This week in dance is like a lowbrow sandwich – on highbrow bread. Lincoln Center Festival is presenting some very high concept works on Tuesday and Thursday, but in between (on Wednesday night at 8 p.m.) Fox launches its deliciously silly television show “So You Think You Can Dance?”

The goal of the program is to find America’s best dancer, and the contestants come from a wide field that includes hip-hop, jazz, ballroom, and “krumping” (spastic, clown-inspired hip-hop). But whoever wins, they’re still up against some stiff competition. Fox’s Web site for the show offers a poll that asks the question: “Who is the greatest contemporary dancer?”

You may legitimately wonder what sense of the word “contemporary” was intended here. Well, you won’t get any clarification from the choices, though you might get a laugh: Usher, Janet Jackson, Justin Timberlake, Baryshinkov, Savion Glover, Gregory Hines, Twyla Tharp, or Debbie Allen. (I am not making this up; if I were, Jennifer Lopez would definitely be on this list. )

But this dose of nonsense should be a welcome change from the intensity of performances by the contemporary dance companies Shen Wei Dance Arts and Random Dance.

Shen Wei’s work is intense in a way that foie gras is intense: rich, smooth, and meant to be savored. His dances combine arts like modern dance, painting, and sculpture with a touch of the Chinese artistic traditions that he absorbed while growing up in Hunan. I’ve said it before, and I’ll repeat it: The man is one of the most talented people in all of the arts, not just dance.

On the program that opens tonight (and is repeated on the weekend), Shen Wei Dance Arts will present two works: the world premiere of “Map” and the New York premiere of “Near the Terrace, Part 1.”

The latter, set to music by Arvo Part, was inspired by the work of Belgian painter Paul Delvaux. The mood is cool, blue, and surreal.

“Map” is divided into seven sections that follow the patterns in Steve Reich’s piece “The Desert Music.” Each section explores a different type of movement, such as rotation, bouncing, or internal isolation.

Given Mr. Shen’s ability to look within and create a new style, this work – commissioned by Lincoln Center Festival – should be one of the highlights of the week.

On Thursday night and again on Friday, the British company Random Dance presents the U.S. premiere of its 70-minute work “AtaXia.” Choreographed by artistic director Wayne McGregor, “AtaXia” is an exploration of a neurological condition that affects the body’s control over movement.

This piece is the result of an unusual overlap of art and science. Mr. McGregor spent six months as a research fellow at the experimental psychology department at Cambridge University. During his time there, he and lab scientists studied the interaction between the body and the brain.

Though dancers have exquisite control over their bodies, this piece considers movement that is out of control. The moves are fast, sometimes flailing, often totally unconnected to each other: an arm that shoots off in one direction, a foot that flops in another.

Part of Mr. McGregor’s research included talking with people who have ataxia, including Sarah Seddon Jenner, who then wrote a first-person essay about becoming involved with the work. Ms. Jenner heard through the grapevine that Mr. McGregor was creating the piece, but she wound up meeting him when she discovered that they shared the same Pilates instructor.

After a long discussion with him, Ms. Jenner was asked back and discussed her world at even greater length with the entire company. Some of her movements – such as the way she scoots across the floor- even made it into the final product.

While the movement is searing, the music is the really aggressive part of this piece. The score – “Trance” by Michael Gordon – will be performed live by the 12-piece British group Icebreaker, known for its contemporary, edge-pushing sound. Fair warning: From reading the international press, I get the sense this may be very loud.

But the loudness has a point. The music combines with the work’s visual display of lights and electronic images for a bit of sensory overload. This piece should make you think about the brain, how it absorbs reality, and how you react to information that you take in. Or, for those with ataxia, how the body cannot react to that same information.

Random Dance and Shen Wei Dance Arts are both at New York State Theater, and there’s a good way to see both. The “Dance Lovers Package” offers two tickets to Random Dance and two tickets to Shen Wei for $100. For tickets call CenterCharge at 212-721-6500 or visit the box office of Avery Fisher Hall, which is the festival’s box office HQ.

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First it was Peter Boal, then Jock Soto. Now James Fayette is the latest male principal to leave New York City Ballet. If I had any teeth left to gnash, I would. But we don’t even get to have a send-off at State Theater. Mr. Fayette’s farewell performance took place on July 14 at the Saratoga Performing Arts Center, the company’s summer home.

Mr. Fayette was charmingly seductive in his dancing, especially when onstage with his dancer wife, Jenifer Ringer. Watching them together was a thrill: She projected more brilliantly than Times Square, he was a rock who never failed. In his own dancing, he had a manly appeal; he’s an American-looking guy with the build of a fit, muscle-bound athlete and the spark of a team captain.

Which, it turns out, he actually is (a team captain, not an athlete; though who knows?). Mr. Fayette is retiring to go to work for the American Guild of Musical Artists, the union that represents City Ballet’s dancers. Mr. Fayette was asked to become the New York Area Dance Executive. This follows his tenure as the chairman of the Dancer’s Committee for AGMA.

Will he quickly tire of a desk job and yearn for a return to the stage? We can only hope.