In his paintings of a century ago, Georges Seurat demanded that the world look at art in a shocking new way. In "Sunday in the Park With George," their new show about Seurat, the songwriter Stephen Sondheim and the playwright-director James Lapine demand that an audience radically change its whole way of looking at the Broadway musical. Seurat, the authors remind us, never sold a painting; it's anyone's guess whether the public will be shocked or delighted by "Sunday in the Park." What I do know is that Mr. Sondheim and Mr. Lapine have created an audacious, haunting and, in its own intensely personal way, touching work. Even when it fails—as it does on occasion—"Sunday in the Park" is setting the stage for even more sustained theatrical innovations yet to come.

If anything, the show … owes more to the Off Broadway avant-garde than it does to past groundbreaking musicals, Mr. Sondheim's included. "Sunday" is not a bridge to opera, like "Sweeney Todd"; nor is it in the tradition of the dance musicals of Jerome Robbins and Michael Bennett. There is, in fact, no dancing in "Sunday," and while there's a book, there's little story. In creating a work about a pioneer of modernist art, Mr. Lapine and Mr. Sondheim have made a contemplative modernist musical that, true to form, is as much about itself and its creators as it is about the universe beyond.

The show's inspiration is Seurat's most famous canvas, "A Sunday Afternoon on the Island of La Grande Jatte." That huge painting shows a crowd of bourgeois 19th-century Parisians relaxing in a park on their day off. But "La Grande Jatte" was also a manifesto by an artist in revolt against Impressionism….

[Seurat] could well be a stand-in for Mr. Sondheim, who brings the same fierce, methodical intellectual precision to musical and verbal composition that the artist brought to his pictorial realm. In one number in "Sunday," Seurat's work is dismissed by contemporaries as having "no passion, no life"—a critique frequently leveled at Mr. Sondheim. But unlike the last Sondheim show, "Merrily We Roll Along," this one is usually not a whiny complaint about how hard it is to be a misunderstood, underappreciated genius. Instead of a showbiz figure's self-martyrdom we get an artist's self-revelation.

As is often the case in Sondheim musicals, we don't care about the characters—and here, more than ever, it's clear we're not meant to care. To Seurat, these people are just models for a meditative composition that's not intended to tell any story: In his painting, the figures are silent and expressionless, and even Dot is but fodder for dots. Mr. Lapine and Mr. Sondheim tease us with their characters' various private lives—which are rife with betrayals—only to sever those stories abruptly the moment Seurat's painting has found its final shape. It's the authors' way of saying that they, too, regard their "characters" only as forms to be manipulated into a theatrical composition whose content is more visual and musical than dramatic.

As a result, when Seurat finishes "La Grande Jatte" at the end of Act I, we're moved not because a plot has been resolved but because a harmonic work of art has been born.

[In Act II, the] show jumps a full century to focus on a present-day American artist also named George…. This protagonist is possibly a double, for Mr. Sondheim at his most self-doubting. George makes large, multimedia conceptual sculptures that, like Broadway musicals, require collaborators, large budgets and compromises….

The fanciful time-travel conceits that link this George to Seurat are charming. Rather less successful is the authors' reversion to a compressed, conventional story about how the modern George overcomes his crisis of confidence to regenerate himself as a man and artist. When George finally learns how to "connect" with other people and rekindles his esthetic vision, his breakthrough is ordained by two pretty songs, "Children and Art" and "Move On," which seem as inorganic as the equivalent inspirational number ("Being Alive") that redeems the born-again protagonist in Mr. Sondheim's "Company."

The show's most moving song is "Finishing the Hat"—which, like many of Mr. Sondheim's best, is about being disconnected. Explaining his emotional aloofness to Dot, Seurat sings how he watches "the rest of the world from a window" while he's obsessively making art. And if the maintenance of that solitary emotional distance means that Seurat's art (and, by implication, Mr. Sondheim's) is "cold," even arrogant, so be it. "Sunday" argues that the esthetic passion in the cerebrally ordered classicism of modern artists is easily as potent as the sentimental passion of romantic paintings or conventional musicals….

[The] lyrics can be brilliantly funny. Mr. Sondheim exploits the homonyms "kneads" and "needs" to draw a razor-sharp boundary between sex and love; a song in which Seurat's painted figures break their immortal poses to complain about "sweating in a picture that was painted by a genius" is a tour de force. But there's often wisdom beneath the cleverness….

Both at the show's beginning and end, the hero is embracing not a woman, but the empty white canvas that he really loves—for its "many possibilities." Look closely at that canvas—or at "Sunday in the Park" itself—and you'll get lost in a sea of floating dots. Stand back and you'll see that this evening's two theater artists, Mr. Sondheim and Mr. Lapine, have woven all those imaginative possibilities into a finished picture with a startling new glow.