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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

NEAL FOX FOR NEW STATESMAN
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They know where you live

Imagine your house being raided by armed police. That’s what happened to Mumsnet’s Justine Roberts after she fell victim to an internet hoaxer.

At around midnight on Tuesday 11 August 2015, a man dialled 999 to report a murder. A woman had been killed in her London home, he said, before hanging up without offering his name. A second call followed. This time, the man claimed to be the killer. He told the operator that he had now taken the woman’s children hostage at the Islington address. They were locked with him inside a room in the house, he said. The police responded with reassuring speed. Fifteen minutes later, eight officers, five of them armed with automatic weapons, accompanied by saliva-flecked dogs, arrived at the scene and took up position in neighbouring front gardens. When one officer banged on the front door of the house, the team was greeted, moments later, not by a masked murderer but by a blinking and bewildered au pair.

Justine Roberts, the woman whom the caller claimed to have killed, was in fact nearly 2,000 kilometres away – in Italy, holidaying with her husband and children. After explaining this to the police, the au pair called Roberts, who assumed that the incident was an unfortunate misunderstanding, one that could be unpicked after the vacation. It was no mistake. Roberts had been the victim of “swatting”, the term given to a false emergency call designed to bait an armed unit of police officers to storm someone’s home. It wasn’t until a few days later, as the family was preparing to return to London, that Roberts discovered that she had been the target of a planned and sustained attack, not only on her household, but also on her business.

Roberts is the founder of Mumsnet, the popular British internet discussion forum on which parents share advice and information. A few days before the swatting incident, members of 8chan, a chat room that prides itself on being an open, anonymous platform for free speech, no matter how distasteful, had registered accounts on Mums­net with the aim of trolling people there. When legitimate Mumsnet users identified and then ridiculed the trolls, some retreated to 8chan to plot more serious vengeance in a thread that the police later discovered. Roberts wasn’t involved in the online skirmish but, as the public face of the site, she was chosen as the first target.

After the initial armed response, Roberts’s perception was that the police were unconcerned about the swatting attack. “We were told that there was no victim, so there was not much that could be done,” she told me. The hoax caller, however, was not finished. In the days after the incident, there was chatter on Mumsnet and Twitter about what had happened. A Mumsnet user whom I will call Jo Scott – she requested anonymity for her own safety – exchanged heated messages with a hacker who claimed responsibility for the 999 call.

“It descended into jokes and silliness, like many things do,” Scott said. “I didn’t take it seriously when the hacker said he had big surprises in store.” She doesn’t believe that what happened next was personal. “I think I was just easy to find.”

A few days after police were called to Roberts’s home, Scott was in her bedroom while her husband was sitting downstairs playing video games. At 11pm, she heard a noise outside. “I looked out of the window and saw blue flashing lights in the street,” she recalled. “I could hear shouting but I didn’t pay it much notice.” Then she heard her husband open the front door. Police rushed into the house. An armed officer shouted upstairs, asking Scott if she was hurt. When she replied that she was fine, he told her to fetch her two young children: he needed to see them. Scott shook her sons awake, explaining, so as not to alarm them, that the police had come to show the boys their cars. As the three of them went downstairs, the officers swept up through the house, repeatedly asking if there were any weapons on the property.

“I was beyond confused by this point,” Scott said. “Everyone was carrying a gun. They had little cutaway bits so you could see the bullets. My eldest asked one of the officers if he could have a go on his gun and went to touch it.”

As Scott sat with an officer downstairs, she asked what had happened to her husband. “I later found out that the noises I’d heard were the police calling for him to come outside,” she said. “He dropped the PlayStation controller as he left the room. It was only later that we realised it’s a good job he did: in the dark, the controller might have looked like a weapon.”

Outside, Scott’s husband had been surrounded and arrested. Other police ­officers were on the lookout in the front gardens of nearby properties, having warned the couple’s neighbours to stay indoors, away from their windows. “One of the officers said it was beginning to look like a hoax,” Scott said. “Then he mentioned swatting. As soon as he said that word, I twigged that I’d seen the term that day on Twitter in relation to the Mumsnet hack.”

***

The term “swatting” has been used by the FBI since 2008. “Swat” is an acronym of “Special Weapons and Tactics”, the American police squads routinely called to intervene in hostage situations. It is, in a sense, a weaponised version of a phoney order of pizza, delivered as a prank to a friend’s home, albeit one that carries the possibility of grave injury at the hands of police. For perpetrators, the appeal is the ease with which the hoax can be set in motion and the severity of the results. With a single, possibly untraceable phone call, dialled from anywhere in the world, it is possible to send an armed unit to any address, be it the home of a high-profile actor whom you want to prank or that of someone you want to scare.

In America, where swatting originated, the practice has become so widespread – targets have included Tom Cruise, Taylor Swift, Clint Eastwood and the Californian congressman Ted Lieu – that it is now classed as an act of domestic terrorism. In the UK, where Justine Roberts’s was one of the first recorded cases, swatting is classed as harassment, though that may change if these and other forms of internet vigilante attacks, such as doxxing, become increasingly commonplace.

Doxxing involves the publication of someone’s personal details – usually their home address, phone numbers, bank details and, in some cases, email address – on the internet. It is often the prelude to swatting: after all, the perpetrator of a hoax cannot direct the police to the target’s home address until this is known. (During the week of the Mumsnet attacks, one of the perpetrators attempted to locate another target using their computer’s IP address, which can identify where a person is connected to the internet, often with alarming precision. Their calculation, however, was slightly out; police were called to a neighbour’s address.)

Though doxxing has a less dramatic outcome than swatting, the psychological effects can be just as severe. For victims – usually people who are active on the internet and who have outspoken opinions or who, in the eyes of an internet mob, have committed some kind of transgression – the mere threat of having their personal information made available on the web can cause lasting trauma. A Canadian software developer whose home address, bank details, social security number and email history were published online in 2014 told me that he now keeps an axe by his front door. “I still don’t feel safe here,” he said. “It’s terrifying.”

Christos Reid, a social media manager for a software company, was doxxed last year. Reid’s information came from a website he had registered seven years earlier. “I woke up one morning to find a tweet announcing my personal details,” he told me. When he asked the Twitter account holder to take down the address, he was told to commit suicide. Reid said he was “OK for about half an hour”; but then, after he went out, he broke down in the street. “I’ve become more paranoid,” he said. He no longer gives out business cards with personal information.

Reid lives in London, but at the time of the doxx he was attending an event in Nottingham, home to the British police’s largest cybercrime division. He was impressed with the police response, even though they told him that they had not heard of the term “doxxing” before. “I was interviewed by two separate people about my experiences who then compiled everything into a case file and transferred it to the Met. When I arrived home, an officer visited me to discuss what happened and my options.”

The policeman explained harassment law to Reid, and offered advice on how to improve security at his flat and what to do if someone hostile turned up at the address. Reid shouldered the repercussions of what had happened alone; no suspects were identified. A spokesperson for the Metropolitan Police similarly said that although detectives from Islington CID have investigated the swatting attacks made on Roberts and Scott, no suspects have been identified “at this time”, even as “inquiries continue”.

Doxxing may seem to be a mild form of harassment but it carries with it an implicit threat of impending violence; the worrying message is: “We know where you live.” Unlike swatting, which is always malicious, doxxing is sometimes viewed by its perpetrators as virtuous. In November 2014, hackers claiming to be aligned with the internet group Anonymous published personal information allegedly belonging to a Ku Klux Klan member from Missouri. The hackers said that their action was a response to the KKK’s threat to use lethal force against demonstrators in the city of Ferguson, Missouri, protesting against the killing of the unarmed black teenager Michael Brown by a white police officer. In January 2015 hackers claiming to be from Isis took over US Central Command’s Twitter account and posted information about senior military officers, including phone numbers and email addresses. In each case, those carrying out the doxxing believed, however mistakenly, in the virtue of their actions and hoped that the information could be used to bring punishment or ruin to the subject.

The term “doxxing” may be new but the practice is an old one. The Hollywood blacklist revealed the political beliefs and associations of actors and directors in the late 1940s as a way to invite shame, deny employment and dissuade others from following their example. “But it has become a lot easier to find people’s private details with the help of the internet,” Jeroen Vader told me. Vader owns Pastebin, a website that allows users to upload and distribute text documents, and where much of the personal data is anonymously uploaded and shared. “People post their private information on social networks,” he said. “A lot of people aren’t aware that their information is so easily available to others.”

In Justine Roberts’s case, the perpetrator may not even have needed to look at social networks to mine her personal information. “If you’re on the electoral roll, you’re easy to find,” she said. “There’s not much you can do to stop people getting hold of your data one way or another, whether it’s for nefarious reasons or simply to better advertise to you. We live in a world that is constantly trying to gather more information about us.”

Jeroen Vader said he has noticed an “upward trend” in the number of doxxing posts uploaded to Pastebin in recent months, but insisted that when someone uses the site’s abuse report system these offending posts are removed immediately.

Across social media companies, action is more often reactive than proactive. Victoria Taylor, a former director at Reddit, one of the largest community-driven websites in the world, said that the rule against publishing other users’ personal information has been “consistently one of the site’s most basic policies” and that “any violation of this rule is taken extremely seriously by the team and community”. Still, she was only able to recommend that victims of doxxing send a message to the site’s administrators. Similarly, when asked what a person can do to remove personal details that have been published without permission, a Twitter spokesperson said: “Use our help form.”

The spokesperson added: “There has def­initely been an overall increase in doxxing since 2006, both on Twitter and on the internet more generally.” She attributed this rise to the emergence of search engines such as Intelius and Spokeo, services designed to locate personal information.

***

The surge in the number of dox­xing and swatting attacks is in part a result of the current lack of legal protection for victims. Confusion regarding the law on doxxing is pervasive; the term is even not mentioned in either US or European law. In a tutorial posted on Facebook in 2013, the writer claims: “Doxxing isn’t illegal as all the information you have obtained is public,” and adds: “But posting of the doxx might get you in a little trouble.”

Phil Lee, a partner in the privacy, security and information department of Fieldfisher based at the law firm’s office in Silicon Valley, said that differing privacy laws around the world were part of the problem. “Various countries have laws that cover illegal or unauthorised obtaining of data. Likewise, some of the consequences of releasing that data, such as defamation or stalking, cover elements of what we now term doxxing. But there is no global law covering what is a global phenomenon.” Indeed, Roberts believes that her London address was targeted from America – the 999 call was routed through a US proxy number.

One challenge to creating a law on doxxing is that the sharing of personal information without permission has already become so widespread in the digital age. “If a law was to state something like, ‘You must not post personal information about another person online without their consent,’ it wouldn’t reflect how people use the internet,” Lee said. “People post information about what their friends and family members have been doing all the time without their consent.

“Such a law could have a potentially detrimental effect on freedom of speech.”

Lee believes that a specific law is unnecessary, because its potentially harmful effects are already covered by three discrete pieces of legislation dealing with instances where a person’s private information is obtained illegally, when that information is used to carry out illegal acts and when the publication of the information is accompanied by a threat to incite hatred. However, this does not adequately account for cases in which the information is obtained legally, and then used to harass the individual in a more legally ambiguous manner, either with prank phone calls or with uninvited orders of pizza.

Susan Basko, an independent lawyer who practises in California and who has been doxxed in the course of her frequent clashes with internet trolls, believes that the onus should be on the law, rather than the public. She points out that in the US it is a crime to publicise information about a government employee such as their home address, their home and cellphone numbers, or their social security number, even if the information is already online. “This law should apply to protect all people, not just federal employees,” she said. “And websites, website-hosting companies and other ISPs should be required to uphold this law.”

Basko said that doxxing will continue to increase while police have inadequate resources to follow up cases. For now, it is up to individuals to take preventative measures. Zoë Quinn, an American game designer and public speaker who was doxxed in 2014, has launched Crash Override, a support network and assistance group for targets of online harassment, “composed entirely of experienced survivors”.

Quinn, who spoke about the problem at a congressional hearing in Washington, DC in April last year, recently posted a guide on how to reduce the likelihood of being doxxed. “If you are worried you might some day be targeted,” she wrote, “consider taking an evening to stalk yourself online, deleting and opting out of anything you’re not comfortable with.”

Both Scott and Roberts have changed their privacy habits following the attacks. Scott is more careful about interacting with strangers online, while Roberts uses scrambler software, which ensures that she never uses the same password for more than one online site or service.

For both women’s families, the effects of their encounters with armed police have also lingered. When one day recently Roberts’s husband returned home early from work, the au pair called the police, believing it was an intruder. And Scott is haunted by what happened.

“What if my husband had made a sudden move or resisted in some way? What if my eldest had grabbed the gun instead of gently reaching for it? What if people locally believed that my husband did actually have guns in the house?” she asks. “I don’t think the people making these sorts of hoax calls realise the impact.” 

This article first appeared in the 28 April 2016 issue of the New Statesman, The new fascism