That ability to connect the most disparate of dots has helped Shorter become one of the finest composers in the history of American jazz — and when he receives the Kennedy Center Honors on Sunday night, he’ll be recognized for all of that, and then some. Because when you listen to the sweep of his music — whether he made it with Miles Davis, or in Weather Report, or on his own — you can practically hear Shorter’s concept of “everything” growing wide enough to include what lies beyond our perception.

“There are colors we can’t see, but they’re connected to the ones we can,” he says, gesturing toward an open window on a breezy October afternoon in his California living room. “There’s a connection between everything.”

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As a conversationalist, Shorter still likes to jump around, but he’s easier to follow than he used to be. At 85, he’s been struggling with respiratory issues, and he doesn’t speak as briskly. But his mind still zips. That much becomes evident the moment he starts talking about “Dolores,” a dashing, venturesome tune he recorded with Davis in 1966. Shorter had once said that writing the song was more like writing DNA — he wasn’t creating the organism, just the code for it to exist.

What an idea. Could he say a little more about it? Sure he could, but what follows isn’t an answer so much as a daisy chain of axioms that seem to have animated his life’s work:

“DNA is, like, not to be finished. So I wrote a piece called ‘Dolores,’ right? It’s not finished yet. I think beginnings and endings are consensual. There’s no such thing as a short story. . . . The DNA, some people say, is the signature — and every composer has a signature. A lot of people don’t know that Beethoven, when he wrote the Fifth Symphony, that second movement” — and here, Shorter begins humming in a happy rasp, then resumes — “He took eight years to figure that out! But to suffer is not right, either. There just has to be something in the music that knocks at the door, that challenges the gatekeepers. Art induces a kind of funniness. Or a tickle, or jingle bells — laughing all the way. . . . And without ever giving up. Never giving up: That means playing for a long time? No! [laughs] . . . ‘Potential’ is another way of saying ‘mystery.’ ”

The Newark Flash

You could almost plot out the vast totality of Shorter’s life as a three-dimensional thing — a multidirectional creative expanse marked with monumental artistic triumphs and fathomless personal tragedies (Shorter lost a daughter, Iska, to a grand mal seizure when she was 14; he later lost a wife, Ana Maria, in the crash of TWA Flight 800). But these days, Shorter’s legacy is secure, and his life appears peaceful and calm. He lives with his wife of nearly 20 years, Carolina, in a house high in the Hollywood Hills, where the maestro awakes each day around 5:30 a.m. to compose on a Nord synthesizer the color of an Atomic Fireball.

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He’s always been tenacious with his music. Raised in Newark, N.J., he took up clarinet at 15, and by the time he switched over the saxophone a year later, his skills were surging. But in his mind, Shorter couldn’t improve fast enough. “I knew that people start on instruments when they’re 5 years old, so I did think I had a lot of catching up to do,” he says. “But when things started to move, opportunities came at a pace I hadn’t seen.”

He spent his teenage years playing in groups with his older brother, Alan, and the two proudly carried themselves around Newark as outcasts. Wayne had his nickname, “Mr. Weird,” painted on his saxophone case, and he developed an outsize musical reputation to match. He turned down a tour with Sonny Stitt so that he could graduate from high school in 1951, and while studying music education at New York University and working the clubs of Manhattan and its vicinity, he earned himself a new nickname: the Newark Flash.

After a stint in the Army, he landed a spot in Art Blakey’s Jazz Messengers — a group in which Shorter says he learned to think of musical narrative as an act of collective storytelling. “Art Blakey would sit behind the drum-kit and say, “T ell me that story!,” Shorter says, transporting himself into a nightclub, holding an invisible saxophone in his hands. “So the narrative spreads throughout the group.”

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Around that time, Shorter was developing a friendship with John Coltrane, who would eventually bequeath Shorter his place in Miles Davis’s group — a new quintet that would feature drummer Tony Williams, bassist Ron Carter, and Shorter’s soon-to-be best friend, the pianist Herbie Hancock. Almost instantly, the quintet became one of the most elastic and exploratory groups jazz had ever seen.

“The first day I played with Miles, he called me to the Hollywood Bowl,” Shorter says of his high-wire audition. “I walked into the dressing room and Miles said, ‘You know my music?’ I said, ‘Yeah.’ He said, ‘Uh-oh.’ ”

But Shorter managed to ace his onstage tryout, allowing him to spend the next five years alongside the deep and unknowable Davis. Together, they generated some of the most well-known jazz of the 20th century, with Shorter composing many of the group’s sturdiest songs — “E.S.P.,” “Footprints,” “Nefertiti” and others. Up on the bandstand, the players embraced an improvisational approach they called “anti-music” — a refusal to do whatever might be expected of them at any given moment. Reminiscing about it in “Footprints,” an illuminating 2004 biography of Shorter written by Michelle Mercer, Shorter said, “This is what freedom means.”

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The quintet dissolved in 1968, but Shorter stuck with Davis long enough to toss a few clean ideas into the psychedelic muck of Davis’s big crossover album, 1970’s “Bitches Brew.” That same year, Shorter co-founded Weather Report, a wildly successful fusion group in which the anti-music veteran converted himself into a sort of anti-bandleader, taking up the role of a benevolent, centering presence rather than the group’s guiding force. Critics complained that Shorter was becoming tentative. He thought he was simply cultivating his own awareness.

The years that followed were Shorter’s starriest, dotted with recording sessions with Steely Dan (1977’s “Aja”), the Rolling Stones (1997’s “Bridges to Babylon”) and Joni Mitchell (every album she released between 1977 and 2002). At first, Shorter was leery of being seen as a legitimizer-for-hire, but he ultimately remembers those studio hours as little exercises in empathy — especially when it comes to the delicate magic he made with Mitchell.

“I believe in everyone staying as they are, and when you meld together, you get something more accurate and democratic,” Shorter says, evoking the sanctity of the republic before pivoting to a sci-fi idea: “That’s where the portal is.”

Jumping into those pop-portals might not have resulted in Shorter’s most cosmic playing, but strangely, his rock-and-roll dalliances only support his reputation in the greater jazz consciousness as an empath whose preternatural sense of economy sets him apart from the busy heroism of Coltrane, Sonny Rollins and other saxophone colossi. His simpatico approach seems to permeate our 21st-century ego-stripped jazz ecosystem, where so many of today’s most astonishing players value cooperation over command.

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Mark Turner is one of them, a saxophonist of sublime clarity who explains Shorter’s influence in terms of altruism and equanimity. “It’s less about the self and more about things like, ‘What can we make together?’,” Turner says. “If he only needs to play one note, that’s what he does. He’s not a checklist player. He’s not one of those people who needs to do this and do that.”

That aura of necessity radiates from Shorter’s greatest compositions, with durable lines of melody often bending into irregular shapes. “I’m working on something right now, and I’m in a spot where I’m asking, ‘Should I make this regular?’ ” Shorter says, pointing at an unruly stack of sheet music (an opera he’s currently writing with the bassist Esperanza Spalding). “But if you make something irregular for the sake of irregularity, that’s not cool, either. Sometimes when you get to something irregular, you have to start sculpting it, shaping it. It depends what’s out there. The notes are hanging around each other the way we’re hanging around each other.”

That sculpted quality is something many musicians cherish in Shorter’s songbook, including the flutist Nicole Mitchell, a visionary composer whose visions are much different from Shorter’s, but who still finds the architecture of his music to be deeply instructive.

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“I really admire his ability to look at a song as a shape,” Mitchell says. “It’s almost like fractalism. There’s a seed that exists in the whole piece, but in different ways, different permutations of that idea.”

So yes, everything is connected, but “everything” can also be a vast network of indivisible somethings. Here’s how Shorter once put it to the critic Greg Tate: “I like this phrase: A million dollars does not exist without one penny, but one penny can exist without a million dollars. I like that, brother!”

Superheroes of jazz

In September, Shorter released “Emanon,” a triple-disc packaged inside a graphic novel that may or may not be named after a tune that Shorter once saw Dizzy Gillespie introduce from the bandstand in a cryptic shout: “ ‘Emanon’ is ‘no name’ backwards!”

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The recording itself features Shorter’s acolyte-band of the past decade, the drummer Brian Blade, the bassist John Patitucci and the pianist Danilo Perez, often working in grand gestures without ever really stepping over the line into grandeur. Some of the music correlates to the comic book, which depicts Shorter’s titular superhero leaping across different sectors of the multiverse, shaking societies free from their received knowledge. “I made sure he didn’t get his power from outside of himself,” Shorter says of his protagonist. “No profound, omnipotent force came and gave it to him. It emerged from within.”

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It’s a full-circle gesture. Shorter grew up reading comics voraciously. He even drew one when he was 15 — an interplanetary romance titled “Other Worlds.” But once bebop took over his teen brain, he stopped idolizing Captain Marvel and started worshiping Charlie Parker.

Still, as the decades wore on, Shorter began to spot resemblances between the guys with the trumpets and the guys with the capes. In a 1992 interview with Jazz Forum, he compared Miles Davis to Batman, describing Davis as “a crusader for justice and for value” who “had to be a dual personality, too, like he knew the criminal mind.”

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So what about Wayne Shorter? What about that kid who transformed from Mr. Weird into the Newark Flash into one of the greatest composers American music has ever known? He was an outsider whose extraordinary abilities never stopped him from cultivating an abiding sensitivity to how human beings think, listen and feel. That makes him Superman, right?