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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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The English Revolt

Brexit, Euroscepticism and the future of the United Kingdom.

English voters have led – some would say forced – the United Kingdom towards exit from the European Union. Was this an English revolt, the result of an ­upsurge over decades of a more assertive, perhaps resentful, sense of English identity? At one level, clearly so. Surveys indicate that individuals who most often describe themselves as “English”, and regions where this is common, were more inclined to vote Leave on 23 June. Some of these are poorer regions where marginalised people think that their voices are more likely to be heard in a national democracy than in an international trading bloc, and for whom patriotism is a source of self-respect. But it would only make sense to regard Leave as essentially an English reaction if discontent with the EU were confined to England, or specifically linked with feelings of Englishness.

In fact, negative opinions about the EU, and especially about its economic policy, are now more widespread in other countries than they are in England. Polls by the Pew Research Centre last month showed that disapproval of the EU was as high in Germany and the Netherlands as in Britain, and higher in France, Greece and Spain. Though aggravated by the 2007-2008 crash and enforced policies of austerity, a decline in support was clear earlier. France’s referendum of May 2005 gave a 55 per cent No to the proposed EU constitution after thorough debate, and a now familiar pattern emerged: enthusiastic Europeanism was confined to the wealthiest suburbs and quarters of Paris, and the only professional groups that strongly voted Yes were big business, the liberal professions and academics.

Going far beyond the atavistic and incoherent English revolt that some think they discern, our referendum result is partly a consequence of transnational political phenomena across the democratic world: the disaffection of citizens from conventional politics, shown by falling turnouts for elections, shrinking party membership and the rise of new, sometimes extreme political movements; as well as the simultaneous detachment of a professional political class from civil society, and its consequent retreat into a closed world of institutions.

The EU embodies these phenomena in uniquely acute form. In several cases its central bodies have opposed – or, if one prefers, have been forced to deny – democratically expressed wishes. In Greece and Italy, the EU has enforced changes of government and policy, and in Denmark, Ireland and the Netherlands it has pressed countries to ignore or reverse popular referendums. Its own representative body, the European Parliament, has gained neither power nor legitimacy. Crucial decisions are taken in secret, making the EU a hiding place for beleaguered politicians as well as a source of lavish financial reward for insiders. In the words of the historian John Gillingham, Europe is now being governed by neither its peoples nor its ideals, but by a bank board. This is not the “superstate” of Eurosceptic mythology. Though it drains power and legitimacy away from national governments, it is incapable of exercising power effectively itself, whether to cope with short-term emergencies such as an inflow of refugees, or to solve chronic failings such as the creation of mass unemployment in southern Europe. The result is paralysis, the inability either to extricate itself from failing institutions or to make them work.

If popular discontent with the EU continues to increase (and it is hard to see how it could not) sooner or later there will be some unmanageable political or social crisis. The response of too many supporters of the EU is to screw the lid down tighter, including now by promising to make life difficult for the United Kingdom, pour décourager les autres. This is the organisation – unpopular, unaccountable, secretive, often corrupt, and economically failing – from which our decision to depart apparently causes people to weep in the streets.

***

Why this decision? Why in Britain? The simplest and perhaps the best answer is that we have had a referendum. If France, Greece, Italy and some other countries had been given the same choice, they might well have made the same decision. But of course they have not been and will not be given such a choice, barring severe political crisis. This is most obviously because countries that have adopted the euro – even those such as Greece, for which the IMF has predicted high unemployment at least until the 2040s – have no clear way out.

I make this obvious point to emphasise that the immediate explanation of what has happened lies not only and not mainly in different feelings about the EU in Britain, but in different political opportunities and levels of fear. The contrasting votes in Scotland and Northern Ireland have particular explanations. Scottish nationalists – like their counterparts in Catalonia – see the EU as an indispensable support for independence. Northern Ireland sees the matter primarily as one affecting its own, still tense domestic politics and its relations with the Republic. In a European perspective, Scotland and Northern Ireland are the outliers, not England and Wales. Indeed, Scotland’s vote makes it stand out as one of the most pro-EU countries in Europe. If ever there is another referendum to see whether Scots prefer the EU to the UK, it will show whether this level of support for the EU is solid.

If England is exceptional, it is not in its disaffection from the EU, nor in the political divisions the referendum vote has exposed (if France, for instance, had such a vote, one could expect blood in the streets). Rather, its exceptional characteristic is its long-standing and settled scepticism about the European project in principle, greater than in any other EU country. Every ­member has a specific history that shapes its attitude to the theoretical idea of European integration. As John Gillingham, one of the most perceptive historians of the EU, describes its beginnings: “to the French [supranationalism was] a flag of convenience, to the Italians it was preferable (by definition) to government by Rome, to the Germans a welcome escape route, and to the Benelux nations a better choice than being dominated by powerful neighbours”.

Subsequently, for the eastern European states, it was a decisive step away from communist dictatorship, and for southern Europe a line drawn under a traumatic history of civil conflict. There is also a widespread belief, powerful though fanciful, that the EU prevents war between the European states. All these are important reasons why there remains considerable support for unification as an aspiration. But all these reasons are weaker, and some of them non-existent, in Britain, and especially in England. The simple reason for this is that Britain’s experience of the 20th century was far less traumatic. Moreover, during that time loyalty to the nation was not tarnished with fascism, but was rather the buttress of freedom and democracy. Conversely, the vision of a European “superstate” is seen less as a guarantee of peace and freedom, and rather as the latest in a five-century succession of would-be continental hegemons.

Given all this, an obvious question is why the United Kingdom ever joined in the European project in the first place. The answer helps to explain the country’s subsequent lack of enthusiasm. Its first response to the creation of the European Economic Community in 1957 was not to join, but to agree to establish a separate European Free Trade Association (Efta) in 1959 with Austria, Denmark, Norway, Portugal, Sweden and Switzerland; over the next three decades the seven founder members were joined by Finland, Iceland and Liechtenstein. This worked efficiently, cheaply and amicably, and, in time, Efta and the EEC would doubtless have created trading arrangements and systems of co-operation. But then the historic mistake was made. Efta was considered too small to provide the diplomatic clout craved by Whitehall at a time of severe post-imperial jitters. A cabinet committee warned in 1960 that “if we try to remain aloof from [the EEC] – bearing in mind that this will be happening simultaneously with the contraction of our overseas possessions – we shall run the risk of losing political influence and of ceasing to be able to exercise any real claim to be a world Power”.

Besides, Washington disliked Efta as a barrier to its aim of a federal Europe, and the Americans put heavy pressure on London to apply to accede to the Treaty of Rome, which it duly did in August 1961. “It is only full membership, with the possibility of controlling and dominating Europe,” wrote an optimistic British cabinet official, “that is really attractive.”

As the former US secretary of state Dean Acheson (one of the early backers of European integration) put it, in a now celebrated comment in December 1962: “Great Britain has lost an empire, and has not yet found a role. The attempt to play a separate power role . . . apart from Europe . . . based on a ‘special relationship’ with the United States [or] on being the head of a ‘Commonwealth’ . . . – this role is about played out.”

Acheson’s words long haunted British policymakers; perhaps they still do. And yet Britain remains one of the half-dozen strongest and most assertive states anywhere in the world, just as it has been for the past three centuries.

To fear of diplomatic marginalisation was added fear of economic decline. A government report in 1953 warned of “relegation of the UK to the second division”. Over the next 30 years there was a chorus of dismay about “the sick man of Europe”. Belief that EEC membership at any price was the only cure for Britain’s perceived economic ills became the orthodoxy in official circles: Britain was “the sinking Titanic”, and “Europe” the lifeboat.

So, on 1 January 1973 Britain formally entered the EEC with Denmark and Ireland. Other Efta members remained outside the Community – Switzerland and Norway for good. Harold Wilson’s 1975 referendum on whether to stay in the EEC in effect turned on Europe’s superior economic performance – which, though no one realised it at the time, had just ended.

This memory of apparent British economic weakness half a century ago still seems to weigh with older Remainers. Yet it was based on a fundamental misconception: that European growth rates were permanently higher than in a supposedly outdated and declining Britain. In reality, faster growth on the mainland in the 1950s and 1960s was due to one-off structural modernisation: the large agricultural workforce shifted into more productive industrial employment. From the mid-1940s to the early 1970s this gave several European countries “windfall growth” at a higher rate than was possible in Britain, which since the 19th century had had no large agricultural sector to convert. By the early 1970s, once that catching up was finished, European growth rates became the same as, or slightly lower than, Britain’s. When measured over the whole half-century from 1950 to 2000, Britain’s economic performance was no different from the ­European norm. By the mid-1980s, growth was faster than in France and Germany, and today Britain’s economic fundamentals remain strong.

Slower European growth lessened the perceived attractiveness of EU integration. In 1992, on Black Wednesday (16 September), hesitant participation in the European Exchange Rate Mechanism led to forced devaluations in Finland, Sweden, Italy, Spain and, finally, Britain. This was a huge political shock, though an economic boost.

Black Wednesday subsequently made it politically difficult for Britain to join the eurozone – allowing us a narrow escape, attributable more to circumstance than to policy, as vocal political and economic lobbies urged joining.

Moreover, Britain’s trade with the rest of the EU was declining as a proportion of its global activity: as Gordon Brown observed in 2005, 80 per cent of the UK’s potential trade lay outside the EU. The EU’s single market proved not very effective at increasing trade between its members even before the crash of 2007-2008, and prolonged austerity thereafter made it stagnant. Consequently, in the 2016 referendum campaign, more emphasis was placed on the dangers of leaving the single market than on the precise benefits of being in it.

But the days when Britain seemed the Titanic and Europe the lifeboat were long gone. On the contrary, Britain, with its fluid and largely unregulated labour market, had become the employer of last resort for the depressed countries of the eurozone. The sustained importation of workers since the 1990s had become, for a large part of Britain’s working class, the thing that most obviously outweighed whatever legal or economic advantages the EU might theoretically offer.

***

What galvanised the vote for Brexit, I think, was a core attachment to national democracy: the only sort of democracy that exists in Europe. That is what “getting our country back” essentially means. Granted, the slogan covers a multitude of concerns and wishes, some of them irreconcilable; but that is what pluralist democracy involves. Britain has long been the country most ­resistant to ceding greater powers to the EU: opinion polls in the lead-up to the referendum showed that only 6 per cent of people in the UK (compared to 34 per cent in France, for instance, and 26 per cent in Germany) favoured increased centralisation – a measure of the feebleness of Euro-federalism in Britain.

In contrast, two-thirds wanted powers returned from the EU to the British government, with a majority even among the relatively Europhile young. This suggests a much greater opposition to EU centralisation than shown by the 52 per cent vote for Brexit. The difference may be accounted for by the huge pressure put on the electorate during the campaign. Indeed, arithmetic suggests that half even of Remain voters oppose greater powers being given to the EU. Yet its supporters regard an increase of EU control over economic and financial decisions – the basics of politics – as indispensable if the EU is to survive, because of the strains inherent in the eurozone system. This stark contradiction between the decentralisation that many of the peoples of Europe – and above all the British – want to see and the greater centralisation that the EU as an institution needs is wilfully ignored by Remain supporters. Those who deplore the British electorate’s excessive attachment to self-government as some sort of impertinence should be clear (not least with themselves) about whether they believe that the age of democracy in Europe is over, and that great decisions should be left to professional politicians, bureaucracies and large corporations.

Some have dismissed the Leave vote as an incoherent and anarchic protest against “the establishment”, or as a xenophobic reaction against immigrants. Some of the media in Britain and abroad have been doing their best to propagate this view. Yet xenophobia has not been a significant feature of British politics since the 1960s, and certainly far less so than in many obedient EU member states, including France, Germany, Greece and the Netherlands. As for the anti-establishment “revolt”, this emerged when parts of the establishment began to put organised pressure on the electorate to vote Remain. Would-be opinion-formers have hardly covered themselves in glory in recent weeks. They have been out of touch and out of sympathy with opinion in the country, unwilling or unable to engage in reasoned debate, and resorting to collective proclamations of institutional authority which proved embarrassingly ineffective.

Worst of all, their main argument – whether they were artists, actors, film-makers, university vice-chancellors or prestigious learned societies – was one of unabashed self interest: the EU is our milch-cow, and hence you must feed it. This was a lamentable trahison des clercs. The reaction to the referendum result by some Remain partisans has been a monumental fit of pique that includes talking up economic crisis (which, as Keynes showed, is often self-fulfilling) and smearing 17 million Leave voters as xenophobes. This is both irresponsible and futile, and paves the way to political marginalisation.

The Queen’s call for “deeper, cooler consideration” is much needed. I recall Victor Hugo’s crushing invective against French elitists who rejected the verdict of democracy, when in 1850 he scorned “your ignorance of the country today, the antipathy that you feel for it and that it feels for you”.

This antipathy has reduced English politics to a temporary shambles. It is too early to say whether there will be some realignment of the fragments: One-Nation Toryism, Conservative neoliberalism, “new” and “old” Labour, the hibernating Liberal Democrats and Greens, the various nationalists and, of course, the unpredictable Ukip. When in the past there were similar crises – such as Labour’s rift over the national government in 1931, the Liberals’ split over Irish home rule in 1886, or the Tory fragmentation over the repeal of the Corn Laws in 1846 – the political balance was permanently changed.

***

Many Europeans fear that a breakdown of the EU could slide into a return to the horrors of the mid-20th century. Most people in Britain do not. The fundamental feature of the referendum campaign was that the majority was not frightened out of voting for Leave, either by political or by economic warnings. This is testimony to a significant change since the last referendum in 1975: most people no longer see Britain as a declining country dependent on the EU.

A Eurobarometer poll in 2013 showed that Britain was the only EU member state in which most citizens felt that they could face the future better outside the Union. Last month’s referendum reflected this view, which was not reversed by reiterated predictions of doom.

In retrospect, joining the Common Market in 1973 has proved an immense historic error. It is surely evident that we would not have been applying to join the EU in 2016 had we, like Norway or Switzerland, remained outside it. Yet the political and possibly economic costs of leaving it now are considerable. Even though discontent with the EU across much of Europe has recently overtaken sentiment in Britain, Britain is unique, in that, ever since the 1970s, its public has been consistently far less ­favourable to the idea of European integration than the electorate in any other country. Hence the various “opt-outs” and the critically important decision to remain outside the euro.

Now, by a great historic irony, we are heading towards the sort of associate status with the EU that we had in the late 1960s as the leading member of Efta, and which we could have kept. Instead, this country was led by its political elite, for reasons of prestige and because of exaggerated fears of national decline and marginalisation, into a vain attempt to be “at the heart of Europe”. It has been a dangerous illusion, born of the postwar declinist obsession, that Britain must “punch above its weight” both by following in the footsteps of the United States and by attaching itself to the EU.

For some, money, blood and control over our own policy were sacrifices worth making for a “seat at the top table”. This dual strategy has collapsed. In future we shall have to decide what is the appropriate and desirable role for Britain to play in the world, and we shall have to decide it for ourselves.

Robert Tombs is Professor of French History at Cambridge University. His most recent book is “The English and Their History” (Penguin)

This article first appeared in the 21 July 2016 issue of the New Statesman, The English Revolt