Beyonce live at Madison Square Garden

There were five months between last November’s release of Beyonce's last record, “I Am ... Sasha Fierce,” and the April beginning of her world tour, which made its first American stop at Madison Square Garden on Sunday. It’s reasonable to suppose that it took that long to prepare for it. It would be reasonable to suppose that it took twice that long to prepare for it. The whole point of the dazzling show was to make you ask how she does it. Not just physically, but organizationally. A long time from now, when this stretch of the history of pop is written, someone will have to pay close attention to Beyoncé’s laptop and smartphone files, as well as those of her managers and producers. From there we might find the trail of communication, the co-opting and planning and execution. The YouTube research, the conversations with choreographers and stunt coordinators and the fashion designer Thierry Mugler, the tour’s creative adviser. The cast’s 71 costumes. The aerial somersaults. The titanium robot glove. And the unwieldy mother concept of the tour: the duality of well-meaning good girl and rapacious animal-robot-dance-titan.

The two-hour show worked with conventions, and a few felt off-the-rack. A variation of the tall riser at the front of the stage was in Tina Turner’s show a few months back. Moving to a small stage in the middle of the arena is an old and effective rolling stones trick, but Beyoncé got there through the air, lifted out of a 20-foot train by a harness. (She high-stepped in slow motion and front-flipped along the way; there is a breathtaking elegance in her acute desire to entertain.) And some conventions were her own — the medley of Destiny’s Child songs, who emerged to deafening applause, rapping a verse from his “I Just Wanna Love U (Give It 2 Me),” in the middle of her “Crazy in Love.”

Beyoncé is the high priestess of upward mobility: there’s always something better for herself (“Irreplaceable”) and those she loves (“Upgrade U”). The good-girl songs of the new album and tour are staged attempts to temper all that ambition with humility and empathy. And she’s fine at it, as she is fine at everything, though sometimes the songs seem like public-service announcements when they aren’t banging tracks. “I don’t want to play the brokenhearted girl,” she sang in one of them. That was the evening’s most comical moment, in a concert involving a bustier made with motorcycle lights.

di Clarissa Falzone