Stanley Milgram designed an experiment in 1967 where he gave a message to people living in the mid-west of the United States asking them to send it to a stockbroker living in Boston. Rather than just posting it, if they did not personally know the stockbroker, they had to post it to someone they knew on a first-name basis, who was more likely to know them. That person had to hand it on in the same way until the message finally arrived at the stockbroker. He was interested to know how many steps were needed on average to make such a link.  

We might be tempted to think, given the population of the United States that many steps would be needed. Of course, small-world network dynamics tell us that if we can get our message out of our local cluster, we soon have potential links with an exponentially growing list of people at each step. If we can link in with a “hub person”, who knows many more people than most, the process may be sped up even more.

Stanley Milgram found the number of steps on average was six. From which the saying “six degrees of separation” has come into our common language. We can all think of “coincidental” occasions that have arisen where unlikely connections are made. I was traveling at the opposite end of New Zealand when a seeming stranger called out, “You’re Victor aren’t you.” It was someone who had been a child of a friend from many years ago” Obviously, it is more likely to happen here with a population of only five million but it is surprising just how closely linked we are.

There has been some controversy over Milgram’s work because later researchers found that around 95% of the messages sent never actually arrived at the destination, suggesting that perhaps the idea had grown into an urban myth.

There may well have been shorter steps between the people that nobody knew about that would have reduced the degrees of separation needed. Since 2001, Duncan Watts through the University of Columbia has been replicating Milgram’s experiment using emails, which are more likely to be passed on. He has worked with 48,000 senders and 19 targets covering 157 countries. His results suggest six is actually around the average number of steps to link any two people anywhere on the planet.

A variant of this experiment links movie actors in the “Bacon Game”. In this, a person is deemed to be linked to another if they have starred in a movie with another actor. Each actor is given a Bacon Number depending on the number of steps to link back to the actor, Kevin Bacon. He was chosen as the starting point because he has starred in so many movies. He has a number of zero, while Elvis Presley has a Bacon number of two because he starred in Change of Habit with Edward Asner, who starred in the movie JFK with Kevin Bacon.

There is a similar number called an Erdős number named after Paul Erdős, a Hungarian mathematician. He traveled widely around Europe writing mathematical papers with other scientists and mathematicians. A link is defined by having collaborated with another person on a scientific paper. Benoit Mandelbrot has an Erdős number of two, while Stephen Hawking’s number is three.