Manhattan is all about movement. This summer the Museum of Modern Art mounted a retrospective of the work of Richard Serra, who crafts enormous plates of steel into sculptures. When you enter one of the spiraling shapes, you're led to no visible destination; the tilted walls sometimes open up invitingly, sometimes close in claustrophobically. This is a museum encounter that demands not just observation but experience—the experience of merging into a crowd as it flows through a work of art.
A couple of blocks up from the exhibit, along Columbus Circle, the preoccupation is with the art of efficient customer flow. There, Whole Foods, the gourmet supermarket, has abandoned separate checkout lines, including those that turn out to be inevitably and annoyingly slow-moving, in favor of a single, serpentine line. As soon as a cash register becomes available, the next customer is summoned. In a front-page article, The New York Times called the process an emblem of “queue management.”
Wherever a flow system is involved, Adrian Bejan has something to say about it. A decade ago, Bejan, J.A. Jones Professor of mechanical engineering, coined the term “constructal theory,” originally as an idea applied to thermodynamics. How might heat be dispersed in small electrical devices, he wondered, so they wouldn't burn up? He found that in many cases, the answer is to let the heat spread out like a tree's limbs and leaves or like a river's tributaries. In a book published by Cambridge University Press in 2000, Shape and Structure, From Engineering to Nature, Bejan found parallels between engineering principles and mechanisms in natural flow systems. An optimal engineering system, he argued, hinges on the ability to minimize all the resistances to internal flows—whether those are the flows of heat, fluid, or electricity.
Writing in the January 2006 International Journal of Heat and Mass Transfer, Bejan and geophysicist A. Heitor Reiss of the University of Évora in Portugal turned to constructal thinking in an audacious application of the theory. They wanted to predict the climate, the large-scale movement of air that distributes heat on the surface of the Earth—the grandest of all flow systems. “Nothing flows ideally,” Bejan says. “Every flow system is destined to remain imperfect. The struggle of nature is to be the least imperfect it can be.”
From thermodynamics, constructal theory has morphed into a theory of pretty much everything, natural or manmade. Bejan says it unites physics with Darwinian evolution. According to the theory, if free to do so, a flow system—a river basin, a blood stream, or city traffic—will evince a pattern that allows for optimal movement.
That's also true of things that fly, run, and swim. To fly at optimal speed is to strike a balance between the vertical and horizontal loss of energy, says Bejan. “The bird is basically a falling body, a rock. In every time interval that the bird falls, the bird has two jobs. One is to lift itself vertically back to where it was. But it also has to advance horizontally, which means it has to overcome drag. When the cruising is fast, it takes a little work to lift itself up. But it takes a lot of work to go forward. Once you put your finger on that, you know the optimal flapping frequency for the wings.” Larger birds, then, fly faster and flap their wings less frequently, though with greater force.
The same tasks are demanded of a running or a swimming animal. And the same mechanisms that produce flying efficiency produce efficiency in runners and swimmers. “The runner has to get off the ground, which is vertical work. And then the runner has to advance against the horizontal ground and air friction; at higher speeds, the gazelle or the cheetah struggles mightily against drag.” In Bejan's view, all forms of locomotion, managing as they do to surmount obstacles in physics through a balancing act of good design, are essentially identical. And that fact illustrates the presence of a universal principle.
“People didn't copy a bird to make an airplane. They tried all sorts of shapes, and are still trying. And, as it turns out, the ones that are better and better look more and more birdlike.”
At a constructal-theory conference held at Duke this past spring, a mathematician gave a presentation that considered a dog with a seeming capacity to calculate in constructal terms. That capacity actually is an aspect of survival: When a lion is going to chase down an antelope, or when that dog is going to retrieve a stick thrown from a lakeside beach into the water, it has to calculate precisely the most efficient way to perform the feat, given its properties of locomotion. So the dog doesn't make a direct-line approach; at some point, it dashes into the water and swims at an angle toward the stick. The dog finds the optimal path to retrieving its object.
In a book published this year, Constructal Theory of Social Dynamics (Springer Science+
Business Media), Bejan and his co-editor, Gilbert W. Merkx, a sociologist and the vice provost for international affairs at Duke, take the theory across new intellectual boundaries. In the book's preface, Bejan and Merkx declare that the theory is so “commonsense, concise, and useful” that it applies to the social sciences, as well as to engineering science. Merkx contributed a chapter on “Constructal Models in Social Processes.” Duke colleagues Kenneth Manton A.M. '71, Ph.D. '74, Kenneth Land, and Eric Stallard wrote on “Human Aging and Mortality”; Edward Tiryakian on “Sociology Theory, Constructal Theory, and Globalization”; and John Staddon on “Is Animal Learning Optimal?”
Merkx, in his chapter, scrutinizes Mexican migration to the United States. The migration stream began to develop rapidly with World War II, he points out, when the U.S. responded to labor shortages by recruiting Mexicans. Originally, labor would flow north over the border for planting and harvest, and flow back over the border in the off seasons. Merkx argues that as the U.S. clamped down on the natural flow system—that is, the move across borders, including the easy flow of Mexicans back to their home country—the system lost its efficiency.
“There will be less flow through big channels,” he says. “But the flow of people will still leak through in other ways, and they won't go back, because the transaction costs are so high. That means they want to bring their families over, too, so you're actually moving more people and creating more and more of a one-way flow by closing the border. Another effect is, once the border is sealed, you begin to see this sort of washing-through effect: The population spreads out and disperses beyond border areas to places like New England and North Carolina.”
Having grown up in Venezuela, Merkx came with his family to the U.S. when he was eleven. His childhood across borders, he says, “gave me a lifelong interest in viewing things from a comparative perspective.” As a Harvard undergraduate, he studied both sociology and cultural anthropology, which whetted his appetite for understanding social processes. The sociology department at Harvard at the time was led by Talcott Parsons, who was committed to uncovering “pattern variables,” the basic attributes or properties that characterize all social systems.
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