Chances are you're a friend of a friend of a friend of Mark Zuckerberg — at least according to Facebook.
A well-known theory holds that most people, at least in the US and perhaps in the world, are six degrees of separation away from each other. Pick a random stranger anywhere in the country, the theory goes, and chances are you can build a chain of acquaintances between the two of you in no more than six hops.
The idea of "six degrees of separation" rests on a scientific foundation that's dubious at best. But Facebook, because its users give it access to possibly the richest data set ever on how 1.6 billion people know and interact with each other, set out to prove it with a statistical algorithm.
The researchers found that the world is connected enough that six degrees of separation might be too many. The average Facebook user is three and a half degrees of separation away from every other user, and the social network's post tells you your own distance from everyone else on the site.
Mark Zuckerberg is 3.17 degrees of separation from all Facebook users.
The 1967 experiment that proved "six degrees of separation"
How people define a Facebook "friend" varies widely, so how connected you are presumably depends in part on how generous you are with your Facebook friendship.
The typical Facebook user has 155 friends, but only describes 50 of them as friends in real life, according to a 2014 study from the Pew Research Center. Thirty-five percent of people have Facebook friends they've never met in person.
The original "six degrees of separation" experiment required people to know each other fairly well: They had to be on a first-name basis, at a time when society was slightly more formal, in order for the connection to count.
Social psychologist Stanley Milgram conducted an experiment in 1967 around the "small world problem": How are two randomly selected people within the United States connected?
Milgram picked a stockbroker in Sharon, Massachusetts, a Boston suburb, as his target, and three groups of volunteers, two in Nebraska and one in Boston, as a starting point. The volunteers got the stockbroker's name, occupation, address, college and year of graduation, and dates of service in the military. They were also told the name and hometown of the stockbroker's wife, and that he worked in Boston proper.
Volunteers were given an impressive-looking document that was supposed to reach the stockbroker, and were instructed to send it to someone they knew on a first-name basis who they thought could get them closer to the stockbroker. That person was then supposed to send it to someone, and so on, until the document arrived.
About one-third of the documents eventually reached the stockbroker, after a chain of, on average, six people — the six degrees of separation. It's a small world after all, Milgram concluded.
Class and race mean we might be more separate than we think
Judith Kleinfeld, a professor of psychology at the University of Alaska Fairbanks, studied Milgram's unpublished archives in 2002, planning to try to create a new version of the experiment using email.
She found instead that Milgram's conclusions rested on a shaky foundation, and that class and race divided Americans more than his original paper admitted.
The majority of Milgram's letters didn't make it to the Boston stockbroker. And further experiments that factored in class and race suggested that making connections across those barriers was even more challenging.
A later experiment of Milgram's, in which white people in Los Angeles tried to reach white and black people in New York, found that 27 percent of the intraracial chains eventually arrived, while only 13 percent of the interracial ones did.
Another study in the late 1960s, not by Milgram, asked people in Ohio from low-, middle-, and high-income households to try to reach people in Los Angeles.
While middle- and high-income people were able to find their targets regardless of their household income, low-income people could only connect with other low-income families, Kleinfeld wrote in a 2002 article in the journal Society.
The correct interpretation of Milgram, she argued, was not the optimistic conclusion that we're all only a few degrees of separation away. Instead, it's that there are still barriers that are insurmountable.
"We live in a world where social capital, the ability to make personal connections, is not widespread and more apt to be a possession of high-income, white people or people with exceptional social intelligence," Kleinfeld wrote.
Does the Facebook analysis mean that technology has helped overcome those barriers? It's hard to tell. People making more than $75,000 per year are overrepresented among Facebook users, according to Pew, as are younger people. African Americans use Facebook at slightly lower rates than white people.
But the real divide is between people who are on Facebook and those who aren't on the internet at all. Facebook users make up about 62 percent of American adults but 72 percent of all internet users. Americans without the internet are disproportionately older, rural, and less educated. As Facebook users get closer, they might be becoming ever more isolated.
Correction: An earlier version of this article said Stanley Milgram conducted the Stanford Prison Experiment. He didn't; he conducted the Milgram Obedience Study, in which volunteers were asked to play the role of a teacher and shock students who gave an incorrect answer.