Wayne Shorter at his home in Los Angeles. (Bret Hartman/For The Washington Post)

Wayne Shorter has been a potent and sometimes perplexing force in jazz for more than five decades, both as a saxophonist and as a composer. But every few years, he sheds his old skin, assumes a new identity and steers the music in provocative new directions.

You might remember him from Weather Report, when he helped make jazz fusion the hipster music of the 1970s. Or maybe you recall his quicksilver solo with the Miles Davis Quintet of the 1960s, the group that made the “Live at the Plugged Nickel” recordings that helped shape improvisational music for years to come.

Even before that, Shorter was part of Art Blakey’s Jazz Messengers of the early 1960s, when he helped move jazz out of the hard-bop past and into a future that is still being defined. He was named a Jazz Master by the National Endowment of the Arts — the country’s highest honor for a jazz musician — in 1998 and has long been hailed as the finest living jazz composer.

He’s won nine Grammy Awards and, after stoking the furnace of jazz for so long, has earned the right to sit back and play a few of his greatest hits — if jazz musicians actually had hit records — for old time’s sake. He turned 80 last month, after all, and he’s spent the past months on a celebratory worldwide tour that has taken him from Panama across Europe to the Hollywood Bowl and now to the Kennedy Center, where he’ll appear Thursday with his quartet.

But if you’ve paid any attention to Wayne Shorter, you’d know that this is no nostalgia tour.

Jazz saxophonist Wayne Shorter performs during Tokyo Jazz 2002 in Chofu, a northwestern suburb of Tokyo, in this Aug 24, 2002 photo. (Naokazu Oinuma/AP)

Remember “Speak No Evil,” “E.S.P.” and “Infant Eyes” from in the ’60s? You used to bop to Weather Report’s “Birdland” and “Mysterious Traveler”? Well, enjoy the memories, because Shorter isn’t going to relive the past for you.

Since 2001, with his new acoustic quartet, he’s been embarking on a musical journey that seldom looks back at the familiar signposts. Most of the pieces he performs these days are new, including “Gaia,” a composition he wrote for the dazzling young bassist-singer Esperanza Spalding, who will also appear Thursday with the National Symphony Orchestra.

Just don’t expect to leave the Kennedy Center humming any of Shorter’s new tunes. The sinuous melodies that used to crawl into your ear have given way to dashes, drops and flashing blades of aural color. His most recent recording, “Without a Net,” has been heaped with praise by critics, but it can be difficult to warm to, especially if you haven’t been following his recent music. The only tune on the disc that could be called a standard, “Flying Down to Rio,” was written for a Fred Astaire movie in 1933, the same year Shorter was born.

But he’s turned it inside out, with a darting, percussive quality that skitters along on the edge of dissonance. He keeps you on your toes and — sort of like Astaire, come to think of it — makes you admire his musicality and, even more, the sheer audacity of his performance. You marvel at how he can defy gravity and spin through impossible turns and still keep his balance.

“I have my own meaning for jazz,” Shorter says. “Jazz means, ‘I dare you.’ I dare you to get out of your comfort zone.”

‘Open. And courageous.’

The presence of an old movie theme is hardly an accident, since film has been a big part of Shorter’s life, ever since he skipped class for 56 days one year in high school in Newark. He would sneak around the corner to watch matinee movies and the jazz bands that shared the billing: Duke Ellington, Jimmie Lunceford, Stan Kenton and others.

To keep him focused, his teachers put him in a music class, where he took up the clarinet before switching to saxophone. It was like turning on a light. He was 16, and ever since Shorter has been creating what he calls the soundtrack of his life.

He knows all about music theory, chord intervals and the technical things musicians talk about among themselves, of course, but he seldom talks about them. He’s worked with many of the finest musicians of the past half-century, from John Coltrane and Miles to Freddie Hubbard, Herbie Hancock, Pat Metheny, Jaco Pastorius, Carlos Santana, Joni Mitchell and Brad Mehldau. But don’t expect Shorter to drop any of their names.

“When you go onstage,” he says, “you have to put away all your Grammys, your accolades, put away all your newspaper articles. Go out there in your pajamas and tell a story.”

His current quartet, with pianist Danilo Perez, bassist John Patitucci and drummer Brian Blade, has been together since 2001, but the group has seldom had a rehearsal. He’ll send them new music, let them ponder it on their own, then hit the bandstand with the raw materials for an untried experiment.

“How do you negotiate the unexpected and the unknown?” is the way Shorter puts it, speaking from his home in Los Angeles. “You have to be open. And courageous.”

Instead of practicing together, he might ask his musicians to watch the same movie, such as “Alien.” Shorter views the shocking moment in the film, when a creature emerges from a human body, as a metaphor of creativity.

“You see that?” he said, according to an interview pianist Renee Rosnes gave to Jazz Times this year. “That’s how I want my band to sound!”

Shorter has been a dedicated practitioner of Buddhism for more than 30 years and has learned to talk in a gnomic style that flows around a question. If you want an answer from him, you can’t expect to find it by standing on the river bank: You have wade in with him and peer through the ripples in the current.

Asked whether he thinks of his musical ancestors and mentors while performing — Charlie Parker, Blakey, Coltrane, Davis — Shorter does not answer the question directly. His elliptical response is cast almost in the form of an aphorism.

“When you’re becoming new, you’re not changing your original essence,” he says. “You’re gaining knowledge and insights. Knowledge is nothing without wisdom.”

Then after an intellectual voyage through the cosmos — or, more to the point, like a wildly searching saxophone solo that returns to its original theme — Shorter says, without mentioning his jazz heroes by name: “I celebrate them. I celebrate the camaraderie. I celebrate not just the musicians, but the mystery of us.”

There are times with his current quartet, he says, when a kind of mystical quality emerges, a sense in which the music is somehow inhabited by the spirits of other people and other times.

“With the quartet,” he says, “something happens, and I’ll say, ‘Did you feel somebody’s grandmother in there?’ ”

Perez, Shorter’s Panamanian-born pianist, had early apprenticeships with Dizzy Gillespie, Roy Haynes and Gary Burton and is one of the most accomplished musicians in jazz. But something about working with Shorter is different.

“Other experiences were rewarding but were steppingstones guiding me to this moment,” Perez says. “Working with Wayne has been rewarding in other areas besides just musical. It’s been rewarding in a human way. I’ve gained another father in my life.”

‘Eternal adventure’

For someone who became a musician almost by accident, Shorter had a sudden ascent to acclaim. After graduating from New York University in 1956, he played in an Army band in New Jersey — where he also qualified as a top marksman.

When his commanding officers asked him to extend his military service, Shorter said thanks, but no: “I have urgent business in New York City.”

That business? “To get into the music world.”

He became close to Coltrane, the volcanic saxophonist who inspired a generation with his torrents of sound.

“He came to my place, and we just started trading ideas,” Shorter recalls. “He’d play a little bit, I’d play a little bit, and we’d talk. He said, ‘You’re playing all over the horn, like I am.’ He meant ‘exploring.’ ”

Working with the Jazz Messengers and in his own groups in the 1960s, Shorter became perhaps the leading tenor saxophonist following in Coltrane’s style. (Another tenor titan of the era, Sonny Rollins, developed his style before Coltrane’s influence emerged.) When Davis formed his “second great quintet” in 1964, Shorter took over the tenor saxophone position that Coltrane had held in the 1950s.

His playing contained a blend of energy and sensitivity that has influenced virtually every major tenor player who came after him, including Joe Lovano, Branford Marsalis and Joshua Redman. And all the while, he was writing tunes, such as “Footprints,” “Nefertiti” and “Night Dreamer,” that pushed jazz toward new levels of refinement.

“They’re a very gifted combination of conventional jazz tonality and ambiguity,” says Scott DeVeaux, a University of Virginia music professor and jazz historian. “Those records from the ’60s are going to be studied as long as people are studying improvised music.”

In the late 1960s, Shorter followed Davis into experiments in electronic music and appeared on “Bitches Brew,” Davis’s influential recording released in 1970. About that time, Shorter joined with keyboardist Joe Zawinul to form Weather Report, a seminal jazz fusion group.

For almost 30 years, Shorter worked in the world of jazz-rock music — something his early fans never really forgave him for — and increasingly abandoned his dark-toned tenor saxophone for the lighter, sketchier sounds of the soprano.

During those years, Shorter went through a private transformation, as well, cultivating his interest in Buddhism and enduring several painful losses. He had a 14-year-old developmentally disabled daughter who died in 1986. In 1996, his wife, Ana Maria, died on TWA Flight 800, which crashed off Long Island.

The tragedies only made Shorter more philosophical and caused him to burrow more deeply into his music.

“When one close to you passes away,” he says, “driving your car over a cliff or drinking yourself to death is a slap in the face. You will strive to be the happiest person in the world for her sake, and yours. We have to see the tragedy as temporary and not make the tragedy the constant in our lives.”

One other thing helped spur Shorter’s creativity, as well. Shortly before Davis died in 1991, the mercurial trumpet player summoned Shorter to his side and told him that he needed to do more to put his music before the public — that, in effect, he had a gift that the world needed to hear.

For the past dozen years, Shorter has returned to the acoustic jazz format on which he built his name. He’s dusted off his tenor saxophone again, playing it almost as much as the soprano. His music may be difficult and challenging, but Shorter and his quartet are universally acclaimed as one of the top working groups in jazz.

“As a quartet, we have become truly a family,” Perez, the pianist, says. “Our level of telepathy is scary at times.”

For Wayne Shorter, the journey continues to reveal itself, day by day. He has overcome his natural reclusiveness to step out front as one of the grand oracles of jazz, playing that ever-evolving soundtrack of what he calls the “eternal adventure” of his life.

“Tell me your story,” he says, “and I’ll tell you mine.”

NSO Pops: Wayne Shorter 80th Birthday Celebration

with the Wayne Shorter Quartet and special guest Esperanza Spalding. Vince Mendoza, conductor. 8 p.m. Thursday. Concert Hall, Kennedy Center. 202-467-4600. www.kennedy-center.org.