The Anti-gravity Men.(Tate Modern)

The most striking feature of Tate Modern--the huge art museum in a converted power station on the south bank of the Thames, in London--is the Turbine Hall, a cathedral-like space five hundred feet long, seventy-five feet wide, and a hundred and fifteen feet tall. Each year, the Tate invites an artist to create a monumental piece specifically for the hall. When, a few years ago, this commission was given to Anish Kapoor, whose works include "Cloud Gate," a hundred-and-ten-ton kidney-shaped stainless-steel sculpture in Chicago's Millennium Park, he did something that artists don't usually do: he hired a structural engineer.

The man he chose was Cecil Balmond, who is a trustee of Arup, an international engineering firm based in London. Arup has offices in thirty-seven countries, and its engineers are, at any moment, involved in several thousand large projects worldwide--a six-lane expressway in Singapore, a master plan for a new city in China, an automotive redesign in the United Kingdom, the long-awaited Second Avenue subway line in Manhattan. Balmond is sixty-four. He has a disarming, slightly gap-toothed smile and a trim gray chinstrap beard, which he uses as a pointing device and rhetorical aid. He dresses as casually as a literature professor, and when he thinks about something difficult he runs a hand over his head, the top of which is bald. He is a talented musician and, early in his career, considered leaving Arup to make his living as a classical guitarist.

Kapoor was used to working with full-time assistants, but he came to feel an unusual imaginative harmony with Balmond. "The traditional role of the engineer is to perform, so to speak, the ideas of the architect, or of the artist, or whatever," Kapoor told me not long ago. "But Cecil and I decided, quite clearly, that we were going to put that aside and invent together." For five months, the two men spent half the week in an Arup office in London, engaged in a sort of high-level play date. They would sit at a table and sketch, while the Advanced Geometry Unit--a small engineering, architecture, and research practice that Balmond has set up within Arup--used computers to explore the structural ramifications of their ideas. Computer science has revolutionized work at many engineering firms, but Balmond feels that design software is often used lazily or for mere effect, whereas he hopes that the A.G.U., which he calls "an investigation into a new aesthetic," can make rational principles the basis for generating designs. During the planning for the Tate piece, one team member modified a video game so that Kapoor and Balmond, wearing 3-D glasses, could navigate a simulated Turbine Hall. The A.G.U. turned promising ideas into prototypes using a machine that lays down thin layers of a rapidly hardening liquid polymer, like a three-dimensional printer, to convert computer drawings into solid objects.

The resulting work, which Kapoor named "Marsyas," after the satyr who challenged Apollo to a flute-playing contest and was flayed for his hubris, was a four-hundred-and-sixty-foot-long attenuated tubular form made from twenty thousand square yards of blood-red PVC fabric. The material was stretched between three massive steel rings--two standing vertically at either end of the hall and the third hovering horizontally in the middle. The weight of the center ring pulled the entire membrane into high tension, and the piece looked like a tremendous uncoiled trumpet with three bells and no mouthpiece. "Marsyas" was designed to seem as if it had had to be squeezed into the hall, and its shape was so complex that Arup had to write new software to predict how the finished skin would behave when it was stretched. Fabric has often been used in architecture, usually in roofs or canopies, but it is generally a secondary element, supported by cables, trusses, or other structural components. In "Marsyas," by contrast, the membrane was the structure.

The piece was erected in the Turbine Hall by a large team of professional riggers, some of whom used rock-climbing gear to dangle from the roof. The job took more than a week, and was completed just an hour or two before the exhibition's opening cocktail party. The huge red central orifice floated ominously above a pedestrian bridge, like a spaceship preparing to land, or like an enormous mouth about to make a meal of the crowd beneath. There was much speculation about what was holding it up. Michael Hopkins, an architect who has made a specialty of fabric structures, asked Balmond where the supporting cables were. The Iraqi-born architect Zaha Hadid, who in 2004 became the first woman to win the Pritzker Prize, speculated that the red skin was made of steel; Balmond took Hadid aside and told her to punch it.

Balmond has achieved a great reputation as a structural engineer, but his most exceptional talent may be a sort of genius for collaboration. During the past twenty years, he has worked with Philip Johnson, Rem Koolhaas, Daniel Libeskind, James Stirling, Ben van Berkel, Toyo Ito, and several other celebrated architects. These are all powerful figures, with very different personalities and architectural styles, yet Balmond has managed to work productively with all of them. Johnson, who was born some four decades before Balmond, called him a mentor. Koolhaas told me recently that he and Balmond are able to engage in "a kind of telepathic communication, almost." Ito has often said that his first building with Balmond, in 2002, changed the course of his career, and he told me that the "meaning and influence" of Balmond's work is comparable to that of Le Corbusier's seminal 1923 manifesto, "Vers une Architecture."

A characteristic Balmond collaboration was the Portuguese National Pavilion for Expo '98, in Lisbon, where he worked with Alvaro Siza, who is often described as Portugal's greatest architect. The pavilion consists of a simple two-story box with a large covered entrance plaza at one end. The plaza measures an acre and a half, and Balmond originally thought of covering it with a thin metal canopy. He worried, though, that this might be too insubstantial for the pavilion's harborside location and that it might seem out of character with Siza's other work. He had a different idea: What about a thin, curving sheet of concrete, suspended above the plaza like a broad hammock? Siza, incredulous, asked whether unsupported concrete could really be used over such a span. Balmond said that it could. An eminent Portuguese engineer disagreed, and told the building authorities that the canopy would crack catastrophically. "That was a difficult moment, because this was a very good person," Balmond told me. "So I got a young guy from my team, from Australia, and we spent two months analyzing that simple sheet, proving that there wasn't a problem."