One constant of David Byrne’s long and prolific career is his ability to grow a seemingly simple idea into something brilliant, whether it’s the melody of “Road to Nowhere” or the concept of the “Stop Making Sense” tour some 36 years ago, where the premise of bringing out nine musicians, one at a time per song, grew into one of the most iconic tours in modern music history. What is perhaps most remarkable is his ability to keep coming up new ideas that seem obvious, but obviously aren’t.

To that end, the concept underpinning “American Utopia,” his 16-week Broadway show that officially launched Sunday, is equally simple in theory: A completely bare stage with “untethered” performers, bound by no wires or stationary equipment, moving more or less constantly throughout the show. As he described the concept to the audience at the Hudson Theater on Wednesday night, “It’s just us — and you.”

And while the show shares a title with his latest album, songs from it make up less than a quarter of the 21-track setlist, which acts more as a selective career retrospective, reaching all the way back to the Talking Heads’ 1977 debut and spanning crowd-pleasers like “Once in a Lifetime” and “Naïve Melody (This Must Be the Place)” to deeper cuts like “I Should Watch TV” (from his 2012 collaborative album with St. Vincent) and “Toe Jam” (a relatively obscure 2009 song with grime act BPA), and even a Janelle Monae cover. However, it’s not a greatest-hits set; notable by its absence is “Psycho Killer,” which is probably not a song Byrne cares to revisit at this stage of American history.

The show also has a thematic throughline — spawned from the concept that human brains have many more neural connections when we’re babies, which are gradually lost as we age — along with an unexpectedly and uncharacteristically political subtext that unspools as the evening progresses.

While “American Utopia” is essentially the same production that Byrne toured around the world for much of last year, it is far more suited to a Broadway theater than, say, a festival — in the intimate, seated confines of the Hudson, the staging, sound, colors and sense of movement have no distractions. But the show is hardly sedate: Before launching into “Burning Down the House,” Byrne encouraged the audience to dance (while staying out of the aisles, in deference to the fire marshal).

The show opens with Byrne seated at a table, holding a plastic human brain and musing on the neural-connection theory: “Does this mean babies are smarter than us, and we get stupider as we grow older? Where do those lost connections go?” Three sides of the stage are enclosed by curtains made of hundreds of small, hanging metal chains, which rise from the floor as the show opens. They are not only used to section off the stage but also occasionally as props — during one song, the musicians’ seemingly disembodied hands hold out their instruments from behind the curtain, to comic effect.

The musicians — totaling 12, including Byrne — come onstage gradually, wearing headset microphones and matching grey suits and grey shirts, and all are barefoot (except for one, who was inexplicably wearing shoes designed to look like bare feet). The lighting is stark; there aren’t even any colored lights until midway through the show, and even then they’re single colors to suit the mood of a song.

The instrumentation is also deceptively simple: A guitarist (joined by Byrne on a few songs), bassist, keyboardist, two singer/dancers, and everyone else plays percussion, with the instruments harnessed to their bodies, marching-band style. The musicians are in more or less constant motion, performing choreography (designed by Annie-B Parson) that is deceptively elaborate yet almost never ostentatious: It’s all designed to be part of an overall effect, with lots of synchronized movement, walking in unison, and simple hand gestures.

At times the group looks like a single organism: During one song, the musicians are huddled together on the left side of the stage, moving in a crouch across the stage as the song progresses while Byrne backs away from them, singing. During “Blind,” the stage is illuminated by a single bright white light on the floor, with Byrne and the group throwing dramatic shadows onto the curtains; during the final chorus of “Once in a Lifetime,” the musicians, arrayed evenly across the stage, march slowly toward the audience in unison — a simple but spine-tinglingly effective tactic.

Throughout, Byrne is the gracious ringleader, always the frontman and always in charge but happily ceding the spotlight to musicians or dancers for solos, and twice taking comical, wordless vocal solos himself (like “Bip b-b-bip, B-bip-bip, B-bip” — you get the idea).

The political content comes into the show gradually. While introducing the band, Byrne says “We’ve got people from Brazil, from Jamaica,” and notes that he himself is a naturalized American citizen who emigrated from Scotland with his family as a boy. “We are all immigrants, and we couldn’t do this show without them.” Later, he speaks about working for voter registration in North Carolina before the 2016 election and notes that the highest percentage of the population in decades voted that year: 55%. “In most local elections, it’s 20%: To put that in some perspective” — a spotlight shone on a small sliver of the audience — “in this room, that number of people decide what the rest of you do — and most of them are 55 and over. Global warming? They’re not too worried about it. Kids? You’re f—ed.” (Voter-registration workers were stationed in the theater lobby.)

But the calls for activism ramp up late in the show, particularly with the percussion-and-vocal cover of Janelle Monae’s “Hell You Talmbout.” Byrne spoke of hearing Monae perform the song at the 2017 Women’s March in Washington, D.C., and asking her if she would mind if a “white man of a certain age” covered it. He said she was delighted, and the band performs a rousing version of the stark song, which is simply a chant of “Say his name” and listing the names of many black people murdered in America, ranging from Emmett Till to Atatiana Jefferson, who was killed by a police officer in Texas just last week. Much of the song’s power comes from the fact that the tragically familiar names just keep coming — Amadou Diallo, Eric Garner, Trayvon Martin — in painful, unrelenting succession.

However, the show ends up a hopeful note with the song “One Fine Day,” bringing the theme full circle. “Despite everything that’s happened and is happening in the world, I think we’ve got a chance,” Byrne says. “The connections in our brains can be re-established — and that extends to the connections between us all.”

Continuing that theme, the musicians return for an encore of the Talking Heads’ 1985 hit “Road to Nowhere” — a fittingly paradoxical close to a stunning show from an artist whose much-vaunted quirkiness masks his intensely focused and disciplined creativity. While Byrne’s more recent solo recordings may not always approach the brilliance of his earlier work — really, not many creators’ work does — particularly in concert, he remains a vital, compelling and deeply relevant artist who, at 67, continues to challenge his audience and himself.

I Know Sometimes a Man Is Wrong
Don’t Worry About the Government
This Must Be the Place (Naive Melody)
I Zimbra
Slippery People
I Should Watch TV
Everybody’s Coming to My House
Once in a Lifetime
Glass, Concrete & Stone
Toe Jam
Born Under Punches (The Heat Goes On)
I Dance Like This
Every Day Is a Miracle
Burning Down the House
Hell You Talmbout
One Fine Day
Road to Nowhere