Colum McCann’s new novel, “Apeirogon,” is based on an uplifting true story. It’s about two fathers — Rami Elhanan, an Israeli, and Bassam Aramin, a Palestinian — who each lost a young daughter to senseless violence. They have become friends and work together, through an organization called Combatants for Peace, to bring the opposing sides together.

McCann takes their story and drops it to the ground, where it shatters. To read “Apeirogon” is to watch him pick up the shards. As befits a writer who ruminates about the nature of storytelling, there are 1,001 of these shards, each numbered, in a homage to “One Thousand and One Nights,” the collection of Middle Eastern folk tales.

This is an early warning sign. It is possible to admire “One Thousand and One Nights” while having learned through hard experience that a writer who derives too much inspiration from it is generally one to avoid, unless what’s desired is a self-inflicted intellectual glitter-bombing. The Time magazine film critic Stephanie Zacharek, writing on Twitter, recently called “storytelling” a “jazz-hands word.” “Apeirogon” is a jazz-hands novel.

In many of McCann’s 1,001 shards, we follow Rami and Bassam in something like real time. They attend meetings, give lectures, worry about crossing border checkpoints. In others, we flash back to earlier points in their lives. From multiple angles, we witness the events that led to their daughters being killed.