Ali Smith’s playfully brilliant new novel makes me both excited and wary of recommending it. This gender-blending, genre-blurring story, which was shortlisted for the Booker Prize, bounces across centuries, tossing off profound reflections on art and grief, without getting tangled in its own postmodern wires. It’s the sort of death-defying storytelling acrobatics that don’t seem entirely possible — How did she get here from there? — but you’ve got to be willing to hang on.

The games start even before you know it, as soon as you pick up a copy. In a flight of whimsy that is far too rare in publishing, “How to Be Both” is being released like some kind of literary Pushmi-pullyu: In half of the editions, a historical novella precedes a contemporary one; in the other half, the order is reversed. You won’t know which version you’ve bought until you begin reading. The two novellas make frequent references to each other, but how you interpret those references will depend on whether they’re looking forward or backward. (What a perfect complication for the adventuresome book group!) As one character says, it’s a lesson in “how to tell a story, but tell it more than one way at once, and tell another underneath it up-rising through the skin of it.”

The 15th-century story is narrated in a stream-of-consciousness monologue by the impish ghost of Francesco del Cossa (c. 1430-c. 1477). An Italian painter about whom little is known, del Cossa worked on the frescos inside the Palazzo Schifanoia in Ferrara, Italy, until he apparently became annoyed with the meager wages. On the scrawny skeleton of that historical record, Smith fleshes out the life of a precocious young artist who binds her chest with linen, takes the name Francescho and pretends to be a man so she can get commissions.

It’s a fascinating bricolage of history and speculation enriched with Francescho’s audacious patter, often comically incongruous with the Renaissance. Freely mixing genders and pigments, the young artist distinguishes herself early as a magician with paints — and she knows it. “I’m good at the real and the true and the beautiful,” she tells us. She can capture human figures in suspended motion, and she has mastered a sense of depth that transfixes the eye.

That self-taught skill gets Francescho a job painting panoramic frescos at the Palazzo Schifanoia, and there we follow her working with the more famous Cosimo Tura. Amid her boasts and complaints about her artistic rival, we learn much about the way Francescho — and, by implication, Smith — relishes the trompe l’oeil effect of great art: “I like very much a foot,” she says, “or a hand, coming over the edge and over the frame into the world beyond the picture, cause a picture is a real thing in the world and this shift is a marker of this reality: and I like a figure to shift into that realm between the picture and the world just like I like a body really to be present under painted clothes where something, a breast, a chest, an elbow, a knee, presses up from beneath and brings life to a fabric.”

"How to be both" by Ali Smith. (Pantheon)

The most delightful — and admittedly absurd — scene is one involving her trip to a whorehouse with her best friend, a male, who has no idea Francescho is approaching their sexual adventure with entirely different expectations. But soon the ladies are asking for Francescho (she paints their portraits behind closed doors). Francescho’s friend assumes his fine-featured buddy must be quite the stud. “Love and painting both are works of skill and aim,” she confesses to us.

Francescho’s half of the novel follows a bumblebee’s flight pattern, darting forward and backward through memories of childhood and old age, alighting on certain sweet or painful experiences for a moment. “We go out anonymous into the insect air,” she says, “and all we are is the dust of colour, brief engineering of wings towards a glint of light on a blade of grass or a leaf in a summer dark.” Francescho assumes that she is dead, hovering in purgatory, but she has no idea how she got here. (Do any of us?)

The most perplexing visions that pass before her involve a young man — no, wait, a young woman — in the year 2013. There, during unpredictable and baffling moments, Francescho can see her and her mother looking at paintings in a Ferrer museum and carrying a “holy votive tablet” upon which appear an impossible number of quickly changing portraits. Shifting through space and time, Francescho tenderly observes this teenager studying the little square images she has affixed to her bedroom wall.

In the second novella — or the first, depending on your particular edition of this book — we follow the life of a 16-year-old girl, George, an acerbic high school student in contemporary England. Although it is told in the third person, George’s story, like Francescho’s, moves freely through time, circling back on significant moments and themes that gradually come into focus. Among her most cherished memories is a family trip to Italy, where she and her mother saw frescoes created by del Cossa. (See where this is going? Believe me, you don’t.)

In the hazy months following her mother’s unexpected death, George returns to that happy trip, with its witty banter about art and feminism. Those memories are a respite from her father’s drunken sorrow and the platitudes of her well-meaningschool therapist. Left largely alone in a fog of despair, George struggles to grasp the surprising dimensions of her mother’s life as a loving parent and a well-known online anarchist.

This sounds like a novel freighted with postmodern gimmicks, but Smith knows how to be both fantastically complex and incredibly touching. Just as Francescho’s story is laced with insights about the nature and power of painting, George’s story offers its own tender exploration of the baffling and clarifying power of grief. How can a loved one suddenly not exist? And how can a painting bring ground pigment and oil to life? Standing in the Palazzo Schifanoia, George looks up at the frescoes and says, “What there is . . . is so full of life happening that it’s actually like life.” To which her mother responds, “Whenever it’s sardonic, a moment later it’s generous again.” So, too, with this swirling, panoramic vision of two women’s lives, separated by more than 500 years, impossibly connected by their fascination with the mystery of existence.

Charles is the editor of Book World. His reviews appear every Wednesday in Style. You can follow him on Twitter @RonCharles.

HOW TO BE BOTH

By Ali Smith

Pantheon. 372 pp. $25.95