Kleinfeld made some disconcerting discoveries in Milgram’s papers:
Very few of his folders reached their targets. In his first, unpublished, study, only three of 60 letters–five percent–made it. Even in Milgram’s published studies, less than 30 percent of folders got through…
Perhaps people didn’t bother sending the letters on. That was Milgram’s explanation. But that seems unlikely. The folder was not a simple chain letter, but an official-looking document with heavy blue binding and a gold logo. If the subjects knew how to reach the targets, they probably would have.
Kleinfeld also scrutinised Milgram’s samples. In the Nebraska survey, only half of the almost two hundred ‘starters’ were randomly selected. The others were stock investors, which gave them a natural affinity with the target, the Boston stockbroker. And of the ninety-six folders that started their journey with people who had been randomly selected and so met Milgram’s condition of social and physical distance, only eighteen reached the broker!
Kleinfeld concluded that the evidence was inconclusive–maybe we live in a small world; maybe we don’t.
So who was right–Milgram or Kleinfeld? New evidence arrived shortly after Kleinfeld penned her critique. Professor Duncan Watts and colleagues did what Kleinfeld had originally intended to do–they organised a massive email exercise to retest the small-world hypothesis. Volunteers registered online and were randomly allocated one of eighteen targets in thirteen countries. The targets included a professor at an Ivy League university, an archivist in Estonia, a consultant in India and a policeman in Australia.6 Participants were simply asked to send the message to an acquaintance who was ‘closer’ to the target than they were.
On the whole, the results vindicated Milgram and the small-world thesis. An impressive total of 24,163 message chains were started, and while a mere 384 were completed (a success rate of only 1.6 per cent), the average completed chain length–4.05 intermediaries–was short. The researchers looked hard at why there were so many incomplete chains. They concluded that chains were aborted not because it was too difficult to find the targets, or because the appropriate links didn’t exist, but because of individual apathy or disinclination to participate. One reason for this conclusion was direct research: recipients who did not forward the message after a week were asked why they had not participated. ‘Less than 0.3 per cent of those contacted claimed that they could not think of an appropriate recipient, suggesting that lack of interest or incentive, not difficulty, was the main reason for chain termination.’
The other intriguing finding was that one of the eighteen targets–the Ivy League professor–received nearly half of all the completed chains. Now, 85 per cent of senders were college educated and more than half were American, so it seems likely that most senders anticipated little difficulty in reaching him. The researchers believed that the professor’s ‘true’ accessibility was ‘little different from that of other targets’, but the belief that he could be reached encouraged the participants to proceed. ‘Network structure’, they concluded, ‘is not everything’–the motivation of the people in the network matters as well. If someone believed that the target could be reached, he could be.
So, Watts and his colleagues largely validated the small-world idea. Above all, his retest lets us stop worrying about Milgram’s low response rates. In fact, in comparison with Watts’ study, Milgram’s response rate was quite high; and to expect unpaid volunteers to be highly motivated to complete each chain is unrealistic. In any case, an incomplete chain didn’t prove that the linkage doesn’t exist, just that it wasn’t found or used.
As for Milgram’s sample sizes, we’ve looked at all the evidence again and concluded they were satisfactory–there were sixty-four completed chains, with an average length of 5.2 intermediaries. The Watts study corroborates this: 384 completed chains, with a similar number of intermediaries in the US, and slightly more, around seven, for international chains.7
Then researchers found the easy way to generate large samples. In 2008 the Microsoft Messenger project was completed by Eric Horvitz and Jure Leskovec. They had the benefit of a vast database of personal conversations–all 30 billion Microsoft instant-message communications sent between 180 million people for the month of June 2006, comprising about half of all the world’s instant-messaging traffic at that time. With a complete map of senders and recipients, the researchers were able to calculate the ‘degrees of separation’ for all 180 million people.
What do you think the average degrees of separation were? The magic number six crops up again–to be precise, 6.6.
‘To me, it was pretty shocking,’ says Horvitz. ‘What we’re seeing suggests there may be a social connectivity constant for humanity. People have had this suspicion that we are really close. But we are showing on a very large scale that this idea goes beyond folklore.’
But there was a kicker in the results, showing that not everyone is that well connected. While nearly four out of five pairs of people in the database could be connected in seven or fewer hops, at the other extreme there were some pairs requiring twenty-nine hops to connect. So most of the 180 million people sending instant messages live in a small world, but more than a fifth of them do not. Some poor souls manage the amazing feat of being connected to the Internet and instant-messaging, yet significantly isolated from other inhabitants of cyberspace.
So what? If we live in a small world, what does that mean, and how can we benefit from it?
It’s important to be realistic about what a small world does and does not imply. We may all be a few short hops from our president or prime minister, but that doesn’t mean he’s about to invite us round for tea. As Stanley Milgram said in his article, five sounds like a small number, but in this experiment that’s misleading. It really means ‘five circles of acquaintances’ apart. Almost all Americans were probably only a few removes from Nelson Rockefeller, but very few integrated their lives with his. ‘Even in a small world,’ Milgram said, ‘geographical and social differences are still important.’
As we’ll see later, many people remain relatively isolated–through geographical remoteness, poverty or lack of social connections.
Or simply by not feeling part of a small world. In a very real sense, the world is small if we think it is. In Watts’ email experiment, the college professor received such a large proportion of completed chains principally because people felt they could link to him. We will try to connect if we believe our efforts will be successful. And this is a virtuous circle, because they are likely to be successful if we try to connect. It’s easier than we think to reach almost anyone; the main barrier is in our heads.
Why is it better to live in a small, more connected world? Consider two extreme scenarios. In one, you are a hermit. In the other, you know everyone else in the world. Which life is likely to be richer, more interesting, with more opportunity?
A historical perspective helps. Imagine spending your entire life in a cave, knowing only a few fellow cave people. There could be millions of other caves and tens of millions of other people around the planet, but they are completely irrelevant if you cannot reach them. No contact, no trade, no sharing of knowledge, no friends from beyond your own cave. A large, unknowable and forbidding world outside. And inside? Isolated. Poor. Dangerous.
Now, envision new communications technology connecting the cave people–roads, explorers, merchants, boats, bicycles, cars, trains, planes, telephones, fax machines, inter-cave videoconferencing, cave cyberspace. A small world. Connected. Specialised. Interdependent. Infinitely richer in every way.