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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

CLIVE BARDA
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The lost magic of England

The great conservative journalist Peregrine Worsthorne reflects on a long life at the heart of the establishment.

In a recent editorial meeting, our subscriptions manager happened to mention that Peregrine Worsthorne was still a New Statesman subscriber. A former editor of the Sunday Telegraph and, during a long Fleet Street career, a self-styled “romantic reactionary” scourge of liberals and liberalism, Worsthorne used to be something of a pantomime villain for the left, a role he delighted in. He had close friends among the “Peterhouse right”, the group of High Tory intellectuals who gathered around Maurice Cowling at the small, conspiratorial Cambridge college. He was a frequent contributor to Encounter (which turned out to be funded by the CIA) and an ardent cold warrior. His social conservatism and lofty affectations offended lefty Islingtonian sensibilities. On several occasions he was the Guardian’s reviewer of choice for its annual collection of journalism, The Bedside Guardian, and he invariably delivered the required scornful appraisal while praising its witty television critic, Nancy Banks-Smith. There is no suggestion, he wrote in 1981, that the “Guardian ever sees itself as part of the problem; itself as having some responsibility for the evils its writers described so well”.

His prose style was Oxbridge high table, more Walter Pater than George Orwell. It was essential not to take Worsthorne too seriously, because he delighted in mischief-making and wilful provocation – one of his targets for remorseless ridicule was Andrew Neil, when Neil edited the abrasively Thatcherite Sunday Times. He ended up suing Worsthorne, who was famous for his silk shirts and Garrick Club lunches, for libel; he was awarded damages of £1, the then cover price of the Sunday Times.

“I wrote that in the old days editors of distinguished Sunday papers could be found dining at All Souls, and something must have changed when they’re caught with their trousers down in a nightclub,” Worsthorne told me when we met recently. “I had no idea he was going to sue. I was teasing. I occasionally run into him and we smile at each other, so it’s all forgotten and forgiven.”

After his retirement in 1989, Worsthorne, although he remained a resolute defender of aristocracy, seemed to mellow, and even mischievously suggested that the Guardian had replaced the Times as the newspaper of record. In the 1990s he began writing occasionally for the New Statesman – the then literary editor, Peter Wilby, commissioned book reviews from him, as I did after I succeeded Wilby. Like most journalists of his generation, Worsthorne was a joy to work with; he wrote to length, delivered his copy on time and was never precious about being edited. (Bill Deedes and Tony Howard were the same.) He might have had the mannerisms of an old-style toff but he was also a tradesman, who understood that journalism was a craft.

Shortly before Christmas, I rang Wors­thorne at the home in Buckinghamshire he shares with his second wife, Lucinda Lambton, the charming architectural writer. I asked how he was. “I’m like a squeezed lemon: all used up,” he said. Lucy described him as being “frail but not ill”. I told him that I would visit, so one recent morning I did. Home is a Grade II-listed old rectory in the village of Hedgerley. It is grand but dishevelled and eccentrically furnished. A sign on the main gates warns you to “Beware of the Dog”. But the dog turns out to be blind and moves around the house uneasily, poignantly bumping into objects and walls. At lunch, a small replica mosque in the dining room issues repeated mechanised calls to prayer. “Why does it keep doing that?” Perry asks. “Isn’t it fun,” Lucy says. She then turns to me: “Have some more duck pâté.”

As a student, I used to read Worsthorne’s columns and essays with pleasure. I did not share his positions and prejudices but I admired the style in which he articulated them. “The job of journalism is not to be scholarly,” he wrote in 1989. “The most that can be achieved by an individual newspaper or journalist is the articulation of an intelligent, well-thought-out, coherent set of prejudices – ie, a moral position.”

His Sunday Telegraph, which he edited from 1986 to 1989, was like no other newspaper. The recondite and reactionary comment pages (the focus of his energies) were unapologetically High Tory, contrary to the prevailing Thatcherite orthodoxies of the time, but were mostly well written and historically literate. Bruce Anderson was one of the columnists. “You never knew what you were going to get when you opened the paper,” he told me. “Perry was a dandy, a popinjay, and of course he didn’t lack self-esteem. He had a nostalgia for Young England. In all the time I wrote for him, however, I never took his approval for granted. I always felt a tightening of the stomach muscles when I showed him something.”

***

Worsthorne is 92 now and, though his memory is failing, he remains a lucid and engaging conversationalist. Moving slowly, in short, shuffling steps, he has a long beard and retains a certain dandyish glamour. His silver hair is swept back from a high, smooth forehead. He remains a stubborn defender of the aristocracy – “Superiority is a dread word, but we are in very short supply of superiority because no one likes the word” – but the old hauteur has gone, replaced by humility and a kind of wonder and bafflement that he has endured so long and seen so much: a journalistic Lear, but one who is not raging against the dying of the light.

On arrival, I am shown through to the drawing room, where Perry sits quietly near an open fire, a copy of that morning’s Times before him. He moves to a corner armchair and passes me a copy of his book Democracy Needs Aristocracy (2005). “It’s all in there,” he says. “I’ve always thought the English aristocracy so marvellous compared to other ruling classes. It seemed to me that we had got a ruling class of such extraordinary historical excellence, which is rooted in England
almost since the Norman Conquest.

“Just read the 18th-century speeches – the great period – they’re all Whig or Tory, but all come from that [the aristocracy]. If they didn’t come directly from the aristocracy, they turned themselves very quickly into people who talk in its language. Poetic. If you read Burke, who’s the best in my view, it’s difficult not to be tempted to think what he says has a lot of truth in it . . .”

His voice fades. He has lost his way and asks what we were talking about. “Oh, yes,” he says. “It survived when others – the French and Russians and so on – were having revolutions. It was absolutely crazy to set about destroying that. There was something magical . . . the parliamentary speeches made by Burke and so on – this is a miracle! No other country has it apart from America in the early days. And I thought to get rid of it, to undermine it, was a mistake.”

I ask how exactly the aristocracy was undermined. Even today, because of the concentration of the ownership of so much land among so few and because of the enduring influence of the old families, the great schools and Oxbridge, Britain remains a peculiar hybrid: part populist hyper-democracy and part quasi-feudal state. The Tory benches are no longer filled by aristocrats but the old class structures remain.

“Equality was the order of the day after the war,” Worsthorne replies. “And in a way it did a lot of good, equalising people’s chances in the world. But it didn’t really get anywhere; the ruling class went happily on. But slowly, and I think unnecessarily dangerously, it was destroyed – and now there are no superior people around [in politics]. The Cecil family – Lord Salisbury, he was chucked out of politics. The Cecil family is being told they are not wanted. The institutions are falling apart . . .

“But there were people who had natural authority, like Denis Healey. I’m not saying it’s only aristocrats – a lot of Labour people had it. But now we haven’t got any Denis Healeys.”

Born in 1923, the younger son of Alexander Koch de Gooreynd, a Belgian banker, Worsthorne (the family anglicised its name) was educated at Stowe and was an undergraduate at both Cambridge (Peterhouse, where he studied under the historian Herbert Butterfield, the author of The Whig Interpretation of History) and Oxford (Magdalen College). “I have always felt slightly underprivileged and de-classed by having gone to Stowe, unlike my father who went to Eton,” Worsthorne wrote in 1985.

Yet his memories of Stowe remain pellucid. There he fell under the influence of the belle-lettrist John Davenport, who later became a close friend of Dylan Thomas. “He was a marvellous man, a famous intellectual of the 1930s, an ex-boxer, too. But in the war he came to Stowe and he was preparing me for a scholarship to Cambridge. He told me to read three books, and find something to alleviate the boredom of an examiner, some little thing you’ll pick up. And I duly did and got the scholarship.”

Can you remember which three books he recommended?

“Tawney. Something by Connolly, um . . . that’s the terrible thing about getting old, extremely old – you forget. And by the time you die you can’t remember your brother’s name. It’s a terrible shock. I used to think old age could be a joy because you’d have more time to read. But if you push your luck and get too far, and last too long, you start finding reading really quite difficult. The connections go, I suppose.”

Was the Connolly book Enemies of Promise (1938)?

“Yes, that’s right. It was. And the other one was . . . Hang on, the writer of the book . . . What’s the country invaded by Russia, next to Russia?

Finland, I say. Edmund Wilson’s To the Finland Station (1940)?

“Yes. Wilson. How did you get that?”

We both laugh.

***

Worsthorne is saddened but not surprised that so many Scots voted for independence and his preference is for Britain to remain a member of the European Union. “What’s happening is part of the hopelessness of English politics. It’s horrible. I can’t think why the Scots would want to be on their own but it might happen. The youth will vote [for independence]. This is part of my central theme: the Scots no longer think it’s worthwhile belonging to England. The magic of England has gone – and it’s the perversity of the Tory party to want to get us out of the European Union when of course we’re much more than ever unlikely to be able to look after ourselves as an independent state because of the quality of our political system.

“The people who want to get us out are obviously of an undesirable kind. That the future should depend on [Nigel] Farage is part of the sickness. I mean the real horror is for him to have any influence at all. And when you think of the great days of the Labour Party, the giants who strode the stage – famous, lasting historical figures, some of them: Healey, Attlee, who was probably the greatest, [Ernest] Bevin. I’m well aware that Labour in the good days produced people who were superior.”

He digresses to reflect on his wartime experience as a soldier – he served in Phantom, the special reconnaissance unit, alongside Michael Oakeshott, the philosopher of English conservatism who became a close friend, and the actor David Niven, our “prize colleague”.

“I remember Harold Macmillan saying to me, after the Second World War, the British people needed their belt enlarged; they’d done their job and they deserved a reward. And that’s what he set about doing. And he wasn’t a right-wing, unsympathetic man at all. But he didn’t – and this is what is good about conservatism – he didn’t turn it into an ‘ism’. It was a sympathetic feel, an instinctive feel, and of course people in the trenches felt it, too: solidarity with the rest of England and not just their own brotherhood. Of course he didn’t get on with Margaret Thatcher at all.”

Worsthorne admired Thatcher and believed that the “Conservatives required a dictator woman” to shake things up, though he was not a Thatcherite and denounced what he called her “bourgeois triumphalism”. He expresses regret at how the miners were treated during the bitter strike of 1984-85. “I quarrelled with her about the miners’ strike, and the people she got around her to conduct it were a pretty ropey lot.

“I liked her as a person. I was with her that last night when she wasn’t prime minister any more, but she was still in Downing Street and had everything cut off. The pressman [Bernard Ingham] got several of us to try to take her mind off her miseries that night. There’s a photograph of me standing at the top of the stairs.”

In the summer of 1989, Peregrine Wors­thorne was sacked as the editor of the Sunday Telegraph by Andrew Knight, a former journalist-turned-management enforcer, over breakfast at Claridge’s. He wrote about the experience in an elegant diary for the Spectator: “I remember well the exact moment when this thunderbolt, coming out of a blue sky, hit me. It was when the waiter had just served two perfectly poached eggs on buttered toast . . . In my mind I knew that the information just imparted was a paralysingly painful blow: pretty well a professional death sentence.”

He no longer reads the Telegraph.

“Politically they don’t have much to say of interest. But I can’t put the finger on exactly what it is I don’t like about it. Boredom, I think!”

You must read Charles Moore?

“He is my favourite. Interesting fellow. He converted to Catholicism and started riding to hounds in the same week.”

He has no regrets about pursuing a long career in journalism rather than, say, as a full-time writer or academic, like his friends Cowling and Oakeshott. “I was incredibly lucky to do journalism. What people don’t realise – and perhaps you don’t agree – but it’s really a very easy life, compared to many others. And you have good company in other journalists and so on. I was an apprentice on the Times, after working [as a sub-editor] on the Glasgow Herald.”

How does he spend the days?

“Living, I suppose. It takes an hour to get dressed because all the muscles go. Then I read the Times and get bored with it halfway through. Then there’s a meal to eat. The ­answer is, the days go. I used to go for walks but I can’t do that now. But Lucy’s getting me all kinds of instruments to facilitate people with no muscles, to help you walk. I’m very sceptical about it working, but then again, better than the alternative.”

He does not read as much as he would wish. He takes the Statesman, the Spectator and the Times but no longer the Guardian. He is reading Niall Ferguson’s biography of Kissinger, The Maisky Diaries by Ivan Maisky, Stalin’s ambassador to London from 1932 to 1943, and Living on Paper, a selection of letters by Iris Murdoch, whom he knew. “I get these massive books, thinking of a rainy day, but once I pick them up they are too heavy, physically, so they’re stacked up, begging to be read.”

He watches television – the news (we speak about Isis and the Syrian tragedy), the Marr show on Sunday mornings, and he has been enjoying War and Peace on BBC1. “Andrew Marr gave my book a very good review. He’s come back. He’s survived [a stroke] through a degree of hard willpower to get back to that job, almost as soon as he came out of surgery. But I don’t know him; he was a Guardian man.” (In fact, Marr is more closely associated with the Independent.)

Of the celebrated Peterhouse historians, both Herbert Butterfield (who was a Methodist) and Maurice Cowling were devout Christians. For High Tories, who believe in and accept natural inequalities and the organic theory of society, Christianity was a binding force that held together all social classes, as some believe was the order in late-Victorian England.

“I was a very hardened Catholic,” Worsthorne says, when I mention Cowling’s book Religion and Public Doctrine in Modern England. “My mother was divorced [her second marriage was to Montagu Norman, then the governor of the Bank of England] and she didn’t want my brother and me to be Catholic, so she sent us to Stowe. And I used to annoy her because I read [Hilaire] Belloc. I tried to annoy the history master teaching us Queen Elizabeth I. I said to him: ‘Are you covering up on her behalf: don’t you know she had syphilis?’

“Once I felt very angry about not being made Catholic. But then I went to Cambridge and there was a very Catholic chaplain and he was very snobbish. And in confession I had to tell him I masturbated twice that morning or something, and so it embarrassed me when half an hour later I had to sit next to him at breakfast. I literally gave up going to Mass to get out of this embarrassing situation. But recently I’ve started again. I haven’t actually gone to church but I’ve made my confessions, to a friendly bishop who came to the house.”

So you are a believer?

“Yes. I don’t know which bit I believe. But as Voltaire said: ‘Don’t take a risk.’”

He smiles and lowers his head. We are ready for lunch. 

Jason Cowley is editor of the New Statesman. He has been the editor of Granta, a senior editor at the Observer and a staff writer at the Times.

This article first appeared in the 11 February 2016 issue of the New Statesman, The legacy of Europe's worst battle