and a half years. The authors put its central day, Friday the thirteenth of November, in their title.

Press Run the clock to watch the curve race upward, and compare it with the real head counts.

The idea behind it was daring. In most growing things, each member adds offspring at a steady rate, so the total grows exponentially, by the same percentage every year.

Von Foerster argued that people are not like other living things: the more of us there are, the more we cooperate and share what we learn, so the growth rate itself should rise as the population rises. Mathematicians call that hyperbolic growth.

And for two thousand years, it looked right. Until about 1700, the world grew by roughly four hundredths of one percent a year. By 1963, growth had reached two point three percent a year, the fastest ever.

The fear itself was much older. In 1798, the English clergyman Thomas Malthus published An Essay on the Principle of Population.

He wrote that population, when unchecked, increases in a geometrical ratio: one, two, four, eight, sixteen. Food, he said, grows only in an arithmetical ratio: one, two, three, four, five.

Press Next generation and watch the gap open. Malthus argued that something must always hold population back to what the land can feed.

Exponential growth has a simple rule of thumb. Divide seventy by the yearly growth rate in percent, and you get roughly the number of years it takes to double.

At four hundredths of a percent, the long average before 1700, doubling takes about seventeen hundred years. At nine tenths of a percent, today's rate, about seventy-seven. At two point three percent, the peak of the 1960s, only about thirty.

Press Race to watch all three at once. A doubling time that kept shrinking is exactly what von Foerster saw in his data, and why his curve bent so sharply upward.

Look at how the billions arrived. Humanity reached its first billion around 1804. Twelve thousand years earlier, there had been only about four million people on Earth.

The second billion took a hundred and twenty-three years, to 1927. The third took thirty-three, to 1960, the very year the doomsday paper appeared. Then fourteen years, thirteen, twelve.

Press Add a billion. The eighth arrived in November 2022, about a decade after the seventh. But look at the next gaps: the United Nations expects them to get longer, not shorter.

Now put von Foerster's curve next to the real numbers. Until about 1960 they track each other closely. Then they part ways.

World growth peaked in the early 1960s and has slowed ever since. The formula had no way of knowing that, within a generation, families almost everywhere would start having far fewer children.

Instead of the sixty-three billion people the formula gives for 2024, there were about eight point two billion. The doomsday paper described the past remarkably well. It could not see the turn coming.

So why did the real curve not keep shooting up? Demographers describe a pattern first set out by the American Warren Thompson in 1929. It is called the demographic transition.

In the first stage, births and deaths are both high, and population barely grows. Then cleaner water, better food, vaccines and medicine cut deaths, above all among children.

Births stay high for a while, so for a generation or two the gap between births and deaths becomes a population boom. Press Next stage to step through.

In the third stage, births begin to fall as well: the fertility rate, the average number of children per woman, drops. When most children survive, families no longer need many births to be sure that some will grow up.

Education, especially for girls, life in cities, paid work and access to contraception all push the same way. In the fourth stage, births and deaths are both low again, and growth slows almost to a stop.

North-western Europe went first, from the late eighteenth century. Much of Asia, Latin America and Africa entered the transition later, in the twentieth century.

You can see the transition in a population pyramid, which stacks people by age, with the youngest at the bottom, men on one side and women on the other.

With many births, the pyramid has a wide base and a narrow top. As births fall and people live longer, the base shrinks, the middle fills out, and the shape turns into a column.

Press Young country and Ageing country to compare. Worldwide, a baby born in 2024 could expect to live about seventy-three years, and by the mid-2030s the UN expects more people over eighty than babies under one.

The United Nations' latest projections, from 2024, expect world population to keep rising for about sixty more years, to a peak of around ten point three billion in the mid-2080s.

Then it is projected to drift down, to about ten point two billion by 2100. Women today have on average about two and a quarter children each, down from about three point three in 1990.

Sixty-three countries and areas, including China, Germany, Japan and Russia, have already passed their peak. Projections are not prophecies, but they are built from births, deaths and migration that are measured every year.

Thailand shows how fast a transition can run. Around 1970, Thai women had about six children each, and the population was growing about three percent a year.

In 1970 the government made family planning the main way to slow that growth. Within about two decades, fertility had fallen to about two point two children per woman.

Today it is about one. In 2024, Thailand registered about four hundred and sixty-two thousand births, the first time below half a million since 1949, and more deaths than births for the fourth year running.

So the doomsday of the title is a date on the calendar, not a prediction to fear. Commentators have suggested the dramatic title was partly a provocation, to make people pay attention.

Its lesson still holds: a curve that fits the past very well can still fail, because people can change the very trend that is being measured.

The question for this century is no longer how to stop explosive growth, but how to live well in a world that is older, and that is projected one day to begin shrinking.