Robin Dunbar came up with his eponymous number almost by accident. The University of Oxford anthropologist and psychologist (then at University College London) was trying to solve the problem of why primates devote so much time and effort to grooming. In the process of figuring out the solution, he chanced upon a potentially far more intriguing application for his research. At the time, in the nineteen-eighties, the Machiavellian Intelligence Hypothesis (now known as the Social Brain Hypothesis) had just been introduced into anthropological and primatology discourse. It held that primates have large brains because they live in socially complex societies: the larger the group, the larger the brain. Thus, from the size of an animal’s neocortex, the frontal lobe in particular, you could theoretically predict the group size for that animal.

Looking at his grooming data, Dunbar made the mental leap to humans. “We also had humans in our data set so it occurred to me to look to see what size group that relationship might predict for humans,” he told me recently. Dunbar did the math, using a ratio of neocortical volume to total brain volume and mean group size, and came up with a number. Judging from the size of an average human brain, the number of people the average person could have in her social group was a hundred and fifty. Anything beyond that would be too complicated to handle at optimal processing levels. For the last twenty-two years, Dunbar has been “unpacking and exploring” what that number actually means—and whether our ever-expanding social networks have done anything to change it.

The Dunbar number is actually a series of them. The best known, a hundred and fifty, is the number of people we call casual friends—the people, say, you’d invite to a large party. (In reality, it’s a range: a hundred at the low end and two hundred for the more social of us.) From there, through qualitative interviews coupled with analysis of experimental and survey data, Dunbar discovered that the number grows and decreases according to a precise formula, roughly a “rule of three.” The next step down, fifty, is the number of people we call close friends—perhaps the people you’d invite to a group dinner. You see them often, but not so much that you consider them to be true intimates. Then there’s the circle of fifteen: the friends that you can turn to for sympathy when you need it, the ones you can confide in about most things. The most intimate Dunbar number, five, is your close support group. These are your best friends (and often family members). On the flipside, groups can extend to five hundred, the acquaintance level, and to fifteen hundred, the absolute limit—the people for whom you can put a name to a face. While the group sizes are relatively stable, their composition can be fluid. Your five today may not be your five next week; people drift among layers and sometimes fall out of them altogether.

When Dunbar consulted the anthropological and historical record, he found remarkable consistency in support of his structure. The average group size among modern hunter-gatherer societies (where there was accurate census data) was 148.4 individuals. Company size in professional armies, Dunbar found, was also remarkably close to a hundred and fifty, from the Roman Empire to sixteenth-century Spain to the twentieth-century Soviet Union. Companies, in turn, tended to be broken down into smaller units of around fifty then further divided into sections of between ten and fifteen. At the opposite end, the companies formed battalions that ranged from five hundred and fifty to eight hundred, and even larger regiments.

Dunbar then decided to go beyond the existing evidence and into experimental methods. In one early study, the first empirical demonstration of the Dunbar number in action, he and the Durham University anthropologist Russell Hill examined the destinations of Christmas cards sent from households all over the U.K.—a socially pervasive practice, Dunbar explained to me, carried out by most typical households. Dunbar and Hill had each household list its Christmas card recipients and rate them on several scales. “When you looked at the pattern, there was a sense that there were distinct subgroups in there,” Dunbar said. If you considered the number of people in each sending household and each recipient household, each individual’s network was composed of about a hundred and fifty people. And within that network, people fell into circles of relative closeness—family, friends, neighbors, and work colleagues. Those circles conformed to Dunbar’s breakdown.

As constant use of social media has become the new normal, however, people have started challenging the continued relevance of Dunbar’s number: Isn’t it easier to have more friends when we have Facebook, Twitter, and Instagram to help us to cultivate and maintain them? Some, like the University of California, Berkeley, professor Morten Hansen, have pointed out that social media has facilitated more effective collaborations. Our real-world friends tend to know the same people that we do, but, in the online world, we can expand our networks strategically, leading to better business outcomes. Yet, when researchers tried to determine whether virtual networks increase our strong ties as well as our weak ones (the ones that Hansen had focussed on), they found that, for now, the essential Dunbar number, a hundred and fifty, has remained constant. When Bruno Gonçalves and his colleagues at Indiana University at Bloomington looked at whether Twitter had changed the number of relationships that users could maintain over a six-month period, they found that, despite the relative ease of Twitter connections as opposed to face-to-face one, the individuals that they followed could only manage between one and two hundred stable connections. When the Michigan State University researcher Nicole Ellison surveyed a random sample of undergraduates about their Facebook use, she found, while that their median number of Facebook friends was three hundred, they only counted an average of seventy-five as actual friends.

There’s no question, Dunbar agrees, that networks like Facebook are changing the nature of human interaction. “What Facebook does and why it’s been so successful in so many ways is it allows you to keep track of people who would otherwise effectively disappear,” he said. But one of the things that keeps face-to-face friendships strong is the nature of shared experience: you laugh together; you dance together; you gape at the hot-dog eaters on Coney Island together. We do have a social-media equivalent—sharing, liking, knowing that all of your friends have looked at the same cat video on YouTube as you did—but it lacks the synchronicity of shared experience. It’s like a comedy that you watch by yourself: you won’t laugh as loudly or as often, even if you’re fully aware that all your friends think it’s hysterical. We’ve seen the same movie, but we can’t bond over it in the same way.

With social media, we can easily keep up with the lives and interests of far more than a hundred and fifty people. But without investing the face-to-face time, we lack deeper connections to them, and the time we invest in superficial relationships comes at the expense of more profound ones. We may widen our network to two, three, or four hundred people that we see as friends, not just acquaintances, but keeping up an actual friendship requires resources. “The amount of social capital you have is pretty fixed,” Dunbar said. “It involves time investment. If you garner connections with more people, you end up distributing your fixed amount of social capital more thinly so the average capital per person is lower.” If we’re busy putting in the effort, however minimal, to “like” and comment and interact with an ever-widening network, we have less time and capacity left for our closer groups. Traditionally, it’s a sixty-forty split of attention: we spend sixty per cent of our time with our core groups of fifty, fifteen, and five, and forty with the larger spheres. Social networks may be growing our base, and, in the process, reversing that balance.