THE MÖBIUS BOOK, by Catherine Lacey

The first thing to know about “The Möbius Book,” by Catherine Lacey, is that it is actually two books. One is a novella with a hint of murder mystery. Start from the opposite side, flipping upside down — how will this work on a Kindle? — and you’ll find the other: a memoir of breakup and friendship during the pandemic, interspersed with musings on religion.

Where will bookstores put this loopy blue thing? Amazon, with unusual resourcefulness, has nested it for now under Self-Help/Relationships/Love & Loss (though I’d wager the author’s core audience avoids Amazon).

One has come to expect such formal experiments from Lacey, especially after her bravura “Biography of X”: not a biography of anyone real, but a footnoted, name-dropping, time-melting fourth novel that made many best lists in 2023.

There are plenty of names pelted into “The Möbius Book,” too — author friends like Heidi Julavits and Sarah Manguso, and many others — but one notably missing in the memoir part is that of Lacey’s ex, which gentle Googling reveals is yet another writer, Jesse Ball. Here he is referred to as The Reason: the literary-circle equivalent, maybe, of The Weeknd.

He is the “reason” why she has become a visitor to, rather than a resident of, the house they bought together, after receiving an email he sent from another room, composed on his phone, telling her he’d met another woman. (At least not a Post-it?) He is also, or so she believed, a pillar of masculine rationality. With tattoos.

The Reason has control and anger issues. He noticed when Lacey, or her memoiristic avatar, put on weight and advised her how to take it off. After they split she found it hard to eat for a time.

The Reason, unreasonably, refused to use a laptop, so she had done most of his paperwork, participating “in the long lineage of women licking stamps for their geniuses.” He once called her “a crazy, sexist autocrat” when she wanted to leave a light on in a stairwell for a female guest. Sometimes he would surprise her — “playfully,” he insisted; unpleasantly, she felt — with a smack on the rear. When not threatening or cold, he seems a little absurd in this telling, playing funeral hymns on a shakuhachi.

There was a time when such narratives were lightning bolts cast down on the world of letters, causing considerable shock waves. (I’m thinking of Catherine Texier’s 1998 “Breakup,” about the dissolution of her marriage to Joel Rose, and even Rachel Cusk’s 2012 divorce memoir “Aftermath.”) But Lacey isn’t scorching earth — she’s sifting it, flinging fistfuls of dirt and thought at us.

With characteristic keenness she notes how “The Reason’s name had burrowed into everything, like glitter in shag carpet.” How mundane language pops out with new meaning in the fog of post-relationship grief (“Even the copy on a jar of peanut butter tried to offer advice — Separation is natural”). She reflects on her religious childhood and her once-authoritarian, now-infirm father. She consults — and sometimes curses — Simone Weil, Seneca and William Gass. She hooks up with a new fellow she dubs, naturally, The Bad Idea.

Lacey runs the same list of acknowledgments and credits at the end of both novella and memoir. There are similar themes, but also an element of “Hey, you got your chocolate in my peanut butter!” in their juxtaposition. The fiction is shorter, noirish and elliptical. Was yoking it to the fiction an organic, creative act — whatever that is, we’re maybe meant to consider — or a clever packaging solution for two not-quite stand-alones?

A woman named Marie welcomes a friend, Edie, into her grim apartment on Christmas, noticing — is this a nightmare? — a pool of blood spreading outside a neighbor’s door. They both write it off as “just paint” so they can sip mezcal, eat crustless sandwiches and talk about failed relationships, some mediated or complicated through another, friend, Kafkaesquely called K.

They are both reputed in their circle to be in some kind of “crisis.” (Marie’s Crisis happens to be an excellent piano bar in the West Village of Manhattan, but, as Lacey writes, “no one cares about anyone else’s coincidences.”) Their interlocked stories drip with aphorism (“it is a fact that when one living thing rests its chin on another living thing, everything is fine”), defy summary and might all be a fever dream anyway.

“The Möbius Book” invites the reader to consider the overlaps between its two parts, an exercise both frustrating — all that turning back, forth and upside down — and exhilarating, because Lacey is imaginative and whimsical when considering reality, and sees truth in make-believe. The curving strip is like Lewis Carroll’s looking glass. Both halves share a broken teacup. Twins! A violent man. Bursts of sarcastic laughter. A dying dog (God?) with important spiritual wisdom to share.

Depending on how you twist, this book — defying the linear story, homage to the messy middle — is either delightfully neo-Dada or utterly maddening.

Or, as Lacey puts it: “Symbolism is both hollow and solid, a crutch, yes, but what’s so wrong with needing help to get around?”

THE MÖBIUS BOOK | By Catherine Lacey | Farrar, Straus & Giroux | 240 pp. | $27