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Torque, Tension, Turns

Balancing on the balls of her feet, her arms in a wide circle, senior Katrina Wisdom begins a ballet move called an attitude. She raises one leg, slightly bent, to ninety degrees without a wobble, to show how ballerinas intuitively feel physics.

The dancers don't often know the mathematical equations describing their moves, but they know how to execute them with grace. If ballerinas didn't feel physics, they'd fall over.

As an engineering major at Duke who has been dancing since the age of four, Wisdom sees the math in her mind as she expresses it with her body.

"Ballet teachers often say, 'keep extending as if you're never quite going to get to the end of a move,' " she says. As she learned more complex math in her engineering classes, Wisdom began to see each step as "a kind of exponential, one that accelerates quickly at first and then slows down towards the end, like an equation that asymptotically approaches, but never quite reaches, an end value."

ballet performanceThe imagery grew so powerful that Wisdom began to notice small improvements in the flow of her ballet. Eager to bend, flex and turn with added grace, she looked more critically at the intersections of engineering and dance.

She says the connections became even more important to explore when, at the 2009 NAE Grand Challenge Summit conference, she heard that most Americans grade themselves a C or lower in math and science, according to a National Academy of Engineering survey. Engineering, in particular, was boring, inaccessible and unrelated to their lives, those surveyed said.

“Now, how can that be," she asks, "when engineers build cell phones and computers to keep us connected, design rockets to go into space and invent the miraculous medical devices that save our lives? Clearly, engineering communication is in dire need of a facelift.”

The elegance and grace of ballet is one cosmetic device Wisdom thinks engineers could use to improve their communication.

In the spring of her junior year, Wisdom tested this idea, giving a public talk called “Fouetté Turns and Fourier Series" in the Ark, Duke's dance studio in a century-old, converted gym and cafeteria on East campus. She explored five intersections of ballet and engineering while surrounded by ballet bars, a screen and projector.  Wisdom demonstrated basic ballet moves and recruited three other ballerinas in leotards and ballet shoes to be her test subjects.

One of her first experiments was on turns. As two of the ballerinas began to spin, their arms flowed in and out, their legs flexed and extended and their eyes focused at a point on the wall, leaving that spot only long enough for the women to whip their heads around and return their eyes to the same place.

Wisdom explained that their legs, arms and head are oscillating as they turn – moving back and forth in seemingly separate patterns. However, to be "on” in turns, she continued, “Everything really must move at the same rhythm."

Engineering systems with many parts that oscillate in rhythm are capable of highly energy-efficient fluctuations, a physical phenomenon called resonance. Wisdom asked the ballerinas to try their turns again, this time focusing on syncing their movements to create a sort of “resonance” among the oscillations of their arms, legs and heads.

The ballerinas began to spin, timing their arm and leg movements carefully. At half a dozen turns, they seemed to spin faster and longer with less effort.

"One of the most compelling elements in Katrina's presentation was the way she articulated the fact that dancers deal with engineering and physics concepts all the time, and in real time, without necessarily thinking of their work in that way," says Tyler Walters, an associate professor of ballet in the university's dance program and one of Wisdom's instructors.

He says that many of the aesthetic foundations of western classical dance are rooted in the geometry, science and architecture of the renaissance and baroque periods, which is not generally associated with modern ballet.

Reasserting those historical connections or, at the very least rediscovering humans' intuitive understanding of physics, could provide a bridge between the arts and science to better communicate engineering.

Relating a ballerina's turns to resonance, or her leg extensions to torque and tension, may make it easier for an engineer to explain to the public engineering failures like the Tacoma Narrows Bridge collapse or the complexity of new systems and designs, Wisdom says.

This could work in the opposite direction too, Walters says. Focusing on fundamental physics could provide dancers a new way of understanding and doing ballet.

"The boundaries in ballet are constantly being pushed in every way," Wisdom says. Choreographers and companies are experimenting with all kinds of ways to make the performing experience fresh, so thinking of dance in terms of engineering is a tool to equip ballerinas to be competitive in a world full of situations they've never seen before. It's a way, she says, to master new and impressive feats of artistry and performance.