It’s important to remember — and this theme is stressed in each of the books — that small-world theory findings are the direct result of interdisciplinary interaction and observation. Empirical observation is just as important as clever theory. The beauty of the small-world hypotheses is that they can be tested in the real world very quickly.
Random geometries of small worlds is just one network law that commands respect. While ambitious managers read Machiavelli to better understand the laws of social and political power, effective executives need to understand that mathematical “power laws” profoundly shape laws of personal power.
“If you are not a physicist or mathematician, most likely you have never heard of power laws,” asserts Barabási. In Linked, executives will recognize their importance, because power laws can reveal as much about marketing and finance as they do about math and physics.
The “power” in power laws is not a function of Machiavellian manipulation but the “power” found in exponential functions; numbers squared or cubed or taken to the 10th power, etc. Power laws strike at the heart of what businesspeople think they understand about playing the odds and managing risk. Why? Because power laws are the sworn enemy of a basic statistical concept: the notion that probabilities present themselves in the average distribution of bell-shaped curves. In a networked world ruled by power laws, the bell curve is a dangerous lie.
In fact, power laws describe a radically different kind of distribution. There are no peaks; no symmetries; no bell curve. Power laws look nothing like traditional school-taught statistics. Yet they do a far better job of reflecting how much of the real world behaves. The distinguishing feature of a power law, Barabási writes, is that its distribution is wildly skewed: numerous tiny events coexist within the few very large ones that actually matter.
The distribution of individual wealth in the United States is an excellent example of a power law; a relatively tiny number of people account for the overwhelming majority of individual net worth. The distribution of American and European height, however, is not a power law. There are not a few hundred giants over 1,000 feet tall and millions of pygmies; there’s a more comforting and symmetrical bell curve distribution. Power laws explain why computing “the average” — the means, medians, and modes — for insight is so frequently a fool’s errand.
Power laws are thus crucial to understand because they force us to look at those few critical hubs — the O’Hares and Heathrows — that dominate either the creation of network value or its destruction. “If Watts and Strogatz’s discovery of random connections was a first step into the world of disorderly and complex networks,” Buchanan comments, “then the recognition of hubs and power law patterns for the distribution of links is second.”
But recall the Southwest Airlines network evolution question: Precisely when does a lowly node evolve into a hub? When should small worlds–oriented sociologists, economists, or mathematicians declare a cluster of nodes a hub? How can we be sure a network’s links and hubs are distributed by power laws instead of bell curves? When do a few random connections between networks create more chaos than cost-effectiveness?
The answers to those questions aren’t yet known. Networks have laws, all right, but even laws are subject to interpretation and experimentation. The true test of the laws in the context of business and economics will come from the technologies used and abused by Rheingold’s “smart mobs.”
Reputation Marks the Spot
Smart mobs are a sociological phenomenon that Rheingold persuasively argues will become an everyday reality. These aren’t the mobs that storm the Bastille or riot in the streets (although they could); they’re small worlds of individuals linked and melded by technological networks, especially through mobile communications. Smart mobs don’t just mediate information and analysis; they mediate passion and behavior.