

The theory that everyone in the world is six friendships away from everyone else is regarded by many as a myth. So what happens when the theory is put to the test? The thought that all 6.9 billion people on the planet could be closely connected to one another through their network of friends has a long-held fascination. For decades, scientists have tried to prove that the world is made up of social networks that are ultimately interconnected. The theory that there were "six degrees of separation" between everyone - with each degree being a person they knew - entered the mainstream when John Guare wrote a play of that name, followed by a 1993 film starring Will Smith. The following year, a group of US students came up with the party game Six Degrees of Kevin Bacon, apparently after a late-night viewing of back-to-back films starring the actor. They began to pick random Hollywood names and then connect the actors to Bacon via films in which both had appeared. IT'S A SMALL WORLD In 1967, Stanley Milgram asked 160 people in Nebraska to get a parcel to a named person in Boston He found that some people have three links of separation, some have 100 and some have none In 1973, American sociologist Mark Granovetter discovered society is made up of clusters of people, with strong and weak links British photographer Andy Gotts spent eight years taking pictures of 115 actors linked by friendship That sparked a website, a board game and a book, and the phenomenon was born, although many dismissed its accuracy. So how true is it? Recreating a famous experiment done in the 1960s, 40 parcels were given to people randomly picked around the world, as part of a BBC programme testing the "six degrees" theory. They then had to try and get the parcel to a scientist called Marc Vidal based in Boston, via someone they knew on a first-name basis. Three of the parcels made it to Mr Vidal, and on average took six steps to get there. Organisers of the experiment believe the other 37 chains broke because of the apathy of individuals who failed to send the parcel on. One that made it started off in the remote village of Nyamware in Kenya, where Nyaloka Auma gave it to her aunt in Nairobi. Margaret Owino then sent it to a friend in New York state who used to live in Nairobi, who in turn sent it to another friend in Boston. Eventually it arrived in the hands of the right person, through seven people in total. The parcel went from Nyaloka Auma to Marc Vidal in six steps

Its success, and the fact that two other parcels also reached their destination within six links, proves that the theory can work, even if it does not always. There have been many other attempts to test how "small" the world really is. Last year, Microsoft examined its instant-messenger network of 30 billion electronic conversations between 180 million people. Its researchers concluded that any two people are on average apart by 6.6 degrees of separation, meaning that they could be linked by a string of seven or fewer acquaintances. Swine flu spread The six degrees theory has had a huge impact on other areas of science. When mathematician Steven Strogatz and his PhD student Duncan Watts set out to investigate why some crickets chirp in unison the young Australian got inspired by his father's words in a phone call: "Did you know that you are only six handshakes from any person on Earth?" Watts thought this might explain why his crickets are such good synchronizers but he had no idea that this question would lead him to a major discovery in an emerging branch of research - network science. FIND OUT MORE... Six Degrees of Separation is broadcast on BBC Two on Tuesday 5 May at 1900BST Or catch up using the iPlayer If the phenomenon applies to cricket synchronisation, what are the consequences for the way disease spreads throughout a human population, or the dynamics of markets, he asked. These sorts of questions seem to have something to do with networks. Teaming up with Strogatz, the two scientists used data from the online trivia game Six Degrees of Kevin Bacon to see if there was a mathematical basis for this complex set of relationships. They discovered a formula for the invisible links that make the big world small, and another scientist Albert-Laszlo Barabasi examined the importance of hubs in how networks evolved. A new discipline - network science - was established and other scientists gladly applied these universal laws to other kinds of networks, such as the world-wide web, the growth of cities, global travel, sexual relations between people, wealth and property distribution, and protein molecules in cells. If I start with my favourite protein and I ask what does it interact with, I'm now back to basically a problem of six degrees of separation

Marc Vidal, who is road-mapping human cells Professor Alex Vespignani, of Indiana University, says network theory is having a huge impact on predicting how swine flu will spread. His work is being used by the European Community and authorities in the US. How people go from one place to another - what he calls mobility networks - is at the heart of his predictions, and involve long-range journeys (such as by plane), short-range commutes, and how we move around small spaces like the workplace or the home. "We can identify the pathways along which the disease will spread and therefore the next places to observe the cases. "That gives you time and where you can focus. With limited resources you need to make choices and focus on certain routes. Network theory can tell you and it's not just about looking at the obvious." WHY KEVIN BACON? Name loosely rhymes with 'separation' Students who invented the game watched two of his films that night Bacon said in an interview that he had worked with everyone Marc Vidal, the "target" of the parcel experiment, is creating the first "roadmap" of the human cell - how proteins interact - in order to find the origin of disease. "If I start with my favourite protein and I ask what does it interact with, I'm now back to basically a problem of six degrees of separation - who is connected to whom." Although scientists may disagree on how much emphasis they give network theory, it is now a well established principle. And it's all down to Kevin Bacon. Below is a selection of your comments. I used to play a variant of this game when I was on the train from London to Southampton to visit my folks for the weekend. I used to sit in the smoking carriage - though I didn't smoke because the people were friendlier there and it was next to the bar. The idea was to identify a mutual acquaintance - something we were able to do probably 3/4 of the time. (Though, to be fair, geography and lifestyles narrowed the field considerably.)

Alex C, London The six degree theory may explain how mathematics and astronomy calculations have run a parallel course in separate cultures like the Mayas, the Egyptians, the Minoans in Crete, China and India. Their application of mathematics and astrology in the construction of pyramids and temples, as well as their water distribution systems can't be explained by the "random chance" theory or a common provider.

William F Pennock, Puerto Rico The parcel experiment isn't particularly sound - it might tend to over estimate the length of such chains. I might be six degrees (or less) of separation from a specified person in Boston... but I probably don't know the exact form of that chain in advance - so I don't know which of my friends to send the parcel to. I might send the parcel to a friend in Pennsylvania (on the assumption that its closer than me to Boston) without knowing that one of my good friends in the UK actually knows the named person in Boston. The instant messenger analysis is a bit more sound as they can find the most efficient chain of links between 2 people.

Martyn Gay, London I think it is impressive that 3 out of 40 parcels made it to the Professor at an average of 6 steps. However, the Professor is presumably a well known figure, in a well known institution. In other words he is likely to be a "well connected" individual in the literal sense. Kevin Bacon is likewise substantially more connected than the average. The theory falls down when we talk about isolated individuals in remote communities. That said we spend a lot of time and effort building connections. For instance, we are all connected (or used to be) by the phonebook.

Gordon Lewis, Reading, UK Finally, the billions of pounds spent by the UK government for GCHQ to have complete visibility of internet traffic will enable the UK to be the foremost country in the investigation of this theory.

Clark Ellis, Sheffield I started writing a book about this very subject in Jan of this year, I have set myself the challenge of meeting 7 people admire using the 6 degrees theory, so far I am on step 3 with 3 of them and step 2 with the other 4. It will be interesting to see how it all pans out.

Derek Devayya, London I fall into the 6 degrees of separation from Kevin Bacon. My ex housemate went to school with a girl. This girl's brother ended up in Hollywood working on films as a make up artist. He worked on films involving Angelina Jolie, who I am pretty sure would know Kevin Bacon.

Andrew Johnson, Guildford I once had the opportunity to meet with Kevin Bacon to discuss the whole phenomena, but decided that it might be better if a friend of mine was to question him... who in turn asked a work colleague... who asked her brother-in-law...

Richard, Sheffield Milgram's experiment was a really terrible piece of science: the methodology was bad and the data analysis was bad. First, the methodology doesn't measure the right thing. As Martyn Gay says, it will tend to overestimate the length of the chain between two people because, at each stage on the chain, it's likely that the package won't be forwarded in an optimal way. Second, as the chain gets longer, it's increasingly likely that somebody will not bother to forward the package. Therefore, only looking at the packages that actually arrived at the destination biases toward small chains and gives an underestimate of the average chain length. So, all that Milgram's experiment actually tells us is that the average number of links between two people is smaller than some number that's bigger than six. And that's no information at all because every number is smaller than some number bigger than six.

David Richerby, Leeds, UK Facebook is surely a useful medium to prove this theory.

Eddie, York I think the theory works quite well for most people in the developed world. Not sure how it would apply to Amazonian rainforest dwellers. I live in South Africa and I'm not particularly well connected, yet I can get to almost any celebrity or world leader within 6 degrees - even Sadaam Hussein!

Joe de Lange, cape town Mathematicians had thought about this long before Kevin Bacon fans. Your journalists should look up "Erdos number", which was described in The American Mathematical Monthly in 1969.

Richard Tobin, Edinburgh This is an interesting parlour game that I've played many times, on the basis that a handshake and a proper face to face conversation establish the necessary connection. The key to connecting oneself to people, some of whom can be reasonably recent historical figures is to find people who are 'nodes'. If you've ever met your MP, that will get you a long way. If you know someone, who knows someone, who knows someone who has been a guest of Parkinson, or Jonathon Ross etc, then you really are in business. I can get Mohammed Ali in four, Tony Blair in two [so George Bush in three], the Queen in three, and amazingly, frighteningly, Adolf Hitler in three!!!

John Francis, London Something that was strange when a friend of mine moved up from London was he, his friend and I coming to the realisation that though we are all from different parts of the country that we have a sizable number of shared friends, or friends who've worked together.

James B, Sheffield, UK



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