In arriving at our funding priorities—including criminal justice reform, farm animal welfare, pandemic preparedness, health-related science, and artificial intelligence safety—Open Philanthropy has pondered profound questions. How much should we care about people who will live far in the future? Or about chickens today? What events could extinguish civilization? Could artificial intelligence (AI) surpass human intelligence?
One strand of analysis that has caught our attention is about the pattern of growth of human society over many millennia, as measured by number of people or value of economic production. Perhaps the mathematical shape of the past tells us about the shape of the future. I dug into that subject. A draft of my technical paper is here. (Comments welcome.) In this post, I’ll explain in less technical language what I learned.
It’s extraordinary that the larger the human economy has become—the more people and the more goods and services they produce—the faster it has grown on average. Now, especially if you’re reading quickly, you might think you know what I mean. And you might be wrong, because I’m not referring to exponential growth. That happens when, for example, the number of people carrying a virus doubles every week. Then the growth rate (100% increase per week) holds fixed. The human economy has grown super-exponentially. The bigger it has gotten, the faster it has doubled, on average. The global economy churned out $74 trillion in goods and services in 2019, twice as much as in 2000.1 Such a quick doubling was unthinkable in the Middle Ages and ancient times. Perhaps our earliest doublings took millennia.
If global economic growth keeps accelerating, the future will differ from the present to a mind-boggling degree. The question is whether there might be some plausibility in such a prospect. That is what motivated my exploration of the mathematical patterns in the human past and how they could carry forward. Having now labored long on the task, I doubt I’ve gained much perspicacity. I did come to appreciate that any system whose rate of growth rises with its size is inherently unstable. The human future might be one of explosion, perhaps an economic upwelling that eclipses the industrial revolution as thoroughly as it eclipsed the agricultural revolution. Or the future could be one of implosion, in which environmental thresholds are crossed or the creative process that drives growth runs amok, as in an AI dystopia. More likely, these impulses will mix.
I now understand more fully a view that shapes the work of Open Philanthropy. The range of possible futures is wide. So it is our task as citizens and funders, at this moment of potential leverage, to lower the odds of bad paths and raise the odds of good ones.
Humans are better than viruses at multiplying. If a coronavirus particle sustains an advantageous mutation (lowering the virulence of the virus, one hopes), it cannot transmit that innovation to particles around the world. But humans have language, which is the medium of culture. When someone hits upon a new idea in science or political philosophy (lowering the virulence of humans, one hopes) that intellectual mutation can disseminate quickly. And some new ideas, such as the printing press and the World Wide Web, let other ideas spread even faster. Through most of human history, new insights about how to grow wheat or raise sheep ultimately translated into population increases. The material standard of living did not improve much and may even have declined. In the last century or so, the pattern has flipped. In most of the world, women are having fewer children while material standards are higher for many, enough that human economic activity, in aggregate, has continued to swell. When the global economy is larger, it has more capacity to innovate, and potentially to double even faster.
To the extent that superexponential growth is a good model for history, it comes with a strange corollary when projected forward: the human system will go infinite in finite time. Cyberneticist Heinz Von Foerster and colleagues highlighted this implication in 1960. They graphed world population since the birth of Jesus, fit a line to the data, projected it, and foretold an Armageddon of infinite population in 2026. They evidently did so tongue in cheek, for they dated the end times to Friday the 13th of November. As we close in on 2026, the impossible prophecy is not looking more possible. In fact, the world population growth rate peaked at 2.1%/year in 1968 and has since fallen by half.
That a grand projection went off track so fast should instill humility in anyone trying to predict the human trajectory. And it’s fine to laugh at the absurdity of an infinite doomsday. Nevertheless, those responses seem incomplete. What should we make of the fact that good models of the past project an impossible future? While population growth has slowed, growth in aggregate economic activity has not slackened as much. Historically poor countries such as China are catching up with wealthier ones, adding to the global totals. Of course, there is only so much catching up to do. And economically important ideas may be getting harder to find. For instance, keeping up with Moore’s law of computer chip improvement is getting more expensive. But history records other slowdowns, each of which ended with a burst of innovation such as the European Enlightenment. Is this time different? It’s possible, to be sure. But it’s impossible to be sure.
Since 1960, when Von Foerster and colleagues published, other analysts have worked the same vein—now including me. I was influenced by writings of Michael Kremer in 1993 and Robin Hanson in 2000. Building on work by demographer Ronald Lee, Kremer brought ideas about “endogenous technology” (explained below) to population data like that of Von Foerster and his coauthors. Except Kremer’s population numbers went back not 2,000 years, but a million years. Hanson was the first to look at economic output, rather than population, over such a stretch, relying mainly on numbers from Brad De Long.
You might wonder how anyone knows how many people lived in 5000 BCE and how much “gross product” they produced. Scholars have formed rough ideas from the available evidence. Ancient China and Rome conducted censuses, for example. McEvedy and Jones, whose historical population figures are widely used, put it this way:
[T]here is something more to statements about the size of classical and early medieval populations than simple speculation….[W]e wouldn’t attempt to disguise the hypothetical nature of our treatment of the earlier periods. But we haven’t just pulled numbers out of the sky. Well, not often.
Meanwhile, until 1800 most people lived barely above subsistence; before then the story of GWP growth was mostly the story of population growth, which simplifies the task of estimating GWP through most of history.
I focused on GWP from 10,000 BCE to 2019. I chose GWP over population because I think economic product is a better indicator of capacity for innovation, which seems central to economic history. And I prefer to start in 10,000 BCE rather 1 million or 2 million years ago because the numbers become especially conjectural that far back. In addition, it seems problematic to start before the evolution of language 40,000–50,000 years ago. Arguably, it was then that the development of human society took on its modern character. Before, hominins had developed technologies such as handaxes, intellectual mutations that may have spread no faster than the descendants of those who wrought them. After, innovations could diffuse through human language, a novel medium of arbitrary expressiveness—one built on a verbal “alphabet” whose letters could be strung together in limitless, meaningful ways. Human language is the first new, arbitrarily expressive medium on Earth since DNA.2
Here is the data series I studied the most3:
The series looks like a hockey stick. It starts at $1.6 billion in 10,000 BCE, in inflation-adjusted dollars of 1990: that is 4 million people times $400 per person per year, Angus Maddison’s quantification of subsistence living. For clarity, here is the same graph but with $1 billion, $10 billion, $100 billion, etc., equally spaced. When the vertical axis is scaled this way, exponentially growing quantities—ones with fixed doubling times—follow straight lines. So to show how poorly human history corresponds to exponential growth, I’ve also drawn a best-fit line:
Finally, just as in that 1960 paper, I do something similar to the horizontal axis, so that 10,000, 1,000, 100, and 10 years before 2047 are equally spaced. (Below, I’ll explain how I chose 2047.) The horizontal stretching and compression changes the contour of the data once again. And it bends the line that represented exponential growth. But I’ve fit another line under the new scaling:
