I often joke that I plan to live forever. After all, only about 93% of humans have ever died, and I'm part of the 7%. Everybody I know is! We're clearly destined to live forever: the human condition is only about 93% fatal after all, and with a sample size of around 100,000,000,000 that's surely extremely statistically significant.

This stupid joke does raise some interesting questions though, a few of which I address here.

Figuring it Out

Lots of people have seen a hockey-stick graph of human population, with a huge upward swing starting within the past 100 years. It's the lead graphic on Wikipedia's world population article and the source of considerable consternation about the carrying capacity of the planet, given some reasonably foreseeable level of technical sophistication on the part of all these billions of us. Some people have even seen Randal Munroe's musings on fairy demographics which discusses — in a roundabout way — the cumulative number of people to have ever lived. So at least a few people other than me are thinking about this.

But what percentage of that hundred billion or so people to have ever lived are dead? We know that in antiquity nearly everyone who'd ever lived up to that point was dead. The human population was small and had been small for tens of thousands of years. A population that isn't growing is tallying up dead people as the years go by without increasing the number of live people, so clearly the proportion of folks who are dead must be going up. From there, it's a race: as the population rises, the percentage of currently-alive people rises, but so does the rate at which dead people are being generated. Still, if the population rises 10% in less time than it takes to add 10% more dead people - not an impossible task, if you add a little basic agriculture - then you're well on your way to fixing the nearly-everyone's-dead problem. So when was the peak? When was the largest fraction of all homo sapiens dead? The answer, as they say, may surprise you.

In principle, it's easy to figure out what percent of all humans are dead at any particular point in time: how many had ever lived up to that point, and what was the then-current world population? Sadly, determining those two numbers in order to do the simple arithmetic is somewhat difficult, particularly in the distant past. Estimates of global human population in antiquity vary wildly, but I'm going to use data from the Population Reference Bureau and the aforementioned Wikipedia article. A little bit of interpolation gets us current and cumulative-to-date human populations from about 10,000 BCE to the present.

As of about 12,000 years ago, the human condition was about 99.3% fatal. It would have been difficult for an early Neolithic person to imagine living forever on the basis of human performance to date. But it got even worse from there! Over the next six thousand years, the human population had not even doubled, while the number of humans who'd ever lived increased roughly five-fold, with the overall mortality rate climbing to almost 99.8%. But then humans seem to have gotten better at survival, and the estimated population roughly doubled every millennium for about the next five thousand years to finally drive the mortality rate below what it was in 10,000 BCE. Since then, and dramatically since the 19th century, the rising population of the living has outpaced the rising population of the dead, with overall mortality falling from 99% at the start of the 19th century, to 98% in about 1910, 97% in 1960, 95% in 1990, and on target for 93% in 2020 and about 92% in another decade. We're winning!

What If?

What if the death rate had not gone up, nor down? What if population growth had precisely kept up with growth in the number of humans to have ever lived? What does that population curve look like? The curve depends on two parameters: initial populations (alive and dead), and life expectancy. The faster people are dying and being added to the count of dead people, the faster they'll need to be replaced to keep the living population at the target percentage of the total. For the first parameter, let's take the ten-thousand-years-ago values of 5 million living humans, and 1,138 million dead ones. For the second parameter, once again, Wikipedia has some data which I will approximate as 30 years for a reasonable long-term average (world life expectancy at birth didn't significantly exceed that until well into the 20th century). So as a slight simplification, 1/30th of the population would die every year and be added to the cumulative total of humans who have ever lived. On a log scale, the graph of living humans and total humans in this scenario is a pair of parallel lines. The slope of those lines depends on how fast we're adding dead people, and thus how fast we need to add new live ones to keep things in balance.

With these starting conditions, population growth is extremely slow. It takes just shy of 5,000 years for the population to double, which is actually reasonably close to best-estimate values for the human population during the period between five and ten thousand years ago. But whereas human population rose more rapidly thereafter, here we continue at our slow pace, taking right around 50,000 years to reach the world's current population of a bit shy of eight billion.

The Future

Though demographic projections vary wildly, from approximately a doubling of the world population by 2100 to maybe a halving, it's clear that the living will keep gaining for at least a little while. With approximately 117 billion total dead humans, and a current death rate of about 55 million per year, world population only needs to grow by more than 0.047% per year for the population of the living to rise faster than the population of the dead. That is comparable to the population growth rate in antiquity. Projections from Our World in Data estimate that by about the year 2060, the death rate will be about 100 million per year, which will require global population to rise by almost 0.1% per year to keep up. That is roughly one tenth of the current population growth rate, or a quarter of the projected growth rate in 2060.

Barring some catastrophe (I write this during the early days of the COVID-19 pandemic), the world population will over the next several decades continue growing far faster than required to maintain the current overall mortality rate. So rejoice: we live in a golden age, and maths says your chance of living forever is the best it has ever been!