In one pivotal scene of “Phantom Thread,” a beguiling and clever new film from writer-director Paul Thomas Anderson, a character asks, “What precisely is the nature of my game?” In the context of the film, this question is equal parts a threat, a tease and a genuine inquiry. It also feels like a subtle break of the fourth wall: Anderson might as well have asked the audience the same question. This film’s literal narrative is easy to follow, but much of Anderson’s deeper explorations, obsession, creativity and intimacy lie well below the surface. Several moments of the film are sure to spark passionate debates. Even after finishing “Phantom Thread” I feel unsure of the exact nature of Anderson’s game. This game, as strange and inscrutable as it can be at times, is well worth playing.

Set among the excessive wealth and glamour of the upper class in 1950s London, the film focuses on Reynolds Woodstock (Daniel Day-Lewis), a dress designer for princesses and socialites. His designs are lavishly beautiful, and Reynolds treats his work with utmost seriousness, refusing to tolerate any distractions. He cycles through romantic partners with disinterest — the only constant presence is his sister Cyril (Lesley Manville) who both tolerates and tempers Reynolds’s exactitude. When Reynolds brings the pretty young Alma (Vicky Krieps) home, it seems that she will be just another temporary love interest, but Alma asserts herself, demanding attention and a real relationship from Reynolds. As the film progresses, Reynolds’ beloved routine is disrupted by Alma’s presence, and he is alarmed by his strong emotional response as their relationship becomes more intense and twisted.

I will not spoil the exact turns their relationship takes, as those details are one of the film’s several bizarre surprises. The narrative turns are deliciously unexpected, subverting any notions one might have about the relationship between an artist and his muse. Anderson is refreshingly clear-eyed about his protagonist’s sharp edges. While it is always clear that Reynolds is a genuinely brilliant artist, the narrative never adopts the trope of the “tortured artist” nor does it sugarcoat his many pathologies as lovable quirks. The film also adopts an endlessly fascinating view of gender dynamics. This is not a story where the women surrounding a male genius are either supportive stalwarts or shrewish wet blankets. Instead, Alma, Cyril and Reynolds share a complicated and ever-shifting relationship, blurring lines between power and vulnerability, love and disdain and respect and fetishism. All three actors give subtle, engrossing performances, portraying their characters’ messy dynamics without betraying easy answers.

“Phantom Thread” is slowly paced, especially in the first act, and Anderson’s insistence on challenging his audience can sometimes be trying. Luckily, every moment of the film is exquisitely designed — this film is easy to get lost in. The costumes, designed by Mark Bridges, are endlessly gorgeous — this is a surprisingly rare film about an artistic mastermind where the talent is evident on screen. The score, from Radiohead member Jonny Greenwood, is a constant presence in the film, and its alternations between baroque beauty and discordant intensity become an integral building block of the show’s tone. Anderson, a famous perfectionist, makes this film a sumptuous sensory experience, building up pretty exteriors that suggest a polite period drama. Of course, “Phantom Thread” is much more than that, and the screenplay possesses a jagged wit, as well as complex psychological observations. Like Reynolds’ dresses, this film can be admired as a beautiful physical object, with the details lovingly crafted.

One detail has overshadowed the press coverage of “Phantom Thread:” the beloved Day-Lewis has stated that this performance will be his last ever. Day-Lewis is famous for his intense dedication to method acting — his work as an artist is on par with his character’s in terms of brilliance and obsessiveness. If Day-Lewis is truly done with acting, this film is a more than fitting farewell. It feels appropriate that his career grand finale is both an ode to and a warning against creativity as an all-consuming passion.