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Now you see it, now you don't: what optical illusions tell us about our brains

Illusions can offer insights into how the visual system processes images.

Maurits Escher: where do the staircases lead?

The human brain is a network of about 20 billion neurons – nerve cells – linked by several trillion connections. Not to mention glial cells, which scientists used to think were inactive scaffolding, but increasingly view as an essential part of how the brain works. Our brains give us movement, language, senses, memories, consciousness and personality. We know a lot more about the brain than we used to, but it still seems far too complicated for human understanding.

Fortunately, the brain contains many small networks of neurons that carry out some specific function: vision, hearing, movement. It makes sense to tackle these simple modules first. Moreover, we have good mathematical models of nerve cell behaviour. In 1952, Alan Hodgkin and Andrew Huxley wrote down the “Hodgkin-Huxley equations” for the transmission of a nerve impulse, which won them the 1963 Nobel Prize in Medicine. We also have effective techniques for understanding small networks’ components and how they are linked.

Many of these simple networks occur in the visual system. We used to think that the eye was like a camera, taking a “snapshot” of the outside world that was stored in the brain like a photo stuck in an album. It uses a lens to focus an image on to the retina at the back of the eye, which functions a bit like a roll of film – or, in today’s digital cameras, a charge-coupled device, storing an image pixel by pixel. But we now know that when the retina sends information to the brain’s visual cortex, the similarity to a camera ends.

Although we get a strong impression that what we are seeing is “out there” in front of us, what determines that perception resides inside our own heads. The brain decomposes images into simple pieces, works out what they are, “labels” them with that information, and reassembles them. When we see three sheep and two pigs in a field, we “know” which bits are sheep, which are pigs, and how many of each there are. If you try to program a computer to do that, you quickly realise how tricky the process is. Only very recently have computers been able to distinguish between faces, let alone sheep and pigs.

Probing the brain’s detailed activity is difficult. Rapid progress is being made, but it still takes a huge effort to get reliable information. But when science cannot observe something directly, it infers it, working indirectly. An effective way to infer how something functions is to see what it does when it goes wrong. It may be hard to understand a bridge while it stays up, but you can learn a lot about strength of materials when it collapses.

The visual system can “go wrong” in several interesting ways. Hallucinogenic drugs can change how neurons behave, producing dramatic images such as spinning spirals, which originate not in the eye, but in the brain. Some images even cause the brain to misinterpret what it’s seeing without outside help. We call them optical illusions.

One of the earliest was discovered in Renaissance Italy in the 16th century. Giambattista della Porta was the middle of three surviving sons of a wealthy merchant nobleman who became secretary to the Holy Roman emperor Charles V. The father was an intellectual, and Giambattista grew up in a house in Naples that hosted innumerable mathematicians, scientists, poets and musicians. He became an outstanding polymath, with publications on secret codes (including writing on the inside of eggshells), physiology, botany, agriculture, engineering, and much else. He wrote more than 20 plays.

Della Porta was particularly interested in the science of light. He made definitive improvements to the camera obscura, a device that projects an image of the outside world into a darkened room; he claimed to have invented the telescope before Galileo, and very likely did. His De refractione optices of 1593 contained the first report of a curious optical effect. He arranged two books so that one was visible to one eye only and the other to the other eye. Instead of seeing a combination of the two images, he perceived them alternately. He discovered that he could select either image at will by consciously switching his attention. This phenomenon is known today as binocular rivalry.

Two other distinct but related effects are impossible figures and visual illusions. In rivalry, each image appears unambiguous, but the eyes are shown conflicting images. In the other two phenomena, both eyes see the same image, but in one case it doesn’t make sense, and in the other it makes sense but is ambiguous.

Impossible figures at first sight seem to be entirely normal, but depict things that cannot exist – such as Roger Shepard’s 1990 drawing of an elephant in which everything above the knees makes sense, and everything below the knees makes sense, but the two regions do not fit together correctly. The Dutch artist Maurits Escher made frequent use of this kind of visual quirk.

In 1832, the Swiss crystallographer Louis Necker invented his “Necker cube” illusion, a skeletal cube that seems to switch its orientation repeatedly. An 1892 issue of the humorous German magazine Fliegende Blätter contains a picture with the caption “Which animals are most like each other?” and the answer “Rabbit and duck”. In a 1915 issue of the American magazine Puck, the cartoonist Ely William Hill published “My wife and my mother-in-law”, based on an 1888 German postcard. The image can be seen either as a young lady looking back over her shoulder, or as an elderly woman facing forwards. Several of Salvador Dalí’s paintings include illusions; especially Slave Market With the Apparition of the Invisible Bust of Voltaire, where a number of figures and everyday objects, carefully arranged, combine to give the impression of the French writer’s face.

Illusions offer insights into how the visual system processes images. The first few stages are fairly well understood. The top layer in the visual cortex detects edges of objects and the direction in which they are pointing. This information is passed to lower layers, which detect places where the direction suddenly changes, such as corners. Eventually some region in the cortex detects that you are looking at a human face and that it belongs to Aunt Matilda. Other parts of the brain are alerted, and you belatedly remember that tomorrow is her birthday and hurry off to buy a present.

These things don’t happen by magic. They have a very definite rationale, and that’s where the mathematics comes in. The top layer of the visual cortex contains innumerable tiny stacks of nerve cells. Each stack is like a pile of pancakes, and each pancake is a network of neurons that is sensitive to edges that point in one specific direction: one o’clock, two o’clock and so on.

For simplicity, call this network a cell; it does no harm to think of it as a single neuron. Roughly speaking, the cell at the top of the stack senses edges at the one o’clock position, the next one down corresponds to the two o’clock angle, and so on. If one cell receives a suitable input signal, it “fires”, telling all the other cells in its stack: “I’ve seen a boundary in the five o’clock direction.” However, another cell in the same stack might disagree, claiming the direction is at seven o’clock. How to resolve this conflict?

Neurons are linked by two kinds of connection, excitatory and inhibitory. If a neuron activates an excitatory connection, those at the other end of it are more likely to fire themselves. An inhibitory connection makes them less likely to fire. The cortex uses inhibitory connections to reach a definite decision. When a cell fires, it sends inhibitory signals to all of the other cells in its stack. These signals compete for attention. If the five o’clock signal is stronger than the seven o’clock one, for instance, the seven o’clock one gets shut down. The cells in effect “vote” on which direction they are detecting and the winner takes all.

Many neuroscientists think that something very similar is going on in visual illusions and rivalry. Think of the duck and rabbit with two possible interpretations. Hugh R Wilson, a neuroscientist at the Centre for Vision Research at York University, Toronto, proposed the simplest model, one stack with just two cells. Rodica Curtu, a mathematician at the University of Iowa, John Rinzel, a biomathematician then at the National Institutes of Health, and several other scientists have analysed this model in more detail. The basic idea is that one cell fires if the picture looks like a duck, the other if it resembles a rabbit. Because of the inhibitory connections, the winner should take all. Except that, in this illusion, it doesn’t quite work, because the two choices are equally plausible. That’s what makes it an illusion. So both cells want to fire. But they can’t, because of those inhibitory connections. Yet neither can they both remain quiescent, because the incoming signals encourage them to fire.

One possibility is that random signals coming from elsewhere in the brain might introduce a bias of perception, so that one cell still wins. However, the mathematical model predicts that, even without such bias, the signals in both cells should oscillate from active to inactive and back again, each becoming active when the other is not. It’s as if the network is dithering: the two cells take turns to fire and the network perceives the image as a duck, then as a rabbit, and keeps switching from one to the other. Which is what happens in reality.

Generalising from this observation, Wilson proposed a similar type of network that can model decision-making in the brain – which political party to support, for instance. But now the network consists of several stacks. Maybe one stack represents immigration policy, another unemployment, a third financial regulation, and so on. Each stack consists of cells that “recognise” a distinct policy feature. So the financial regulation stack has cells that recognise state regulation by law, self-regulation by the industry, or free-market economics.

The overall political stance of any given political party is a choice of one cell from each stack – one policy decision on each issue. Each prospective voter has his or her preferences, and these might not match those of any particular party. If these choices are used as inputs to the network, it will identify the party that most closely fits what the voter prefers. That decision can then be passed to other areas of the brain. Some voters may find themselves in a state akin to a visual illusion, vacillating between Labour and Liberal Democrat, or Conservative and Ukip.

This idea is speculative and it is not intended to be a literal description of how we decide whom to vote for. It is a schematic outline of something more complex, involving many regions of the brain. However, it provides a simple and flexible model for decision-making by a neural network, and in particular it shows that simple networks can do the job quite well. Martin Golubitsky of the Mathematical Biosciences Institute at Ohio State University and Casey O Diekman of the University of Michigan wondered whether Wilson’s networks could be used to model more complex examples of rivalry and illusions. Crucially, the resulting models allow specific predictions about experiments that have not yet been performed, making the whole idea scientifically testable.

The first success of this approach helped to explain an experiment that had already been carried out, with puzzling results. When the brain reassembles the separate bits of an image, it is said to “bind” these pieces. Rivalry provides evidence that binding occurs, by making it go wrong. In a rivalry experiment carried out in 2006 by S W Hong and S K Shevell, the subject’s left eye is shown a horizontal grid of grey and pink lines while the right eye sees a vertical grid of grey and green lines. Many subjects perceive an alternation between the images, just as della Porta did with his books. But some see two different images alternating: pink and green vertical lines, and pink and green horizontal lines – images shown to neither eye. This effect is called colour misbinding; it tells us that the reassembly process has matched colour to grid direction incorrectly. It is as if della Porta had ended up seeing another book altogether.

Golubitsky and Diekman studied the simplest Wilson network corresponding to this experiment. It has two stacks: one for colour, one for grid direction. Each stack has two cells. In the “colour” stack one cell detects pink and the other green; in the “orientation” stack one cell detects vertical and the other horizontal. As usual, there are inhibitory connections within each stack to ensure a winner-takes-all decision.

Following Wilson’s general scheme, they also added excitatory connections between cells in distinct stacks, representing the combinations of colour and direction that occur in the two “learned” images – those actually presented to the two eyes. Then they used recent mathematical techniques to list the patterns that arise in such a network. They found two types of oscillatory pattern. One corresponds to alternation between the two learned images. The other corresponds precisely to alternation between the two images seen in colour misbinding.

Colour misbinding is therefore a natural feature of the dynamics of Wilson networks. Although the network is “set up” to detect the two learned images, its structure produces an unexpected side effect: two images that were not learned. The rivalry experiment reveals hints of the brain’s hidden wiring. The same techniques apply to many other experiments, including some that have not yet been performed. They lead to very specific predictions, including more circumstances in which subjects will observe patterns that were not presented to either eye.

Similar models also apply to illusions. However, the excitatory connections cannot be determined by the images shown to the two eyes, because both eyes see the same image. One suggestion is that the connections may be determined by what your visual system already “knows” about real objects.

Take the celebrated moving illusion called “the spinning dancer”. Some observers see the solid silhouette of a dancer spinning anticlockwise, others clockwise. Sometimes, the direction of spin seems to switch suddenly.

We know that the top half of a spinning dancer can spin either clockwise or anticlockwise. Ditto for the bottom half. In principle, if the top half spins one way but the bottom half spins the other way, you would see the same silhouette, as if both were moving together. When people are shown “the spinning dancer”, no one sees the halves moving independently. If the top half spins clockwise, so does the bottom half.

Why do our brains do this? We can model that information using a series of stacks that correspond to different parts of the dancer’s body. The brain’s prior knowledge sets up a set of excitatory connections between all cells that sense clockwise motion, and another set of excitatory connections between all “anticlockwise” cells. We can also add inhibitory connections between the “clockwise” and the “anticlockwise” cells. These connections collectively tell the network that all parts of the object being perceived must spin in the same direction at any instant. Our brains don’t allow for a “half and half” interpretation.

When we analyse this network mathematically, it turns out that the cells switch repeatedly between a state in which all clockwise cells are firing but the anticlockwise ones are quiescent, and a state in which all anticlockwise cells are firing but the clockwise ones are quiescent. The upshot is that we perceive the whole figure of the dancer switching directions. Similar networks provide sensible models for many other illusions, including some in which there are three different inputs.

These models provide a common framework for both rivalry and illusion, and they unify many experiments, explain otherwise puzzling results and make new predictions that can be tested. They also tell us that in principle the brain can carry out some apparently complex tasks using simple networks. (What it does in practice is probably different in detail, but could well follow the same general lines.)

This could help make sense of a real brain, as new experiments improve our ability to observe its “wiring diagram”. It might not be as ambitious as trying to model the whole thing on a computer, but modesty can be a virtue. Since simple networks behave in strange and unexpected ways, what incomprehensible quirks might a complicated network have?

Perhaps Dalí, and Escher, and the spinning dancer can help us find out. 

Ian Stewart is Emeritus Professor of Mathematics and Digital Media Fellow at the University of Warwick

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Why the elites always rule

Since an Italian sociologist coined the word “elite” in 1902, it has become a term of abuse. But history is the story of one elite replacing another – as the votes for Trump and Brexit have shown.

Donald Trump’s successful presidential campaign was based on the rejection of the “establishment”. Theresa May condemned the rootless “international elites” in her leader’s speech at last October’s Conservative party conference. On the European continent, increasingly popular right-wing parties such as Marine Le Pen’s Front National and the German Alternative für Deutschland, as well as Poland’s ruling Law and Justice party, delight in denouncing the “Eurocratic” elites. But where does the term “elite” come from, and what does it mean?

It was Vilfredo Pareto who, in 1902, gave the term the meaning that it has today. We mostly think of Pareto as the economist who came up with ideas such as “Pareto efficiency” and the “Pareto principle”. The latter – sometimes known as the “power law”, or the “80/20 rule” – stipulates that 80 per cent of the land always ends up belonging to 20 per cent of the population. Pareto deduced this by studying land distribution in Italy at the turn of the 20th century. He also found that 20 per cent of the pea pods in his garden produced 80 per cent of the peas. Pareto, however, was not only an economist. In later life, he turned his hand to sociology, and it was in this field that he developed his theory of the “circulation of elites”.

The term élite, used in its current socio­logical sense, first appeared in his 1902 book Les systèmes socialistes (“socialist systems”). Its aim was to analyse Marxism as a new form of “secular” religion. And it was the French word élite that he used: naturally, one might say, for a book written in French. Pareto, who was bilingual, wrote in French and Italian. He was born in Paris in 1848 to a French mother and an Italian father; his father was a Genoese marquis who had accompanied the political activist Giuseppe Mazzini into exile. In honour of the revolution that was taking place in Germany at the time, Pareto was at first named Fritz Wilfried. This was latinised into Vilfredo Federico on the family’s return to Italy in 1858.

When Pareto wrote his masterpiece – the 3,000-page Trattato di sociologia ­generale (“treatise on general sociology”) – in 1916, he retained the French word élite even though the work was in Italian. Previously, he had used “aristocracy”, but that didn’t seem to fit the democratic regime that had come into existence after Italian unification. Nor did he want to use his rival Gaetano Mosca’s term “ruling class”; the two had bitter arguments about who first came up with the idea of a ruling minority.

Pareto wanted to capture the idea that a minority will always rule without recourse to outdated notions of heredity or Marxist concepts of class. So he settled on élite, an old French word that has its origins in the Latin eligere, meaning “to select” (the best).

In the Trattato, he offered his definition of an elite. His idea was to rank everyone on a scale of one to ten and that those with the highest marks in their field would be considered the elite. Pareto was willing to judge lawyers, politicians, swindlers, courtesans or chess players. This ranking was to be morally neutral: beyond “good and evil”, to use the language of the time. So one could identify the best thief, whether that was considered a worthy profession or not.

Napoleon was his prime example: whether he was a good or a bad man was irrelevant, as were the policies he might have pursued. Napoleon had undeniable political qualities that, according to Pareto, marked him out as one of the elite. Napoleon is important
because Pareto made a distinction within the elite – everyone with the highest indices within their branch of activity was a member of an elite – separating out the governing from the non-governing elite. The former was what interested him most.

This is not to suggest that the non-governing elite and the non-elite were of no interest to him, but they had a specific and limited role to play, which was the replenishment of the governing elite. For Pareto, this group was the key to understanding society as a whole – for whatever values this elite incarnated would be reflected in society. But he believed that there was an inevitable “physiological” law that stipulated the continuous decline of the elite, thereby making way for a new elite. As he put it in one of his most memorable phrases, “History is the graveyard of elites.”

***

Pareto’s thesis was that elites always rule. There is always the domination of the minority over the majority. And history is just the story of one elite replacing another. This is what he called the “circulation of elites”. When the current elite starts to decline, it is challenged and makes way for another. Pareto thought that this came about in two ways: either through assimilation, the new elite merging with elements of the old, or through revolution, the new elite wiping out the old. He used the metaphor of a river to make his point. Most of the time, the river flows continuously, smoothly incorporating its tributaries, but sometimes, after a storm, it floods and breaks its banks.

Drawing on his Italian predecessor Machiavelli, Pareto identified two types of elite rulers. The first, whom he called the “foxes”, are those who dominate mainly through combinazioni (“combination”): deceit, cunning, manipulation and co-optation. Their rule is characterised by decentralisation, plurality and scepticism, and they are uneasy with the use of force. “Lions”, on the other hand, are more conservative. They emphasise unity, homogeneity, established ways, the established faith, and rule through small, centralised and hierarchical bureaucracies, and they are far more at ease with the use of force than the devious foxes. History is the slow swing of the pendulum from one type of elite to the other, from foxes to lions and back again.

The relevance of Pareto’s theories to the world today is clear. After a period of foxes in power, the lions are back with renewed vigour. Donald Trump, as his behaviour during the US presidential campaign confirmed, is perfectly at ease with the use of intimidation and violence. He claimed that he wants to have a wall built between the United States and Mexico. His mooted economic policies are largely based on protectionism and tariffs. Regardless of his dubious personal ethics – a classic separation between the elite and the people – he stands for the traditional (white) American way of life and religion.

This is in stark contrast to the Obama administration and the Cameron government, both of which, compared to what has come since the votes for Trump and Brexit, were relatively open and liberal. Pareto’s schema goes beyond the left/right divide; the whole point of his Systèmes socialistes was to demonstrate that Marxism, as a secular religion, signalled a return to faith, and thus the return of the lions in politics.

In today’s context, the foxes are the forces of globalisation and liberalism – in the positive sense of developing an open, inter­connected and tolerant world; and in the negative sense of neoliberalism and the dehumanising extension of an economic calculus to all aspects of human life. The lions represent the reaction, centring themselves in the community, to which they may be more attentive, but bringing increased xenophobia, intolerance and conservatism. For Pareto, the lions and foxes are two different types of rule, both with strengths and weaknesses. Yet the elite is always composed of the two elements. The question is: which one dominates at any given time?

What we know of Theresa May’s government suggests that she runs a tight ship. She has a close – and closed – group of confidants, and she keeps a firm grip on the people under her. She is willing to dispense with parliament in her negotiation of Brexit, deeming it within the royal prerogative. Nobody yet knows her plan.

The European Union is a quintessentially foxlike project, based on negotiation, compromise and combination. Its rejection is a victory of the lions over the foxes. The lions are gaining prominence across the Western world, not just in Trumpland and Brexit Britain. Far-right movements have risen by rejecting the EU. It should come as no surprise that many of these movements (including Trump in the US) admire Vladimir Putin, at least for his strongman style.

Asia hasn’t been spared this movement, either. After years of tentative openness in China, at least with the economy, Xi Jinping has declared himself the “core” leader, in the mould of the previous strongmen Mao Zedong and Deng Xiaoping. Japan’s prime minister, Shinzo Abe, has also hardened his stance, and he was the first world leader to meet with President-Elect Donald Trump. Narendra Modi in India and Rodrigo Duterte in the Philippines are in the same mould, the latter coming to power on the back of promising to kill criminals and drug dealers. After the failed coup against him in July, Recep Tayyip Erdogan has also been cracking down on Turkey.

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In Les systèmes socialistes, Pareto elaborated on how a new elite replaces the old. A, the old elite, would be challenged by B, the new, in alliance with C, the people. B would win the support of C by making promises that, once in power, it wouldn’t keep. If that sounds like the behaviour of most politicians, that is because it probably is. But what Pareto was pointing out was how, in its struggle for power, the new elite politicised groups that were not political before.

What we know of Trump supporters and Brexiteers is that many feel disenfranchised: the turnout in the EU referendum could not have been greater than in the 2015 general election otherwise, and significant numbers of those who voted for Trump had never voted before. There is no reason to think that they, too, won’t be betrayed by the new leaders they helped to bring to power.

In the last years of his life, Pareto offered a commentary on Italy in the 1920s. He denounced the state’s inability to enforce its decisions and the way that Italians spent their time flaunting their ability to break the law and get away with it. He coined the phrase “demagogic plutocracy” to characterise the period, in which the rich ruled behind a façade of democratic politics. He thought this particularly insidious for two reasons: those in power were more interested in siphoning off wealth for their personal ends than encouraging the production of new wealth, and consequently undermined national prosperity (remember Pareto’s training as an economist); and, as the demagogic elites govern through deceit and cunning, they are able to mask their rule for longer periods.

Much has been made of Trump’s “populism”, but the term “demagogic plutocrat” seems particularly apt for him, too: he is a wealthy man who will advance the interests of his small clique to the detriment of the well-being of the nation, all behind the smokescreen of democratic politics.

There are other ways in which Pareto can help us understand our predicament. After all, he coined the 80/20 rule, of which we hear an intensified echo in the idea of “the One Per Cent”. Trump is a fully paid-up member of the One Per Cent, a group that he claims to be defending the 99 Per Cent from (or, perhaps, he is an unpaid-up member, given that what unites the One Per Cent is its reluctance to pay taxes). When we perceive the natural inequality of the distribution of resources as expressed through Pareto’s “power law”, we are intellectually empowered to try to do something about it.

Those writings on 1920s Italy landed Pareto in trouble, as his theory of the circulation of elites predicted that a “demagogic plutocracy”, dominated by foxes, would necessarily make way for a “military plutocracy”, this time led by lions willing to restore the power of the state. In this, he was often considered a defender of Mussolini, and Il Duce certainly tried to make the best of that possibility by making Pareto a senator. Yet there is a difference between prediction and endorsement, and Pareto, who died in 1923, had already been living as a recluse in Céligny in Switzerland for some time – earning him the nickname “the hermit of Céligny” – with only his cats for company, far removed from day-to-day Italian politics. He remained a liberal to his death, content to stay above the fray.

Like all good liberals, Pareto admired Britain above all. As an economist, he had vehemently defended its system of free trade in the face of outraged opposition in Italy. He also advocated British pluralism and tolerance. Liberalism is important here: in proposing to set up new trade barriers and restrict freedom of movement, exacerbated by their more or less blatant xenophobia, Trump and Brexit challenge the values at the heart of the liberal world.

***


What was crucial for Pareto was that new elites would rise and challenge the old. It was through the “circulation of elites” that history moved. Yet the fear today is that history has come to a standstill, that elites have ­become fossilised. Electors are fed up with choosing between the same old candidates, who seem to be proposing the same old thing. No wonder people are willing to try something new.

This fear of the immobility of elites has been expressed before. In 1956, the American sociologist C Wright Mills published The Power Elite. The book has not been out of print since. It is thanks to him that the term was anglicised and took on the pejorative sense it has today. For Mills, Cold War America had come to be dominated by a unified political, commercial and military elite. With the 20th century came the growth of nationwide US corporations, replacing the older, more self-sufficient farmers of the 19th century.

This made it increasingly difficult to ­distinguish between the interests of large US companies and those of the nation as a whole. “What’s good for General Motors,” as the phrase went, “is good for America.” As a result, political and commercial interests were becoming ever more intertwined. One had only to add the Cold War to the mix to see how the military would join such a nexus.

Mills theorised what President Dwight D Eisenhower denounced in his January 1961 farewell speech as the “military-industrial complex” (Eisenhower had wanted to add the word “congressional”, but that was thought to be too risky and was struck out of the speech). For Mills, the circulation of elites – a new elite rising to challenge the old – had come to an end. If there was any circulation at all, it was the ease with which this new power elite moved from one part of the elite to the other: the “revolving door”.

The Cold War is over but there is a similar sense of immobility at present concerning the political elite. Must one be the child or wife of a past US president to run for that office? After Hillary Clinton, will Chelsea run, too? Must one have gone to Eton, or at least Oxford or Cambridge, to reach the cabinet? In France is it Sciences Po and Éna?

The vote for Brexit, Trump and the rise of the far right are, beyond doubt, reactions to this sentiment. And they bear out Pareto’s theses: the new elites have aligned themselves with the people to challenge the old elites. The lions are challenging the foxes. Needless to say, the lions, too, are prototypically elites. Trump is a plutocrat. Boris Johnson, the co-leader of the Leave campaign, is as “establishment” as they come (he is an Old Etonian and an Oxford graduate). Nigel Farage is a public-school-educated, multimillionaire ex-stockbroker. Marine Le Pen is the daughter of Jean-Marie Le Pen. Putin is ex-KGB.

Pareto placed his hopes for the continuing circulation of elites in technological, economic and social developments. He believed that these transformations would give rise to new elites that would challenge the old political ruling class.

We are now living through one of the biggest ever technological revolutions, brought about by the internet. Some have argued that social media tipped the vote in favour of Brexit. Arron Banks’s Leave.EU website relentlessly targeted disgruntled blue-collar workers through social media, using simple, sometimes grotesque anti-immigration messages (as a recent profile of Banks in the New Statesman made clear) that mimicked the strategies of the US hard right.

Trump’s most vocal supporters include the conspiracy theorist Alex Jones, who has found the internet a valuable tool for propagating his ideas. In Poland, Jarosław Kaczynski, the leader of the Law and Justice party, claims that the Russian plane crash in 2010 that killed his twin brother (then the country’s president) was a political assassination, and has accused the Polish prime minister of the time, Donald Tusk, now the president of the European Council, of being “at least morally” responsible. (The official explanation is that the poorly trained pilots crashed the plane in heavy fog.)

It need not be like this. Silicon Valley is a world unto itself, but when some of its members – a new technological elite – start to play a more active role in politics, that might become a catalyst for change. In the UK, it has been the legal, financial and technological sectors that so far have led the pushback against a “hard” Brexit. And we should not forget how the social movements that grew out of Occupy have already been changing the nature of politics in many southern European countries.

The pendulum is swinging back to the lions. In some respects, this might be welcome, because globalisation has left too many behind and they need to be helped. However, Pareto’s lesson was one of moderation. Both lions and foxes have their strengths and weaknesses, and political elites are a combination of the two, with one element dominating temporarily. Pareto, as he did in Italy in the 1920s, would have predicted a return of the lions. But as a liberal, he would have cautioned against xenophobia, protectionism and violence.

If the lions can serve as correctives to the excesses of globalisation, their return is salutary. Yet the circulation of elites is a process more often of amalgamation than replacement. The challenge to liberal politics is to articulate a balance between the values of an open, welcoming society and of one that takes care of its most vulnerable members. Now, as ever, the task is to find the balance between the lions and the foxes. l

Hugo Drochon is the author of “Nietzsche’s Great Politics” (Princeton University Press)

This article first appeared in the 12 January 2017 issue of the New Statesman, Putin's revenge