In the opening chapter of Book 1 of My Struggle, by Karl Ove Knausgaard, the 8-year-old narrator sees a ghost in the waves. He is watching a televised report of a rescue effort at sea—“the sky is overcast, the gray-green swell heavy but calm”—when suddenly, on the surface of the water, “the outline of a face emerges.”

We might guess from this anecdote that Karl, our protagonist, is both creative and troubled. His limber mind discerns patterns in chaos, but the patterns are illusions. “The lunatic, the lover, and the poet,” Shakespeare wrote, “have such seething brains, such shaping fantasies.” Their imaginations give “to airy nothing a local habitation and a name.” A seething brain can be a great asset for an artist, but, like Knausgaard’s churning, gray-green swell, it can be dangerous too. Inspired metaphors, paranormal beliefs, conspiracy theories, and delusional episodes may all exist on a single spectrum, recent research suggests. The name for the concept that links them is apophenia.

A German scientist named Klaus Conrad coined apophanie (from the Greek apo, away, and phaenein, to show) in 1958. He was describing the acute stage of schizophrenia, during which unrelated details seem saturated in connections and meaning. Unlike an epiphany—a true intuition of the world’s interconnectedness—an apophany is a false realization. Swiss psychologist Peter Brugger introduced the term into English when he penned a chapter in a 2001 book on hauntings and poltergeists. Apophenia, he said, was a weakness of human cognition: the “pervasive tendency … to see order in random configurations,” an “unmotivated seeing of connections,” the experience of “delusion as revelation.” On the phone he unveiled his favorite formulation yet: “the tendency to be overwhelmed by meaningful coincidences.”

In statistics, a problem akin to apophenia is a Type I error, or false positive. It means believing something is real when it isn’t, based on a misleading pattern in the data. The equal and opposite misstep, a Type II error, involves attributing a true relationship to chance. Defaulting to Type I thinking may have once conferred a survival advantage: Assume every rustle in the grass is a tiger, and you’ll last a lot longer than the carefree naïf who chalks each disturbance up to the wind. So, the theory goes, human brains evolved into “belief engines” and “pattern-recognition machines,” keen to organize jumbled sensory inputs into meaningful data. We are also expert detectors of conspiracies in random events, whispers in radio static, and the Virgin Mary in grilled cheese. Sometimes these false positives create an orderly perceptual continuum that helps us think. They aren’t strictly necessary, but they are at least usually benign. When I see a scowling man in the moon, or you see clouds that remind you of fluffy lambs, our brains are making the world a more diverse and beautiful place. Plus, every now and then, chaos offers up glimmers of order.

Yet apophenia can also lure us into false and damaging convictions. Take the gambler’s fallacy, which states—erroneously—that in a sequence of random events, past outcomes will affect future outcomes. A player imagines he sees flickers of cosmic logic in the heads-tails-tails pattern of successive coin flips; he places his bets accordingly and loses a bundle of cash. Or a trail of tea leaves in the vague shape of a skull causes a woman to cancel her social engagements and spend the rest of the day in bed. Or someone pieces together random news clippings and decides that the Sept. 11 terrorist attacks were an inside job. Or a kid studies the headlights sliding over her bedroom wall, thinks they constitute a code, and concludes that UFOs are real. (I did that.)

So apophenia cuts both ways—it’s a profoundly human habit of mind that can underlie adaptive behaviors and reward flights of fancy, or induce all kinds of paranoia and silliness.

In 2001, scientists from the KEY Institute for Brain-Mind Research in Zurich found that a “hyper-associative cognitive style” both nourished “belief in magical or psychic phenomena” and prompted divergent thinking—a measure of creativity. Apophenia’s defenders cite Leonardo da Vinci, who urged his students:

Look at walls covered with many stains … with the idea of imagining some scene, you will see in it a similarity to landscapes adorned with mountains, rivers, rocks, trees, plains, broad valleys, and hills of all kinds … [also] battles and figures with lively gestures and strange faces and costumes and an infinity of things which you can reduce to separate and complex forms.

Or Wordsworth, who wrote in his Prelude:

The curious traveller, who, from open day, hath passed with torches into some huge cave … he looks around and sees the vault widening on all sides; sees, or thinks he sees … the massy roof above his head, that instantly unsettles and recedes—substance and shadow, light and darkness, all commingled, making up a canopy of shapes and forms … that shift and vanish, change and interchange like spectres—ferment silent and sublime!

Recently, though, psychologists have looked more closely at the link between apophenia and mental illness. It is not just poets and the supernaturally suggestible (believers in witchcraft, Bigfoot, or psychic auras) who seem disposed to find signals in static. It is men and women suffering from schizophrenia, and perhaps bipolar disorder and post-traumatic stress disorder as well.

According to the researchers at University College, London, “[t]here is now considerable evidence that high schizotypes … show a greater tendency to see patterns in random configurations and perceive meaning in coincidental events.” In one study, adult participants were divided into groups based on their scores on the Schizotypal Personality Scale, which measures “proneness to psychosis.” The volunteers watched animations of two shapes motoring across a screen. In some cases, the shapes moved independently of each other, but in others, a “prime mover” bumped or launched a “reactive mover.” Asked whether they believed there was a relationship between the motion of the two shapes, so-called high schizotypes were far more likely than low schizotypes to say yes, even when the shapes’ paths were unrelated. In another experiment, people who scored high on a test of delusional thinking attributed qualities of mind to triangles randomly floating around a screen. They claimed that one triangle “saw” another one—that was why it “ran away” or crept closer to investigate. A similar study with paranoid schizophrenics revealed that some participants suspected triangles of “hiding from” or “tricking” one another, as though in a vast conspiracy.

Brain imaging studies by Brugger and his colleagues hint that garden-variety apophenia may result from overactivation of the brain’s right hemisphere. This neural real estate, which governs certain metaphorical or associative aspects of language, stores conceptual knowledge in a looser, more diffuse network than the left hemisphere. When one concept is ignited in the right hemisphere, Brugger explained, distantly related concepts may come to mind as well—producing a sense of meaningful connection. Brugger told me about a study he conducted several years back in which he and his colleagues flashed haphazard configurations of dots into people’s left and right visual fields (so that the images would be processed by their right and left brain hemispheres, respectively). Those who viewed the dots presented to the right hemisphere were more likely to perceive in them an underlying structure or design. Meanwhile, the left-hemisphere group saw only anarchy.

Another possible culprit in apophenia is dopamine. A 2002 experiment revealed that people with high levels of dopamine more often extract meaning from coincidences than those with lower dopamine levels. And when self-described skeptics (team “UFOs are fake”) were given the drug L-dopa, which ups the brain’s dopamine supply, they began to perform more like self-described believers (team “I can speak to spirits”) on the same pattern-finding tasks. Likewise, when Brugger and his colleagues administered dopamine to a group of healthy adult men, that group proved more likely than a control group to notice visual similarities between random pairs of shapes.

Personal accounts from manic patients fizz with an almost compulsive meaning-making, but the research on connections between apophenia and bipolar disorder is thin. One clue: Just like people with schizotypal tendencies, people at risk for bipolar disorder often ace creativity tests. They seem to excel especially at the type of “intuitive, open-minded thinking” that results in surprising associations. (Though he hasn’t studied apophenia and bipolar disorder, Brugger says he would “assume that you see connections everywhere in a manic state.”) A symptom of mania known as clanging, in which ideas are strung together not in a logical order but because of how the words sound, has an apophenic aura. Was Charlotte Perkins Gilman bipolar? The jury is still out on the troubled author who brought forth “The Yellow Wallpaper” after a period of postpartum psychosis. Yet her most famous story revolves around a housewife who begins to see ghastly, phantom shapes in her interior décor. “There is a recurrent spot where the pattern lolls like a broken neck and two bulbous eyes stare at you upside down,” the fictional madwoman reports, in one of literature’s most chilling apophenic moments. Virginia Woolf, a famous manic-depressive, once listened to the nonsense chirping of the birds in her garden and grew convinced they were speaking Greek.

The literature about post-traumatic stress disorder is also suggestive of a role for apophenia. A study by Margaret McKinnon and Brian Levine showed that people with PTSD often fail to screen out irrelevant details when recalling past events. That’s why a woman who develops the syndrome after a harrowing plane landing might tell a questioner not only what the flight attendants were wearing but how old she was when she first drove a car. Her brain, tracing an illusory connection between the two facts, dredges up the second while retrieving the first.

Though apophenia has long been considered a perceptual error, Brugger is curious as to how it might play out in the domain of memory. “People conflate apophenia with having a hallucination, as if it is merely sensory,” he said. “But meaning is the result of so many sensory and cognitive processes. It is far more complicated than we think.”

David J. Morris would agree. A former Marine officer, Morris has written a book—The Evil Hours—that functions as “a biography of post-traumatic stress disorder.” He says he was surprised at how apophenia became an organizing principle not just for the text but for his own experiences in Iraq. “In a war zone,” he told me, “you run into people with a heightened sense of superstition, people trying to find ways to deal with the uncertainty of death.” Morris hallucinated that he had a doppelganger while in Iraq and developed an obsession with anniversaries. He thinks shattering experiences have a way of remaking the world, sending survivors into frenzies of analysis as they encounter each thing anew. “Trauma destroys your connection to the universe,” he suggested. “You can no longer make sense of the social and moral order; it’s as if reality has turned on you in a paranormal way.” A victim’s brain can respond by going into overdrive: “You try to explain what happened, why you … what are the laws of cause and effect.”

Sometimes, the military encourages this rewiring. The official U.S. manual for counterinsurgency urges troops to “attend to intangibles”—the vibe on the streets, the presence or absence of kids playing soccer, microevents, and their own gut feelings. “We’re supposed to be hyperaware of ‘atmospherics,’ ” Morris told me, pinpointing the sticky problem of apophenia, its grace and peril. “But when does that alertness save your life, and when does it mean you’re insane?”

And when does it make the world better, not worse? Unplug the lamp of imagination and you will stumble around in darkness, like the Wordsworth cave-goer if he’d never bothered to light his torch. Without attempting to resolve whether apophenia is good or evil, I will note that Western culture hallows a lot of notions about the singularity of creative genius, even as we boast a long and dangerous tradition of romanticizing madness. Is that just a coincidence … or something more?