“Everyone on this planet is separated by only six other people”. So says a character in John Guare’s 1990 play Six Degrees of Separation. It’s a maxim that has come to define our ideas about the reach of social networks – and there’s some truth in it too. The average number of friends-of-friends connecting you to any other random person might not be exactly six – it depends on how you define links, for one thing – but it is a small number of about that size.

But has it always been such a small world? It’s tempting to think so. Jazz musicians in the early 20th Century were united by barely three degrees of separation. Much further back, scientists in the 17th Century maintained a dense social network via letters, as did humanist scholars of the Renaissance. But those were specialised groups. Intellectual and aristocratic elites in history might have all known one another, but was it always a small world for ordinary folk too? Studying such social networks is difficult, because the relationships of the average person living in pre-industrial times were rarely documented. Yet there could be an indirect way to find out – by studying the spread of disease.

The modern understanding of small-world social networks has come largely from direct experiments. Guare took his idea from experiments conducted in the late 1960s by social scientist Stanley Milgram of Harvard University and colleagues. In one study, they attempted to get letters to a Boston stockbroker by sending them to random people in Omaha, Nebraska, bearing only the addressee’s name and profession and the fact that he worked in Boston. Those who received the letter were asked to forward it to anyone they knew who might be better placed to help it on its way.

Most of the letters didn’t arrive at all. But of those that did, an average of only six journeys were needed to get them there. A much larger-scale re-run of the experiment in 2003 using email forwarding found an almost identical result: the average “chain length” for messages delivered to the target was between five and seven. More recently, other researchers have claimed that in the age of Facebook we are only four degrees apart.

Going viral

Needless to say, it’s not possible to conduct epistolary experiments to deduce the human social networks of former ages. But there are other ways to figure out what they looked like, according to Mark Newman of the University of Michigan at Ann Arbor and his coworkers. These networks don’t only spread news, information and rumour, but also things that are decidedly less welcome, such as disease. Many bugs are passed between individuals by direct, sometime intimate contact – could spread of an epidemic reflect the web of human relationships on which it happens?

Newman and colleagues admit that the spread of disease is only an approximate proxy for social networks. Disease can be transmitted by rats, fleas or strangers, for example, rather than among friends or acquaintances. Still, the team argues that in pre-industrial times, the transmission of pathogens would have roughly reflected the nature of human contact. Rats and fleas never travelled far unless carried by humans, and since many people lived in small communities, meeting strangers may have been less common than today.

Despite the caveats, the researchers propose that the spread of the Black Death in the 14th Century could offer some clues about social networks at the time. It took at least three years for the disease to spread through Europe, Scandinavia and Russia in the 14th Century, beginning in the Levant and the Mediterranean ports. They argue that the crucial point is not how quickly or slowly the disease spread, but what the pattern was like.

Historical documents have already shown that the Black Death moved through the Western world rather like an ink blot spreading across a map of Europe: a steady advance of the “disease front”. In a pre-print paper on the physics arxiv, the team’s computer simulations and calculations show that the Black Death’s stain-like spread is possible only if people in the network were more poorly connected than today – in other words, if it wasn’t a small world. While they didn’t calculate a specific number for the degrees of separation, it was clear that there were essentially no “shortcuts” linking geographically distant individuals, so people must have further apart than six degrees. The pattern would have looked more blotchy – like modern disease epidemics – if people had been more connected, because new outbreaks would have seeded well outside the initial infected region.

So if the world was still “large” in the 14th Century, when did it become “small”? Newman and colleagues hope that other epidemiological data might reveal that, but they guess that it happened with the advent of long-distance transportation in the 19th Century, which seems also to have been the time that rapidly spreading epidemics appeared. There’s always a price for progress.

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