Dana Tai Soon Burgess Dance Company members Alvaro Palau and Christin Arthur. (Jeff Watts/Handout)

How powerful art is when it shows us our spiritual self, the part that gazes beyond this tottering world for meaning. Dance, with its embodied emotion, is optimal for this. The best dance pieces register with an immediacy that is like an ancient knowledge, a shared language of gesture and feeling that transcends the stage and inspires the imagination.

But to do all that simply is the Holy Grail. There were magnificent glimpses of such simplicity in Dana Tai Soon Burgess’s works, performed Friday at the Kennedy Center Terrace Theater.

The basis of Burgess’s choreography is sympathy with what we struggle not to show. He can portray, uncannily, the flickers and stabs of feeling that swarm through us as we try to stay calm under stress. Those nameless feelings figured in all four pieces on the program. Along with two new pieces, there were two gems created a decade ago: “Leaving Pusan,” which takes us through a Korean emigre’s anguish at leaving her family behind, and the luminous solo “Khaybet.”

In each of the works, the most effective moments were motionless. In “Khaybet,” Connie Lin Fink-Hammack stood under a sheer, dust-colored shroud, at once delicately beautiful and unsettling. The faint aspect of decay in her attire presaged her doom. (The gifted Judy Hansen created this and all the evening’s costumes.) But Fink-Hammack was not going easily.

With the first guttural notes of Philip Glass’s strings, we saw her eclipsed in shadow, her face averted, which was already a poignant scene. But something in the way she abruptly thrashed at the darkened space, and just as suddenly stopped, delivered a chill. As her dance progressed in this stop-start way, you saw her lash out in rebellion, then clear her mind, reset and shift little by little toward an acceptance of death that ultimately freed her.

Both of the new pieces, “Homage” and “Revenant Elegy,” were inspired by recent museum exhibitions of dance photos, artifacts and costumes. Burgess homed in on a fascinating aspect of such shows: the bittersweet feelings they arouse as you stand surrounded by the ghostly leftovers of past times. His “Revenant Elegy” was a kind of dance-play, commissioned by the National Gallery of Art in conjunction with its 2013 show, “Diaghilev and the Ballets Russes, 1909-29: When Art Danced With Music.” The gowns evoked another century, but the subject was eternal: the jilted lover reliving her pain.

You felt the sharpest sting at the end when, in the central role, Maria Del Carmen Valle Riestra doubled over, her breath and her will sucked away when her boyfriend leaves her.

As the first resident choreographer at the Smithsonian’s National Portrait Gallery, Burgess created “Homage” in connection with the gallery’s “Dancing the Dream” exhibit (continuing through July 13) on dance in American movies, theaters and concert arenas. Here, too, the strongest section featured stillness: As two couples waltz to Elvis Presley’s “Can’t Help Falling in Love,” dancer Alvaro Palau watches in silent absorption, and an attitude of longing. Was he the stand-in for the lonely choreographer, for all the ones whose sound bites we heard on a voice-over?

Once again, Burgess proved that it is a wise artist who knows the power of simplicity. When Palau finally moved, it was to take another dancer’s hand and walk with her slowly across the stage. The look of rapture on his face, and Presley’s melted-caramel voice: vicarious delight, and candy for the soul.