Sonny Rollins remembers the weather. Sunshine. He remembers the band, too. Erskine Hawkins and Dud Bascomb each on trumpet, Paul Bascomb and Julian Dash both blowing tenor sax. But the other details come back blurry, rosy or deleted.

“It’s a fantasy land for me now,” says Rollins. “It’s in my dreams, in my mind.”

It’s 1942. Probably. That would make Rollins 11 years old, down from Harlem to spend the summer in Annapolis with his father, a chief petty officer in the Navy. It’s a gorgeous afternoon at Carr’s Beach — a segregated strip on the Severn River where black musicians regularly performed for black audiences. Rollins is listening carefully to Hawkins and his big band, an Alabama group whose work the kid knows well. But he’s got his eyes locked on Marjorie Brown, a woman he’s been following around town.

“They used to have people sitting on chairs on the stage, right next to the band,” Rollins says, flashing back seven decades. “Sure enough, when I went there that day, there was Marjorie Brown sitting next to the Erskine Hawkins band. The implications were that she was friendly with the band. So that crushed my heart, you know?”

No, not really. How does an 11-year-old fall in love with a woman 10 years his senior? Laughter peals over the telephone from Europe, where the 81-year-old has spent the past month on tour. “I was a mature 11,” he says.

Mature, precocious, cultured and determined. Aside from a few summers in Maryland, Rollins spent his childhood in Harlem, a cultural epicenter that would shape him into a jazz icon who would steer the trajectory of the genre and the concept of improvisation writ large. As Rollins looks back, the chapters of his life often slice into neat little halves — separate realities where he toggled between success and struggle, renown and solitude. He apprenticed with the bop gods (Charlie Parker, Miles Davis) while battling the dark forces of addiction. At his highest levels of acclaim, he took mysterious sabbaticals that felt like vanishing acts. Today, Rollins says he gets through “this world full of problems” by reaching for higher spiritual plateaus that he “can almost touch,” but never quite does.

His worlds started dividing during those formative Maryland summers. He remembers going to a movie theater in Annapolis to see “ Cabin in the Sky,” a musical whose title track Rollins still likes to perform today. Lena Horne, Louis Armstrong, Ethel Waters and Duke Ellington all starred in the film. So did Ford Lee Washington and John William Sublett, a duo Rollins had seen perform as Buck and Bubbles at the Apollo Theater back home.

In Annapolis, Rollins had to watch the film from the balcony. But he doesn’t remember feeling the ugly sting of segregation that day — only the magic he saw glimmering on screen. “A great experience,” he says. “And at the end of the picture, the guy woke up and realized it was all a dream.”

* * *

In the 1958 essay “Sonny Rollins and the Challenge of Thematic Improvisation,” jazz writer and composer Gunther Schuller famously declared, “Today we have reached another juncture in the constant evolution of improvisation and the central figure of this present renewal is Sonny Rollins.” The world soon heard what Schuller was hearing. As Rollins searched for fresh melodic phrases in his solos, his playing became more untethered and more articulate, possessing the rhythm and authority of human speech. Since then, thousands of Smith-Corona ribbons and laptop batteries have died in the service of explaining its impact.

“Hearing him really awakened me to the true power and potential of jazz improvisation,” says Joshua Redman, the 42-year-old tenor saxophonist who has called Rollins his greatest influence. “He made me realize that improvisation could at once be completely in the moment and spontaneous and full of ad­ven­ture and daring and surprise — but at the same time could have an incredible amount of structure and really tell a very, very logical and organized story.”

Rollins describes the mysteries of improvisation plainly: “You make what might seem like a breakthrough. And then . . . you have to take a step back. You take a step forward. Then you have to take a step or two to the side. The idea that, ‘Oh, gee, now I’ve got it, I’m right on the track’ — that never really materializes.”

He remains hypercritical of his own work, but says he knew at a young age that he was destined to be “prominent.” Born in Harlem on Sept. 7, 1930, Walter Theodore Rollins was the son of a working mom and a Navy dad, both born in the Virgin Islands. His grandmother often looked after him as a child, but in many ways, he was raised by the city. As a jazz-obsessed teen, he would hound saxophonist Coleman Hawkins and persuade Thelonious Monk to sneak him into bars.

“I think I was just born at the right time and the right place because everything around me was music,” Rollins says. As a young child, he listened to the blues records of his uncle’s girlfriend. He watched his older siblings practice violin and piano. He’d walk past the Cotton Club on the way to school. He took up saxophone at 13 and a few years later was playing alongside future jazz great Jackie McLean. His family remained skeptical.

“They didn’t think much of jazz,” Rollins says. “Later, when I began smoking pot and all this stuff, it really confirmed their views that music was really nothing and I wasn’t going anyplace.”

By 1953, he was proving them wrong and right. He had already served jail time for an armed robbery in 1950, but his star was rising as Monk’s prize sideman — all while nursing a heroin addiction that he managed to kick for good in 1955. “ Saxophone Colossus ” came the following year, the album that would cement his eminence in jazz.

But in 1959, when the praise began to feel heavy, Rollins stopped his career to work in solitude. On an afternoon stroll down Delancey Street in Manhattan, he stumbled upon his new rehearsal space, the Willliamsburg Bridge.

“It was just a perfect thing,” Rollins says of the steel expanse stretching across the East River to Brooklyn. There, he would spend days and nights practicing in complete anonymity, hidden in a nook from the passing cars and trains. “I used to blow my horn back at the boats when the boats would blow. All of that was great. I was in a place where nobody could see me,” he says. “This was heaven. This was heaven.”

When he came down in 1962, it still felt premature. “I could have probably spent the rest of my life just going up on the bridge,” he says. “I realized, no, I have to get back into the real world.”

That meant a new contract with RCA and a streak of adventurous recordings. But before long, he started hearing that same “inner voice” that told him to scale the bridge. “I was a little disillusioned,” says Rollins of the music business at the time. “Jazz is dead every 10 years. That was part of it.” He’d also grown curious about meditation, yoga, Rosicrucianism and “things of the spirit.” In 1970, he checked in at an ashram near Bombay.

“I took this trip because I wanted to find out for myself — and sort of be in the atmosphere and the ambiance — where all these people supposedly made all of these great revelations,” he says. But Rollins’s revelation couldn’t have been more simple.

“I have a lot of trouble meditating,’’ he says. “A lot of these practices have to do with meditating and trying to get away from ordinary life. The swami said, ‘Well, Sonny, when you’re playing your horn, you’re meditating.’ A light came on in my head. ‘Wow, that’s true!’ It seems like it might be obvious, but some of these things, even though they seem to be so plain, you need something to sort of light them up.”

Rollins says he’s kept the lights on ever since. “I was playing and I was thinking positive thoughts and I was really getting deep inside of my music,” he says. “Which is really what I do when I improvise, anyway. The idea is to get into a subconscious state.”

* * *

He kept leaping from one world to another. After the towers of the World Trade Center crumbled not far from his apartment building, Rollins and his wife, Lucille, moved to a farm in Upstate New York. When Lucille died in 2004, he found comfort in endless rehearsing and founded a label to release his recordings. Today, Rollins lives both at home and on the road. His current tour ends on Sunday at the Kennedy Center, where he’ll be given a medal with a rainbow ribbon hopefully big enough to lasso the cumulonimbus of hair atop his head.

Rollins doesn’t see the recognition as any kind of trophy or happy ending. It simply allows his work to go on. “I might get better jobs so I can continue my life and what I’m doing,” he says of receiving the Kennedy Center award. “Pursuing that musical thing that I’m looking for and, at the same time, representing this great music that is so much bigger than I am.”

It’s a pursuit that has no endpoint.

“I’ll never realize perfection — I realize that,” Rollins says. “But I want to get closer than where I am now.”

See the rest of this year’s Kennedy Center Honorees:

Meryl Streep | photos

Neil Diamond | photos

Yo-Yo Ma| photos

Barbara Cook | photos