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The Small World Phenomenon

We are all familiar with the experience of meeting a complete stranger in an unfamiliar location and discovering that he or she shares a mutual aquaintance with us. At such times, we might remark that "it's a small world." What surprises us is that this random person, out of the billions of people we could meet, happens to have a connection to us even though we only personally know a miniscule fraction of the world's population.

This phenomenon is not just a by-product of our imaginations. In a 1967 study, the psychologist Stanley Milgram created a number of chain letters. These letters were first given to people in Kansas and Nebraska. Each was intended for a target person in Massachussetts, unknown to the original holders. The subjects were instructed to send the letter to someone they knew on a first name basis who they thought would be most likely to know the target person. These next recipients were then given the same instructions and the pattern continued.

Remarkably, a substantial number of letters reached their intended targets. In fact, of those that did succeed, the median number of times the letter was passed on was only six. This gave birth to the popular notion of "six degrees of separation," the idea that any two people on earth are connected by a chain of no more than six links.

The question that motivates us is how this is possible given that we know very few people and furthermore that our friends typically know mostly the same people that we do.

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