5, 6, 7, 8 …

Young dancers gather at the Ark on East Campus. Michael Zirkle

A young man in sweats and a white T-shirt stands perfectly still, staring intently at the piece of paper he holds in his hand. He takes a deep breath, and lets his arm fall. The paper flutters to the floor.

Nearby, a red-haired woman wearing blue leg-warmers positions herself face-up, on hands and feet, as it ready to begin a crabwalk.

She slowly raises her left leg, then her left arm, stretching them slowly to the right. Just before gravity makes her fall, she flips herself over and touches down on the other side. A slow-motion break dance.

Like the young man in sweats, she takes long pauses between moves to pore over a sheet of paper covered with a diagram of some sort. As if any two-dimensional sketch could adequately describe their strange motions.

Young dancers perfecting their pirouettes and accomplished professionals working on world premieres descend on campus to learn and teach during the American Dance Festival's annual summer school. Michael Zirkle

In the world of dance as envisioned by legendary choreographer William Forsythe, it does just that. These dancers, students in the six-week school convened on Duke's campus every summer by the American Dance Festival, have gathered with about a dozen others at the Ark on East Campus to work on one of the dances from Forsythe's Hypothetical Stream. The piece, which Forsythe created in 1996 for Daniel Larrieu and his company, is based on a series of sketches by the eighteenth-century Venetian painter Giovanni Battista Tiepolo, known for paintings filled with dazzling spatial illusions.

On a copy of each sketch, Forsythe numbered Tiepolo's figures, so that each came to represent a dancer. Forsythe drew arrows from the figures' heads, hands, and legs as a way to signal the arc of a movement, leaving its exact form, duration, direction, and order open to interpretation by individual dancers who would "solve" the puzzle he created.

As the students go about crafting dances based on the arrows emanating from a single amorino, or cupid, in a single sketch, instructor Richard Siegal watches from one side of the room. He is seated against the wall with his knees pulled up, his arms raised and hands gripping the barre mounted above his head. Every minute or so, he unconsciously flexes and unflexes his calves.

Siegal, who danced in Forsythe's Ballett Frankfurt from 1997 until it disbanded in 2004, is trying to teach his students something of Forsythe's method of improvisation, a system that has been highly influential in modern dance.

"It isn't a canon of steps that a dancer has to learn and master," Siegal says. "It's more like grammar, but without the vocabulary. You are free to insert your own language." Most of the students, he says, are familiar with Forsythe, who now directs the Frankfurt-based Forsythe Company, but few have studied his methods in depth.

The festival's school, part of ADF since its founding seventy-five years ago, is all about understanding dance. The school attracts some 500 students each year to its three programs: weeklong workshops for professional dancers, a six-week school for students sixteen and up (most are college students), and a four-week school for students ages twelve to fifteen. Most students in the six-week and four-week schools live in East Campus dorms.

Students in the six-week school have a full slate of courses in composition, dance technique, and improvisation that meet for two hours each on Mondays, Tuesdays, Thursdays, and Fridays. They study various modern styles, as well as ballet and contemporary African dance. On Wednesdays, Friday evenings, Saturdays, and Sundays, they are free to pursue a variety of elective classes, like the Forsythe Project. Other options include several forms of yoga, as well as a class in which students study the archive of choreographer and anthropologist Pearl Primas and use the material she created to inspire new works.

On a sultry summer afternoon in mid-session, all of East Campus is bustling with ADF people. The Ark is a prime practice and performance venue, but classes are also held daily in Baldwin Auditorium, Brodie recreation center, and various other buildings.

Just across the parking lot from the Ark, Wilson dorm, with its unusual layout of suites, provides a temporary headquarters for the festival's offices. During the summer, ADF's New York City office largely shuts down; its staff members make the trek to Durham and settle here.

In the lobby of Wilson, colorful fliers advertising an upcoming series of performances by Japanese dance companies are taped to pillars and walls. A bulletin board features news clippings about the festival that  boast of world premieres (dateline: Durham) from The New York Times, as well as the local Herald-Sun and News & Observer. This week's schedule of classes and events, which include "improv jams," a showing from the "rock band dance class," and performances of works by pioneers like Laura Dean, Mark Dendy, Erick Hawkins, and Hanya Holm, is posted on one wall.

Outside, ADF dancers, students, and administrators crisscross the East Campus quad, heading to class or the bus stop, or perhaps making a run to the Whole Foods on Broad Street. There is a sense of camaraderie among ADF participants that often tends to erase the boundaries between students, instructors, and performers. The students attend the professional companies' shows most nights, as well as master classes and lecture series, but there are also opportunities for less formal interaction. Many students have been here before; they recognize old instructors in passing between classes and stop to say hi.

Siegal is here teaching for the fourth year in a row. "I've been going to see performances, watching other people's classes," he says. "As an expat—I've been living abroad for twelve years—this is a great mainline into the American modern dance.

"I feel like I've got water in the desert," he says. "I'm soaking it right up."

The following week, the Forsythe Project students gather for a Friday night viewing of a DVD of Hypothetical Stream performed by Ballett Frankfurt. In the audience is Tyler Eash, a student who is studying dance and architecture at the University of California at Davis and is a big fan of Forsythe. There's something about the geometry of the dances that he finds intellectually stimulating, he says later. "As far as innovation goes, he's definitely number one."

During the viewing, Forsythe's wife, dancer Dana Caspersen, stops by to chat about her husband's work and her own involvement with the company. She is enrolled in ADF's master of fine arts program and invites the students to attend two video presentations she's making the following week that highlight Forsythe's work as well as her own.

Caspersen sits to watch part of Hypothetical Stream. The dancers, in pastel colors, move about a dimly lit stage. The music consists of discordant noises from synthesized instruments—organs, horns—like the soundtrack of a suspenseful movie. Some steps are precise, taken on pointed toe, but many of the movements are looser, choppier than those of ballet. A dancer's arms pull him in one direction, while his legs twist in the opposite. His arms stop moving, but his legs continue.

"Look at how their heads are connected to their bodies," Caspersen tells the students. "Look at the curve as it comes out of their pelvises."

The students watch with rapt attention, not saying much, perhaps envisioning how they might integrate some of what they are seeing into their own performances. Eash, who is hard at work on the choreography for an original piece, acknowledges he is heavily influenced by Forsythe's methods. "He gives you systems you can apply," Eash says, "without feeling like you are stealing from him."