How Small is the World?

The science of networks doesn't sound interesting, but how about the idea that you are only six degrees away from anyone in the world? Nexus: Small Worlds and the Groundbreaking Science of Networks by Mark Buchanan and Six Degrees: The Science of a Connected Age by Duncan Watts deal the popular notion with scientific inquiry that help us to see the hidden desire and fear of our time.

Psychologist Stanley Milgram is the first scholar to bring up the "small world". In 1967, Milgram conducted an experiment in which he sent letters to 300 people in the U.S. and ask them to forward the letter to a designated target, a stock broker in Boston. To his and everyone's surprise, the average number of letter travel is six-- the world is much smaller than we thought! The idea of a small world got more and more popular and was adopted in a play and a movie.

Milgram had always been a controversial figure, but his flawed theory didn't get busted this time until 2002. Klienfeld examined Milgram's data and found that it was not random at all. There were 100 of them lived in Boston instead of alleged Nebraska; and another 100 persons were investors of stock who reasonably have a fair chance to know how to reach a stock broker. There were 96 persons out of 300 qualified as "random"; and only 18 among them successfully completed the assignment.

Milgram was proved to be defective, but the six degrees of separation survived. Duncan Watts applies mathematical approach on social network and supposes that six may be the right figure. But is a world with six degrees of separation a small world? Is six small at all? Watts says no, six is huge.

Start it from me, the first degree of separation would be someone I personally know, say, a friend Ling, a social activist devoted to migrant workers' rights. The second degree is one of her acquaintance whom I don't know, it could be a Philippine woman working in Taiwan. The third degree could be the father of the Philippine woman, a farmer or a coal-miner; and I can hardly go on because I am dragged to a world that I know almost nothing about and this is just the third degrees of separation. I will be easily connected to a Martian in the eighth degree.

Mathematicians who set foot in this sociological arena do acknowledge the fact that human network doesn't exactly resemble a piece of paper with a few dots on it. There are some factors to be known that segregate people into clusters, like class, gender, geography, language, etc. It turns out to be that the link between clusters is extremely powerful, sometimes determinant.

Here comes another fascinating concept: "the strength of weak ties", as Mark Granovetter called it. When looking for a job, your acquaintances will be more helpful compared with close friends, because your acquaintances are capable of taking this information to another "cluster" while your friends probably locate in the same cluster. Weak ties are especially important in creating a trend, a fashion, or a craze.

I wonder how many weak tie is used connecting two persons in six degrees of separation? None of the studies mentioned in these two books seems to answer this question. A weak tie is actually a giant leap between clusters, and the average number of weak tie may be an even better indicator than the number of degrees of separation.

Another interesting question would be the definition of "connection" or "link". In mathematics it's easy: You draw a couple of nodes and take a ruler to draw a line to connect them, you create connections or links. But human connection is more complicated than that: how weak is the weak tie? In psychological experiments mentioned above, they use the lowest level of interaction, which is the conveyance of insensitive information, and my assumption is that it could be the maximum load of a weak tie. Add a little debate on it and it will split-- that's what makes it a "weak" tie in the first place.

The prevalence of six degrees of separation is itself a phenomenon worthy of exploring. There seems to be little resistance since it was introduced. The idea of a small world is comforting when in reality we feel intimidated by the world's immensity and by people's indifference; we need a theory to tell us: in a mystical way we ALL are connected; nobody is alone although it appears to be so.

--An old entry from an old blog, before Erasmus Mundus

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