Apeirogon: a shape with a countably infinite number of sides. With this figure — in the title, and then in expanding definitions — Colum McCann offers us a template for reading his new book, which is a novel but not in any traditional sense. McCann, acclaimed author of “TransAtlantic” and the National Book Award-winning “Let the Great World Spin,” has taken for his subject the countably infinite facets of the Israeli-Palestinian conundrum, as embodied in the stories of two real-world characters, Bassam Aramin, a 52-year-old Palestinian, and Rami Elhanan, a 70-year-old Israeli Jew.

Both men have played a part in the seemingly intractable violence of their homeland: Bassam as a teenager jailed for seven years for a grenade attack on an Israeli jeep; Rami as a soldier in the 1973 Yom Kippur War. But what ultimately links the two is the death of their daughters: 14-year-old Smadar Elhanan, killed by a suicide bomber; and 10-year-old Abir Aramin, felled by a rubber bullet fired by an 18-year-old Israel border guard.

As the men join forces, first in an organization called Combatants for Peace, and then in the Parents Circle, which brings together bereaved Palestinians and Israelis, the details of their respective histories and daily lives conjure a picture of the endless differences and indignities that foment misunderstanding and obstruct empathy at every turn in this Holy Land at odds with its people and itself.

Pieced together in a sort of narrative pastiche, these facts and features and events are told and retold, alluded to and expanded on, until we have seen them from so many angles that the picture they finally make seems at once comprehensively complete and incomprehensibly complex. And interspersed with the story of Rami and Bassam, and Smadar and Abir, are numbered chapters of pages, paragraphs and often single lines that further enhance and complicate the picture: anecdotes from history; notes on religion, politics and art; extended meditations on saltpeter and gunpowder, bird behavior, mathematics and language; quotes from poetry and songs; glimpses of Artaud and Anais Nin; Kalashnikov on his deathbed and George Mitchell in Ireland; riffs on words like “operation” and “morgue”; the Song of Solomon, the Song of Songs, the Canticle of Canticles; solitaire.

Among these many references and digressions, more models for understanding “Apeirogon” emerge — for instance in the Moebius strip of “One Thousand and One Nights,” in the word puzzles of Jorge Luis Borges, the compositions of John Cage. “What interested Cage,” McCann tells us, “was the idea of the aleatoric, in which the course of music may be determined in a general direction, but the details rely on associations discovered by the performer or the audience or even the sounds themselves.”

The associations that “Apeirogon” suggests are inescapable, of course, not random at all, but as wide as they ripple and as heady as they sometimes seem, they always come back to the book’s human heart, two grieving fathers and the power of their love in the face of countably infinite odds.

 Ellen Akins is a writer and teacher of writing in Wisconsin.

By: Colum McCann.
Publisher: Random House, 463 pages, $28.

Correction: Previous versions of this article misstated the year of the Yom Kippur War.