They are weightless, colorless, and odorless … something you rarely recognize, and don’t give a second thought about when you do. And yet they structure your life, your relationships, your beliefs, and the universe. Welcome to the world of gaps.

In the mid-1970s three U.S. researchers ran an experiment in a men’s latrine, testing a theory that micturation—peeing—is inhibited by “personal space invasions.” Lurking in a nearby stall, with a periscope hidden in a stack of books (ethical standards were a bit different then), the researchers observed subjects relieving themselves with 1) a stranger close by, 2) a stranger slightly farther away, or 3) no stranger present (the control).

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They found that, with a stranger positioned at the adjacent urinal—shoulder to shoulder—the onset of peeing was delayed by, on average, 8.4 seconds, compared with 6.2 seconds with subject and stranger separated by one urinal, and 4.9 seconds with no one else around. Space invasion also affected the duration of urination, which lasted for 17.4 seconds with a stranger close by, 23.4 seconds with the subject given a wider berth, and 24.8 seconds in unbroken solitude.

Predictable as those findings might appear, they offer an insight into the phenomenon of “gaps.” Gaps, the spaces between people, things and concepts, mostly go unnoticed. After all, our attention is generally required elsewhere. But as the peeing experiment shows, gaps sometimes represent more than just absences—and they can tell us a lot about how things work. At their most obvious, gaps are physical, comprising the space between two points, but they can also be intangible, as with, for instance, the ideological chasm between present-day Republicans and Democrats. As well as defining and dividing, gaps connect: consider the conspiratorial fresh air between two friends sitting across the table from each other in a cafe.

Although gaps might at first glance seem insignificant—just a void, or an absence—they can provide a novel and rewarding way of looking at the world. Take human relationships. The British anthropologist Robin Dunbar argued in the 1990s that the number of people we can relate to in a meaningful way at any one time is no higher than, on average, 150. Beyond that, we hit a biologically determined “intimacy gap,” and any additional relationships must be shallow. Dunbar discovered that 150 has always been a significant figure, being about the size of a hunter-gatherer clan, a basic fighting unit and a branch of government or business. It’s higher than for most other group animals, including apes, reflecting our ability to manage much more complex social structures. (Dunbar links it to our relatively large neocortex—the outer lining of the brain.)

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Clearly, the quality of relationships within that 150—and while not all anthropologists agree with Dunbar’s figure, most accept the principle—differs greatly. Social networks are often depicted as concentric circles, starting with an inner nucleus of close friends and family, and with classmates, work colleagues and more peripheral friends represented by ever bigger radiating circles. Between each circle is blank space: a gap in people’s relationship groups.

These days, thanks to widespread use of social media, we feel connected with virtually infinite numbers of people. Yet the average number of Facebook friends, according to recent data, is 200—not all that far away from Dunbar’s hypothesis. Even Facebookers with 500 “friends” interact regularly with only a handful of them. As for offline relations, our innermost circles contain two people, on average, compared with three a few decades ago. Despite Twitter, Instagram and Tumblr, the intimacy gap hasn’t shrunk—all that has increased is our number of casual connections.

For as long as I can remember, I’ve been riveted by gaps and their intrinsic power. I can still recall the illogical fear I felt in my early 20s, seated in a window seat of a Boeing 747, watching the horizon fall steeply away as the plane banked at 32,000 feet. In later life, I climbed the staircase inside the Basilica di Santa Maria del Fiore, Florence’s Renaissance-era domed cathedral, known to Italians all over simply as “Il Duomo,” only to freeze as I emerged into an open-air deck with views over the red-roofed city and Tuscany countryside. Even as recently as last January, I stood with irrational trepidation behind a low wall overlooking the southern rim of the Grand Canyon, unable to think of much except the mess I’d create at the bottom if I fell.

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As you may have gathered, I’m not just afraid of heights but acrophobic, a condition that affects about 3 percent of the population. We are afraid of the gap between the height we’re at and the plummet to the earth, but the deep psychology of this probably has something to do with the sudden death that would ensue. The old joke is falling doesn’t kill you. Although the scariness on the way down is a big concern, it’s the sudden stop at the bottom that proves decisive.

Yet I’ve always been struck by non-physical gaps, too. The yawning divide between political viewpoints, for instance. Between the different versions of Christianity and Islam. Between the tribes that follow rival football or baseball or hockey teams. Between intellectual theories, such as capitalism versus labor. Between men and women. And so on.

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In fact, as I’ve found, when you think hard about gaps, you start to see them nearly everywhere, and to comprehend how integral they are to almost everything. Gaps act as both links and separators. Nature’s go-betweens, they connect features in the landscape, but also people within social structures, workplaces and institutions. They delineate different ideas and mind-sets, too. Significant in all our endeavors, they frame our lives, limiting, stretching and provoking us. Powerful forces are at work across gaps, often evoking strong responses—thwarting the mundane necessity of taking a pee, as we’ve seen.

Gaps define, inform and motivate. They define by forming distinct boundaries. They inform because, intuitively, we glean meaning from them—when we drive, for example, we continually judge physical gaps between vehicles. They motivate, impelling us to work to plug a financial gap, for instance, or to fill an emotional gap by finding a congenial mate. Governments respond to gaps with policy. Artists respond with creativity. Inventors respond with products. Scientists respond with knowledge. Nature responds with evolution. And the universe responds to gaps with matter.

Throughout history, what has distinguished the most gifted and outstanding individuals has been their innate grasp of the importance of what lies in-between. Plato, the Greek philosopher, was captivated by the dichotomy between perception and reality. Mother Teresa was appalled by the gulf between rich and poor. Steve Jobs saw a gaping hole in the market for user-friendly mass computing.

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These “gap thinkers”—and others, such as Galileo Galilei, Charles Darwin, Marie Curie and Martin Luther King—understood that gaps contain critical information. Reflect on Isaac Newton, for a moment. For thousands of years, farmers had been watching apples drop from trees—but it was not until Newton thought about what separates branch from ground that he hit upon something elemental: gravity. Like the other intellectual giants, he possessed, as well as a brilliant, enquiring mind, an urge to delve into what is mostly overlooked and to uncover what I call “the surprising truth hiding in-between.”

Unlike those innovative individuals who recognize and exploit gaps, and who are constantly alert to the surprising truth hiding in-between, most people are not natural gap thinkers. Yet while most of us might not consciously register gaps, we all have an innate knowledge of them. We mediate them unconsciously every day—otherwise, we’d bump into walls and burn ourselves while lifting a cup of coffee to our mouths. If we didn’t understand work hierarchies, with all their built-in gaps, we would get lost in the labyrinth of office politics. If we couldn’t accommodate the ideological, social and personality quirks that differentiate us from others, we would be friendless.

And just think about the space between musical notes: those brief silences that are so crucial to a melody. About the seemingly huge, terrifying gap we have to lean across to kiss someone for the first time. About the enormous void through which we hurtle if we jump out of a plane, trusting in our parachute as a brake—well, those of us who can, that is.

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While a gap’s-eye view offers a fresh perspective—and the realization that it’s often what we don’t see that counts—gaps themselves are nothing new. In fact, a gap-defining moment occurred about 500 million years ago, when early organisms, until then rooted to the seabed, went out to find food. They created a radical gap by severing their connection with their home base. Then these creatures grew nerve cells, some of which helped them to distinguish movement around them and evade predators—the first example of gap processing. Over the millennia, the nerve cells evolved to become eyes, and as brains grew increasingly sophisticated, dealing with spaces became mostly automatic.

With gaps hard-wired into our brains, we can process them without really having to think about it. One of the most intriguing gaps is that 3 pounds of jello-like mass inside our craniums—the brain. As most people know, the brain consists of two halves: a right hemisphere, responsible for spatial navigation and for processing sights, sounds, faces and emotions, and a left hemisphere, responsible for speech, language, numbers and practical skills. While the right side is associated with fantasy, creativity and risk, the left equips us for an intellectual conversation. So, in addition to the physical gap between the two halves, there is a gap between the contrasting and complementary functions they perform.

At the same time, the brain—being extremely plastic—is able to bridge those functional gaps. Most dramatically, gaps between hemispheres can even be bridged when one half is removed, usually as a last-ditch measure to treat children suffering from violent and drug-resistant seizures. When the parents of 7-year-old Cameron Mott of North Carolina were told that their daughter’s only chance of living a life without seizures was to have the right hemisphere of her brain removed, their initial reaction was like any parents': abject horror. As often happens following such surgery on kids, however, Cameron’s remaining hemisphere compensated by taking over most of the functions of the excised half. She’s now a bright, cheerful 14-year-old.

Other abnormalities in the brain can create new gaps, and new gap-solutions. One morning in Boston in 1996, Jill Bolte Taylor woke up with a stabbing pain behind her left eye. For the love of a brother with schizophrenia, Bolte Taylor—then a neuroanatomist in Harvard University’s Department of Psychiatry—spent her days mapping the brain’s microcircuitry and her weekends advocating for the National Alliance on Mental Illness. On that winter morning, she collapsed in the shower, her right arm paralyzed. A blood vessel had exploded in the left side of her brain.

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It was eight years before Bolte Taylor recovered normal speech and mobility. The damage to her left hemisphere meant she could no longer work as a scientist. In the wake of the stroke, though, thanks to an intensification of activity in her right hemisphere, her sense of color and visual creativity was heightened. She now uses art and music to promote brain research and brain trauma recovery programs—filling a massive treatment gap.

Bolte Taylor’s experience echoes the findings of UCSF neurologist Bruce Miller’s work with dementia patients. Miller has found that as the left brain-linked capabilities of such patients deteriorate, and their ability to communicate diminishes, they suddenly develop new artistic and musical talents. His theory is that the left hemisphere, when fully functioning, dominates the right, constraining creativity. And when the left becomes less powerful, through injury or disease, the right fills the gap.

Perhaps the most fundamental gap of all is the one between our private and public selves—between the person only we properly know, and whom we talk to continually inside our heads—and the persona we project, whether at work or in the company of friends, family, lovers or strangers. It’s a gap we endlessly negotiate as we move between home, workplace and social situations endeavoring, variously, to belong, stand out, be liked or succeed, and exposing our “true” selves to varying degrees.

That’s also the gap on stark display, as it were, in the men’s lavatory, where a bodily function generally performed in private is transposed to a semi-public arena … and, well, you know the rest.