In terms of his methods, director Hirokazu Kore-eda (“Nobody Knows”) is algebraic. His latest film “Shoplifters” interrogates every axiom that has been used to define family. Is it childbirth that makes a mother? Does calling someone mom, dad, sister or brother automatically baptize that person into fulfilling the corresponding role? Do these titles even encompass all that a person actually means to us? Can family be chosen, or renegotiated or be anything other than an unalterable birthright?

At the same time that Kore-eda reevaluates these supposed axioms, he applies selective coefficients within the formula for family drama, focusing specifically on the effect of poverty. The family in “Shoplifters” consists of couple Osamu (Lily Franky, “The Devil’s Path”) and Nobuyo (Sakura Andô, “100 Yen Love”), as well as the various dependents with whom they share their lives: A young boy named Shota (Jyo Kairi, “Erased”), a young woman named Aki (Mayu Matsuoka, “A Silent Voice”), Aki’s grandmother Hatsue (Kirin Kiki, “Returner”) and the most recent addition to the nontraditional family, a young girl named Yuri (Miyu Sasaki, “Samurai Gourmet”). The nontraditional family is united in their shared victimization, each one clinging to the bottom rung of the economic ladder; they also share the burden of finding a way to survive in spite of their poverty (usually taking the form of the titular practice of shoplifting). All the while, the constant pressure of their precarious financial situation threatens to erode the unquestionable care they have for one another and instead compel selfishness.

Other filmmakers would do well to pay attention to Kore-eda’s cinematic arithmetic, especially others who also endeavor to tell insightful stories about families. It is tempting to try to account for each of the countless variables that shape family dynamics but, as “Shoplifters” attests, much more rewarding to zero in on a few.

While his approach is mathematical, Kore-eda’s results are poetic. For example, he structures his investigation of family dynamics in what could be described as a series of couplets. He pairs off members of the nontraditional family and devotes to these duos scenes like stanzas, each one poignant enough to stand alone but each one also working together to form a more resonant whole. And through all these stanzas, “Shoplifters” speaks with a steady tone of composure, inflecting characters’s exchanges with unselective compassion. As if to say, “So what if we shoplift? So what if break the rules? We are trying to survive. We are trying to take care of one another.”

So take, for instance, one of the most thoughtful of the aforementioned couplets: The relationship between Aki and her grandmother. When Yuri wets the bed the first night she stays with her new family and Aki’s grandmother offers to sleep next to Yuri, Aki protests, insisting on her rightful place beside her grandmother. Aki’s jealousy is not conveyed as dispassionate but rather a childish, touching manifestation of fierce love and loyalty – a familial dynamic too subtle for other directors to capture on screen.

Or take the design of a recurring set in “Shoplifters”: that is, the shabby place this nontraditional family calls home. It houses the dregs of consumerist capitalism. Every room is congested with cheap goods, to the point that the scenes in this house always border on inducing claustrophobia. And yet, it is in one of these cluttered rooms that Aki’s grandmother tends to Yuri’s wounds from her abusive upbringing. It is here that every member of Yuri’s new family strives to reteach her what it means to love and be loved. It is here that this family somehow finds room and reason to breathe and continue to live in spite of their living conditions.

Take any scene, any conversation, any shot in “Shoplifters.” Revel in its careful calculation and pore over its resonant results.

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