A Guy Who Rules at Math Explains the Theory

The idea of a web of relationships linking everyone on earth dates back to a 1929 story called “Chains” by a Hungarian, Frigyes Karinthy, and seems to have been independently re-invented at least a dozen times in the twentieth century by psychologists, mathematicians, playwrights, bored engineers and sci-fi writers. At its basis is elementary combinatrics, probably the last math subject I thoroughly understood before discovering hallucinogens. In crudest terms, it’s obvious that if everyone has on average one hundred people they are directly connected to (via friends, family or work), and those people in turn have a hundred people they are connected to, after six steps you’re talking about 1 gazillion (1,000,000,000,000) people (10 to the power of 12). As the real population is less than a hundredth of that, there is an enormous amount of space for redundancy, which is where the math gets more interesting and the combinatrics comes in. Namely, if everyone you know also has 100 people they know, but half of them are redundant (i.e. already known to you) and so on, then it works out differently, at 100 * 50 * 50 * 50 etc. Which with six steps gives 31.25 billion. Again, more than enough to include the whole population of the world. However not everyone is equal. The most important people in your phonebook from the six-degrees point of view are the outliers, the people you probably know least about, because they are the ones with the least redundancy. It’s the exchange student who worked in an orphanage in Ecuador for three weeks in order to pad out his CV—whose number you copied down in a bar and forgot to delete—who brings most of South America in a couple of hops, or Ajay, the emergency plumber from Sri Lanka who connects you to all of Wall Street via his second cousin, the resourceful Ahilan Ariyapala. The closest we’ve come to an objective test of the concept is Facebook, which sets the average separation of all users at 5.73 degrees. Small, closely knit groups are more isolated and have higher levels of redundancy. If you are in a Papua New Guinean hill tribe, say in Goroka, living with a hermaphrodite goat, you are at a serious disadvantage. Most of the people you know don’t know anyone outside the village. Except for the headhunter couple down the road who named their baby Kevin Rudd after a visit from the Australian Prime Minister (see Vice Vol 6, Number 8), which then links you to the entire Australian population within three steps. What The Hell? So, if it’s such an obvious thought experiment, what’s the attraction? Chiefly, it seems to be that most people, when they think of the six degrees, imagine themselves at the centre of a circle of a hundred people, who are in turn surrounded by 10,000 friends of friends, and so on, until the whole world is there, linking hands, beaming, staring towards the centre. This confirms what most people have suspected all along: I am the centre of the universe. Six degrees of separation teaches us how intimately we are all connected. When being introduced to new people, remember that they are not strangers, they are friends of friends that you haven’t met yet, and probably have had sex with monkeys.