The Dutch dance group Oxygen. Trae Patton/NBC

After watching the impeccable tutting routine by a group called Geometrie Variable, Ne-Yo had one question for his fellow judges on NBC’s “World of Dance.”

“Did you catch the chin-ography?”

Of course they caught it. They’d all whooped when one of the dancers hammered his chin like a sewing-machine needle along the extended forearm of another. It was creative, witty and unexpected. It also expressed an important aesthetic principle in dance: The smallest movements can rock the crowd if they surprise the eye, connect with the music and touch some aspect of our own humanity.

In the absence of live dancing, all but extinguished by the pandemic, viewers can learn quite a bit about solid performance values on Season 4 of “World of Dance,” which airs Tuesday nights. (There are four more episodes left to the season – which was filmed just before the pandemic-related shutdowns – including the finale, which is Aug. 12.)

For one thing, crowd appeal – a key factor that judges Jennifer Lopez, Derek Hough and Ne-Yo are measuring – isn’t confined to extreme, acrobatic tricks, even here. It doesn’t matter whether dancers are competing before millions of TV viewers for a $1 million prize, as they’re doing on this show, or whether they’re soaring in an opera house or they’ve micro-calibrated for the small screens of Instagram and TikTok. What sets the most interesting dancers apart is a yin-yang tension of musical responsiveness (watching them, we want to be swept away) and astonishment (we also want to be pulled up short).

“World of Dance” judges Ne-Yo, Jennifer Lopez and Derek Hough. Trae Patton/NBC

That’s why a small-scale dance style like tutting, which focuses on angular shapes of the arms, hands and fingers, can project unexpectedly if it’s inventive and well-directed. The three French street dancers of Geometrie Variable proved this in “WOD’s” “duel” round on July 14.

They took tutting beyond the crisp two-dimensionality inspired by Egyptian hieroglyphics (the King Tut roots of its name). Responding to Flume’s stuttering, bittersweet “Never Be Like You,” the trio sculpted itself into a fast-paced fantasy of machines and hinged contraptions and even, eerily, a guillotine matched to a chilling sound effect.

The three men barely moved apart, working together in a tightknit brotherhood. They didn’t explode with crazy energy or take up a lot of space. They created corporeal pictures that grew and transformed not by virtue of muscular force, but through intricate interconnections. That was the human, and the most moving, dimension.

It was a taut, compact starburst of a performance, which Hough rightly praised as “surgical.” And at the end, after all the fine-tuned detail, came a surprise that made you catch your breath: One of the dancers broke from the others and flew into a flip, spinning smoothly like a coin tossed in water.

The throughline of “WOD” is: Show us something we’ve never seen before. As a dance critic, I want to see that, too, whenever I’m in the theater. What new revelation jumps out in a premiere, or in a reinterpretation of a classic work? What fresh response is there to the music, the setting, the story? Part of “new” involves sheer novelty, but part of it is also framing – how the choreographer and the dancer set up a moment for the best impact. Like the tutter’s scene-stealing chin, or the group breaking apart for a sudden solo backflip.

On “WOD,” there’s not a lot of time to shine: The format is a two-minute performance followed by instant appraisal. So the judges are focused and get right to the point. This is one of the show’s great strengths. Hough’s forte is identifying the elements that succeed or fail. Ne-Yo has an eye for unusual moments. J-Lo, with her hearty, buoyant good humor, nevertheless cuts to the bone: Are you going to wow America? Can you compete against all the others? Do you have what it takes to win? It’s not for nothing that she’s the boss judge (and one of the show’s executive producers). She makes the simplest, clearest case for who belongs on the show, or doesn’t, and she draws on honest values: the elements of her own starpower.

For example, J-Lo told one group that when she’s putting her own concerts together, a ballad might be a nice part of the package. “But if I’m going to come out for only two minutes,” she said while narrowing her eyes at the lead dancer, “I’m gonna need to slay.”

Got that, “WOD” hopefuls? You have a very tiny window to impress. Don’t fill it with anything less than killer material.

All of the judges zero in on the art of drawing the eye, the ability to make an action leap out at us because we’ve been directed to see it. In the qualifying rounds, the all-female group Pumpfidence did this the wrong way. They strutted and twisted in heels to a J-Lo song, but J-Lo, who knows more than a little about performing in heels, told them theirs were so high that they were distracting.

She faulted the Dutch popping group Oxygen for not “pushing the boundaries” and losing the beautifully coordinated weirdness that had made them stand out.

Styles & Emma, a ballet duo on the show. Trae Patton/NBC

All three judges swooned over Styles & Emma, a highly attractive ballet duo that combined long, stretchy flexibility with powerful lifts and jumps. Guest judge Stephen “tWitch” Boss was their biggest advocate when it came to the “redemption” round, where they competed against Oxygen. Comparing ballet and hip-hop sounds untenable, but this show is pretty consistent in what it values – surprise, clean execution, a vivid relationship to the music – so you could kind of compare the dance styles on those points.

Oxygen, donning hats and gloves, fired off a snappy, stylish number with cascades of syncopated precision hits rippling through the group, and they left everyone gasping. By contrast, there was a sameness about Styles & Emma, with one leggy, gorgeously extended move after another. The basic structure never changed: He was the target, and she was the projectile. Boss had seemed to note this when he lamented after an earlier performance that he “wanted to see y’all dance together more.”

It’s a request for simple human harmony, not just the tricks. Boss brought the emphasis back to an essential performance value: the ability to touch our own humanity. He reminded us how good it feels when we can connect with dancers vicariously, on a plain, earthy, human level. When we can see something of ourselves in them. I’m glad Boss brought this to the fore; it’s a grounding value, quite different from jaw-dropping extremes of physicality. Styles & Emma were eliminated, and while I was sorry to see them go – as Boss said, their art form is underrepresented on the show – I can understand why they were cut. They didn’t take his note.

A sense of harmony and oneness ran throughout Geometrie Variable’s routine, especially in that chin-ography bit, with its wacky, chummy connection between two men. The evident unity among the three dancers helped create a performance that was emotionally moving as well as astonishing technique-wise.

Dancing together: On a show that loves surprises, that may be the biggest one of all.

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