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We live in an era that puts little stock in stability. Solidity and permanence read as rigidity and torpor. The future will be only more unruly, tossed and pulled by disparate forces like a piece of bread among sea gulls. So where does this leave architects, whose work is all about permanence? Buildings are supposed to be hefty, purposeful and unyielding. How can you create structures that embody a quicksilver society when they have to stand still?

Asymptote, a husband-and-wife team of architects in New York City, has spent more than a decade grappling with that question and in the process has become recognized as a master of high-wire acts of digital architecture. When a corporation — say, the New York Stock Exchange — has a blue-sky project that no one else seems to understand, Asymptote tends to head the to-call list. As a result, most of the firm's architectural projects — it also dabbles in art — are not buildings but acrobatic proposals for buildings that push the limits of architectural theory. After all, in the computer, a building can yawn, swivel its hips and shimmy. No matter how much you subvert the principles of engineering, it won't crumble.

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For Asymptote — otherwise known as Hani Rashid, 45, and Lise Anne Couture, 44--the ultimate challenge is connecting the digital world to the one we actually live in. The firm has attempted this with several projects, and perhaps its purest piece of digi-tecture is the Guggenheim Virtual Museum: an Internet-only gallery that would enable art lovers anywhere to swoop through interlocking coils and interact with the Guggenheim's collection of digital art. "Would," that is, because the museum, in a funding crunch, has yet to put up the website for public viewing.

The New York Stock Exchange, however, was so impressed with the virtual control center Asymptote created to communicate reams of data about the trading floor clearly and simultaneously that it commissioned the firm to build a version on its trading floor. That, to Rashid and Couture, is the sweetest moment: when virtual and real coexist. Because real by itself just doesn't do it for them. They're working on two unlikely projects: developing ceramic tiles that can change color and creating entrances to the New York City subway that look inviting. And consider Rashid's take on the outlandishly curvaceous, Frank Gehry — designed Guggenheim Bilbao: "It's a very contemporary and fascinating building but still somewhat classical, rooted in the world as we know it." But he can fix that: "Wouldn't it be fantastic if it revolved, if the skin mutated, if you could tell what kind of shows were going on inside, if it was dematerialized?"

And how, exactly, does a building mutate? The closest the duo has come to answering that is with HydraPier, an exhibition pavilion that Asymptote built (yes, actually built) last year at Harlemmermeer, in the Netherlands. The two-winged structure sits on an artificial lake created on land reclaimed from the sea. Embracing this quirky history, the roof of each wing is covered in a film of water so that as the wings dip toward each other visitors pass through a water alley formed by the runoff from the roof running down glass walls. That is, they walk through water — on dry land that was once underwater — to an artificial lake. The little pavilion doesn't change (unless you count the play of light through the liquid on the glass), but it acknowledges change.

One thing Asymptote has not developed is a recognizable style, although it's fluid in most of the current "isms." It toyed with deconstructivism in early designs, such as the steel cloud Rashid proposed as a gateway for Los Angeles in 1988. (The cloud registers the heaviness of the traffic and converts it into music.) The firm has also flirted with folded geometry, designing a store interior for Brazilian fashion designer Carlos Miele in New York City that's both chunky and smooth, as if carved out of ice that's melting and setting the clothes afloat.

This stylelessness is intentional on the firm's part, and Rashid, in particular, scorns architects who return constantly to the same design language. "Architecture is much more complex than a formal statement or a symbolic gesture," he says in Asymptote's book-cum-manifesto, Flux. "What we are most focused on is building inspired worlds, be they domestic, institutional, urban or digital." And in a world where boundaries are blurring, we might need all four at once.

• Belinda Luscombe