The notion that there are an average of six degrees of separation between any pair of individuals in the world helped inspire a play and movie, which mangled the numbers by claiming that we’re all connected by no more than six degrees. It also gave rise to related connectedness theories for subsets of the world, among mathematicians or film actors.
If you believed news reports this week, you’d think that the six-degrees theory — first advanced in a test using the mail in 1967 — had been proven. Microsoft researchers announced that a study of the company’s instant-message traffic in June 2006 showed that the average number of people needed to bridge any pair of users was 6.6. The median number was 7, and the longest was 29.
The authors readily agreed with me that this is far from proof of the average distance between any two people on Earth. Some limitations of the study cause it to overstate our connectedness, while others serve to understate it. Still, the Microsoft numbers represent a major advance in our knowledge about the fragmentary nature of the online population, and certainly are more rigorous than the original six-degrees experiment from more than four decades ago.
Some 240 million people used Microsoft’s instant-message product, Messenger, in the month in question — meaning about 96.3% of the world’s population didn’t. Those who didn’t were disproportionately located in Africa and parts of South America, Asia and Eastern Europe. Excluding people can cut both ways: Some of those excluded might have helped bridge the gap between those people in the study. On the other hand, some of those excluded may not have access to telecommunications devices, and these relatively isolated people may be many degrees removed from each other, driving up the numbers. Including only Messenger users accounts for “part of the bias that is there,” Jure Leskovec, a graduate student in machine learning at Carnegie Mellon University and a study co-author, told me.
Meanwhile, the study covered just one month and counted only messages, not buddy-membership, as connections. “Grandparents probably don’t speak to grandchildren using Messenger, yet those are very strong communication links,” Eric Horvitz, principal researcher at Microsoft Research and a study co-author, told me. “Whole sets of real-world communications are removed.”
But improving on the study would be tough. Email networks are even more fragmented, so doing a similar study using only, say, Hotmail addresses would miss a lot of connections that involved Gmail addresses. Phone numbers can be shared among multiple people. And accessing this kind of data raises privacy issues. Typically, Microsoft doesn’t collect this kind of information. The researchers made a request to access just the age, gender and location of users, and it was approved. “It would take a lot of effort to go back and grab more data,” Mr. Horvitz said. Linking the email database with instant messages would pose other privacy hurdles, as well.
Mr. Horvitz mentioned another possibility: Take a sample of the people in the study and examine their other forms of communication to get an estimate of the links that are missed. But Mr. Leskovec cautioned, “Any random sampling will destroy the structure of the network.” That’s because some of the people who connect those in the sample won’t be in the sample.
The study is certainly an improvement on the 1967 experiment conducted by Jeffrey Travers and Stanley Milgram, which would have provided ample material for this blog had it and its author existed at the time. It was based on just 296 people, in Boston and Nebraska. They were asked to try to reach other by mail, using only close acquaintances as go-betweens to form a chain. Just 64 of the mailings reached their intended target. And an unpublished study by Prof. Milgram found a much greater degree of separation and a much lower rate of completion. As of today we’re closer to the true level of separation — but still far removed from that goal.