On 27 March 2009, President Barack Obama met a group of bank CEOs. Known for his cool head, on this occasion he lost his patience, though not because he was an enemy of the sector – the previous year, when he was still a senator, he had voted for a $700 billion bank bailout. After listening to the attempts by the CEOs to justify their sky-high salaries, the president interrupted them. ‘My administration’, he told them, ‘is the only thing between you and the pitchforks.’

It was a good line. At the time it sounded like the kind of exaggeration that is commonplace in politics. But as the recession took its toll, Obama’s words began to feel less like hyperbole than prophecy. By 2011, the typical US family was $5,000 a year worse off than before the recession. Working-class wages in the hardest-hit areas were permanently reduced. So-called ‘deaths of despair’, caused by suicide, alcohol or drug overdoses, skyrocketed, especially in working-class communities. Anger at establishment institutions rose. Populist movements gained momentum, and not just in the United States but around the world.

We know the rest of the story. Or at least, we know how it goes up to 2023. But how will it end? Probably not well, according to Peter Turchin, a Russian-American ‘complexity scientist’, best known as one of the founders of ‘cliodynamics’, a movement in historical scholarship that uses complex statistical models to predict the trajectories of societies (Clio is the Greek muse of history). Drawing on big data for societies across time and space, Turchin shows that periods of political instability are inevitable. Typically, they are the result of a cyclical process: ‘The most common pattern is an alternation of integrative and disintegrative phases lasting for roughly a century.’

The idea of history moving in cycles is as old as history itself. Both Plato and Aristotle offered a version of this thesis, and the Greek historian Polybius, writing in the second century BC, argued that societies move through a cycle of democracy, aristocracy and monarchy, each of which enters a period of degeneration before the next stage begins.

Hegel also argued that societies develop in a series of cycles, each of which is characterised by a certain spirit, or zeitgeist. Hegel used the metaphor of a plant to illustrate his idea of natural cycles in social history. (Appropriately enough, Turchin started his career as an ecologist.) Hegel influenced Marx and Engels, who emphasised the role of class conflict in providing the energy for each cycle of growth.

All of these thinkers were progressives at heart. Each turn of the historical wheel, in their view, drives us forward, one way or another. Turchin is less romantic. His models suggest that societies have periods where things are good (‘integrative phases’), followed by periods where everything goes to hell (‘disintegrative phases’), and so on. There’s nothing good about disintegration. The only thing to do is try to delay the disintegration phase, or to make it shorter and less costly.

The integrative phases are characterised by ‘internal peace, social stability, and relatively cooperative elites’. Crucially, in Turchin’s models, these are also periods where the proceeds of economic growth are reasonably evenly shared. Disintegrative phases, by contrast, are marked by ‘social instability, breakdown of cooperation among the elites, and persistent outbreaks of political violence, such as rebellions, revolutions, and civil wars’.

Turchin identifies four key early warning signs of a disintegrative phase. First, ‘popular immiseration’, which creates the conditions for mass anti-establishment movements. Immiseration can be tracked by economic indicators, especially the relative wage, a measure of how far wage levels for the typical worker track economic growth as a whole. In the United States, relative wages have been falling in recent decades after rising rapidly in the middle decades of the 20th century. ‘Relative wages have not declined in such a sustained manner since the three decades between 1830 and 1860,’ Turchin writes.

The second warning sign is ‘failing fiscal health and weakened legitimacy of the state’. As I write, the United States is embroiled yet again in an embarrassing political wrangle over the debt ceiling. Only 2 per cent of Americans trust the federal government to do what is right ‘just about always’, and only 19 per cent say they trust it ‘most of the time’.

The third warning sign is turbulence in external affairs, marked specifically by disruptive foreign wars or revolutions. It looks like the war in Ukraine counts here.

So far, so familiar. But the fourth factor is much less so. According to Turchin, ‘intraelite competition and conflict’ is the single biggest predictor of instability. The condition to watch for here is ‘elite overproduction’. This occurs when there are not enough elite roles for the number of people who feel entitled to them. A contemporary example is the gap between the number of college graduates and the number of jobs that actually require a degree.

According to Turchin’s models, the ‘frustrated elite aspirant class’ is ‘the most dangerous class for societal stability’. That is because it can form an anti-establishment counter-elite, often drawing strength from the discontented masses, with destabilising effects. That was true for ancient Rome, where Tiberius founded a so-called populist party (populares in Latin), and it is true for the modern United States, where a populist movement has taken shape under Donald Trump, a man with a chip on his shoulder too large for any amount of money to dislodge.

Turchin explains why, in spite of the overproduction of elites there, Britain in the 19th century managed to avoid a period of disintegration: the mother country simply exported the surplus elite overseas to run the colonies. He also offers an explanation of why integrative phases last an average of two centuries in monogamous societies but only one century in polygamous ones. In polygamous societies, high-status men are able to produce many more offspring, which accelerates the process of elite overproduction.

The bad news is that Turchin’s model suggests that the 2020s are unavoidably set to be a period of disintegration. Our goal has to be to minimise the damage, the social equivalent of building levees to hold back the rising seas. The better news is that we can avoid another, perhaps deeper, period of social breakdown later in the century. That, though, will require a more equitable sharing of economic resources, greater fiscal responsibility, geopolitical stabilisation and a reduction in the oversupply of elites, perhaps by slowing the educational arms race. As it happens, these are all good things to do in and of themselves.

Obama’s warning to the bankers evoked an image of proletarian uprising. But, as Turchin points out, the counter-elites are usually formed of professionals – teachers, like Hong Xiuquan, the leader of the 19th-century Taiping rebellion, or lawyers, like Robespierre, Lenin and Castro. They might be real-estate moguls, financiers or journalists. Revolutionaries almost always have more credentials than callouses. They don’t carry pitchforks. They do, however, bear grudges, which makes them all the more dangerous.