As a passionate young singer, Joan La Barbara attended a 1972 Berlin Philharmonic performance of experimental composer John Cage’s music that disturbed her deeply. Musicians argued politics with the audience instead of playing their instruments. There was an orchestra in the lobby, a cacophony of noise, milling crowds and apparent confusion.

“I really didn’t know what to make of it,” La Barbara says. “So I walked up to Cage and said, ‘With all the chaos in the world, why do you want to make more?’ ”

The circle of admirers surrounding him gasped, and La Barbara walked off thinking she’d offended the famous composer. Instead, she felt a tap on her shoulder and turned to see Cage beaming. “Perhaps now when you go out into the world,” he told her, “it won’t seem so chaotic anymore.”

Exploring how one of the most influential and controversial artists of the 20th century found music in the world’s chaos is the goal of the New World Symphony’s Making the Right Choices: A John Cage Centennial Celebration next weekend at the New World Center in Miami Beach.

Conceived by the symphony’s artistic director, Michael Tilson Thomas, the three-night festival is among the more ambitious and creative of the many events commemorating the 100th anniversary of Cage’s 1912 birth. There will be projections on a giant helium balloon and the curved “sails” of the main concert hall, musicians playing simultaneously in multiple rooms and new stagings of rarely done dances by Merce Cunningham, Cage’s longtime creative and personal partner.

Guest artists include La Barbara (who became a frequent Cage collaborator), soprano Jessye Norman and contemporary singer Meredith Monk. Works range from meticulous recreations of early solo pieces for prepared piano to a dramatic re-imagining of Renga, one of Cage’s most ambitious and complex orchestral works.

With all its multimedia bells and whistles, the festival is “Cirque du Soleil for the intellectual set,” NWS president Howard Herring says.

Tilson Thomas, a passionate, longtime advocate for Cage and contemporary music, hopes it will draw audiences into a musical world that is as rich and rewarding as it is complex and misunderstood.

“I think people have taken the freedom in [Cage’s] music to do whatever they want,” Tilson Thomas said. “But that’s not at all his intention. He’s trying to create a situation, an opportunity for music to come into existence.”

Opportunities to hear Cage’s music remain rare. Two decades after his 1992 death, many people still find his work baffling and disturbing, not “really” music. And yet he is widely regarded as one of the pivotal artists of the 20th century, a man whose ideas about the definition and role of art and performance, about creativity, about our awareness of and relationship to the world, were key drivers in the cultural shift to post-modernism.

Cage used chance, most famously with the I-Ching, to structure his pieces, freeing them from emotions and biases and seeking to tap into larger life forces. By juxtaposing multiple musical elements, or, in his half-century collaboration with Cunningham, independently created dance, music and décor, he opened up the use of collage and foreshadowed the way we process simultaneous stimuli in our Internet-linked lives. DJs, hip-hop producers and electronic music mavens owe him a debt for his pioneering use of electronic sounds and sampling. The way he structured his compositions to embody ideas and raise questions has become the primary ethos of the conceptually driven contemporary art world.