The Information - James Gleick [204]
Then came Google. Brin and Page moved their fledgling company from their Stanford dorm rooms into offices in 1998. Their idea was that cyberspace possessed a form of self-knowledge, inherent in the links from one page to another, and that a search engine could exploit this knowledge. As other scientists had done before, they visualized the Internet as a graph, with nodes and links: by early 1998, 150 million nodes joined by almost 2 billion links. They considered each link as an expression of value—a recommendation. And they recognized that all links are not equal. They invented a recursive way of reckoning value: the rank of a page depends on the value of its incoming links; the value of a link depends on the rank of its containing page. Not only did they invent it, they published it. Letting the Internet know how Google worked did not hurt Google’s ability to leverage the Internet’s knowledge.
At the same time, the rise of this network of all networks was inspiring new theoretical work on the topology of interconnectedness in very large systems. The science of networks had many origins and evolved along many paths, from pure mathematics to sociology, but it crystallized in the summer of 1998, with the publication of a letter to Nature from Duncan Watts and Steven Strogatz. The letter had three things that combined to make it a sensation: a vivid catchphrase, a nice result, and a surprising assortment of applications. It helped that one of the applications was All the World’s People. The catchphrase was small world. When two strangers discover that they have a mutual friend—an unexpected connection—they may say, “It’s a small world,” and it was in this sense that Watts and Strogatz talked about small-world networks.
The defining quality of a small-world network is the one unforgettably captured by John Guare in his 1990 play, Six Degrees of Separation. The canonical explanation is this:
I read somewhere that everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everyone else on this planet. The President of the United States. A gondolier in Venice. Fill in the names.♦
The idea can be traced back to a 1967 social-networking experiment by the Harvard psychologist Stanley Milgram and, even further, to a 1929 short story by a Hungarian writer, Frigyes Karinthy, titled “Láncszemek”—Chains.♦ Watts and Strogatz took it seriously: it seems to be true, and it is counterintuitive, because in the kinds of networks they studied, nodes tended to be highly clustered. They are cliquish. You may know many people, but they tend to be your neighbors—in a social space, if not literally—and they tend to know mostly the same people. In the real world, clustering is ubiquitous in complex networks: neurons in the brain, epidemics of infectious disease, electric power grids, fractures and channels in oil-bearing rock. Clustering alone means fragmentation: the oil does not flow, the epidemics sputter out. Faraway strangers remain estranged.
But some nodes may have distant links, and some nodes may have an exceptional degree of connectivity. What Watts and Strogatz discovered in their mathematical models is that it takes astonishingly few of these exceptions—just a few distant links, even in a tightly clustered network—to collapse the average separation to almost nothing and create a small world.♦ One of their test cases was a global epidemic: “Infectious diseases are predicted to spread much more easily and quickly in a small world; the alarming and less obvious point is how few short cuts are needed to make the world small.”♦ A few sexually active flight attendants might be enough.
In cyberspace, almost everything lies in the shadows. Almost everything is connected, too, and the connectedness comes from a relatively few nodes, especially well linked or especially well trusted. However, it is one