Alana Kane is lost. She’s a 25-year-old woman halfway between adolescence and adulthood. She has a real job – a photographer’s assistant at a school, meaning she spends most of her day surrounded by pimply teenage boys believing they’re way older than they actually are. One such pimply teenage boy is the appropriately named Gary Valentine.

Gary has a confidence both beyond his years yet perfectly fitting of a child actor dreaming of the magic, limitless opportunity of adulthood. His eyes light up when he sees Alana for the first time, and throughout the film’s long opening tracking shot, they dance and sparkle, never leaving her. It’s love at first sight.

Licorice Pizza sees Paul Thomas Anderson return home, back to the San Fernando Valley where he grew up. Back to the 1970s, the decade of his birth. And back to the fringes of show business he knows so well – his father Ernie Anderson was a famous TV and radio personality who introduced horror movies.

Like many filmmakers, Anderson has always loved love. From John C. Reilly’s naively lovelorn John Finnegan in Hard Eight to the gripping co-dependency of Reynolds and Alma at the heart of Phantom Thread, Anderson has always been captured by the wild emotions of love. The love that flutters a heart a few beats quicker, that turns us all to infantile, tantrum-prone babies, the type of love that is so all-consuming that bodies pain, hearts break and eyes water. All of his films (yes, including There Will Be Blood) are about people looking for love in the world, some kind of beautiful connection that transcends the often isolating reality of life on this planet.

“Being in love is the most difficult challenge of your life,” Anderson recently told The Guardian and his films certainly reflect that view. The youthfulness of Licorice Pizza generally heightens that challenge. Neither Gary (played by Cooper Hoffman) nor Alana (Alana Haim in a debut performance channeling the electric energy of Jennifer Lawrence in Silver Linings Playbook) appear to have known love before. Alana seems to have had a line of boyfriends that have never outlasted the “we’ll see where things are going” stage, and Gary’s charm offensive sits somewhere between insurance salesman pitch and publicly singing a Shakespearean sonnet – and yet their entanglement is about the most natural thing in the world.

Part of why Alana and Gary’s relationship is so effective is the psychological realism with which it is portrayed. She is very aware that he is “just a kid” and yet, he has the confidence of a grown man. He’s bolshy, and brings with him a number of attributes that would actually make him attractive – he’s charismatic, independent and relentless with flattery. She likes the attention. She doesn’t let on, but it’s clear she does. Alana is intrigued by Gary and she points out the age difference repeatedly during their first encounter, but the more he talks, the more she pushes herself towards him. To be crushed on is one of the most remarkable things about the human condition, to do the crushing is a remarkably vulnerable state of being yet there’s something ethereal about both sides.

In Boogie Nights, Anderson’s first major film after the release debacle of his debut feature Hard Eight, Scotty J (Philip Seymour Hoffman) has a crush on his friend Dirk Diggler (Mark Wahlberg). Scotty has an anguishing love for Dirk that is never reciprocated and never can be (Dirk isn’t gay) and Hoffman wears the irrationality of a crush in every fibre of his performance. The way he holds his body, the way his eyes search to look anywhere but where they want to – it’s immediately familiar to somebody who has loved without receipt.

Punch Drunk Love, perhaps the film in Anderson’s filmography closest to Licorice Pizza, is an offbeat, slightly surreal, undoubtedly melancholic gaze into the emotion of love. It’s centred around a pair of polar opposites. There’s Adam Sandler’s childlike, anxiety-ridden Barry Egan, often bullied by his seven merciless sisters. And then there’s Emily Watson’s seemingly well-balanced Lena. Apart they are nothing but together, they’re everything. Their love frees Barry, and he finds comfort in a world that had previously brought him nothing but pain.

“I have a love in my life. It makes me stronger than anything you can imagine,” Barry says at one point, and has a truer line ever been written about what it feels like to give yourself to someone, and how much bigger you become as a result? Being in love is a superpower – especially when you’re young – and Anderson has never stopped seeing the beauty of connection. Indeed, the pacing of his films often capture the whirl of love. Punch Drunk Love clocks in at 90 minutes and pinpoints the rush of falling for someone in such a beautiful but violently seismic way, while Phantom Thread with all its acerbic toing and froing is nearly an hour longer.

Unlike many other relationships depicted in Anderson’s film, Alana and Gary are harder to define. What they are to one another is a question that lingers, but maybe it’s a question that misses the point. It doesn’t matter. Alana chaperones Gary for a trip to New York and later enters into business with him, because it doesn’t matter what label they put on their relationship as long as there is one.

Numerous threats do present themselves. Idiot men being idiot men, a clash of age and expectation or a lecherous Sean Penn (playing a William Holden stand-in) – but love remains undefeated. During the Sean Penn section of the film (also featuring a guzzling and grizzly Tom Waits seemingly doing a John Huston impression), Gary and Alana confront their innermost feelings for each other. We see the stabs of jealousy in glances across the room, and then the breakneck sprint of protectiveness. That’s love, and it’s all soundtracked by Paul McCartney. “You gave me something I understand / You gave me lovin’ in the palm of my hand / I can’t tell you how I feel / my heart is like a wheel / let me roll it to you,” he sings.

Licorice Pizza mimics the cosmic coincidences of Punch Drunk Love. The chances of Barry and Lena finding each other how they do, when they do, would give you long odds with a bookmaker. And it’s the same for Gary and Alana. Her looking for directions just as she passes him – what are the odds? But that’s love, that’s all the special relationships you have in your life. They all seem to drop from the sky like a frog.