How long will America last?

An impossible question, answered with math.

by Samuel Arbesman

The Boston Globe

With all the chatter about the rise of China, our possible economic collapse, and climate change, it is little wonder that Americans might be growing preoccupied with our nation’s staying power. Is the rise of the United States a fleeting moment in world history, or simply the beginning of many centuries of American ascendancy?

Souvenirs of empires past: the Byzantine Empress Theodora, circa 530 AD.

It might seem like a question for pundits to argue over, pessimists against optimists. But there is another way to answer the question as well: with some data.

History is filled with examples of powers much like America - nations whose wealth and influence allowed them outsized effects on the world. In the past, they were empires; America doesn’t usually see itself that way, but its wealth and influence put it in this peer group. And once we place it there, we can look at the lifetimes of lots of empires, see how long they’ve lasted, and use this to gain a bit of insight into our American situation.

This kind of approach, using a quantitative approach to understand history, is part of what has recently begun to be called cliodynamics. The field of cliodynamics - a term coined by the mathematician, biologist, and social scientist Peter Turchin from the name Clio, the muse of history - uses mathematics to understand the shape of history, and has been around for centuries. With a pedigree dating back to such approaches as that of Francis Galton, a relative of Darwin, who used math to understand the extinction of Victorian aristocratic surnames, a cliodynamic approach can be used to understand the ebb and flow of entire civilizations on a grand scale. Now, with the advent of the digitization of vast amounts of data, we can apply a certain precision to history that wasn’t possible before.

So that’s what I set out to do.

Using a data set of empires that spans over 3,000 years, I wanted to create a model that could show us, statistically, what the lifetimes of empires look like. There are many more complex and intricate models of how civilizations grow and decay, but perhaps something could be gained by creating a very simple model that looks only at life span.

This data set is expansive, including everything from the Babylonian Empire of ancient Mesopotomia - known for such contributions as Hammurabi’s Code - to the Byzantine Empire, which has provided us with the eponymous word for red tape. Some of the world’s empires lasted an exceptionally long time: The ancient, and now little known, Elam empire located in present-day Iran lasted a thousand years. Others were short-lived, for all their power: The Phrygian and Lydian empires were around for only about six decades each. (The data set, based on earlier research in empires, ends at 600 A.D.)

If you crunch these all together, the first thing you discover is that the average lifetime of these powers is 215 years.

If you’re playing at home, this number is pessimistically eerie: It’s been 223 years since the ratification of the US Constitution. And that should perhaps give us some pause. To make this explicit, the United States has now outlasted the majority of the empires in my historical data set, and is now crossing the threshold into hoary old age.

Attila the Hun, circa 450 AD.

But there is a more interesting way to look at it than simply taking an average. By putting all the life spans together, we can see a pattern that statisticians call a distribution — the underlying shape of the “density” of the life spans. Distributions give us a much better sense than the average because, just as with incomes, life spans needn’t be distributed like a bell-shaped curve. They can be skewed towards one end or the other.

In the case of empires, their life spans seem to follow what’s called an exponential distribution. The exponential distribution is special for a particular reason: Of all the different types of probability distribution, it is the only one that is “memoryless.” This means that if something’s life span adheres to an exponential distribution, the likelihood of it ending next year - or even tomorrow - is the same no matter how long it has lasted. It has no “memory.” If something has lasted for a hundred years, it is no more or less likely to go extinct next year than something that has only lasted a single decade. This is quite unlike, for example, human life span, where the older you get, the more likely you are to die. An empire’s chance of death is the same each year.

It can be chastening to look at a 200-year history of success - or a millennium, as Elamites once could - and realize that it simply doesn’t matter; that the numbers tell us we have no better chance than we did 100 years ago. It violates our sense of how things work - how the strength of institutions and tradition creates a powerful foundation of stability; or in the past, how a dynasty’s long history could confer a legitimacy that placed it in the realm of the gods.

But we are also in good company. This memoryless property is not unique to empires. It turns out that it also applies to biological species - not individuals, but the whole species. How long will elephants last? How long did the dodo survive? How long will there be fruit flies?

It turns out that, despite a species having acquired beneficial mutations over millions of years, it still has the same likelihood of vanishing every year. The origins of this phenomenon have occasioned a certain amount of debate and research in evolutionary biology. One of the earliest hypotheses for why this might be so is because each species is not evolving to survive within an unchanging environment.

Our environments are continually changing, whether the climate is in flux, or other species are also competing for resources, in a sort of escalating arms race. So no matter how impressive a species is today, it still has to try to survive in tomorrow’s world. This constant evolution and co-evolution is known by the name of the Red Queen hypothesis, from Lewis Carroll’s “Through The Looking-Glass.” As the Red Queen states, “It takes all the running you can do, to keep in the same place.”

Hittite sculpture of horse and ride, circa 1,000 B.C.

And so it goes with world powers. No matter how adapted an empire is to its environment and neighboring civilizations, everyone else is trying to do more or less the same thing. As a result, the likelihood of continuing to survive doesn’t change. To quote mutual fund brochures, “past performance is not indicative of future results.” Any civilization, America or otherwise, either adapts or dies.

Each civilization thinks that it is exceptional, and it might be frustrating to see the survival of empires as so deeply unpredictable. But it’s also deeply humanizing to think about history this way. The human story is full of individual details, but it also has pattern and overall mathematical shape. And when we start to see it that way, we recognize that each civilization, no matter how alien or familiar it may seem, is but a single value within an overall distribution that enfolds us all.

Samuel Arbesman is a senior fellow at the Ewing Marion Kauffman Foundation. He is a regular contributor to Ideas. Follow him on Twitter @arbesm