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And those patterns are everywhere, including human creations like street blocks and airports. Merkx, Bejan's co-editor on the new book, observes that a well-laid-out block or a well-planned airport, like Atlanta's, minimizes the average time, effort, and energy expended for a traveler between each mode of travel. “Different block lengths and house heights and sizes also evolve to minimize the time required for the average traveler from point to point,” he says. If walking is the primary mode, as it would have been in the time before cars ruled the roadways, streets can be relatively narrow, and houses will not be too deep nor have many stories.
“Let's say you add the horse and buggy, plus walking. Then streets must be wider and blocks longer, but houses will remain not too large or high. If you add a slow elevator to the mix, then houses can efficiently rise in height without sacrificing time. If you add cars and high-speed elevators instead of buggies, blocks can get longer and buildings much taller, with the same time efficiency. But the speed of walking does not change. Therefore, the buildings tend to go higher more rapidly than they get wider or deeper, because the time required for walking limits the horizontal distances.”
As Merkx sees it, the Pentagon, with its endless horizontal corridors and modest vertical scale, is a case study of inefficient flow. (According to a new history of the Pentagon, the five-sided plan conformed to the shape of the plot of land, while the low height of the building was meant to keep it in harmony with the low Washington skyline.) “If you want to have a building that is really huge in terms of the horizontal dimensions, like an airport terminal, then you have to put in high-speed people-movers, like trams, to minimize the time or maximize the efficiency.”
In constructal terms, is language a high-speed ideas-mover? That was the research starting point for Cyrus Amoozegar, a former student of Bejan's who is a Duke senior majoring in biomedical engineering and mechanical engineering and with minors in chemistry and Chinese. In a chapter he contributed to the book, he examines the flow paths of modern languages and two of the earliest languages, ancient Egyptian and Chinese.
“Through time, written language develops a set of pieces from which the most basic ideas are constructed,” he says. “In English, these pieces are the alphabet. The forms and uses of these pieces change through time so that they are easy enough to remember but complex enough to be distinguishable from one another and numerous enough so that ideas can be conveyed easily.”
According to constructal theory, a written language evolves to “connect” better to the masses, even as it's able to provide a more accurate description of the world. If the elements that constitute a language are complicated, the language will take too long to write and will be more difficult to remember. The global resistance will increase. On the other hand, if the language elements are too simple, the users of the language will lack precision. The meaning of words will be misconstrued. The natural evolution of written language, then, must head for a balance between the complicated and the simple.
With interests in history and engineering, another former student, Gideon Weinerth '07, wrote a term paper in Bejan and Lorente's course applying constructal theory to ancient warfare. Weinerth says that warfare can be understood, after all, in terms of flow systems. The Greek phalanx, for example, would maximize its effectiveness by taking on the same shape that Bejan noticed in riverbeds, that is, a semi-circle. A deeper phalanx of soldiers offered more pushing power than a narrow formation. But in making its flanks wider and thinner, a phalanx could build a strong defense. Those two actions would be at cross-purposes, so the idea was to find the perfect geometric balance. By the Roman period, the phalanx had been reorganized into an independent, highly mobile, and rapidly adjustable unit. “This is simply a validation of the freedom of design providing advantages in efficiency,” Weinerth writes.
In class Bejan compared the optimization of the material in a cantilevered beam designed by Galileo with how the Roman army maximized the strength of all of its soldiers. By that account, Galileo was unconsciously a constructal theorist. The class discussion “began to tip me off to possible avenues for investigation,” Weinerth recalls. He says he was surprised to find that studies of military strategy have been largely devoid of references to math or physics.
Today Bejan is interested in linking constructal theory and another sort of global phenomenon, higher education. Universities always have been a morphing flow system, he says. Through the centuries, ideas, and the people who generate them, have moved through channels from centers of learning in Bologna, then Padua, then Paris, then the United Kingdom, now the U.S. Those channels may swell or shrink, and the nodules—the learning centers—along the channels may grow or diminish in importance. But, as in any effective flow system, the hierarchy remains essentially fixed and recognizable.
Bejan worries that engineering itself may be too fixed and recognizable for its own good; and part of his crusade is to get the profession to think in grander terms. In his earlier book, he observes that engineering “ranks either low or not at all on the ladder of respect.” He adds, “Biologists and physicists are describing what nature is and how it works. What do engineers bring to this apparently full table? Engineers describe how a system changes its configuration in time so that its global performance improves.”
With figures like Gustave Eiffel and Leonardo da Vinci as his models, he suggests that engineers can blur the lines between the natural and the artificial, that they can define the theoretical agenda for the life sciences. It's just a matter of going with the flow of good ideas —or against the flow of conventional thinking.
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