I’m sure you know the idea of six degrees of separation. Or perhaps you know it better as the six degrees of Kevin Bacon. The idea is simple: everyone on Earth is connected to every other person by six or fewer links. A link is someone you know, who knows someone else, who knows someone else and so on. You are one degree away from everyone you know, and two degrees away from everyone they know. According to the theory, you are just six introductions away from anyone on the planet. The idea was first proposed in 1929, but is six still the correct number of links in today’s connected world? And does it matter?

Six degrees of Kevin Bacon

It’s a small world

In 1929, Hungarian writer Frigyes Karinthy published his short story Chains. In it, one of the characters suggests a game to test whether the population of Earth is closer than ever before. The game is a familiar one: can you link any two people on earth by no more than five individuals?

Basic maths tells us this idea is certainly plausible. Do you know 45 people? Do each of those 45 people know another 45 people that you don’t know etc? If this were true for everyone on Earth, in just six steps any one person could theoretically be connected to 8.3 billion people – more than the 7.4 billion alive today.

The first research to test this ‘Small World Problem’ was published in the 60s. Stanley Milgram asked 300 randomly-selected people to attempt to send a package to a particular stockbroker living in Boston via their acquaintances. The result? On average it took 6.2 links to reach the Boston target.

Bam! Is that all the proof we need for our six degrees theory? Not so fast. In fact, Milgram’s research has been heavily criticised. For example, two hundred of the original people weren’t randomly selected at all: 100 were stockbrokers and 100 lived in Boston. And we have no idea how many links there were in the chains that never successfully reached their target: the stockbroker only received 64 packages.

How many degrees to Kevin Bacon?

In 1994, three college students created the game Six Degrees of Kevin Bacon. They came up with the idea after Kevin Bacon suggested he had worked with everyone in Hollywood. The aim of the game is to link Kevin Bacon to anyone in the Hollywood film industry via their film roles in six or fewer steps.

As a result, the Bacon number of an actor is the number of degrees of separation he or she has from Kevin Bacon. The game led to the Oracle of Bacon, where you can find out the Bacon number for any actor, director or producer you care to name. There are also Six Degrees apps that allow you to explore the number of degrees of separation between any two actors.

So does it hold up? According to the Oracle of Bacon, Kevin Bacon has appeared in films with 3,031 actors and more than 99% of 1.91 million other actors have a Bacon number of five or less. And although Bacon apparently didn’t like the game initially, he later launched a website to bring together people who want to support good causes.

Enter email, Instant Messaging and YouTube

In 2003, researchers at Columbia University set out to test the six degrees theory using email. They asked more than 61,000 volunteers from 166 countries to use their email networks to reach one of 18 different target people. These included an Australian police officer, a Norwegian army vet and an Estonian archive inspector. More than 224,000 email chains started, and only 384 arrived in the prescribed inbox. But right on target: the typical chain length was between five and seven.

Microsoft had a go at testing the theory too. They analysed 30 billion Instant Messaging conversations among 240 million people from the month of June 2006. They found that the average path length among Messenger users was 6.6.

Science YouTuber Derek Muller pondered the science of six degrees and ended his video with a challenge: he asked his viewers to try and get an email to him by only contacting people they knew and had met in person. At the time Derek reported back, about 750,000 people had watched his video and he received 350 emails, with an average of only 2.75 steps in each email chain. But let’s be clear: people who watch science videos aren’t a random selection to begin with. On top of that, Derek has no idea how many email chains were started but never successfully reached him.

Has the internet shrunk our world?

Fifty percent of the world’s population actively and regularly uses the internet, and it is often said that social media use brings connectedness. Earlier this year Facebook announced that when it comes to Facebook users, each person in the world is in fact separated by only three and a half degrees. It’s not surprising the number of degrees is smaller: this calculation includes only the 1.59 billion Facebook users of the world, ignoring the other 5.8 billion people we share this planet with. But are we really more connected to one another as a result of the online world?

If you are a Facebook user, you can quickly find out your own average degree of separation from everyone else. But perhaps a more pertinent question to ask yourself is exactly how many of your Facebook friends are truly your friends? Evolutionary biologists have long argued that around 150 is our limit when it comes to meaningful and genuine friendships. Our brains simply didn’t evolve to cope with any more.

Links and stuff

• Veritasium: Science of Six Degrees of Separation video
• Facebook research blog: Three and a half degrees of separation
• Kevin Bacon’s Six Degrees social fundraiser website
• Six degrees of Francis Bacon: a website to explore the British early modern social network