What is the meaning of the phrase 'Six Degrees of Separation'?

In 1967, social psychologist Stanley Milgrim published a groundbreaking article in the inaugural issue of *Psychology Today* titled "The Small World Problem". Milgrim had already earned fame with his controversial "obedience to authority" experiment, where ordinary people were instructed to deliver increasingly powerful electric shocks to strangers, all in the name of obeying orders.

Milgrim's 1967 article reached a surprising conclusion: Everyone in the world was connected through no more than six people on average. A person in Iowa could be linked to someone in Belarus through a chain of six or fewer acquaintances. It truly was a small world after all!

Milgrim's study made a significant impact in the '60s, but it truly entered popular culture with the 1990 play *Six Degrees of Separation* and the subsequent 1993 film featuring a young Will Smith. Since then, the concept of 'six degrees of separation' has been embraced as a fundamental principle of social networks. But just how reliable is it?

The Problems with the Original Experiment

Milgrim's original 1967 experiment was conducted as follows: he enlisted "starters" in Kansas and Nebraska and instructed them to send an envelope to a "target" individual in Massachusetts. The starters were to forward the envelope to someone they knew well who might have a better chance of knowing the target. This process continued until the envelope reached the target.

Milgrim reported that "chains ranged from two to 10 intermediaries, with the median being five." If there were an average of five intermediaries connecting strangers, it would mean they were linked by six degrees.

However, when scrutinizing Milgrim's data from the first envelope experiment, the results were underwhelming. Of the 60 envelopes sent to the 'starters' in Kansas, only three ever reached the intended target. This resulted in a 5 percent success rate. Worse yet, these envelopes passed through an average of eight people, meaning nine degrees of separation.

In the follow-up study conducted in Nebraska, Milgrim achieved a 30 percent success rate and an average of six degrees. However, Judith Kleinfeld, a psychology professor at the University of Alaska, pointed out that Milgrim used a "passport" made from thick blue cardboard, embossed with the words "Harvard University" in gold, which may have increased the likelihood that senders would go the extra mile to find someone to deliver it. She also noted that most of the senders and targets were from higher-income backgrounds, making them more likely to have a broader network of acquaintances compared to those from lower-income backgrounds.

Kleinfeld referred to the evidence from Milgrim's pivotal 1967 study as "insufficient" and questioned whether the concept of six degrees of separation was simply an "academic urban legend."

Mathematics Reveals a Small World After All

Long before Milgrim’s experiment, mathematicians had already been grappling with the 'small world problem.' They sought to calculate the mathematical probability that two completely unrelated people might have a common acquaintance. "You also know Brianna from Boise? What a small world!"

Milgrim's social experiment seemed to confirm that "small world moments" like this weren't as uncommon or surprising as they seemed, yet mathematicians still struggled to explain how the phenomenon worked.

It wasn't until the late 1990s that two mathematicians created a computer model that accurately recreated Milgrim's results. They discovered that the key was that most people possess one or more "long-range connections" in addition to numerous local connections. One of the mathematicians, for instance, was a professor in New York who played online chess with a friend in Holland. As a result, all the professor's New York acquaintances were only two steps away from everyone his Dutch friend knew.

Modern experiments involving email chains (who still sends letters these days?) have supported the idea that any two people in the world are connected through six to seven acquaintances. Additionally, in 2011, Facebook discovered that its billions of users were linked by an average of 4.57 "friends" or 7 intermediaries. Facebook referred to this as " degrees of separation."

While Milgrim's initial experiments may have had their flaws, they hinted at mathematical realities that now underpin "network theory." The unexpected tightness of our social networks — both offline and online — helps explain phenomena like the rapid spread of COVID-19 or how misinformation can go viral and sway presidential elections.