Keeping Our Distance

Bad News for the Small-World Crowd: More Than 6 Degrees Separate Us

You know that whole six degrees of separation idea, the global-village notion that we're all interconnected like Tinkertoys and everybody pretty much knows everybody? Or at least that you know somebody who knows the person who knows a guy . . . who actually knows Britney Spears? You've felt that warm fuzzy sense you get that you are only a half-dozen people removed from anybody in the world?

Forget about it, says Judith Kleinfeld, a sociologist at the University of Alaska-Fairbanks. She doesn't believe it for a second.

"We live in a world where social capital, the ability to make personal connections, is not widespread but more apt to be a possession of people of higher social status," Kleinfeld writes in the current issue of Society.

So how do you explain the fact that your sister's friend's mother in Tacoma knows someone you know in Asheville?

Ever heard of coincidence? "We have a poor mathematical, as well as a poor intuitive, understanding of the nature of coincidence," Kleinfeld writes in her article "The Small World Problem."

But for some reason, you get goose bumps when you have a brush with a celebrity. You feel toasty when you find you have friends in common with a stranger. You go out of your way on vacation to seek out people you've only heard about. You believe that such a connection could possibly get you a new job. Or could help you find a doctor who could cure your disease.

The small-world notion "is such an attractive idea," Kleinfeld says. "It sailed into the imagination." She says that believing in such an unproven premise is a "positive illusion" to those who want to believe that there is a master plan and those who take solace in the thought that we're all in this together. It gives Earthlings a sense of security.

But it's impossible to prove. How will we ever know that some guy in the Gobi Desert is connected to a woman in Soweto? We won't. But people still keep trying to establish that it is, as the Disney robots sing, a small world after all.

The latest attempt is the Small World Research Project,smallworld.sociology.columbia.edu, an Internet-driven experiment launched in the fall by Duncan Watts at Columbia University. Watts wants to explore the idea that the world is tinier than it seems and that every one of its 6 billion residents is separated by only a handful of social acquaintances.

He hopes to use the Internet to show that we are all linked. "At the level of connectivity we are looking at," he says, "we are finding that the world is pretty connected."

To distinguish hype from hypothesis, Watts, an assistant professor of sociology, chose a diverse set of anonymous "targets" around the world. Internet users are invited to register at the site. They receive a little information about a target and, with guidance from the Web site, they send an e-mail to someone they already know who might be closer to the target than they are. And so on.

Watts wonders just how many e-mails it will take for a volunteer to reach a target. He says that people are slow to dive in because it seems like a lot of trouble. "We are getting there," he says. "We have about 20,000 signed up to participate. We have 16 targets and soon we will have more all around the world."

He has pursued targets "who are not just academics and computer industry types." An ex-flight attendant and someone who works in a pizza parlor, for instance. Those people, he says, might indeed find out that they are connected to faraway lands and people in ways they never envisioned.

"People have a difficult time understanding this problem because they tend to only think about the people they are directly connected to -- who often are a lot like them," Watts says. "What they don't necessarily understand is that if one of their friends has just a single friend who has just a single friend who is quite different from them, then a path exists -- no matter how counterintuitive that may seem. That path may be very hard to find and may be impossible to use."

It all depends on what you mean by "friend." The intensity of our connections fluctuates. You know a lot of people by face. You know fewer on a first-name basis. A smaller number might go to your funeral and you've only kissed a fistful. You feel differently toward each of them.

The small-world hypothesis was first proposed by Stanley Milgram, a social psychologist at Harvard University in the 1960s. Milgram -- who went on to teach at Yale and the City University of New York -- was famous for a series of controversial mock-shock experiments pitting obedience to authority against humane responsibility. In the experiments, people were asked to mete out electric-shock punishment to other people as part of a learning experiment. The "other people," as it turns out, were actors pretending to receive voltage.

Milgram also is responsible for loosing the six degrees of separation theory on the world. He pinpointed the "small world problem" by telling a story:

"Fred Jones of Peoria, sitting in a sidewalk cafe in Tunis, and needing a light for his cigarette, asks the man at the next table for a match. They fall into conversation; the stranger is an Englishman who, it turns out, spent several months in Detroit studying the operation of an interchangeable-bottlecap-factory.

" 'I know it's a foolish question,' says Jones, 'but did you ever by any chance run into a fellow named Ben Arkadian? He's an old friend of mine, manages a chain of supermarkets in Detroit . . .'

" 'Arkadian, Arkadian,' the Englishman mutters. 'Why, upon my soul, I believe I do! Small chap, very energetic, raised merry hell with the factory over a shipment of defective bottlecaps.'

" 'No kidding!' Jones exclaims in amazement. 'Good lord, it's a small world, isn't it?' This experience is so surprising, yet at the same time so familiar, that we have coined a phrase to describe it: It's a small world, isn't it?"

In the mid-1960s, Milgram sent several hundred letters to everyday folks in Midwestern places such as Nebraska and Kansas, asking them to try to forward the letters to a specific person, a target, in Northeastern urban places such as Boston. He told each sender a little bit about the target -- name, location and occupation. In the most-likely event that a sender did not know the target, the sender was asked to mail the letter to someone -- an acquaintance whom they knew on a first-name basis -- who might know the target or at least move it closer to the target. And so the chain of letters continued until the target was reached.

One target person was the wife of a student at the Episcopal Theological Seminary in Cambridge. She received a brown folder -- originally sent to a Kansas wheat farmer -- in an astounding four days. Degrees of separation: three! The farmer had passed it to an Episcopal priest who had mailed it to a professor at the seminary who had handed it to the target.

Milgram discovered that the average number of steps involved in his studies was six or so and that's where the overused phrase "six degrees of separation" comes from.

The phrase gave rise to "Six Degrees of Separation," a popular play by John Guare -- and subsequently a movie -- in which a young man in a bloodstained shirt shows up at the Fifth Avenue home of a rich art dealer and his wife. The man claims to be a friend of their kids at Harvard. He cooks them a meal and tells them elaborate stories. They discover the next morning that he is not who he said he is.

The saying has entered American parlance. And parlors. Six Degrees of Kevin Bacon is a popular game in which players are given the name of an actor and asked to connect the dots to Bacon using movies that the actors have appeared in. For example, Alfre Woodard. Alfre Woodard was in the 1999 movie "Mumford" with Pruitt Taylor Vince, who is in the upcoming "24 Hours" with Kevin Bacon. Degrees of separation: Two.

The computer science department at the University of Virginia has designed a Web site testing the Kevin Bacon proposition:www.oracleofbacon.org, and in a popular Visa ad that first ran during the Super Bowl, Bacon proved his identity to a cashier using the six degrees theory.

Watts has tested the small-world notion from another angle. In 1998, he and Cornell mathematician Steven H. Strogatz published a mathematical response in the scientific journal Nature. They contended that by adding or moving around at random a few of the existing connections in any kind of network, you dramatically reduce the number of links between individual nodes, vertexes or individuals. That means if someone you know moves to Houston, the degrees of separation between you and a whole host of Houstonians drops substantially.

But Judith Kleinfeld says that no matter how many ways you come at the question, you're dealing with a premise that was flawed from the get-go.

While digging through Milgram's work in the archives of the Yale University library, she discovered material that "was disconcerting and cast doubt on the validity of his findings."

"He stacked the deck," she says.

Milgram published the story of the divinity student's wife in the premiere issue of Psychology Today in May 1967. The story, Kleinfeld says, was a statistical anomaly. Here is what Milgram did not report: Some 60 starters were recruited in Kansas. Fifty chains were started. Only three (5 percent) of the original 60 documents reached the woman in Cambridge. The average number of degrees of separation: nine.

Milgram's studies, Kleinfeld says, "strongly favored chain completion." She says that Milgram worded his recruitment advertisement for the Kansas experiment so as to attract "particularly sociable people proud of their social skills and confident of their powers to reach someone across class barriers." In other studies, he bought names from mailing lists of people who were affluent enough to have been put on mailing lists in the first place.

To boot, Kleinfeld points out, another study in the archives, perhaps sent to Milgram for inspection, "not only showed extremely low chain completion rates (below 18 percent) but also suggested that people are actually separated quite dramatically by social class." In the study of 151 Crestline, Ohio, volunteers -- of various income groups -- senders were asked to reach targets -- also of various incomes -- in Los Angeles. While some of the upper-income senders were able to reach their California targets, none of the low income senders were successful.

"These patterns," Kleinfeld writes, "suggest a world divided by social class, with low-income people more apt to be disconnected." People who run in the same circles are more likely to know one another and one another's friends.

She cites several small world studies by other researchers that were not successful.

Kleinfeld found another study, a 1978 experiment in the urbanized Northeast, in which a substantial number of documents reached the targets -- about 30 percent. But the successes were mostly within racial groups. The authors concluded, "Crossing the racial boundary is less likely to be attempted and less likely to be effective."

The new Small World Research Project on the Internet "is a great effort to understand the world of connections of people . . . who are on computer," Kleinfeld says. "Such as the chattering classes."

No one is more swept up by small-world possibilities than members of the media. In part, because we inhabit such a small world -- of sources and subjects and ideas and interests.

In fact, get this: I have a colleague whose former wife was vacationing in Anguilla. Her son, Adrian, was running on a pier at a restaurant and bumped headlong into a tall stranger.

Adrian looked up and did a double take. Before he could say a word, the tall man smiled and nodded.

"Yep," the man said. "Kevin Bacon. How are you doing?"

And Bacon walked on.

So I am four degrees from Kevin Bacon.

But who's counting?