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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 biggest blunder of them all

It was a catastrophic error of judgement that produced the referendum – and now the British political class is paying the price.

AAs dawn broke on Friday morning and I turned over in bed to grab my phone and Twitter, I thought immediately of G K Chesterton’s poem from 1915, about the secret people of England:

 

Smile at us, pay us, pass us; but do not quite forget.
For we are the people of England, that never have spoken yet.
There is many a fat farmer that drinks less cheerfully,
There is many a free French peasant who is richer and sadder than we.
There are no folk in the whole world so helpless or so wise.
There is hunger in our bellies, there is laughter in our eyes;
You laugh at us and love us, both mugs and eyes are wet:
Only you do not know us. For we have not spoken yet.

 

Well, they have spoken now. This was a quietly devastating revolt by the English heartlands – southern and western suburbs; the urban sprawls of the Midlands and the north; former mining areas and devastated ex-industrial towns – against London, Scotland, Northern Ireland and the so-called elites. Looking at the numbers, one sees that it was a revolt also by older voters against younger voters and by poorer against richer, better-educated voters. It was, of course, a great democratic moment. Apart from the hideous and probably unconnected murder of Jo Cox, it was accomplished peacefully, and by a majority of well over a million. That sets it aside from Chesterton’s vision, which moves on from benign, bucolic defiance to outright anti-Semitism and warnings of blood-drenched revolution. Well, that’s the beauty of modern democracy . . .

The decision by the British people to leave the European Union is this country’s single biggest democratic act in modern times – indeed, as far as I can make out, the biggest ever. But it is also one of the elite’s most significant blunders, provoked by the most senior politicians for the wrong reasons and then pursued in what (to use a crude but apposite phrase) is the biggest establishment cock-up in my lifetime.

We should not fall into the trap, though, of seeing this as a purely British story. It is also about the EU, now looking more fragile than at any other time since the 1950s, and about what is still our common European home. There are calls for national revolt against the EU coming from across the continent. Far too many of the continent’s leaders welcoming our decision were the wrong sort of people. Mostly, the congratulations are coming from far-right parties, whose most lurid and upsetting rhetoric has emerged from central and eastern Europe. If you think I’m exaggerating, go on to YouTube, type “Visegrad”, and spend ten minutes watching. If this vote presages a process of messy and angry dissolution, it’s a story that will have started here. But that is only the beginning. If Marine Le Pen wins the French presidential election, then a French exit from the EU looks very likely – and that really is the end of it all.

Hurrah, many people will say: but we should reflect that this will demand negotiation of many individual trade deals with the leaders of angry and fractured European nations, which will clearly be a lot harder than any single deal with the EU. And then, there are the darker forebodings about Europe, which has never managed to stay at peace with itself for long as a constellation of independent countries. Immigration pressures and the Russian threat are just a couple of possible sources of future conflict.

But there are better outcomes. For the UK the optimal one now is clearly “Norway-plus”: meaning, in essence, restrictions on the free movement of people but access to the single market. Unless the victorious team of Brexit Tories is bonkers, this is what they will try to negotiate. It would minimise the threat of all-out economic disruption, which has already begun, and answer the biggest complaint from Leave voters. To which the obvious retort is: “Why in a million years would they give us that?” Well, as leaders in France, Germany, the Netherlands and other countries contemplate their own populist insurgencies, they must know that a rethink of freedom to work across borders is their best card against the insurgent right. There is a slim, but not entirely negligible, chance that a much wider rethink across the EU will now be prompted by the British decision.

This is not something that will be decided here. Is it possible that leaders in Brussels will eventually react, once the anger has cooled, to take a different path: to listen much more acutely to the sounds of pain caused by the euro experiment; to do a proper deal for Greece; to reassert democratic accountability (much more Council of Ministers, much less Commission); and to reassess free movement? Writing it, I know that I sound like a deluded optimist, but the possibility deserves to be filed alongside all the grimmest alternatives.

Keeping all this cautiously in mind, let’s look at the British establishment cock-up. According to one of those involved, this all started at a pizza restaurant at Chicago O’Hare Airport at the time of a Nato conference in 2012, when David Cameron and his closest political allies decided that the only way of scuppering Ukip and the Euro-hostile right of the Conservative Party was to give the British people a referendum.

The brutal way of putting this is that Cameron decided to put party management and tactics ahead of grand strategy, grossly overrated his own negotiating skills, and has been badly bitten in the bottom accordingly. He has often looked like a chess player who plays the next move brilliantly yet fails to see three moves ahead. There is, however, a more generous explanation – which is simply that this referendum was inevitable; that it was more than time for restless British voters to reassess their membership of a union that has changed dramatically since we joined, both in extent and in depth.

***

At any rate, whatever his mixed motives, Cameron believed that he could negotiate a deal with his EU partners so good that he would win a subsequent referendum. A great deal of this was based on a second huge miscalculation – about his friend Angela Merkel.

As a result, the whole referendum process was fixed around the negotiation. In other words, the feeling was: “Give the plebs their plebiscite. It’s pretty safe. The Continentals will be scared enough to give us a great deal and, therefore, the people will vote for Nurse.” As soon as it became clear that Mrs Merkel was not prepared to countenance an end to the free movement of people, the plan began to fall apart. I vividly remember interviewing Cameron as the details of the negotiation became clear and thinking to myself, between his explanations: “This isn’t nearly enough.”

This mistake was followed by another – one that the Scottish National Party leader, Nicola Sturgeon, publicly warned against months ago. Those running the Remain campaign always believed in “Project Fear”; that a barrage of warnings by the Treasury, big business, banks and international organisations would simply terrify ordinary voters – pensioners and workers alike – and pulverise the arguments for leaving.

It had worked, after all, hadn’t it, in Scotland in 2014? A close confidant of the Prime Minister told me, when I questioned him about the wisdom of this: “On the contrary, we need more fear. Fear is the only thing that can win it for us . . . We need lots of fear. We need as much fear as we can get.”

But the Scottish parallel proved to be a delusion. First, this kind of “you will lose your pensions, you will lose your jobs” warning infuriated many Scottish voters in 2014, who stuck their fingers in their ears and moved over to the Yes campaign. Second, although in the end threats of doom may have swung things, Scotland was a country of five million people, suffering from a falling oil price and taking a decision about a union that had been around for three centuries. If, right at the end and by a narrow margin, Scots voted two years ago to stay inside the UK, that was not a close enough comparison for this referendum; there were far more people involved, a bigger country, a much looser and more recent union.

It was the specificity of the Project Fear warnings that did most damage: households £4,300 worse off, house prices falling by 18 per cent, and so forth. By being incredibly detailed, the Remain campaigners lost the ear of a dubious public. That meant that the much more frightening warnings by business leaders, talking about companies they knew and understood, didn’t get enough traction. Granted, we still don’t know; Project Fear may be vindicated yet. (The early falls on the money markets and stock markets tell us very little – they may be an overreaction to previous and recent complacency.)

But the most significant reason Project Fear failed was that it was confronted by a larger project of fear: the fear of uncontrolled and uncontrollable migration running, cumulatively, into the millions for many years ahead. Frank lies were told. Gross exaggeration ran riot. This was a fight between people who like living among migrants from Europe and employing them, on the one hand, and those competing against migrants (and failing) for jobs and wages. Neither David Cameron nor Theresa May seemed to have a plausible response to “uncontrolled immigration”. That may be because, inside the EU, there wasn’t one. Jeremy Corbyn responded with interesting ideas about wage rates and employment laws which did not address, at all, central fears about numbers and identity.

It is on this, above all issues, that “the plain people of England” spoke most compellingly against the elites, from Westminster politicians and Whitehall mandarins to London actresses, pop stars and media grandees. Boris Johnson, Michael Gove and Nigel Farage were absolutely right to point out that immigration from eastern Europe – though it has hugely benefited people who employ drivers and domestic servants, and who want to pay less for their electrical or plumbing repairs – keeps down the wages of indigenous working-class people and, in many cases, makes it harder for them to find work in hotels, in restaurants, on farms and elsewhere. Aggregated economic statistics mean nothing compared to personal experience. If you’ve got nothing, you’ve got nothing to lose. (Well, in fact, you have got something, but it feels that way.) When George Osborne warned of an economic apocalypse, people with nothing who felt they had no opportunities just put their fingers in their ears and went “la-la-la”.

There were people who saw what was happening and understood that disregarded Lower and Middle Britain was fed up to the back teeth and ready to revolt: some trade union leaders – whose job it was, after all, to represent them – and some Labour MPs.

***

The Labour leadership, however, seems to have got the message far too late and far too weakly, and that was a function of its own political philosophy. Labour leaders of the Jeremy Corbyn era don’t like to talk about immigration and have based much of their inner-city politics on the rights and causes of migrant communities already in the UK. The menacing noises about a leadership challenge grew louder by the hour and then turned into open revolt.

There is something tragicomic about this. The Corbyn revolution was about the overthrow of the last remnants of the Blairites, accused by party activists of not thinking enough or caring enough about ordinary Labour voters – of becoming too rich, too close to the elites, and infatuated by neoliberal, post-Thatcher economic solutions. The Corbyn movement began as an anti-elitist rebellion. But now, from their base among Londoners and students whose politics are a million miles away from the views of angry, white, non-metropolitan, working-class voters the Corbynistas, too, found themselves unable to get a hearing.

So, what is the result of all this? Wherever one looks, the British political class has come close to destroying itself. There is no source of authority. As Kenneth Clarke has noted, we have a hole, in effect, where a government should be.

The Remain faction of Tory MPs has no leader now. Many of them are bruised and livid against the triumphant Brexiteers. Boris Johnson, Michael Gove, Iain Duncan Smith and the rest now have to deal with outraged Tories who accused them of lying, a panicky and angry City, big business leaders who feel betrayed, and an EU in a dark mood. All of this is taking place during the inevitable turmoil and struggle of a Conservative leadership campaign. It is no doubt hyperbole to say we have absolutely no government at the moment: there is still a prime minister, there is a cabinet, and there is a party with a paper majority in the Commons. But if “government” means a group of people with a mandate and a plan, and the parliamentary authority to carry it through – well, we certainly don’t have that.

What happens in Scotland and Northern Ireland now adds to the sense of crisis. Nicola Sturgeon has this problem: she would very much like to secure terms for Scotland staying inside the EU before the rest of the UK leaves. That would minimise disruption, give Scots a secure alternative haven and prepare perfectly for a successful referendum on independence. The problem is that the EU is unlikely to countenance this. First, Scotland may be a country but it is not a nation in EU terms, and therefore has no locus. At the very least, under current EU law, Scotland would need to be a customs union – which it isn’t.

The alternative is that Scotland leaves alongside the rest of the UK and then has to reapply, after an independence referendum. The problems here multiply: Nicola Sturgeon and the SNP may have lost momentum and because new applicants have to join the euro, and will be under great pressure to ­accept the Schengen Agreement, she would be going to the Scottish electorate offering an independent Scotland using the euro (not the world’s most popular currency at the moment, to put it gently) and requiring a hard border with England. This seems to me a hard sell to Scottish voters, especially long after the initial Brexit shock will have faded. What we don’t know is how enthusiastic the rest of the European Union would be about bringing in an independent Scotland briskly, to punish Westminster, and how threateningly Spain’s Catalan/Basque difficulties will loom.

In Northern Ireland, Sinn Fein is calling for an all-Ireland referendum. There is now a border problem there as well, for the first time since the 1998 peace agreement. Tory ministers dismiss this but the dynamics of Irish politics, too, have been dramatically changed by the Brexit vote.

The UK could, naturally, survive all of this completely intact. But the possibility, at least, of a relatively lonely England is something that the new and victorious Brexit Tories now have to confront.

In usual circumstances, we would expect an early general election. There is a strong basic democratic case for one: otherwise, we get a prime minister, never chosen by the country, attempting to enact a manifesto no party has ever stood on in a general election. But we don’t really have the political parties to contest it, do we? Ukip is in chipper form. Like so many nationalist movements, it may survive achieving its goal. But the Conservatives are hopelessly divided. The outgoing Prime Minister believes the likely incoming Tory leader – a certain flaxen-haired fellow – is going to put a bomb under the British economy and has told outright untruths. He is trying hard to stop Boris but Boris may well be unstoppable. Another (former) prime minister, Sir John Major, tells us we cannot trust the National Health Service into the hands of Johnson, Gove and Duncan Smith. The amiable Alistair Burt, the MP for North-East Bedfordshire, has promised Brexit Tories that what is to come will make the Maastricht rebellion seem like a tea party.

No, on the whole, they don’t look like a party aching to face the electorate. You might expect the Labour leader to fight for an early election and try to rally the Commons to his side. But then Jeremy Corbyn faces his own rebellion.

At the moment, the coup against him seems to face insuperable hurdles. There isn’t a plausible alternative candidate so far. Above all, he retains the support of most Labour members, and it is they and trade unionists who will have the final say, whatever the Parliamentary Labour Party does.

If Corbyn sees off the plotters, what next? A united Labour opposition could go into a general election saying explicitly that it rejected the Brexit decision – that the vote was based on lies and scaremongering – and that, if elected, they would not implement Article 50: in effect, not leave the EU. That is what the Liberal Democrats are doing. For Labour, it would be a huge gamble. It would be a slap in the face for the majority who voted on 23 June and could lead to a different kind of revolt. But it would give the Labour Party a very clear purpose and agenda that could reach out into parts of Britain Corbyn has no chance of reaching just now.

Naturally, the politicians have noticed all this. So we are hearing a great deal of optimistic whistling from leading Conservatives, insisting that they can work together happily and cordially for the rest of this parliament – trying to persuade us that they’ve forgotten everything they said about each other during the referendum campaign, and that people who believe Brexit is an economic catastrophe will nevertheless roll up their sleeves and . . . er . . . make it happen.

Clearly, the best hope for the Conservatives is that such warnings turn out to be piffle and that we are soon enjoying an economic upswing, even as the EU continues to struggle. If Boris Johnson or another leader is indeed able to achieve “Norway-plus” then the Brexiteers are close to being home free. Yet there are signs already that the Boris camp is slightly panicky – as well it might be – about a rash of racist and xenophobic politics immediately after the results. He is right, of course, to call for inclusion and calm, though it is fatuous to suggest that immigration was not a critical issue in the campaign. If he wants to win long term, he has to get a different deal from Brussels, much better than the one that Cameron got – a long shot, but not impossible. For the Brexiteers, time is very short. They have to stay together, and yet there will be tensions: Rupert Murdoch is running Gove against Johnson, or, at any rate, would like to.

My guess is that parliamentary chaos and an overwhelming sense of drift at the centre of politics will nevertheless propel us into an election later this year or early next year. If so, that will mean that, tactically, the Brexiteers, who don’t want to trigger Article 50 just yet, must do so before the people are asked for their view again.

And, of course, if it turns out that George Osborne’s blood-curdling warnings about jobs and investment turn out to be even half accurate, then those same cheerful gentlemen will have many personal apologies to make to people who do lose their jobs, or see prices rise and their pensions fall. There is plenty of anger still to come.

That’s not so surprising: after all, this was a kind of revolution. It has been a very British revolution, accomplished through the ballot box and after a great deal of nonsense spoken on all sides. The plain people, of England, mainly, have spoken at last and their voice has blown over not just a constitutional link with the European continent but also almost the entire political class – and most of the pollsters – and oh, go on, then – us clever-Dick journalists as well.

Andrew Marr presents “The Andrew Marr Show” on BBC1. His Brexit thriller, “Head of State”, is published by Fourth Estate

Andrew Marr is a broadcaster and journalist. Formerly the BBC’s Political Editor, he presents the Andrew Marr Show on BBC1 on Sundays and Start the Week on Monday mornings on Radio 4.

This article first appeared in the 30 June 2016 issue of the New Statesman, The Brexit lies