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Are you average and know 290 people?

Sunday, March 24, 2002

By Mackenzie Carpenter, Post-Gazette Staff Writer

How many people do you know named Nicole?

How many with pilot's licenses? Or people on dialysis?

These seemingly trivial queries actually have helped a couple of researchers come up with the answer to an unusual question: How many total people, on average, does a typical person know?

Russell Bernard, Peter Killworth and several of their colleagues have spent the past 15 years trying to unravel that mystery, and now, they say, they've solved it.

The average circle of acquaintances, they say, is 290 -- plus or minus a few people.

It might seem like one of those fascinating but useless bits of knowledge in some esoteric trivia game, but Bernard and Killworth believe that the mathematical model they've developed may one day provide government agencies and other organizations with an easy, inexpensive way to estimate hard-to-count populations, such as the homeless, abused children, rape victims, heroin users and people with HIV.

Their work, along with that of other researchers who are increasingly using computer models to study the intricacies of human interaction, illustrates a new trend toward collaboration by researchers in the "hard" sciences such as physics and mathematics, and those from the "softer" sciences, such as anthropology and sociology.

The method for answering the "How many people do you know?" question worked this way.

First, Bernard and Killworth surveyed people in the United States about 29 "populations" in which they might know someone -- people named Nicole or postal workers, for instance, and for which the two researchers had accurate counts from government data or other sources.

If the person being surveyed said, "I know three people named Nicole," the researchers determined what percentage of all Nicoles that person knew. The process was repeated across each of the 29 groups to give a pattern of percentages for the person being surveyed.

Then the researchers used those findings to estimate what percentage of the entire population the average person might know.

While the 290 figure is just an average, it's a surprisingly robust one, Bernard and Killworth said, because it kept appearing over many surveys covering nationally representative samples of people.

Bernard and Killworth found there was no obvious connection between the kind of life someone leads and how many people he or she knows. But they also believe our circle of acquaintances isn't just a matter of random luck.

"God isn't going to throw 600 people at Peter [Killworth] when he's born and two at me. ... We believe there are rules that govern who people know, and how they know each other," Bernard said -- rules the two are still trying to discover.

An oceanic encounter

Bernard, an anthropology professor at the University of Florida, and Killworth, an oceanographer and physicist at the Southampton Oceanography Centre in England, are an unusual pair of collaborators.

Bernard has always been fascinated with a branch of anthropology called social network analysis, which looks at how members of societies or groups, from tribal village inhabitants to Vietnam veterans, interact with each other. Killworth, as an ocean physicist, uses mathematical models to study how ocean currents and the atmosphere interact.

The two men met in 1972, when both were spending a year at the Scripps Institution of Oceanography in La Jolla, Calif. Bernard had just returned from a sojourn on a research vessel, where he was studying how social structures formed among the people on board.

Killworth was intrigued with what the anthropologist had found. He suggested that he could apply something known as the Baltimore traffic problem algorithm, designed to find the shortest distance between any two points in a traffic-clogged city, to Bernard's research to see if it could find the shortest social distance between people in a group.

The pair would ask each person in a group to list whom he had the most contact with, and then use the algorithm to calculate the cliques within each group.

At one point, they found themselves working with staffers at two federal penitentiaries.

"Prison staff would look at the output [from the algorithm] and see the patterns: These people in this group here are all whites from big cities in the North, these people are all Southern blacks, these people all committed the same crime," Bernard recalled.

In one case, though, the model turned up a group of three strongly linked people whose connections made little apparent sense: the three had committed different crimes, were racially mixed and were from Northern, Southern, rural and urban backgrounds. Everyone was stumped, and the researchers feared that their model had malfunctioned -- until the following week, when the three prisoners escaped together.

Six degrees

To further refine their knowledge, Bernard and Killworth examined what is today widely known as the "small world" or the "six degrees of separation" problem popularized by social psychologist Stanley Milgram in the 1960s. He was curious about how human beings were linked and whether we were tied together in a closely knit web.

To test that theory, he sent several hundred letters to people randomly chosen in the rural Midwest, asking them to forward the letters to another person living in the urban Northeast -- a "target," identified only by name, general location and occupation.

If the sender didn't know the target, he or she was asked to mail the letter to someone most likely to know the target. That person would then send the letter to someone he thought might know the target, and so on, creating a chain of letters. On average, it took between five and six letters before the target was reached.

As a result of Milgram's experiment, the term "six degrees of separation" was coined, eventually becoming the basis for a parlor game featuring actor Kevin Bacon and a play and a movie.

Yet even though many are familiar with the idea that we are removed from most people in the world by a chain of only five or six others, many people still think the small-world phenomenon is an example of extraordinary chance, said Bernard.

So Bernard and Killworth decided to turn Milgram's experiment on its head.

Instead of asking a group of people to find one target person, they would ask individuals which people they would initially get in touch with to find a large group of targets.

Using that approach, they had their first breakthrough in the early 1980s, after interviewing people from Morgantown, W.Va. -- their representative sample of ordinary Americans. They concluded that each person in this group would call upon about 250 people in their social networks to begin reaching their "targets."

But that number was still not as accurate as they would have liked, and so they came up with a new technique -- asking people how many others they knew in certain defined populations, and then computing their overall "social circle" from that information.

And that's what has led them to their estimate that most of us know, on average, 290 other people.

One challenge to their model, Bernard and Killworth have come to realize, is that people don't always know all the facts about their acquaintances.

For instance, people can be fairly accurate in saying how many priests they know, because priests tend to be highly visible, but they are less accurate in saying how many twins they know, because it often takes years for people to learn that an acquaintance has a twin sibling.

It also was vital, they realized, to get a good national sample to correct for regional variations. People in Oklahoma might know a lot more American Indians than others would, while Western Pennsylvanians might know more people of Croatian descent than others do.

Knowing terror victims

With their research becoming better known, it was no surprise that a reporter called them after Sept. 11 and asked them to estimate how many people in the United States knew someone who died in the terror attacks.

In an article published recently in the journal Connections, the two said the answer was about a half-million people.

If 3,000 people died in the attacks, and each one of them had a social network averaging 290, multiplying those two numbers would result in about 900,000 people knowing someone who died. But they estimated there would be considerable overlap within those social networks. Often, if you know someone in a population, the person you work with also knows that person. Accounting for this overlap reduced the figure to about 500,000.

What's the good of these kind of calculations?

Killworth has one answer: "Before we decide how much money to spend on a social problem, we need to know how big the problem is. It may not matter to anyone but scientists whether the typical American knows 290 people or 2,900, but it matters a lot if we can tell whether populations like the homeless are increasing or decreasing."
