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 / Spring 2004 / Issue 34(originally published by Booz & Company)


Power Laws & the New Science of Complexity Management

In an intricately networked world, the study of “nonequilibrium” systems is teaching companies how to overcome risk.

Illustration by Guy Billout
In 1972, the (future) Nobel Prize–winning physicist Philip Anderson published an article in the journal Science titled “More Is Different.” Dr. Anderson was exploring what happens when a number of elements — atoms or molecules, but perhaps ants or even people — interact with one another. Interactions lead to messy interdependence; for observers, they ratchet up the difficulty of understanding what goes on and why. But Dr. Anderson’s point was that interactions also lead to “emergence” — to the spontaneous appearance of features that cannot be traced to the character of the individual parts.

Today, science is increasingly concerned with understanding not only how more is different, but how “more” becomes “different” — how thousands of genes and proteins interact to create the human organism, or how an ant colony organizes its members into an intelligent community. This research, broadly associated with the term complexity science, is gathering attention in the business world as well, as executives and scholars recognize that conventional theories of management, forged in the era of industrialization, vertically integrated companies, and relatively impermeable institutional borders, can no longer cope with the immensely complex organizations that have emerged during two decades of rising globalization and decentralization. With the global economy now far more integrated than it has ever been, chains of economic cause and effect reach across the world with disconcerting speed, exposing individuals, firms, and governments to a new kind of “interdependence risk” — to the possibility that events quite far away can undermine the activities on which their security and prosperity depend.

Does the specter of ever-increasing complexity mean senior executives must succumb to rising unpredictability, uncertainty, and loss of managerial control? Not necessarily. During the three decades of its development, complexity science has not only chronicled the phenomenon of interdependence: It has also opened paths to understanding and handling its challenges. Although complex systems are frequently unpredictable — inevitably so, in many instances — they also exhibit precise regularities. Relatively simple patterns, known as power laws and observed in disparate settings from astrophysics to evolutionary biology, as well as in  human society, suggest strategies by which well-managed organizations can deal with uncertainty and navigate the discontinuities of contemporary business.

Modern science has moved well beyond a fixation on exact prediction and control; it has learned to accept unpredictability as an unavoidable and, at times, even beneficial aspect of the world, as a resource that can sometimes be harnessed. Businesses can also learn to adapt to complexity, in ways that can help them both reduce risk and expand opportunities.

The Simplicity Behind
From trees and coastlines to the rough surface of a broken brick, the natural world is at home with irregularity. Many natural structures violate the tidy principles of Euclidean geometry and appear to lack any identifiable order. However, as mathematician Benoit Mandelbrot pointed out decades ago, they do possess a kind of hidden organization. Small portions of a tree or a cloud or a brick’s fractured surface resemble larger parts, and these larger parts in turn resemble the whole. Irregular structures in nature are often “self-similar” in this way; they are what Mandelbrot called fractals.

Physicists have learned that hidden order of this sort comes with a very simple mathematical signature. A power law is a relationship in which one quantity A is proportional to another B taken to some power n; that is, A~Bn. Trees, clouds, and fractured surfaces all conform to power laws, as do river drainage basins, fluctuations in Internet traffic, the response of the immune system, and a vast range of other natural phenomena. Surprisingly, power laws also arise in the statistics of events that would seem to be utterly random, such as earthquakes and forest fires. For example, the number of earthquakes that release energy E — a measure of their strength — is simply proportional to 1/E2.

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