Can a new mathematical model predict the endgame of empires? Peter Turchin says his work shows why the US is in crisis, and what will happen next

“Spending by the elite, who control the coffers, spirals until order cannot be maintained” (Image: AP Photo/Evan Vucci)

Editorial: “Can science stop government shutdowns?“

ON THE surface it seems inexplicable. The government of the most powerful country on earth has shut down and is dangerously close to defaulting on its debt. Its people and economy are feeling the consequences, and a new global financial crisis might not be far behind. And all this because a minority faction of one house of Congress will not approve a budget unless a healthcare measure that has already been passed into law is suspended.

But for Peter Turchin, a mathematical ecologist at the University of Connecticut in Storrs, the stand-off was predictable. He is one of a small group of people applying the mathematics of complex systems to political instability. They have been anticipating events just like this – and they say that if we don’t find some way to respond to the warning signs and change course, things are bound to get a lot worse before they get better.


Turchin has found what he believes to be historical cycles, two to three centuries long, of political instability and breakdown affecting states and empires from Rome to Russia. In a book he is finishing, he argues that similar cycles are evident in US history, and that they are playing out to this day. He admits that his theory, built on a model that combines social and economic data, must be tested against real events – but unlike most historical theories, it can be. Meanwhile, he says, it “predicts the long-term conditions that led to this shutdown”.

Workers or employees make up the bulk of any society, with a minority of employers constituting the top few per cent of earners. By mathematically modelling historical data, Turchin finds that as population grows, workers start to outnumber available jobs, driving down wages. The wealthy elite then end up with an even greater share of the economic pie, and inequality soars. This is borne out in the US, for example, where average wages have stagnated since the 1970s although gross domestic product has steadily climbed.

This process also creates new avenues – such as increased access to higher education – that allow a few workers to join the elite, swelling their ranks. Eventually this results in what Turchin calls “elite overproduction” – there being more people in the elite than there are top jobs. “Then competition starts to get ugly,” he says.

The richest continue to become richer: as in many complex systems, whether in nature or in society, existing advantage feeds back positively to create yet more. The rest of the elite fight it out, with rival patronage networks battling ever more fiercely. “There are always ideological differences, but elite overproduction explains why competition becomes so bitter, with no one willing to compromise,” Turchin says. This means the squabbling in Congress that precipitated the current shutdown is a symptom of societal forces at work, rather than the primary problem.

In Turchin’s theory, such political acrimony is paralleled by rising discontent among workers left with less and less, and increasing state bankruptcy as spending by the elite who control the government coffers spirals. Ultimately, the situation gets so bad that order cannot be maintained and the state collapses. A new cycle begins.

Spending by the elite, who control the coffers, spirals until order cannot be maintained

It may sound far-fetched. But in the last century, a slew of variables ranging from labour supply to public health indices, income inequality and the numbers and behaviour of the elite rose and fell in sync and as predicted by the theory. And with each glut of workers and peak in inequality came a surge in political violence.

Turchin finds that a simple mathematical model, combining economic output per person, the balance of labour demand and supply, and changes in attitudes towards redistributing wealth – the minimum wage level is one proxy for this – generates a curve that exactly matches the change in real wages since 1930, including complex rises and falls since 1980. Such close agreement between model and reality is exceptional in social sciences, says Turchin, and shows that all three factors control the rise of inequality, as predicted.

A set of 1590 instances of political violence in the US reveals peaceful periods around 1820 and 1950, with instability rising in between. Social data reflecting labour supply, inequality and elite overproduction match that basic fluctuation. Turchin thinks these changes explain the American civil war in the 1860s. The statistics also show that we are now in another phase of rising instability that began in the 1970s, just when, as his theory predicts, labour supply started outstripping demand.

In Turchin’s theory, this phase in the cycle should also be marked by political polarisation and rising government debt – both current crises in Washington. Real wages, the minimum wage, trade union suppression, the share of wealth owned by the richest one per cent, even filibusters and fights over judicial appointments – all have changed at the same time in ways reflecting reduced social consensus. Meanwhile, the elite class has grown sharply. Between the 1970s and 2010, college fees rose, yet the numbers of doctors and lawyers qualifying per head of population nearly trebled. Workers have steadily lost out. The “real shocker”, says Turchin, is that the average height of Americans peaked in 1975. It has actually declined in black women since then – a fact that could be down to falling nutrition standards linked to lower incomes. None of the trends shows any sign of reversing.

Yaneer Bar-Yam of the New England Complex Systems Institute in Cambridge, Massachusetts, agrees with Turchin’s finding of repeated cycles in history. However, he believes our current experience also reflects something new: technology has brought about the emergence of a complex, networked society, one that, he argues, existing democratic institutions are too simplistic to govern.

“The fall of the Soviet Union wasn’t the end of the story,” says Bar-Yam. He says that the US government could also fall apart unless its citizens choose to adapt by evolving decentralised, networked institutions more suited to managing complexity.

Dirk Helbing of the Swiss Federal Institute of Technology in Zurich agrees. He says what’s needed are fluid institutions that allow citizens to collaborate in a direct democracy to solve problems using next-generation social media. It works in a small country like Switzerland, and the time is ripe for it to be exported to larger states. “The technology that allows this is growing,” he says.

Shutdown in the time of cholera What does a cholera outbreak in Mexico have to do with the US government shutdown? Plenty. The Centers for Disease Control and Prevention (CDC) in Atlanta, Georgia, would normally monitor the situation to help prevent the disease spreading across the border. But the shutdown has put the agency out of action. The outbreak began just north of Mexico City in August and was exacerbated by flooding after Hurricane Ingrid last month. So far 75 cases have been reported in the state of Hidalgo, including one death, and two in Mexico City. People who are apparently healthy can spread the cholera bug. The Mexican outbreak is related to the strain introduced into Haiti in 2010 by travellers who appeared well, and which has since spread to Cuba and the Dominican Republic. Cholera could therefore spread in the US for some time undetected, warns James Wilson, who heads Ascel Bio, an epidemiology consultancy in Delta, Colorado, that is tracking the Mexican outbreak. In the absence of CDC monitoring, state public health agencies will do their best to be on the lookout for unusual outbreaks. But they need federal leadership, says Wilson. “With CDC effectively offline for situational awareness, our country is missing that heads-up.” Correction: When this article was first published on 9 October, it gave an incorrect figure for the cholera cases reported to date in Hidalgo state, Mexico. This has now been corrected.

This article appeared in print under the headline “Pattern behind the shutdown”