HOW many Facebook friends do you have? For some, the answer can be a signal of social success, and the numbers claimed can be enormous: Facebook permits 5,000 of them (though these might include products and companies as well as people). But Robin Dunbar, a psychologist at Oxford University, has long reckoned that claims of vast numbers of Facebook friends do not say much about actual human relationships. This week, as he describes in a paper in Royal Society Open Science, he is even more certain.

Dr Dunbar is the eponymous originator of Dunbar’s number, a rough measure of the number of stable relationships that individuals can maintain. He came up with it in 1993, when he was studying the brains of social primates. He found a correlation between the average size of each species’s neocortex (a recently evolved part of the brain) and that of their social groups. Extrapolating the results to humans, he reckoned, meant they should have social circles—of close friends and relatives, and frequently seen acquaintances—of about 150 people. And that is what he found. From the sizes of Neolithic villages to the centuries of Roman legions, humans seem to have organised themselves in the past into groups of 100-200.

Things have changed a bit since Neolithic and Roman times, though, and many wonder what effects modern technology might have on the size of such circles. Perhaps there is indeed a cognitive limit, imposed by the brain’s internal architecture, on how large a social structure can be maintained. But there may also be another limit: time. Maintaining 150 friendships face-to-face consumes a lot of that. Cobbling together many times this number of connections online, though, is a doddle.

Previous attempts to decide between these possibilities have tended to come down on the cognitive-limit side of the fence. But they have been criticised for looking at unrepresentative groups of people: students (inevitably), scientists and particularly heavy users of social networks. The latest try, in which Dr Dunbar piggybacked on a survey organised by a biscuit-maker, has overcome that. It is the first national-scale, randomly sampled study to investigate the matter.

The survey asked 2,000 people, chosen because they were regular social-network users, and a further 1,375 adults in full-time employment, who might or might not have been such users, how many friends they had on Facebook. The results showed, to no surprise whatsoever on the part of Dr Dunbar, that the average number of Facebook friends in the two groups were Dunbar-sized numbers: 155 and (when those who did not use Facebook at all were excluded) 187, respectively.

Other details matched Dr Dunbar’s earlier work, too. This described a pair of smaller socially relevant numbers—a support clique (people you would rely on in a crisis) of about five and a sympathy group (those you would call close friends) of about 15. Such cliques and groups turned up in detailed answers to questions about Facebook users’ relations with others.

These results, then, confirm that what constrains an individual’s number of friends is neurological. Even though social networks like Facebook could help people handle far more social interactions than Dunbar’s number describes, it seems the human brain simply cannot keep up.